Subgroups — C₂₃×#62572 #19210198

Order 5888.

1652 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3554	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3374	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3371	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3331	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3327	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3317	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3316	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3315	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3312	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3244	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3223	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3185	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3178	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3142	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3137	C₂	1	2	yes	maximal, complemented
19	C₂₃×#2967	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#564	—	2	1	no	—
21	C₂₃×#563	—	2	1	no	—
22	C₂₃×#562	—	2	2	no	—
23	C₂₃×#559	—	2	1	no	—
24	C₂₃×#559	C₂²	1	1	yes	characteristic
25	C₂₃×#557	C₂²	1	1	yes	characteristic
26	C₂₃×#557	C₂²	1	2	yes	—
27	C₂₃×#554	—	2	1	no	—
28	C₂₃×#554	C₂²	1	2	yes	—
29	C₂₃×#552	—	2	2	no	—
30	C₂₃×#552	C₂²	1	2	yes	—
31	C₂₃×#552	C₂²	1	2	yes	—
32	C₂₃×#550	C₂²	1	1	yes	characteristic
33	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
34	C₂₃×#548	C₂²	1	2	yes	—
35	C₂₃×#547	C₂²	1	2	yes	—
36	C₂₃×#544	—	2	1	no	—
37	C₂₃×#544	C₂²	1	2	yes	—
38	C₂₃×#542	—	2	1	no	—
39	C₂₃×#542	C₂²	1	2	yes	—
40	C₂₃×#541	—	2	2	no	—
41	C₂₃×#541	C₂²	1	2	yes	—
42	C₂₃×#540	—	2	1	no	—
43	C₂₃×#539	—	2	2	no	—
44	C₂₃×#539	—	2	1	no	—
45	C₂₃×#536	C₂²	1	2	yes	—
46	C₂₃×#533	C₂²	1	1	yes	characteristic
47	C₂₃×#533	C₂²	1	1	yes	characteristic
48	C₂₃×#532	C₂²	1	1	yes	characteristic
49	C₂₃×#529	C₂²	1	1	yes	characteristic
50	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
51	C₂₃×#501	C₂²	1	2	yes	—
52	C₂₃×#498	C₂²	1	1	yes	characteristic
53	C₂₃×#497	C₂²	1	2	yes	—
54	C₂₃×#494	C₂²	1	1	yes	characteristic
55	C₂₃×#491	C₂²	1	2	yes	—
56	C₂₃×#491	C₂²	1	2	yes	—
57	C₂₃×#491	C₂²	1	2	yes	—
58	C₂₃×#490	C₂²	1	2	yes	—
59	C₂₃×#489	C₂²	1	2	yes	—
60	C₂₃×#489	C₂²	1	2	yes	—
61	C₂₃×#488	C₂²	1	2	yes	—
62	C₂₃×#488	C₂²	1	2	yes	—
63	C₂₃×#488	C₂²	1	2	yes	—
64	C₂₃×#487	C₂²	1	1	yes	characteristic
65	C₂₃×#487	C₂²	1	1	yes	characteristic
66	C₂₃×#487	C₂²	1	2	yes	—
67	C₂₃×#485	C₂²	1	2	yes	—
68	C₂₃×#484	C₂²	1	1	yes	characteristic
69	C₂₃×#484	C₂²	1	1	yes	characteristic
70	C₂₃×#483	C₂²	1	1	yes	characteristic
71	C₂₃×#483	C₂²	1	1	yes	characteristic
72	C₂₃×#483	C₂²	1	2	yes	—
73	C₂₃×#482	C₂²	1	2	yes	—
74	C₂₃×#481	C₂²	1	2	yes	—
75	C₂₃×#479	C₂²	1	2	yes	—
76	C₂₃×#479	C₂²	1	2	yes	—
77	C₂₃×#479	C₂²	1	2	yes	—
78	C₂₃×#478	C₂²	1	2	yes	—
79	C₂₃×#476	C₂²	1	2	yes	—
80	C₂₃×#475	C₂²	1	2	yes	—
81	C₂₃×#470	C₂²	1	2	yes	—
82	C₂₃×#470	C₂²	1	2	yes	—
83	C₂₃×#470	C₂²	1	2	yes	—
84	C₂₃×#468	C₂²	1	2	yes	—
85	C₂₃×#467	C₂²	1	2	yes	—
86	C₂₃×#465	C₂²	1	2	yes	—
87	C₂₃×#464	C₂²	1	2	yes	—
88	C₂₃×#464	C₂²	1	2	yes	—
89	C₂₃×#462	C₂²	1	2	yes	—
90	C₂₃×#462	C₂²	1	2	yes	—
91	C₂₃×#462	C₂²	1	2	yes	—
92	C₂₃×#460	C₂²	1	2	yes	—
93	C₂₃×#452	C₂²	1	2	yes	—
94	C₂₃×#452	C₂²	1	2	yes	—
95	C₂₃×#452	C₂²	1	2	yes	—
96	C₂₃×#452	C₂²	1	2	yes	—
97	C₂₃×#451	C₂²	1	2	yes	—
98	C₂₃×#451	C₂²	1	2	yes	—
99	C₂₃×#446	C₂²	1	2	yes	—
100	C₂₃×#441	C₂²	1	2	yes	—
101	C₂₃×#441	C₂²	1	2	yes	—
102	C₂₃×#441	C₂²	1	2	yes	—
103	C₂₃×#440	C₂²	1	2	yes	—
104	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
105	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
106	C₂₃×#436	C₂²	1	2	yes	—
107	C₂₃×#435	C₂²	1	2	yes	—
108	C₂₃×#435	C₂²	1	2	yes	—
109	C₂₃×#433	C₂²	1	2	yes	—
110	C₂₃×#432	C₂²	1	1	yes	characteristic
111	C₂₃×#419	C₂²	1	2	yes	—
112	C₂₃×#417	C₂²	1	2	yes	—
113	C₂₃×#417	C₂²	1	2	yes	—
114	C₂₃×#417	C₂²	1	2	yes	—
