Subgroups — C₂₃×#60925 #19208551

Order 5888.

1748 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3461	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3261	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3258	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3255	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3252	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3249	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3248	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3082	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3063	C₂	1	2	yes	maximal
13	C₂₃×#3059	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3044	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×#137	C₂²	1	2	yes	—
19	C₂²×Q₁₆×C₂₃	C₂²	1	2	yes	—
20	C₂×C₂₃×#131	C₂²	1	2	yes	—
21	C₂₃×#557	—	2	1	no	—
22	C₂₃×#557	—	2	1	no	—
23	C₂₃×#556	—	2	1	no	—
24	C₂₃×#556	—	2	1	no	—
25	C₂₃×#552	—	2	2	no	—
26	C₂₃×#552	—	2	2	no	—
27	C₂₃×#544	C₂²	1	1	yes	characteristic
28	C₂₃×#542	—	2	1	no	—
29	C₂₃×#542	C₂²	1	2	yes	—
30	C₂₃×#541	—	2	1	no	—
31	C₂₃×#541	C₂²	1	2	yes	—
32	C₂₃×#541	C₂²	1	4	yes	—
33	C₂₃×#539	—	2	2	no	—
34	C₂₃×#537	C₂²	1	1	yes	characteristic
35	C₂₃×#536	C₂²	1	1	yes	characteristic
36	C₂₃×#536	C₂²	1	1	yes	characteristic
37	C₂₃×#536	C₂²	1	2	yes	—
38	C₂₃×#533	—	2	1	no	—
39	C₂₃×#533	C₂²	1	2	yes	—
40	C₂₃×#533	C₂²	1	2	yes	—
41	C₂₃×#533	C₂²	1	2	yes	—
42	C₂₃×#533	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₂₃×#529	—	2	2	no	—
45	C₂₃×#529	—	2	1	no	—
46	C₂₃×#529	C₂²	1	2	yes	—
47	C₂₃×#519	C₂²	1	2	yes	—
48	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
49	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
51	C₂₃×#479	C₂²	1	4	yes	—
52	C₂₃×#479	C₂²	1	4	yes	—
53	C₂₃×#479	C₂²	1	4	yes	—
54	C₂₃×#479	C₂²	1	2	yes	—
55	C₂₃×#478	C₂²	1	2	yes	—
56	C₂₃×#477	C₂²	1	1	yes	characteristic
57	C₂₃×#477	C₂²	1	2	yes	—
58	C₂₃×#477	C₂²	1	4	yes	—
59	C₂₃×#476	C₂²	1	1	yes	characteristic
60	C₂₃×#475	C₂²	1	2	yes	—
61	C₂₃×#475	C₂²	1	1	yes	characteristic
62	C₂₃×#475	C₂²	1	4	yes	—
63	C₂₃×#474	C₂²	1	1	yes	characteristic
64	C₂₃×#470	C₂²	1	4	yes	—
65	C₂₃×#470	C₂²	1	4	yes	—
66	C₂₃×#470	C₂²	1	4	yes	—
67	C₂₃×#468	C₂²	1	4	yes	—
68	C₂₃×#467	C₂²	1	4	yes	—
69	C₂₃×#467	C₂²	1	4	yes	—
70	C₂₃×#467	C₂²	1	4	yes	—
71	C₂₃×#465	C₂²	1	4	yes	—
72	C₂₃×#464	C₂²	1	4	yes	—
73	C₂₃×#464	C₂²	1	4	yes	—
74	C₂₃×#462	C₂²	1	2	yes	—
75	C₂₃×#462	C₂²	1	2	yes	—
76	C₂₃×#462	C₂²	1	4	yes	—
77	C₂₃×#462	C₂²	1	2	yes	—
78	C₂₃×#462	C₂²	1	4	yes	—
79	C₂₃×#462	C₂²	1	4	yes	—
80	C₂₃×#462	C₂²	1	2	yes	—
81	C₂₃×#461	C₂²	1	2	yes	—
82	C₂₃×#461	C₂²	1	2	yes	—
83	C₂₃×#428	C₂²	1	2	yes	—
84	C₂₃×#427	C₂²	1	2	yes	—
85	C₂₃×#424	C₂²	1	4	yes	—
86	C₂₃×#424	C₂²	1	2	yes	—
87	C₂₃×#423	C₂²	1	2	yes	—
88	C₂₃×#423	C₂²	1	1	yes	characteristic
89	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
90	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
91	C₂₃×#419	C₂²	1	2	yes	—
92	C₂₃×#419	C₂²	1	2	yes	—
93	C₂₃×#416	C₂²	1	2	yes	—
94	C₂×C₂₃×#103	C₂²	1	2	yes	—
95	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
96	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
99	C₂₃×#137	—	4	4	no	—
100	C₂×Q₁₆×C₂₃	—	4	4	no	—
101	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
102	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
