Subgroups — C₂₃×#62835 #19210461

Order 5888.

7148 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3561	C₂	1	4	yes	maximal, complemented
2	C₂₃×#3559	C₂	1	4	yes	maximal, complemented
3	C₂₃×#3554	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3550	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3548	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3547	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3536	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3522	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3520	C₂	1	4	yes	maximal, complemented
10	C₂₃×#3511	C₂	1	4	yes	maximal, complemented
11	C₂₃×#3511	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3508	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3507	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3506	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3503	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3501	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3499	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3497	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3494	C₂	1	4	yes	maximal, complemented
20	C₂₃×#3489	C₂	1	4	yes	maximal, complemented
21	C₂₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₂₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₂₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	4	yes	complemented
25	C₂²×#41×C₂₃	C₂²	1	2	yes	—
26	C₂₃×#563	C₂²	1	8	yes	complemented
27	C₂₃×#562	C₂²	1	16	yes	complemented
28	C₂₃×#562	C₂²	1	8	yes	complemented
29	C₂₃×#559	C₂²	1	8	yes	complemented
30	C₂₃×#559	C₂²	1	4	yes	complemented
31	C₂₃×#559	C₂²	1	4	yes	complemented
32	Q₈²×C₂₃	C₂²	1	4	yes	complemented
33	C₂₃×#557	C₂²	1	4	yes	complemented
34	C₂₃×#556	C₂²	1	4	yes	complemented
35	C₂₃×#556	C₂²	1	8	yes	complemented
36	C₂₃×#556	C₂²	1	4	yes	complemented
37	C₂₃×#555	C₂²	1	8	yes	complemented
38	C₂₃×#555	C₂²	1	4	yes	complemented
39	C₂₃×#554	C₂²	1	8	yes	—
40	C₂₃×#554	C₂²	1	4	yes	complemented
41	C₂₃×#554	C₂²	1	4	yes	complemented
42	C₂₃×#554	C₂²	1	8	yes	complemented
43	C₂₃×#554	C₂²	1	8	yes	complemented
44	C₂₃×#554	C₂²	1	4	yes	complemented
45	C₂₃×#553	C₂²	1	8	yes	complemented
46	C₂₃×#553	C₂²	1	8	yes	complemented
47	C₂₃×#553	C₂²	1	8	yes	complemented
48	C₂₃×#552	C₂²	1	8	yes	complemented
49	C₂₃×#551	C₂²	1	16	yes	—
50	C₂₃×#550	C₂²	1	4	yes	complemented
51	C₂₃×#550	C₂²	1	4	yes	complemented
52	C₂₃×#550	C₂²	1	4	yes	complemented
53	D₄×Q₈×C₂₃	C₂²	1	8	yes	—
54	D₄×Q₈×C₂₃	C₂²	1	4	yes	complemented
55	D₄×Q₈×C₂₃	C₂²	1	4	yes	complemented
56	D₄×Q₈×C₂₃	C₂²	1	4	yes	complemented
57	D₄×Q₈×C₂₃	C₂²	1	4	yes	complemented
58	C₂₃×#548	C₂²	1	8	yes	complemented
59	C₂₃×#548	C₂²	1	8	yes	complemented
60	C₂₃×#548	C₂²	1	8	yes	complemented
61	C₂₃×#548	C₂²	1	8	yes	complemented
62	C₂₃×#547	C₂²	1	8	yes	complemented
63	C₂₃×#547	C₂²	1	16	yes	complemented
64	C₂₃×#547	C₂²	1	8	yes	complemented
65	C₂₃×#547	C₂²	1	4	yes	complemented
66	C₂₃×#547	C₂²	1	4	yes	complemented
67	C₂₃×#547	C₂²	1	8	yes	complemented
68	C₂₃×#547	C₂²	1	4	yes	complemented
69	C₂₃×#546	C₂²	1	16	yes	—
70	C₂₃×#546	C₂²	1	8	yes	—
71	C₂₃×#546	C₂²	1	8	yes	—
72	C₂₃×#544	C₂²	1	4	yes	—
73	C₂₃×#544	C₂²	1	8	yes	complemented
74	C₂₃×#543	C₂²	1	8	yes	—
75	C₂₃×#542	C₂²	1	8	yes	complemented
76	C₂₃×#542	C₂²	1	8	yes	complemented
77	C₂₃×#542	C₂²	1	8	yes	complemented
78	C₂₃×#542	C₂²	1	8	yes	complemented
79	C₂₃×#542	C₂²	1	16	yes	complemented
80	C₂₃×#540	C₂²	1	8	yes	complemented
81	C₂₃×#540	C₂²	1	8	yes	complemented
82	C₂₃×#539	C₂²	1	8	yes	complemented
83	C₂₃×#539	C₂²	1	16	yes	complemented
84	C₂₃×#538	C₂²	1	8	yes	—
85	C₂₃×#537	C₂²	1	4	yes	complemented
86	C₂₃×#537	C₂²	1	8	yes	complemented
87	C₂₃×#537	C₂²	1	8	yes	complemented
88	C₂₃×#537	C₂²	1	8	yes	complemented
89	C₂₃×#536	C₂²	1	4	yes	complemented
90	C₂₃×#536	C₂²	1	8	yes	complemented
91	C₂₃×#536	C₂²	1	8	yes	complemented
92	C₂₃×#535	C₂²	1	4	yes	—
93	C₂₃×#533	C₂²	1	2	yes	—
94	C₂₃×#533	C₂²	1	2	yes	—
95	C₂₃×#533	C₂²	1	2	yes	—
96	C₂₃×#533	C₂²	1	2	yes	—
97	C₂₃×#533	C₂²	1	1	yes	characteristic
98	C₂₃×#533	C₂²	1	2	yes	complemented
99	C₂₃×#533	C₂²	1	2	yes	complemented
100	C₂₃×#533	C₂²	1	2	yes	complemented
101	C₂₃×#533	C₂²	1	2	yes	complemented
102	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
104	C₂₃×#533	C₂²	1	4	yes	complemented
105	C₂₃×#532	C₂²	1	2	yes	—
106	C₂₃×#532	C₂²	1	2	yes	—
107	C₂₃×#532	C₂²	1	2	yes	—
108	C₂₃×#532	C₂²	1	2	yes	—
109	C₂₃×#532	C₂²	1	2	yes	—
110	C₂₃×#532	C₂²	1	2	yes	—
111	C₂₃×#532	C₂²	1	2	yes	—
112	C₂₃×#532	C₂²	1	2	yes	—
113	C₂₃×#532	C₂²	1	1	yes	characteristic
114	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
115	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
116	C₂₃×#532	C₂²	1	8	yes	complemented
117	C₂₃×#532	C₂²	1	4	yes	complemented
118	C₂₃×#532	C₂²	1	4	yes	complemented
119	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
120	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₂₃×C₄⋊Q₈	C₂²	1	4	yes	complemented
123	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
124	C₂₃×#529	C₂²	1	2	yes	—
125	C₂₃×#529	C₂²	1	2	yes	—
126	C₂₃×#529	C₂²	1	2	yes	complemented
127	C₂₃×#529	C₂²	1	2	yes	complemented
128	C₂₃×#529	C₂²	1	2	yes	complemented
129	C₂₃×#529	C₂²	1	2	yes	complemented
130	C₂₃×#529	C₂²	1	8	yes	complemented
131	C₂×C₂₃×#125	C₂²	1	2	yes	complemented
132	C₂×C₂₃×#124	C₂²	1	2	yes	—
133	C₂₃×#525	C₂²	1	2	yes	—
134	C₂₃×#525	C₂²	1	2	yes	—
135	C₂₃×#525	C₂²	1	2	yes	—
136	C₂₃×#525	C₂²	1	8	yes	—
137	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
138	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
139	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	8	yes	—
140	C₂×C₂₃×#121	C₂²	1	2	yes	—
141	C₂×C₂₃×#121	C₂²	1	2	yes	—
142	C₂₃×#520	C₂²	1	4	yes	—
143	C₂₃×#520	C₂²	1	4	yes	complemented
144	C₂₃×#520	C₂²	1	8	yes	complemented
145	C₂₃×#518	C₂²	1	4	yes	—
146	C₄×#41×C₂₃	C₂²	1	2	yes	—
147	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
148	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
149	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
150	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
151	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
152	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
153	C₂×C₂₃×#117	C₂²	1	2	yes	—
154	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
155	C₂₃×2₋¹⁺⁴	—	4	16	no	—
156	C₂×#41×C₂₃	—	4	8	no	—
157	C₂×#41×C₂₃	C₂³	1	4	yes	—
158	C₂×#41×C₂₃	C₂³	1	2	yes	—
159	C₂×#41×C₂₃	C₂³	1	2	yes	—
160	C₂×#41×C₂₃	C₂³	1	4	yes	—
161	C₂×#41×C₂₃	C₂³	1	16	yes	—
162	C₂×#41×C₂₃	C₂³	1	4	yes	—
163	C₂×#41×C₂₃	C₂³	1	8	yes	—
164	C₂×#41×C₂₃	C₂³	1	8	yes	—
165	C₂×#41×C₂₃	C₂³	1	8	yes	—
166	C₂×#41×C₂₃	C₂³	1	4	yes	—
167	C₂×#41×C₂₃	C₂³	1	2	yes	—
168	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
169	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
170	C₂²×Q₈×C₂₃	C₂³	1	8	yes	—
171	C₂²×Q₈×C₂₃	C₂³	1	8	yes	—
172	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
173	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
174	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
175	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
176	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
177	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
178	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
179	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
180	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
182	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
183	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
184	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
185	C₂₃×C₄⋊Q₈	C₂³	1	16	yes	—
186	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
187	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
188	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
189	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
190	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
191	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
192	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
193	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