115	C₂₃×#416	C₂²	1	2	yes	—
116	C₂×C₂₃×#103	C₂²	1	2	yes	—
117	C₂₃×#405	C₂²	1	2	yes	—
118	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
119	C₂×#41×C₂₃	C₂³	1	2	yes	—
120	C₂×#41×C₂₃	C₂³	1	2	yes	—
121	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
122	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
124	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
128	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
129	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
130	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
131	C₂₃×C₄⋊Q₈	—	2	2	no	—
132	C₂₃×C₄⋊Q₈	—	2	1	no	—
133	C₂₃×C₄⋊Q₈	—	2	2	no	—
134	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
136	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
137	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₂₃×#127	—	2	1	no	—
142	C₂₃×#127	C₂³	1	1	yes	characteristic
143	C₂₃×#126	—	2	2	no	—
144	C₂₃×#126	—	2	2	no	—
145	C₂₃×#126	—	2	2	no	—
146	C₂₃×#126	—	2	2	no	—
147	C₂₃×#126	—	2	2	no	—
148	C₂₃×#126	D₄	1	2	yes	—
149	C₂₃×#125	—	2	2	no	—
150	C₂₃×#125	—	2	2	no	—
151	C₂₃×#125	—	2	2	no	—
152	C₂₃×#125	—	2	2	no	—
153	C₂₃×#125	—	2	2	no	—
154	C₂₃×#125	—	2	1	no	—
155	C₂₃×#125	—	2	2	no	—
156	C₂₃×#125	—	2	2	no	—
157	C₂₃×#125	—	2	2	no	—
158	C₂₃×#125	—	2	2	no	—
159	C₂₃×#125	—	2	1	no	—
160	C₂₃×#125	—	2	1	no	—
161	C₂₃×#125	—	2	1	no	—
162	C₂₃×#125	—	2	1	no	—
163	C₂₃×#125	D₄	1	1	yes	characteristic
164	C₂₃×#125	C₂³	1	2	yes	—
165	C₂₃×#125	C₂³	1	2	yes	—
166	C₂₃×#125	C₂³	1	2	yes	—
167	C₂₃×#124	—	2	1	no	—
168	C₂₃×#124	—	2	2	no	—
169	C₂₃×#124	—	2	2	no	—
170	C₂₃×#124	D₄	1	1	yes	characteristic
171	C₂₃×#124	C₂³	1	2	yes	—
172	C₂₃×#124	C₂³	1	2	yes	—
173	C₂₃×#123	—	2	2	no	—
174	C₂₃×#123	—	2	2	no	—
175	C₂₃×#123	—	2	2	no	—
176	C₂₃×#123	—	2	2	no	—
177	C₂₃×#123	—	2	2	no	—
178	C₂₃×#123	—	2	2	no	—
179	C₂₃×#123	—	2	2	no	—
180	C₂₃×#123	—	2	2	no	—
181	C₂₃×#123	D₄	1	2	yes	—
182	C₂₃×C₂²⋊Q₈	—	2	1	no	—
183	C₂₃×C₂²⋊Q₈	—	2	1	no	—
184	C₂₃×C₂²⋊Q₈	—	2	2	no	—
185	C₂₃×C₂²⋊Q₈	—	2	2	no	—
186	C₂₃×C₂²⋊Q₈	—	2	2	no	—
187	C₂₃×C₂²⋊Q₈	—	2	2	no	—
188	C₂₃×C₂²⋊Q₈	—	2	2	no	—
189	C₂₃×C₂²⋊Q₈	—	2	2	no	—
190	C₂₃×C₂²⋊Q₈	—	2	2	no	—
191	C₂₃×C₂²⋊Q₈	—	2	2	no	—
192	C₂₃×C₂²⋊Q₈	—	2	2	no	—
193	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
194	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
195	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
197	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₂₃×#121	—	2	2	no	—
201	C₂₃×#121	—	2	2	no	—
202	C₂₃×#121	—	2	1	no	—
203	C₂₃×#121	—	2	1	no	—
204	C₂₃×#121	—	2	2	no	—
205	C₂₃×#121	D₄	1	1	yes	characteristic
206	C₂₃×#121	C₂³	1	2	yes	—
207	C₄×Q₈×C₂₃	—	2	1	no	—
208	C₄×Q₈×C₂₃	—	2	2	no	—
209	C₄×Q₈×C₂₃	—	2	1	no	—
210	C₄×Q₈×C₂₃	—	2	1	no	—
211	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
212	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
213	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
214	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
215	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
216	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
217	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
218	C₄×D₄×C₂₃	—	2	1	no	—
219	C₄×D₄×C₂₃	—	2	2	no	—
220	C₄×D₄×C₂₃	—	2	1	no	—
221	C₄×D₄×C₂₃	—	2	1	no	—
222	C₄×D₄×C₂₃	—	2	2	no	—
223	C₄×D₄×C₂₃	—	2	1	no	—
224	C₄×D₄×C₂₃	—	2	1	no	—
225	C₄×D₄×C₂₃	C₂³	1	2	yes	—
226	C₄×D₄×C₂₃	C₂³	1	2	yes	—
227	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
228	C₂₃×#117	—	2	1	no	—
229	C₂₃×#117	—	2	1	no	—
230	C₂₃×#117	—	2	2	no	—
231	C₂₃×#117	—	2	2	no	—
232	C₂₃×#117	C₂³	1	2	yes	—
233	C₂₃×#117	C₂³	1	2	yes	—
234	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
235	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
236	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
237	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
239	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
240	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
