Subgroups — C₂₃×#62821 #19210447

Order 5888.

7338 conjugacy classes of subgroups.

The subgroup lattice has 1538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3542	C₂	1	4	yes	maximal, complemented
2	C₂₃×#3541	C₂	1	4	yes	maximal, complemented
3	C₂₃×#3540	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3539	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3533	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3532	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3520	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3519	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3513	C₂	1	8	yes	maximal, complemented
10	C₂₃×#3506	C₂	1	4	yes	maximal, complemented
11	C₂₃×#3505	C₂	1	4	yes	maximal, complemented
12	C₂₃×#3495	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3494	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3493	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3489	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3488	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3487	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3485	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₂₃×#525	C₂	1	2	yes	maximal, complemented
20	C₂×C₂₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
23	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
24	C₂²×#41×C₂₃	C₂²	1	2	yes	complemented
25	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
26	C₂₃×#563	C₂²	1	4	yes	complemented
27	C₂₃×#562	C₂²	1	8	yes	complemented
28	C₂₃×H(3,𝔽₄)	C₂²	1	4	yes	complemented
29	C₂₃×#560	C₂²	1	4	yes	complemented
30	C₂₃×#560	C₂²	1	8	yes	complemented
31	C₂₃×#560	C₂²	1	4	yes	complemented
32	C₂₃×#559	C₂²	1	4	yes	complemented
33	C₂₃×#559	C₂²	1	8	yes	complemented
34	C₂₃×#556	C₂²	1	4	yes	complemented
35	C₂₃×#556	C₂²	1	4	yes	complemented
36	C₂₃×#556	C₂²	1	4	yes	complemented
37	C₂₃×#555	C₂²	1	4	yes	complemented
38	C₂₃×#555	C₂²	1	4	yes	complemented
39	C₂₃×#555	C₂²	1	4	yes	complemented
40	C₂₃×#554	C₂²	1	4	yes	complemented
41	C₂₃×#554	C₂²	1	8	yes	complemented
42	C₂₃×#553	C₂²	1	4	yes	complemented
43	C₂₃×#553	C₂²	1	8	yes	complemented
44	C₂₃×#553	C₂²	1	4	yes	complemented
45	C₂₃×#553	C₂²	1	4	yes	complemented
46	C₂₃×#553	C₂²	1	4	yes	complemented
47	C₂₃×#553	C₂²	1	8	yes	complemented
48	C₂₃×#553	C₂²	1	8	yes	complemented
49	C₂₃×#553	C₂²	1	8	yes	complemented
50	C₂₃×#552	C₂²	1	8	yes	complemented
51	C₂₃×#552	C₂²	1	4	yes	complemented
52	C₂₃×#552	C₂²	1	4	yes	complemented
53	C₂₃×#552	C₂²	1	4	yes	complemented
54	C₂₃×#552	C₂²	1	4	yes	complemented
55	C₂₃×#551	C₂²	1	8	yes	complemented
56	C₂₃×#551	C₂²	1	4	yes	complemented
57	C₂₃×#551	C₂²	1	8	yes	complemented
58	C₂₃×#551	C₂²	1	8	yes	complemented
59	C₂₃×#551	C₂²	1	4	yes	complemented
60	C₂₃×#551	C₂²	1	8	yes	complemented
61	C₂₃×#550	C₂²	1	4	yes	complemented
62	C₂₃×#550	C₂²	1	4	yes	complemented
63	C₂₃×#550	C₂²	1	4	yes	complemented
64	D₄×Q₈×C₂₃	C₂²	1	4	yes	complemented
65	C₂₃×#548	C₂²	1	4	yes	complemented
66	C₂₃×#548	C₂²	1	4	yes	complemented
67	C₂₃×#548	C₂²	1	4	yes	complemented
68	C₂₃×#548	C₂²	1	4	yes	complemented
69	C₂₃×#547	C₂²	1	8	yes	complemented
70	C₂₃×#547	C₂²	1	4	yes	complemented
71	C₂₃×#547	C₂²	1	4	yes	complemented
72	C₂₃×#547	C₂²	1	4	yes	complemented
73	C₂₃×#547	C₂²	1	4	yes	complemented
74	C₂₃×#546	C₂²	1	8	yes	complemented
75	C₂₃×#546	C₂²	1	8	yes	complemented
76	C₂₃×#546	C₂²	1	8	yes	complemented
77	C₂₃×#546	C₂²	1	4	yes	complemented
78	C₂₃×#546	C₂²	1	8	yes	complemented
79	C₂₃×#546	C₂²	1	8	yes	complemented
80	C₂₃×#546	C₂²	1	4	yes	complemented
81	C₂₃×#546	C₂²	1	4	yes	complemented
82	C₂₃×#546	C₂²	1	4	yes	complemented
83	D₄²×C₂₃	C₂²	1	8	yes	complemented
84	D₄²×C₂₃	C₂²	1	4	yes	complemented
85	D₄²×C₂₃	C₂²	1	4	yes	complemented
86	C₂₃×#544	C₂²	1	2	yes	complemented
87	C₂₃×#542	C₂²	1	4	yes	complemented
88	C₂₃×#542	C₂²	1	4	yes	complemented
89	C₂₃×#542	C₂²	1	8	yes	complemented
90	C₂₃×#542	C₂²	1	8	yes	complemented
91	C₂₃×#541	C₂²	1	4	yes	complemented
92	C₂₃×#540	C₂²	1	4	yes	complemented
93	C₂₃×#540	C₂²	1	8	yes	complemented
94	C₂₃×#540	C₂²	1	8	yes	complemented
95	C₂₃×#539	C₂²	1	8	yes	complemented
96	C₂₃×#539	C₂²	1	8	yes	complemented
97	C₂₃×#539	C₂²	1	8	yes	complemented
98	C₂₃×#538	C₂²	1	8	yes	complemented
99	C₂₃×#538	C₂²	1	8	yes	complemented
100	C₂₃×#538	C₂²	1	8	yes	complemented
101	C₂₃×#538	C₂²	1	8	yes	complemented
102	C₂₃×#538	C₂²	1	8	yes	complemented
103	C₂₃×#538	C₂²	1	8	yes	complemented
104	C₂₃×#537	C₂²	1	2	yes	complemented
105	C₂₃×#537	C₂²	1	4	yes	complemented
106	C₂₃×#537	C₂²	1	4	yes	complemented
107	C₂₃×#536	C₂²	1	2	yes	complemented
108	C₂₃×#536	C₂²	1	4	yes	complemented
109	C₂₃×#535	C₂²	1	4	yes	complemented
110	C₂₃×#535	C₂²	1	8	yes	complemented
111	C₂₃×#535	C₂²	1	2	yes	complemented
112	C₂₃×#535	C₂²	1	4	yes	complemented
113	C₂₃×#534	C₂²	1	4	yes	complemented
114	C₂₃×#534	C₂²	1	8	yes	complemented
115	C₂₃×#533	C₂²	1	4	yes	complemented
116	C₂₃×#532	C₂²	1	4	yes	complemented
117	C₂₃×#529	C₂²	1	8	yes	complemented
118	C₂₃×#529	C₂²	1	4	yes	complemented
119	C₂₃×#529	C₂²	1	4	yes	complemented
120	C₂₃×#525	C₂²	1	2	yes	—
121	C₂₃×#525	C₂²	1	2	yes	complemented
122	C₂₃×#525	C₂²	1	2	yes	complemented
123	C₂₃×#525	C₂²	1	2	yes	complemented
124	C₂₃×#525	C₂²	1	2	yes	complemented
125	C₂₃×#525	C₂²	1	4	yes	complemented
126	C₂₃×#525	C₂²	1	2	yes	complemented
127	C₂₃×#525	C₂²	1	4	yes	complemented
128	C₂₃×#525	C₂²	1	4	yes	complemented
129	C₂₃×#525	C₂²	1	4	yes	complemented
130	C₂₃×#525	C₂²	1	2	yes	complemented
131	C₂₃×#525	C₂²	1	4	yes	complemented
132	C₂₃×#525	C₂²	1	4	yes	complemented
133	C₂₃×#525	C₂²	1	2	yes	complemented
134	C₂₃×#525	C₂²	1	4	yes	complemented
135	C₂₃×#525	C₂²	1	4	yes	complemented
136	C₂₃×#525	C₂²	1	4	yes	complemented
137	C₂₃×#525	C₂²	1	4	yes	complemented
138	C₂₃×#525	C₂²	1	4	yes	complemented
139	C₂×C₂₃×#123	C₂²	1	4	yes	complemented
140	C₂×C₂₃×#123	C₂²	1	2	yes	complemented
141	C₂×C₂₃×#123	C₂²	1	4	yes	complemented
142	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
143	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
144	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
145	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
146	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
147	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
148	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
149	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
150	C₂×C₂₃×#120	C₂²	1	4	yes	complemented
151	C₂×C₂₃×#120	C₂²	1	2	yes	complemented
152	C₂₃×#520	C₂²	1	2	yes	complemented
153	C₂₃×#520	C₂²	1	2	yes	complemented
154	C₂₃×#520	C₂²	1	8	yes	complemented
155	C₂₃×#519	C₂²	1	1	yes	characteristic, complemented
156	C₂₃×#518	C₂²	1	1	yes	characteristic, complemented
157	C₂₃×#518	C₂²	1	8	yes	complemented
158	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
159	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
160	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
161	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
162	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
163	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
164	C₂₃×2₋¹⁺⁴	—	4	4	no	—
165	C₂₃×H(5,𝔽₂)	—	4	4	no	—
166	C₂×#41×C₂₃	—	4	4	no	—
167	C₂×#41×C₂₃	—	4	8	no	—
168	C₂×#41×C₂₃	C₂³	1	2	yes	—
169	C₂×#41×C₂₃	C₂³	1	2	yes	—
170	C₂×#41×C₂₃	C₂³	1	2	yes	—
171	C₂×#41×C₂₃	C₂³	1	4	yes	—
172	C₂×#41×C₂₃	C₂³	1	4	yes	—
173	C₂×#41×C₂₃	C₂³	1	4	yes	—
174	C₂×#41×C₂₃	C₂³	1	4	yes	—
175	C₂×#41×C₂₃	C₂³	1	8	yes	—
176	C₂×#41×C₂₃	C₂³	1	2	yes	—
177	C₂×#41×C₂₃	C₂³	1	4	yes	—
178	C₂×#41×C₂₃	C₂³	1	4	yes	complemented
179	C₂×#41×C₂₃	C₂³	1	4	yes	complemented
180	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
181	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
182	C₂²×Q₈×C₂₃	C₂³	1	4	yes	complemented
183	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
184	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
185	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
186	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
187	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
188	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
189	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
190	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
191	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
192	C₂²×D₄×C₂₃	C₂³	1	4	yes	complemented
193	C₂³×C₄×C₂₃	—	4	4	no	—
194	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
195	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
196	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
197	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
198	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
199	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
200	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
201	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
202	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
203	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
204	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
205	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
206	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
207	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
208	C₂₃×#127	C₂³	1	4	yes	—
209	C₂₃×#127	C₂³	1	4	yes	—
210	C₂₃×#127	C₂³	1	8	yes	—
211	C₂₃×#127	C₂³	1	4	yes	complemented
212	C₂₃×#126	C₂³	1	8	yes	—
213	C₂₃×#126	C₂³	1	8	yes	—
214	C₂₃×#126	C₂³	1	8	yes	—
215	C₂₃×#126	C₂³	1	8	yes	—
216	C₂₃×#126	C₂³	1	8	yes	complemented
217	C₂₃×#126	C₂³	1	8	yes	complemented
218	C₂₃×#126	C₂³	1	8	yes	complemented
219	C₂₃×#126	C₂³	1	8	yes	complemented
220	C₂₃×#126	C₂³	1	8	yes	complemented
221	C₂₃×#126	C₂³	1	8	yes	complemented
222	C₂₃×#125	C₂³	1	4	yes	complemented
223	C₂₃×#125	C₂³	1	8	yes	complemented
224	C₂₃×#125	C₂³	1	8	yes	complemented
225	C₂₃×#125	C₂³	1	8	yes	complemented
226	C₂₃×#125	C₂³	1	4	yes	complemented
227	C₂₃×#125	C₂³	1	8	yes	complemented
