Subgroups — C₂₃×#61779 #19209405

Order 5888.

1678 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3493	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3352	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3351	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3349	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3348	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3329	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3328	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3320	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3312	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3242	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3201	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3196	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3196	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3120	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3097	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3095	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3095	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2978	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#563	—	2	2	no	—
21	C₂₃×#556	—	2	1	no	—
22	C₂₃×#556	C₂²	1	2	yes	—
23	C₂₃×#555	—	2	1	no	—
24	C₂₃×#555	C₂²	1	2	yes	—
25	C₂₃×#553	—	2	1	no	—
26	C₂₃×#553	C₂²	1	2	yes	—
27	C₂₃×#552	—	2	1	no	—
28	C₂₃×#552	C₂²	1	2	yes	—
29	C₂₃×#552	C₂²	1	2	yes	—
30	C₂₃×#552	C₂²	1	2	yes	—
31	C₂₃×#551	—	2	2	no	—
32	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
33	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
34	C₂₃×#544	—	2	1	no	—
35	C₂₃×#544	—	2	1	no	—
36	C₂₃×#544	C₂²	1	1	yes	characteristic
37	C₂₃×#541	C₂²	1	2	yes	—
38	C₂₃×#539	—	2	1	no	—
39	C₂₃×#539	—	2	1	no	—
40	C₂₃×#538	—	2	2	no	—
41	C₂₃×#537	C₂²	1	1	yes	characteristic
42	C₂₃×#536	C₂²	1	2	yes	—
43	C₂₃×#529	—	2	2	no	—
44	C₂₃×#525	C₂²	1	1	yes	characteristic
45	C₂₃×#525	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
48	C₂₃×#520	C₂²	1	1	yes	characteristic
49	C₂₃×#520	C₂²	1	1	yes	characteristic
50	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
51	C₂₃×#501	C₂²	1	2	yes	complemented
52	C₂₃×#499	C₂²	1	2	yes	complemented
53	C₂₃×#491	C₂²	1	2	yes	complemented
54	C₂₃×#487	C₂²	1	2	yes	complemented
55	C₂₃×#485	C₂²	1	2	yes	—
56	C₂₃×#485	C₂²	1	2	yes	—
57	C₂₃×#485	C₂²	1	2	yes	—
58	C₂₃×#485	C₂²	1	2	yes	—
59	C₂₃×#485	C₂²	1	2	yes	—
60	C₂₃×#485	C₂²	1	2	yes	—
61	C₂₃×#485	C₂²	1	2	yes	complemented
62	C₂₃×#485	C₂²	1	2	yes	complemented
63	C₂₃×#485	C₂²	1	2	yes	complemented
64	C₂₃×#484	C₂²	1	1	yes	characteristic
65	C₂₃×#484	C₂²	1	1	yes	characteristic
66	C₂₃×#484	C₂²	1	2	yes	—
67	C₂₃×#484	C₂²	1	2	yes	—
68	C₂₃×#484	C₂²	1	2	yes	complemented
69	C₂₃×#483	C₂²	1	2	yes	—
70	C₂₃×#483	C₂²	1	2	yes	—
71	C₂₃×#483	C₂²	1	2	yes	complemented
72	C₂₃×#482	C₂²	1	2	yes	complemented
73	C₂₃×#481	C₂²	1	1	yes	characteristic
74	C₂₃×#481	C₂²	1	1	yes	characteristic
75	C₂₃×#479	C₂²	1	2	yes	complemented
76	C₂₃×#479	C₂²	1	2	yes	complemented
77	C₂₃×#479	C₂²	1	2	yes	complemented
78	C₂₃×#478	C₂²	1	2	yes	complemented
79	C₂₃×#477	C₂²	1	2	yes	complemented
80	C₂₃×#475	C₂²	1	2	yes	complemented
81	C₂₃×#470	C₂²	1	2	yes	—
82	C₂₃×#470	C₂²	1	2	yes	—
83	C₂₃×#470	C₂²	1	2	yes	complemented
84	C₂₃×#468	C₂²	1	2	yes	—
85	C₂₃×#468	C₂²	1	2	yes	—
86	C₂₃×#468	C₂²	1	2	yes	complemented
87	C₂₃×#467	C₂²	1	2	yes	complemented
88	C₂₃×#465	C₂²	1	2	yes	complemented
89	C₂₃×#462	C₂²	1	2	yes	complemented
90	C₂₃×#461	C₂²	1	2	yes	complemented
91	C₂₃×#452	C₂²	1	2	yes	—
92	C₂₃×#452	C₂²	1	2	yes	—
93	C₂₃×#451	C₂²	1	1	yes	characteristic
94	C₂₃×#451	C₂²	1	1	yes	characteristic
95	C₂₃×#451	C₂²	1	2	yes	complemented
96	C₂₃×#448	C₂²	1	1	yes	characteristic
97	C₂₃×#448	C₂²	1	1	yes	characteristic
98	C₂₃×#448	C₂²	1	2	yes	complemented
99	C₂₃×#441	C₂²	1	2	yes	complemented
100	C₂₃×#440	C₂²	1	2	yes	complemented
101	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
103	C₂₃×#436	C₂²	1	2	yes	—
104	C₂₃×#436	C₂²	1	2	yes	—
105	C₂₃×#435	C₂²	1	2	yes	—
106	C₂₃×#435	C₂²	1	2	yes	—
107	C₂₃×#433	C₂²	1	2	yes	—
108	C₂₃×#428	C₂²	1	2	yes	—
109	C₂₃×#428	C₂²	1	2	yes	—
110	C₂₃×#428	C₂²	1	2	yes	complemented
111	C₂₃×#427	C₂²	1	2	yes	complemented
112	C₂₃×#419	C₂²	1	2	yes	—
113	C₂₃×#419	C₂²	1	2	yes	—
114	C₂₃×#419	C₂²	1	2	yes	complemented