241	C₂₃×#107	C₂³	1	2	yes	—
242	C₂₃×#107	C₂³	1	2	yes	—
243	C₂₃×#106	C₂³	1	2	yes	—
244	C₂₃×#106	C₂³	1	2	yes	—
245	C₂₃×#106	C₂³	1	2	yes	—
246	C₂₃×#106	C₂³	1	2	yes	—
247	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
248	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
249	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
250	C₂₃×#103	C₂³	1	2	yes	—
251	C₂₃×#103	C₂³	1	2	yes	—
252	C₂₃×#103	C₂³	1	2	yes	—
253	C₂₃×#103	C₂³	1	2	yes	—
254	C₂₃×#103	C₂³	1	2	yes	—
255	C₂₃×#103	C₂³	1	2	yes	—
256	C₂₃×#103	C₂³	1	2	yes	—
257	C₂₃×#103	C₂³	1	2	yes	—
258	C₂₃×#103	C₂³	1	2	yes	—
259	C₂₃×#103	C₂³	1	2	yes	—
260	C₂₃×#103	C₂³	1	2	yes	—
261	C₂₃×#103	C₂³	1	2	yes	—
262	C₂₃×#103	C₂³	1	2	yes	—
263	C₂₃×#103	C₂³	1	2	yes	—
264	C₂₃×#102	C₂³	1	2	yes	—
265	C₂₃×#102	C₂³	1	2	yes	—
266	C₂₃×#102	C₂³	1	2	yes	—
267	C₂₃×#102	C₂³	1	2	yes	—
268	C₂₃×#102	C₂³	1	2	yes	—
269	C₂₃×#102	C₂³	1	2	yes	—
270	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₂₃×#97	C₂³	1	2	yes	—
275	C₂₃×#97	C₂³	1	2	yes	—
276	C₂₃×#97	C₂³	1	2	yes	—
277	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
278	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
279	C₄×C₈×C₂₃	C₂³	1	2	yes	—
280	#41×C₂₃	—	4	2	no	—
281	#41×C₂₃	—	4	2	no	—
282	#41×C₂₃	—	4	2	no	—
283	#41×C₂₃	—	4	2	no	—
284	C₂×Q₈×C₂₃	—	2	1	no	—
285	C₂×Q₈×C₂₃	—	2	1	no	—
286	C₂×Q₈×C₂₃	—	2	2	no	—
287	C₂×Q₈×C₂₃	—	2	2	no	—
288	C₂×Q₈×C₂₃	—	4	2	no	—
289	C₂×Q₈×C₂₃	—	4	2	no	—
290	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
291	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
292	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
293	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
294	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
295	C₂×D₄×C₂₃	—	2	2	no	—
296	C₂×D₄×C₂₃	—	2	2	no	—
297	C₂×D₄×C₂₃	—	2	2	no	—
298	C₂×D₄×C₂₃	—	2	1	no	—
299	C₂×D₄×C₂₃	—	2	1	no	—
300	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
301	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
302	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₂₃	—	2	1	no	—
304	C₂²×C₄×C₂₃	—	2	1	no	—
305	C₂²×C₄×C₂₃	—	2	2	no	—
306	C₂²×C₄×C₂₃	—	2	2	no	—
307	C₂²×C₄×C₂₃	—	2	2	no	—
308	C₂²×C₄×C₂₃	—	2	2	no	—
309	C₂²×C₄×C₂₃	—	2	2	no	—
310	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
314	Q₁₆×C₂₃	—	4	2	no	—
315	Q₁₆×C₂₃	—	4	2	no	—
316	Q₁₆×C₂₃	—	4	2	no	—
317	Q₁₆×C₂₃	—	4	2	no	—
318	SD₁₆×C₂₃	—	4	2	no	—
319	SD₁₆×C₂₃	—	4	2	no	—
320	M₁₆×C₂₃	—	4	2	no	—
321	M₁₆×C₂₃	—	4	2	no	—
322	C₂×C₈×C₂₃	—	4	2	no	—
323	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
324	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
325	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
326	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
327	C₄⋊C₄×C₂₃	—	2	1	no	—
328	C₄⋊C₄×C₂₃	—	2	2	no	—
329	C₄⋊C₄×C₂₃	—	2	2	no	—
330	C₄⋊C₄×C₂₃	—	2	2	no	—
331	C₄⋊C₄×C₂₃	—	2	2	no	—
332	C₄⋊C₄×C₂₃	—	2	2	no	—
333	C₄⋊C₄×C₂₃	—	2	2	no	—
334	C₄⋊C₄×C₂₃	—	2	1	no	—
335	C₄⋊C₄×C₂₃	—	2	2	no	—
336	C₄⋊C₄×C₂₃	—	2	1	no	—
337	C₄⋊C₄×C₂₃	—	2	1	no	—
338	C₄⋊C₄×C₂₃	—	2	1	no	—
339	C₄⋊C₄×C₂₃	—	2	2	no	—
340	C₄⋊C₄×C₂₃	—	2	2	no	—
341	C₄⋊C₄×C₂₃	—	2	2	no	—
342	C₄⋊C₄×C₂₃	—	2	1	no	—
343	C₄⋊C₄×C₂₃	—	2	1	no	—
344	C₄⋊C₄×C₂₃	—	2	1	no	—
345	C₄⋊C₄×C₂₃	—	2	1	no	—
346	C₄⋊C₄×C₂₃	—	2	1	no	—
347	C₄⋊C₄×C₂₃	—	2	2	no	—
348	C₄⋊C₄×C₂₃	—	2	1	no	—
349	C₄⋊C₄×C₂₃	—	2	2	no	—
350	C₄⋊C₄×C₂₃	—	2	2	no	—
351	C₄⋊C₄×C₂₃	—	2	2	no	—
352	C₄⋊C₄×C₂₃	—	2	1	no	—
353	C₄⋊C₄×C₂₃	—	2	1	no	—
354	C₄⋊C₄×C₂₃	—	2	2	no	—
355	C₄⋊C₄×C₂₃	—	2	1	no	—
356	C₄⋊C₄×C₂₃	—	2	2	no	—
357	C₄⋊C₄×C₂₃	—	2	2	no	—
358	C₄⋊C₄×C₂₃	—	2	2	no	—
359	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
364	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
365	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
369	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
370	C₂²⋊C₄×C₂₃	—	2	2	no	—
371	C₂²⋊C₄×C₂₃	—	2	1	no	—
372	C₂²⋊C₄×C₂₃	—	2	1	no	—
373	C₂²⋊C₄×C₂₃	—	2	2	no	—