228	C₂₃×#124	C₂³	1	4	yes	—
229	C₂₃×#124	C₂³	1	4	yes	—
230	C₂₃×#124	C₂³	1	8	yes	—
231	C₂₃×#124	C₂³	1	8	yes	—
232	C₂₃×#124	C₂³	1	8	yes	—
233	C₂₃×#124	C₂³	1	8	yes	—
234	C₂₃×#124	C₂³	1	8	yes	—
235	C₂₃×#124	C₂³	1	4	yes	complemented
236	C₂₃×#124	C₂³	1	8	yes	complemented
237	C₂₃×#124	C₂³	1	4	yes	complemented
238	C₂₃×#124	C₂³	1	8	yes	complemented
239	C₂₃×#124	C₂³	1	8	yes	complemented
240	C₂₃×#123	C₂³	1	4	yes	—
241	C₂₃×#123	C₂³	1	4	yes	—
242	C₂₃×#123	C₂³	1	4	yes	—
243	C₂₃×#123	C₂³	1	8	yes	—
244	C₂₃×#123	C₂³	1	8	yes	—
245	C₂₃×#123	C₂³	1	8	yes	—
246	C₂₃×#123	C₂³	1	8	yes	—
247	C₂₃×#123	C₂³	1	4	yes	—
248	C₂₃×#123	C₂³	1	8	yes	—
249	C₂₃×#123	C₂³	1	8	yes	—
250	C₂₃×#123	C₂³	1	4	yes	—
251	C₂₃×#123	C₂³	1	8	yes	—
252	C₂₃×#123	C₂³	1	4	yes	—
253	C₂₃×#123	C₂³	1	8	yes	—
254	C₂₃×#123	C₂³	1	4	yes	—
255	C₂₃×#123	C₂³	1	4	yes	—
256	C₂₃×#123	C₂³	1	4	yes	—
257	C₂₃×#123	C₂³	1	4	yes	—
258	C₂₃×#123	C₂³	1	4	yes	—
259	C₂₃×#123	C₂³	1	8	yes	—
260	C₂₃×#123	C₂³	1	4	yes	—
261	C₂₃×#123	C₂³	1	8	yes	complemented
262	C₂₃×#123	C₂³	1	8	yes	complemented
263	C₂₃×#123	C₂³	1	8	yes	complemented
264	C₂₃×#123	C₂³	1	8	yes	complemented
265	C₂₃×#123	C₂³	1	8	yes	complemented
266	C₂₃×#123	C₂³	1	8	yes	complemented
267	C₂₃×#123	C₂³	1	8	yes	complemented
268	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
269	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
270	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
271	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
272	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
273	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
274	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
275	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
276	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
277	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
278	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
279	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
280	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
281	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
282	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
283	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
284	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
285	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
286	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
287	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
288	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
289	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
290	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
291	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
292	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
293	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
294	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
295	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
296	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
297	C₂₃×#121	C₂³	1	4	yes	—
298	C₂₃×#121	C₂³	1	8	yes	—
299	C₂₃×#121	C₂³	1	8	yes	—
300	C₂₃×#121	C₂³	1	8	yes	—
301	C₂₃×#121	C₂³	1	8	yes	—
302	C₂₃×#121	C₂³	1	8	yes	—
303	C₂₃×#121	C₂³	1	8	yes	—
304	C₂₃×#121	C₂³	1	8	yes	—
305	C₂₃×#121	C₂³	1	8	yes	—
306	C₂₃×#121	C₂³	1	2	yes	—
307	C₂₃×#121	C₂³	1	2	yes	—
308	C₂₃×#121	C₂³	1	4	yes	—
309	C₂₃×#121	C₂³	1	8	yes	—
310	C₂₃×#121	C₂³	1	8	yes	—
311	C₂₃×#121	C₂³	1	8	yes	—
312	C₂₃×#121	C₂³	1	4	yes	—
313	C₂₃×#121	C₂³	1	2	yes	—
314	C₂₃×#121	C₂³	1	8	yes	—
315	C₂₃×#121	C₂³	1	8	yes	—
316	C₂₃×#121	C₂³	1	8	yes	—
317	C₂₃×#121	C₂³	1	8	yes	—
318	C₂₃×#121	C₂³	1	2	yes	—
319	C₂₃×#121	C₂³	1	4	yes	—
320	C₂₃×#121	C₂³	1	2	yes	—
321	C₂₃×#121	C₂³	1	4	yes	—
322	C₂₃×#121	C₂³	1	2	yes	—
323	C₂₃×#121	C₂³	1	2	yes	—
324	C₂₃×#121	C₂³	1	4	yes	—
325	C₂₃×#121	C₂³	1	2	yes	—
326	C₂₃×#121	C₂³	1	4	yes	—
327	C₂₃×#121	C₂³	1	4	yes	—
328	C₂₃×#121	C₂³	1	4	yes	complemented
329	C₂₃×#121	C₂³	1	8	yes	complemented
330	C₂₃×#121	C₂³	1	4	yes	complemented
331	C₂₃×#121	C₂³	1	4	yes	complemented
332	C₂₃×#121	C₂³	1	8	yes	complemented
333	C₂₃×#121	C₂³	1	8	yes	complemented
334	C₂₃×#121	C₂³	1	4	yes	complemented
335	C₂₃×#121	C₂³	1	8	yes	complemented
336	C₂₃×#120	C₂³	1	4	yes	—
337	C₂₃×#120	C₂³	1	4	yes	—
338	C₂₃×#120	C₂³	1	8	yes	—
339	C₂₃×#120	C₂³	1	4	yes	—
340	C₂₃×#120	C₂³	1	8	yes	—
341	C₂₃×#120	C₂³	1	8	yes	—
342	C₂₃×#120	C₂³	1	4	yes	—
343	C₂₃×#120	C₂³	1	4	yes	—
344	C₂₃×#120	C₂³	1	4	yes	—
345	C₂₃×#120	C₂³	1	4	yes	—
346	C₂₃×#120	C₂³	1	4	yes	—
347	C₂₃×#120	C₂³	1	4	yes	—
348	C₂₃×#120	C₂³	1	8	yes	—
349	C₂₃×#120	C₂³	1	4	yes	—
350	C₂₃×#120	C₂³	1	4	yes	—
351	C₂₃×#120	C₂³	1	4	yes	—
352	C₂₃×#120	C₂³	1	8	yes	—
353	C₂₃×#120	C₂³	1	8	yes	complemented
354	C₄×Q₈×C₂₃	C₂³	1	4	yes	complemented
355	C₄×Q₈×C₂₃	C₂³	1	4	yes	complemented
356	C₄×Q₈×C₂₃	C₂³	1	4	yes	complemented
357	C₄×Q₈×C₂₃	C₂³	1	4	yes	complemented
358	C₄×Q₈×C₂₃	C₂³	1	8	yes	complemented
359	C₄×Q₈×C₂₃	C₂³	1	8	yes	complemented
360	C₄×D₄×C₂₃	C₂³	1	4	yes	—
361	C₄×D₄×C₂₃	C₂³	1	4	yes	—
362	C₄×D₄×C₂₃	C₂³	1	8	yes	—
363	C₄×D₄×C₂₃	C₂³	1	4	yes	—
364	C₄×D₄×C₂₃	C₂³	1	4	yes	—
365	C₄×D₄×C₂₃	C₂³	1	4	yes	—
366	C₄×D₄×C₂₃	C₂³	1	4	yes	—
367	C₄×D₄×C₂₃	C₂³	1	8	yes	—
368	C₄×D₄×C₂₃	C₂³	1	4	yes	—
369	C₄×D₄×C₂₃	C₂³	1	8	yes	—
370	C₄×D₄×C₂₃	C₂³	1	4	yes	—
371	C₄×D₄×C₂₃	C₂³	1	4	yes	—
372	C₄×D₄×C₂₃	C₂³	1	4	yes	—
373	C₄×D₄×C₂₃	C₂³	1	8	yes	—
374	C₄×D₄×C₂₃	C₂³	1	8	yes	—
375	C₄×D₄×C₂₃	C₂³	1	8	yes	—
376	C₄×D₄×C₂₃	C₂³	1	8	yes	—
377	C₄×D₄×C₂₃	C₂³	1	4	yes	—
378	C₄×D₄×C₂₃	C₂³	1	4	yes	—
379	C₄×D₄×C₂₃	C₂³	1	8	yes	—
380	C₄×D₄×C₂₃	C₂³	1	4	yes	—
381	C₄×D₄×C₂₃	C₂³	1	8	yes	—
382	C₄×D₄×C₂₃	C₂³	1	4	yes	—
383	C₄×D₄×C₂₃	C₂³	1	4	yes	—
384	C₄×D₄×C₂₃	C₂³	1	8	yes	—
385	C₄×D₄×C₂₃	C₂³	1	4	yes	—
386	C₄×D₄×C₂₃	C₂³	1	4	yes	complemented
387	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
388	C₄×D₄×C₂₃	C₂³	1	4	yes	complemented
389	C₄×D₄×C₂₃	C₂³	1	4	yes	complemented
390	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
391	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
392	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
393	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
394	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
395	C₄×D₄×C₂₃	C₂³	1	4	yes	complemented
396	C₂₃×#117	C₂³	1	8	yes	—
397	C₂₃×#117	C₂³	1	4	yes	—
398	C₂₃×#117	C₂³	1	4	yes	—
399	C₂₃×#117	C₂³	1	2	yes	—
400	C₂₃×#117	C₂³	1	4	yes	—
401	C₂₃×#117	C₂³	1	4	yes	—
402	C₂₃×#117	C₂³	1	2	yes	—
403	C₂₃×#117	C₂³	1	2	yes	—
404	C₂₃×#117	C₂³	1	2	yes	—
405	C₂₃×#117	C₂³	1	4	yes	—
406	C₂₃×#117	C₂³	1	8	yes	complemented
407	C₂₃×#117	C₂³	1	8	yes	complemented
408	C₂₃×#117	C₂³	1	8	yes	complemented
409	C₂₃×#117	C₂³	1	8	yes	complemented
410	C₂₃×#117	C₂³	1	4	yes	complemented
411	C₂₃×#117	C₂³	1	4	yes	complemented
412	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
413	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
414	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
415	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
416	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
417	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
418	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	complemented
419	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	complemented
420	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
421	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
422	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
423	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
424	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
425	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
426	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
427	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
428	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
429	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
430	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
431	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
432	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	complemented
433	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	complemented
434	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
435	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
436	C₂⁴×C₂₃	—	4	2	no	—
437	C₂⁴×C₂₃	—	4	4	no	—
438	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
439	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
440	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
441	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
442	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
443	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
444	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
445	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
446	#41×C₂₃	—	2	8	no	—
447	#41×C₂₃	—	2	8	no	—
448	#41×C₂₃	—	4	8	no	—
449	#41×C₂₃	—	4	8	no	—
450	#41×C₂₃	—	4	16	no	—
451	#41×C₂₃	—	4	8	no	—
452	#41×C₂₃	—	4	8	no	—
453	#41×C₂₃	—	4	8	no	—
454	#41×C₂₃	—	4	4	no	—
455	#41×C₂₃	—	4	4	no	—
456	#41×C₂₃	—	4	8	no	—
457	#41×C₂₃	—	4	8	no	—
458	C₂×Q₈×C₂₃	—	2	4	no	—
459	C₂×Q₈×C₂₃	—	4	4	no	—
460	C₂×Q₈×C₂₃	—	4	8	no	—
461	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
462	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
463	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
464	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
465	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
466	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
467	C₂×D₄×C₂₃	—	2	4	no	—
468	C₂×D₄×C₂₃	—	4	4	no	—
469	C₂×D₄×C₂₃	—	4	8	no	—
470	C₂×D₄×C₂₃	—	4	8	no	—
471	C₂×D₄×C₂₃	—	4	4	no	—
472	C₂×D₄×C₂₃	—	4	16	no	—
473	C₂×D₄×C₂₃	—	4	8	no	—
474	C₂×D₄×C₂₃	—	4	8	no	—
475	C₂×D₄×C₂₃	—	4	8	no	—
476	C₂×D₄×C₂₃	—	4	8	no	—
477	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
478	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
479	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