194	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
195	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
196	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
197	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
198	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
199	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
200	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
201	C₂₃×#127	C₂³	1	1	yes	characteristic
202	C₂₃×#127	C₂³	1	8	yes	—
203	C₂₃×#127	C₂³	1	2	yes	—
204	C₂₃×#127	C₂³	1	2	yes	—
205	C₂₃×#127	C₂³	1	2	yes	—
206	C₂₃×#127	C₂³	1	2	yes	—
207	C₂₃×#126	C₂³	1	16	yes	—
208	C₂₃×#126	C₂³	1	16	yes	—
209	C₂₃×#126	C₂³	1	16	yes	—
210	C₂₃×#126	C₂³	1	4	yes	—
211	C₂₃×#126	C₂³	1	4	yes	—
212	C₂₃×#125	C₂³	1	2	yes	—
213	C₂₃×#125	C₂³	1	16	yes	—
214	C₂₃×#125	C₂³	1	4	yes	—
215	C₂₃×#125	C₂³	1	8	yes	—
216	C₂₃×#125	C₂³	1	2	yes	—
217	C₂₃×#125	C₂³	1	8	yes	—
218	C₂₃×#125	C₂³	1	4	yes	—
219	C₂₃×#125	C₂³	1	2	yes	—
220	C₂₃×#125	C₂³	1	4	yes	—
221	C₂₃×#125	C₂³	1	4	yes	—
222	C₂₃×#124	C₂³	1	2	yes	—
223	C₂₃×#124	C₂³	1	16	yes	—
224	C₂₃×#124	C₂³	1	4	yes	—
225	C₂₃×#124	C₂³	1	16	yes	—
226	C₂₃×#124	C₂³	1	16	yes	—
227	C₂₃×#124	C₂³	1	8	yes	—
228	C₂₃×#124	C₂³	1	8	yes	—
229	C₂₃×#124	C₂³	1	8	yes	—
230	C₂₃×#124	C₂³	1	2	yes	—
231	C₂₃×#124	C₂³	1	2	yes	—
232	C₂₃×#124	C₂³	1	4	yes	—
233	C₂₃×#124	C₂³	1	4	yes	—
234	C₂₃×#124	C₂³	1	4	yes	—
235	C₂₃×#123	C₂³	1	4	yes	—
236	C₂₃×#123	C₂³	1	16	yes	—
237	C₂₃×#123	C₂³	1	16	yes	—
238	C₂₃×#123	C₂³	1	16	yes	—
239	C₂₃×#123	C₂³	1	16	yes	—
240	C₂₃×#123	C₂³	1	16	yes	—
241	C₂₃×#123	C₂³	1	16	yes	—
242	C₂₃×#123	C₂³	1	16	yes	—
243	C₂₃×#123	C₂³	1	4	yes	—
244	C₂₃×#123	C₂³	1	16	yes	—
245	C₂₃×#123	C₂³	1	4	yes	—
246	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
247	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
248	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
249	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
250	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
251	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
252	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
253	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
254	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
255	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
256	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
257	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
258	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
259	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
260	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
261	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
262	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
263	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
264	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
265	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
266	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
267	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
268	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
269	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
270	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
271	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
272	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
273	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
274	C₂₃×#121	C₂³	1	4	yes	—
275	C₂₃×#121	C₂³	1	8	yes	—
276	C₂₃×#121	C₂³	1	4	yes	—
277	C₂₃×#121	C₂³	1	8	yes	—
278	C₂₃×#121	C₂³	1	8	yes	—
279	C₂₃×#121	C₂³	1	16	yes	—
280	C₂₃×#121	C₂³	1	16	yes	—
281	C₂₃×#121	C₂³	1	16	yes	—
282	C₂₃×#121	C₂³	1	8	yes	—
283	C₂₃×#121	C₂³	1	16	yes	—
284	C₂₃×#121	C₂³	1	16	yes	—
285	C₂₃×#121	C₂³	1	16	yes	—
286	C₂₃×#121	C₂³	1	8	yes	—
287	C₂₃×#121	C₂³	1	4	yes	—
288	C₂₃×#121	C₂³	1	4	yes	—
289	C₂₃×#121	C₂³	1	4	yes	—
290	C₂₃×#121	C₂³	1	4	yes	—
291	C₂₃×#121	C₂³	1	4	yes	—
292	C₂₃×#121	C₂³	1	4	yes	—
293	C₂₃×#121	C₂³	1	2	yes	—
294	C₂₃×#121	C₂³	1	2	yes	—
295	C₂₃×#121	C₂³	1	2	yes	—
296	C₂₃×#121	C₂³	1	2	yes	—
297	C₂₃×#121	C₂³	1	2	yes	—
298	C₂₃×#121	C₂³	1	2	yes	—
299	C₂₃×#120	C₂³	1	16	yes	—
300	C₂₃×#120	C₂³	1	4	yes	—
301	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
302	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
303	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
304	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
305	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
306	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
307	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
308	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
309	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
310	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
311	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
312	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
313	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
314	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
315	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
316	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
317	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
318	C₄×D₄×C₂₃	C₂³	1	2	yes	—
319	C₄×D₄×C₂₃	C₂³	1	4	yes	—
320	C₄×D₄×C₂₃	C₂³	1	4	yes	—
321	C₄×D₄×C₂₃	C₂³	1	4	yes	—
322	C₄×D₄×C₂₃	C₂³	1	4	yes	—
323	C₄×D₄×C₂₃	C₂³	1	2	yes	—
324	C₄×D₄×C₂₃	C₂³	1	16	yes	—
325	C₄×D₄×C₂₃	C₂³	1	16	yes	—
326	C₄×D₄×C₂₃	C₂³	1	8	yes	—
327	C₄×D₄×C₂₃	C₂³	1	4	yes	—
328	C₄×D₄×C₂₃	C₂³	1	8	yes	—
329	C₄×D₄×C₂₃	C₂³	1	8	yes	—
330	C₄×D₄×C₂₃	C₂³	1	2	yes	—
331	C₄×D₄×C₂₃	C₂³	1	16	yes	—
332	C₄×D₄×C₂₃	C₂³	1	4	yes	—
333	C₄×D₄×C₂₃	C₂³	1	4	yes	—
334	C₄×D₄×C₂₃	C₂³	1	16	yes	—
335	C₄×D₄×C₂₃	C₂³	1	2	yes	—
336	C₄×D₄×C₂₃	C₂³	1	4	yes	—
337	C₄×D₄×C₂₃	C₂³	1	8	yes	—
338	C₄×D₄×C₂₃	C₂³	1	8	yes	—
339	C₄×D₄×C₂₃	C₂³	1	2	yes	—
340	C₄×D₄×C₂₃	C₂³	1	8	yes	—
341	C₄×D₄×C₂₃	C₂³	1	2	yes	—
342	C₄×D₄×C₂₃	C₂³	1	4	yes	—
343	C₄×D₄×C₂₃	C₂³	1	4	yes	—
344	C₄×D₄×C₂₃	C₂³	1	8	yes	—
345	C₄×D₄×C₂₃	C₂³	1	4	yes	—
346	C₄×D₄×C₂₃	C₂³	1	4	yes	—
347	C₄×D₄×C₂₃	C₂³	1	4	yes	—
348	C₄×D₄×C₂₃	C₂³	1	4	yes	—
349	C₂₃×#117	C₂³	1	4	yes	—
350	C₂₃×#117	C₂³	1	16	yes	—
351	C₂₃×#117	C₂³	1	8	yes	—
352	C₂₃×#117	C₂³	1	4	yes	—
353	C₂₃×#117	C₂³	1	8	yes	—
354	C₂₃×#117	C₂³	1	4	yes	—
355	C₂₃×#117	C₂³	1	4	yes	—
356	C₂₃×#117	C₂³	1	2	yes	—
357	C₂₃×#117	C₂³	1	4	yes	—
358	C₂₃×#117	C₂³	1	2	yes	—
359	C₂₃×#117	C₂³	1	4	yes	—
360	C₂₃×#117	C₂³	1	2	yes	—
361	C₂₃×#117	C₂³	1	4	yes	—
362	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
363	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
364	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
365	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
366	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
367	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	—
368	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
369	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
370	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
371	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
372	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
373	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
374	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
375	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	—
376	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
377	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
378	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
379	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
380	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
381	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
382	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
383	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
384	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
385	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
386	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
387	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
388	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
389	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