115	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
116	C₂₃×#408	C₂²	1	2	yes	—
117	C₂₃×#407	C₂²	1	1	yes	characteristic
118	C₂₃×#407	C₂²	1	1	yes	characteristic
119	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
120	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
121	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
122	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
125	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
126	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
129	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
130	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
131	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
132	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
133	C₂₃×C₄⋊Q₈	—	2	2	no	—
134	C₂₃×C₄⋊Q₈	—	2	2	no	—
135	C₂₃×C₄⋊Q₈	—	2	2	no	—
136	C₂₃×C₄⋊Q₈	—	2	1	no	—
137	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₂₃×#126	—	2	2	no	—
140	C₂₃×#126	—	2	2	no	—
141	C₂₃×#126	—	2	2	no	—
142	C₂₃×#126	—	2	2	no	—
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×#125	—	2	2	no	—
148	C₂₃×#125	—	2	1	no	—
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	C₂³	1	2	yes	—
154	C₂₃×#125	C₂³	1	2	yes	—
155	C₂₃×#124	—	2	2	no	—
156	C₂₃×#124	—	2	2	no	—
157	C₂₃×#124	—	2	2	no	—
158	C₂₃×#124	—	2	2	no	—
159	C₂₃×#123	—	2	2	no	—
160	C₂₃×#123	—	2	2	no	—
161	C₂₃×#123	—	2	2	no	—
162	C₂₃×#123	—	2	2	no	—
163	C₂₃×#123	—	2	2	no	—
164	C₂₃×#123	—	2	1	no	—
165	C₂₃×#123	—	2	2	no	—
166	C₂₃×#123	D₄	1	2	yes	—
167	C₂₃×C₂²⋊Q₈	—	2	1	no	—
168	C₂₃×C₂²⋊Q₈	—	2	1	no	—
169	C₂₃×C₂²⋊Q₈	—	2	1	no	—
170	C₂₃×C₂²⋊Q₈	—	2	1	no	—
171	C₂₃×C₂²⋊Q₈	—	2	1	no	—
172	C₂₃×C₂²⋊Q₈	—	2	2	no	—
173	C₂₃×C₂²⋊Q₈	—	2	2	no	—
174	C₂₃×C₂²⋊Q₈	—	2	2	no	—
175	C₂₃×C₂²⋊Q₈	—	2	2	no	—
176	C₂₃×C₂²⋊Q₈	—	2	2	no	—
177	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
178	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
179	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
180	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
181	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
182	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
183	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
184	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
185	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
186	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
187	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
188	C₂₃×#121	—	2	1	no	—
189	C₂₃×#121	—	2	2	no	—
190	C₂₃×#121	—	2	2	no	—
191	C₂₃×#121	—	2	2	no	—
192	C₂₃×#121	D₄	1	1	yes	characteristic
193	C₂₃×#121	D₄	1	1	yes	characteristic
194	C₂₃×#121	C₂³	1	1	yes	characteristic
195	C₂₃×#121	C₂³	1	2	yes	—
196	C₂₃×#121	C₂³	1	1	yes	characteristic
197	C₂₃×#120	—	2	1	no	—
198	C₂₃×#120	D₄	1	2	yes	—
199	C₄×Q₈×C₂₃	—	2	1	no	—
200	C₄×Q₈×C₂₃	—	2	2	no	—
201	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
202	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
203	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
204	C₄×D₄×C₂₃	—	2	2	no	—
205	C₄×D₄×C₂₃	—	2	2	no	—
206	C₄×D₄×C₂₃	—	2	1	no	—
207	C₄×D₄×C₂₃	—	2	2	no	—
208	C₄×D₄×C₂₃	—	2	1	no	—
209	C₄×D₄×C₂₃	—	2	1	no	—
210	C₄×D₄×C₂₃	—	2	2	no	—
211	C₄×D₄×C₂₃	—	2	2	no	—
212	C₄×D₄×C₂₃	C₂³	1	2	yes	—
213	C₄×D₄×C₂₃	C₂³	1	2	yes	—
214	C₄×D₄×C₂₃	C₂³	1	2	yes	—
215	C₂₃×#117	—	2	1	no	—
216	C₂₃×#117	—	2	1	no	—
217	C₂₃×#117	—	2	2	no	—
218	C₂₃×#117	—	2	1	no	—
219	C₂₃×#117	—	2	2	no	—
220	C₂₃×#117	—	2	2	no	—
221	C₂₃×#117	—	2	2	no	—
222	C₂₃×#117	C₂³	1	2	yes	—
223	C₂₃×#117	C₂³	1	2	yes	—
224	C₂₃×#117	C₂³	1	2	yes	—
225	C₂₃×#117	C₂³	1	2	yes	—
226	C₂₃×#117	C₂³	1	1	yes	characteristic
227	C₂₃×#117	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
229	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
230	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
231	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
234	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
236	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
237	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
239	C₂×C₄²×C₂₃	—	2	1	no	—
240	C₂₃×#107	C₂³	1	2	yes	—
241	C₂₃×#107	C₂³	1	2	yes	—
242	C₂₃×#107	C₂³	1	2	yes	—
243	C₂₃×#107	C₂³	1	2	yes	—
244	C₂₃×#107	C₂³	1	2	yes	—
245	C₂₃×#107	C₂³	1	2	yes	—
246	C₂₃×#106	C₂³	1	2	yes	—
247	C₂₃×#106	C₂³	1	2	yes	—
