Subgroups — C₂₃×#61000 #19208626

Order 5888.

1802 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3494	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3250	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3247	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3245	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3243	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3241	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3224	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3220	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3191	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3188	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3186	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3180	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3124	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3122	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3119	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3118	C₂	1	2	yes	maximal, complemented
19	C₂×C₂₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#555	—	2	2	no	—
21	C₂₃×#553	—	2	2	no	—
22	C₂₃×#553	—	2	2	no	—
23	C₂₃×#551	—	2	2	no	—
24	C₂₃×#551	—	2	2	no	—
25	C₂₃×#547	—	2	2	no	—
26	C₂₃×#546	—	2	2	no	—
27	C₂₃×#546	—	2	2	no	—
28	C₂₃×#544	C₂²	1	2	yes	complemented
29	C₂₃×#542	C₂²	1	2	yes	—
30	C₂₃×#542	C₂²	1	2	yes	—
31	C₂₃×#540	C₂²	1	2	yes	—
32	C₂₃×#540	C₂²	1	2	yes	—
33	C₂₃×#535	C₂²	1	2	yes	complemented
34	C₂₃×#532	C₂²	1	2	yes	complemented
35	C₂₃×#532	C₂²	1	2	yes	complemented
36	C₂₃×#529	C₂²	1	2	yes	complemented
37	C₂₃×#529	C₂²	1	2	yes	complemented
38	C₂₃×#525	C₂²	1	2	yes	—
39	C₂×C₂₃×#121	C₂²	1	2	yes	—
40	C₂₃×#520	C₂²	1	2	yes	complemented
41	C₂₃×#518	C₂²	1	2	yes	complemented
42	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
43	C₂₃×#501	C₂²	1	2	yes	complemented
44	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#499	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#496	C₂²	1	2	yes	complemented
47	C₂₃×#495	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×#493	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#490	C₂²	1	2	yes	complemented
50	C₂₃×#489	C₂²	1	2	yes	complemented
51	C₂₃×#488	C₂²	1	2	yes	complemented
52	C₂₃×#486	C₂²	1	2	yes	complemented
53	C₂₃×#485	C₂²	1	2	yes	complemented
54	C₂₃×#484	C₂²	1	2	yes	complemented
55	C₂₃×#482	C₂²	1	2	yes	—
56	C₂₃×#482	C₂²	1	2	yes	—
57	C₂₃×#482	C₂²	1	2	yes	complemented
58	C₂₃×#481	C₂²	1	2	yes	complemented
59	C₂₃×#480	C₂²	1	2	yes	—
60	C₂₃×#480	C₂²	1	2	yes	—
61	C₂₃×#479	C₂²	1	2	yes	complemented
62	C₂₃×#478	C₂²	1	2	yes	complemented
63	C₂₃×#478	C₂²	1	2	yes	complemented
64	C₂₃×#478	C₂²	1	2	yes	complemented
65	C₂₃×#477	C₂²	1	2	yes	complemented
66	C₂₃×#476	C₂²	1	2	yes	complemented
67	C₂₃×#474	C₂²	1	2	yes	complemented
68	C₂₃×#474	C₂²	1	2	yes	complemented
69	C₂₃×#467	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×#466	C₂²	1	1	yes	characteristic
71	C₂₃×#466	C₂²	1	1	yes	characteristic
72	C₂₃×#466	C₂²	1	2	yes	—
73	C₂₃×#466	C₂²	1	2	yes	complemented
74	C₂₃×#466	C₂²	1	1	yes	characteristic, complemented
75	C₂₃×#466	C₂²	1	2	yes	complemented
76	C₂₃×#465	C₂²	1	2	yes	complemented
77	C₂₃×#465	C₂²	1	2	yes	complemented
78	C₂₃×#465	C₂²	1	2	yes	complemented
79	C₂₃×#464	C₂²	1	2	yes	complemented
80	C₂₃×#463	C₂²	1	2	yes	complemented
81	C₂₃×#463	C₂²	1	2	yes	complemented
82	C₂₃×#463	C₂²	1	2	yes	complemented
83	C₂₃×#460	C₂²	1	2	yes	complemented
84	C₂₃×#459	C₂²	1	2	yes	complemented
85	C₂₃×#459	C₂²	1	2	yes	complemented
86	C₂₃×#459	C₂²	1	2	yes	complemented
87	C₂₃×#452	C₂²	1	2	yes	complemented
88	C₂₃×#450	C₂²	1	2	yes	complemented
89	C₂₃×#449	C₂²	1	2	yes	—
90	C₂₃×#449	C₂²	1	2	yes	—
91	C₂₃×#449	C₂²	1	2	yes	complemented
92	C₂₃×#447	C₂²	1	2	yes	—
93	C₂₃×#447	C₂²	1	2	yes	—
94	C₂₃×#447	C₂²	1	2	yes	complemented
95	C₂₃×#442	C₂²	1	2	yes	complemented
96	C₂₃×#442	C₂²	1	2	yes	complemented
97	C₂₃×#440	C₂²	1	2	yes	complemented
98	C₂₃×#440	C₂²	1	2	yes	complemented
99	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
100	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
101	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
102	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
103	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
104	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
105	C₂₃×#433	C₂²	1	2	yes	complemented
106	C₂₃×#433	C₂²	1	2	yes	complemented
107	C₂₃×#433	C₂²	1	2	yes	complemented
108	C₂₃×#433	C₂²	1	2	yes	complemented