390	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
391	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
392	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
393	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
394	#41×C₂₃	—	2	16	no	—
395	#41×C₂₃	—	2	8	no	—
396	#41×C₂₃	—	2	8	no	—
397	#41×C₂₃	—	4	8	no	—
398	#41×C₂₃	—	4	4	no	—
399	#41×C₂₃	—	4	8	no	—
400	#41×C₂₃	—	4	32	no	—
401	#41×C₂₃	—	4	8	no	—
402	#41×C₂₃	—	4	16	no	—
403	#41×C₂₃	—	4	16	no	—
404	#41×C₂₃	—	4	16	no	—
405	C₂×Q₈×C₂₃	—	2	8	no	—
406	C₂×Q₈×C₂₃	—	4	4	no	—
407	C₂×Q₈×C₂₃	—	4	4	no	—
408	C₂×Q₈×C₂₃	—	4	16	no	—
409	C₂×Q₈×C₂₃	—	4	16	no	—
410	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
411	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
412	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
413	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
414	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
415	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
416	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
417	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
418	C₂×Q₈×C₂₃	C₂⁴	1	16	yes	—
419	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
420	C₂×D₄×C₂₃	—	2	8	no	—
421	C₂×D₄×C₂₃	—	4	4	no	—
422	C₂×D₄×C₂₃	—	4	4	no	—
423	C₂×D₄×C₂₃	—	4	8	no	—
424	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
425	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
426	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
427	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
428	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
429	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
430	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
431	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
432	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
433	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
434	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
435	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
436	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
437	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
438	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
439	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
440	C₂²×C₄×C₂₃	—	2	4	no	—
441	C₂²×C₄×C₂₃	—	2	4	no	—
442	C₂²×C₄×C₂₃	—	4	2	no	—
443	C₂²×C₄×C₂₃	—	4	8	no	—
444	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
445	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
446	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
447	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
448	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
449	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
450	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
451	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
452	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
453	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
454	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
455	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
456	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
457	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
458	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
459	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
460	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
461	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
462	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
463	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
464	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
465	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
466	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
467	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
468	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
469	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
470	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
471	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
472	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
473	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
474	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
475	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
476	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
477	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
478	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
479	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
480	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
481	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
482	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
483	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
484	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
485	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
486	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
487	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
488	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
489	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
490	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
491	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
492	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
493	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
494	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
495	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
496	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
497	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
498	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
499	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
500	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
501	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
502	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
503	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
504	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
505	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
506	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
507	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
508	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
509	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
510	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
511	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
512	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
513	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
514	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
515	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
516	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
517	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
518	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
519	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
520	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
521	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
522	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
523	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
524	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
525	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
526	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
527	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
528	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
529	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
530	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
531	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
532	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
533	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
534	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
535	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
536	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
537	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
538	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