248	C₂₃×#106	C₂³	1	2	yes	—
249	C₂₃×#106	C₂³	1	2	yes	—
250	C₂₃×#106	C₂³	1	2	yes	—
251	C₂₃×#106	C₂³	1	2	yes	—
252	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
253	C₂₃×C₄⋊C₈	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×#103	C₂³	1	2	yes	—
265	C₂₃×#103	C₂³	1	2	yes	—
266	C₂₃×#103	C₂³	1	2	yes	—
267	C₂₃×#103	C₂³	1	2	yes	—
268	C₂₃×#102	C₂³	1	2	yes	—
269	C₂₃×#102	C₂³	1	2	yes	—
270	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
271	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
272	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
274	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
275	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
276	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₂₃×#97	C₂³	1	2	yes	—
279	C₄×C₈×C₂₃	C₂³	1	2	yes	—
280	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
281	#41×C₂₃	—	4	2	no	—
282	#41×C₂₃	—	4	2	no	—
283	C₂×Q₈×C₂₃	—	2	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	—	4	2	no	—
288	C₂×Q₈×C₂₃	—	4	2	no	—
289	C₂×Q₈×C₂₃	—	4	2	no	—
290	C₂×Q₈×C₂₃	—	4	2	no	—
291	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
292	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
293	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
294	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
295	C₂×D₄×C₂₃	—	2	1	no	—
296	C₂×D₄×C₂₃	—	2	1	no	—
297	C₂×D₄×C₂₃	—	2	1	no	—
298	C₂×D₄×C₂₃	—	2	2	no	—
299	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
300	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
301	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
302	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
303	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₂₃	—	2	1	no	—
305	C₂²×C₄×C₂₃	—	2	1	no	—
306	C₂²×C₄×C₂₃	—	2	1	no	—
307	C₂²×C₄×C₂₃	—	2	1	no	—
308	C₂²×C₄×C₂₃	—	2	1	no	—
309	C₂²×C₄×C₂₃	—	2	1	no	—
310	C₂²×C₄×C₂₃	—	2	2	no	—
311	C₂²×C₄×C₂₃	—	2	2	no	—
312	C₂²×C₄×C₂₃	—	2	1	no	—
313	C₂²×C₄×C₂₃	—	2	2	no	—
314	C₂²×C₄×C₂₃	—	4	2	no	—
315	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
322	Q₁₆×C₂₃	—	4	2	no	—
323	Q₁₆×C₂₃	—	4	2	no	—
324	SD₁₆×C₂₃	—	4	2	no	—
325	SD₁₆×C₂₃	—	4	2	no	—
326	M₁₆×C₂₃	—	4	2	no	—
327	M₁₆×C₂₃	—	4	2	no	—
328	M₁₆×C₂₃	—	4	2	no	—
329	C₂×C₈×C₂₃	—	4	2	no	—
330	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
331	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
332	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
333	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
334	C₄⋊C₄×C₂₃	—	2	1	no	—
335	C₄⋊C₄×C₂₃	—	2	2	no	—
336	C₄⋊C₄×C₂₃	—	2	2	no	—
337	C₄⋊C₄×C₂₃	—	2	2	no	—
338	C₄⋊C₄×C₂₃	—	2	2	no	—
339	C₄⋊C₄×C₂₃	—	2	2	no	—
340	C₄⋊C₄×C₂₃	—	2	1	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	2	no	—
346	C₄⋊C₄×C₂₃	—	2	2	no	—
347	C₄⋊C₄×C₂₃	—	2	2	no	—
348	C₄⋊C₄×C₂₃	—	2	2	no	—
349	C₄⋊C₄×C₂₃	—	2	2	no	—
350	C₄⋊C₄×C₂₃	—	2	2	no	—
351	C₄⋊C₄×C₂₃	—	2	1	no	—
352	C₄⋊C₄×C₂₃	—	2	2	no	—
353	C₄⋊C₄×C₂₃	—	2	2	no	—
354	C₄⋊C₄×C₂₃	—	2	2	no	—
355	C₄⋊C₄×C₂₃	—	2	2	no	—
356	C₄⋊C₄×C₂₃	—	2	2	no	—
357	C₄⋊C₄×C₂₃	—	2	2	no	—
358	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
359	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
360	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
368	C₂²⋊C₄×C₂₃	—	2	2	no	—
369	C₂²⋊C₄×C₂₃	—	2	2	no	—
370	C₂²⋊C₄×C₂₃	—	2	2	no	—
371	C₂²⋊C₄×C₂₃	—	2	2	no	—
372	C₂²⋊C₄×C₂₃	—	2	2	no	—
373	C₂²⋊C₄×C₂₃	—	2	2	no	—
374	C₂²⋊C₄×C₂₃	—	2	2	no	—
375	C₂²⋊C₄×C₂₃	—	2	1	no	—
376	C₂²⋊C₄×C₂₃	—	2	2	no	—
377	C₂²⋊C₄×C₂₃	—	2	2	no	—
378	C₂²⋊C₄×C₂₃	—	2	1	no	—
379	C₂²⋊C₄×C₂₃	—	2	1	no	—
380	C₂²⋊C₄×C₂₃	—	2	2	no	—
381	C₂²⋊C₄×C₂₃	—	2	2	no	—
382	C₂²⋊C₄×C₂₃	—	2	1	no	—
383	C₂²⋊C₄×C₂₃	—	2	2	no	—
384	C₂²⋊C₄×C₂₃	—	2	2	no	—
385	C₂²⋊C₄×C₂₃	—	2	1	no	—
386	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
387	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
389	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
391	C₄²×C₂₃	—	2	2	no	—
392	C₄²×C₂₃	—	2	2	no	—
393	C₄²×C₂₃	—	2	2	no	—
394	C₄²×C₂₃	—	2	2	no	—
395	C₄²×C₂₃	—	2	2	no	—
396	C₄²×C₂₃	—	2	2	no	—
397	C₄²×C₂₃	—	2	2	no	—
398	C₄²×C₂₃	—	2	1	no	—
399	C₄²×C₂₃	C₂⁴	1	2	yes	—
400	#61779	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
401	C₂³×C₂₃	—	2	1	no	—
402	C₂³×C₂₃	—	4	1	no	—
403	C₂³×C₂₃	—	4	1	no	—
404	C₂³×C₂₃	—	4	1	no	—