109	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
112	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
113	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₂₃	—	2	2	no	—
116	C₂×#41×C₂₃	—	2	2	no	—
117	C₂×#41×C₂₃	C₂³	1	2	yes	—
118	C₂²×D₄×C₂₃	—	2	2	no	—
119	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
120	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
122	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
125	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
126	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
127	C₂×D₈×C₂₃	C₂³	1	2	yes	—
128	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
129	C₂×D₈×C₂₃	C₂³	1	2	yes	—
130	C₂×D₈×C₂₃	C₂³	1	2	yes	—
131	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
135	C₂₃×C₄⋊Q₈	—	2	2	no	—
136	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₂₃×#127	C₂³	1	2	yes	—
139	C₂₃×#127	C₂³	1	2	yes	—
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×#125	—	2	2	no	—
145	C₂₃×#125	C₂³	1	2	yes	—
146	C₂₃×#125	C₂³	1	2	yes	—
147	C₂₃×#124	—	2	2	no	—
148	C₂₃×#124	—	2	2	no	—
149	C₂₃×#124	—	2	2	no	—
150	C₂₃×#124	—	2	2	no	—
151	C₂₃×#124	C₂³	1	2	yes	—
152	C₂₃×#124	C₂³	1	2	yes	—
153	C₂₃×#123	—	2	2	no	—
154	C₂₃×#123	—	2	2	no	—
155	C₂₃×#123	—	2	2	no	—
156	C₂₃×#123	—	2	2	no	—
157	C₂₃×#123	—	2	2	no	—
158	C₂₃×#123	—	2	2	no	—
159	C₂₃×#123	—	2	2	no	—
160	C₂₃×#123	—	2	2	no	—
161	C₂₃×#123	—	2	2	no	—
162	C₂₃×C₂²⋊Q₈	—	2	2	no	—
163	C₂₃×C₂²⋊Q₈	—	2	2	no	—
164	C₂₃×C₂²⋊Q₈	—	2	2	no	—
165	C₂₃×C₂²⋊Q₈	—	2	2	no	—
166	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
167	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
168	C₂₃×#121	—	2	2	no	—
169	C₂₃×#121	—	2	2	no	—
170	C₂₃×#121	—	2	2	no	—
171	C₂₃×#121	—	2	2	no	—
172	C₂₃×#121	—	2	2	no	—
173	C₂₃×#121	—	2	2	no	—
174	C₂₃×#121	—	2	2	no	—
175	C₂₃×#121	—	2	2	no	—
176	C₂₃×#121	—	2	2	no	—
177	C₂₃×#121	—	2	2	no	—
178	C₂₃×#121	C₂³	1	2	yes	—
179	C₂₃×#121	C₂³	1	2	yes	—
180	C₂₃×#121	C₂³	1	2	yes	—
181	C₂₃×#121	C₂³	1	2	yes	—
182	C₂₃×#121	C₂³	1	2	yes	—
183	C₂₃×#121	C₂³	1	2	yes	—
184	C₂₃×#120	—	2	2	no	—
185	C₂₃×#120	—	2	2	no	—
186	C₂₃×#120	—	2	2	no	—
187	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
188	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
189	C₄×D₄×C₂₃	—	2	2	no	—
190	C₄×D₄×C₂₃	—	2	2	no	—
191	C₄×D₄×C₂₃	—	2	2	no	—
192	C₄×D₄×C₂₃	—	2	2	no	—
193	C₄×D₄×C₂₃	—	2	2	no	—
194	C₄×D₄×C₂₃	—	2	2	no	—
195	C₄×D₄×C₂₃	—	2	2	no	—
196	C₄×D₄×C₂₃	—	2	2	no	—
197	C₄×D₄×C₂₃	—	2	2	no	—
198	C₄×D₄×C₂₃	—	2	2	no	—
199	C₄×D₄×C₂₃	C₂³	1	2	yes	—
200	C₄×D₄×C₂₃	C₂³	1	2	yes	—
201	C₄×D₄×C₂₃	C₂³	1	2	yes	—
202	C₄×D₄×C₂₃	C₂³	1	2	yes	—
203	C₄×D₄×C₂₃	C₂³	1	2	yes	—
204	C₄×D₄×C₂₃	C₂³	1	2	yes	—
205	C₂₃×#117	—	2	2	no	—
206	C₂₃×#117	—	2	2	no	—
207	C₂₃×#117	—	2	2	no	—
208	C₂₃×#117	D₄	1	2	yes	—
209	C₂₃×#117	D₄	1	2	yes	—
210	C₂₃×#117	C₂³	1	2	yes	—
211	C₂₃×#117	C₂³	1	2	yes	—
212	C₂₃×#117	C₂³	1	2	yes	—
213	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
214	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
215	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
216	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
218	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
219	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
220	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
222	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
224	C₂₃×#107	C₂³	1	1	yes	characteristic
225	C₂₃×#107	C₂³	1	1	yes	characteristic
226	C₂₃×#107	C₂³	1	2	yes	—
227	C₂₃×#107	C₂³	1	1	yes	characteristic
228	C₂₃×#107	C₂³	1	1	yes	characteristic
229	C₂₃×#107	C₂³	1	2	yes	—
230	C₂₃×#107	C₂³	1	2	yes	—
231	C₂₃×#106	C₂³	1	2	yes	—
232	C₂₃×#106	C₂³	1	2	yes	—
233	C₂₃×#106	C₂³	1	2	yes	—
234	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
235	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
236	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
237	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
238	C₂₃×#103	C₂³	1	2	yes	—
239	C₂₃×#103	C₂³	1	2	yes	—
240	C₂₃×#103	C₂³	1	2	yes	—
241	C₂₃×#103	C₂³	1	2	yes	—
242	C₂₃×#102	C₂³	1	2	yes	—
243	C₂₃×#102	C₂³	1	2	yes	—
244	C₂₃×#102	C₂³	1	2	yes	—
245	C₂₃×#102	C₂³	1	2	yes	—
246	C₂₃×#102	C₂³	1	2	yes	—
247	C₂₃×#102	C₂³	1	2	yes	—
248	C₂₃×#102	C₂³	1	2	yes	—
249	C₂₃×#102	C₂³	1	2	yes	—
250	C₂₃×#102	C₂³	1	2	yes	—
251	C₂₃×#102	C₂³	1	2	yes	—
252	C₂₃×#102	C₂³	1	2	yes	—
253	C₂₃×#102	C₂³	1	2	yes	—
254	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
255	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
