Subgroups — C₂₃×#60918 #19208544

Order 5888.

1888 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3255	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3254	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3252	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3249	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3248	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3246	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3079	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3078	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3056	C₂	1	4	yes	maximal, complemented
12	C₂₃×#3039	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3037	C₂	1	2	yes	maximal, complemented
14	C₂×C₂₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#137	C₂²	1	4	yes	—
16	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
17	C₂₃×#533	—	2	1	no	—
18	C₂₃×#533	—	2	1	no	—
19	C₂₃×#533	—	2	1	no	—
20	C₂₃×#533	—	2	1	no	—
21	C₂₃×#533	C₂²	1	2	yes	—
22	C₂₃×#533	C₂²	1	2	yes	—
23	C₂₃×#533	C₂²	1	2	yes	—
24	C₂₃×#533	C₂²	1	2	yes	—
25	C₂₃×#533	C₂²	1	1	yes	characteristic
26	C₂₃×#533	C₂²	1	1	yes	characteristic
27	C₂₃×#533	C₂²	1	1	yes	characteristic
28	C₂₃×#532	C₂²	1	1	yes	characteristic
29	C₂₃×#532	C₂²	1	1	yes	characteristic
30	C₂₃×#532	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂₃×#529	—	2	1	no	—
34	C₂₃×#529	—	2	1	no	—
35	C₂₃×#529	—	2	1	no	—
36	C₂₃×#529	—	2	1	no	—
37	C₂₃×#529	C₂²	1	2	yes	—
38	C₂₃×#529	C₂²	1	2	yes	—
39	C₂×C₂₃×#125	—	2	1	no	—
40	C₂₃×#525	—	2	1	no	—
41	C₂₃×#525	—	2	1	no	—
42	C₂₃×#525	C₂²	1	2	yes	—
43	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
44	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
45	C₄×#41×C₂₃	—	2	1	no	—
46	C₄×#41×C₂₃	—	2	1	no	—
47	C₄×#41×C₂₃	C₂²	1	2	yes	—
48	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
49	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
50	C₂×C₂₃×#117	—	2	1	no	—
51	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
52	C₂₃×#479	C₂²	1	8	yes	complemented
53	C₂₃×#477	C₂²	1	4	yes	complemented
54	C₂₃×#477	C₂²	1	4	yes	complemented
55	C₂₃×#476	C₂²	1	4	yes	complemented
56	C₂₃×#475	C₂²	1	4	yes	complemented
57	C₂₃×#475	C₂²	1	4	yes	complemented
58	C₂₃×#474	C₂²	1	4	yes	complemented
59	C₂₃×#470	C₂²	1	8	yes	—
60	C₂₃×#468	C₂²	1	8	yes	—
61	C₂₃×#467	C₂²	1	8	yes	—
62	C₂₃×#465	C₂²	1	8	yes	—
63	C₂₃×#464	C₂²	1	8	yes	complemented
64	C₂₃×#462	C₂²	1	4	yes	complemented
65	C₂₃×#462	C₂²	1	4	yes	complemented
66	C₂₃×#462	C₂²	1	4	yes	complemented
67	C₂₃×#461	C₂²	1	4	yes	complemented
68	C₂₃×#461	C₂²	1	4	yes	complemented
69	C₂₃×#460	C₂²	1	4	yes	complemented
70	C₂₃×#428	C₂²	1	4	yes	—
71	C₂₃×#423	C₂²	1	2	yes	—
72	C₂₃×#423	C₂²	1	2	yes	—
73	C₂₃×#423	C₂²	1	2	yes	—
74	C₂₃×#423	C₂²	1	2	yes	—
75	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