480	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
481	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
482	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
483	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
484	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
485	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
486	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
487	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
488	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
489	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
490	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
491	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
492	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
493	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
494	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
495	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
496	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
497	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
498	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
499	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
500	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
501	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
502	C₂²×C₄×C₂₃	—	2	4	no	—
503	C₂²×C₄×C₂₃	—	2	8	no	—
504	C₂²×C₄×C₂₃	—	4	4	no	—
505	C₂²×C₄×C₂₃	—	4	4	no	—
506	C₂²×C₄×C₂₃	—	4	4	no	—
507	C₂²×C₄×C₂₃	—	4	4	no	—
508	C₂²×C₄×C₂₃	—	4	8	no	—
509	C₂²×C₄×C₂₃	—	4	4	no	—
510	C₂²×C₄×C₂₃	—	4	2	no	—
511	C₂²×C₄×C₂₃	—	4	4	no	—
512	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
513	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
514	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
515	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
516	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
517	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
518	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
519	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
520	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
521	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
522	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
523	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
524	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
525	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
526	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
527	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
528	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
529	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
530	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
531	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
532	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
533	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
534	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
535	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
536	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
537	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
538	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
539	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
540	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
541	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
542	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
543	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
544	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
545	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
546	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
547	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
548	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
549	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
550	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
551	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
552	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
553	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
554	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
555	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
556	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
557	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
558	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
559	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
560	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
561	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
562	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
563	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
564	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
565	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
566	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
567	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
568	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
569	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
570	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
571	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
572	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
573	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
574	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
575	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
576	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
577	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
578	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
579	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
580	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
581	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
582	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
583	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
584	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
585	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
586	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
587	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
588	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
589	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
590	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
591	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
592	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
593	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
594	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
595	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
596	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
597	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
598	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
599	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
600	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
601	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
602	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
603	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
604	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
605	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
606	C₄²×C₂₃	C₂⁴	1	4	yes	—
607	C₄²×C₂₃	C₂⁴	1	8	yes	—
608	C₄²×C₂₃	C₂⁴	1	4	yes	—
609	C₄²×C₂₃	C₂⁴	1	4	yes	—
610	C₄²×C₂₃	C₂⁴	1	4	yes	—
611	C₄²×C₂₃	C₂⁴	1	4	yes	—
612	C₄²×C₂₃	C₂⁴	1	4	yes	—
613	C₄²×C₂₃	C₂⁴	1	8	yes	—
614	C₄²×C₂₃	C₂⁴	1	8	yes	—
615	#62821	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
616	C₂³×C₂₃	—	2	4	no	—
617	C₂³×C₂₃	—	2	2	no	—
618	C₂³×C₂₃	—	2	4	no	—
619	C₂³×C₂₃	—	2	4	no	—
620	C₂³×C₂₃	—	2	4	no	—
621	C₂³×C₂₃	—	2	4	no	—
622	C₂³×C₂₃	—	2	8	no	—
623	C₂³×C₂₃	—	4	1	no	—
624	C₂³×C₂₃	—	4	2	no	—
625	C₂³×C₂₃	—	4	1	no	—
626	C₂³×C₂₃	—	4	2	no	—
627	C₂³×C₂₃	—	4	2	no	—
628	C₂³×C₂₃	—	4	2	no	—
629	C₂³×C₂₃	—	4	2	no	—
630	C₂³×C₂₃	—	4	4	no	—
631	C₂³×C₂₃	—	4	4	no	—
632	C₂³×C₂₃	—	4	4	no	—
633	C₂³×C₂₃	—	4	4	no	—
634	C₂³×C₂₃	—	4	8	no	—
635	C₂³×C₂₃	—	4	16	no	—
636	C₂³×C₂₃	C₂⁵	1	2	yes	—
637	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
638	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
639	C₂³×C₂₃	C₂⁵	1	4	yes	—
640	C₂³×C₂₃	C₂⁵	1	4	yes	—
641	C₂³×C₂₃	C₂⁵	1	4	yes	—
642	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
643	C₂³×C₂₃	C₂⁵	1	2	yes	—
644	Q₈×C₂₃	—	2	8	no	—
645	Q₈×C₂₃	—	2	4	no	—
646	Q₈×C₂₃	—	2	4	no	—
647	Q₈×C₂₃	—	4	4	no	—
648	Q₈×C₂₃	—	4	4	no	—
649	Q₈×C₂₃	—	4	8	no	—
650	D₄×C₂₃	—	2	8	no	—
651	D₄×C₂₃	—	2	8	no	—
652	D₄×C₂₃	—	2	8	no	—
653	D₄×C₂₃	—	2	16	no	—
654	D₄×C₂₃	—	2	8	no	—
655	D₄×C₂₃	—	2	8	no	—
656	D₄×C₂₃	—	2	4	no	—
657	D₄×C₂₃	—	2	4	no	—
658	D₄×C₂₃	—	4	8	no	—
659	D₄×C₂₃	—	4	4	no	—
660	D₄×C₂₃	—	4	4	no	—
661	D₄×C₂₃	—	4	4	no	—
662	D₄×C₂₃	—	4	4	no	—
663	D₄×C₂₃	—	4	4	no	—
664	D₄×C₂₃	—	4	8	no	—
665	D₄×C₂₃	—	4	8	no	—
666	D₄×C₂₃	—	4	8	no	—
667	D₄×C₂₃	—	4	4	no	—
668	D₄×C₂₃	—	4	4	no	—
669	D₄×C₂₃	—	4	4	no	—
670	D₄×C₂₃	—	4	4	no	—
671	D₄×C₂₃	—	4	4	no	—
672	D₄×C₂₃	—	4	4	no	—
673	D₄×C₂₃	—	4	8	no	—
674	D₄×C₂₃	—	4	4	no	—
675	C₂×C₄×C₂₃	—	2	2	no	—
676	C₂×C₄×C₂₃	—	2	4	no	—
677	C₂×C₄×C₂₃	—	2	4	no	—
678	C₂×C₄×C₂₃	—	2	8	no	—
679	C₂×C₄×C₂₃	—	2	4	no	—
680	C₂×C₄×C₂₃	—	2	4	no	—
681	C₂×C₄×C₂₃	—	2	4	no	—
682	C₂×C₄×C₂₃	—	2	4	no	—
683	C₂×C₄×C₂₃	—	2	4	no	—
684	C₂×C₄×C₂₃	—	2	4	no	—
685	C₂×C₄×C₂₃	—	2	8	no	—
686	C₂×C₄×C₂₃	—	2	8	no	—
687	C₂×C₄×C₂₃	—	4	2	no	—
688	C₂×C₄×C₂₃	—	4	2	no	—
689	C₂×C₄×C₂₃	—	4	1	no	—
690	C₂×C₄×C₂₃	—	4	2	no	—
691	C₂×C₄×C₂₃	—	4	2	no	—
692	C₂×C₄×C₂₃	—	4	2	no	—
693	C₂×C₄×C₂₃	—	4	1	no	—
694	C₂×C₄×C₂₃	—	4	4	no	—
695	C₂×C₄×C₂₃	—	4	4	no	—
696	C₂×C₄×C₂₃	—	4	4	no	—
697	C₂×C₄×C₂₃	—	4	8	no	—
698	C₂×C₄×C₂₃	—	4	8	no	—
699	C₂×C₄×C₂₃	—	4	4	no	—
700	C₂×C₄×C₂₃	—	4	4	no	—
701	C₂×C₄×C₂₃	—	4	4	no	—
702	C₂×C₄×C₂₃	—	4	8	no	—
703	C₂×C₄×C₂₃	—	4	8	no	—
704	C₂×C₄×C₂₃	—	4	8	no	—
705	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
706	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
707	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