256	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₂₃×#97	C₂³	1	2	yes	—
259	C₂₃×#97	C₂³	1	2	yes	—
260	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
264	C₂⁴×C₂₃	—	2	2	no	—
265	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
266	#41×C₂₃	—	4	2	no	—
267	#41×C₂₃	—	4	2	no	—
268	#41×C₂₃	—	8	4	no	—
269	#41×C₂₃	—	8	4	no	—
270	C₂×Q₈×C₂₃	—	2	2	no	—
271	C₂×Q₈×C₂₃	—	2	2	no	—
272	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
273	C₂×D₄×C₂₃	—	2	2	no	—
274	C₂×D₄×C₂₃	—	2	2	no	—
275	C₂×D₄×C₂₃	—	2	2	no	—
276	C₂×D₄×C₂₃	—	2	2	no	—
277	C₂×D₄×C₂₃	—	2	2	no	—
278	C₂×D₄×C₂₃	—	2	2	no	—
279	C₂×D₄×C₂₃	—	2	2	no	—
280	C₂×D₄×C₂₃	—	2	2	no	—
281	C₂×D₄×C₂₃	—	2	2	no	—
282	C₂×D₄×C₂₃	—	2	2	no	—
283	C₂×D₄×C₂₃	—	2	2	no	—
284	C₂×D₄×C₂₃	—	2	2	no	—
285	C₂×D₄×C₂₃	—	4	2	no	—
286	C₂×D₄×C₂₃	—	4	2	no	—
287	C₂×D₄×C₂₃	—	8	4	no	—
288	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
289	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
290	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₂₃	—	2	2	no	—
292	C₂²×C₄×C₂₃	—	2	2	no	—
293	C₂²×C₄×C₂₃	—	2	2	no	—
294	C₂²×C₄×C₂₃	—	2	2	no	—
295	C₂²×C₄×C₂₃	—	2	2	no	—
296	C₂²×C₄×C₂₃	—	2	2	no	—
297	C₂²×C₄×C₂₃	—	2	2	no	—
298	C₂²×C₄×C₂₃	—	2	2	no	—
299	C₂²×C₄×C₂₃	—	4	1	no	—
300	C₂²×C₄×C₂₃	—	4	1	no	—
301	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
306	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
309	Q₁₆×C₂₃	—	4	1	no	—
310	SD₁₆×C₂₃	—	4	2	no	—
311	SD₁₆×C₂₃	—	4	2	no	—
312	SD₁₆×C₂₃	—	4	2	no	—
313	D₈×C₂₃	—	4	2	no	—
314	D₈×C₂₃	—	4	1	no	—
315	D₈×C₂₃	—	4	1	no	—
316	D₈×C₂₃	—	4	2	no	—
317	D₈×C₂₃	—	4	2	no	—
318	D₈×C₂₃	—	4	1	no	—
319	C₂×C₈×C₂₃	—	4	1	no	—
320	C₂×C₈×C₂₃	—	4	1	no	—
321	C₂×C₈×C₂₃	—	4	1	no	—
322	C₂×C₈×C₂₃	—	4	1	no	—
323	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
324	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
325	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
326	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
327	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
328	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
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	2	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	C₂×D₄	1	2	yes	—
341	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
342	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
343	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
344	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
346	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
347	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
348	C₂²⋊C₄×C₂₃	—	2	2	no	—
349	C₂²⋊C₄×C₂₃	—	2	2	no	—
350	C₂²⋊C₄×C₂₃	—	2	2	no	—
351	C₂²⋊C₄×C₂₃	—	2	2	no	—
352	C₂²⋊C₄×C₂₃	—	2	2	no	—
353	C₂²⋊C₄×C₂₃	—	2	2	no	—
354	C₂²⋊C₄×C₂₃	—	2	2	no	—
355	C₂²⋊C₄×C₂₃	—	2	2	no	—
356	C₂²⋊C₄×C₂₃	—	2	2	no	—
357	C₂²⋊C₄×C₂₃	—	2	2	no	—
358	C₂²⋊C₄×C₂₃	—	2	2	no	—
359	C₂²⋊C₄×C₂₃	—	2	2	no	—
360	C₂²⋊C₄×C₂₃	—	2	2	no	—
361	C₂²⋊C₄×C₂₃	—	2	2	no	—
362	C₂²⋊C₄×C₂₃	—	2	2	no	—
363	C₂²⋊C₄×C₂₃	—	2	2	no	—
364	C₂²⋊C₄×C₂₃	—	2	2	no	—
365	C₂²⋊C₄×C₂₃	—	2	2	no	—
366	C₂²⋊C₄×C₂₃	—	2	2	no	—
367	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
368	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
369	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
370	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
371	C₄²×C₂₃	—	2	2	no	—
372	C₄²×C₂₃	—	2	2	no	—
373	C₄²×C₂₃	—	2	2	no	—
374	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₂₃	C₂×D₄	1	2	yes	—
376	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
377	C₄²×C₂₃	C₂⁴	1	2	yes	—
378	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
379	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
380	#61000	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
381	C₂³×C₂₃	—	2	2	no	—
382	C₂³×C₂₃	—	2	2	no	—
383	C₂³×C₂₃	—	2	2	no	—
384	C₂³×C₂₃	—	2	2	no	—
385	C₂³×C₂₃	—	4	1	no	—
386	C₂³×C₂₃	—	4	1	no	—
387	C₂³×C₂₃	—	4	4	no	—
388	C₂³×C₂₃	—	8	2	no	—
389	C₂³×C₂₃	—	8	2	no	—
390	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
391	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
392	Q₈×C₂₃	—	2	2	no	—
393	Q₈×C₂₃	—	2	2	no	—
394	Q₈×C₂₃	—	8	2	no	—
395	Q₈×C₂₃	—	8	2	no	—
396	D₄×C₂₃	—	2	2	no	—
397	D₄×C₂₃	—	2	2	no	—
398	D₄×C₂₃	—	2	2	no	—
399	D₄×C₂₃	—	2	2	no	—
400	D₄×C₂₃	—	2	2	no	—
401	D₄×C₂₃	—	2	2	no	—
402	D₄×C₂₃	—	4	4	no	—
403	D₄×C₂₃	—	4	4	no	—
404	D₄×C₂₃	—	4	4	no	—
405	D₄×C₂₃	—	4	4	no	—
406	D₄×C₂₃	—	4	4	no	—
407	D₄×C₂₃	—	8	2	no	—
408	D₄×C₂₃	—	8	2	no	—
409	D₄×C₂₃	—	8	2	no	—
410	D₄×C₂₃	—	8	2	no	—
411	D₄×C₂₃	—	8	2	no	—