103	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
105	C₂₃×#131	—	4	4	no	—
106	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
107	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
108	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
109	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
110	C₂₃×C₄⋊Q₈	—	2	2	no	—
111	C₂₃×C₄⋊Q₈	—	2	1	no	—
112	C₂₃×C₄⋊Q₈	—	2	1	no	—
113	C₂₃×C₄⋊Q₈	—	2	1	no	—
114	C₂₃×C₄⋊Q₈	—	2	1	no	—
115	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₂₃×#126	—	2	2	no	—
122	C₂₃×#126	—	2	4	no	—
123	C₂₃×#126	—	2	4	no	—
124	C₂₃×#126	—	2	2	no	—
125	C₂₃×#126	—	2	2	no	—
126	C₂₃×#126	—	2	2	no	—
127	C₂₃×#125	—	2	4	no	—
128	C₂₃×#125	—	2	4	no	—
129	C₂₃×#125	—	2	2	no	—
130	C₂₃×#125	—	2	1	no	—
131	C₂₃×#125	—	2	2	no	—
132	C₂₃×#125	—	2	2	no	—
133	C₂₃×#125	—	2	2	no	—
134	C₂₃×#125	—	2	2	no	—
135	C₂₃×#125	C₂³	1	2	yes	—
136	C₂₃×#125	C₂³	1	2	yes	—
137	C₂₃×#124	—	2	2	no	—
138	C₂₃×#124	—	2	1	no	—
139	C₂₃×#124	—	2	2	no	—
140	C₂₃×#124	C₂³	1	2	yes	—
141	C₂₃×#123	—	2	4	no	—
142	C₂₃×#123	—	2	2	no	—
143	C₂₃×#123	—	2	2	no	—
144	C₂₃×#123	—	2	2	no	—
145	C₂₃×#123	—	2	2	no	—
146	C₂₃×C₂²⋊Q₈	—	2	1	no	—
147	C₂₃×C₂²⋊Q₈	—	2	1	no	—
148	C₂₃×C₂²⋊Q₈	—	2	1	no	—
149	C₂₃×C₂²⋊Q₈	—	2	2	no	—
150	C₂₃×C₂²⋊Q₈	—	2	2	no	—
151	C₂₃×C₂²⋊Q₈	—	2	2	no	—
152	C₂₃×C₂²⋊Q₈	—	2	1	no	—
153	C₂₃×C₂²⋊Q₈	—	2	1	no	—
154	C₂₃×C₂²⋊Q₈	—	2	2	no	—
155	C₂₃×C₂²⋊Q₈	—	2	2	no	—
156	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
157	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
158	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
159	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
160	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
161	C₂₃×#121	—	2	2	no	—
162	C₂₃×#121	—	2	1	no	—
163	C₂₃×#121	C₂³	1	2	yes	—
164	C₄×Q₈×C₂₃	—	2	2	no	—
165	C₄×Q₈×C₂₃	—	2	2	no	—
166	C₄×Q₈×C₂₃	—	2	2	no	—
167	C₄×Q₈×C₂₃	—	2	2	no	—
168	C₄×Q₈×C₂₃	—	2	1	no	—
169	C₄×Q₈×C₂₃	—	2	1	no	—
170	C₄×Q₈×C₂₃	—	2	1	no	—
171	C₄×Q₈×C₂₃	—	2	1	no	—
172	C₄×Q₈×C₂₃	—	2	2	no	—
173	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
174	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
175	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
176	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
177	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
178	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
179	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
180	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
181	C₄×D₄×C₂₃	—	2	1	no	—
182	C₄×D₄×C₂₃	—	2	1	no	—
183	C₄×D₄×C₂₃	—	2	2	no	—
184	C₄×D₄×C₂₃	D₄	1	2	yes	—
185	C₄×D₄×C₂₃	D₄	1	2	yes	—
186	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
187	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
188	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
190	C₂₃×#117	—	2	2	no	—
191	C₂₃×#117	—	2	2	no	—
192	C₂₃×#117	—	2	2	no	—
193	C₂₃×#117	—	2	4	no	—
194	C₂₃×#117	—	2	1	no	—
195	C₂₃×#117	—	2	2	no	—
196	C₂₃×#117	C₂³	1	2	yes	—
197	C₂₃×#117	C₂³	1	1	yes	characteristic
198	C₂₃×#117	C₂³	1	1	yes	characteristic
199	C₂₃×#117	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
201	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
202	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