708	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
709	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
710	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
711	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
712	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
713	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
714	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
715	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
716	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
717	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
718	#3542	C₂×C₂₃	1	4	yes	complemented
719	#3541	C₂×C₂₃	1	4	yes	complemented
720	#3540	C₂×C₂₃	1	4	yes	complemented
721	#3539	C₂×C₂₃	1	4	yes	complemented
722	#3533	C₂×C₂₃	1	4	yes	complemented
723	#3532	C₂×C₂₃	1	4	yes	complemented
724	#3520	C₂×C₂₃	1	4	yes	complemented
725	#3519	C₂×C₂₃	1	4	yes	complemented
726	#3513	C₂×C₂₃	1	8	yes	complemented
727	#3506	C₂×C₂₃	1	4	yes	complemented
728	#3505	C₂×C₂₃	1	4	yes	complemented
729	#3495	C₂×C₂₃	1	2	yes	complemented
730	#3494	C₂×C₂₃	1	2	yes	complemented
731	#3493	C₂×C₂₃	1	2	yes	complemented
732	#3489	C₂×C₂₃	1	2	yes	complemented
733	#3488	C₂×C₂₃	1	2	yes	complemented
734	#3487	C₂×C₂₃	1	1	yes	characteristic, complemented
735	#3485	C₂×C₂₃	1	1	yes	characteristic, complemented
736	C₂×#525	C₂×C₂₃	1	2	yes	complemented
737	C₂×#525	C₂×C₂₃	1	1	yes	characteristic, complemented
738	C₂²×C₂₃	—	2	2	no	—
739	C₂²×C₂₃	—	2	2	no	—
740	C₂²×C₂₃	—	2	2	no	—
741	C₂²×C₂₃	—	2	1	no	—
742	C₂²×C₂₃	—	2	2	no	—
743	C₂²×C₂₃	—	2	1	no	—
744	C₂²×C₂₃	—	2	4	no	—
745	C₂²×C₂₃	—	2	4	no	—
746	C₂²×C₂₃	—	2	4	no	—
747	C₂²×C₂₃	—	2	4	no	—
748	C₂²×C₂₃	—	2	4	no	—
749	C₂²×C₂₃	—	2	8	no	—
750	C₂²×C₂₃	—	2	4	no	—
751	C₂²×C₂₃	—	2	4	no	—
752	C₂²×C₂₃	—	2	2	no	—
753	C₂²×C₂₃	—	2	2	no	—
754	C₂²×C₂₃	—	2	2	no	—
755	C₂²×C₂₃	—	2	2	no	—
756	C₂²×C₂₃	—	4	8	no	—
757	C₂²×C₂₃	—	4	4	no	—
758	C₂²×C₂₃	—	4	4	no	—
759	C₂²×C₂₃	—	4	8	no	—
760	C₂²×C₂₃	—	4	4	no	—
761	C₂²×C₂₃	—	8	4	no	—
762	C₂²×C₂₃	—	8	8	no	—
763	C₂²×C₂₃	—	16	4	no	—
764	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
765	C₂²×C₂₃	#585	1	4	yes	—
766	C₂²×C₂₃	C₂⁶	1	1	yes	characteristic
767	C₄×C₂₃	—	2	2	no	—
768	C₄×C₂₃	—	2	2	no	—
769	C₄×C₂₃	—	2	2	no	—
770	C₄×C₂₃	—	2	4	no	—
771	C₄×C₂₃	—	2	4	no	—
772	C₄×C₂₃	—	2	4	no	—
773	C₄×C₂₃	—	2	4	no	—
774	C₄×C₂₃	—	2	4	no	—
775	C₄×C₂₃	—	2	4	no	—
776	C₄×C₂₃	—	2	8	no	—
777	C₄×C₂₃	—	2	4	no	—
778	C₄×C₂₃	C₂×H(5,𝔽₂)	1	4	yes	—
779	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic, complemented
780	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic, complemented
781	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
782	C₂²×#41	C₂²×C₂₃	1	2	yes	complemented
783	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
784	#563	C₂²×C₂₃	1	4	yes	complemented
785	#562	C₂²×C₂₃	1	8	yes	complemented
786	H(3,𝔽₄)	C₂²×C₂₃	1	4	yes	complemented
787	#560	C₂²×C₂₃	1	4	yes	complemented
788	#560	C₂²×C₂₃	1	8	yes	complemented
789	#560	C₂²×C₂₃	1	4	yes	complemented
790	#559	C₂²×C₂₃	1	4	yes	complemented
791	#559	C₂²×C₂₃	1	8	yes	complemented
792	#556	C₂²×C₂₃	1	4	yes	complemented
793	#556	C₂²×C₂₃	1	4	yes	complemented
794	#556	C₂²×C₂₃	1	4	yes	complemented
795	#555	C₂²×C₂₃	1	4	yes	complemented
796	#555	C₂²×C₂₃	1	4	yes	complemented
797	#555	C₂²×C₂₃	1	4	yes	complemented
798	#554	C₂²×C₂₃	1	4	yes	complemented
799	#554	C₂²×C₂₃	1	8	yes	complemented
800	#553	C₂²×C₂₃	1	4	yes	complemented
801	#553	C₂²×C₂₃	1	8	yes	complemented
802	#553	C₂²×C₂₃	1	4	yes	complemented
803	#553	C₂²×C₂₃	1	4	yes	complemented
804	#553	C₂²×C₂₃	1	4	yes	complemented
805	#553	C₂²×C₂₃	1	8	yes	complemented
806	#553	C₂²×C₂₃	1	8	yes	complemented
807	#553	C₂²×C₂₃	1	8	yes	complemented
808	#552	C₂²×C₂₃	1	8	yes	complemented
809	#552	C₂²×C₂₃	1	4	yes	complemented
810	#552	C₂²×C₂₃	1	4	yes	complemented
811	#552	C₂²×C₂₃	1	4	yes	complemented
812	#552	C₂²×C₂₃	1	4	yes	complemented
813	#551	C₂²×C₂₃	1	8	yes	complemented
814	#551	C₂²×C₂₃	1	4	yes	complemented
815	#551	C₂²×C₂₃	1	8	yes	complemented
816	#551	C₂²×C₂₃	1	8	yes	complemented
817	#551	C₂²×C₂₃	1	4	yes	complemented
818	#551	C₂²×C₂₃	1	8	yes	complemented
819	#550	C₂²×C₂₃	1	4	yes	complemented
820	#550	C₂²×C₂₃	1	4	yes	complemented
821	#550	C₂²×C₂₃	1	4	yes	complemented
822	D₄×Q₈	C₂²×C₂₃	1	4	yes	complemented
823	#548	C₂²×C₂₃	1	4	yes	complemented
824	#548	C₂²×C₂₃	1	4	yes	complemented
825	#548	C₂²×C₂₃	1	4	yes	complemented
826	#548	C₂²×C₂₃	1	4	yes	complemented
827	#547	C₂²×C₂₃	1	8	yes	complemented
828	#547	C₂²×C₂₃	1	4	yes	complemented
829	#547	C₂²×C₂₃	1	4	yes	complemented
830	#547	C₂²×C₂₃	1	4	yes	complemented
831	#547	C₂²×C₂₃	1	4	yes	complemented
832	#546	C₂²×C₂₃	1	8	yes	complemented
833	#546	C₂²×C₂₃	1	8	yes	complemented
834	#546	C₂²×C₂₃	1	8	yes	complemented
835	#546	C₂²×C₂₃	1	4	yes	complemented
836	#546	C₂²×C₂₃	1	8	yes	complemented
837	#546	C₂²×C₂₃	1	8	yes	complemented
838	#546	C₂²×C₂₃	1	4	yes	complemented
839	#546	C₂²×C₂₃	1	4	yes	complemented
840	#546	C₂²×C₂₃	1	4	yes	complemented
841	D₄²	C₂²×C₂₃	1	8	yes	complemented
842	D₄²	C₂²×C₂₃	1	4	yes	complemented
843	D₄²	C₂²×C₂₃	1	4	yes	complemented
844	#544	C₂²×C₂₃	1	2	yes	complemented
845	#542	C₂²×C₂₃	1	4	yes	complemented
846	#542	C₂²×C₂₃	1	4	yes	complemented
847	#542	C₂²×C₂₃	1	8	yes	complemented
848	#542	C₂²×C₂₃	1	8	yes	complemented
849	#541	C₂²×C₂₃	1	4	yes	complemented
850	#540	C₂²×C₂₃	1	4	yes	complemented
851	#540	C₂²×C₂₃	1	8	yes	complemented
852	#540	C₂²×C₂₃	1	8	yes	complemented
853	#539	C₂²×C₂₃	1	8	yes	complemented
854	#539	C₂²×C₂₃	1	8	yes	complemented
855	#539	C₂²×C₂₃	1	8	yes	complemented
856	#538	C₂²×C₂₃	1	8	yes	complemented
857	#538	C₂²×C₂₃	1	8	yes	complemented
858	#538	C₂²×C₂₃	1	8	yes	complemented
859	#538	C₂²×C₂₃	1	8	yes	complemented
860	#538	C₂²×C₂₃	1	8	yes	complemented
861	#538	C₂²×C₂₃	1	8	yes	complemented
862	#537	C₂²×C₂₃	1	2	yes	complemented
863	#537	C₂²×C₂₃	1	4	yes	complemented
864	#537	C₂²×C₂₃	1	4	yes	complemented
865	#536	C₂²×C₂₃	1	2	yes	complemented
866	#536	C₂²×C₂₃	1	4	yes	complemented
867	#535	C₂²×C₂₃	1	4	yes	complemented
868	#535	C₂²×C₂₃	1	8	yes	complemented
869	#535	C₂²×C₂₃	1	2	yes	complemented
870	#535	C₂²×C₂₃	1	4	yes	complemented
871	#534	C₂²×C₂₃	1	4	yes	complemented
872	#534	C₂²×C₂₃	1	8	yes	complemented
873	#533	C₂²×C₂₃	1	4	yes	complemented
874	#532	C₂²×C₂₃	1	4	yes	complemented
875	#529	C₂²×C₂₃	1	8	yes	complemented
876	#529	C₂²×C₂₃	1	4	yes	complemented
877	#529	C₂²×C₂₃	1	4	yes	complemented
878	#525	C₂²×C₂₃	1	2	yes	—
879	#525	C₂²×C₂₃	1	2	yes	complemented
880	#525	C₂²×C₂₃	1	2	yes	complemented
881	#525	C₂²×C₂₃	1	2	yes	complemented
882	#525	C₂²×C₂₃	1	2	yes	complemented
883	#525	C₂²×C₂₃	1	4	yes	complemented
884	#525	C₂²×C₂₃	1	2	yes	complemented
885	#525	C₂²×C₂₃	1	4	yes	complemented
886	#525	C₂²×C₂₃	1	4	yes	complemented
887	#525	C₂²×C₂₃	1	4	yes	complemented
888	#525	C₂²×C₂₃	1	2	yes	complemented
889	#525	C₂²×C₂₃	1	4	yes	complemented
890	#525	C₂²×C₂₃	1	4	yes	complemented
891	#525	C₂²×C₂₃	1	2	yes	complemented
892	#525	C₂²×C₂₃	1	4	yes	complemented
893	#525	C₂²×C₂₃	1	4	yes	complemented
894	#525	C₂²×C₂₃	1	4	yes	complemented
895	#525	C₂²×C₂₃	1	4	yes	complemented
896	#525	C₂²×C₂₃	1	4	yes	complemented
897	C₂×#123	C₂²×C₂₃	1	4	yes	complemented
898	C₂×#123	C₂²×C₂₃	1	2	yes	complemented
899	C₂×#123	C₂²×C₂₃	1	4	yes	complemented
900	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
901	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
902	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
903	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	complemented
904	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
905	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
906	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
907	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
908	C₂×#120	C₂²×C₂₃	1	2	yes	complemented
909	C₂×#120	C₂²×C₂₃	1	4	yes	complemented
910	#520	C₂²×C₂₃	1	2	yes	complemented
911	#520	C₂²×C₂₃	1	2	yes	complemented
912	#520	C₂²×C₂₃	1	8	yes	complemented
913	#519	C₂²×C₂₃	1	1	yes	characteristic, complemented
914	#518	C₂²×C₂₃	1	1	yes	characteristic, complemented
915	#518	C₂²×C₂₃	1	8	yes	complemented
916	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	complemented
917	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	complemented
918	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	complemented
919	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic, complemented
920	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
921	C₂×C₂₃	—	2	2	no	—
922	C₂×C₂₃	—	2	4	no	—
923	C₂×C₂₃	—	4	2	no	—
924	C₂×C₂₃	—	4	1	no	—
925	C₂×C₂₃	—	4	1	no	—
926	C₂×C₂₃	—	4	4	no	—
927	C₂×C₂₃	—	4	4	no	—
928	C₂×C₂₃	—	4	4	no	—
929	C₂×C₂₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
930	C₂×C₂₃	C₂×#585	1	2	yes	—
931	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
932	2₋¹⁺⁴	—	4	4	no	—
933	H(5,𝔽₂)	—	4	4	no	—
934	C₂×#41	—	4	4	no	—
935	C₂×#41	—	4	8	no	—
936	C₂×#41	C₂³×C₂₃	1	2	yes	—
937	C₂×#41	C₂³×C₂₃	1	2	yes	—
938	C₂×#41	C₂³×C₂₃	1	8	yes	—
939	C₂×#41	C₂³×C₂₃	1	4	yes	—
940	C₂×#41	C₂³×C₂₃	1	4	yes	—
941	C₂×#41	C₂³×C₂₃	1	2	yes	—
942	C₂×#41	C₂³×C₂₃	1	4	yes	—
943	C₂×#41	C₂³×C₂₃	1	4	yes	—
944	C₂×#41	C₂³×C₂₃	1	2	yes	—
945	C₂×#41	C₂³×C₂₃	1	4	yes	—
946	C₂×#41	C₂³×C₂₃	1	4	yes	complemented
947	C₂×#41	C₂³×C₂₃	1	4	yes	complemented
948	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
949	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
950	C₂²×Q₈	C₂³×C₂₃	1	4	yes	complemented
951	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
952	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
953	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
954	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
955	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
956	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