412	D₄×C₂₃	—	8	2	no	—
413	D₄×C₂₃	—	8	2	no	—
414	C₂×C₄×C₂₃	—	2	2	no	—
415	C₂×C₄×C₂₃	—	2	2	no	—
416	C₂×C₄×C₂₃	—	2	1	no	—
417	C₂×C₄×C₂₃	—	2	1	no	—
418	C₂×C₄×C₂₃	—	2	2	no	—
419	C₂×C₄×C₂₃	—	2	2	no	—
420	C₂×C₄×C₂₃	—	2	2	no	—
421	C₂×C₄×C₂₃	—	2	2	no	—
422	C₂×C₄×C₂₃	—	2	2	no	—
423	C₂×C₄×C₂₃	—	2	2	no	—
424	C₂×C₄×C₂₃	—	2	2	no	—
425	C₂×C₄×C₂₃	—	4	1	no	—
426	C₂×C₄×C₂₃	—	4	2	no	—
427	C₂×C₄×C₂₃	—	4	1	no	—
428	C₂×C₄×C₂₃	—	4	1	no	—
429	C₂×C₄×C₂₃	—	4	4	no	—
430	C₂×C₄×C₂₃	—	8	2	no	—
431	C₂×C₄×C₂₃	—	8	2	no	—
432	C₂×C₄×C₂₃	—	8	2	no	—
433	C₂×C₄×C₂₃	—	8	2	no	—
434	C₂×C₄×C₂₃	—	8	2	no	—
435	C₂×C₄×C₂₃	—	8	2	no	—
436	C₂×C₄×C₂₃	—	8	2	no	—
437	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
439	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
440	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
444	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
446	C₈×C₂₃	—	2	1	no	—
447	C₈×C₂₃	—	2	1	no	—
448	C₈×C₂₃	—	2	2	no	—
449	C₈×C₂₃	—	2	2	no	—
450	C₈×C₂₃	—	2	1	no	—
451	C₈×C₂₃	—	2	1	no	—
452	#3494	C₂×C₂₃	1	2	yes	complemented
453	#3250	C₂×C₂₃	1	1	yes	characteristic, complemented
454	#3247	C₂×C₂₃	1	2	yes	complemented
455	#3245	C₂×C₂₃	1	1	yes	characteristic, complemented
456	#3243	C₂×C₂₃	1	2	yes	complemented
457	#3241	C₂×C₂₃	1	2	yes	complemented
458	#3224	C₂×C₂₃	1	2	yes	complemented
459	#3220	C₂×C₂₃	1	2	yes	complemented
460	#3191	C₂×C₂₃	1	1	yes	characteristic, complemented
461	#3188	C₂×C₂₃	1	2	yes	complemented
462	#3186	C₂×C₂₃	1	1	yes	characteristic, complemented
463	#3180	C₂×C₂₃	1	2	yes	complemented
464	#3169	C₂×C₂₃	1	1	yes	characteristic, complemented
465	#3168	C₂×C₂₃	1	1	yes	characteristic, complemented
466	#3124	C₂×C₂₃	1	2	yes	complemented
467	#3122	C₂×C₂₃	1	2	yes	complemented
468	#3119	C₂×C₂₃	1	2	yes	complemented
469	#3118	C₂×C₂₃	1	2	yes	complemented
470	C₂×#433	C₂×C₂₃	1	1	yes	characteristic, complemented
471	C₂²×C₂₃	—	2	1	no	—
472	C₂²×C₂₃	—	2	1	no	—
473	C₂²×C₂₃	—	2	2	no	—
474	C₂²×C₂₃	—	2	2	no	—
475	C₂²×C₂₃	—	2	2	no	—
476	C₂²×C₂₃	—	4	2	no	—
477	C₂²×C₂₃	—	4	2	no	—
478	C₂²×C₂₃	—	4	2	no	—
479	C₂²×C₂₃	—	4	2	no	—
480	C₂²×C₂₃	—	4	2	no	—
481	C₂²×C₂₃	—	4	2	no	—
482	C₂²×C₂₃	—	4	2	no	—
483	C₂²×C₂₃	—	4	2	no	—
484	C₂²×C₂₃	—	4	2	no	—
485	C₂²×C₂₃	—	8	2	no	—
486	C₂²×C₂₃	—	16	4	no	—
487	C₂²×C₂₃	#576	1	2	yes	—
488	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
489	C₄×C₂₃	—	2	1	no	—
490	C₄×C₂₃	—	2	2	no	—
491	C₄×C₂₃	—	2	1	no	—
492	C₄×C₂₃	—	2	2	no	—
493	C₄×C₂₃	—	2	1	no	—
494	C₄×C₂₃	—	2	1	no	—
495	C₄×C₂₃	—	2	2	no	—
496	C₄×C₂₃	—	2	1	no	—
497	C₄×C₂₃	—	4	2	no	—
498	C₄×C₂₃	—	4	2	no	—
499	C₄×C₂₃	—	4	2	no	—
500	C₄×C₂₃	—	4	2	no	—
501	C₄×C₂₃	—	4	2	no	—
502	C₄×C₂₃	#585	1	1	yes	characteristic
503	C₄×C₂₃	#585	1	1	yes	characteristic
504	#555	—	2	2	no	—
505	#553	—	2	2	no	—
506	#553	—	2	2	no	—
507	#551	—	2	2	no	—
508	#551	—	2	2	no	—
509	#547	—	2	2	no	—
510	#546	—	2	2	no	—
511	#546	—	2	2	no	—
512	#544	C₂²×C₂₃	1	2	yes	complemented
513	#542	C₂²×C₂₃	1	2	yes	—
514	#542	C₂²×C₂₃	1	2	yes	—
515	#540	C₂²×C₂₃	1	2	yes	—
516	#540	C₂²×C₂₃	1	2	yes	—
517	#535	C₂²×C₂₃	1	2	yes	complemented
518	#532	C₂²×C₂₃	1	2	yes	complemented
519	#532	C₂²×C₂₃	1	2	yes	complemented
520	#529	C₂²×C₂₃	1	2	yes	complemented
521	#529	C₂²×C₂₃	1	2	yes	complemented
522	#525	C₂²×C₂₃	1	2	yes	—
523	C₂×#121	C₂²×C₂₃	1	2	yes	—
524	#520	C₂²×C₂₃	1	2	yes	complemented
525	#518	C₂²×C₂₃	1	2	yes	complemented
526	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
527	#501	C₂²×C₂₃	1	2	yes	complemented
528	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
529	#499	C₂²×C₂₃	1	1	yes	characteristic, complemented
530	#496	C₂²×C₂₃	1	2	yes	complemented
531	#495	C₂²×C₂₃	1	1	yes	characteristic, complemented
532	#493	C₂²×C₂₃	1	1	yes	characteristic, complemented
533	#490	C₂²×C₂₃	1	2	yes	complemented
534	#489	C₂²×C₂₃	1	2	yes	complemented
535	#488	C₂²×C₂₃	1	2	yes	complemented
536	#486	C₂²×C₂₃	1	2	yes	complemented
537	#485	C₂²×C₂₃	1	2	yes	complemented
538	#484	C₂²×C₂₃	1	2	yes	complemented
539	#482	C₂²×C₂₃	1	2	yes	—
540	#482	C₂²×C₂₃	1	2	yes	—
541	#482	C₂²×C₂₃	1	2	yes	complemented
542	#481	C₂²×C₂₃	1	2	yes	complemented
543	#480	C₂²×C₂₃	1	2	yes	—
544	#480	C₂²×C₂₃	1	2	yes	—
545	#479	C₂²×C₂₃	1	2	yes	complemented
546	#478	C₂²×C₂₃	1	2	yes	complemented
547	#478	C₂²×C₂₃	1	2	yes	complemented
548	#478	C₂²×C₂₃	1	2	yes	complemented
549	#477	C₂²×C₂₃	1	2	yes	complemented
550	#476	C₂²×C₂₃	1	2	yes	complemented
551	#474	C₂²×C₂₃	1	2	yes	complemented
552	#474	C₂²×C₂₃	1	2	yes	complemented
553	#467	C₂²×C₂₃	1	1	yes	characteristic, complemented