539	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
540	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
541	C₄²×C₂₃	C₂⁴	1	8	yes	—
542	C₄²×C₂₃	C₂⁴	1	4	yes	—
543	C₄²×C₂₃	C₂⁴	1	4	yes	—
544	C₄²×C₂₃	C₂⁴	1	4	yes	—
545	C₄²×C₂₃	C₂⁴	1	8	yes	—
546	C₄²×C₂₃	C₂⁴	1	16	yes	—
547	#62835	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
548	C₂³×C₂₃	—	2	2	no	—
549	C₂³×C₂₃	—	2	2	no	—
550	C₂³×C₂₃	—	2	8	no	—
551	C₂³×C₂₃	—	4	1	no	—
552	C₂³×C₂₃	—	4	4	no	—
553	C₂³×C₂₃	—	4	4	no	—
554	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
555	C₂³×C₂₃	C₂⁵	1	8	yes	—
556	C₂³×C₂₃	C₂⁵	1	4	yes	—
557	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
558	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
559	Q₈×C₂₃	—	2	8	no	—
560	Q₈×C₂₃	—	2	8	no	—
561	Q₈×C₂₃	—	2	4	no	—
562	Q₈×C₂₃	—	2	8	no	—
563	Q₈×C₂₃	—	2	4	no	—
564	Q₈×C₂₃	—	2	8	no	—
565	Q₈×C₂₃	—	4	16	no	—
566	Q₈×C₂₃	—	4	4	no	—
567	Q₈×C₂₃	—	4	4	no	—
568	Q₈×C₂₃	—	4	2	no	—
569	D₄×C₂₃	—	2	16	no	—
570	D₄×C₂₃	—	2	8	no	—
571	D₄×C₂₃	—	2	8	no	—
572	D₄×C₂₃	—	2	8	no	—
573	D₄×C₂₃	—	2	4	no	—
574	D₄×C₂₃	—	2	8	no	—
575	D₄×C₂₃	—	2	8	no	—
576	D₄×C₂₃	—	2	4	no	—
577	D₄×C₂₃	—	2	8	no	—
578	D₄×C₂₃	—	4	4	no	—
579	D₄×C₂₃	—	4	4	no	—
580	D₄×C₂₃	—	4	8	no	—
581	D₄×C₂₃	—	4	4	no	—
582	D₄×C₂₃	—	4	2	no	—
583	D₄×C₂₃	—	4	16	no	—
584	D₄×C₂₃	—	4	16	no	—
585	C₂×C₄×C₂₃	—	2	2	no	—
586	C₂×C₄×C₂₃	—	2	8	no	—
587	C₂×C₄×C₂₃	—	2	2	no	—
588	C₂×C₄×C₂₃	—	2	2	no	—
589	C₂×C₄×C₂₃	—	2	2	no	—
590	C₂×C₄×C₂₃	—	2	2	no	—
591	C₂×C₄×C₂₃	—	2	2	no	—
592	C₂×C₄×C₂₃	—	2	16	no	—
593	C₂×C₄×C₂₃	—	2	8	no	—
594	C₂×C₄×C₂₃	—	2	2	no	—
595	C₂×C₄×C₂₃	—	2	2	no	—
596	C₂×C₄×C₂₃	—	2	2	no	—
597	C₂×C₄×C₂₃	—	2	2	no	—
598	C₂×C₄×C₂₃	—	2	8	no	—
599	C₂×C₄×C₂₃	—	2	2	no	—
600	C₂×C₄×C₂₃	—	2	2	no	—
601	C₂×C₄×C₂₃	—	2	2	no	—
602	C₂×C₄×C₂₃	—	2	8	no	—
603	C₂×C₄×C₂₃	—	4	1	no	—
604	C₂×C₄×C₂₃	—	4	1	no	—
605	C₂×C₄×C₂₃	—	4	1	no	—
606	C₂×C₄×C₂₃	—	4	4	no	—
607	C₂×C₄×C₂₃	—	4	8	no	—
608	C₂×C₄×C₂₃	—	4	4	no	—
609	C₂×C₄×C₂₃	—	4	16	no	—
610	C₂×C₄×C₂₃	—	4	16	no	—
611	C₂×C₄×C₂₃	—	4	16	no	—
612	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
613	C₂×C₄×C₂₃	2₋¹⁺⁴	1	4	yes	complemented
614	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
615	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
616	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
617	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
618	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
619	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
620	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
621	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
622	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
623	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
624	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
625	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
626	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
627	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
628	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
629	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
630	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
631	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
632	#3561	C₂×C₂₃	1	4	yes	complemented
633	#3559	C₂×C₂₃	1	4	yes	complemented
634	#3554	C₂×C₂₃	1	4	yes	complemented
635	#3550	C₂×C₂₃	1	2	yes	complemented
636	#3548	C₂×C₂₃	1	2	yes	complemented
637	#3547	C₂×C₂₃	1	4	yes	complemented
638	#3536	C₂×C₂₃	1	4	yes	complemented
639	#3522	C₂×C₂₃	1	4	yes	complemented
640	#3520	C₂×C₂₃	1	4	yes	complemented
641	#3511	C₂×C₂₃	1	2	yes	complemented
642	#3511	C₂×C₂₃	1	4	yes	complemented
643	#3508	C₂×C₂₃	1	2	yes	complemented
644	#3507	C₂×C₂₃	1	2	yes	complemented
645	#3506	C₂×C₂₃	1	2	yes	complemented
646	#3503	C₂×C₂₃	1	2	yes	complemented
647	#3501	C₂×C₂₃	1	2	yes	complemented
648	#3499	C₂×C₂₃	1	2	yes	complemented
649	#3497	C₂×C₂₃	1	2	yes	complemented
650	#3494	C₂×C₂₃	1	4	yes	complemented
651	#3489	C₂×C₂₃	1	4	yes	complemented
652	#3444	C₂×C₂₃	1	1	yes	characteristic, complemented
653	C₂×#533	C₂×C₂₃	1	1	yes	characteristic, complemented
654	C₂×#532	C₂×C₂₃	1	1	yes	characteristic, complemented
655	C₂²×C₂₃	—	2	1	no	—
656	C₂²×C₂₃	—	2	1	no	—
657	C₂²×C₂₃	—	2	1	no	—
658	C₂²×C₂₃	—	2	1	no	—
659	C₂²×C₂₃	—	2	1	no	—
660	C₂²×C₂₃	—	2	4	no	—
661	C₂²×C₂₃	—	2	8	no	—
662	C₂²×C₂₃	—	2	1	no	—
663	C₂²×C₂₃	—	2	4	no	—
664	C₂²×C₂₃	—	2	8	no	—
665	C₂²×C₂₃	—	2	1	no	—
666	C₂²×C₂₃	—	2	4	no	—
667	C₂²×C₂₃	—	2	8	no	—
668	C₂²×C₂₃	—	4	4	no	—
669	C₂²×C₂₃	—	8	8	no	—
670	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
671	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
672	C₂²×C₂₃	C₂⁶	1	1	yes	characteristic
673	C₄×C₂₃	—	2	1	no	—
674	C₄×C₂₃	—	2	1	no	—
675	C₄×C₂₃	—	2	8	no	—
676	C₄×C₂₃	—	2	4	no	—
677	C₄×C₂₃	—	2	8	no	—
678	C₄×C₂₃	—	2	1	no	—
679	C₄×C₂₃	—	2	1	no	—
680	C₄×C₂₃	—	2	4	no	—
681	C₄×C₂₃	—	2	4	no	—
682	C₄×C₂₃	—	2	1	no	—
683	C₄×C₂₃	—	2	1	no	—
684	C₄×C₂₃	—	2	1	no	—
685	C₄×C₂₃	—	2	8	no	—
686	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
687	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
688	C₄×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
689	C₄×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
690	C₄×C₂₃	#585	1	2	yes	—
691	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	4	yes	complemented
692	C₂²×#41	C₂²×C₂₃	1	2	yes	—
693	#563	C₂²×C₂₃	1	8	yes	complemented
694	#562	C₂²×C₂₃	1	16	yes	complemented
695	#562	C₂²×C₂₃	1	8	yes	complemented
696	#559	C₂²×C₂₃	1	8	yes	complemented
697	#559	C₂²×C₂₃	1	4	yes	complemented
698	#559	C₂²×C₂₃	1	4	yes	complemented
699	Q₈²	C₂²×C₂₃	1	4	yes	complemented
700	#557	C₂²×C₂₃	1	4	yes	complemented
701	#556	C₂²×C₂₃	1	4	yes	complemented
702	#556	C₂²×C₂₃	1	8	yes	complemented
703	#556	C₂²×C₂₃	1	4	yes	complemented
704	#555	C₂²×C₂₃	1	8	yes	complemented
705	#555	C₂²×C₂₃	1	4	yes	complemented
706	#554	C₂²×C₂₃	1	8	yes	—
707	#554	C₂²×C₂₃	1	4	yes	complemented
708	#554	C₂²×C₂₃	1	4	yes	complemented
709	#554	C₂²×C₂₃	1	8	yes	complemented
710	#554	C₂²×C₂₃	1	8	yes	complemented
711	#554	C₂²×C₂₃	1	4	yes	complemented
712	#553	C₂²×C₂₃	1	8	yes	complemented
713	#553	C₂²×C₂₃	1	8	yes	complemented
714	#553	C₂²×C₂₃	1	8	yes	complemented
715	#552	C₂²×C₂₃	1	8	yes	complemented
716	#551	C₂²×C₂₃	1	16	yes	—
717	#550	C₂²×C₂₃	1	4	yes	complemented
718	#550	C₂²×C₂₃	1	4	yes	complemented
719	#550	C₂²×C₂₃	1	4	yes	complemented
720	D₄×Q₈	C₂²×C₂₃	1	8	yes	—
721	D₄×Q₈	C₂²×C₂₃	1	4	yes	complemented
722	D₄×Q₈	C₂²×C₂₃	1	4	yes	complemented
723	D₄×Q₈	C₂²×C₂₃	1	4	yes	complemented
724	D₄×Q₈	C₂²×C₂₃	1	4	yes	complemented
725	#548	C₂²×C₂₃	1	8	yes	complemented
726	#548	C₂²×C₂₃	1	8	yes	complemented
727	#548	C₂²×C₂₃	1	8	yes	complemented
728	#548	C₂²×C₂₃	1	8	yes	complemented
729	#547	C₂²×C₂₃	1	8	yes	complemented
730	#547	C₂²×C₂₃	1	16	yes	complemented
731	#547	C₂²×C₂₃	1	8	yes	complemented
732	#547	C₂²×C₂₃	1	4	yes	complemented
733	#547	C₂²×C₂₃	1	4	yes	complemented
734	#547	C₂²×C₂₃	1	8	yes	complemented
735	#547	C₂²×C₂₃	1	4	yes	complemented
736	#546	C₂²×C₂₃	1	16	yes	—
737	#546	C₂²×C₂₃	1	8	yes	—
738	#546	C₂²×C₂₃	1	8	yes	—
739	#544	C₂²×C₂₃	1	4	yes	—
740	#544	C₂²×C₂₃	1	8	yes	complemented
741	#543	C₂²×C₂₃	1	8	yes	—
742	#542	C₂²×C₂₃	1	8	yes	complemented
743	#542	C₂²×C₂₃	1	8	yes	complemented
744	#542	C₂²×C₂₃	1	8	yes	complemented
745	#542	C₂²×C₂₃	1	8	yes	complemented
746	#542	C₂²×C₂₃	1	16	yes	complemented
747	#540	C₂²×C₂₃	1	8	yes	complemented
748	#540	C₂²×C₂₃	1	8	yes	complemented
749	#539	C₂²×C₂₃	1	8	yes	complemented
750	#539	C₂²×C₂₃	1	16	yes	complemented
751	#538	C₂²×C₂₃	1	8	yes	—
752	#537	C₂²×C₂₃	1	4	yes	complemented
753	#537	C₂²×C₂₃	1	8	yes	complemented
754	#537	C₂²×C₂₃	1	8	yes	complemented
755	#537	C₂²×C₂₃	1	8	yes	complemented
756	#536	C₂²×C₂₃	1	4	yes	complemented
757	#536	C₂²×C₂₃	1	8	yes	complemented
758	#536	C₂²×C₂₃	1	8	yes	complemented
759	#535	C₂²×C₂₃	1	4	yes	—
760	#533	C₂²×C₂₃	1	2	yes	—
761	#533	C₂²×C₂₃	1	2	yes	—
762	#533	C₂²×C₂₃	1	2	yes	—
763	#533	C₂²×C₂₃	1	2	yes	—
764	#533	C₂²×C₂₃	1	1	yes	characteristic
765	#533	C₂²×C₂₃	1	2	yes	complemented
766	#533	C₂²×C₂₃	1	2	yes	complemented