957	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
958	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
959	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
960	C₂²×D₄	C₂³×C₂₃	1	4	yes	complemented
961	C₂³×C₄	—	4	4	no	—
962	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
963	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
964	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
965	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
966	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
967	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
968	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
969	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
970	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
971	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
972	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	complemented
973	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	complemented
974	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	complemented
975	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
976	#127	C₂³×C₂₃	1	4	yes	—
977	#127	C₂³×C₂₃	1	8	yes	—
978	#127	C₂³×C₂₃	1	4	yes	—
979	#127	C₂³×C₂₃	1	4	yes	complemented
980	#126	C₂³×C₂₃	1	8	yes	—
981	#126	C₂³×C₂₃	1	8	yes	—
982	#126	C₂³×C₂₃	1	8	yes	—
983	#126	C₂³×C₂₃	1	8	yes	—
984	#126	C₂³×C₂₃	1	8	yes	complemented
985	#126	C₂³×C₂₃	1	8	yes	complemented
986	#126	C₂³×C₂₃	1	8	yes	complemented
987	#126	C₂³×C₂₃	1	8	yes	complemented
988	#126	C₂³×C₂₃	1	8	yes	complemented
989	#126	C₂³×C₂₃	1	8	yes	complemented
990	#125	C₂³×C₂₃	1	8	yes	complemented
991	#125	C₂³×C₂₃	1	4	yes	complemented
992	#125	C₂³×C₂₃	1	4	yes	complemented
993	#125	C₂³×C₂₃	1	8	yes	complemented
994	#125	C₂³×C₂₃	1	8	yes	complemented
995	#125	C₂³×C₂₃	1	8	yes	complemented
996	#124	C₂³×C₂₃	1	4	yes	—
997	#124	C₂³×C₂₃	1	8	yes	—
998	#124	C₂³×C₂₃	1	8	yes	—
999	#124	C₂³×C₂₃	1	4	yes	—
1000	#124	C₂³×C₂₃	1	8	yes	—
1001	#124	C₂³×C₂₃	1	8	yes	—
1002	#124	C₂³×C₂₃	1	8	yes	—
1003	#124	C₂³×C₂₃	1	4	yes	complemented
1004	#124	C₂³×C₂₃	1	4	yes	complemented
1005	#124	C₂³×C₂₃	1	8	yes	complemented
1006	#124	C₂³×C₂₃	1	8	yes	complemented
1007	#124	C₂³×C₂₃	1	8	yes	complemented
1008	#123	C₂³×C₂₃	1	4	yes	—
1009	#123	C₂³×C₂₃	1	4	yes	—
1010	#123	C₂³×C₂₃	1	4	yes	—
1011	#123	C₂³×C₂₃	1	4	yes	—
1012	#123	C₂³×C₂₃	1	8	yes	—
1013	#123	C₂³×C₂₃	1	4	yes	—
1014	#123	C₂³×C₂₃	1	4	yes	—
1015	#123	C₂³×C₂₃	1	4	yes	—
1016	#123	C₂³×C₂₃	1	4	yes	—
1017	#123	C₂³×C₂₃	1	4	yes	—
1018	#123	C₂³×C₂₃	1	4	yes	—
1019	#123	C₂³×C₂₃	1	8	yes	—
1020	#123	C₂³×C₂₃	1	8	yes	—
1021	#123	C₂³×C₂₃	1	8	yes	—
1022	#123	C₂³×C₂₃	1	4	yes	—
1023	#123	C₂³×C₂₃	1	8	yes	—
1024	#123	C₂³×C₂₃	1	4	yes	—
1025	#123	C₂³×C₂₃	1	8	yes	—
1026	#123	C₂³×C₂₃	1	8	yes	—
1027	#123	C₂³×C₂₃	1	8	yes	—
1028	#123	C₂³×C₂₃	1	8	yes	—
1029	#123	C₂³×C₂₃	1	8	yes	complemented
1030	#123	C₂³×C₂₃	1	8	yes	complemented
1031	#123	C₂³×C₂₃	1	8	yes	complemented
1032	#123	C₂³×C₂₃	1	8	yes	complemented
1033	#123	C₂³×C₂₃	1	8	yes	complemented
1034	#123	C₂³×C₂₃	1	8	yes	complemented
1035	#123	C₂³×C₂₃	1	8	yes	complemented
1036	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
1037	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
1038	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
1039	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
1040	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
1041	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
1042	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
1043	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
1044	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
1045	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
1046	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
1047	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
1048	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
1049	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
1050	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
1051	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
1052	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
1053	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
1054	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
1055	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	complemented
1056	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	complemented
1057	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
1058	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	complemented
1059	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	complemented
1060	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
1061	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
1062	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
1063	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
1064	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
1065	#121	C₂³×C₂₃	1	2	yes	—
1066	#121	C₂³×C₂₃	1	4	yes	—
1067	#121	C₂³×C₂₃	1	2	yes	—
1068	#121	C₂³×C₂₃	1	2	yes	—
1069	#121	C₂³×C₂₃	1	4	yes	—
1070	#121	C₂³×C₂₃	1	2	yes	—
1071	#121	C₂³×C₂₃	1	4	yes	—
1072	#121	C₂³×C₂₃	1	4	yes	—
1073	#121	C₂³×C₂₃	1	4	yes	—
1074	#121	C₂³×C₂₃	1	4	yes	—
1075	#121	C₂³×C₂₃	1	2	yes	—
1076	#121	C₂³×C₂₃	1	2	yes	—
1077	#121	C₂³×C₂₃	1	4	yes	—
1078	#121	C₂³×C₂₃	1	2	yes	—
1079	#121	C₂³×C₂₃	1	2	yes	—
1080	#121	C₂³×C₂₃	1	4	yes	—
1081	#121	C₂³×C₂₃	1	8	yes	—
1082	#121	C₂³×C₂₃	1	8	yes	—
1083	#121	C₂³×C₂₃	1	8	yes	—
1084	#121	C₂³×C₂₃	1	8	yes	—
1085	#121	C₂³×C₂₃	1	8	yes	—
1086	#121	C₂³×C₂₃	1	8	yes	—
1087	#121	C₂³×C₂₃	1	8	yes	—
1088	#121	C₂³×C₂₃	1	8	yes	—
1089	#121	C₂³×C₂₃	1	8	yes	—
1090	#121	C₂³×C₂₃	1	8	yes	—
1091	#121	C₂³×C₂₃	1	8	yes	—
1092	#121	C₂³×C₂₃	1	8	yes	—
1093	#121	C₂³×C₂₃	1	8	yes	—
1094	#121	C₂³×C₂₃	1	8	yes	—
1095	#121	C₂³×C₂₃	1	8	yes	—
1096	#121	C₂³×C₂₃	1	4	yes	complemented
1097	#121	C₂³×C₂₃	1	4	yes	complemented
1098	#121	C₂³×C₂₃	1	8	yes	complemented
1099	#121	C₂³×C₂₃	1	4	yes	complemented
1100	#121	C₂³×C₂₃	1	4	yes	complemented
1101	#121	C₂³×C₂₃	1	8	yes	complemented
1102	#121	C₂³×C₂₃	1	8	yes	complemented
1103	#121	C₂³×C₂₃	1	8	yes	complemented
1104	#120	C₂³×C₂₃	1	4	yes	—
1105	#120	C₂³×C₂₃	1	4	yes	—
1106	#120	C₂³×C₂₃	1	4	yes	—
1107	#120	C₂³×C₂₃	1	8	yes	—
1108	#120	C₂³×C₂₃	1	4	yes	—
1109	#120	C₂³×C₂₃	1	4	yes	—
1110	#120	C₂³×C₂₃	1	4	yes	—
1111	#120	C₂³×C₂₃	1	4	yes	—
1112	#120	C₂³×C₂₃	1	4	yes	—
1113	#120	C₂³×C₂₃	1	4	yes	—
1114	#120	C₂³×C₂₃	1	4	yes	—
1115	#120	C₂³×C₂₃	1	8	yes	—
1116	#120	C₂³×C₂₃	1	8	yes	—
1117	#120	C₂³×C₂₃	1	8	yes	—
1118	#120	C₂³×C₂₃	1	4	yes	—
1119	#120	C₂³×C₂₃	1	8	yes	—
1120	#120	C₂³×C₂₃	1	4	yes	—
1121	#120	C₂³×C₂₃	1	8	yes	complemented
1122	C₄×Q₈	C₂³×C₂₃	1	4	yes	complemented
1123	C₄×Q₈	C₂³×C₂₃	1	4	yes	complemented
1124	C₄×Q₈	C₂³×C₂₃	1	4	yes	complemented
1125	C₄×Q₈	C₂³×C₂₃	1	8	yes	complemented
1126	C₄×Q₈	C₂³×C₂₃	1	4	yes	complemented
1127	C₄×Q₈	C₂³×C₂₃	1	8	yes	complemented
1128	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1129	C₄×D₄	C₂³×C₂₃	1	8	yes	—
1130	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1131	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1132	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1133	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1134	C₄×D₄	C₂³×C₂₃	1	8	yes	—
1135	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1136	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1137	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1138	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1139	C₄×D₄	C₂³×C₂₃	1	8	yes	—
1140	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1141	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1142	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1143	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1144	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1145	C₄×D₄	C₂³×C₂₃	1	8	yes	—
1146	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1147	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1148	C₄×D₄	C₂³×C₂₃	1	8	yes	—
1149	C₄×D₄	C₂³×C₂₃	1	8	yes	—
1150	C₄×D₄	C₂³×C₂₃	1	8	yes	—
1151	C₄×D₄	C₂³×C₂₃	1	8	yes	—
1152	C₄×D₄	C₂³×C₂₃	1	8	yes	—
1153	C₄×D₄	C₂³×C₂₃	1	8	yes	—
1154	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
1155	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
1156	C₄×D₄	C₂³×C₂₃	1	4	yes	complemented
1157	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
1158	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
1159	C₄×D₄	C₂³×C₂₃	1	4	yes	complemented
1160	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
1161	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
1162	C₄×D₄	C₂³×C₂₃	1	4	yes	complemented
1163	C₄×D₄	C₂³×C₂₃	1	4	yes	complemented
1164	#117	C₂³×C₂₃	1	2	yes	—
1165	#117	C₂³×C₂₃	1	2	yes	—
1166	#117	C₂³×C₂₃	1	4	yes	—
1167	#117	C₂³×C₂₃	1	4	yes	—
1168	#117	C₂³×C₂₃	1	2	yes	—
1169	#117	C₂³×C₂₃	1	4	yes	—
1170	#117	C₂³×C₂₃	1	4	yes	—
1171	#117	C₂³×C₂₃	1	2	yes	—
1172	#117	C₂³×C₂₃	1	4	yes	—
1173	#117	C₂³×C₂₃	1	8	yes	—
1174	#117	C₂³×C₂₃	1	8	yes	complemented
1175	#117	C₂³×C₂₃	1	8	yes	complemented
1176	#117	C₂³×C₂₃	1	4	yes	complemented
1177	#117	C₂³×C₂₃	1	4	yes	complemented
1178	#117	C₂³×C₂₃	1	8	yes	complemented
1179	#117	C₂³×C₂₃	1	8	yes	complemented
1180	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
1181	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
1182	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
1183	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
1184	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
1185	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
1186	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	complemented
1187	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	complemented
1188	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	complemented
1189	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	complemented