203	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₂₃	—	2	1	no	—
205	C₂×C₄²×C₂₃	—	2	1	no	—
206	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
208	C₂₃×#107	C₂³	1	2	yes	—
209	C₂₃×#107	C₂³	1	2	yes	—
210	C₂₃×#107	C₂³	1	4	yes	—
211	C₂₃×#106	C₂³	1	2	yes	—
212	C₂₃×#106	C₂³	1	2	yes	—
213	C₂₃×#106	C₂³	1	4	yes	—
214	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
216	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
217	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
218	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
219	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
220	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
221	C₂₃×#103	C₂³	1	4	yes	—
222	C₂₃×#103	C₂³	1	4	yes	—
223	C₂₃×#103	C₂³	1	2	yes	—
224	C₂₃×#103	C₂³	1	2	yes	—
225	C₂₃×#103	C₂³	1	4	yes	—
226	C₂₃×#103	C₂³	1	4	yes	—
227	C₂₃×#103	C₂³	1	4	yes	—
228	C₂₃×#103	C₂³	1	4	yes	—
229	C₂₃×#102	C₂³	1	2	yes	—
230	C₂₃×#102	C₂³	1	2	yes	—
231	#41×C₂₃	—	2	2	no	—
232	#41×C₂₃	—	2	2	no	—
233	#41×C₂₃	—	2	2	no	—
234	#41×C₂₃	—	2	2	no	—
235	C₂×Q₈×C₂₃	—	2	1	no	—
236	C₂×Q₈×C₂₃	—	2	1	no	—
237	C₂×Q₈×C₂₃	—	2	1	no	—
238	C₂×Q₈×C₂₃	—	2	2	no	—
239	C₂×Q₈×C₂₃	—	2	2	no	—
240	C₂×Q₈×C₂₃	—	2	2	no	—
241	C₂×Q₈×C₂₃	—	2	4	no	—
242	C₂×Q₈×C₂₃	—	2	2	no	—
243	C₂×Q₈×C₂₃	—	2	4	no	—
244	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
247	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₂₃	—	2	1	no	—
249	C₂×D₄×C₂₃	—	2	2	no	—
250	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
251	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
252	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₂₃	—	2	1	no	—
254	C₂²×C₄×C₂₃	—	2	2	no	—
255	C₂²×C₄×C₂₃	—	2	1	no	—
256	C₂²×C₄×C₂₃	—	2	1	no	—
257	C₂²×C₄×C₂₃	—	2	1	no	—
258	C₂²×C₄×C₂₃	—	2	1	no	—
259	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
265	Q₁₆×C₂₃	—	4	4	no	—
266	Q₁₆×C₂₃	—	4	4	no	—
267	Q₁₆×C₂₃	—	4	4	no	—
268	SD₁₆×C₂₃	—	4	4	no	—
269	M₁₆×C₂₃	—	2	4	no	—
270	M₁₆×C₂₃	—	4	4	no	—
271	C₂×C₈×C₂₃	—	2	4	no	—
272	C₂×C₈×C₂₃	—	4	4	no	—
273	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
274	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
275	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
276	C₄⋊C₄×C₂₃	—	2	2	no	—
277	C₄⋊C₄×C₂₃	—	2	2	no	—
278	C₄⋊C₄×C₂₃	—	2	2	no	—
279	C₄⋊C₄×C₂₃	—	2	2	no	—
280	C₄⋊C₄×C₂₃	—	2	2	no	—
281	C₄⋊C₄×C₂₃	—	2	2	no	—
282	C₄⋊C₄×C₂₃	—	2	1	no	—
283	C₄⋊C₄×C₂₃	—	2	1	no	—
284	C₄⋊C₄×C₂₃	—	2	1	no	—
285	C₄⋊C₄×C₂₃	—	2	1	no	—
286	C₄⋊C₄×C₂₃	—	2	1	no	—
287	C₄⋊C₄×C₂₃	—	2	4	no	—
288	C₄⋊C₄×C₂₃	—	2	4	no	—
289	C₄⋊C₄×C₂₃	—	2	2	no	—
290	C₄⋊C₄×C₂₃	—	2	2	no	—
291	C₄⋊C₄×C₂₃	—	2	2	no	—
292	C₄⋊C₄×C₂₃	—	2	2	no	—
293	C₄⋊C₄×C₂₃	—	2	2	no	—
294	C₄⋊C₄×C₂₃	—	2	2	no	—
295	C₄⋊C₄×C₂₃	—	2	2	no	—
296	C₄⋊C₄×C₂₃	—	2	2	no	—
297	C₄⋊C₄×C₂₃	—	2	2	no	—
298	C₄⋊C₄×C₂₃	—	2	2	no	—
299	C₄⋊C₄×C₂₃	—	2	4	no	—
300	C₄⋊C₄×C₂₃	—	2	4	no	—
301	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
302	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
303	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
304	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
306	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
307	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
308	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