767	#533	C₂²×C₂₃	1	2	yes	complemented
768	#533	C₂²×C₂₃	1	2	yes	complemented
769	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
770	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
771	#533	C₂²×C₂₃	1	4	yes	complemented
772	#532	C₂²×C₂₃	1	2	yes	—
773	#532	C₂²×C₂₃	1	2	yes	—
774	#532	C₂²×C₂₃	1	2	yes	—
775	#532	C₂²×C₂₃	1	2	yes	—
776	#532	C₂²×C₂₃	1	2	yes	—
777	#532	C₂²×C₂₃	1	2	yes	—
778	#532	C₂²×C₂₃	1	2	yes	—
779	#532	C₂²×C₂₃	1	2	yes	—
780	#532	C₂²×C₂₃	1	1	yes	characteristic
781	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
782	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
783	#532	C₂²×C₂₃	1	8	yes	complemented
784	#532	C₂²×C₂₃	1	4	yes	complemented
785	#532	C₂²×C₂₃	1	4	yes	complemented
786	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
787	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
788	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
789	C₂×C₄⋊Q₈	C₂²×C₂₃	1	4	yes	complemented
790	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
791	#529	C₂²×C₂₃	1	2	yes	—
792	#529	C₂²×C₂₃	1	2	yes	—
793	#529	C₂²×C₂₃	1	2	yes	complemented
794	#529	C₂²×C₂₃	1	2	yes	complemented
795	#529	C₂²×C₂₃	1	2	yes	complemented
796	#529	C₂²×C₂₃	1	2	yes	complemented
797	#529	C₂²×C₂₃	1	8	yes	complemented
798	C₂×#125	C₂²×C₂₃	1	2	yes	complemented
799	C₂×#124	C₂²×C₂₃	1	2	yes	—
800	#525	C₂²×C₂₃	1	2	yes	—
801	#525	C₂²×C₂₃	1	2	yes	—
802	#525	C₂²×C₂₃	1	2	yes	—
803	#525	C₂²×C₂₃	1	8	yes	—
804	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
805	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
806	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	8	yes	—
807	C₂×#121	C₂²×C₂₃	1	2	yes	—
808	C₂×#121	C₂²×C₂₃	1	2	yes	—
809	#520	C₂²×C₂₃	1	4	yes	—
810	#520	C₂²×C₂₃	1	4	yes	complemented
811	#520	C₂²×C₂₃	1	8	yes	complemented
812	#518	C₂²×C₂₃	1	4	yes	—
813	C₄×#41	C₂²×C₂₃	1	2	yes	—
814	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
815	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
816	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
817	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
818	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
819	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
820	C₂×#117	C₂²×C₂₃	1	2	yes	—
821	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
822	C₂×C₂₃	—	2	2	no	—
823	C₂×C₂₃	—	2	2	no	—
824	C₂×C₂₃	—	4	4	no	—
825	C₂×C₂₃	—	4	1	no	—
826	C₂×C₂₃	—	4	8	no	—
827	C₂×C₂₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
828	C₂×C₂₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
829	C₂×C₂₃	C₂×#585	1	1	yes	characteristic
830	2₋¹⁺⁴	—	4	16	no	—
831	C₂×#41	—	4	8	no	—
832	C₂×#41	C₂³×C₂₃	1	2	yes	—
833	C₂×#41	C₂³×C₂₃	1	2	yes	—
834	C₂×#41	C₂³×C₂₃	1	4	yes	—
835	C₂×#41	C₂³×C₂₃	1	2	yes	—
836	C₂×#41	C₂³×C₂₃	1	8	yes	—
837	C₂×#41	C₂³×C₂₃	1	8	yes	—
838	C₂×#41	C₂³×C₂₃	1	4	yes	—
839	C₂×#41	C₂³×C₂₃	1	4	yes	—
840	C₂×#41	C₂³×C₂₃	1	4	yes	—
841	C₂×#41	C₂³×C₂₃	1	8	yes	—
842	C₂×#41	C₂³×C₂₃	1	16	yes	—
843	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
844	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
845	C₂²×Q₈	C₂³×C₂₃	1	8	yes	—
846	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
847	C₂²×Q₈	C₂³×C₂₃	1	8	yes	—
848	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
849	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
850	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
851	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
852	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
853	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
854	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
855	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
856	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
857	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
858	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
859	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
860	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
861	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
862	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
863	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
864	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
865	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
866	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
867	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
868	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
869	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
870	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
871	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
872	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
873	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
874	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
875	C₄⋊Q₈	C₂³×C₂₃	1	16	yes	—
876	#127	C₂³×C₂₃	1	2	yes	—
877	#127	C₂³×C₂₃	1	2	yes	—
878	#127	C₂³×C₂₃	1	2	yes	—
879	#127	C₂³×C₂₃	1	2	yes	—
880	#127	C₂³×C₂₃	1	1	yes	characteristic
881	#127	C₂³×C₂₃	1	8	yes	—
882	#126	C₂³×C₂₃	1	4	yes	—
883	#126	C₂³×C₂₃	1	4	yes	—
884	#126	C₂³×C₂₃	1	16	yes	—
885	#126	C₂³×C₂₃	1	16	yes	—
886	#126	C₂³×C₂₃	1	16	yes	—
887	#125	C₂³×C₂₃	1	4	yes	—
888	#125	C₂³×C₂₃	1	4	yes	—
889	#125	C₂³×C₂₃	1	4	yes	—
890	#125	C₂³×C₂₃	1	4	yes	—
891	#125	C₂³×C₂₃	1	2	yes	—
892	#125	C₂³×C₂₃	1	2	yes	—
893	#125	C₂³×C₂₃	1	2	yes	—
894	#125	C₂³×C₂₃	1	8	yes	—
895	#125	C₂³×C₂₃	1	8	yes	—
896	#125	C₂³×C₂₃	1	16	yes	—
897	#124	C₂³×C₂₃	1	4	yes	—
898	#124	C₂³×C₂₃	1	4	yes	—
899	#124	C₂³×C₂₃	1	4	yes	—
900	#124	C₂³×C₂₃	1	4	yes	—
901	#124	C₂³×C₂₃	1	2	yes	—
902	#124	C₂³×C₂₃	1	2	yes	—
903	#124	C₂³×C₂₃	1	2	yes	—
904	#124	C₂³×C₂₃	1	8	yes	—
905	#124	C₂³×C₂₃	1	8	yes	—
906	#124	C₂³×C₂₃	1	8	yes	—
907	#124	C₂³×C₂₃	1	16	yes	—
908	#124	C₂³×C₂₃	1	16	yes	—
909	#124	C₂³×C₂₃	1	16	yes	—
910	#123	C₂³×C₂₃	1	4	yes	—
911	#123	C₂³×C₂₃	1	4	yes	—
912	#123	C₂³×C₂₃	1	4	yes	—
913	#123	C₂³×C₂₃	1	16	yes	—
914	#123	C₂³×C₂₃	1	16	yes	—
915	#123	C₂³×C₂₃	1	16	yes	—
916	#123	C₂³×C₂₃	1	16	yes	—
917	#123	C₂³×C₂₃	1	16	yes	—
918	#123	C₂³×C₂₃	1	16	yes	—
919	#123	C₂³×C₂₃	1	16	yes	—
920	#123	C₂³×C₂₃	1	16	yes	—
921	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
922	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
923	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
924	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
925	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
926	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
927	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
928	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
929	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
930	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
931	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
932	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
933	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
934	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
935	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
936	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
937	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
938	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
939	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
940	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
941	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
942	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
943	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
944	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
945	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
946	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
947	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
948	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
949	#121	C₂³×C₂₃	1	4	yes	—
950	#121	C₂³×C₂₃	1	4	yes	—
951	#121	C₂³×C₂₃	1	4	yes	—
952	#121	C₂³×C₂₃	1	4	yes	—
953	#121	C₂³×C₂₃	1	4	yes	—
954	#121	C₂³×C₂₃	1	4	yes	—
955	#121	C₂³×C₂₃	1	4	yes	—
956	#121	C₂³×C₂₃	1	4	yes	—
957	#121	C₂³×C₂₃	1	2	yes	—