554	#466	C₂²×C₂₃	1	1	yes	characteristic
555	#466	C₂²×C₂₃	1	1	yes	characteristic
556	#466	C₂²×C₂₃	1	2	yes	—
557	#466	C₂²×C₂₃	1	2	yes	complemented
558	#466	C₂²×C₂₃	1	1	yes	characteristic, complemented
559	#466	C₂²×C₂₃	1	2	yes	complemented
560	#465	C₂²×C₂₃	1	2	yes	complemented
561	#465	C₂²×C₂₃	1	2	yes	complemented
562	#465	C₂²×C₂₃	1	2	yes	complemented
563	#464	C₂²×C₂₃	1	2	yes	complemented
564	#463	C₂²×C₂₃	1	2	yes	complemented
565	#463	C₂²×C₂₃	1	2	yes	complemented
566	#463	C₂²×C₂₃	1	2	yes	complemented
567	#460	C₂²×C₂₃	1	2	yes	complemented
568	#459	C₂²×C₂₃	1	2	yes	complemented
569	#459	C₂²×C₂₃	1	2	yes	complemented
570	#459	C₂²×C₂₃	1	2	yes	complemented
571	#452	C₂²×C₂₃	1	2	yes	complemented
572	#450	C₂²×C₂₃	1	2	yes	complemented
573	#449	C₂²×C₂₃	1	2	yes	—
574	#449	C₂²×C₂₃	1	2	yes	—
575	#449	C₂²×C₂₃	1	2	yes	complemented
576	#447	C₂²×C₂₃	1	2	yes	—
577	#447	C₂²×C₂₃	1	2	yes	—
578	#447	C₂²×C₂₃	1	2	yes	complemented
579	#442	C₂²×C₂₃	1	2	yes	complemented
580	#442	C₂²×C₂₃	1	2	yes	complemented
581	#440	C₂²×C₂₃	1	2	yes	complemented
582	#440	C₂²×C₂₃	1	2	yes	complemented
583	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
584	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
585	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
586	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
587	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
588	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
589	#433	C₂²×C₂₃	1	2	yes	complemented
590	#433	C₂²×C₂₃	1	2	yes	complemented
591	#433	C₂²×C₂₃	1	2	yes	complemented
592	#433	C₂²×C₂₃	1	2	yes	complemented
593	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
594	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
595	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
596	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
597	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
598	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
599	C₂×C₂₃	—	2	2	no	—
600	C₂×C₂₃	—	4	2	no	—
601	C₂×C₂₃	—	8	2	no	—
602	C₂×C₂₃	—	8	2	no	—
603	C₂×C₂₃	—	8	2	no	—
604	C₂×C₂₃	#3449	1	1	yes	characteristic
605	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
606	C₂×C₂₃	#3584	1	1	yes	characteristic
607	C₂×#41	—	2	2	no	—
608	C₂×#41	—	2	2	no	—
609	C₂×#41	C₂³×C₂₃	1	2	yes	—
610	C₂²×D₄	—	2	2	no	—
611	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
612	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
613	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
614	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
615	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
616	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
617	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
618	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
619	C₂×D₈	C₂³×C₂₃	1	2	yes	—
620	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
621	C₂×D₈	C₂³×C₂₃	1	2	yes	—
622	C₂×D₈	C₂³×C₂₃	1	2	yes	—
623	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
624	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
625	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
626	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
627	C₄⋊Q₈	—	2	2	no	—
628	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
629	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
630	#127	C₂³×C₂₃	1	2	yes	—
631	#127	C₂³×C₂₃	1	2	yes	—
632	#126	—	2	2	no	—
633	#126	—	2	2	no	—
634	#126	—	2	2	no	—
635	#126	—	2	2	no	—
636	#125	—	2	2	no	—
637	#125	C₂³×C₂₃	1	2	yes	—
638	#125	C₂³×C₂₃	1	2	yes	—
639	#124	—	2	2	no	—
640	#124	—	2	2	no	—
641	#124	—	2	2	no	—
642	#124	—	2	2	no	—
643	#124	C₂³×C₂₃	1	2	yes	—
644	#124	C₂³×C₂₃	1	2	yes	—
645	#123	—	2	2	no	—
646	#123	—	2	2	no	—
647	#123	—	2	2	no	—
648	#123	—	2	2	no	—
649	#123	—	2	2	no	—
650	#123	—	2	2	no	—
651	#123	—	2	2	no	—
652	#123	—	2	2	no	—
653	#123	—	2	2	no	—
654	C₂²⋊Q₈	—	2	2	no	—
655	C₂²⋊Q₈	—	2	2	no	—
656	C₂²⋊Q₈	—	2	2	no	—
657	C₂²⋊Q₈	—	2	2	no	—
658	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
659	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
660	#121	—	2	2	no	—
661	#121	—	2	2	no	—
662	#121	—	2	2	no	—
663	#121	—	2	2	no	—
664	#121	—	2	2	no	—
665	#121	—	2	2	no	—
666	#121	—	2	2	no	—
667	#121	—	2	2	no	—
668	#121	—	2	2	no	—
669	#121	—	2	2	no	—
670	#121	C₂³×C₂₃	1	2	yes	—
671	#121	C₂³×C₂₃	1	2	yes	—
672	#121	C₂³×C₂₃	1	2	yes	—
673	#121	C₂³×C₂₃	1	2	yes	—
674	#121	C₂³×C₂₃	1	2	yes	—
675	#121	C₂³×C₂₃	1	2	yes	—
676	#120	—	2	2	no	—
677	#120	—	2	2	no	—
678	#120	—	2	2	no	—
