Subgroups — C₂₃×#62836 #19210462

Order 5888.

7254 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3562	C₂	1	8	yes	maximal, complemented
2	C₂₃×#3554	C₂	1	4	yes	maximal, complemented
3	C₂₃×#3546	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3542	C₂	1	8	yes	maximal, complemented
5	C₂₃×#3517	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3514	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3513	C₂	1	8	yes	maximal, complemented
8	C₂₃×#3511	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3510	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3508	C₂	1	4	yes	maximal, complemented
13	C₂₃×#3500	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3487	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3485	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₂₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
22	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	2	yes	—
23	C₂²×#41×C₂₃	C₂²	1	2	yes	complemented
24	C₂₃×#562	C₂²	1	16	yes	complemented
25	C₂₃×#560	C₂²	1	16	yes	complemented
26	C₂₃×#559	C₂²	1	8	yes	complemented
27	C₂₃×#559	C₂²	1	8	yes	complemented
28	C₂₃×#559	C₂²	1	4	yes	complemented
29	C₂₃×#557	C₂²	1	4	yes	complemented
30	C₂₃×#556	C₂²	1	4	yes	complemented
31	C₂₃×#556	C₂²	1	8	yes	complemented
32	C₂₃×#555	C₂²	1	8	yes	complemented
33	C₂₃×#554	C₂²	1	8	yes	complemented
34	C₂₃×#553	C₂²	1	8	yes	complemented
35	C₂₃×#553	C₂²	1	8	yes	complemented
36	C₂₃×#553	C₂²	1	16	yes	complemented
37	C₂₃×#552	C₂²	1	8	yes	complemented
38	C₂₃×#551	C₂²	1	16	yes	complemented
39	C₂₃×#551	C₂²	1	16	yes	complemented
40	C₂₃×#550	C₂²	1	8	yes	complemented
41	C₂₃×#550	C₂²	1	8	yes	complemented
42	C₂₃×#550	C₂²	1	4	yes	complemented
43	C₂₃×#550	C₂²	1	8	yes	complemented
44	C₂₃×#550	C₂²	1	4	yes	complemented
45	D₄×Q₈×C₂₃	C₂²	1	4	yes	complemented
46	C₂₃×#548	C₂²	1	8	yes	complemented
47	C₂₃×#548	C₂²	1	8	yes	complemented
48	C₂₃×#548	C₂²	1	8	yes	complemented
49	C₂₃×#547	C₂²	1	8	yes	complemented
50	C₂₃×#547	C₂²	1	8	yes	complemented
51	C₂₃×#547	C₂²	1	8	yes	complemented
52	C₂₃×#547	C₂²	1	4	yes	complemented
53	C₂₃×#546	C₂²	1	8	yes	complemented
54	C₂₃×#546	C₂²	1	8	yes	complemented
55	C₂₃×#546	C₂²	1	8	yes	complemented
56	C₂₃×#546	C₂²	1	16	yes	complemented
57	C₂₃×#546	C₂²	1	8	yes	complemented
58	C₂₃×#546	C₂²	1	8	yes	complemented
59	C₂₃×#546	C₂²	1	8	yes	complemented
60	D₄²×C₂₃	C₂²	1	8	yes	—
61	D₄²×C₂₃	C₂²	1	4	yes	complemented
62	C₂₃×#542	C₂²	1	8	yes	complemented
63	C₂₃×#542	C₂²	1	8	yes	complemented
64	C₂₃×#542	C₂²	1	8	yes	complemented
65	C₂₃×#541	C₂²	1	4	yes	complemented
66	C₂₃×#540	C₂²	1	8	yes	complemented
67	C₂₃×#540	C₂²	1	8	yes	complemented
68	C₂₃×#540	C₂²	1	4	yes	complemented
69	C₂₃×#540	C₂²	1	16	yes	complemented
70	C₂₃×#539	C₂²	1	16	yes	complemented
71	C₂₃×#538	C₂²	1	16	yes	complemented
72	C₂₃×#538	C₂²	1	16	yes	complemented
73	C₂₃×#537	C₂²	1	8	yes	complemented
74	C₂₃×#536	C₂²	1	2	yes	—
75	C₂₃×#536	C₂²	1	2	yes	complemented
76	C₂₃×#536	C₂²	1	4	yes	complemented
77	C₂₃×#536	C₂²	1	4	yes	complemented
78	C₂₃×#535	C₂²	1	2	yes	—
79	C₂₃×#535	C₂²	1	2	yes	complemented
80	C₂₃×#535	C₂²	1	8	yes	complemented
81	C₂₃×#535	C₂²	1	4	yes	complemented
82	C₂₃×#535	C₂²	1	4	yes	complemented
83	C₂₃×#535	C₂²	1	8	yes	complemented
84	C₂₃×#534	C₂²	1	8	yes	complemented
85	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
86	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
87	C₂₃×#533	C₂²	1	2	yes	complemented
88	C₂₃×#533	C₂²	1	2	yes	complemented
89	C₂₃×#533	C₂²	1	4	yes	complemented
90	C₂₃×#532	C₂²	1	1	yes	characteristic
91	C₂₃×#532	C₂²	1	1	yes	characteristic
92	C₂₃×#532	C₂²	1	4	yes	complemented
93	C₂₃×#532	C₂²	1	4	yes	complemented
94	C₂₃×#532	C₂²	1	4	yes	complemented
95	C₂₃×#532	C₂²	1	4	yes	complemented
96	C₂₃×#532	C₂²	1	2	yes	complemented
97	C₂₃×#532	C₂²	1	2	yes	complemented
98	C₂₃×#532	C₂²	1	2	yes	complemented
99	C₂₃×#532	C₂²	1	2	yes	complemented
100	C₂₃×#532	C₂²	1	4	yes	complemented
101	C₂₃×#532	C₂²	1	4	yes	complemented
102	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
103	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
104	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
105	C₂×C₂₃×#127	C₂²	1	2	yes	complemented
106	C₂₃×#529	C₂²	1	4	yes	complemented
107	C₂₃×#529	C₂²	1	4	yes	complemented
108	C₂₃×#529	C₂²	1	2	yes	complemented
109	C₂₃×#529	C₂²	1	2	yes	complemented
110	C₂₃×#529	C₂²	1	4	yes	complemented
111	C₂₃×#529	C₂²	1	4	yes	complemented
112	C₂₃×#529	C₂²	1	4	yes	complemented
113	C₂₃×#529	C₂²	1	8	yes	complemented
114	C₂×C₂₃×#124	C₂²	1	2	yes	complemented
115	C₂×C₂₃×#124	C₂²	1	4	yes	complemented
116	C₂₃×#525	C₂²	1	1	yes	characteristic
117	C₂₃×#525	C₂²	1	2	yes	complemented
118	C₂₃×#525	C₂²	1	1	yes	characteristic, complemented
119	C₂₃×#525	C₂²	1	4	yes	complemented
120	C₂₃×#525	C₂²	1	4	yes	complemented
121	C₂₃×#525	C₂²	1	8	yes	complemented
122	C₂×C₂₃×#123	C₂²	1	8	yes	complemented
123	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
124	C₂₃×#520	C₂²	1	8	yes	complemented
125	C₂₃×#519	C₂²	1	2	yes	complemented
126	C₂₃×#518	C₂²	1	2	yes	complemented
127	C₂₃×#518	C₂²	1	8	yes	complemented
128	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
129	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
130	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
131	C₄×#41×C₂₃	C₂²	1	4	yes	complemented
132	C₄×#41×C₂₃	C₂²	1	4	yes	complemented
133	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
134	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
135	C₂₃×2₋¹⁺⁴	—	4	8	no	—
136	C₂₃×H(5,𝔽₂)	—	4	8	no	—
137	C₂×#41×C₂₃	—	4	8	no	—
138	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
139	C₂×#41×C₂₃	C₂³	1	2	yes	—
140	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
141	C₂×#41×C₂₃	C₂³	1	4	yes	—
142	C₂×#41×C₂₃	C₂³	1	4	yes	—
143	C₂×#41×C₂₃	C₂³	1	4	yes	—
144	C₂×#41×C₂₃	C₂³	1	8	yes	—
145	C₂×#41×C₂₃	C₂³	1	8	yes	—
146	C₂×#41×C₂₃	C₂³	1	8	yes	—
147	C₂×#41×C₂₃	C₂³	1	4	yes	—
148	C₂×#41×C₂₃	C₂³	1	4	yes	—
149	C₂×#41×C₂₃	C₂³	1	8	yes	—
150	C₂×#41×C₂₃	C₂³	1	4	yes	—
151	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
152	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
153	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
154	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
155	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
156	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
157	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
158	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
159	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
160	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
161	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
162	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
163	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
164	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
165	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
166	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