405	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
406	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
407	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
408	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
409	Q₈×C₂₃	—	2	2	no	—
410	Q₈×C₂₃	—	2	2	no	—
411	Q₈×C₂₃	—	2	2	no	—
412	Q₈×C₂₃	—	2	2	no	—
413	Q₈×C₂₃	—	2	2	no	—
414	Q₈×C₂₃	—	4	1	no	—
415	Q₈×C₂₃	—	8	2	no	—
416	Q₈×C₂₃	—	8	1	no	—
417	Q₈×C₂₃	—	8	1	no	—
418	Q₈×C₂₃	—	8	2	no	—
419	D₄×C₂₃	—	2	2	no	—
420	D₄×C₂₃	—	4	2	no	—
421	D₄×C₂₃	—	4	2	no	—
422	D₄×C₂₃	—	4	1	no	—
423	D₄×C₂₃	—	4	2	no	—
424	D₄×C₂₃	—	4	2	no	—
425	D₄×C₂₃	—	8	1	no	—
426	D₄×C₂₃	—	8	2	no	—
427	D₄×C₂₃	—	8	1	no	—
428	C₂×C₄×C₂₃	—	2	2	no	—
429	C₂×C₄×C₂₃	—	2	2	no	—
430	C₂×C₄×C₂₃	—	2	2	no	—
431	C₂×C₄×C₂₃	—	2	2	no	—
432	C₂×C₄×C₂₃	—	2	2	no	—
433	C₂×C₄×C₂₃	—	2	2	no	—
434	C₂×C₄×C₂₃	—	2	1	no	—
435	C₂×C₄×C₂₃	—	2	2	no	—
436	C₂×C₄×C₂₃	—	2	2	no	—
437	C₂×C₄×C₂₃	—	2	1	no	—
438	C₂×C₄×C₂₃	—	2	2	no	—
439	C₂×C₄×C₂₃	—	2	1	no	—
440	C₂×C₄×C₂₃	—	2	2	no	—
441	C₂×C₄×C₂₃	—	2	2	no	—
442	C₂×C₄×C₂₃	—	4	1	no	—
443	C₂×C₄×C₂₃	—	4	1	no	—
444	C₂×C₄×C₂₃	—	4	1	no	—
445	C₂×C₄×C₂₃	—	4	2	no	—
446	C₂×C₄×C₂₃	—	4	2	no	—
447	C₂×C₄×C₂₃	—	4	2	no	—
448	C₂×C₄×C₂₃	—	8	2	no	—
449	C₂×C₄×C₂₃	—	8	1	no	—
450	C₂×C₄×C₂₃	—	8	2	no	—
451	C₂×C₄×C₂₃	—	8	1	no	—
452	C₂×C₄×C₂₃	—	8	1	no	—
453	C₂×C₄×C₂₃	—	8	1	no	—
454	C₂×C₄×C₂₃	—	8	2	no	—
455	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
459	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
460	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
462	C₈×C₂₃	—	2	2	no	—
463	C₈×C₂₃	—	2	2	no	—
464	C₈×C₂₃	—	2	2	no	—
465	C₈×C₂₃	—	2	2	no	—
466	#3538	C₂×C₂₃	1	1	yes	characteristic, complemented
467	#3493	C₂×C₂₃	1	1	yes	characteristic
468	#3352	C₂×C₂₃	1	2	yes	complemented
469	#3351	C₂×C₂₃	1	2	yes	complemented
470	#3349	C₂×C₂₃	1	2	yes	complemented
471	#3348	C₂×C₂₃	1	2	yes	complemented
472	#3329	C₂×C₂₃	1	2	yes	complemented
473	#3328	C₂×C₂₃	1	2	yes	complemented
474	#3320	C₂×C₂₃	1	2	yes	complemented
475	#3312	C₂×C₂₃	1	2	yes	complemented
476	#3242	C₂×C₂₃	1	2	yes	complemented
477	#3201	C₂×C₂₃	1	2	yes	complemented
478	#3196	C₂×C₂₃	1	1	yes	characteristic, complemented
479	#3196	C₂×C₂₃	1	1	yes	characteristic, complemented
480	#3120	C₂×C₂₃	1	2	yes	complemented
481	#3097	C₂×C₂₃	1	2	yes	complemented
482	#3095	C₂×C₂₃	1	1	yes	characteristic, complemented
483	#3095	C₂×C₂₃	1	1	yes	characteristic, complemented
484	#2978	C₂×C₂₃	1	1	yes	characteristic, complemented
485	C₂²×C₂₃	—	2	1	no	—
486	C₂²×C₂₃	—	2	1	no	—
487	C₂²×C₂₃	—	2	2	no	—
488	C₂²×C₂₃	—	2	1	no	—
489	C₂²×C₂₃	—	2	1	no	—
490	C₂²×C₂₃	—	2	2	no	—
491	C₂²×C₂₃	—	2	1	no	—
492	C₂²×C₂₃	—	2	1	no	—
493	C₂²×C₂₃	—	2	1	no	—
494	C₂²×C₂₃	—	2	1	no	—
495	C₂²×C₂₃	—	2	1	no	—
496	C₂²×C₂₃	—	2	2	no	—
497	C₂²×C₂₃	—	4	1	no	—
498	C₂²×C₂₃	—	4	1	no	—
499	C₂²×C₂₃	—	4	1	no	—
500	C₂²×C₂₃	—	8	2	no	—
501	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
502	C₄×C₂₃	—	2	2	no	—
503	C₄×C₂₃	—	2	2	no	—
504	C₄×C₂₃	—	2	1	no	—
505	C₄×C₂₃	—	2	1	no	—
506	C₄×C₂₃	—	2	1	no	—
507	C₄×C₂₃	—	2	2	no	—
508	C₄×C₂₃	—	4	2	no	—
509	C₄×C₂₃	—	4	2	no	—
510	C₄×C₂₃	—	4	2	no	—
511	C₄×C₂₃	—	4	1	no	—
512	C₄×C₂₃	—	4	2	no	—
513	C₄×C₂₃	—	4	1	no	—
514	C₄×C₂₃	—	4	1	no	—
515	C₄×C₂₃	—	4	2	no	—
516	C₄×C₂₃	—	4	2	no	—
517	C₄×C₂₃	#585	1	2	yes	—
518	#563	—	2	2	no	—
519	#556	—	2	1	no	—
520	#556	C₂²×C₂₃	1	2	yes	—
521	#555	—	2	1	no	—
522	#555	C₂²×C₂₃	1	2	yes	—
523	#553	—	2	1	no	—
524	#553	C₂²×C₂₃	1	2	yes	—
525	#552	—	2	1	no	—
526	#552	C₂²×C₂₃	1	2	yes	—
527	#552	C₂²×C₂₃	1	2	yes	—
528	#552	C₂²×C₂₃	1	2	yes	—
529	#551	—	2	2	no	—
530	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
531	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
532	#544	—	2	1	no	—
533	#544	—	2	1	no	—
534	#544	C₂²×C₂₃	1	1	yes	characteristic
535	#541	C₂²×C₂₃	1	2	yes	—
536	#539	—	2	1	no	—
537	#539	—	2	1	no	—
538	#538	—	2	2	no	—
539	#537	C₂²×C₂₃	1	1	yes	characteristic
540	#536	C₂²×C₂₃	1	2	yes	—
541	#529	—	2	2	no	—
542	#525	C₂²×C₂₃	1	1	yes	characteristic
543	#525	C₂²×C₂₃	1	1	yes	characteristic
544	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
545	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
546	#520	C₂²×C₂₃	1	1	yes	characteristic
547	#520	C₂²×C₂₃	1	1	yes	characteristic
548	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
549	#501	C₂²×C₂₃	1	2	yes	complemented