309	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
310	C₂²⋊C₄×C₂₃	—	2	2	no	—
311	C₂²⋊C₄×C₂₃	—	2	2	no	—
312	C₂²⋊C₄×C₂₃	—	2	2	no	—
313	C₂²⋊C₄×C₂₃	—	2	4	no	—
314	C₂²⋊C₄×C₂₃	—	2	4	no	—
315	C₂²⋊C₄×C₂₃	—	2	1	no	—
316	C₂²⋊C₄×C₂₃	—	2	2	no	—
317	C₂²⋊C₄×C₂₃	—	2	1	no	—
318	C₂²⋊C₄×C₂₃	—	2	1	no	—
319	C₂²⋊C₄×C₂₃	—	2	2	no	—
320	C₂²⋊C₄×C₂₃	—	2	2	no	—
321	C₂²⋊C₄×C₂₃	—	2	2	no	—
322	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
324	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
325	C₄²×C₂₃	—	2	2	no	—
326	C₄²×C₂₃	—	2	1	no	—
327	C₄²×C₂₃	—	2	1	no	—
328	C₄²×C₂₃	—	2	1	no	—
329	C₄²×C₂₃	—	2	2	no	—
330	C₄²×C₂₃	—	2	4	no	—
331	C₄²×C₂₃	—	2	4	no	—
332	C₄²×C₂₃	—	2	2	no	—
333	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₂₃	C₂×D₄	1	2	yes	—
335	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₂₃	C₂×D₄	1	2	yes	—
337	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
338	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
339	C₄²×C₂₃	C₂⁴	1	2	yes	—
340	#60925	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
341	C₂³×C₂₃	—	2	1	no	—
342	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
343	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
344	Q₈×C₂₃	—	2	2	no	—
345	Q₈×C₂₃	—	2	4	no	—
346	Q₈×C₂₃	—	2	2	no	—
347	Q₈×C₂₃	—	2	1	no	—
348	Q₈×C₂₃	—	2	2	no	—
349	Q₈×C₂₃	—	2	4	no	—
350	Q₈×C₂₃	—	2	1	no	—
351	Q₈×C₂₃	—	4	2	no	—
352	Q₈×C₂₃	—	4	2	no	—
353	Q₈×C₂₃	—	4	4	no	—
354	Q₈×C₂₃	—	4	2	no	—
355	Q₈×C₂₃	—	8	2	no	—
356	D₄×C₂₃	—	2	4	no	—
357	D₄×C₂₃	—	2	2	no	—
358	D₄×C₂₃	—	2	1	no	—
359	D₄×C₂₃	—	2	1	no	—
360	D₄×C₂₃	—	4	2	no	—
361	D₄×C₂₃	—	8	2	no	—
362	C₂×C₄×C₂₃	—	2	2	no	—
363	C₂×C₄×C₂₃	—	2	4	no	—
364	C₂×C₄×C₂₃	—	2	2	no	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	2	2	no	—
367	C₂×C₄×C₂₃	—	2	2	no	—
368	C₂×C₄×C₂₃	—	2	1	no	—
369	C₂×C₄×C₂₃	—	2	2	no	—
370	C₂×C₄×C₂₃	—	2	1	no	—
371	C₂×C₄×C₂₃	—	2	1	no	—
372	C₂×C₄×C₂₃	—	2	4	no	—
373	C₂×C₄×C₂₃	—	2	2	no	—
374	C₂×C₄×C₂₃	—	4	1	no	—
375	C₂×C₄×C₂₃	—	4	2	no	—
376	C₂×C₄×C₂₃	—	4	2	no	—
377	C₂×C₄×C₂₃	—	4	4	no	—
378	C₂×C₄×C₂₃	—	4	2	no	—
379	C₂×C₄×C₂₃	—	4	2	no	—
380	C₂×C₄×C₂₃	—	8	1	no	—
381	C₂×C₄×C₂₃	—	8	1	no	—
382	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
391	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
392	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
393	C₈×C₂₃	—	2	2	no	—
394	C₈×C₂₃	—	2	2	no	—
395	C₈×C₂₃	—	2	4	no	—
396	#3509	C₂×C₂₃	1	1	yes	characteristic, complemented
397	#3461	C₂×C₂₃	1	1	yes	characteristic
398	#3261	C₂×C₂₃	1	4	yes	complemented
399	#3258	C₂×C₂₃	1	4	yes	complemented
400	#3255	C₂×C₂₃	1	2	yes	complemented
401	#3252	C₂×C₂₃	1	2	yes	complemented
402	#3249	C₂×C₂₃	1	2	yes	complemented
403	#3248	C₂×C₂₃	1	2	yes	complemented
404	#3082	C₂×C₂₃	1	2	yes	complemented
405	#3078	C₂×C₂₃	1	1	yes	characteristic, complemented
406	#3076	C₂×C₂₃	1	1	yes	characteristic, complemented
407	#3063	C₂×C₂₃	1	2	yes	—
408	#3059	C₂×C₂₃	1	2	yes	complemented
409	#3044	C₂×C₂₃	1	2	yes	complemented
410	#3039	C₂×C₂₃	1	1	yes	characteristic, complemented
411	C₂×#462	C₂×C₂₃	1	1	yes	characteristic, complemented
412	#2906	C₂×C₂₃	1	1	yes	characteristic, complemented
413	C₂²×C₂₃	—	2	1	no	—
414	C₂²×C₂₃	—	2	1	no	—
415	C₂²×C₂₃	—	2	2	no	—
416	C₂²×C₂₃	—	2	2	no	—