679	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
680	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
681	C₄×D₄	—	2	2	no	—
682	C₄×D₄	—	2	2	no	—
683	C₄×D₄	—	2	2	no	—
684	C₄×D₄	—	2	2	no	—
685	C₄×D₄	—	2	2	no	—
686	C₄×D₄	—	2	2	no	—
687	C₄×D₄	—	2	2	no	—
688	C₄×D₄	—	2	2	no	—
689	C₄×D₄	—	2	2	no	—
690	C₄×D₄	—	2	2	no	—
691	C₄×D₄	C₂³×C₂₃	1	2	yes	—
692	C₄×D₄	C₂³×C₂₃	1	2	yes	—
693	C₄×D₄	C₂³×C₂₃	1	2	yes	—
694	C₄×D₄	C₂³×C₂₃	1	2	yes	—
695	C₄×D₄	C₂³×C₂₃	1	2	yes	—
696	C₄×D₄	C₂³×C₂₃	1	2	yes	—
697	#117	—	2	2	no	—
698	#117	—	2	2	no	—
699	#117	—	2	2	no	—
700	#117	D₄×C₂₃	1	2	yes	—
701	#117	D₄×C₂₃	1	2	yes	—
702	#117	C₂³×C₂₃	1	2	yes	—
703	#117	C₂³×C₂₃	1	2	yes	—
704	#117	C₂³×C₂₃	1	2	yes	—
705	C₂×C₄⋊C₄	—	2	2	no	—
706	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
707	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
708	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
709	C₂×C₂²⋊C₄	—	2	2	no	—
710	C₂×C₂²⋊C₄	—	2	2	no	—
711	C₂×C₂²⋊C₄	—	2	2	no	—
712	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
713	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
714	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
715	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
716	#107	C₂³×C₂₃	1	1	yes	characteristic
717	#107	C₂³×C₂₃	1	1	yes	characteristic
718	#107	C₂³×C₂₃	1	2	yes	—
719	#107	C₂³×C₂₃	1	1	yes	characteristic
720	#107	C₂³×C₂₃	1	1	yes	characteristic
721	#107	C₂³×C₂₃	1	2	yes	—
722	#107	C₂³×C₂₃	1	2	yes	—
723	#106	C₂³×C₂₃	1	2	yes	—
724	#106	C₂³×C₂₃	1	2	yes	—
725	#106	C₂³×C₂₃	1	2	yes	—
726	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
727	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
728	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
729	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
730	#103	C₂³×C₂₃	1	2	yes	—
731	#103	C₂³×C₂₃	1	2	yes	—
732	#103	C₂³×C₂₃	1	2	yes	—
733	#103	C₂³×C₂₃	1	2	yes	—
734	#102	C₂³×C₂₃	1	2	yes	—
735	#102	C₂³×C₂₃	1	2	yes	—
736	#102	C₂³×C₂₃	1	2	yes	—
737	#102	C₂³×C₂₃	1	2	yes	—
738	#102	C₂³×C₂₃	1	2	yes	—
739	#102	C₂³×C₂₃	1	2	yes	—
740	#102	C₂³×C₂₃	1	2	yes	—
741	#102	C₂³×C₂₃	1	2	yes	—
742	#102	C₂³×C₂₃	1	2	yes	—
743	#102	C₂³×C₂₃	1	2	yes	—
744	#102	C₂³×C₂₃	1	2	yes	—
745	#102	C₂³×C₂₃	1	2	yes	—
746	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
747	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
748	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
749	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
750	#97	C₂³×C₂₃	1	2	yes	—
751	#97	C₂³×C₂₃	1	2	yes	—
752	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
753	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
754	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
755	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
756	C₂₃	#61000	1	1	yes	characteristic, direct product factor, Sylow
757	C₂⁴	—	2	2	no	—
758	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
759	#41	—	4	2	no	—
760	#41	—	4	2	no	—
761	#41	—	8	4	no	—
762	#41	—	8	4	no	—
763	C₂×Q₈	—	2	2	no	—
764	C₂×Q₈	—	2	2	no	—
765	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	2	no	—
775	C₂×D₄	—	2	2	no	—
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	4	2	no	—
779	C₂×D₄	—	4	2	no	—
780	C₂×D₄	—	8	4	no	—
781	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
782	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
783	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	4	1	no	—
793	C₂²×C₄	—	4	1	no	—
794	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
795	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
796	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
797	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
798	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
799	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
802	Q₁₆	—	4	1	no	—
803	SD₁₆	—	4	2	no	—
804	SD₁₆	—	4	2	no	—
805	SD₁₆	—	4	2	no	—
806	D₈	—	4	2	no	—
807	D₈	—	4	1	no	—
808	D₈	—	4	1	no	—
809	D₈	—	4	2	no	—
810	D₈	—	4	2	no	—
811	D₈	—	4	1	no	—
812	C₂×C₈	—	4	1	no	—
813	C₂×C₈	—	4	1	no	—
814	C₂×C₈	—	4	1	no	—
815	C₂×C₈	—	4	1	no	—
816	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
817	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
818	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
819	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
820	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
821	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
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	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