958	#121	C₂³×C₂₃	1	2	yes	—
959	#121	C₂³×C₂₃	1	2	yes	—
960	#121	C₂³×C₂₃	1	2	yes	—
961	#121	C₂³×C₂₃	1	2	yes	—
962	#121	C₂³×C₂₃	1	2	yes	—
963	#121	C₂³×C₂₃	1	8	yes	—
964	#121	C₂³×C₂₃	1	8	yes	—
965	#121	C₂³×C₂₃	1	8	yes	—
966	#121	C₂³×C₂₃	1	16	yes	—
967	#121	C₂³×C₂₃	1	8	yes	—
968	#121	C₂³×C₂₃	1	8	yes	—
969	#121	C₂³×C₂₃	1	16	yes	—
970	#121	C₂³×C₂₃	1	16	yes	—
971	#121	C₂³×C₂₃	1	16	yes	—
972	#121	C₂³×C₂₃	1	16	yes	—
973	#121	C₂³×C₂₃	1	16	yes	—
974	#120	C₂³×C₂₃	1	4	yes	—
975	#120	C₂³×C₂₃	1	16	yes	—
976	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
977	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
978	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
979	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
980	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
981	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
982	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
983	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
984	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
985	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
986	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
987	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
988	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
989	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
990	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
991	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
992	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
993	C₄×D₄	C₂³×C₂₃	1	4	yes	—
994	C₄×D₄	C₂³×C₂₃	1	4	yes	—
995	C₄×D₄	C₂³×C₂₃	1	4	yes	—
996	C₄×D₄	C₂³×C₂₃	1	4	yes	—
997	C₄×D₄	C₂³×C₂₃	1	4	yes	—
998	C₄×D₄	C₂³×C₂₃	1	4	yes	—
999	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1000	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1001	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1002	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1003	C₄×D₄	C₂³×C₂₃	1	2	yes	—
1004	C₄×D₄	C₂³×C₂₃	1	2	yes	—
1005	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1006	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1007	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1008	C₄×D₄	C₂³×C₂₃	1	4	yes	—
1009	C₄×D₄	C₂³×C₂₃	1	2	yes	—
1010	C₄×D₄	C₂³×C₂₃	1	2	yes	—
1011	C₄×D₄	C₂³×C₂₃	1	2	yes	—
1012	C₄×D₄	C₂³×C₂₃	1	2	yes	—
1013	C₄×D₄	C₂³×C₂₃	1	8	yes	—
1014	C₄×D₄	C₂³×C₂₃	1	8	yes	—
1015	C₄×D₄	C₂³×C₂₃	1	8	yes	—
1016	C₄×D₄	C₂³×C₂₃	1	8	yes	—
1017	C₄×D₄	C₂³×C₂₃	1	16	yes	—
1018	C₄×D₄	C₂³×C₂₃	1	8	yes	—
1019	C₄×D₄	C₂³×C₂₃	1	16	yes	—
1020	C₄×D₄	C₂³×C₂₃	1	16	yes	—
1021	C₄×D₄	C₂³×C₂₃	1	8	yes	—
1022	C₄×D₄	C₂³×C₂₃	1	8	yes	—
1023	C₄×D₄	C₂³×C₂₃	1	16	yes	—
1024	#117	C₂³×C₂₃	1	4	yes	—
1025	#117	C₂³×C₂₃	1	4	yes	—
1026	#117	C₂³×C₂₃	1	4	yes	—
1027	#117	C₂³×C₂₃	1	4	yes	—
1028	#117	C₂³×C₂₃	1	2	yes	—
1029	#117	C₂³×C₂₃	1	4	yes	—
1030	#117	C₂³×C₂₃	1	2	yes	—
1031	#117	C₂³×C₂₃	1	4	yes	—
1032	#117	C₂³×C₂₃	1	2	yes	—
1033	#117	C₂³×C₂₃	1	4	yes	—
1034	#117	C₂³×C₂₃	1	8	yes	—
1035	#117	C₂³×C₂₃	1	8	yes	—
1036	#117	C₂³×C₂₃	1	16	yes	—
1037	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
1038	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
1039	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
1040	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
1041	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
1042	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
1043	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
1044	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
1045	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
1046	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
1047	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	—
1048	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
1049	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
1050	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
1051	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
1052	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	—
1053	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
1054	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1055	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1056	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1057	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1058	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1059	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
1060	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1061	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1062	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1063	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1064	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1065	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1066	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1067	C₂₃	#62835	1	1	yes	characteristic, direct product factor, Sylow
1068	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1069	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
1070	#41	—	2	16	no	—
1071	#41	—	2	8	no	—
1072	#41	—	2	8	no	—
1073	#41	—	4	8	no	—
1074	#41	—	4	4	no	—
1075	#41	—	4	8	no	—
1076	#41	—	4	32	no	—
1077	#41	—	4	8	no	—
1078	#41	—	4	16	no	—
1079	#41	—	4	16	no	—
1080	#41	—	4	16	no	—
1081	C₂×Q₈	—	2	8	no	—
1082	C₂×Q₈	—	4	4	no	—
1083	C₂×Q₈	—	4	16	no	—
1084	C₂×Q₈	—	4	16	no	—
1085	C₂×Q₈	—	4	4	no	—
1086	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
1087	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
1088	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
1089	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
1090	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
1091	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
1092	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
1093	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
1094	C₂×Q₈	C₂⁴×C₂₃	1	16	yes	—
1095	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
1096	C₂×D₄	—	2	8	no	—
1097	C₂×D₄	—	4	4	no	—
1098	C₂×D₄	—	4	4	no	—
1099	C₂×D₄	—	4	8	no	—
1100	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1101	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1102	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1103	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1104	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1105	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1106	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
1107	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1108	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1109	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1110	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
1111	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1112	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1113	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
1114	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
1115	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
1116	C₂²×C₄	—	2	4	no	—
1117	C₂²×C₄	—	2	4	no	—
1118	C₂²×C₄	—	4	8	no	—
1119	C₂²×C₄	—	4	2	no	—
1120	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1121	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1122	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1123	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1124	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1125	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1126	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1127	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1128	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1129	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1130	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1131	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1132	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1133	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
1134	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
1135	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