417	C₂²×C₂₃	—	2	2	no	—
418	C₂²×C₂₃	—	4	1	no	—
419	C₂²×C₂₃	—	4	1	no	—
420	C₂²×C₂₃	—	4	1	no	—
421	C₂²×C₂₃	#537	1	2	yes	—
422	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
423	C₄×C₂₃	—	2	1	no	—
424	C₄×C₂₃	—	2	1	no	—
425	C₄×C₂₃	—	2	2	no	—
426	C₄×C₂₃	—	2	2	no	—
427	C₄×C₂₃	—	2	1	no	—
428	C₄×C₂₃	—	2	2	no	—
429	C₄×C₂₃	—	4	2	no	—
430	C₄×C₂₃	—	4	1	no	—
431	C₄×C₂₃	—	4	2	no	—
432	C₄×C₂₃	—	4	1	no	—
433	C₄×C₂₃	—	4	2	no	—
434	C₄×C₂₃	—	4	4	no	—
435	C₄×C₂₃	—	4	1	no	—
436	C₄×C₂₃	—	4	2	no	—
437	C₄×C₂₃	#537	1	2	yes	—
438	C₄×C₂₃	#578	1	2	yes	—
439	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
440	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
441	C₂×#137	C₂²×C₂₃	1	2	yes	—
442	C₂²×Q₁₆	C₂²×C₂₃	1	2	yes	—
443	C₂×#131	C₂²×C₂₃	1	2	yes	—
444	#557	—	2	1	no	—
445	#557	—	2	1	no	—
446	#556	—	2	1	no	—
447	#556	—	2	1	no	—
448	#552	—	2	2	no	—
449	#552	—	2	2	no	—
450	#544	C₂²×C₂₃	1	1	yes	characteristic
451	#542	—	2	1	no	—
452	#542	C₂²×C₂₃	1	2	yes	—
453	#541	—	2	1	no	—
454	#541	C₂²×C₂₃	1	2	yes	—
455	#541	C₂²×C₂₃	1	4	yes	—
456	#539	—	2	2	no	—
457	#537	C₂²×C₂₃	1	1	yes	characteristic
458	#536	C₂²×C₂₃	1	1	yes	characteristic
459	#536	C₂²×C₂₃	1	1	yes	characteristic
460	#536	C₂²×C₂₃	1	2	yes	—
461	#533	—	2	1	no	—
462	#533	C₂²×C₂₃	1	2	yes	—
463	#533	C₂²×C₂₃	1	2	yes	—
464	#533	C₂²×C₂₃	1	2	yes	—
465	#533	C₂²×C₂₃	1	1	yes	characteristic
466	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
467	#529	—	2	2	no	—
468	#529	—	2	1	no	—
469	#529	C₂²×C₂₃	1	2	yes	—
470	#519	C₂²×C₂₃	1	2	yes	—
471	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
472	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
473	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
474	#479	C₂²×C₂₃	1	2	yes	—
475	#479	C₂²×C₂₃	1	4	yes	—
476	#479	C₂²×C₂₃	1	4	yes	—
477	#479	C₂²×C₂₃	1	4	yes	—
478	#478	C₂²×C₂₃	1	2	yes	—
479	#477	C₂²×C₂₃	1	1	yes	characteristic
480	#477	C₂²×C₂₃	1	2	yes	—
481	#477	C₂²×C₂₃	1	4	yes	—
482	#476	C₂²×C₂₃	1	1	yes	characteristic
483	#475	C₂²×C₂₃	1	1	yes	characteristic
484	#475	C₂²×C₂₃	1	2	yes	—
485	#475	C₂²×C₂₃	1	4	yes	—
486	#474	C₂²×C₂₃	1	1	yes	characteristic
487	#470	C₂²×C₂₃	1	4	yes	—
488	#470	C₂²×C₂₃	1	4	yes	—
489	#470	C₂²×C₂₃	1	4	yes	—
490	#468	C₂²×C₂₃	1	4	yes	—
491	#467	C₂²×C₂₃	1	4	yes	—
492	#467	C₂²×C₂₃	1	4	yes	—
493	#467	C₂²×C₂₃	1	4	yes	—
494	#465	C₂²×C₂₃	1	4	yes	—
495	#464	C₂²×C₂₃	1	4	yes	—
496	#464	C₂²×C₂₃	1	4	yes	—
497	#462	C₂²×C₂₃	1	2	yes	—
498	#462	C₂²×C₂₃	1	2	yes	—
499	#462	C₂²×C₂₃	1	4	yes	—
500	#462	C₂²×C₂₃	1	2	yes	—
501	#462	C₂²×C₂₃	1	4	yes	—
502	#462	C₂²×C₂₃	1	4	yes	—
503	#462	C₂²×C₂₃	1	2	yes	—
504	#461	C₂²×C₂₃	1	2	yes	—
505	#461	C₂²×C₂₃	1	2	yes	—
506	#428	C₂²×C₂₃	1	2	yes	—
507	#427	C₂²×C₂₃	1	2	yes	—
508	#424	C₂²×C₂₃	1	2	yes	—
509	#424	C₂²×C₂₃	1	4	yes	—
510	#423	C₂²×C₂₃	1	1	yes	characteristic
511	#423	C₂²×C₂₃	1	2	yes	—
512	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
513	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
514	#419	C₂²×C₂₃	1	2	yes	—
515	#419	C₂²×C₂₃	1	2	yes	—
516	#416	C₂²×C₂₃	1	2	yes	—
517	C₂×#103	C₂²×C₂₃	1	2	yes	—
518	C₂×C₂₃	—	2	2	no	—
519	C₂×C₂₃	—	4	2	no	—
520	C₂×C₂₃	—	8	1	no	—
521	C₂×C₂₃	C₂×#537	1	1	yes	characteristic
522	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
523	C₂×C₂₃	#3586	1	1	yes	characteristic