76	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
77	C₂₃×#419	C₂²	1	4	yes	—
78	C₂₃×#417	C₂²	1	4	yes	—
79	C₂×#41×C₂₃	—	2	1	no	—
80	C₂×#41×C₂₃	—	2	1	no	—
81	C₂×#41×C₂₃	C₂³	1	2	yes	—
82	C₂²×Q₈×C₂₃	—	2	1	no	—
83	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
85	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
86	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂₃×#137	—	4	8	no	—
88	C₂×Q₁₆×C₂₃	C₂³	1	8	yes	—
89	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
90	C₂×M₁₆×C₂₃	—	4	4	no	—
91	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
92	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
93	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
94	C₂₃×C₄⋊Q₈	—	2	1	no	—
95	C₂₃×C₄⋊Q₈	—	2	1	no	—
96	C₂₃×C₄⋊Q₈	—	2	1	no	—
97	C₂₃×C₄⋊Q₈	—	2	1	no	—
98	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
100	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
101	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
102	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
104	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₂₃×#127	C₂³	1	1	yes	characteristic
106	C₂₃×#126	—	2	2	no	—
107	C₂₃×#126	—	2	2	no	—
108	C₂₃×#125	—	2	2	no	—
109	C₂₃×#125	—	2	2	no	—
110	C₂₃×#125	—	2	2	no	—
111	C₂₃×#125	—	2	2	no	—
112	C₂₃×#125	—	2	1	no	—
113	C₂₃×#125	—	2	1	no	—
114	C₂₃×#125	C₂³	1	2	yes	—
115	C₂₃×#124	—	2	1	no	—
116	C₂₃×#124	—	2	1	no	—
117	C₂₃×#124	C₂³	1	2	yes	—
118	C₂₃×#123	—	2	2	no	—
119	C₂₃×#123	—	2	2	no	—
120	C₂₃×#123	—	2	2	no	—
121	C₂₃×C₂²⋊Q₈	—	2	2	no	—
122	C₂₃×C₂²⋊Q₈	—	2	2	no	—
123	C₂₃×C₂²⋊Q₈	—	2	2	no	—
124	C₂₃×C₂²⋊Q₈	—	2	2	no	—
125	C₂₃×C₂²⋊Q₈	—	2	2	no	—
126	C₂₃×C₂²⋊Q₈	—	2	2	no	—
127	C₂₃×C₂²⋊Q₈	—	2	1	no	—
128	C₂₃×C₂²⋊Q₈	—	2	1	no	—
129	C₂₃×C₂²⋊Q₈	—	2	1	no	—
130	C₂₃×C₂²⋊Q₈	—	2	1	no	—
131	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
132	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
133	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₂₃×#121	—	2	1	no	—
136	C₂₃×#121	—	2	1	no	—
137	C₂₃×#121	—	2	1	no	—
138	C₂₃×#121	—	2	1	no	—
139	C₂₃×#121	C₂³	1	2	yes	—
140	C₂₃×#121	C₂³	1	2	yes	—
141	C₂₃×#120	—	2	2	no	—
142	C₄×Q₈×C₂₃	—	2	2	no	—
143	C₄×Q₈×C₂₃	—	2	2	no	—
144	C₄×Q₈×C₂₃	—	2	2	no	—
145	C₄×Q₈×C₂₃	—	2	2	no	—
146	C₄×Q₈×C₂₃	—	2	2	no	—
147	C₄×Q₈×C₂₃	—	2	2	no	—
148	C₄×Q₈×C₂₃	—	2	1	no	—
149	C₄×Q₈×C₂₃	—	2	1	no	—
150	C₄×Q₈×C₂₃	—	2	1	no	—
151	C₄×Q₈×C₂₃	—	2	1	no	—
152	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
153	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
154	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
155	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
156	C₄×D₄×C₂₃	—	2	2	no	—
157	C₄×D₄×C₂₃	—	2	2	no	—
158	C₄×D₄×C₂₃	—	2	2	no	—
159	C₄×D₄×C₂₃	—	2	2	no	—
160	C₄×D₄×C₂₃	—	2	2	no	—
161	C₄×D₄×C₂₃	—	2	2	no	—
162	C₄×D₄×C₂₃	—	2	1	no	—
163	C₄×D₄×C₂₃	—	2	1	no	—