374	C₂²⋊C₄×C₂₃	—	2	2	no	—
375	C₂²⋊C₄×C₂₃	—	2	2	no	—
376	C₂²⋊C₄×C₂₃	—	2	2	no	—
377	C₂²⋊C₄×C₂₃	—	2	2	no	—
378	C₂²⋊C₄×C₂₃	—	2	2	no	—
379	C₂²⋊C₄×C₂₃	—	2	2	no	—
380	C₂²⋊C₄×C₂₃	—	2	2	no	—
381	C₂²⋊C₄×C₂₃	—	2	2	no	—
382	C₂²⋊C₄×C₂₃	—	2	2	no	—
383	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
384	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
385	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
386	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
387	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
388	C₄²×C₂₃	—	2	2	no	—
389	C₄²×C₂₃	—	2	2	no	—
390	C₄²×C₂₃	—	2	1	no	—
391	C₄²×C₂₃	—	2	1	no	—
392	C₄²×C₂₃	—	2	2	no	—
393	C₄²×C₂₃	—	2	2	no	—
394	C₄²×C₂₃	—	2	2	no	—
395	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
396	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
398	C₄²×C₂₃	C₂⁴	1	2	yes	—
399	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
400	#62572	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
401	C₂³×C₂₃	—	2	2	no	—
402	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
403	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
404	Q₈×C₂₃	—	2	2	no	—
405	Q₈×C₂₃	—	2	2	no	—
406	Q₈×C₂₃	—	2	2	no	—
407	Q₈×C₂₃	—	2	2	no	—
408	Q₈×C₂₃	—	2	2	no	—
409	Q₈×C₂₃	—	2	2	no	—
410	Q₈×C₂₃	—	4	1	no	—
411	Q₈×C₂₃	—	8	1	no	—
412	Q₈×C₂₃	—	8	1	no	—
413	Q₈×C₂₃	—	8	2	no	—
414	Q₈×C₂₃	—	8	2	no	—
415	D₄×C₂₃	—	2	2	no	—
416	D₄×C₂₃	—	2	2	no	—
417	D₄×C₂₃	—	4	1	no	—
418	D₄×C₂₃	—	4	2	no	—
419	D₄×C₂₃	—	4	2	no	—
420	D₄×C₂₃	—	8	1	no	—
421	D₄×C₂₃	—	8	2	no	—
422	D₄×C₂₃	—	8	2	no	—
423	D₄×C₂₃	—	8	2	no	—
424	C₂×C₄×C₂₃	—	2	2	no	—
425	C₂×C₄×C₂₃	—	2	2	no	—
426	C₂×C₄×C₂₃	—	2	2	no	—
427	C₂×C₄×C₂₃	—	2	2	no	—
428	C₂×C₄×C₂₃	—	2	1	no	—
429	C₂×C₄×C₂₃	—	2	2	no	—
430	C₂×C₄×C₂₃	—	2	2	no	—
431	C₂×C₄×C₂₃	—	2	1	no	—
432	C₂×C₄×C₂₃	—	2	1	no	—
433	C₂×C₄×C₂₃	—	2	2	no	—
434	C₂×C₄×C₂₃	—	2	2	no	—
435	C₂×C₄×C₂₃	—	2	1	no	—
436	C₂×C₄×C₂₃	—	4	1	no	—
437	C₂×C₄×C₂₃	—	4	1	no	—
438	C₂×C₄×C₂₃	—	4	2	no	—
439	C₂×C₄×C₂₃	—	8	2	no	—
440	C₂×C₄×C₂₃	—	8	2	no	—
441	C₂×C₄×C₂₃	—	8	2	no	—
442	C₂×C₄×C₂₃	—	8	1	no	—
443	C₂×C₄×C₂₃	—	8	2	no	—
444	C₂×C₄×C₂₃	—	8	2	no	—
445	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
448	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
449	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
450	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
454	C₈×C₂₃	—	2	2	no	—
455	C₈×C₂₃	—	2	2	no	—
456	C₈×C₂₃	—	2	2	no	—
457	C₈×C₂₃	—	2	2	no	—
458	#3563	C₂×C₂₃	1	1	yes	characteristic, complemented
459	#3554	C₂×C₂₃	1	1	yes	characteristic
460	#3374	C₂×C₂₃	1	2	yes	complemented
461	#3371	C₂×C₂₃	1	2	yes	complemented
462	#3331	C₂×C₂₃	1	2	yes	complemented
463	#3327	C₂×C₂₃	1	2	yes	complemented
464	#3317	C₂×C₂₃	1	2	yes	complemented
465	#3316	C₂×C₂₃	1	2	yes	complemented
466	#3315	C₂×C₂₃	1	2	yes	complemented
467	#3312	C₂×C₂₃	1	2	yes	complemented
468	#3244	C₂×C₂₃	1	2	yes	complemented
469	#3236	C₂×C₂₃	1	1	yes	characteristic, complemented
470	#3223	C₂×C₂₃	1	2	yes	complemented
471	#3216	C₂×C₂₃	1	1	yes	characteristic, complemented
472	#3185	C₂×C₂₃	1	1	yes	characteristic, complemented
473	#3178	C₂×C₂₃	1	2	yes	complemented
474	#3142	C₂×C₂₃	1	1	yes	characteristic, complemented
475	#3137	C₂×C₂₃	1	2	yes	complemented
476	#2967	C₂×C₂₃	1	1	yes	characteristic, complemented
477	C₂²×C₂₃	—	2	1	no	—
478	C₂²×C₂₃	—	2	1	no	—
479	C₂²×C₂₃	—	2	2	no	—
480	C₂²×C₂₃	—	2	2	no	—
481	C₂²×C₂₃	—	2	2	no	—
482	C₂²×C₂₃	—	2	1	no	—
483	C₂²×C₂₃	—	4	2	no	—
484	C₂²×C₂₃	—	4	2	no	—
485	C₂²×C₂₃	—	4	2	no	—
486	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
487	C₄×C₂₃	—	2	1	no	—
488	C₄×C₂₃	—	2	1	no	—
489	C₄×C₂₃	—	2	1	no	—
490	C₄×C₂₃	—	2	1	no	—
491	C₄×C₂₃	—	2	2	no	—
492	C₄×C₂₃	—	2	2	no	—
493	C₄×C₂₃	—	2	1	no	—
494	C₄×C₂₃	—	2	2	no	—
495	C₄×C₂₃	—	4	2	no	—
496	C₄×C₂₃	—	4	1	no	—
497	C₄×C₂₃	—	4	2	no	—
498	C₄×C₂₃	—	4	2	no	—
499	C₄×C₂₃	—	4	1	no	—
500	C₄×C₂₃	—	4	1	no	—
501	C₄×C₂₃	—	4	2	no	—