550	#499	C₂²×C₂₃	1	2	yes	complemented
551	#491	C₂²×C₂₃	1	2	yes	complemented
552	#487	C₂²×C₂₃	1	2	yes	complemented
553	#485	C₂²×C₂₃	1	2	yes	—
554	#485	C₂²×C₂₃	1	2	yes	—
555	#485	C₂²×C₂₃	1	2	yes	—
556	#485	C₂²×C₂₃	1	2	yes	—
557	#485	C₂²×C₂₃	1	2	yes	—
558	#485	C₂²×C₂₃	1	2	yes	—
559	#485	C₂²×C₂₃	1	2	yes	complemented
560	#485	C₂²×C₂₃	1	2	yes	complemented
561	#485	C₂²×C₂₃	1	2	yes	complemented
562	#484	C₂²×C₂₃	1	1	yes	characteristic
563	#484	C₂²×C₂₃	1	2	yes	—
564	#484	C₂²×C₂₃	1	2	yes	—
565	#484	C₂²×C₂₃	1	1	yes	characteristic
566	#484	C₂²×C₂₃	1	2	yes	complemented
567	#483	C₂²×C₂₃	1	2	yes	—
568	#483	C₂²×C₂₃	1	2	yes	—
569	#483	C₂²×C₂₃	1	2	yes	complemented
570	#482	C₂²×C₂₃	1	2	yes	complemented
571	#481	C₂²×C₂₃	1	1	yes	characteristic
572	#481	C₂²×C₂₃	1	1	yes	characteristic
573	#479	C₂²×C₂₃	1	2	yes	complemented
574	#479	C₂²×C₂₃	1	2	yes	complemented
575	#479	C₂²×C₂₃	1	2	yes	complemented
576	#478	C₂²×C₂₃	1	2	yes	complemented
577	#477	C₂²×C₂₃	1	2	yes	complemented
578	#475	C₂²×C₂₃	1	2	yes	complemented
579	#470	C₂²×C₂₃	1	2	yes	—
580	#470	C₂²×C₂₃	1	2	yes	—
581	#470	C₂²×C₂₃	1	2	yes	complemented
582	#468	C₂²×C₂₃	1	2	yes	—
583	#468	C₂²×C₂₃	1	2	yes	—
584	#468	C₂²×C₂₃	1	2	yes	complemented
585	#467	C₂²×C₂₃	1	2	yes	complemented
586	#465	C₂²×C₂₃	1	2	yes	complemented
587	#462	C₂²×C₂₃	1	2	yes	complemented
588	#461	C₂²×C₂₃	1	2	yes	complemented
589	#452	C₂²×C₂₃	1	2	yes	—
590	#452	C₂²×C₂₃	1	2	yes	—
591	#451	C₂²×C₂₃	1	1	yes	characteristic
592	#451	C₂²×C₂₃	1	1	yes	characteristic
593	#451	C₂²×C₂₃	1	2	yes	complemented
594	#448	C₂²×C₂₃	1	1	yes	characteristic
595	#448	C₂²×C₂₃	1	1	yes	characteristic
596	#448	C₂²×C₂₃	1	2	yes	complemented
597	#441	C₂²×C₂₃	1	2	yes	complemented
598	#440	C₂²×C₂₃	1	2	yes	complemented
599	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
600	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
601	#436	C₂²×C₂₃	1	2	yes	—
602	#436	C₂²×C₂₃	1	2	yes	—
603	#435	C₂²×C₂₃	1	2	yes	—
604	#435	C₂²×C₂₃	1	2	yes	—
605	#433	C₂²×C₂₃	1	2	yes	—
606	#428	C₂²×C₂₃	1	2	yes	—
607	#428	C₂²×C₂₃	1	2	yes	—
608	#428	C₂²×C₂₃	1	2	yes	complemented
609	#427	C₂²×C₂₃	1	2	yes	complemented
610	#419	C₂²×C₂₃	1	2	yes	—
611	#419	C₂²×C₂₃	1	2	yes	—
612	#419	C₂²×C₂₃	1	2	yes	complemented
613	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
614	#408	C₂²×C₂₃	1	2	yes	—
615	#407	C₂²×C₂₃	1	1	yes	characteristic
616	#407	C₂²×C₂₃	1	1	yes	characteristic
617	C₂×C₂₃	—	4	2	no	—
618	C₂×C₂₃	—	4	1	no	—
619	C₂×C₂₃	—	4	1	no	—
620	C₂×C₂₃	—	4	1	no	—
621	C₂×C₂₃	—	8	1	no	—
622	C₂×C₂₃	#3485	1	1	yes	characteristic
623	C₂×C₂₃	#3586	1	1	yes	characteristic
624	C₂×C₂₃	#3586	1	1	yes	characteristic
625	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
626	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
627	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
628	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
629	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
630	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
631	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
632	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
633	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
634	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
635	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
636	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
637	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
638	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
639	C₄⋊Q₈	—	2	2	no	—
640	C₄⋊Q₈	—	2	2	no	—
641	C₄⋊Q₈	—	2	2	no	—
642	C₄⋊Q₈	—	2	1	no	—
643	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
644	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
645	#126	—	2	2	no	—
646	#126	—	2	2	no	—
647	#126	—	2	2	no	—
648	#126	—	2	2	no	—
649	#126	—	2	2	no	—
650	#126	—	2	2	no	—
651	#126	—	2	2	no	—
652	#126	—	2	2	no	—
653	#125	—	2	2	no	—
654	#125	—	2	2	no	—
655	#125	—	2	2	no	—
656	#125	—	2	2	no	—
657	#125	—	2	2	no	—
658	#125	—	2	1	no	—
659	#125	C₂³×C₂₃	1	2	yes	—
660	#125	C₂³×C₂₃	1	2	yes	—
661	#124	—	2	2	no	—
662	#124	—	2	2	no	—
663	#124	—	2	2	no	—
664	#124	—	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	1	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	1	no	—
676	C₂²⋊Q₈	—	2	1	no	—