524	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
525	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
526	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
527	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
528	#137	—	4	4	no	—
529	C₂×Q₁₆	—	4	4	no	—
530	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
531	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
532	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
533	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
534	#131	—	4	4	no	—
535	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
536	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
537	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
538	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
539	C₄⋊Q₈	—	2	1	no	—
540	C₄⋊Q₈	—	2	2	no	—
541	C₄⋊Q₈	—	2	1	no	—
542	C₄⋊Q₈	—	2	1	no	—
543	C₄⋊Q₈	—	2	1	no	—
544	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
545	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
546	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
547	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
548	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
549	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
550	#126	—	2	2	no	—
551	#126	—	2	2	no	—
552	#126	—	2	2	no	—
553	#126	—	2	4	no	—
554	#126	—	2	4	no	—
555	#126	—	2	2	no	—
556	#125	—	2	2	no	—
557	#125	—	2	1	no	—
558	#125	—	2	2	no	—
559	#125	—	2	4	no	—
560	#125	—	2	4	no	—
561	#125	—	2	2	no	—
562	#125	—	2	2	no	—
563	#125	—	2	2	no	—
564	#125	C₂³×C₂₃	1	2	yes	—
565	#125	C₂³×C₂₃	1	2	yes	—
566	#124	—	2	1	no	—
567	#124	—	2	2	no	—
568	#124	—	2	2	no	—
569	#124	C₂³×C₂₃	1	2	yes	—
570	#123	—	2	2	no	—
571	#123	—	2	4	no	—
572	#123	—	2	2	no	—
573	#123	—	2	2	no	—
574	#123	—	2	2	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	1	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	1	no	—
582	C₂²⋊Q₈	—	2	1	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
586	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
587	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
588	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
589	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
590	#121	—	2	2	no	—
591	#121	—	2	1	no	—
592	#121	C₂³×C₂₃	1	2	yes	—
593	C₄×Q₈	—	2	2	no	—
594	C₄×Q₈	—	2	2	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	—	2	2	no	—
598	C₄×Q₈	—	2	2	no	—
599	C₄×Q₈	—	2	2	no	—
600	C₄×Q₈	—	2	1	no	—
601	C₄×Q₈	—	2	1	no	—
602	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
603	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
604	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
605	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
606	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
607	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
608	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
609	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	D₄×C₂₃	1	2	yes	—
614	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
615	C₄×D₄	D₄×C₂₃	1	2	yes	—
616	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
617	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
618	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