167	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
168	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
170	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
171	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
173	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
174	C₂₃×#127	C₂³	1	4	yes	—
175	C₂₃×#127	C₂³	1	16	yes	—
176	C₂₃×#127	C₂³	1	4	yes	—
177	C₂₃×#127	C₂³	1	4	yes	—
178	C₂₃×#127	C₂³	1	8	yes	—
179	C₂₃×#127	C₂³	1	2	yes	—
180	C₂₃×#127	C₂³	1	2	yes	—
181	C₂₃×#127	C₂³	1	1	yes	characteristic
182	C₂₃×#127	C₂³	1	1	yes	characteristic
183	C₂₃×#126	C₂³	1	4	yes	—
184	C₂₃×#126	C₂³	1	16	yes	—
185	C₂₃×#126	C₂³	1	16	yes	—
186	C₂₃×#126	C₂³	1	16	yes	—
187	C₂₃×#126	C₂³	1	4	yes	—
188	C₂₃×#126	C₂³	1	8	yes	—
189	C₂₃×#125	C₂³	1	8	yes	—
190	C₂₃×#125	C₂³	1	16	yes	—
191	C₂₃×#125	C₂³	1	4	yes	—
192	C₂₃×#125	C₂³	1	2	yes	—
193	C₂₃×#125	C₂³	1	4	yes	—
194	C₂₃×#125	C₂³	1	2	yes	—
195	C₂₃×#124	C₂³	1	16	yes	—
196	C₂₃×#124	C₂³	1	4	yes	—
197	C₂₃×#124	C₂³	1	4	yes	—
198	C₂₃×#124	C₂³	1	16	yes	—
199	C₂₃×#124	C₂³	1	8	yes	—
200	C₂₃×#124	C₂³	1	16	yes	—
201	C₂₃×#124	C₂³	1	4	yes	—
202	C₂₃×#124	C₂³	1	4	yes	—
203	C₂₃×#124	C₂³	1	4	yes	—
204	C₂₃×#124	C₂³	1	8	yes	—
205	C₂₃×#124	C₂³	1	1	yes	characteristic
206	C₂₃×#124	C₂³	1	4	yes	—
207	C₂₃×#124	C₂³	1	4	yes	—
208	C₂₃×#124	C₂³	1	1	yes	characteristic
209	C₂₃×#124	C₂³	1	2	yes	—
210	C₂₃×#124	C₂³	1	4	yes	—
211	C₂₃×#123	C₂³	1	8	yes	—
212	C₂₃×#123	C₂³	1	16	yes	—
213	C₂₃×#123	C₂³	1	16	yes	—
214	C₂₃×#123	C₂³	1	16	yes	—
215	C₂₃×#123	C₂³	1	16	yes	—
216	C₂₃×#123	C₂³	1	16	yes	—
217	C₂₃×#123	C₂³	1	16	yes	—
218	C₂₃×#123	C₂³	1	16	yes	—
219	C₂₃×#123	C₂³	1	8	yes	—
220	C₂₃×#123	C₂³	1	16	yes	—
221	C₂₃×#123	C₂³	1	8	yes	—
222	C₂₃×#123	C₂³	1	2	yes	—
223	C₂₃×#123	C₂³	1	4	yes	—
224	C₂₃×#123	C₂³	1	2	yes	—
225	C₂₃×#123	C₂³	1	4	yes	—
226	C₂₃×#123	C₂³	1	4	yes	—
227	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
228	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
229	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
230	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
231	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
232	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
233	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
234	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
235	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
236	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
237	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
238	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
239	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
240	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
241	C₂₃×#121	C₂³	1	8	yes	—
242	C₂₃×#121	C₂³	1	4	yes	—
243	C₂₃×#121	C₂³	1	16	yes	—
244	C₂₃×#121	C₂³	1	16	yes	—
245	C₂₃×#121	C₂³	1	8	yes	—
246	C₂₃×#121	C₂³	1	8	yes	—
247	C₂₃×#121	C₂³	1	16	yes	—
248	C₂₃×#121	C₂³	1	16	yes	—
249	C₂₃×#121	C₂³	1	16	yes	—
250	C₂₃×#121	C₂³	1	2	yes	—
251	C₂₃×#121	C₂³	1	16	yes	—
252	C₂₃×#121	C₂³	1	4	yes	—
253	C₂₃×#121	C₂³	1	8	yes	—
254	C₂₃×#121	C₂³	1	8	yes	—
255	C₂₃×#121	C₂³	1	16	yes	—
256	C₂₃×#121	C₂³	1	16	yes	—
257	C₂₃×#121	C₂³	1	16	yes	—
258	C₂₃×#121	C₂³	1	8	yes	—
259	C₂₃×#121	C₂³	1	4	yes	—
260	C₂₃×#121	C₂³	1	8	yes	—
261	C₂₃×#121	C₂³	1	8	yes	—
262	C₂₃×#121	C₂³	1	8	yes	—
263	C₂₃×#121	C₂³	1	2	yes	—
264	C₂₃×#121	C₂³	1	4	yes	—
265	C₂₃×#121	C₂³	1	4	yes	—
266	C₂₃×#120	C₂³	1	8	yes	—
267	C₂₃×#120	C₂³	1	16	yes	—
268	C₂₃×#120	C₂³	1	16	yes	—
269	C₂₃×#120	C₂³	1	16	yes	—
270	C₂₃×#120	C₂³	1	2	yes	—
271	C₂₃×#120	C₂³	1	4	yes	—
272	C₂₃×#120	C₂³	1	2	yes	—
273	C₂₃×#120	C₂³	1	8	yes	—
274	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
275	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
276	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
277	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
278	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
279	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
280	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
281	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
282	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
283	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
284	C₄×D₄×C₂₃	C₂³	1	2	yes	—
285	C₄×D₄×C₂₃	C₂³	1	4	yes	—
286	C₄×D₄×C₂₃	C₂³	1	4	yes	—
287	C₄×D₄×C₂₃	C₂³	1	8	yes	—
288	C₄×D₄×C₂₃	C₂³	1	4	yes	—
289	C₄×D₄×C₂₃	C₂³	1	8	yes	—
290	C₄×D₄×C₂₃	C₂³	1	8	yes	—
291	C₄×D₄×C₂₃	C₂³	1	8	yes	—
292	C₄×D₄×C₂₃	C₂³	1	4	yes	—
293	C₄×D₄×C₂₃	C₂³	1	4	yes	—
294	C₄×D₄×C₂₃	C₂³	1	16	yes	—
295	C₄×D₄×C₂₃	C₂³	1	16	yes	—
296	C₄×D₄×C₂₃	C₂³	1	16	yes	—
297	C₄×D₄×C₂₃	C₂³	1	4	yes	—
298	C₄×D₄×C₂₃	C₂³	1	16	yes	—
299	C₄×D₄×C₂₃	C₂³	1	8	yes	—
300	C₄×D₄×C₂₃	C₂³	1	8	yes	—
301	C₄×D₄×C₂₃	C₂³	1	8	yes	—
302	C₄×D₄×C₂₃	C₂³	1	4	yes	—
303	C₄×D₄×C₂₃	C₂³	1	4	yes	—
304	C₄×D₄×C₂₃	C₂³	1	8	yes	—
305	C₄×D₄×C₂₃	C₂³	1	8	yes	—
306	C₄×D₄×C₂₃	C₂³	1	4	yes	—
307	C₄×D₄×C₂₃	C₂³	1	2	yes	—
308	C₄×D₄×C₂₃	C₂³	1	4	yes	—
309	C₄×D₄×C₂₃	C₂³	1	8	yes	—
310	C₄×D₄×C₂₃	C₂³	1	8	yes	—
311	C₄×D₄×C₂₃	C₂³	1	4	yes	—
312	C₄×D₄×C₂₃	C₂³	1	8	yes	—
313	C₂₃×#117	C₂³	1	8	yes	—
314	C₂₃×#117	C₂³	1	8	yes	—
315	C₂₃×#117	C₂³	1	16	yes	—
316	C₂₃×#117	C₂³	1	8	yes	—
317	C₂₃×#117	C₂³	1	4	yes	—
318	C₂₃×#117	C₂³	1	1	yes	characteristic
319	C₂₃×#117	C₂³	1	2	yes	—
320	C₂₃×#117	C₂³	1	1	yes	characteristic
321	C₂₃×#117	C₂³	1	4	yes	—
322	C₂₃×#117	C₂³	1	2	yes	—
323	C₂₃×#117	C₂³	1	4	yes	—
324	C₂₃×#117	C₂³	1	4	yes	—
325	C₂₃×#117	C₂³	1	4	yes	—
326	C₂₃×#117	C₂³	1	2	yes	—
327	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
328	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
329	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	—
330	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
331	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
332	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	—
333	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	—
334	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
335	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
336	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
337	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
338	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
339	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
340	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
341	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
342	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
343	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
344	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
345	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
346	C₂⁴×C₂₃	C₂⁴	1	8	yes	—
347	#41×C₂₃	—	2	4	no	—
348	#41×C₂₃	—	2	8	no	—
349	#41×C₂₃	—	2	4	no	—
350	#41×C₂₃	—	4	8	no	—
351	#41×C₂₃	—	4	16	no	—
352	#41×C₂₃	—	4	16	no	—
353	#41×C₂₃	—	4	16	no	—
354	#41×C₂₃	—	4	8	no	—
355	#41×C₂₃	—	4	16	no	—
356	#41×C₂₃	—	4	8	no	—
357	#41×C₂₃	—	4	8	no	—
358	#41×C₂₃	—	4	8	no	—
359	#41×C₂₃	—	4	8	no	—
360	C₂×Q₈×C₂₃	—	2	8	no	—