834	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
835	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
836	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
837	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
838	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
839	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
840	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
861	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
862	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
863	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	2	no	—
867	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
868	C₄²	C₂×D₄×C₂₃	1	2	yes	—
869	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
870	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
871	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
872	C₄²	C₂⁴×C₂₃	1	2	yes	—
873	C₂³	—	2	2	no	—
874	C₂³	—	2	2	no	—
875	C₂³	—	2	2	no	—
876	C₂³	—	2	2	no	—
877	C₂³	—	4	1	no	—
878	C₂³	—	4	1	no	—
879	C₂³	—	4	4	no	—
880	C₂³	—	8	2	no	—
881	C₂³	—	8	2	no	—
882	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
883	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
884	Q₈	—	2	2	no	—
885	Q₈	—	2	2	no	—
886	Q₈	—	8	2	no	—
887	Q₈	—	8	2	no	—
888	D₄	—	2	2	no	—
889	D₄	—	2	2	no	—
890	D₄	—	2	2	no	—
891	D₄	—	2	2	no	—
892	D₄	—	2	2	no	—
893	D₄	—	2	2	no	—
894	D₄	—	4	4	no	—
895	D₄	—	4	4	no	—
896	D₄	—	4	4	no	—
897	D₄	—	4	4	no	—
898	D₄	—	4	4	no	—
899	D₄	—	8	2	no	—
900	D₄	—	8	2	no	—
901	D₄	—	8	2	no	—
902	D₄	—	8	2	no	—
903	D₄	—	8	2	no	—
904	D₄	—	8	2	no	—
905	D₄	—	8	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	2	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	4	4	no	—
922	C₂×C₄	—	8	2	no	—
923	C₂×C₄	—	8	2	no	—
924	C₂×C₄	—	8	2	no	—
925	C₂×C₄	—	8	2	no	—
926	C₂×C₄	—	8	2	no	—
927	C₂×C₄	—	8	2	no	—
928	C₂×C₄	—	8	2	no	—
929	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
930	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
931	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
932	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
933	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
934	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
935	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
936	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
937	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
938	C₈	—	2	1	no	—
939	C₈	—	2	1	no	—
940	C₈	—	2	2	no	—
941	C₈	—	2	2	no	—
942	C₈	—	2	1	no	—
943	C₈	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	2	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	8	2	no	—
959	C₂²	—	16	4	no	—
960	C₂²	C₂₃×#576	1	2	yes	—
961	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
962	C₄	—	2	2	no	—
963	C₄	—	2	1	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	2	no	—
966	C₄	—	2	1	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	2	no	—
969	C₄	—	2	1	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	2	no	—
975	C₄	C₂₃×#585	1	1	yes	characteristic
976	C₄	C₂₃×#585	1	1	yes	characteristic
977	C₂	—	2	2	no	—
978	C₂	—	4	2	no	—
979	C₂	—	8	2	no	—
980	C₂	—	8	2	no	—
981	C₂	—	8	2	no	—
982	C₂	C₂₃×#3449	1	1	yes	characteristic
983	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
984	C₂	C₂₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3494	C₂	semidirect
2. C₂₃×#3250	C₂	semidirect
3. C₂₃×#3247	C₂	semidirect
4. C₂₃×#3245	C₂	semidirect
5. C₂₃×#3243	C₂	semidirect
6. C₂₃×#3241	C₂	semidirect
7. C₂₃×#3224	C₂	semidirect
8. C₂₃×#3220	C₂	semidirect
9. C₂₃×#3191	C₂	semidirect
10. C₂₃×#3188	C₂	semidirect
11. C₂₃×#3186	C₂	semidirect
12. C₂₃×#3180	C₂	semidirect
13. C₂₃×#3169	C₂	semidirect
14. C₂₃×#3168	C₂	semidirect
15. C₂₃×#3124	C₂	semidirect
16. C₂₃×#3122	C₂	semidirect
17. C₂₃×#3119	C₂	semidirect
18. C₂₃×#3118	C₂	semidirect
19. C₂×C₂₃×#433	C₂	semidirect
28. C₂₃×#544	C₂²	semidirect
33. C₂₃×#535	C₂²	semidirect
34. C₂₃×#532	C₂²	semidirect
35. C₂₃×#532	C₂²	semidirect
36. C₂₃×#529	C₂²	semidirect
37. C₂₃×#529	C₂²	semidirect
40. C₂₃×#520	C₂²	semidirect
41. C₂₃×#518	C₂²	semidirect
43. C₂₃×#501	C₂²	semidirect
44. C₂₃×#500	C₂²	semidirect
45. C₂₃×#499	C₂²	semidirect
46. C₂₃×#496	C₂²	semidirect
47. C₂₃×#495	C₂²	semidirect
48. C₂₃×#493	C₂²	semidirect
49. C₂₃×#490	C₂²	semidirect
50. C₂₃×#489	C₂²	semidirect
51. C₂₃×#488	C₂²	semidirect
52. C₂₃×#486	C₂²	semidirect
53. C₂₃×#485	C₂²	semidirect
54. C₂₃×#484	C₂²	semidirect
57. C₂₃×#482	C₂²	semidirect