1190	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
1191	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
1192	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
1193	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
1194	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
1195	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
1196	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
1197	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
1198	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
1199	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
1200	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	complemented
1201	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	complemented
1202	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
1203	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
1204	C₂₃	#62821	1	1	yes	characteristic, direct product factor, Sylow
1205	C₂⁴	—	4	2	no	—
1206	C₂⁴	—	4	4	no	—
1207	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
1208	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1209	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
1210	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
1211	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1212	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
1213	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
1214	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1215	#41	—	2	8	no	—
1216	#41	—	2	8	no	—
1217	#41	—	4	8	no	—
1218	#41	—	4	8	no	—
1219	#41	—	4	8	no	—
1220	#41	—	4	16	no	—
1221	#41	—	4	8	no	—
1222	#41	—	4	8	no	—
1223	#41	—	4	4	no	—
1224	#41	—	4	4	no	—
1225	#41	—	4	8	no	—
1226	#41	—	4	8	no	—
1227	C₂×Q₈	—	2	4	no	—
1228	C₂×Q₈	—	4	4	no	—
1229	C₂×Q₈	—	4	8	no	—
1230	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
1231	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
1232	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
1233	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
1234	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
1235	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
1236	C₂×D₄	—	2	4	no	—
1237	C₂×D₄	—	4	4	no	—
1238	C₂×D₄	—	4	8	no	—
1239	C₂×D₄	—	4	4	no	—
1240	C₂×D₄	—	4	8	no	—
1241	C₂×D₄	—	4	8	no	—
1242	C₂×D₄	—	4	8	no	—
1243	C₂×D₄	—	4	16	no	—
1244	C₂×D₄	—	4	8	no	—
1245	C₂×D₄	—	4	8	no	—
1246	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1247	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
1248	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1249	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1250	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1251	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1252	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1253	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1254	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1255	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1256	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1257	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
1258	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1259	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1260	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1261	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
1262	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
1263	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
1264	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1265	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1266	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1267	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1268	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1269	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
1270	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1271	C₂²×C₄	—	2	4	no	—
1272	C₂²×C₄	—	2	8	no	—
1273	C₂²×C₄	—	4	4	no	—
1274	C₂²×C₄	—	4	4	no	—
1275	C₂²×C₄	—	4	4	no	—
1276	C₂²×C₄	—	4	4	no	—
1277	C₂²×C₄	—	4	8	no	—
1278	C₂²×C₄	—	4	4	no	—
1279	C₂²×C₄	—	4	2	no	—
1280	C₂²×C₄	—	4	4	no	—
1281	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1282	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1283	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
1284	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1285	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1286	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1287	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
1288	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
1289	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1290	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1291	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1292	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1293	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
1294	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
1295	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1296	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1297	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
1298	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
1299	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
1300	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
1301	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
1302	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
1303	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
1304	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
1305	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
1306	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1307	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1308	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1309	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1310	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1311	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1312	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1313	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1314	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1315	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1316	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1317	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1318	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1319	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1320	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1321	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1322	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1323	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1324	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1325	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1326	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1327	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1328	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1329	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1330	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1331	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1332	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1333	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1334	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1335	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1336	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1337	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1338	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1339	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1340	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1341	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1342	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1343	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1344	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1345	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1346	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1347	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1348	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1349	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1350	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1351	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1352	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1353	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1354	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1355	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1356	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1357	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1358	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1359	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1360	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1361	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1362	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1363	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1364	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1365	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1366	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1367	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1368	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1369	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1370	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1371	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1372	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1373	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1374	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1375	C₄²	C₂⁴×C₂₃	1	4	yes	—
1376	C₄²	C₂⁴×C₂₃	1	8	yes	—
1377	C₄²	C₂⁴×C₂₃	1	4	yes	—
1378	C₄²	C₂⁴×C₂₃	1	4	yes	—
1379	C₄²	C₂⁴×C₂₃	1	4	yes	—
1380	C₄²	C₂⁴×C₂₃	1	4	yes	—