361	C₂×Q₈×C₂₃	—	4	8	no	—
362	C₂×Q₈×C₂₃	—	4	8	no	—
363	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
364	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
365	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
366	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
367	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
368	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
369	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
370	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
371	C₂×D₄×C₂₃	—	2	8	no	—
372	C₂×D₄×C₂₃	—	4	8	no	—
373	C₂×D₄×C₂₃	—	4	16	no	—
374	C₂×D₄×C₂₃	—	4	8	no	—
375	C₂×D₄×C₂₃	—	4	8	no	—
376	C₂×D₄×C₂₃	—	4	8	no	—
377	C₂×D₄×C₂₃	—	4	16	no	—
378	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
379	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
380	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
381	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
382	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
383	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
384	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
385	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
386	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
387	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
388	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
389	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
390	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
391	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
392	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
393	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
394	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
395	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
396	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
397	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
398	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
399	C₂²×C₄×C₂₃	—	2	4	no	—
400	C₂²×C₄×C₂₃	—	4	4	no	—
401	C₂²×C₄×C₂₃	—	4	8	no	—
402	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
403	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
404	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
405	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
407	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
409	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
410	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
411	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
412	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
413	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
414	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
415	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
416	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
417	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
418	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
419	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
420	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
421	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
422	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
423	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
425	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
426	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
427	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
428	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
429	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
430	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
431	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
432	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
433	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
434	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
435	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
436	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
437	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
438	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
439	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
440	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
441	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
442	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
443	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
444	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
445	C₂²⋊C₄×C₂₃	C₂⁴	1	2	yes	—
446	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
447	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
448	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
449	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
450	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
451	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
452	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
453	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
454	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
455	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
456	C₂²⋊C₄×C₂₃	C₂⁴	1	2	yes	—
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	16	yes	—
461	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
462	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
463	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
464	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
465	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
466	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
467	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
468	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
469	C₄²×C₂₃	C₂⁴	1	2	yes	—
470	C₄²×C₂₃	C₂⁴	1	2	yes	—
471	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
472	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
473	C₄²×C₂₃	C₂⁴	1	2	yes	—
474	C₄²×C₂₃	C₂⁴	1	2	yes	—
475	C₄²×C₂₃	C₂⁴	1	2	yes	—
476	C₄²×C₂₃	C₂⁴	1	2	yes	—
477	C₄²×C₂₃	C₂⁴	1	8	yes	—
478	C₄²×C₂₃	C₂⁴	1	2	yes	—
479	C₄²×C₂₃	C₂⁴	1	4	yes	—
480	C₄²×C₂₃	C₂⁴	1	4	yes	—
481	C₄²×C₂₃	C₂⁴	1	4	yes	—
482	C₄²×C₂₃	C₂⁴	1	2	yes	—
483	C₄²×C₂₃	C₂⁴	1	16	yes	—
484	#62836	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
485	C₂³×C₂₃	—	2	2	no	—
486	C₂³×C₂₃	—	2	8	no	—
487	C₂³×C₂₃	—	4	2	no	—
488	C₂³×C₂₃	—	4	8	no	—
489	C₂³×C₂₃	—	4	8	no	—
490	C₂³×C₂₃	—	4	16	no	—
491	C₂³×C₂₃	C₂⁵	1	2	yes	—
492	C₂³×C₂₃	C₂⁵	1	4	yes	—
493	C₂³×C₂₃	C₂⁵	1	8	yes	—
494	C₂³×C₂₃	C₂⁵	1	2	yes	—
495	C₂³×C₂₃	C₂⁵	1	2	yes	—
496	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
497	Q₈×C₂₃	—	2	8	no	—
498	Q₈×C₂₃	—	2	8	no	—
499	Q₈×C₂₃	—	2	2	no	—
500	Q₈×C₂₃	—	2	4	no	—
501	Q₈×C₂₃	—	2	2	no	—
502	Q₈×C₂₃	—	2	8	no	—
503	Q₈×C₂₃	—	4	8	no	—
504	Q₈×C₂₃	—	4	4	no	—
505	D₄×C₂₃	—	2	4	no	—
506	D₄×C₂₃	—	2	8	no	—
507	D₄×C₂₃	—	2	4	no	—
508	D₄×C₂₃	—	2	8	no	—
509	D₄×C₂₃	—	2	8	no	—
510	D₄×C₂₃	—	2	2	no	—
511	D₄×C₂₃	—	2	4	no	—
512	D₄×C₂₃	—	2	2	no	—
513	D₄×C₂₃	—	2	16	no	—
514	D₄×C₂₃	—	2	8	no	—
515	D₄×C₂₃	—	4	8	no	—
516	D₄×C₂₃	—	4	8	no	—