502	C₄×C₂₃	—	4	1	no	—
503	C₄×C₂₃	—	4	2	no	—
504	C₄×C₂₃	#585	1	2	yes	—
505	#564	—	2	1	no	—
506	#563	—	2	1	no	—
507	#562	—	2	2	no	—
508	#559	—	2	1	no	—
509	#559	C₂²×C₂₃	1	1	yes	characteristic
510	#557	C₂²×C₂₃	1	1	yes	characteristic
511	#557	C₂²×C₂₃	1	2	yes	—
512	#554	—	2	1	no	—
513	#554	C₂²×C₂₃	1	2	yes	—
514	#552	—	2	2	no	—
515	#552	C₂²×C₂₃	1	2	yes	—
516	#552	C₂²×C₂₃	1	2	yes	—
517	#550	C₂²×C₂₃	1	1	yes	characteristic
518	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
519	#548	C₂²×C₂₃	1	2	yes	—
520	#547	C₂²×C₂₃	1	2	yes	—
521	#544	—	2	1	no	—
522	#544	C₂²×C₂₃	1	2	yes	—
523	#542	—	2	1	no	—
524	#542	C₂²×C₂₃	1	2	yes	—
525	#541	—	2	2	no	—
526	#541	C₂²×C₂₃	1	2	yes	—
527	#540	—	2	1	no	—
528	#539	—	2	2	no	—
529	#539	—	2	1	no	—
530	#536	C₂²×C₂₃	1	2	yes	—
531	#533	C₂²×C₂₃	1	1	yes	characteristic
532	#533	C₂²×C₂₃	1	1	yes	characteristic
533	#532	C₂²×C₂₃	1	1	yes	characteristic
534	#529	C₂²×C₂₃	1	1	yes	characteristic
535	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
536	#501	C₂²×C₂₃	1	2	yes	—
537	#498	C₂²×C₂₃	1	1	yes	characteristic
538	#497	C₂²×C₂₃	1	2	yes	—
539	#494	C₂²×C₂₃	1	1	yes	characteristic
540	#491	C₂²×C₂₃	1	2	yes	—
541	#491	C₂²×C₂₃	1	2	yes	—
542	#491	C₂²×C₂₃	1	2	yes	—
543	#490	C₂²×C₂₃	1	2	yes	—
544	#489	C₂²×C₂₃	1	2	yes	—
545	#489	C₂²×C₂₃	1	2	yes	—
546	#488	C₂²×C₂₃	1	2	yes	—
547	#488	C₂²×C₂₃	1	2	yes	—
548	#488	C₂²×C₂₃	1	2	yes	—
549	#487	C₂²×C₂₃	1	2	yes	—
550	#487	C₂²×C₂₃	1	1	yes	characteristic
551	#487	C₂²×C₂₃	1	1	yes	characteristic
552	#485	C₂²×C₂₃	1	2	yes	—
553	#484	C₂²×C₂₃	1	1	yes	characteristic
554	#484	C₂²×C₂₃	1	1	yes	characteristic
555	#483	C₂²×C₂₃	1	1	yes	characteristic
556	#483	C₂²×C₂₃	1	2	yes	—
557	#483	C₂²×C₂₃	1	1	yes	characteristic
558	#482	C₂²×C₂₃	1	2	yes	—
559	#481	C₂²×C₂₃	1	2	yes	—
560	#479	C₂²×C₂₃	1	2	yes	—
561	#479	C₂²×C₂₃	1	2	yes	—
562	#479	C₂²×C₂₃	1	2	yes	—
563	#478	C₂²×C₂₃	1	2	yes	—
564	#476	C₂²×C₂₃	1	2	yes	—
565	#475	C₂²×C₂₃	1	2	yes	—
566	#470	C₂²×C₂₃	1	2	yes	—
567	#470	C₂²×C₂₃	1	2	yes	—
568	#470	C₂²×C₂₃	1	2	yes	—
569	#468	C₂²×C₂₃	1	2	yes	—
570	#467	C₂²×C₂₃	1	2	yes	—
571	#465	C₂²×C₂₃	1	2	yes	—
572	#464	C₂²×C₂₃	1	2	yes	—
573	#464	C₂²×C₂₃	1	2	yes	—
574	#462	C₂²×C₂₃	1	2	yes	—
575	#462	C₂²×C₂₃	1	2	yes	—
576	#462	C₂²×C₂₃	1	2	yes	—
577	#460	C₂²×C₂₃	1	2	yes	—
578	#452	C₂²×C₂₃	1	2	yes	—
579	#452	C₂²×C₂₃	1	2	yes	—
580	#452	C₂²×C₂₃	1	2	yes	—
581	#452	C₂²×C₂₃	1	2	yes	—
582	#451	C₂²×C₂₃	1	2	yes	—
583	#451	C₂²×C₂₃	1	2	yes	—
584	#446	C₂²×C₂₃	1	2	yes	—
585	#441	C₂²×C₂₃	1	2	yes	—
586	#441	C₂²×C₂₃	1	2	yes	—
587	#441	C₂²×C₂₃	1	2	yes	—
588	#440	C₂²×C₂₃	1	2	yes	—
589	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
590	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
591	#436	C₂²×C₂₃	1	2	yes	—
592	#435	C₂²×C₂₃	1	2	yes	—
593	#435	C₂²×C₂₃	1	2	yes	—
594	#433	C₂²×C₂₃	1	2	yes	—
595	#432	C₂²×C₂₃	1	1	yes	characteristic
596	#419	C₂²×C₂₃	1	2	yes	—
597	#417	C₂²×C₂₃	1	2	yes	—
598	#417	C₂²×C₂₃	1	2	yes	—
599	#417	C₂²×C₂₃	1	2	yes	—
600	#416	C₂²×C₂₃	1	2	yes	—
601	C₂×#103	C₂²×C₂₃	1	2	yes	—
602	#405	C₂²×C₂₃	1	2	yes	—
603	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
604	C₂×C₂₃	—	4	1	no	—
605	C₂×C₂₃	—	4	2	no	—
606	C₂×C₂₃	—	8	2	no	—
607	C₂×C₂₃	#3500	1	1	yes	characteristic
608	C₂×C₂₃	#3586	1	1	yes	characteristic
609	C₂×C₂₃	#3586	1	1	yes	characteristic
610	C₂×#41	C₂³×C₂₃	1	2	yes	—
611	C₂×#41	C₂³×C₂₃	1	2	yes	—
612	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
613	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
614	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
615	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
616	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
617	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
618	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
619	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
620	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