1381	C₄²	C₂⁴×C₂₃	1	4	yes	—
1382	C₄²	C₂⁴×C₂₃	1	8	yes	—
1383	C₄²	C₂⁴×C₂₃	1	8	yes	—
1384	C₂³	—	2	4	no	—
1385	C₂³	—	2	2	no	—
1386	C₂³	—	2	4	no	—
1387	C₂³	—	2	4	no	—
1388	C₂³	—	2	4	no	—
1389	C₂³	—	2	4	no	—
1390	C₂³	—	2	8	no	—
1391	C₂³	—	4	1	no	—
1392	C₂³	—	4	2	no	—
1393	C₂³	—	4	1	no	—
1394	C₂³	—	4	2	no	—
1395	C₂³	—	4	2	no	—
1396	C₂³	—	4	2	no	—
1397	C₂³	—	4	2	no	—
1398	C₂³	—	4	4	no	—
1399	C₂³	—	4	4	no	—
1400	C₂³	—	4	4	no	—
1401	C₂³	—	4	4	no	—
1402	C₂³	—	4	8	no	—
1403	C₂³	—	4	16	no	—
1404	C₂³	C₂⁵×C₂₃	1	2	yes	—
1405	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1406	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1407	C₂³	C₂⁵×C₂₃	1	4	yes	—
1408	C₂³	C₂⁵×C₂₃	1	4	yes	—
1409	C₂³	C₂⁵×C₂₃	1	4	yes	—
1410	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1411	C₂³	C₂⁵×C₂₃	1	2	yes	—
1412	Q₈	—	2	8	no	—
1413	Q₈	—	2	4	no	—
1414	Q₈	—	2	4	no	—
1415	Q₈	—	4	4	no	—
1416	Q₈	—	4	4	no	—
1417	Q₈	—	4	8	no	—
1418	D₄	—	2	8	no	—
1419	D₄	—	2	8	no	—
1420	D₄	—	2	8	no	—
1421	D₄	—	2	16	no	—
1422	D₄	—	2	8	no	—
1423	D₄	—	2	8	no	—
1424	D₄	—	2	4	no	—
1425	D₄	—	2	4	no	—
1426	D₄	—	4	8	no	—
1427	D₄	—	4	4	no	—
1428	D₄	—	4	4	no	—
1429	D₄	—	4	4	no	—
1430	D₄	—	4	4	no	—
1431	D₄	—	4	4	no	—
1432	D₄	—	4	4	no	—
1433	D₄	—	4	4	no	—
1434	D₄	—	4	4	no	—
1435	D₄	—	4	4	no	—
1436	D₄	—	4	4	no	—
1437	D₄	—	4	8	no	—
1438	D₄	—	4	8	no	—
1439	D₄	—	4	8	no	—
1440	D₄	—	4	4	no	—
1441	D₄	—	4	4	no	—
1442	D₄	—	4	8	no	—
1443	C₂×C₄	—	2	2	no	—
1444	C₂×C₄	—	2	4	no	—
1445	C₂×C₄	—	2	4	no	—
1446	C₂×C₄	—	2	8	no	—
1447	C₂×C₄	—	2	4	no	—
1448	C₂×C₄	—	2	4	no	—
1449	C₂×C₄	—	2	4	no	—
1450	C₂×C₄	—	2	4	no	—
1451	C₂×C₄	—	2	4	no	—
1452	C₂×C₄	—	2	4	no	—
1453	C₂×C₄	—	2	8	no	—
1454	C₂×C₄	—	2	8	no	—
1455	C₂×C₄	—	4	2	no	—
1456	C₂×C₄	—	4	2	no	—
1457	C₂×C₄	—	4	1	no	—
1458	C₂×C₄	—	4	2	no	—
1459	C₂×C₄	—	4	2	no	—
1460	C₂×C₄	—	4	2	no	—
1461	C₂×C₄	—	4	1	no	—
1462	C₂×C₄	—	4	4	no	—
1463	C₂×C₄	—	4	4	no	—
1464	C₂×C₄	—	4	4	no	—
1465	C₂×C₄	—	4	8	no	—
1466	C₂×C₄	—	4	4	no	—
1467	C₂×C₄	—	4	8	no	—
1468	C₂×C₄	—	4	4	no	—
1469	C₂×C₄	—	4	4	no	—
1470	C₂×C₄	—	4	8	no	—
1471	C₂×C₄	—	4	8	no	—
1472	C₂×C₄	—	4	8	no	—
1473	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
1474	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
1475	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
1476	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
1477	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
1478	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
1479	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
1480	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
1481	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
1482	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
1483	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
1484	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
1485	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
1486	C₂²	—	2	2	no	—
1487	C₂²	—	2	2	no	—
1488	C₂²	—	2	2	no	—
1489	C₂²	—	2	1	no	—
1490	C₂²	—	2	2	no	—
1491	C₂²	—	2	1	no	—
1492	C₂²	—	2	4	no	—
1493	C₂²	—	2	4	no	—
1494	C₂²	—	2	4	no	—
1495	C₂²	—	2	4	no	—
1496	C₂²	—	2	4	no	—
1497	C₂²	—	2	8	no	—
1498	C₂²	—	2	4	no	—
1499	C₂²	—	2	4	no	—
1500	C₂²	—	2	2	no	—
1501	C₂²	—	2	2	no	—
1502	C₂²	—	2	2	no	—
1503	C₂²	—	2	2	no	—
1504	C₂²	—	4	8	no	—
1505	C₂²	—	4	4	no	—
1506	C₂²	—	4	4	no	—
1507	C₂²	—	4	8	no	—
1508	C₂²	—	4	4	no	—
1509	C₂²	—	8	4	no	—
1510	C₂²	—	8	8	no	—
1511	C₂²	—	16	4	no	—
1512	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
1513	C₂²	C₂₃×#585	1	4	yes	—
1514	C₂²	C₂⁶×C₂₃	1	1	yes	characteristic
1515	C₄	—	2	2	no	—
1516	C₄	—	2	2	no	—
1517	C₄	—	2	2	no	—
1518	C₄	—	2	4	no	—
1519	C₄	—	2	4	no	—
1520	C₄	—	2	4	no	—
1521	C₄	—	2	4	no	—
1522	C₄	—	2	4	no	—
1523	C₄	—	2	4	no	—
1524	C₄	—	2	8	no	—
1525	C₄	—	2	4	no	—
1526	C₄	C₂×C₂₃×H(5,𝔽₂)	1	4	yes	—
1527	C₂	—	2	2	no	—
1528	C₂	—	2	4	no	—
1529	C₂	—	4	2	no	—
1530	C₂	—	4	1	no	—
1531	C₂	—	4	1	no	—
1532	C₂	—	4	4	no	—
1533	C₂	—	4	4	no	—
1534	C₂	—	4	4	no	—
1535	C₂	C₂²×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1536	C₂	C₂×C₂₃×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₂₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂₃×#3542	C₂	semidirect
2. C₂₃×#3541	C₂	semidirect
3. C₂₃×#3540	C₂	semidirect
4. C₂₃×#3539	C₂	semidirect
5. C₂₃×#3533	C₂	semidirect
6. C₂₃×#3532	C₂	semidirect
7. C₂₃×#3520	C₂	semidirect
8. C₂₃×#3519	C₂	semidirect
9. C₂₃×#3513	C₂	semidirect
10. C₂₃×#3506	C₂	semidirect
11. C₂₃×#3505	C₂	semidirect
12. C₂₃×#3495	C₂	semidirect
13. C₂₃×#3494	C₂	semidirect
14. C₂₃×#3493	C₂	semidirect
15. C₂₃×#3489	C₂	semidirect
16. C₂₃×#3488	C₂	semidirect
17. C₂₃×#3487	C₂	semidirect
18. C₂₃×#3485	C₂	semidirect
19. C₂×C₂₃×#525	C₂	semidirect
20. C₂×C₂₃×#525	C₂	semidirect
21. C₂×C₂₃×2₋¹⁺⁴	C₂²	semidirect
22. C₂×C₂₃×H(5,𝔽₂)	C₂²	semidirect
23. C₂²×#41×C₂₃	C₂²	semidirect
24. C₂²×#41×C₂₃	C₂²	semidirect
25. C₂⁴×C₄×C₂₃	C₂²	semidirect
26. C₂₃×#563	C₂²	semidirect
27. C₂₃×#562	C₂²	semidirect
28. C₂₃×H(3,𝔽₄)	C₂²	semidirect
29. C₂₃×#560	C₂²	semidirect
30. C₂₃×#560	C₂²	semidirect
31. C₂₃×#560	C₂²	semidirect
32. C₂₃×#559	C₂²	semidirect
33. C₂₃×#559	C₂²	semidirect
34. C₂₃×#556	C₂²	semidirect
35. C₂₃×#556	C₂²	semidirect
36. C₂₃×#556	C₂²	semidirect
37. C₂₃×#555	C₂²	semidirect
38. C₂₃×#555	C₂²	semidirect
39. C₂₃×#555	C₂²	semidirect
40. C₂₃×#554	C₂²	semidirect
41. C₂₃×#554	C₂²	semidirect
42. C₂₃×#553	C₂²	semidirect
43. C₂₃×#553	C₂²	semidirect
44. C₂₃×#553	C₂²	semidirect
45. C₂₃×#553	C₂²	semidirect
46. C₂₃×#553	C₂²	semidirect
47. C₂₃×#553	C₂²	semidirect
48. C₂₃×#553	C₂²	semidirect
49. C₂₃×#553	C₂²	semidirect
50. C₂₃×#552	C₂²	semidirect
51. C₂₃×#552	C₂²	semidirect
52. C₂₃×#552	C₂²	semidirect
53. C₂₃×#552	C₂²	semidirect
54. C₂₃×#552	C₂²	semidirect
55. C₂₃×#551	C₂²	semidirect
56. C₂₃×#551	C₂²	semidirect
57. C₂₃×#551	C₂²	semidirect
58. C₂₃×#551	C₂²	semidirect
59. C₂₃×#551	C₂²	semidirect
60. C₂₃×#551	C₂²	semidirect
61. C₂₃×#550	C₂²	semidirect
62. C₂₃×#550	C₂²	semidirect
63. C₂₃×#550	C₂²	semidirect
64. D₄×Q₈×C₂₃	C₂²	semidirect
65. C₂₃×#548	C₂²	semidirect
66. C₂₃×#548	C₂²	semidirect
67. C₂₃×#548	C₂²	semidirect
68. C₂₃×#548	C₂²	semidirect
69. C₂₃×#547	C₂²	semidirect
70. C₂₃×#547	C₂²	semidirect
71. C₂₃×#547	C₂²	semidirect
72. C₂₃×#547	C₂²	semidirect
73. C₂₃×#547	C₂²	semidirect
74. C₂₃×#546	C₂²	semidirect
75. C₂₃×#546	C₂²	semidirect
76. C₂₃×#546	C₂²	semidirect
77. C₂₃×#546	C₂²	semidirect
78. C₂₃×#546	C₂²	semidirect
79. C₂₃×#546	C₂²	semidirect
80. C₂₃×#546	C₂²	semidirect
81. C₂₃×#546	C₂²	semidirect
82. C₂₃×#546	C₂²	semidirect
83. D₄²×C₂₃	C₂²	semidirect
84. D₄²×C₂₃	C₂²	semidirect
85. D₄²×C₂₃	C₂²	semidirect
86. C₂₃×#544	C₂²	semidirect
87. C₂₃×#542	C₂²	semidirect
88. C₂₃×#542	C₂²	semidirect
89. C₂₃×#542	C₂²	semidirect
90. C₂₃×#542	C₂²	semidirect
91. C₂₃×#541	C₂²	semidirect
92. C₂₃×#540	C₂²	semidirect
93. C₂₃×#540	C₂²	semidirect
94. C₂₃×#540	C₂²	semidirect
95. C₂₃×#539	C₂²	semidirect
96. C₂₃×#539	C₂²	semidirect
97. C₂₃×#539	C₂²	semidirect
98. C₂₃×#538	C₂²	semidirect
99. C₂₃×#538	C₂²	semidirect
100. C₂₃×#538	C₂²	semidirect
101. C₂₃×#538	C₂²	semidirect
102. C₂₃×#538	C₂²	semidirect
103. C₂₃×#538	C₂²	semidirect
104. C₂₃×#537	C₂²	semidirect
105. C₂₃×#537	C₂²	semidirect
106. C₂₃×#537	C₂²	semidirect
107. C₂₃×#536	C₂²	semidirect
108. C₂₃×#536	C₂²	semidirect
109. C₂₃×#535	C₂²	semidirect
110. C₂₃×#535	C₂²	semidirect
111. C₂₃×#535	C₂²	semidirect
112. C₂₃×#535	C₂²	semidirect
113. C₂₃×#534	C₂²	semidirect
114. C₂₃×#534	C₂²	semidirect
115. C₂₃×#533	C₂²	semidirect
116. C₂₃×#532	C₂²	semidirect
117. C₂₃×#529	C₂²	semidirect
118. C₂₃×#529	C₂²	semidirect
119. C₂₃×#529	C₂²	semidirect
121. C₂₃×#525	C₂²	semidirect
122. C₂₃×#525	C₂²	semidirect
123. C₂₃×#525	C₂²	semidirect
124. C₂₃×#525	C₂²	semidirect
125. C₂₃×#525	C₂²	semidirect
126. C₂₃×#525	C₂²	semidirect
127. C₂₃×#525	C₂²	semidirect
128. C₂₃×#525	C₂²	semidirect
129. C₂₃×#525	C₂²	semidirect
130. C₂₃×#525	C₂²	semidirect
131. C₂₃×#525	C₂²	semidirect
132. C₂₃×#525	C₂²	semidirect
133. C₂₃×#525	C₂²	semidirect
134. C₂₃×#525	C₂²	semidirect
135. C₂₃×#525	C₂²	semidirect
136. C₂₃×#525	C₂²	semidirect
137. C₂₃×#525	C₂²	semidirect
138. C₂₃×#525	C₂²	semidirect
139. C₂×C₂₃×#123	C₂²	semidirect
140. C₂×C₂₃×#123	C₂²	semidirect
141. C₂×C₂₃×#123	C₂²	semidirect
142. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
143. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
144. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
145. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
146. C₂×C₂₃×#121	C₂²	semidirect
147. C₂×C₂₃×#121	C₂²	semidirect
148. C₂×C₂₃×#121	C₂²	semidirect
149. C₂×C₂₃×#121	C₂²	semidirect
150. C₂×C₂₃×#120	C₂²	semidirect
151. C₂×C₂₃×#120	C₂²	semidirect
152. C₂₃×#520	C₂²	semidirect
153. C₂₃×#520	C₂²	semidirect
154. C₂₃×#520	C₂²	semidirect
155. C₂₃×#519	C₂²	semidirect
156. C₂₃×#518	C₂²	semidirect
157. C₂₃×#518	C₂²	semidirect
158. C₂×C₄×D₄×C₂₃	C₂²	semidirect
159. C₂×C₄×D₄×C₂₃	C₂²	semidirect
160. C₂×C₄×D₄×C₂₃	C₂²	semidirect
161. C₂×C₂₃×#117	C₂²	semidirect
162. C₂×C₂₃×#117	C₂²	semidirect
178. C₂×#41×C₂₃	C₂³	semidirect
179. C₂×#41×C₂₃	C₂³	semidirect
182. C₂²×Q₈×C₂₃	C₂³	semidirect
192. C₂²×D₄×C₂₃	C₂³	semidirect
204. C₂₃×C₄⋊Q₈	C₂³	semidirect
205. C₂₃×C₄⋊Q₈	C₂³	semidirect
206. C₂₃×C₄⋊Q₈	C₂³	semidirect
207. C₂₃×C₄⋊Q₈	C₂³	semidirect
211. C₂₃×#127	C₂³	semidirect
216. C₂₃×#126	C₂³	semidirect
217. C₂₃×#126	C₂³	semidirect
218. C₂₃×#126	C₂³	semidirect
219. C₂₃×#126	C₂³	semidirect
220. C₂₃×#126	C₂³	semidirect
221. C₂₃×#126	C₂³	semidirect
222. C₂₃×#125	C₂³	semidirect
223. C₂₃×#125	C₂³	semidirect
224. C₂₃×#125	C₂³	semidirect
225. C₂₃×#125	C₂³	semidirect
226. C₂₃×#125	C₂³	semidirect
227. C₂₃×#125	C₂³	semidirect
235. C₂₃×#124	C₂³	semidirect
236. C₂₃×#124	C₂³	semidirect
237. C₂₃×#124	C₂³	semidirect
238. C₂₃×#124	C₂³	semidirect
239. C₂₃×#124	C₂³	semidirect
261. C₂₃×#123	C₂³	semidirect
262. C₂₃×#123	C₂³	semidirect