517	D₄×C₂₃	—	4	8	no	—
518	D₄×C₂₃	—	4	16	no	—
519	D₄×C₂₃	—	4	16	no	—
520	D₄×C₂₃	—	4	4	no	—
521	D₄×C₂₃	—	4	4	no	—
522	D₄×C₂₃	—	4	4	no	—
523	D₄×C₂₃	—	4	8	no	—
524	D₄×C₂₃	—	4	16	no	—
525	D₄×C₂₃	—	4	8	no	—
526	C₂×C₄×C₂₃	—	2	2	no	—
527	C₂×C₄×C₂₃	—	2	8	no	—
528	C₂×C₄×C₂₃	—	2	4	no	—
529	C₂×C₄×C₂₃	—	2	4	no	—
530	C₂×C₄×C₂₃	—	2	4	no	—
531	C₂×C₄×C₂₃	—	2	8	no	—
532	C₂×C₄×C₂₃	—	2	4	no	—
533	C₂×C₄×C₂₃	—	2	4	no	—
534	C₂×C₄×C₂₃	—	2	4	no	—
535	C₂×C₄×C₂₃	—	2	4	no	—
536	C₂×C₄×C₂₃	—	2	8	no	—
537	C₂×C₄×C₂₃	—	2	8	no	—
538	C₂×C₄×C₂₃	—	4	2	no	—
539	C₂×C₄×C₂₃	—	4	2	no	—
540	C₂×C₄×C₂₃	—	4	2	no	—
541	C₂×C₄×C₂₃	—	4	16	no	—
542	C₂×C₄×C₂₃	—	4	8	no	—
543	C₂×C₄×C₂₃	—	4	8	no	—
544	C₂×C₄×C₂₃	—	4	8	no	—
545	C₂×C₄×C₂₃	—	4	8	no	—
546	C₂×C₄×C₂₃	—	4	16	no	—
547	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
548	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
549	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
550	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
551	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
552	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
553	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
554	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
555	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
556	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
557	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
558	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
559	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
560	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
561	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
562	#3562	C₂×C₂₃	1	8	yes	complemented
563	#3554	C₂×C₂₃	1	4	yes	complemented
564	#3546	C₂×C₂₃	1	4	yes	complemented
565	#3542	C₂×C₂₃	1	8	yes	complemented
566	#3517	C₂×C₂₃	1	4	yes	complemented
567	#3514	C₂×C₂₃	1	4	yes	complemented
568	#3513	C₂×C₂₃	1	8	yes	complemented
569	#3511	C₂×C₂₃	1	4	yes	complemented
570	#3510	C₂×C₂₃	1	2	yes	complemented
571	#3509	C₂×C₂₃	1	1	yes	characteristic, complemented
572	#3508	C₂×C₂₃	1	1	yes	characteristic, complemented
573	#3508	C₂×C₂₃	1	4	yes	complemented
574	#3500	C₂×C₂₃	1	2	yes	complemented
575	#3499	C₂×C₂₃	1	1	yes	characteristic, complemented
576	#3498	C₂×C₂₃	1	1	yes	characteristic, complemented
577	#3487	C₂×C₂₃	1	2	yes	complemented
578	#3485	C₂×C₂₃	1	2	yes	complemented
579	#3444	C₂×C₂₃	1	1	yes	characteristic, complemented
580	#3444	C₂×C₂₃	1	1	yes	characteristic, complemented
581	C₂×#532	C₂×C₂₃	1	1	yes	characteristic, complemented
582	C₂²×C₂₃	—	2	2	no	—
583	C₂²×C₂₃	—	2	2	no	—
584	C₂²×C₂₃	—	2	2	no	—
585	C₂²×C₂₃	—	2	4	no	—
586	C₂²×C₂₃	—	2	2	no	—
587	C₂²×C₂₃	—	2	8	no	—
588	C₂²×C₂₃	—	2	2	no	—
589	C₂²×C₂₃	—	2	2	no	—
590	C₂²×C₂₃	—	2	4	no	—
591	C₂²×C₂₃	—	2	4	no	—
592	C₂²×C₂₃	—	2	16	no	—
593	C₂²×C₂₃	—	2	8	no	—
594	C₂²×C₂₃	—	4	4	no	—
595	C₂²×C₂₃	—	8	8	no	—
596	C₂²×C₂₃	—	16	8	no	—
597	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
598	C₂²×C₂₃	C₂⁶	1	1	yes	characteristic
599	C₄×C₂₃	—	2	2	no	—
600	C₄×C₂₃	—	2	2	no	—
601	C₄×C₂₃	—	2	4	no	—
602	C₄×C₂₃	—	2	2	no	—
603	C₄×C₂₃	—	2	8	no	—
604	C₄×C₂₃	—	2	2	no	—
605	C₄×C₂₃	—	2	4	no	—
606	C₄×C₂₃	—	2	2	no	—
607	C₄×C₂₃	—	2	2	no	—
608	C₄×C₂₃	—	2	4	no	—
609	C₄×C₂₃	—	2	8	no	—
610	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
611	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
612	C₄×C₂₃	#585	1	4	yes	—
613	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	2	yes	complemented
614	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	2	yes	—
615	C₂²×#41	C₂²×C₂₃	1	2	yes	complemented
616	#562	C₂²×C₂₃	1	16	yes	complemented
617	#560	C₂²×C₂₃	1	16	yes	complemented
618	#559	C₂²×C₂₃	1	8	yes	complemented
619	#559	C₂²×C₂₃	1	8	yes	complemented
620	#559	C₂²×C₂₃	1	4	yes	complemented
621	#557	C₂²×C₂₃	1	4	yes	complemented
622	#556	C₂²×C₂₃	1	4	yes	complemented
623	#556	C₂²×C₂₃	1	8	yes	complemented
624	#555	C₂²×C₂₃	1	8	yes	complemented
625	#554	C₂²×C₂₃	1	8	yes	complemented
626	#553	C₂²×C₂₃	1	8	yes	complemented
627	#553	C₂²×C₂₃	1	8	yes	complemented
628	#553	C₂²×C₂₃	1	16	yes	complemented
629	#552	C₂²×C₂₃	1	8	yes	complemented
630	#551	C₂²×C₂₃	1	16	yes	complemented
631	#551	C₂²×C₂₃	1	16	yes	complemented
632	#550	C₂²×C₂₃	1	8	yes	complemented
633	#550	C₂²×C₂₃	1	8	yes	complemented
634	#550	C₂²×C₂₃	1	4	yes	complemented
635	#550	C₂²×C₂₃	1	8	yes	complemented
636	#550	C₂²×C₂₃	1	4	yes	complemented
637	D₄×Q₈	C₂²×C₂₃	1	4	yes	complemented
638	#548	C₂²×C₂₃	1	8	yes	complemented
639	#548	C₂²×C₂₃	1	8	yes	complemented
640	#548	C₂²×C₂₃	1	8	yes	complemented
641	#547	C₂²×C₂₃	1	8	yes	complemented
642	#547	C₂²×C₂₃	1	8	yes	complemented
643	#547	C₂²×C₂₃	1	8	yes	complemented
644	#547	C₂²×C₂₃	1	4	yes	complemented
645	#546	C₂²×C₂₃	1	8	yes	complemented
646	#546	C₂²×C₂₃	1	8	yes	complemented
647	#546	C₂²×C₂₃	1	8	yes	complemented
648	#546	C₂²×C₂₃	1	16	yes	complemented
649	#546	C₂²×C₂₃	1	8	yes	complemented
650	#546	C₂²×C₂₃	1	8	yes	complemented
651	#546	C₂²×C₂₃	1	8	yes	complemented
652	D₄²	C₂²×C₂₃	1	8	yes	—
653	D₄²	C₂²×C₂₃	1	4	yes	complemented
654	#542	C₂²×C₂₃	1	8	yes	complemented
655	#542	C₂²×C₂₃	1	8	yes	complemented
656	#542	C₂²×C₂₃	1	8	yes	complemented
657	#541	C₂²×C₂₃	1	4	yes	complemented
658	#540	C₂²×C₂₃	1	8	yes	complemented
659	#540	C₂²×C₂₃	1	8	yes	complemented
660	#540	C₂²×C₂₃	1	4	yes	complemented
661	#540	C₂²×C₂₃	1	16	yes	complemented
662	#539	C₂²×C₂₃	1	16	yes	complemented
663	#538	C₂²×C₂₃	1	16	yes	complemented
664	#538	C₂²×C₂₃	1	16	yes	complemented
665	#537	C₂²×C₂₃	1	8	yes	complemented
666	#536	C₂²×C₂₃	1	2	yes	—
667	#536	C₂²×C₂₃	1	2	yes	complemented
668	#536	C₂²×C₂₃	1	4	yes	complemented
669	#536	C₂²×C₂₃	1	4	yes	complemented
670	#535	C₂²×C₂₃	1	2	yes	—
671	#535	C₂²×C₂₃	1	2	yes	complemented
672	#535	C₂²×C₂₃	1	8	yes	complemented
673	#535	C₂²×C₂₃	1	4	yes	complemented
674	#535	C₂²×C₂₃	1	4	yes	complemented
675	#535	C₂²×C₂₃	1	8	yes	complemented
676	#534	C₂²×C₂₃	1	8	yes	complemented
677	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
678	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
679	#533	C₂²×C₂₃	1	2	yes	complemented
680	#533	C₂²×C₂₃	1	2	yes	complemented
681	#533	C₂²×C₂₃	1	4	yes	complemented
682	#532	C₂²×C₂₃	1	1	yes	characteristic
683	#532	C₂²×C₂₃	1	1	yes	characteristic
684	#532	C₂²×C₂₃	1	4	yes	complemented
685	#532	C₂²×C₂₃	1	4	yes	complemented
686	#532	C₂²×C₂₃	1	4	yes	complemented
687	#532	C₂²×C₂₃	1	4	yes	complemented
688	#532	C₂²×C₂₃	1	2	yes	complemented
689	#532	C₂²×C₂₃	1	2	yes	complemented
690	#532	C₂²×C₂₃	1	2	yes	complemented
691	#532	C₂²×C₂₃	1	2	yes	complemented
692	#532	C₂²×C₂₃	1	4	yes	complemented
693	#532	C₂²×C₂₃	1	4	yes	complemented
694	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
695	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
696	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
697	C₂×#127	C₂²×C₂₃	1	2	yes	complemented
698	#529	C₂²×C₂₃	1	4	yes	complemented
699	#529	C₂²×C₂₃	1	4	yes	complemented