164	C₄×D₄×C₂₃	—	2	1	no	—
165	C₄×D₄×C₂₃	—	2	1	no	—
166	C₄×D₄×C₂₃	C₂³	1	2	yes	—
167	C₄×D₄×C₂₃	C₂³	1	2	yes	—
168	C₂₃×#117	—	2	2	no	—
169	C₂₃×#117	—	2	2	no	—
170	C₂₃×#117	—	2	2	no	—
171	C₂₃×#117	—	2	2	no	—
172	C₂₃×#117	—	2	1	no	—
173	C₂₃×#117	—	2	1	no	—
174	C₂₃×#117	—	2	2	no	—
175	C₂₃×#117	—	2	2	no	—
176	C₂₃×#117	—	2	2	no	—
177	C₂₃×#117	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
179	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
180	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
181	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
182	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
183	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
185	C₂×C₄²×C₂₃	—	2	2	no	—
186	C₂×C₄²×C₂₃	—	2	2	no	—
187	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
199	C₂₃×#107	C₂³	1	8	yes	—
200	C₂₃×#106	C₂³	1	8	yes	—
201	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
202	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
203	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
204	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
205	C₂₃×#103	C₂³	1	8	yes	—
206	C₂₃×#103	C₂³	1	8	yes	—
207	C₂₃×#103	C₂³	1	8	yes	—
208	C₂₃×#102	C₂³	1	8	yes	—
209	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
210	#41×C₂₃	—	2	4	no	—
211	#41×C₂₃	—	2	4	no	—
212	#41×C₂₃	—	4	4	no	—
213	#41×C₂₃	—	4	4	no	—
214	C₂×Q₈×C₂₃	—	2	1	no	—
215	C₂×Q₈×C₂₃	—	2	1	no	—
216	C₂×Q₈×C₂₃	—	2	2	no	—
217	C₂×Q₈×C₂₃	—	2	2	no	—
218	C₂×Q₈×C₂₃	—	2	2	no	—
219	C₂×Q₈×C₂₃	—	2	4	no	—
220	C₂×Q₈×C₂₃	—	2	4	no	—
221	C₂×Q₈×C₂₃	—	4	4	no	—
222	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
223	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
224	C₂×D₄×C₂₃	—	2	2	no	—
225	C₂×D₄×C₂₃	—	2	2	no	—
226	C₂×D₄×C₂₃	—	2	2	no	—
227	C₂×D₄×C₂₃	—	2	1	no	—
228	C₂×D₄×C₂₃	—	2	1	no	—
229	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₂₃	—	2	4	no	—
231	C₂²×C₄×C₂₃	—	2	2	no	—
232	C₂²×C₄×C₂₃	—	2	2	no	—
233	C₂²×C₄×C₂₃	—	2	2	no	—
234	C₂²×C₄×C₂₃	—	2	2	no	—
235	C₂²×C₄×C₂₃	—	2	2	no	—
236	C₂²×C₄×C₂₃	—	2	2	no	—
237	C₂²×C₄×C₂₃	—	2	2	no	—
238	C₂²×C₄×C₂₃	—	4	2	no	—
239	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
257	Q₁₆×C₂₃	—	4	8	no	—
258	SD₁₆×C₂₃	—	4	8	no	—
259	M₁₆×C₂₃	—	2	8	no	—
260	M₁₆×C₂₃	—	4	4	no	—
261	C₂×C₈×C₂₃	—	4	4	no	—
262	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
263	C₄⋊C₄×C₂₃	—	2	2	no	—
264	C₄⋊C₄×C₂₃	—	2	2	no	—
265	C₄⋊C₄×C₂₃	—	2	2	no	—
266	C₄⋊C₄×C₂₃	—	2	2	no	—
267	C₄⋊C₄×C₂₃	—	2	2	no	—
268	C₄⋊C₄×C₂₃	—	2	2	no	—
269	C₄⋊C₄×C₂₃	—	2	4	no	—
270	C₄⋊C₄×C₂₃	—	2	4	no	—
271	C₄⋊C₄×C₂₃	—	2	4	no	—
272	C₄⋊C₄×C₂₃	—	2	4	no	—
273	C₄⋊C₄×C₂₃	—	2	2	no	—
274	C₄⋊C₄×C₂₃	—	2	1	no	—
275	C₄⋊C₄×C₂₃	—	2	1	no	—
276	C₄⋊C₄×C₂₃	—	2	1	no	—
277	C₄⋊C₄×C₂₃	—	2	1	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	2	no	—
283	C₄⋊C₄×C₂₃	—	2	2	no	—