621	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
622	C₄⋊Q₈	—	2	2	no	—
623	C₄⋊Q₈	—	2	2	no	—
624	C₄⋊Q₈	—	2	1	no	—
625	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
626	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
627	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
628	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
629	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
630	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
631	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
632	#127	—	2	1	no	—
633	#127	C₂³×C₂₃	1	1	yes	characteristic
634	#126	—	2	2	no	—
635	#126	—	2	2	no	—
636	#126	—	2	2	no	—
637	#126	—	2	2	no	—
638	#126	—	2	2	no	—
639	#126	D₄×C₂₃	1	2	yes	—
640	#125	—	2	2	no	—
641	#125	—	2	2	no	—
642	#125	—	2	1	no	—
643	#125	—	2	2	no	—
644	#125	—	2	2	no	—
645	#125	—	2	2	no	—
646	#125	—	2	2	no	—
647	#125	—	2	2	no	—
648	#125	—	2	2	no	—
649	#125	—	2	2	no	—
650	#125	—	2	1	no	—
651	#125	—	2	1	no	—
652	#125	—	2	1	no	—
653	#125	—	2	1	no	—
654	#125	D₄×C₂₃	1	1	yes	characteristic
655	#125	C₂³×C₂₃	1	2	yes	—
656	#125	C₂³×C₂₃	1	2	yes	—
657	#125	C₂³×C₂₃	1	2	yes	—
658	#124	—	2	1	no	—
659	#124	—	2	2	no	—
660	#124	—	2	2	no	—
661	#124	D₄×C₂₃	1	1	yes	characteristic
662	#124	C₂³×C₂₃	1	2	yes	—
663	#124	C₂³×C₂₃	1	2	yes	—
664	#123	—	2	2	no	—
665	#123	—	2	2	no	—
666	#123	—	2	2	no	—
667	#123	—	2	2	no	—
668	#123	—	2	2	no	—
669	#123	—	2	2	no	—
670	#123	—	2	2	no	—
671	#123	—	2	2	no	—
672	#123	D₄×C₂₃	1	2	yes	—
673	C₂²⋊Q₈	—	2	1	no	—
674	C₂²⋊Q₈	—	2	1	no	—
675	C₂²⋊Q₈	—	2	2	no	—
676	C₂²⋊Q₈	—	2	2	no	—
677	C₂²⋊Q₈	—	2	2	no	—
678	C₂²⋊Q₈	—	2	2	no	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
685	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
686	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
687	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
688	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
689	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
690	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
691	#121	—	2	2	no	—
692	#121	—	2	2	no	—
693	#121	—	2	1	no	—
694	#121	—	2	1	no	—
695	#121	—	2	2	no	—
696	#121	D₄×C₂₃	1	1	yes	characteristic
697	#121	C₂³×C₂₃	1	2	yes	—
698	C₄×Q₈	—	2	1	no	—
699	C₄×Q₈	—	2	2	no	—
700	C₄×Q₈	—	2	1	no	—
701	C₄×Q₈	—	2	1	no	—
702	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
703	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
704	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
705	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
706	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
707	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
708	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
709	C₄×D₄	—	2	2	no	—
710	C₄×D₄	—	2	1	no	—
711	C₄×D₄	—	2	1	no	—
712	C₄×D₄	—	2	1	no	—
713	C₄×D₄	—	2	2	no	—
714	C₄×D₄	—	2	1	no	—
715	C₄×D₄	—	2	1	no	—
716	C₄×D₄	C₂³×C₂₃	1	2	yes	—
717	C₄×D₄	C₂³×C₂₃	1	2	yes	—
718	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
719	#117	—	2	1	no	—
720	#117	—	2	1	no	—
721	#117	—	2	2	no	—
722	#117	—	2	2	no	—
723	#117	C₂³×C₂₃	1	2	yes	—
724	#117	C₂³×C₂₃	1	2	yes	—
725	C₂×C₄⋊C₄	—	2	1	no	—
726	C₂×C₄⋊C₄	—	2	1	no	—
727	C₂×C₄⋊C₄	—	2	2	no	—
728	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
729	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
730	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
731	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
732	#107	C₂³×C₂₃	1	2	yes	—
733	#107	C₂³×C₂₃	1	2	yes	—
734	#106	C₂³×C₂₃	1	2	yes	—
735	#106	C₂³×C₂₃	1	2	yes	—
736	#106	C₂³×C₂₃	1	2	yes	—
737	#106	C₂³×C₂₃	1	2	yes	—
738	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
739	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
740	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
741	#103	C₂³×C₂₃	1	2	yes	—
742	#103	C₂³×C₂₃	1	2	yes	—
743	#103	C₂³×C₂₃	1	2	yes	—
744	#103	C₂³×C₂₃	1	2	yes	—
745	#103	C₂³×C₂₃	1	2	yes	—