700	#529	C₂²×C₂₃	1	2	yes	complemented
701	#529	C₂²×C₂₃	1	2	yes	complemented
702	#529	C₂²×C₂₃	1	4	yes	complemented
703	#529	C₂²×C₂₃	1	4	yes	complemented
704	#529	C₂²×C₂₃	1	4	yes	complemented
705	#529	C₂²×C₂₃	1	8	yes	complemented
706	C₂×#124	C₂²×C₂₃	1	2	yes	complemented
707	C₂×#124	C₂²×C₂₃	1	4	yes	complemented
708	#525	C₂²×C₂₃	1	1	yes	characteristic
709	#525	C₂²×C₂₃	1	2	yes	complemented
710	#525	C₂²×C₂₃	1	1	yes	characteristic, complemented
711	#525	C₂²×C₂₃	1	4	yes	complemented
712	#525	C₂²×C₂₃	1	4	yes	complemented
713	#525	C₂²×C₂₃	1	8	yes	complemented
714	C₂×#123	C₂²×C₂₃	1	8	yes	complemented
715	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
716	#520	C₂²×C₂₃	1	8	yes	complemented
717	#519	C₂²×C₂₃	1	2	yes	complemented
718	#518	C₂²×C₂₃	1	2	yes	complemented
719	#518	C₂²×C₂₃	1	8	yes	complemented
720	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
721	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
722	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
723	C₄×#41	C₂²×C₂₃	1	4	yes	complemented
724	C₄×#41	C₂²×C₂₃	1	4	yes	complemented
725	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	complemented
726	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
727	C₂×C₂₃	—	2	2	no	—
728	C₂×C₂₃	—	4	2	no	—
729	C₂×C₂₃	—	4	2	no	—
730	C₂×C₂₃	—	4	8	no	—
731	C₂×C₂₃	—	4	4	no	—
732	C₂×C₂₃	—	4	2	no	—
733	C₂×C₂₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
734	C₂×C₂₃	C₂×#585	1	2	yes	—
735	2₋¹⁺⁴	—	4	8	no	—
736	H(5,𝔽₂)	—	4	8	no	—
737	C₂×#41	—	4	8	no	—
738	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
739	C₂×#41	C₂³×C₂₃	1	2	yes	—
740	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
741	C₂×#41	C₂³×C₂₃	1	4	yes	—
742	C₂×#41	C₂³×C₂₃	1	4	yes	—
743	C₂×#41	C₂³×C₂₃	1	8	yes	—
744	C₂×#41	C₂³×C₂₃	1	8	yes	—
745	C₂×#41	C₂³×C₂₃	1	8	yes	—
746	C₂×#41	C₂³×C₂₃	1	8	yes	—
747	C₂×#41	C₂³×C₂₃	1	4	yes	—
748	C₂×#41	C₂³×C₂₃	1	4	yes	—
749	C₂×#41	C₂³×C₂₃	1	4	yes	—
750	C₂×#41	C₂³×C₂₃	1	4	yes	—
751	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
752	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
753	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
754	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
755	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
756	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
757	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
758	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
759	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
760	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
761	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
762	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
763	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
764	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
765	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
766	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
767	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
768	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
769	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
770	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
771	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
772	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
773	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
774	#127	C₂³×C₂₃	1	2	yes	—
775	#127	C₂³×C₂₃	1	2	yes	—
776	#127	C₂³×C₂₃	1	4	yes	—
777	#127	C₂³×C₂₃	1	1	yes	characteristic
778	#127	C₂³×C₂₃	1	4	yes	—
779	#127	C₂³×C₂₃	1	8	yes	—
780	#127	C₂³×C₂₃	1	1	yes	characteristic
781	#127	C₂³×C₂₃	1	4	yes	—
782	#127	C₂³×C₂₃	1	16	yes	—
783	#126	C₂³×C₂₃	1	8	yes	—
784	#126	C₂³×C₂₃	1	4	yes	—
785	#126	C₂³×C₂₃	1	4	yes	—
786	#126	C₂³×C₂₃	1	16	yes	—
787	#126	C₂³×C₂₃	1	16	yes	—
788	#126	C₂³×C₂₃	1	16	yes	—
789	#125	C₂³×C₂₃	1	2	yes	—
790	#125	C₂³×C₂₃	1	4	yes	—
791	#125	C₂³×C₂₃	1	2	yes	—
792	#125	C₂³×C₂₃	1	4	yes	—
793	#125	C₂³×C₂₃	1	8	yes	—
794	#125	C₂³×C₂₃	1	16	yes	—
795	#124	C₂³×C₂₃	1	1	yes	characteristic
796	#124	C₂³×C₂₃	1	4	yes	—
797	#124	C₂³×C₂₃	1	4	yes	—
798	#124	C₂³×C₂₃	1	8	yes	—
799	#124	C₂³×C₂₃	1	4	yes	—
800	#124	C₂³×C₂₃	1	4	yes	—
801	#124	C₂³×C₂₃	1	16	yes	—
802	#124	C₂³×C₂₃	1	1	yes	characteristic
803	#124	C₂³×C₂₃	1	2	yes	—
804	#124	C₂³×C₂₃	1	4	yes	—
805	#124	C₂³×C₂₃	1	4	yes	—
806	#124	C₂³×C₂₃	1	4	yes	—
807	#124	C₂³×C₂₃	1	4	yes	—
808	#124	C₂³×C₂₃	1	8	yes	—
809	#124	C₂³×C₂₃	1	16	yes	—
810	#124	C₂³×C₂₃	1	16	yes	—
811	#123	C₂³×C₂₃	1	2	yes	—
812	#123	C₂³×C₂₃	1	4	yes	—
813	#123	C₂³×C₂₃	1	8	yes	—
814	#123	C₂³×C₂₃	1	8	yes	—
815	#123	C₂³×C₂₃	1	16	yes	—
816	#123	C₂³×C₂₃	1	16	yes	—
817	#123	C₂³×C₂₃	1	2	yes	—
818	#123	C₂³×C₂₃	1	4	yes	—
819	#123	C₂³×C₂₃	1	4	yes	—
820	#123	C₂³×C₂₃	1	8	yes	—
821	#123	C₂³×C₂₃	1	16	yes	—
822	#123	C₂³×C₂₃	1	16	yes	—
823	#123	C₂³×C₂₃	1	16	yes	—
824	#123	C₂³×C₂₃	1	16	yes	—
825	#123	C₂³×C₂₃	1	16	yes	—
826	#123	C₂³×C₂₃	1	16	yes	—
827	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
828	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
829	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
830	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
831	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
832	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
833	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
834	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
835	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
836	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
837	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
838	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
839	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
840	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
841	#121	C₂³×C₂₃	1	8	yes	—
842	#121	C₂³×C₂₃	1	8	yes	—
843	#121	C₂³×C₂₃	1	8	yes	—
844	#121	C₂³×C₂₃	1	8	yes	—
845	#121	C₂³×C₂₃	1	2	yes	—
846	#121	C₂³×C₂₃	1	4	yes	—
847	#121	C₂³×C₂₃	1	4	yes	—
848	#121	C₂³×C₂₃	1	4	yes	—
849	#121	C₂³×C₂₃	1	4	yes	—
850	#121	C₂³×C₂₃	1	2	yes	—
851	#121	C₂³×C₂₃	1	4	yes	—
852	#121	C₂³×C₂₃	1	16	yes	—
853	#121	C₂³×C₂₃	1	8	yes	—
854	#121	C₂³×C₂₃	1	8	yes	—
855	#121	C₂³×C₂₃	1	8	yes	—
856	#121	C₂³×C₂₃	1	8	yes	—
857	#121	C₂³×C₂₃	1	8	yes	—
858	#121	C₂³×C₂₃	1	16	yes	—
859	#121	C₂³×C₂₃	1	16	yes	—
860	#121	C₂³×C₂₃	1	16	yes	—
861	#121	C₂³×C₂₃	1	16	yes	—
862	#121	C₂³×C₂₃	1	16	yes	—
863	#121	C₂³×C₂₃	1	16	yes	—
864	#121	C₂³×C₂₃	1	16	yes	—
865	#121	C₂³×C₂₃	1	16	yes	—
866	#120	C₂³×C₂₃	1	2	yes	—
867	#120	C₂³×C₂₃	1	4	yes	—
868	#120	C₂³×C₂₃	1	2	yes	—
869	#120	C₂³×C₂₃	1	8	yes	—
870	#120	C₂³×C₂₃	1	8	yes	—
871	#120	C₂³×C₂₃	1	16	yes	—
872	#120	C₂³×C₂₃	1	16	yes	—
873	#120	C₂³×C₂₃	1	16	yes	—
874	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
875	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
876	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
877	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
878	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
879	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