677	C₂²⋊Q₈	—	2	1	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	D₄×C₂₃	1	1	yes	characteristic
684	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
685	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
686	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
687	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
688	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
689	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
690	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
691	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
692	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
693	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
694	#121	—	2	2	no	—
695	#121	—	2	1	no	—
696	#121	—	2	2	no	—
697	#121	—	2	2	no	—
698	#121	D₄×C₂₃	1	1	yes	characteristic
699	#121	D₄×C₂₃	1	1	yes	characteristic
700	#121	C₂³×C₂₃	1	1	yes	characteristic
701	#121	C₂³×C₂₃	1	1	yes	characteristic
702	#121	C₂³×C₂₃	1	2	yes	—
703	#120	—	2	1	no	—
704	#120	D₄×C₂₃	1	2	yes	—
705	C₄×Q₈	—	2	1	no	—
706	C₄×Q₈	—	2	2	no	—
707	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
708	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
709	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
710	C₄×D₄	—	2	2	no	—
711	C₄×D₄	—	2	1	no	—
712	C₄×D₄	—	2	2	no	—
713	C₄×D₄	—	2	2	no	—
714	C₄×D₄	—	2	1	no	—
715	C₄×D₄	—	2	1	no	—
716	C₄×D₄	—	2	2	no	—
717	C₄×D₄	—	2	2	no	—
718	C₄×D₄	C₂³×C₂₃	1	2	yes	—
719	C₄×D₄	C₂³×C₂₃	1	2	yes	—
720	C₄×D₄	C₂³×C₂₃	1	2	yes	—
721	#117	—	2	1	no	—
722	#117	—	2	1	no	—
723	#117	—	2	1	no	—
724	#117	—	2	2	no	—
725	#117	—	2	2	no	—
726	#117	—	2	2	no	—
727	#117	—	2	2	no	—
728	#117	C₂³×C₂₃	1	2	yes	—
729	#117	C₂³×C₂₃	1	2	yes	—
730	#117	C₂³×C₂₃	1	1	yes	characteristic
731	#117	C₂³×C₂₃	1	2	yes	—
732	#117	C₂³×C₂₃	1	2	yes	—
733	#117	C₂³×C₂₃	1	1	yes	characteristic
734	C₂×C₄⋊C₄	—	2	1	no	—
735	C₂×C₄⋊C₄	—	2	1	no	—
736	C₂×C₄⋊C₄	—	2	1	no	—
737	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
738	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
739	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
740	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
741	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
742	C₂×C₂²⋊C₄	—	2	1	no	—
743	C₂×C₂²⋊C₄	—	2	1	no	—
744	C₂×C₂²⋊C₄	—	2	1	no	—
745	C₂×C₄²	—	2	1	no	—
746	#107	C₂³×C₂₃	1	2	yes	—
747	#107	C₂³×C₂₃	1	2	yes	—
748	#107	C₂³×C₂₃	1	2	yes	—
749	#107	C₂³×C₂₃	1	2	yes	—
750	#107	C₂³×C₂₃	1	2	yes	—
751	#107	C₂³×C₂₃	1	2	yes	—
752	#106	C₂³×C₂₃	1	2	yes	—
753	#106	C₂³×C₂₃	1	2	yes	—
754	#106	C₂³×C₂₃	1	2	yes	—
755	#106	C₂³×C₂₃	1	2	yes	—
756	#106	C₂³×C₂₃	1	2	yes	—
757	#106	C₂³×C₂₃	1	2	yes	—
758	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
759	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
760	#103	C₂³×C₂₃	1	2	yes	—
761	#103	C₂³×C₂₃	1	2	yes	—
762	#103	C₂³×C₂₃	1	2	yes	—
763	#103	C₂³×C₂₃	1	2	yes	—
764	#103	C₂³×C₂₃	1	2	yes	—
765	#103	C₂³×C₂₃	1	2	yes	—
766	#103	C₂³×C₂₃	1	2	yes	—
767	#103	C₂³×C₂₃	1	2	yes	—
768	#103	C₂³×C₂₃	1	2	yes	—
769	#103	C₂³×C₂₃	1	2	yes	—
770	#103	C₂³×C₂₃	1	2	yes	—
771	#103	C₂³×C₂₃	1	2	yes	—
772	#103	C₂³×C₂₃	1	2	yes	—
773	#103	C₂³×C₂₃	1	2	yes	—
774	#102	C₂³×C₂₃	1	2	yes	—
775	#102	C₂³×C₂₃	1	2	yes	—
776	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
777	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
778	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
779	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
780	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
781	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
782	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
783	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
784	#97	C₂³×C₂₃	1	2	yes	—
785	C₄×C₈	C₂³×C₂₃	1	2	yes	—
786	C₂₃	#61779	1	1	yes	characteristic, direct product factor, Sylow
787	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
788	#41	—	4	2	no	—
789	#41	—	4	2	no	—
790	C₂×Q₈	—	2	2	no	—
791	C₂×Q₈	—	2	1	no	—
792	C₂×Q₈	—	2	1	no	—
793	C₂×Q₈	—	2	2	no	—
794	C₂×Q₈	—	4	2	no	—
795	C₂×Q₈	—	4	2	no	—
796	C₂×Q₈	—	4	2	no	—
797	C₂×Q₈	—	4	2	no	—
798	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
799	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
800	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
801	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