1136	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
1137	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
1138	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1139	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1140	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1141	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
1142	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
1143	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
1144	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
1145	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
1146	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
1147	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1148	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1149	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1150	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1151	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1152	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1153	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1154	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1155	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1156	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1157	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
1158	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1159	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1160	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1161	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1162	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1163	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1164	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
1165	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
1166	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
1167	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1168	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1169	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1170	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1171	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1172	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1173	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1174	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1175	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1176	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1177	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1178	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1179	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1180	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1181	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1182	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1183	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1184	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1185	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1186	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
1187	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
1188	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1189	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1190	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1191	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1192	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1193	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
1194	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
1195	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1196	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1197	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1198	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
1199	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1200	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1201	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1202	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1203	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1204	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1205	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1206	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1207	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1208	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1209	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1210	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1211	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1212	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1213	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1214	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1215	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1216	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1217	C₄²	C₂⁴×C₂₃	1	8	yes	—
1218	C₄²	C₂⁴×C₂₃	1	4	yes	—
1219	C₄²	C₂⁴×C₂₃	1	4	yes	—
1220	C₄²	C₂⁴×C₂₃	1	4	yes	—
1221	C₄²	C₂⁴×C₂₃	1	8	yes	—
1222	C₄²	C₂⁴×C₂₃	1	16	yes	—
1223	C₂³	—	2	2	no	—
1224	C₂³	—	2	2	no	—
1225	C₂³	—	2	8	no	—
1226	C₂³	—	4	1	no	—
1227	C₂³	—	4	4	no	—
1228	C₂³	—	4	4	no	—
1229	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1230	C₂³	C₂⁵×C₂₃	1	8	yes	—
1231	C₂³	C₂⁵×C₂₃	1	4	yes	—
1232	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1233	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1234	Q₈	—	2	8	no	—
1235	Q₈	—	2	8	no	—
1236	Q₈	—	2	4	no	—
1237	Q₈	—	2	8	no	—
1238	Q₈	—	2	4	no	—
1239	Q₈	—	2	8	no	—
1240	Q₈	—	4	16	no	—
1241	Q₈	—	4	4	no	—
1242	Q₈	—	4	4	no	—
1243	Q₈	—	4	2	no	—
1244	D₄	—	2	16	no	—
1245	D₄	—	2	8	no	—
1246	D₄	—	2	8	no	—
1247	D₄	—	2	8	no	—
1248	D₄	—	2	4	no	—
1249	D₄	—	2	8	no	—
1250	D₄	—	2	8	no	—
1251	D₄	—	2	4	no	—
1252	D₄	—	2	8	no	—
1253	D₄	—	4	4	no	—
1254	D₄	—	4	8	no	—
1255	D₄	—	4	4	no	—
1256	D₄	—	4	16	no	—
1257	D₄	—	4	4	no	—
1258	D₄	—	4	2	no	—
1259	D₄	—	4	16	no	—
1260	C₂×C₄	—	2	2	no	—
1261	C₂×C₄	—	2	8	no	—
1262	C₂×C₄	—	2	2	no	—
1263	C₂×C₄	—	2	2	no	—
1264	C₂×C₄	—	2	2	no	—
1265	C₂×C₄	—	2	2	no	—
1266	C₂×C₄	—	2	2	no	—
1267	C₂×C₄	—	2	16	no	—
1268	C₂×C₄	—	2	8	no	—
1269	C₂×C₄	—	2	2	no	—
1270	C₂×C₄	—	2	2	no	—
1271	C₂×C₄	—	2	2	no	—
1272	C₂×C₄	—	2	2	no	—
1273	C₂×C₄	—	2	8	no	—
1274	C₂×C₄	—	2	2	no	—
1275	C₂×C₄	—	2	2	no	—
1276	C₂×C₄	—	2	2	no	—
1277	C₂×C₄	—	2	8	no	—
1278	C₂×C₄	—	4	4	no	—
1279	C₂×C₄	—	4	8	no	—
1280	C₂×C₄	—	4	1	no	—
1281	C₂×C₄	—	4	1	no	—
1282	C₂×C₄	—	4	1	no	—
1283	C₂×C₄	—	4	16	no	—
1284	C₂×C₄	—	4	16	no	—
1285	C₂×C₄	—	4	4	no	—
1286	C₂×C₄	—	4	16	no	—
1287	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
1288	C₂×C₄	C₂₃×2₋¹⁺⁴	1	4	yes	complemented
1289	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1290	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
1291	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1292	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1293	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1294	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
1295	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1296	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1297	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1298	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
1299	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
1300	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
1301	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
1302	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1303	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1304	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1305	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1306	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1307	C₂²	—	2	1	no	—
1308	C₂²	—	2	1	no	—
1309	C₂²	—	2	1	no	—
1310	C₂²	—	2	1	no	—
1311	C₂²	—	2	1	no	—
1312	C₂²	—	2	4	no	—
1313	C₂²	—	2	8	no	—
1314	C₂²	—	2	1	no	—
1315	C₂²	—	2	4	no	—
1316	C₂²	—	2	8	no	—
1317	C₂²	—	2	1	no	—
1318	C₂²	—	2	4	no	—
1319	C₂²	—	2	8	no	—
1320	C₂²	—	4	4	no	—
1321	C₂²	—	8	8	no	—
1322	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