880	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
881	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
882	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
883	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
884	C₄×D₄	C₂³×C₂₃	1	8	yes	—
885	C₄×D₄	C₂³×C₂₃	1	8	yes	—
886	C₄×D₄	C₂³×C₂₃	1	8	yes	—
887	C₄×D₄	C₂³×C₂₃	1	8	yes	—
888	C₄×D₄	C₂³×C₂₃	1	4	yes	—
889	C₄×D₄	C₂³×C₂₃	1	2	yes	—
890	C₄×D₄	C₂³×C₂₃	1	4	yes	—
891	C₄×D₄	C₂³×C₂₃	1	4	yes	—
892	C₄×D₄	C₂³×C₂₃	1	8	yes	—
893	C₄×D₄	C₂³×C₂₃	1	4	yes	—
894	C₄×D₄	C₂³×C₂₃	1	8	yes	—
895	C₄×D₄	C₂³×C₂₃	1	4	yes	—
896	C₄×D₄	C₂³×C₂₃	1	8	yes	—
897	C₄×D₄	C₂³×C₂₃	1	4	yes	—
898	C₄×D₄	C₂³×C₂₃	1	4	yes	—
899	C₄×D₄	C₂³×C₂₃	1	4	yes	—
900	C₄×D₄	C₂³×C₂₃	1	4	yes	—
901	C₄×D₄	C₂³×C₂₃	1	4	yes	—
902	C₄×D₄	C₂³×C₂₃	1	4	yes	—
903	C₄×D₄	C₂³×C₂₃	1	2	yes	—
904	C₄×D₄	C₂³×C₂₃	1	16	yes	—
905	C₄×D₄	C₂³×C₂₃	1	16	yes	—
906	C₄×D₄	C₂³×C₂₃	1	8	yes	—
907	C₄×D₄	C₂³×C₂₃	1	8	yes	—
908	C₄×D₄	C₂³×C₂₃	1	8	yes	—
909	C₄×D₄	C₂³×C₂₃	1	8	yes	—
910	C₄×D₄	C₂³×C₂₃	1	16	yes	—
911	C₄×D₄	C₂³×C₂₃	1	16	yes	—
912	C₄×D₄	C₂³×C₂₃	1	8	yes	—
913	#117	C₂³×C₂₃	1	1	yes	characteristic
914	#117	C₂³×C₂₃	1	2	yes	—
915	#117	C₂³×C₂₃	1	1	yes	characteristic
916	#117	C₂³×C₂₃	1	4	yes	—
917	#117	C₂³×C₂₃	1	2	yes	—
918	#117	C₂³×C₂₃	1	4	yes	—
919	#117	C₂³×C₂₃	1	4	yes	—
920	#117	C₂³×C₂₃	1	4	yes	—
921	#117	C₂³×C₂₃	1	4	yes	—
922	#117	C₂³×C₂₃	1	2	yes	—
923	#117	C₂³×C₂₃	1	8	yes	—
924	#117	C₂³×C₂₃	1	8	yes	—
925	#117	C₂³×C₂₃	1	8	yes	—
926	#117	C₂³×C₂₃	1	16	yes	—
927	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
928	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	—
929	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
930	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
931	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
932	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	—
933	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	—
934	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
935	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
936	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
937	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
938	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
939	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
940	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
941	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
942	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
943	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
944	C₂₃	#62836	1	1	yes	characteristic, direct product factor, Sylow
945	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
946	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
947	C₂⁴	C₂⁴×C₂₃	1	8	yes	—
948	#41	—	2	4	no	—
949	#41	—	2	8	no	—
950	#41	—	2	4	no	—
951	#41	—	4	8	no	—
952	#41	—	4	16	no	—
953	#41	—	4	16	no	—
954	#41	—	4	16	no	—
955	#41	—	4	8	no	—
956	#41	—	4	8	no	—
957	#41	—	4	8	no	—
958	#41	—	4	8	no	—
959	#41	—	4	8	no	—
960	#41	—	4	16	no	—
961	C₂×Q₈	—	2	8	no	—
962	C₂×Q₈	—	4	8	no	—
963	C₂×Q₈	—	4	8	no	—
964	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
965	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
966	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
967	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
968	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
969	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
970	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
971	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
972	C₂×D₄	—	2	8	no	—
973	C₂×D₄	—	4	8	no	—
974	C₂×D₄	—	4	8	no	—
975	C₂×D₄	—	4	8	no	—
976	C₂×D₄	—	4	16	no	—
977	C₂×D₄	—	4	8	no	—
978	C₂×D₄	—	4	16	no	—
979	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
980	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
981	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
982	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
983	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
984	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
985	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
986	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
987	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
988	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
989	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
990	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
991	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
992	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
993	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
994	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
995	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
996	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
997	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
998	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
999	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
1000	C₂²×C₄	—	2	4	no	—
1001	C₂²×C₄	—	4	4	no	—
1002	C₂²×C₄	—	4	8	no	—
1003	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1004	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1005	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1006	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1007	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1008	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1009	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
1010	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
1011	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1012	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
1013	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1014	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
1015	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1016	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1017	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1018	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
1019	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
1020	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
1021	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
1022	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
1023	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
1024	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1025	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1026	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1027	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1028	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1029	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
1030	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1031	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