802	C₂×D₄	—	2	1	no	—
803	C₂×D₄	—	2	1	no	—
804	C₂×D₄	—	2	1	no	—
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
807	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
808	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
809	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
810	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
811	C₂²×C₄	—	2	1	no	—
812	C₂²×C₄	—	2	1	no	—
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	2	1	no	—
815	C₂²×C₄	—	2	1	no	—
816	C₂²×C₄	—	2	1	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	4	2	no	—
822	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
823	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
824	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
826	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
827	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
829	Q₁₆	—	4	2	no	—
830	Q₁₆	—	4	2	no	—
831	SD₁₆	—	4	2	no	—
832	SD₁₆	—	4	2	no	—
833	M₁₆	—	4	2	no	—
834	M₁₆	—	4	2	no	—
835	M₁₆	—	4	2	no	—
836	C₂×C₈	—	4	2	no	—
837	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
838	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
839	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
840	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
841	C₄⋊C₄	—	2	1	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	1	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	1	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
866	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
867	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
868	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
869	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
870	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
871	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
872	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
873	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
874	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	1	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	1	no	—
886	C₂²⋊C₄	—	2	1	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	1	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	1	no	—
893	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
894	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
895	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
896	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
897	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
898	C₄²	—	2	2	no	—
899	C₄²	—	2	2	no	—
900	C₄²	—	2	2	no	—
901	C₄²	—	2	2	no	—
902	C₄²	—	2	2	no	—
903	C₄²	—	2	2	no	—
904	C₄²	—	2	2	no	—
905	C₄²	—	2	1	no	—
906	C₄²	C₂⁴×C₂₃	1	2	yes	—
907	C₂³	—	2	1	no	—
908	C₂³	—	4	1	no	—
909	C₂³	—	4	1	no	—
910	C₂³	—	4	1	no	—
911	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
912	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
913	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
914	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
915	Q₈	—	2	2	no	—
916	Q₈	—	2	2	no	—
917	Q₈	—	2	2	no	—
918	Q₈	—	2	2	no	—
919	Q₈	—	2	2	no	—
920	Q₈	—	4	1	no	—
921	Q₈	—	8	1	no	—
922	Q₈	—	8	1	no	—
923	Q₈	—	8	2	no	—
924	Q₈	—	8	2	no	—
925	D₄	—	2	2	no	—
926	D₄	—	4	1	no	—
927	D₄	—	4	2	no	—
928	D₄	—	4	2	no	—
929	D₄	—	4	2	no	—
930	D₄	—	4	2	no	—
931	D₄	—	8	1	no	—
932	D₄	—	8	2	no	—
933	D₄	—	8	1	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	4	1	no	—
949	C₂×C₄	—	4	1	no	—
950	C₂×C₄	—	4	1	no	—
951	C₂×C₄	—	4	2	no	—
952	C₂×C₄	—	4	2	no	—
953	C₂×C₄	—	4	2	no	—
954	C₂×C₄	—	8	2	no	—
955	C₂×C₄	—	8	1	no	—
956	C₂×C₄	—	8	1	no	—
957	C₂×C₄	—	8	2	no	—
958	C₂×C₄	—	8	1	no	—
959	C₂×C₄	—	8	2	no	—
960	C₂×C₄	—	8	1	no	—
961	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
962	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
963	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
964	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
965	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
966	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
967	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
968	C₈	—	2	2	no	—
969	C₈	—	2	2	no	—
970	C₈	—	2	2	no	—
971	C₈	—	2	2	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	2	1	no	—
974	C₂²	—	2	1	no	—
975	C₂²	—	2	2	no	—
976	C₂²	—	2	1	no	—