619	#117	—	2	2	no	—
620	#117	—	2	2	no	—
621	#117	—	2	2	no	—
622	#117	—	2	4	no	—
623	#117	—	2	1	no	—
624	#117	—	2	2	no	—
625	#117	C₂³×C₂₃	1	1	yes	characteristic
626	#117	C₂³×C₂₃	1	2	yes	—
627	#117	C₂³×C₂₃	1	1	yes	characteristic
628	#117	C₂³×C₂₃	1	2	yes	—
629	C₂×C₄⋊C₄	—	2	1	no	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
633	C₂×C₄²	—	2	1	no	—
634	C₂×C₄²	—	2	1	no	—
635	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
637	#107	C₂³×C₂₃	1	2	yes	—
638	#107	C₂³×C₂₃	1	2	yes	—
639	#107	C₂³×C₂₃	1	4	yes	—
640	#106	C₂³×C₂₃	1	2	yes	—
641	#106	C₂³×C₂₃	1	2	yes	—
642	#106	C₂³×C₂₃	1	4	yes	—
643	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
644	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
645	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
646	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
647	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
648	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
649	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
650	#103	C₂³×C₂₃	1	4	yes	—
651	#103	C₂³×C₂₃	1	4	yes	—
652	#103	C₂³×C₂₃	1	2	yes	—
653	#103	C₂³×C₂₃	1	2	yes	—
654	#103	C₂³×C₂₃	1	4	yes	—
655	#103	C₂³×C₂₃	1	4	yes	—
656	#103	C₂³×C₂₃	1	4	yes	—
657	#103	C₂³×C₂₃	1	4	yes	—
658	#102	C₂³×C₂₃	1	2	yes	—
659	#102	C₂³×C₂₃	1	2	yes	—
660	C₂₃	#60925	1	1	yes	characteristic, direct product factor, Sylow
661	#41	—	2	2	no	—
662	#41	—	2	2	no	—
663	#41	—	2	2	no	—
664	#41	—	2	2	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	2	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	2	4	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	4	no	—
674	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
675	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
676	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
677	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
681	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
682	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
690	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
691	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
695	Q₁₆	—	4	4	no	—
696	Q₁₆	—	4	4	no	—
697	Q₁₆	—	4	4	no	—
698	SD₁₆	—	4	4	no	—
699	M₁₆	—	2	4	no	—
700	M₁₆	—	4	4	no	—
701	C₂×C₈	—	2	4	no	—
702	C₂×C₈	—	4	4	no	—
703	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
704	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
705	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
732	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
733	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
734	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
735	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
736	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
739	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
753	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
754	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	1	no	—
757	C₄²	—	2	1	no	—
758	C₄²	—	2	1	no	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	4	no	—
761	C₄²	—	2	4	no	—
762	C₄²	—	2	2	no	—
763	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
764	C₄²	C₂×D₄×C₂₃	1	2	yes	—
765	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
766	C₄²	C₂×D₄×C₂₃	1	2	yes	—