263. C₂₃×#123	C₂³	semidirect
264. C₂₃×#123	C₂³	semidirect
265. C₂₃×#123	C₂³	semidirect
266. C₂₃×#123	C₂³	semidirect
267. C₂₃×#123	C₂³	semidirect
287. C₂₃×C₂²⋊Q₈	C₂³	semidirect
288. C₂₃×C₂²⋊Q₈	C₂³	semidirect
289. C₂₃×C₂²⋊Q₈	C₂³	semidirect
290. C₂₃×C₂²⋊Q₈	C₂³	semidirect
291. C₂₃×C₂²⋊Q₈	C₂³	semidirect
292. C₂₃×C₂²⋊Q₈	C₂³	semidirect
293. C₂₃×C₂²⋊Q₈	C₂³	semidirect
294. C₂₃×C₂²⋊Q₈	C₂³	semidirect
295. C₂₃×C₂²⋊Q₈	C₂³	semidirect
296. C₂₃×C₂²⋊Q₈	C₂³	semidirect
328. C₂₃×#121	C₂³	semidirect
329. C₂₃×#121	C₂³	semidirect
330. C₂₃×#121	C₂³	semidirect
331. C₂₃×#121	C₂³	semidirect
332. C₂₃×#121	C₂³	semidirect
333. C₂₃×#121	C₂³	semidirect
334. C₂₃×#121	C₂³	semidirect
335. C₂₃×#121	C₂³	semidirect
353. C₂₃×#120	C₂³	semidirect
354. C₄×Q₈×C₂₃	C₂³	semidirect
355. C₄×Q₈×C₂₃	C₂³	semidirect
356. C₄×Q₈×C₂₃	C₂³	semidirect
357. C₄×Q₈×C₂₃	C₂³	semidirect
358. C₄×Q₈×C₂₃	C₂³	semidirect
359. C₄×Q₈×C₂₃	C₂³	semidirect
386. C₄×D₄×C₂₃	C₂³	semidirect
387. C₄×D₄×C₂₃	C₂³	semidirect
388. C₄×D₄×C₂₃	C₂³	semidirect
389. C₄×D₄×C₂₃	C₂³	semidirect
390. C₄×D₄×C₂₃	C₂³	semidirect
391. C₄×D₄×C₂₃	C₂³	semidirect
392. C₄×D₄×C₂₃	C₂³	semidirect
393. C₄×D₄×C₂₃	C₂³	semidirect
394. C₄×D₄×C₂₃	C₂³	semidirect
395. C₄×D₄×C₂₃	C₂³	semidirect
406. C₂₃×#117	C₂³	semidirect
407. C₂₃×#117	C₂³	semidirect
408. C₂₃×#117	C₂³	semidirect
409. C₂₃×#117	C₂³	semidirect
410. C₂₃×#117	C₂³	semidirect
411. C₂₃×#117	C₂³	semidirect
418. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
419. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
420. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
421. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
432. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
433. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
615. #62821	C₂₃	direct (N × H)
718. #3542	C₂×C₂₃	semidirect
719. #3541	C₂×C₂₃	semidirect
720. #3540	C₂×C₂₃	semidirect
721. #3539	C₂×C₂₃	semidirect
722. #3533	C₂×C₂₃	semidirect
723. #3532	C₂×C₂₃	semidirect
724. #3520	C₂×C₂₃	semidirect
725. #3519	C₂×C₂₃	semidirect
726. #3513	C₂×C₂₃	semidirect
727. #3506	C₂×C₂₃	semidirect
728. #3505	C₂×C₂₃	semidirect
729. #3495	C₂×C₂₃	semidirect
730. #3494	C₂×C₂₃	semidirect
731. #3493	C₂×C₂₃	semidirect
732. #3489	C₂×C₂₃	semidirect
733. #3488	C₂×C₂₃	semidirect
734. #3487	C₂×C₂₃	semidirect
735. #3485	C₂×C₂₃	semidirect
736. C₂×#525	C₂×C₂₃	semidirect
737. C₂×#525	C₂×C₂₃	semidirect
779. C₂×2₋¹⁺⁴	C₂²×C₂₃	semidirect
780. C₂×H(5,𝔽₂)	C₂²×C₂₃	semidirect
781. C₂²×#41	C₂²×C₂₃	semidirect
782. C₂²×#41	C₂²×C₂₃	semidirect
783. C₂⁴×C₄	C₂²×C₂₃	semidirect
784. #563	C₂²×C₂₃	semidirect
785. #562	C₂²×C₂₃	semidirect
786. H(3,𝔽₄)	C₂²×C₂₃	semidirect
787. #560	C₂²×C₂₃	semidirect
788. #560	C₂²×C₂₃	semidirect
789. #560	C₂²×C₂₃	semidirect
790. #559	C₂²×C₂₃	semidirect
791. #559	C₂²×C₂₃	semidirect
792. #556	C₂²×C₂₃	semidirect
793. #556	C₂²×C₂₃	semidirect
794. #556	C₂²×C₂₃	semidirect
795. #555	C₂²×C₂₃	semidirect
796. #555	C₂²×C₂₃	semidirect
797. #555	C₂²×C₂₃	semidirect
798. #554	C₂²×C₂₃	semidirect
799. #554	C₂²×C₂₃	semidirect
800. #553	C₂²×C₂₃	semidirect
801. #553	C₂²×C₂₃	semidirect
802. #553	C₂²×C₂₃	semidirect
803. #553	C₂²×C₂₃	semidirect
804. #553	C₂²×C₂₃	semidirect
805. #553	C₂²×C₂₃	semidirect
806. #553	C₂²×C₂₃	semidirect
807. #553	C₂²×C₂₃	semidirect
808. #552	C₂²×C₂₃	semidirect
809. #552	C₂²×C₂₃	semidirect
810. #552	C₂²×C₂₃	semidirect
811. #552	C₂²×C₂₃	semidirect
812. #552	C₂²×C₂₃	semidirect
813. #551	C₂²×C₂₃	semidirect
814. #551	C₂²×C₂₃	semidirect
815. #551	C₂²×C₂₃	semidirect
816. #551	C₂²×C₂₃	semidirect
817. #551	C₂²×C₂₃	semidirect
818. #551	C₂²×C₂₃	semidirect
819. #550	C₂²×C₂₃	semidirect
820. #550	C₂²×C₂₃	semidirect
821. #550	C₂²×C₂₃	semidirect
822. D₄×Q₈	C₂²×C₂₃	semidirect
823. #548	C₂²×C₂₃	semidirect
824. #548	C₂²×C₂₃	semidirect
825. #548	C₂²×C₂₃	semidirect
826. #548	C₂²×C₂₃	semidirect
827. #547	C₂²×C₂₃	semidirect
828. #547	C₂²×C₂₃	semidirect
829. #547	C₂²×C₂₃	semidirect
830. #547	C₂²×C₂₃	semidirect
831. #547	C₂²×C₂₃	semidirect
832. #546	C₂²×C₂₃	semidirect
833. #546	C₂²×C₂₃	semidirect
834. #546	C₂²×C₂₃	semidirect
835. #546	C₂²×C₂₃	semidirect
836. #546	C₂²×C₂₃	semidirect
837. #546	C₂²×C₂₃	semidirect
838. #546	C₂²×C₂₃	semidirect
839. #546	C₂²×C₂₃	semidirect
840. #546	C₂²×C₂₃	semidirect
841. D₄²	C₂²×C₂₃	semidirect
842. D₄²	C₂²×C₂₃	semidirect
843. D₄²	C₂²×C₂₃	semidirect
844. #544	C₂²×C₂₃	semidirect
845. #542	C₂²×C₂₃	semidirect
846. #542	C₂²×C₂₃	semidirect
847. #542	C₂²×C₂₃	semidirect
848. #542	C₂²×C₂₃	semidirect
849. #541	C₂²×C₂₃	semidirect
850. #540	C₂²×C₂₃	semidirect
851. #540	C₂²×C₂₃	semidirect
852. #540	C₂²×C₂₃	semidirect
853. #539	C₂²×C₂₃	semidirect
854. #539	C₂²×C₂₃	semidirect
855. #539	C₂²×C₂₃	semidirect
856. #538	C₂²×C₂₃	semidirect
857. #538	C₂²×C₂₃	semidirect
858. #538	C₂²×C₂₃	semidirect
859. #538	C₂²×C₂₃	semidirect
860. #538	C₂²×C₂₃	semidirect
861. #538	C₂²×C₂₃	semidirect
862. #537	C₂²×C₂₃	semidirect
863. #537	C₂²×C₂₃	semidirect
864. #537	C₂²×C₂₃	semidirect
865. #536	C₂²×C₂₃	semidirect
866. #536	C₂²×C₂₃	semidirect
867. #535	C₂²×C₂₃	semidirect
868. #535	C₂²×C₂₃	semidirect
869. #535	C₂²×C₂₃	semidirect
870. #535	C₂²×C₂₃	semidirect
871. #534	C₂²×C₂₃	semidirect
872. #534	C₂²×C₂₃	semidirect
873. #533	C₂²×C₂₃	semidirect
874. #532	C₂²×C₂₃	semidirect
875. #529	C₂²×C₂₃	semidirect
876. #529	C₂²×C₂₃	semidirect
877. #529	C₂²×C₂₃	semidirect
879. #525	C₂²×C₂₃	semidirect
880. #525	C₂²×C₂₃	semidirect
881. #525	C₂²×C₂₃	semidirect
882. #525	C₂²×C₂₃	semidirect
883. #525	C₂²×C₂₃	semidirect
884. #525	C₂²×C₂₃	semidirect
885. #525	C₂²×C₂₃	semidirect
886. #525	C₂²×C₂₃	semidirect
887. #525	C₂²×C₂₃	semidirect
888. #525	C₂²×C₂₃	semidirect
889. #525	C₂²×C₂₃	semidirect
890. #525	C₂²×C₂₃	semidirect
891. #525	C₂²×C₂₃	semidirect
892. #525	C₂²×C₂₃	semidirect
893. #525	C₂²×C₂₃	semidirect
894. #525	C₂²×C₂₃	semidirect
895. #525	C₂²×C₂₃	semidirect
896. #525	C₂²×C₂₃	semidirect
897. C₂×#123	C₂²×C₂₃	semidirect
898. C₂×#123	C₂²×C₂₃	semidirect
899. C₂×#123	C₂²×C₂₃	semidirect
900. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
901. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
902. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
903. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
904. C₂×#121	C₂²×C₂₃	semidirect
905. C₂×#121	C₂²×C₂₃	semidirect
906. C₂×#121	C₂²×C₂₃	semidirect
907. C₂×#121	C₂²×C₂₃	semidirect
908. C₂×#120	C₂²×C₂₃	semidirect
909. C₂×#120	C₂²×C₂₃	semidirect
910. #520	C₂²×C₂₃	semidirect
911. #520	C₂²×C₂₃	semidirect
912. #520	C₂²×C₂₃	semidirect
913. #519	C₂²×C₂₃	semidirect
914. #518	C₂²×C₂₃	semidirect
915. #518	C₂²×C₂₃	semidirect
916. C₂×C₄×D₄	C₂²×C₂₃	semidirect
917. C₂×C₄×D₄	C₂²×C₂₃	semidirect
918. C₂×C₄×D₄	C₂²×C₂₃	semidirect
919. C₂×#117	C₂²×C₂₃	semidirect
920. C₂×#117	C₂²×C₂₃	semidirect
946. C₂×#41	C₂³×C₂₃	semidirect
947. C₂×#41	C₂³×C₂₃	semidirect
950. C₂²×Q₈	C₂³×C₂₃	semidirect
960. C₂²×D₄	C₂³×C₂₃	semidirect
972. C₄⋊Q₈	C₂³×C₂₃	semidirect
973. C₄⋊Q₈	C₂³×C₂₃	semidirect
974. C₄⋊Q₈	C₂³×C₂₃	semidirect
975. C₄⋊Q₈	C₂³×C₂₃	semidirect
979. #127	C₂³×C₂₃	semidirect
984. #126	C₂³×C₂₃	semidirect
985. #126	C₂³×C₂₃	semidirect
986. #126	C₂³×C₂₃	semidirect
987. #126	C₂³×C₂₃	semidirect
988. #126	C₂³×C₂₃	semidirect
989. #126	C₂³×C₂₃	semidirect
990. #125	C₂³×C₂₃	semidirect
991. #125	C₂³×C₂₃	semidirect
992. #125	C₂³×C₂₃	semidirect
993. #125	C₂³×C₂₃	semidirect
994. #125	C₂³×C₂₃	semidirect
995. #125	C₂³×C₂₃	semidirect
1003. #124	C₂³×C₂₃	semidirect
1004. #124	C₂³×C₂₃	semidirect
1005. #124	C₂³×C₂₃	semidirect
1006. #124	C₂³×C₂₃	semidirect
1007. #124	C₂³×C₂₃	semidirect
1029. #123	C₂³×C₂₃	semidirect
1030. #123	C₂³×C₂₃	semidirect
1031. #123	C₂³×C₂₃	semidirect
1032. #123	C₂³×C₂₃	semidirect
1033. #123	C₂³×C₂₃	semidirect
1034. #123	C₂³×C₂₃	semidirect
1035. #123	C₂³×C₂₃	semidirect
1055. C₂²⋊Q₈	C₂³×C₂₃	semidirect
1056. C₂²⋊Q₈	C₂³×C₂₃	semidirect
1057. C₂²⋊Q₈	C₂³×C₂₃	semidirect
1058. C₂²⋊Q₈	C₂³×C₂₃	semidirect
1059. C₂²⋊Q₈	C₂³×C₂₃	semidirect
1060. C₂²⋊Q₈	C₂³×C₂₃	semidirect
1061. C₂²⋊Q₈	C₂³×C₂₃	semidirect
1062. C₂²⋊Q₈	C₂³×C₂₃	semidirect
1063. C₂²⋊Q₈	C₂³×C₂₃	semidirect
1064. C₂²⋊Q₈	C₂³×C₂₃	semidirect
1096. #121	C₂³×C₂₃	semidirect
1097. #121	C₂³×C₂₃	semidirect
1098. #121	C₂³×C₂₃	semidirect
1099. #121	C₂³×C₂₃	semidirect
1100. #121	C₂³×C₂₃	semidirect
1101. #121	C₂³×C₂₃	semidirect
1102. #121	C₂³×C₂₃	semidirect
1103. #121	C₂³×C₂₃	semidirect
1121. #120	C₂³×C₂₃	semidirect
1122. C₄×Q₈	C₂³×C₂₃	semidirect
1123. C₄×Q₈	C₂³×C₂₃	semidirect
1124. C₄×Q₈	C₂³×C₂₃	semidirect
1125. C₄×Q₈	C₂³×C₂₃	semidirect
1126. C₄×Q₈	C₂³×C₂₃	semidirect
1127. C₄×Q₈	C₂³×C₂₃	semidirect
1154. C₄×D₄	C₂³×C₂₃	semidirect
1155. C₄×D₄	C₂³×C₂₃	semidirect
1156. C₄×D₄	C₂³×C₂₃	semidirect
1157. C₄×D₄	C₂³×C₂₃	semidirect
1158. C₄×D₄	C₂³×C₂₃	semidirect
1159. C₄×D₄	C₂³×C₂₃	semidirect
1160. C₄×D₄	C₂³×C₂₃	semidirect
1161. C₄×D₄	C₂³×C₂₃	semidirect
1162. C₄×D₄	C₂³×C₂₃	semidirect
1163. C₄×D₄	C₂³×C₂₃	semidirect
1174. #117	C₂³×C₂₃	semidirect
1175. #117	C₂³×C₂₃	semidirect
1176. #117	C₂³×C₂₃	semidirect
1177. #117	C₂³×C₂₃	semidirect
1178. #117	C₂³×C₂₃	semidirect
1179. #117	C₂³×C₂₃	semidirect
1186. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
1187. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
1188. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
1189. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
1200. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
1201. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
1204. C₂₃	#62821	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3542	2
C₂₃×#3541	2
C₂₃×#3540	2
C₂₃×#3539	2
C₂₃×#3533	2
C₂₃×#3532	2
C₂₃×#3520	2
C₂₃×#3519	2
C₂₃×#3513	2
C₂₃×#3506	2
C₂₃×#3505	2
C₂₃×#3495	2
C₂₃×#3494	2
C₂₃×#3493	2
C₂₃×#3489	2
C₂₃×#3488	2
C₂₃×#3487	2
C₂₃×#3485	2
C₂×C₂₃×#525	2
#62821	23

Subgroups — C23×#62821 #19210447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62821 #19210447