1032	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1033	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1034	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1035	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1036	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1037	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1038	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1039	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1040	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1041	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1042	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1043	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1044	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1045	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
1046	C₂²⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1047	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1048	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1049	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1050	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1051	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
1052	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
1053	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
1054	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
1055	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
1056	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
1057	C₂²⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1058	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1059	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1060	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1061	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
1062	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1063	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1064	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1065	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
1066	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1067	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
1068	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1069	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1070	C₄²	C₂⁴×C₂₃	1	2	yes	—
1071	C₄²	C₂⁴×C₂₃	1	2	yes	—
1072	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1073	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1074	C₄²	C₂⁴×C₂₃	1	2	yes	—
1075	C₄²	C₂⁴×C₂₃	1	2	yes	—
1076	C₄²	C₂⁴×C₂₃	1	2	yes	—
1077	C₄²	C₂⁴×C₂₃	1	2	yes	—
1078	C₄²	C₂⁴×C₂₃	1	8	yes	—
1079	C₄²	C₂⁴×C₂₃	1	2	yes	—
1080	C₄²	C₂⁴×C₂₃	1	4	yes	—
1081	C₄²	C₂⁴×C₂₃	1	4	yes	—
1082	C₄²	C₂⁴×C₂₃	1	4	yes	—
1083	C₄²	C₂⁴×C₂₃	1	2	yes	—
1084	C₄²	C₂⁴×C₂₃	1	16	yes	—
1085	C₂³	—	2	2	no	—
1086	C₂³	—	2	8	no	—
1087	C₂³	—	4	2	no	—
1088	C₂³	—	4	8	no	—
1089	C₂³	—	4	8	no	—
1090	C₂³	—	4	16	no	—
1091	C₂³	C₂⁵×C₂₃	1	2	yes	—
1092	C₂³	C₂⁵×C₂₃	1	4	yes	—
1093	C₂³	C₂⁵×C₂₃	1	8	yes	—
1094	C₂³	C₂⁵×C₂₃	1	2	yes	—
1095	C₂³	C₂⁵×C₂₃	1	2	yes	—
1096	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1097	Q₈	—	2	8	no	—
1098	Q₈	—	2	8	no	—
1099	Q₈	—	2	2	no	—
1100	Q₈	—	2	4	no	—
1101	Q₈	—	2	2	no	—
1102	Q₈	—	2	8	no	—
1103	Q₈	—	4	8	no	—
1104	Q₈	—	4	4	no	—
1105	D₄	—	2	4	no	—
1106	D₄	—	2	8	no	—
1107	D₄	—	2	4	no	—
1108	D₄	—	2	8	no	—
1109	D₄	—	2	8	no	—
1110	D₄	—	2	2	no	—
1111	D₄	—	2	4	no	—
1112	D₄	—	2	2	no	—
1113	D₄	—	2	16	no	—
1114	D₄	—	2	8	no	—
1115	D₄	—	4	8	no	—
1116	D₄	—	4	8	no	—
1117	D₄	—	4	16	no	—
1118	D₄	—	4	8	no	—
1119	D₄	—	4	16	no	—
1120	D₄	—	4	8	no	—
1121	D₄	—	4	4	no	—
1122	D₄	—	4	4	no	—
1123	D₄	—	4	4	no	—
1124	D₄	—	4	8	no	—
1125	D₄	—	4	16	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	8	no	—
1128	C₂×C₄	—	2	4	no	—
1129	C₂×C₄	—	2	4	no	—
1130	C₂×C₄	—	2	4	no	—
1131	C₂×C₄	—	2	8	no	—
1132	C₂×C₄	—	2	4	no	—
1133	C₂×C₄	—	2	4	no	—
1134	C₂×C₄	—	2	4	no	—
1135	C₂×C₄	—	2	4	no	—
1136	C₂×C₄	—	2	8	no	—
1137	C₂×C₄	—	2	8	no	—
1138	C₂×C₄	—	4	16	no	—
1139	C₂×C₄	—	4	2	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	4	8	no	—
1143	C₂×C₄	—	4	8	no	—
1144	C₂×C₄	—	4	8	no	—
1145	C₂×C₄	—	4	8	no	—
1146	C₂×C₄	—	4	16	no	—
1147	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
1148	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
1149	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
1150	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
1151	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
1152	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
1153	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
1154	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
1155	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
1156	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
1157	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
1158	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
1159	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1160	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1161	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
1162	C₂²	—	2	2	no	—
1163	C₂²	—	2	2	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	4	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	8	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	2	2	no	—
1170	C₂²	—	2	4	no	—
1171	C₂²	—	2	4	no	—
1172	C₂²	—	2	16	no	—
1173	C₂²	—	2	8	no	—
1174	C₂²	—	4	4	no	—
1175	C₂²	—	8	8	no	—
1176	C₂²	—	16	8	no	—
1177	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
1178	C₂²	C₂⁶×C₂₃	1	1	yes	characteristic
1179	C₄	—	2	2	no	—
1180	C₄	—	2	2	no	—
1181	C₄	—	2	4	no	—
1182	C₄	—	2	2	no	—
1183	C₄	—	2	8	no	—
1184	C₄	—	2	2	no	—
1185	C₄	—	2	4	no	—
1186	C₄	—	2	2	no	—
1187	C₄	—	2	2	no	—
1188	C₄	—	2	4	no	—
1189	C₄	—	2	8	no	—
1190	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
1191	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
1192	C₄	C₂₃×#585	1	4	yes	—
1193	C₂	—	2	2	no	—
1194	C₂	—	4	2	no	—
1195	C₂	—	4	8	no	—
1196	C₂	—	4	2	no	—
1197	C₂	—	4	4	no	—
1198	C₂	—	4	2	no	—
1199	C₂	C₂²×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1200	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×#3562	C₂	semidirect
2. C₂₃×#3554	C₂	semidirect
3. C₂₃×#3546	C₂	semidirect
4. C₂₃×#3542	C₂	semidirect
5. C₂₃×#3517	C₂	semidirect
6. C₂₃×#3514	C₂	semidirect
7. C₂₃×#3513	C₂	semidirect
8. C₂₃×#3511	C₂	semidirect
9. C₂₃×#3510	C₂	semidirect
10. C₂₃×#3509	C₂	semidirect
11. C₂₃×#3508	C₂	semidirect
12. C₂₃×#3508	C₂	semidirect
13. C₂₃×#3500	C₂	semidirect
14. C₂₃×#3499	C₂	semidirect
15. C₂₃×#3498	C₂	semidirect
16. C₂₃×#3487	C₂	semidirect
17. C₂₃×#3485	C₂	semidirect
18. C₂₃×#3444	C₂	semidirect
19. C₂₃×#3444	C₂	semidirect
20. C₂×C₂₃×#532	C₂	semidirect
21. C₂×C₂₃×2₋¹⁺⁴	C₂²	semidirect
23. C₂²×#41×C₂₃	C₂²	semidirect
24. C₂₃×#562	C₂²	semidirect
25. C₂₃×#560	C₂²	semidirect
26. C₂₃×#559	C₂²	semidirect
27. C₂₃×#559	C₂²	semidirect
28. C₂₃×#559	C₂²	semidirect
29. C₂₃×#557	C₂²	semidirect
30. C₂₃×#556	C₂²	semidirect
31. C₂₃×#556	C₂²	semidirect
32. C₂₃×#555	C₂²	semidirect
33. C₂₃×#554	C₂²	semidirect
34. C₂₃×#553	C₂²	semidirect
35. C₂₃×#553	C₂²	semidirect
36. C₂₃×#553	C₂²	semidirect
37. C₂₃×#552	C₂²	semidirect