1323	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
1324	C₂²	C₂⁶×C₂₃	1	1	yes	characteristic
1325	C₄	—	2	1	no	—
1326	C₄	—	2	1	no	—
1327	C₄	—	2	8	no	—
1328	C₄	—	2	4	no	—
1329	C₄	—	2	8	no	—
1330	C₄	—	2	1	no	—
1331	C₄	—	2	1	no	—
1332	C₄	—	2	4	no	—
1333	C₄	—	2	4	no	—
1334	C₄	—	2	1	no	—
1335	C₄	—	2	1	no	—
1336	C₄	—	2	1	no	—
1337	C₄	—	2	8	no	—
1338	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
1339	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
1340	C₄	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
1341	C₄	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
1342	C₄	C₂₃×#585	1	2	yes	—
1343	C₂	—	2	2	no	—
1344	C₂	—	2	2	no	—
1345	C₂	—	4	1	no	—
1346	C₂	—	4	8	no	—
1347	C₂	—	4	4	no	—
1348	C₂	C₂²×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1349	C₂	C₂²×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1350	C₂	C₂×C₂₃×#585	1	1	yes	characteristic

	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×#3561	C₂	semidirect
2. C₂₃×#3559	C₂	semidirect
3. C₂₃×#3554	C₂	semidirect
4. C₂₃×#3550	C₂	semidirect
5. C₂₃×#3548	C₂	semidirect
6. C₂₃×#3547	C₂	semidirect
7. C₂₃×#3536	C₂	semidirect
8. C₂₃×#3522	C₂	semidirect
9. C₂₃×#3520	C₂	semidirect
10. C₂₃×#3511	C₂	semidirect
11. C₂₃×#3511	C₂	semidirect
12. C₂₃×#3508	C₂	semidirect
13. C₂₃×#3507	C₂	semidirect
14. C₂₃×#3506	C₂	semidirect
15. C₂₃×#3503	C₂	semidirect
16. C₂₃×#3501	C₂	semidirect
17. C₂₃×#3499	C₂	semidirect
18. C₂₃×#3497	C₂	semidirect
19. C₂₃×#3494	C₂	semidirect
20. C₂₃×#3489	C₂	semidirect
21. C₂₃×#3444	C₂	semidirect
22. C₂×C₂₃×#533	C₂	semidirect
23. C₂×C₂₃×#532	C₂	semidirect
24. C₂×C₂₃×2₋¹⁺⁴	C₂²	semidirect
26. C₂₃×#563	C₂²	semidirect
27. C₂₃×#562	C₂²	semidirect
28. C₂₃×#562	C₂²	semidirect
29. C₂₃×#559	C₂²	semidirect
30. C₂₃×#559	C₂²	semidirect
31. C₂₃×#559	C₂²	semidirect
32. Q₈²×C₂₃	C₂²	semidirect
33. C₂₃×#557	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
40. C₂₃×#554	C₂²	semidirect
41. C₂₃×#554	C₂²	semidirect
42. C₂₃×#554	C₂²	semidirect
43. C₂₃×#554	C₂²	semidirect
44. C₂₃×#554	C₂²	semidirect
45. C₂₃×#553	C₂²	semidirect
46. C₂₃×#553	C₂²	semidirect
47. C₂₃×#553	C₂²	semidirect
48. C₂₃×#552	C₂²	semidirect
50. C₂₃×#550	C₂²	semidirect
51. C₂₃×#550	C₂²	semidirect
52. C₂₃×#550	C₂²	semidirect
54. D₄×Q₈×C₂₃	C₂²	semidirect
55. D₄×Q₈×C₂₃	C₂²	semidirect
56. D₄×Q₈×C₂₃	C₂²	semidirect
57. D₄×Q₈×C₂₃	C₂²	semidirect
58. C₂₃×#548	C₂²	semidirect
59. C₂₃×#548	C₂²	semidirect
60. C₂₃×#548	C₂²	semidirect
61. C₂₃×#548	C₂²	semidirect
62. C₂₃×#547	C₂²	semidirect
63. C₂₃×#547	C₂²	semidirect
64. C₂₃×#547	C₂²	semidirect
65. C₂₃×#547	C₂²	semidirect
66. C₂₃×#547	C₂²	semidirect
67. C₂₃×#547	C₂²	semidirect
68. C₂₃×#547	C₂²	semidirect
73. C₂₃×#544	C₂²	semidirect
75. C₂₃×#542	C₂²	semidirect
76. C₂₃×#542	C₂²	semidirect
77. C₂₃×#542	C₂²	semidirect
78. C₂₃×#542	C₂²	semidirect
79. C₂₃×#542	C₂²	semidirect
80. C₂₃×#540	C₂²	semidirect
81. C₂₃×#540	C₂²	semidirect
82. C₂₃×#539	C₂²	semidirect
83. C₂₃×#539	C₂²	semidirect
85. C₂₃×#537	C₂²	semidirect
86. C₂₃×#537	C₂²	semidirect
87. C₂₃×#537	C₂²	semidirect
88. C₂₃×#537	C₂²	semidirect
89. C₂₃×#536	C₂²	semidirect
90. C₂₃×#536	C₂²	semidirect
91. C₂₃×#536	C₂²	semidirect
98. C₂₃×#533	C₂²	semidirect
99. C₂₃×#533	C₂²	semidirect
100. C₂₃×#533	C₂²	semidirect
101. C₂₃×#533	C₂²	semidirect
102. C₂₃×#533	C₂²	semidirect
103. C₂₃×#533	C₂²	semidirect
104. C₂₃×#533	C₂²	semidirect
114. C₂₃×#532	C₂²	semidirect
115. C₂₃×#532	C₂²	semidirect
116. C₂₃×#532	C₂²	semidirect
117. C₂₃×#532	C₂²	semidirect
118. C₂₃×#532	C₂²	semidirect
120. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
121. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
122. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
126. C₂₃×#529	C₂²	semidirect
127. C₂₃×#529	C₂²	semidirect
128. C₂₃×#529	C₂²	semidirect
129. C₂₃×#529	C₂²	semidirect
130. C₂₃×#529	C₂²	semidirect
131. C₂×C₂₃×#125	C₂²	semidirect
143. C₂₃×#520	C₂²	semidirect
144. C₂₃×#520	C₂²	semidirect
147. C₄×#41×C₂₃	C₂²	semidirect
148. C₄×#41×C₂₃	C₂²	semidirect
149. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
150. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
547. #62835	C₂₃	direct (N × H)
613. C₂×C₄×C₂₃	2₋¹⁺⁴	semidirect
632. #3561	C₂×C₂₃	semidirect
633. #3559	C₂×C₂₃	semidirect
634. #3554	C₂×C₂₃	semidirect
635. #3550	C₂×C₂₃	semidirect
636. #3548	C₂×C₂₃	semidirect
637. #3547	C₂×C₂₃	semidirect
638. #3536	C₂×C₂₃	semidirect
639. #3522	C₂×C₂₃	semidirect
640. #3520	C₂×C₂₃	semidirect
641. #3511	C₂×C₂₃	semidirect
642. #3511	C₂×C₂₃	semidirect
643. #3508	C₂×C₂₃	semidirect
644. #3507	C₂×C₂₃	semidirect
645. #3506	C₂×C₂₃	semidirect
646. #3503	C₂×C₂₃	semidirect
647. #3501	C₂×C₂₃	semidirect
648. #3499	C₂×C₂₃	semidirect
649. #3497	C₂×C₂₃	semidirect
650. #3494	C₂×C₂₃	semidirect
651. #3489	C₂×C₂₃	semidirect
652. #3444	C₂×C₂₃	semidirect
653. C₂×#533	C₂×C₂₃	semidirect
654. C₂×#532	C₂×C₂₃	semidirect
691. C₂×2₋¹⁺⁴	C₂²×C₂₃	semidirect
693. #563	C₂²×C₂₃	semidirect
694. #562	C₂²×C₂₃	semidirect
695. #562	C₂²×C₂₃	semidirect
696. #559	C₂²×C₂₃	semidirect
697. #559	C₂²×C₂₃	semidirect
698. #559	C₂²×C₂₃	semidirect
699. Q₈²	C₂²×C₂₃	semidirect
700. #557	C₂²×C₂₃	semidirect
701. #556	C₂²×C₂₃	semidirect
702. #556	C₂²×C₂₃	semidirect
703. #556	C₂²×C₂₃	semidirect
704. #555	C₂²×C₂₃	semidirect
705. #555	C₂²×C₂₃	semidirect
707. #554	C₂²×C₂₃	semidirect
708. #554	C₂²×C₂₃	semidirect
709. #554	C₂²×C₂₃	semidirect
710. #554	C₂²×C₂₃	semidirect
711. #554	C₂²×C₂₃	semidirect
712. #553	C₂²×C₂₃	semidirect
713. #553	C₂²×C₂₃	semidirect
714. #553	C₂²×C₂₃	semidirect
715. #552	C₂²×C₂₃	semidirect
717. #550	C₂²×C₂₃	semidirect
718. #550	C₂²×C₂₃	semidirect
719. #550	C₂²×C₂₃	semidirect
721. D₄×Q₈	C₂²×C₂₃	semidirect
722. D₄×Q₈	C₂²×C₂₃	semidirect
723. D₄×Q₈	C₂²×C₂₃	semidirect
724. D₄×Q₈	C₂²×C₂₃	semidirect
725. #548	C₂²×C₂₃	semidirect
726. #548	C₂²×C₂₃	semidirect
727. #548	C₂²×C₂₃	semidirect
728. #548	C₂²×C₂₃	semidirect
729. #547	C₂²×C₂₃	semidirect
730. #547	C₂²×C₂₃	semidirect
731. #547	C₂²×C₂₃	semidirect
732. #547	C₂²×C₂₃	semidirect
733. #547	C₂²×C₂₃	semidirect
734. #547	C₂²×C₂₃	semidirect
735. #547	C₂²×C₂₃	semidirect
740. #544	C₂²×C₂₃	semidirect
742. #542	C₂²×C₂₃	semidirect
743. #542	C₂²×C₂₃	semidirect
744. #542	C₂²×C₂₃	semidirect
745. #542	C₂²×C₂₃	semidirect
746. #542	C₂²×C₂₃	semidirect
747. #540	C₂²×C₂₃	semidirect
748. #540	C₂²×C₂₃	semidirect
749. #539	C₂²×C₂₃	semidirect
750. #539	C₂²×C₂₃	semidirect
752. #537	C₂²×C₂₃	semidirect
753. #537	C₂²×C₂₃	semidirect
754. #537	C₂²×C₂₃	semidirect
755. #537	C₂²×C₂₃	semidirect
756. #536	C₂²×C₂₃	semidirect
757. #536	C₂²×C₂₃	semidirect
758. #536	C₂²×C₂₃	semidirect
765. #533	C₂²×C₂₃	semidirect
766. #533	C₂²×C₂₃	semidirect
767. #533	C₂²×C₂₃	semidirect
768. #533	C₂²×C₂₃	semidirect
769. #533	C₂²×C₂₃	semidirect
770. #533	C₂²×C₂₃	semidirect
771. #533	C₂²×C₂₃	semidirect
781. #532	C₂²×C₂₃	semidirect
782. #532	C₂²×C₂₃	semidirect
783. #532	C₂²×C₂₃	semidirect
784. #532	C₂²×C₂₃	semidirect
785. #532	C₂²×C₂₃	semidirect
787. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
788. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
789. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
793. #529	C₂²×C₂₃	semidirect
794. #529	C₂²×C₂₃	semidirect
795. #529	C₂²×C₂₃	semidirect
796. #529	C₂²×C₂₃	semidirect
797. #529	C₂²×C₂₃	semidirect
798. C₂×#125	C₂²×C₂₃	semidirect
810. #520	C₂²×C₂₃	semidirect
811. #520	C₂²×C₂₃	semidirect
814. C₄×#41	C₂²×C₂₃	semidirect
815. C₄×#41	C₂²×C₂₃	semidirect
816. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
817. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
1067. C₂₃	#62835	direct (N × H)
1288. C₂×C₄	C₂₃×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3561	2
C₂₃×#3559	2
C₂₃×#3554	2
C₂₃×#3550	2
C₂₃×#3548	2
C₂₃×#3547	2
C₂₃×#3536	2
C₂₃×#3522	2
C₂₃×#3520	2
C₂₃×#3511	2
C₂₃×#3508	2
C₂₃×#3507	2
C₂₃×#3506	2
C₂₃×#3503	2
C₂₃×#3501	2
C₂₃×#3499	2
C₂₃×#3497	2
C₂₃×#3494	2
C₂₃×#3489	2
C₂₃×#3444	2
C₂×C₂₃×#533	2
C₂×C₂₃×#532	2
#62835	23

Subgroups — C23×#62835 #19210461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62835 #19210461