746	#103	C₂³×C₂₃	1	2	yes	—
747	#103	C₂³×C₂₃	1	2	yes	—
748	#103	C₂³×C₂₃	1	2	yes	—
749	#103	C₂³×C₂₃	1	2	yes	—
750	#103	C₂³×C₂₃	1	2	yes	—
751	#103	C₂³×C₂₃	1	2	yes	—
752	#103	C₂³×C₂₃	1	2	yes	—
753	#103	C₂³×C₂₃	1	2	yes	—
754	#103	C₂³×C₂₃	1	2	yes	—
755	#102	C₂³×C₂₃	1	2	yes	—
756	#102	C₂³×C₂₃	1	2	yes	—
757	#102	C₂³×C₂₃	1	2	yes	—
758	#102	C₂³×C₂₃	1	2	yes	—
759	#102	C₂³×C₂₃	1	2	yes	—
760	#102	C₂³×C₂₃	1	2	yes	—
761	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
762	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
763	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
764	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
765	#97	C₂³×C₂₃	1	2	yes	—
766	#97	C₂³×C₂₃	1	2	yes	—
767	#97	C₂³×C₂₃	1	2	yes	—
768	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
769	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
770	C₄×C₈	C₂³×C₂₃	1	2	yes	—
771	C₂₃	#62572	1	1	yes	characteristic, direct product factor, Sylow
772	#41	—	4	2	no	—
773	#41	—	4	2	no	—
774	#41	—	4	2	no	—
775	#41	—	4	2	no	—
776	C₂×Q₈	—	2	1	no	—
777	C₂×Q₈	—	2	1	no	—
778	C₂×Q₈	—	2	2	no	—
779	C₂×Q₈	—	2	2	no	—
780	C₂×Q₈	—	4	2	no	—
781	C₂×Q₈	—	4	2	no	—
782	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
783	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
784	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
785	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
786	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	1	no	—
791	C₂×D₄	—	2	1	no	—
792	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
793	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
794	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
795	C₂²×C₄	—	2	1	no	—
796	C₂²×C₄	—	2	1	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
803	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
804	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
806	Q₁₆	—	4	2	no	—
807	Q₁₆	—	4	2	no	—
808	Q₁₆	—	4	2	no	—
809	Q₁₆	—	4	2	no	—
810	SD₁₆	—	4	2	no	—
811	SD₁₆	—	4	2	no	—
812	M₁₆	—	4	2	no	—
813	M₁₆	—	4	2	no	—
814	C₂×C₈	—	4	2	no	—
815	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
816	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
817	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
818	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
819	C₄⋊C₄	—	2	1	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	1	no	—
829	C₄⋊C₄	—	2	1	no	—
830	C₄⋊C₄	—	2	1	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	1	no	—
835	C₄⋊C₄	—	2	1	no	—
836	C₄⋊C₄	—	2	1	no	—
837	C₄⋊C₄	—	2	1	no	—
838	C₄⋊C₄	—	2	1	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	1	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	1	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	1	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
852	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
853	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
854	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
855	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
856	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
857	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
858	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
859	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
860	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
861	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	1	no	—
864	C₂²⋊C₄	—	2	1	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
876	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
877	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
878	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
879	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
880	C₄²	—	2	2	no	—
881	C₄²	—	2	2	no	—
882	C₄²	—	2	1	no	—
883	C₄²	—	2	1	no	—
884	C₄²	—	2	2	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	2	2	no	—
887	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