38. C₂₃×#551	C₂²	semidirect
39. C₂₃×#551	C₂²	semidirect
40. C₂₃×#550	C₂²	semidirect
41. C₂₃×#550	C₂²	semidirect
42. C₂₃×#550	C₂²	semidirect
43. C₂₃×#550	C₂²	semidirect
44. C₂₃×#550	C₂²	semidirect
45. D₄×Q₈×C₂₃	C₂²	semidirect
46. C₂₃×#548	C₂²	semidirect
47. C₂₃×#548	C₂²	semidirect
48. C₂₃×#548	C₂²	semidirect
49. C₂₃×#547	C₂²	semidirect
50. C₂₃×#547	C₂²	semidirect
51. C₂₃×#547	C₂²	semidirect
52. C₂₃×#547	C₂²	semidirect
53. C₂₃×#546	C₂²	semidirect
54. C₂₃×#546	C₂²	semidirect
55. C₂₃×#546	C₂²	semidirect
56. C₂₃×#546	C₂²	semidirect
57. C₂₃×#546	C₂²	semidirect
58. C₂₃×#546	C₂²	semidirect
59. C₂₃×#546	C₂²	semidirect
61. D₄²×C₂₃	C₂²	semidirect
62. C₂₃×#542	C₂²	semidirect
63. C₂₃×#542	C₂²	semidirect
64. C₂₃×#542	C₂²	semidirect
65. C₂₃×#541	C₂²	semidirect
66. C₂₃×#540	C₂²	semidirect
67. C₂₃×#540	C₂²	semidirect
68. C₂₃×#540	C₂²	semidirect
69. C₂₃×#540	C₂²	semidirect
70. C₂₃×#539	C₂²	semidirect
71. C₂₃×#538	C₂²	semidirect
72. C₂₃×#538	C₂²	semidirect
73. C₂₃×#537	C₂²	semidirect
75. C₂₃×#536	C₂²	semidirect
76. C₂₃×#536	C₂²	semidirect
77. C₂₃×#536	C₂²	semidirect
79. C₂₃×#535	C₂²	semidirect
80. C₂₃×#535	C₂²	semidirect
81. C₂₃×#535	C₂²	semidirect
82. C₂₃×#535	C₂²	semidirect
83. C₂₃×#535	C₂²	semidirect
84. C₂₃×#534	C₂²	semidirect
85. C₂₃×#533	C₂²	semidirect
86. C₂₃×#533	C₂²	semidirect
87. C₂₃×#533	C₂²	semidirect
88. C₂₃×#533	C₂²	semidirect
89. C₂₃×#533	C₂²	semidirect
92. C₂₃×#532	C₂²	semidirect
93. C₂₃×#532	C₂²	semidirect
94. C₂₃×#532	C₂²	semidirect
95. C₂₃×#532	C₂²	semidirect
96. C₂₃×#532	C₂²	semidirect
97. C₂₃×#532	C₂²	semidirect
98. C₂₃×#532	C₂²	semidirect
99. C₂₃×#532	C₂²	semidirect
100. C₂₃×#532	C₂²	semidirect
101. C₂₃×#532	C₂²	semidirect
102. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
103. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
105. C₂×C₂₃×#127	C₂²	semidirect
106. C₂₃×#529	C₂²	semidirect
107. C₂₃×#529	C₂²	semidirect
108. C₂₃×#529	C₂²	semidirect
109. C₂₃×#529	C₂²	semidirect
110. C₂₃×#529	C₂²	semidirect
111. C₂₃×#529	C₂²	semidirect
112. C₂₃×#529	C₂²	semidirect
113. C₂₃×#529	C₂²	semidirect
114. C₂×C₂₃×#124	C₂²	semidirect
115. C₂×C₂₃×#124	C₂²	semidirect
117. C₂₃×#525	C₂²	semidirect
118. C₂₃×#525	C₂²	semidirect
119. C₂₃×#525	C₂²	semidirect
120. C₂₃×#525	C₂²	semidirect
121. C₂₃×#525	C₂²	semidirect
122. C₂×C₂₃×#123	C₂²	semidirect
123. C₂×C₂₃×#121	C₂²	semidirect
124. C₂₃×#520	C₂²	semidirect
125. C₂₃×#519	C₂²	semidirect
126. C₂₃×#518	C₂²	semidirect
127. C₂₃×#518	C₂²	semidirect
129. C₄×#41×C₂₃	C₂²	semidirect
130. C₄×#41×C₂₃	C₂²	semidirect
131. C₄×#41×C₂₃	C₂²	semidirect
132. C₄×#41×C₂₃	C₂²	semidirect
133. C₂×C₄×D₄×C₂₃	C₂²	semidirect
134. C₂²×C₄²×C₂₃	C₂²	semidirect
484. #62836	C₂₃	direct (N × H)
562. #3562	C₂×C₂₃	semidirect
563. #3554	C₂×C₂₃	semidirect
564. #3546	C₂×C₂₃	semidirect
565. #3542	C₂×C₂₃	semidirect
566. #3517	C₂×C₂₃	semidirect
567. #3514	C₂×C₂₃	semidirect
568. #3513	C₂×C₂₃	semidirect
569. #3511	C₂×C₂₃	semidirect
570. #3510	C₂×C₂₃	semidirect
571. #3509	C₂×C₂₃	semidirect
572. #3508	C₂×C₂₃	semidirect
573. #3508	C₂×C₂₃	semidirect
574. #3500	C₂×C₂₃	semidirect
575. #3499	C₂×C₂₃	semidirect
576. #3498	C₂×C₂₃	semidirect
577. #3487	C₂×C₂₃	semidirect
578. #3485	C₂×C₂₃	semidirect
579. #3444	C₂×C₂₃	semidirect
580. #3444	C₂×C₂₃	semidirect
581. C₂×#532	C₂×C₂₃	semidirect
613. C₂×2₋¹⁺⁴	C₂²×C₂₃	semidirect
615. C₂²×#41	C₂²×C₂₃	semidirect
616. #562	C₂²×C₂₃	semidirect
617. #560	C₂²×C₂₃	semidirect
618. #559	C₂²×C₂₃	semidirect
619. #559	C₂²×C₂₃	semidirect
620. #559	C₂²×C₂₃	semidirect
621. #557	C₂²×C₂₃	semidirect
622. #556	C₂²×C₂₃	semidirect
623. #556	C₂²×C₂₃	semidirect
624. #555	C₂²×C₂₃	semidirect
625. #554	C₂²×C₂₃	semidirect
626. #553	C₂²×C₂₃	semidirect
627. #553	C₂²×C₂₃	semidirect
628. #553	C₂²×C₂₃	semidirect
629. #552	C₂²×C₂₃	semidirect
630. #551	C₂²×C₂₃	semidirect
631. #551	C₂²×C₂₃	semidirect
632. #550	C₂²×C₂₃	semidirect
633. #550	C₂²×C₂₃	semidirect
634. #550	C₂²×C₂₃	semidirect
635. #550	C₂²×C₂₃	semidirect
636. #550	C₂²×C₂₃	semidirect
637. D₄×Q₈	C₂²×C₂₃	semidirect
638. #548	C₂²×C₂₃	semidirect
639. #548	C₂²×C₂₃	semidirect
640. #548	C₂²×C₂₃	semidirect
641. #547	C₂²×C₂₃	semidirect
642. #547	C₂²×C₂₃	semidirect
643. #547	C₂²×C₂₃	semidirect
644. #547	C₂²×C₂₃	semidirect
645. #546	C₂²×C₂₃	semidirect
646. #546	C₂²×C₂₃	semidirect
647. #546	C₂²×C₂₃	semidirect
648. #546	C₂²×C₂₃	semidirect
649. #546	C₂²×C₂₃	semidirect
650. #546	C₂²×C₂₃	semidirect
651. #546	C₂²×C₂₃	semidirect
653. D₄²	C₂²×C₂₃	semidirect
654. #542	C₂²×C₂₃	semidirect
655. #542	C₂²×C₂₃	semidirect
656. #542	C₂²×C₂₃	semidirect
657. #541	C₂²×C₂₃	semidirect
658. #540	C₂²×C₂₃	semidirect
659. #540	C₂²×C₂₃	semidirect
660. #540	C₂²×C₂₃	semidirect
661. #540	C₂²×C₂₃	semidirect
662. #539	C₂²×C₂₃	semidirect
663. #538	C₂²×C₂₃	semidirect
664. #538	C₂²×C₂₃	semidirect
665. #537	C₂²×C₂₃	semidirect
667. #536	C₂²×C₂₃	semidirect
668. #536	C₂²×C₂₃	semidirect
669. #536	C₂²×C₂₃	semidirect
671. #535	C₂²×C₂₃	semidirect
672. #535	C₂²×C₂₃	semidirect
673. #535	C₂²×C₂₃	semidirect
674. #535	C₂²×C₂₃	semidirect
675. #535	C₂²×C₂₃	semidirect
676. #534	C₂²×C₂₃	semidirect
677. #533	C₂²×C₂₃	semidirect
678. #533	C₂²×C₂₃	semidirect
679. #533	C₂²×C₂₃	semidirect
680. #533	C₂²×C₂₃	semidirect
681. #533	C₂²×C₂₃	semidirect
684. #532	C₂²×C₂₃	semidirect
685. #532	C₂²×C₂₃	semidirect
686. #532	C₂²×C₂₃	semidirect
687. #532	C₂²×C₂₃	semidirect
688. #532	C₂²×C₂₃	semidirect
689. #532	C₂²×C₂₃	semidirect
690. #532	C₂²×C₂₃	semidirect
691. #532	C₂²×C₂₃	semidirect
692. #532	C₂²×C₂₃	semidirect
693. #532	C₂²×C₂₃	semidirect
694. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
695. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
697. C₂×#127	C₂²×C₂₃	semidirect
698. #529	C₂²×C₂₃	semidirect
699. #529	C₂²×C₂₃	semidirect
700. #529	C₂²×C₂₃	semidirect
701. #529	C₂²×C₂₃	semidirect
702. #529	C₂²×C₂₃	semidirect
703. #529	C₂²×C₂₃	semidirect
704. #529	C₂²×C₂₃	semidirect
705. #529	C₂²×C₂₃	semidirect
706. C₂×#124	C₂²×C₂₃	semidirect
707. C₂×#124	C₂²×C₂₃	semidirect
709. #525	C₂²×C₂₃	semidirect
710. #525	C₂²×C₂₃	semidirect
711. #525	C₂²×C₂₃	semidirect
712. #525	C₂²×C₂₃	semidirect
713. #525	C₂²×C₂₃	semidirect
714. C₂×#123	C₂²×C₂₃	semidirect
715. C₂×#121	C₂²×C₂₃	semidirect
716. #520	C₂²×C₂₃	semidirect
717. #519	C₂²×C₂₃	semidirect
718. #518	C₂²×C₂₃	semidirect
719. #518	C₂²×C₂₃	semidirect
721. C₄×#41	C₂²×C₂₃	semidirect
722. C₄×#41	C₂²×C₂₃	semidirect
723. C₄×#41	C₂²×C₂₃	semidirect
724. C₄×#41	C₂²×C₂₃	semidirect
725. C₂×C₄×D₄	C₂²×C₂₃	semidirect
726. C₂²×C₄²	C₂²×C₂₃	semidirect
944. C₂₃	#62836	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×#3562	2
C₂₃×#3554	2
C₂₃×#3546	2
C₂₃×#3542	2
C₂₃×#3517	2
C₂₃×#3514	2
C₂₃×#3513	2
C₂₃×#3511	2
C₂₃×#3510	2
C₂₃×#3509	2
C₂₃×#3508	2
C₂₃×#3500	2
C₂₃×#3499	2
C₂₃×#3498	2
C₂₃×#3487	2
C₂₃×#3485	2
C₂₃×#3444	2
C₂×C₂₃×#532	2
#62836	23

Subgroups — C23×#62836 #19210462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62836 #19210462