767	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
768	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
769	C₄²	C₂⁴×C₂₃	1	2	yes	—
770	C₂³	—	2	1	no	—
771	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
772	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
773	Q₈	—	2	2	no	—
774	Q₈	—	2	4	no	—
775	Q₈	—	2	2	no	—
776	Q₈	—	2	1	no	—
777	Q₈	—	2	2	no	—
778	Q₈	—	2	4	no	—
779	Q₈	—	2	1	no	—
780	Q₈	—	4	2	no	—
781	Q₈	—	4	2	no	—
782	Q₈	—	4	2	no	—
783	Q₈	—	4	4	no	—
784	Q₈	—	8	2	no	—
785	D₄	—	2	4	no	—
786	D₄	—	2	1	no	—
787	D₄	—	2	1	no	—
788	D₄	—	2	2	no	—
789	D₄	—	4	2	no	—
790	D₄	—	8	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	4	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	2	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	8	1	no	—
810	C₂×C₄	—	8	1	no	—
811	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
813	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
819	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
820	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
821	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
822	C₈	—	2	2	no	—
823	C₈	—	2	2	no	—
824	C₈	—	2	4	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	C₂₃×#537	1	2	yes	—
834	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
835	C₄	—	2	2	no	—
836	C₄	—	2	1	no	—
837	C₄	—	2	2	no	—
838	C₄	—	2	1	no	—
839	C₄	—	2	1	no	—
840	C₄	—	2	2	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	4	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	2	no	—
849	C₄	C₂₃×#537	1	2	yes	—
850	C₄	C₂₃×#578	1	2	yes	—
851	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
852	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
853	C₂	—	2	2	no	—
854	C₂	—	4	2	no	—
855	C₂	—	8	1	no	—
856	C₂	C₂×C₂₃×#537	1	1	yes	characteristic
857	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
858	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×#537	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3509	C₂	semidirect
3. C₂₃×#3261	C₂	semidirect
4. C₂₃×#3258	C₂	semidirect
5. C₂₃×#3255	C₂	semidirect
6. C₂₃×#3252	C₂	semidirect
7. C₂₃×#3249	C₂	semidirect
8. C₂₃×#3248	C₂	semidirect
9. C₂₃×#3082	C₂	semidirect
10. C₂₃×#3078	C₂	semidirect
11. C₂₃×#3076	C₂	semidirect
13. C₂₃×#3059	C₂	semidirect
14. C₂₃×#3044	C₂	semidirect
15. C₂₃×#3039	C₂	semidirect
16. C₂×C₂₃×#462	C₂	semidirect
17. C₂₃×#2906	C₂	semidirect
340. #60925	C₂₃	direct (N × H)
396. #3509	C₂×C₂₃	semidirect
398. #3261	C₂×C₂₃	semidirect
399. #3258	C₂×C₂₃	semidirect
400. #3255	C₂×C₂₃	semidirect
401. #3252	C₂×C₂₃	semidirect
402. #3249	C₂×C₂₃	semidirect
403. #3248	C₂×C₂₃	semidirect
404. #3082	C₂×C₂₃	semidirect
405. #3078	C₂×C₂₃	semidirect
406. #3076	C₂×C₂₃	semidirect
408. #3059	C₂×C₂₃	semidirect
409. #3044	C₂×C₂₃	semidirect
410. #3039	C₂×C₂₃	semidirect
411. C₂×#462	C₂×C₂₃	semidirect
412. #2906	C₂×C₂₃	semidirect
660. C₂₃	#60925	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×#3509	2
C₂₃×#3461	2
C₂₃×#3261	2
C₂₃×#3258	2
C₂₃×#3255	2
C₂₃×#3252	2
C₂₃×#3249	2
C₂₃×#3248	2
C₂₃×#3082	2
C₂₃×#3078	2
C₂₃×#3076	2
C₂₃×#3063	2
C₂₃×#3059	2
C₂₃×#3044	2
C₂₃×#3039	2
C₂×C₂₃×#462	2
C₂₃×#2906	2
#60925	23

Subgroups — C23×#60925 #19208551

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60925 #19208551