888	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
889	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
890	C₄²	C₂⁴×C₂₃	1	2	yes	—
891	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
892	C₂³	—	2	2	no	—
893	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
894	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
895	Q₈	—	2	2	no	—
896	Q₈	—	2	2	no	—
897	Q₈	—	2	2	no	—
898	Q₈	—	2	2	no	—
899	Q₈	—	2	2	no	—
900	Q₈	—	2	2	no	—
901	Q₈	—	4	1	no	—
902	Q₈	—	8	2	no	—
903	Q₈	—	8	1	no	—
904	Q₈	—	8	1	no	—
905	Q₈	—	8	2	no	—
906	D₄	—	2	2	no	—
907	D₄	—	2	2	no	—
908	D₄	—	4	1	no	—
909	D₄	—	4	2	no	—
910	D₄	—	4	2	no	—
911	D₄	—	8	1	no	—
912	D₄	—	8	2	no	—
913	D₄	—	8	2	no	—
914	D₄	—	8	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	4	1	no	—
928	C₂×C₄	—	4	1	no	—
929	C₂×C₄	—	4	2	no	—
930	C₂×C₄	—	8	2	no	—
931	C₂×C₄	—	8	2	no	—
932	C₂×C₄	—	8	2	no	—
933	C₂×C₄	—	8	2	no	—
934	C₂×C₄	—	8	1	no	—
935	C₂×C₄	—	8	2	no	—
936	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
937	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
938	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
939	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
940	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
941	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
942	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
943	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
944	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
945	C₈	—	2	2	no	—
946	C₈	—	2	2	no	—
947	C₈	—	2	2	no	—
948	C₈	—	2	2	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	1	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	2	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
959	C₄	—	2	1	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	1	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	1	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	2	no	—
966	C₄	—	2	2	no	—
967	C₄	—	4	1	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	1	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₄	—	4	1	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	1	no	—
976	C₄	C₂₃×#585	1	2	yes	—
977	C₂	—	4	2	no	—
978	C₂	—	4	1	no	—
979	C₂	—	8	2	no	—
980	C₂	C₂₃×#3500	1	1	yes	characteristic
981	C₂	C₂₃×#3586	1	1	yes	characteristic
982	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3554	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3563	C₂	semidirect
3. C₂₃×#3374	C₂	semidirect
4. C₂₃×#3371	C₂	semidirect
5. C₂₃×#3331	C₂	semidirect
6. C₂₃×#3327	C₂	semidirect
7. C₂₃×#3317	C₂	semidirect
8. C₂₃×#3316	C₂	semidirect
9. C₂₃×#3315	C₂	semidirect
10. C₂₃×#3312	C₂	semidirect
11. C₂₃×#3244	C₂	semidirect
12. C₂₃×#3236	C₂	semidirect
13. C₂₃×#3223	C₂	semidirect
14. C₂₃×#3216	C₂	semidirect
15. C₂₃×#3185	C₂	semidirect
16. C₂₃×#3178	C₂	semidirect
17. C₂₃×#3142	C₂	semidirect
18. C₂₃×#3137	C₂	semidirect
19. C₂₃×#2967	C₂	semidirect
400. #62572	C₂₃	direct (N × H)
458. #3563	C₂×C₂₃	semidirect
460. #3374	C₂×C₂₃	semidirect
461. #3371	C₂×C₂₃	semidirect
462. #3331	C₂×C₂₃	semidirect
463. #3327	C₂×C₂₃	semidirect
464. #3317	C₂×C₂₃	semidirect
465. #3316	C₂×C₂₃	semidirect
466. #3315	C₂×C₂₃	semidirect
467. #3312	C₂×C₂₃	semidirect
468. #3244	C₂×C₂₃	semidirect
469. #3236	C₂×C₂₃	semidirect
470. #3223	C₂×C₂₃	semidirect
471. #3216	C₂×C₂₃	semidirect
472. #3185	C₂×C₂₃	semidirect
473. #3178	C₂×C₂₃	semidirect
474. #3142	C₂×C₂₃	semidirect
475. #3137	C₂×C₂₃	semidirect
476. #2967	C₂×C₂₃	semidirect
771. C₂₃	#62572	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×#3563	2
C₂₃×#3554	2
C₂₃×#3374	2
C₂₃×#3371	2
C₂₃×#3331	2
C₂₃×#3327	2
C₂₃×#3317	2
C₂₃×#3316	2
C₂₃×#3315	2
C₂₃×#3312	2
C₂₃×#3244	2
C₂₃×#3236	2
C₂₃×#3223	2
C₂₃×#3216	2
C₂₃×#3185	2
C₂₃×#3178	2
C₂₃×#3142	2
C₂₃×#3137	2
C₂₃×#2967	2
#62572	23

Subgroups — C23×#62572 #19210198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62572 #19210198