284	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
285	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
287	C₂²⋊C₄×C₂₃	—	2	4	no	—
288	C₂²⋊C₄×C₂₃	—	2	4	no	—
289	C₂²⋊C₄×C₂₃	—	2	2	no	—
290	C₂²⋊C₄×C₂₃	—	2	2	no	—
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	C₄²×C₂₃	—	2	2	no	—
299	C₄²×C₂₃	—	2	2	no	—
300	C₄²×C₂₃	—	2	4	no	—
301	C₄²×C₂₃	—	2	4	no	—
302	C₄²×C₂₃	—	2	2	no	—
303	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
316	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
317	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
318	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
319	#60918	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
320	C₂³×C₂₃	—	2	2	no	—
321	C₂³×C₂₃	—	2	2	no	—
322	C₂³×C₂₃	—	2	2	no	—
323	C₂³×C₂₃	—	4	1	no	—
324	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
325	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
326	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
327	Q₈×C₂₃	—	2	4	no	—
328	Q₈×C₂₃	—	2	2	no	—
329	Q₈×C₂₃	—	2	4	no	—
330	Q₈×C₂₃	—	2	2	no	—
331	Q₈×C₂₃	—	4	4	no	—
332	Q₈×C₂₃	—	4	2	no	—
333	Q₈×C₂₃	—	4	4	no	—
334	Q₈×C₂₃	—	4	2	no	—
335	Q₈×C₂₃	—	4	4	no	—
336	D₄×C₂₃	—	2	2	no	—
337	D₄×C₂₃	—	2	2	no	—
338	D₄×C₂₃	—	4	2	no	—
339	D₄×C₂₃	—	4	4	no	—
340	D₄×C₂₃	—	4	4	no	—
341	D₄×C₂₃	—	4	4	no	—
342	D₄×C₂₃	—	4	2	no	—
343	C₂×C₄×C₂₃	—	2	2	no	—
344	C₂×C₄×C₂₃	—	2	2	no	—
345	C₂×C₄×C₂₃	—	2	2	no	—
346	C₂×C₄×C₂₃	—	2	2	no	—
347	C₂×C₄×C₂₃	—	2	2	no	—
348	C₂×C₄×C₂₃	—	2	2	no	—
349	C₂×C₄×C₂₃	—	2	2	no	—
350	C₂×C₄×C₂₃	—	2	2	no	—
351	C₂×C₄×C₂₃	—	2	2	no	—
352	C₂×C₄×C₂₃	—	2	2	no	—
353	C₂×C₄×C₂₃	—	2	2	no	—
354	C₂×C₄×C₂₃	—	2	1	no	—
355	C₂×C₄×C₂₃	—	2	1	no	—
356	C₂×C₄×C₂₃	—	2	1	no	—
357	C₂×C₄×C₂₃	—	2	1	no	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	2	2	no	—
360	C₂×C₄×C₂₃	—	2	2	no	—
361	C₂×C₄×C₂₃	—	2	4	no	—
362	C₂×C₄×C₂₃	—	2	4	no	—
363	C₂×C₄×C₂₃	—	4	1	no	—
364	C₂×C₄×C₂₃	—	4	1	no	—
365	C₂×C₄×C₂₃	—	4	1	no	—
366	C₂×C₄×C₂₃	—	4	4	no	—
367	C₂×C₄×C₂₃	—	4	4	no	—
368	C₂×C₄×C₂₃	—	4	4	no	—
369	C₂×C₄×C₂₃	—	4	4	no	—
370	C₂×C₄×C₂₃	—	4	4	no	—
371	C₂×C₄×C₂₃	#137	1	4	yes	complemented
372	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
384	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
385	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
386	C₈×C₂₃	—	2	8	no	—
387	#3444	C₂×C₂₃	1	1	yes	characteristic
388	C₂×#533	C₂×C₂₃	1	1	yes	characteristic, complemented
389	#3255	C₂×C₂₃	1	2	yes	complemented
390	#3254	C₂×C₂₃	1	2	yes	complemented
391	#3252	C₂×C₂₃	1	4	yes	complemented
392	#3249	C₂×C₂₃	1	2	yes	complemented
393	#3248	C₂×C₂₃	1	4	yes	complemented
394	#3246	C₂×C₂₃	1	2	yes	complemented
395	#3079	C₂×C₂₃	1	2	yes	complemented
396	#3078	C₂×C₂₃	1	2	yes	complemented
397	#3056	C₂×C₂₃	1	4	yes	complemented
398	#3039	C₂×C₂₃	1	2	yes	complemented
399	#3037	C₂×C₂₃	1	2	yes	complemented