977	C₂²	—	2	1	no	—
978	C₂²	—	2	2	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	2	no	—
982	C₂²	—	2	1	no	—
983	C₂²	—	2	1	no	—
984	C₂²	—	4	1	no	—
985	C₂²	—	4	1	no	—
986	C₂²	—	4	1	no	—
987	C₂²	—	8	2	no	—
988	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
989	C₄	—	2	1	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	1	no	—
992	C₄	—	2	2	no	—
993	C₄	—	2	2	no	—
994	C₄	—	2	2	no	—
995	C₄	—	4	1	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	2	no	—
998	C₄	—	4	2	no	—
999	C₄	—	4	2	no	—
1000	C₄	—	4	2	no	—
1001	C₄	—	4	1	no	—
1002	C₄	—	4	2	no	—
1003	C₄	—	4	1	no	—
1004	C₄	C₂₃×#585	1	2	yes	—
1005	C₂	—	4	1	no	—
1006	C₂	—	4	1	no	—
1007	C₂	—	4	1	no	—
1008	C₂	—	4	2	no	—
1009	C₂	—	8	1	no	—
1010	C₂	C₂₃×#3485	1	1	yes	characteristic
1011	C₂	C₂₃×#3586	1	1	yes	characteristic
1012	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×#3493	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3538	C₂	semidirect
3. C₂₃×#3352	C₂	semidirect
4. C₂₃×#3351	C₂	semidirect
5. C₂₃×#3349	C₂	semidirect
6. C₂₃×#3348	C₂	semidirect
7. C₂₃×#3329	C₂	semidirect
8. C₂₃×#3328	C₂	semidirect
9. C₂₃×#3320	C₂	semidirect
10. C₂₃×#3312	C₂	semidirect
11. C₂₃×#3242	C₂	semidirect
12. C₂₃×#3201	C₂	semidirect
13. C₂₃×#3196	C₂	semidirect
14. C₂₃×#3196	C₂	semidirect
15. C₂₃×#3120	C₂	semidirect
16. C₂₃×#3097	C₂	semidirect
17. C₂₃×#3095	C₂	semidirect
18. C₂₃×#3095	C₂	semidirect
19. C₂₃×#2978	C₂	semidirect
51. C₂₃×#501	C₂²	semidirect
52. C₂₃×#499	C₂²	semidirect
53. C₂₃×#491	C₂²	semidirect
54. C₂₃×#487	C₂²	semidirect
61. C₂₃×#485	C₂²	semidirect
62. C₂₃×#485	C₂²	semidirect
63. C₂₃×#485	C₂²	semidirect
68. C₂₃×#484	C₂²	semidirect
71. C₂₃×#483	C₂²	semidirect
72. C₂₃×#482	C₂²	semidirect
75. C₂₃×#479	C₂²	semidirect
76. C₂₃×#479	C₂²	semidirect
77. C₂₃×#479	C₂²	semidirect
78. C₂₃×#478	C₂²	semidirect
79. C₂₃×#477	C₂²	semidirect
80. C₂₃×#475	C₂²	semidirect
83. C₂₃×#470	C₂²	semidirect
86. C₂₃×#468	C₂²	semidirect
87. C₂₃×#467	C₂²	semidirect
88. C₂₃×#465	C₂²	semidirect
89. C₂₃×#462	C₂²	semidirect
90. C₂₃×#461	C₂²	semidirect
95. C₂₃×#451	C₂²	semidirect
98. C₂₃×#448	C₂²	semidirect
99. C₂₃×#441	C₂²	semidirect
100. C₂₃×#440	C₂²	semidirect
101. C₄×Q₁₆×C₂₃	C₂²	semidirect
102. C₄×SD₁₆×C₂₃	C₂²	semidirect
110. C₂₃×#428	C₂²	semidirect
111. C₂₃×#427	C₂²	semidirect
114. C₂₃×#419	C₂²	semidirect
115. C₂×C₂₃×#103	C₂²	semidirect
400. #61779	C₂₃	direct (N × H)
466. #3538	C₂×C₂₃	semidirect
468. #3352	C₂×C₂₃	semidirect
469. #3351	C₂×C₂₃	semidirect
470. #3349	C₂×C₂₃	semidirect
471. #3348	C₂×C₂₃	semidirect
472. #3329	C₂×C₂₃	semidirect
473. #3328	C₂×C₂₃	semidirect
474. #3320	C₂×C₂₃	semidirect
475. #3312	C₂×C₂₃	semidirect
476. #3242	C₂×C₂₃	semidirect
477. #3201	C₂×C₂₃	semidirect
478. #3196	C₂×C₂₃	semidirect
479. #3196	C₂×C₂₃	semidirect
480. #3120	C₂×C₂₃	semidirect
481. #3097	C₂×C₂₃	semidirect
482. #3095	C₂×C₂₃	semidirect
483. #3095	C₂×C₂₃	semidirect
484. #2978	C₂×C₂₃	semidirect
549. #501	C₂²×C₂₃	semidirect
550. #499	C₂²×C₂₃	semidirect
551. #491	C₂²×C₂₃	semidirect
552. #487	C₂²×C₂₃	semidirect
559. #485	C₂²×C₂₃	semidirect
560. #485	C₂²×C₂₃	semidirect
561. #485	C₂²×C₂₃	semidirect
566. #484	C₂²×C₂₃	semidirect
569. #483	C₂²×C₂₃	semidirect
570. #482	C₂²×C₂₃	semidirect
573. #479	C₂²×C₂₃	semidirect
574. #479	C₂²×C₂₃	semidirect
575. #479	C₂²×C₂₃	semidirect
576. #478	C₂²×C₂₃	semidirect
577. #477	C₂²×C₂₃	semidirect
578. #475	C₂²×C₂₃	semidirect
581. #470	C₂²×C₂₃	semidirect
584. #468	C₂²×C₂₃	semidirect
585. #467	C₂²×C₂₃	semidirect
586. #465	C₂²×C₂₃	semidirect
587. #462	C₂²×C₂₃	semidirect
588. #461	C₂²×C₂₃	semidirect
593. #451	C₂²×C₂₃	semidirect
596. #448	C₂²×C₂₃	semidirect
597. #441	C₂²×C₂₃	semidirect
598. #440	C₂²×C₂₃	semidirect
599. C₄×Q₁₆	C₂²×C₂₃	semidirect
600. C₄×SD₁₆	C₂²×C₂₃	semidirect
608. #428	C₂²×C₂₃	semidirect
609. #427	C₂²×C₂₃	semidirect
612. #419	C₂²×C₂₃	semidirect
613. C₂×#103	C₂²×C₂₃	semidirect
786. C₂₃	#61779	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×#3538	2
C₂₃×#3493	2
C₂₃×#3352	2
C₂₃×#3351	2
C₂₃×#3349	2
C₂₃×#3348	2
C₂₃×#3329	2
C₂₃×#3328	2
C₂₃×#3320	2
C₂₃×#3312	2
C₂₃×#3242	2
C₂₃×#3201	2
C₂₃×#3196	2
C₂₃×#3120	2
C₂₃×#3097	2
C₂₃×#3095	2
C₂₃×#2978	2
#61779	23

Subgroups — C23×#61779 #19209405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61779 #19209405