58. C₂₃×#481	C₂²	semidirect
61. C₂₃×#479	C₂²	semidirect
62. C₂₃×#478	C₂²	semidirect
63. C₂₃×#478	C₂²	semidirect
64. C₂₃×#478	C₂²	semidirect
65. C₂₃×#477	C₂²	semidirect
66. C₂₃×#476	C₂²	semidirect
67. C₂₃×#474	C₂²	semidirect
68. C₂₃×#474	C₂²	semidirect
69. C₂₃×#467	C₂²	semidirect
73. C₂₃×#466	C₂²	semidirect
74. C₂₃×#466	C₂²	semidirect
75. C₂₃×#466	C₂²	semidirect
76. C₂₃×#465	C₂²	semidirect
77. C₂₃×#465	C₂²	semidirect
78. C₂₃×#465	C₂²	semidirect
79. C₂₃×#464	C₂²	semidirect
80. C₂₃×#463	C₂²	semidirect
81. C₂₃×#463	C₂²	semidirect
82. C₂₃×#463	C₂²	semidirect
83. C₂₃×#460	C₂²	semidirect
84. C₂₃×#459	C₂²	semidirect
85. C₂₃×#459	C₂²	semidirect
86. C₂₃×#459	C₂²	semidirect
87. C₂₃×#452	C₂²	semidirect
88. C₂₃×#450	C₂²	semidirect
91. C₂₃×#449	C₂²	semidirect
94. C₂₃×#447	C₂²	semidirect
95. C₂₃×#442	C₂²	semidirect
96. C₂₃×#442	C₂²	semidirect
97. C₂₃×#440	C₂²	semidirect
98. C₂₃×#440	C₂²	semidirect
99. C₄×Q₁₆×C₂₃	C₂²	semidirect
100. C₄×SD₁₆×C₂₃	C₂²	semidirect
101. C₄×D₈×C₂₃	C₂²	semidirect
102. C₄×D₈×C₂₃	C₂²	semidirect
103. C₄×D₈×C₂₃	C₂²	semidirect
104. C₄×D₈×C₂₃	C₂²	semidirect
105. C₂₃×#433	C₂²	semidirect
106. C₂₃×#433	C₂²	semidirect
107. C₂₃×#433	C₂²	semidirect
108. C₂₃×#433	C₂²	semidirect
109. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
110. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
113. C₂×C₂₃×#97	C₂²	semidirect
114. C₂×C₄×C₈×C₂₃	C₂²	semidirect
380. #61000	C₂₃	direct (N × H)
452. #3494	C₂×C₂₃	semidirect
453. #3250	C₂×C₂₃	semidirect
454. #3247	C₂×C₂₃	semidirect
455. #3245	C₂×C₂₃	semidirect
456. #3243	C₂×C₂₃	semidirect
457. #3241	C₂×C₂₃	semidirect
458. #3224	C₂×C₂₃	semidirect
459. #3220	C₂×C₂₃	semidirect
460. #3191	C₂×C₂₃	semidirect
461. #3188	C₂×C₂₃	semidirect
462. #3186	C₂×C₂₃	semidirect
463. #3180	C₂×C₂₃	semidirect
464. #3169	C₂×C₂₃	semidirect
465. #3168	C₂×C₂₃	semidirect
466. #3124	C₂×C₂₃	semidirect
467. #3122	C₂×C₂₃	semidirect
468. #3119	C₂×C₂₃	semidirect
469. #3118	C₂×C₂₃	semidirect
470. C₂×#433	C₂×C₂₃	semidirect
512. #544	C₂²×C₂₃	semidirect
517. #535	C₂²×C₂₃	semidirect
518. #532	C₂²×C₂₃	semidirect
519. #532	C₂²×C₂₃	semidirect
520. #529	C₂²×C₂₃	semidirect
521. #529	C₂²×C₂₃	semidirect
524. #520	C₂²×C₂₃	semidirect
525. #518	C₂²×C₂₃	semidirect
527. #501	C₂²×C₂₃	semidirect
528. #500	C₂²×C₂₃	semidirect
529. #499	C₂²×C₂₃	semidirect
530. #496	C₂²×C₂₃	semidirect
531. #495	C₂²×C₂₃	semidirect
532. #493	C₂²×C₂₃	semidirect
533. #490	C₂²×C₂₃	semidirect
534. #489	C₂²×C₂₃	semidirect
535. #488	C₂²×C₂₃	semidirect
536. #486	C₂²×C₂₃	semidirect
537. #485	C₂²×C₂₃	semidirect
538. #484	C₂²×C₂₃	semidirect
541. #482	C₂²×C₂₃	semidirect
542. #481	C₂²×C₂₃	semidirect
545. #479	C₂²×C₂₃	semidirect
546. #478	C₂²×C₂₃	semidirect
547. #478	C₂²×C₂₃	semidirect
548. #478	C₂²×C₂₃	semidirect
549. #477	C₂²×C₂₃	semidirect
550. #476	C₂²×C₂₃	semidirect
551. #474	C₂²×C₂₃	semidirect
552. #474	C₂²×C₂₃	semidirect
553. #467	C₂²×C₂₃	semidirect
557. #466	C₂²×C₂₃	semidirect
558. #466	C₂²×C₂₃	semidirect
559. #466	C₂²×C₂₃	semidirect
560. #465	C₂²×C₂₃	semidirect
561. #465	C₂²×C₂₃	semidirect
562. #465	C₂²×C₂₃	semidirect
563. #464	C₂²×C₂₃	semidirect
564. #463	C₂²×C₂₃	semidirect
565. #463	C₂²×C₂₃	semidirect
566. #463	C₂²×C₂₃	semidirect
567. #460	C₂²×C₂₃	semidirect
568. #459	C₂²×C₂₃	semidirect
569. #459	C₂²×C₂₃	semidirect
570. #459	C₂²×C₂₃	semidirect
571. #452	C₂²×C₂₃	semidirect
572. #450	C₂²×C₂₃	semidirect
575. #449	C₂²×C₂₃	semidirect
578. #447	C₂²×C₂₃	semidirect
579. #442	C₂²×C₂₃	semidirect
580. #442	C₂²×C₂₃	semidirect
581. #440	C₂²×C₂₃	semidirect
582. #440	C₂²×C₂₃	semidirect
583. C₄×Q₁₆	C₂²×C₂₃	semidirect
584. C₄×SD₁₆	C₂²×C₂₃	semidirect
585. C₄×D₈	C₂²×C₂₃	semidirect
586. C₄×D₈	C₂²×C₂₃	semidirect
587. C₄×D₈	C₂²×C₂₃	semidirect
588. C₄×D₈	C₂²×C₂₃	semidirect
589. #433	C₂²×C₂₃	semidirect
590. #433	C₂²×C₂₃	semidirect
591. #433	C₂²×C₂₃	semidirect
592. #433	C₂²×C₂₃	semidirect
593. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
594. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
597. C₂×#97	C₂²×C₂₃	semidirect
598. C₂×C₄×C₈	C₂²×C₂₃	semidirect
756. C₂₃	#61000	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×#3494	2
C₂₃×#3250	2
C₂₃×#3247	2
C₂₃×#3245	2
C₂₃×#3243	2
C₂₃×#3241	2
C₂₃×#3224	2
C₂₃×#3220	2
C₂₃×#3191	2
C₂₃×#3188	2
C₂₃×#3186	2
C₂₃×#3180	2
C₂₃×#3169	2
C₂₃×#3168	2
C₂₃×#3124	2
C₂₃×#3122	2
C₂₃×#3119	2
C₂₃×#3118	2
C₂×C₂₃×#433	2
#61000	23

Subgroups — C23×#61000 #19208626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61000 #19208626