400	C₂×#423	C₂×C₂₃	1	1	yes	characteristic, complemented
401	C₂²×C₂₃	—	2	1	no	—
402	C₂²×C₂₃	—	2	1	no	—
403	C₂²×C₂₃	—	2	1	no	—
404	C₂²×C₂₃	—	2	1	no	—
405	C₂²×C₂₃	—	2	1	no	—
406	C₂²×C₂₃	—	2	1	no	—
407	C₂²×C₂₃	—	2	1	no	—
408	C₂²×C₂₃	—	4	4	no	—
409	C₂²×C₂₃	—	4	2	no	—
410	C₂²×C₂₃	—	4	2	no	—
411	C₂²×C₂₃	—	4	2	no	—
412	C₂²×C₂₃	#537	1	2	yes	—
413	C₂²×C₂₃	C₂×#137	1	2	yes	—
414	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
415	C₄×C₂₃	—	2	1	no	—
416	C₄×C₂₃	—	2	1	no	—
417	C₄×C₂₃	—	2	1	no	—
418	C₄×C₂₃	—	2	1	no	—
419	C₄×C₂₃	—	2	1	no	—
420	C₄×C₂₃	—	2	1	no	—
421	C₄×C₂₃	—	2	1	no	—
422	C₄×C₂₃	—	4	2	no	—
423	C₄×C₂₃	—	4	4	no	—
424	C₄×C₂₃	—	4	2	no	—
425	C₄×C₂₃	—	4	2	no	—
426	C₄×C₂₃	—	4	4	no	—
427	C₄×C₂₃	#537	1	2	yes	—
428	C₄×C₂₃	C₂×#137	1	2	yes	—
429	C₄×C₂₃	C₂×#137	1	2	yes	—
430	C₄×C₂₃	#575	1	2	yes	—
431	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
432	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
433	C₂×#137	C₂²×C₂₃	1	4	yes	—
434	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
435	#533	—	2	1	no	—
436	#533	—	2	1	no	—
437	#533	—	2	1	no	—
438	#533	—	2	1	no	—
439	#533	C₂²×C₂₃	1	2	yes	—
440	#533	C₂²×C₂₃	1	2	yes	—
441	#533	C₂²×C₂₃	1	2	yes	—
442	#533	C₂²×C₂₃	1	2	yes	—
443	#533	C₂²×C₂₃	1	1	yes	characteristic
444	#533	C₂²×C₂₃	1	1	yes	characteristic
445	#533	C₂²×C₂₃	1	1	yes	characteristic
446	#532	C₂²×C₂₃	1	1	yes	characteristic
447	#532	C₂²×C₂₃	1	1	yes	characteristic
448	#532	C₂²×C₂₃	1	1	yes	characteristic
449	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
450	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
451	#529	—	2	1	no	—
452	#529	—	2	1	no	—
453	#529	—	2	1	no	—
454	#529	—	2	1	no	—
455	#529	C₂²×C₂₃	1	2	yes	—
456	#529	C₂²×C₂₃	1	2	yes	—
457	C₂×#125	—	2	1	no	—
458	#525	—	2	1	no	—
459	#525	—	2	1	no	—
460	#525	C₂²×C₂₃	1	2	yes	—
461	C₂×C₂²⋊Q₈	—	2	1	no	—
462	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
463	C₄×#41	—	2	1	no	—
464	C₄×#41	—	2	1	no	—
465	C₄×#41	C₂²×C₂₃	1	2	yes	—
466	C₂×C₄×Q₈	—	2	1	no	—
467	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
468	C₂×#117	—	2	1	no	—
469	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
470	#479	C₂²×C₂₃	1	8	yes	complemented
471	#477	C₂²×C₂₃	1	4	yes	complemented
472	#477	C₂²×C₂₃	1	4	yes	complemented
473	#476	C₂²×C₂₃	1	4	yes	complemented
474	#475	C₂²×C₂₃	1	4	yes	complemented
475	#475	C₂²×C₂₃	1	4	yes	complemented
476	#474	C₂²×C₂₃	1	4	yes	complemented
477	#470	C₂²×C₂₃	1	8	yes	—
478	#468	C₂²×C₂₃	1	8	yes	—
479	#467	C₂²×C₂₃	1	8	yes	—
480	#465	C₂²×C₂₃	1	8	yes	—
481	#464	C₂²×C₂₃	1	8	yes	complemented
482	#462	C₂²×C₂₃	1	4	yes	complemented
483	#462	C₂²×C₂₃	1	4	yes	complemented
484	#462	C₂²×C₂₃	1	4	yes	complemented
485	#461	C₂²×C₂₃	1	4	yes	complemented
486	#461	C₂²×C₂₃	1	4	yes	complemented
487	#460	C₂²×C₂₃	1	4	yes	complemented
488	#428	C₂²×C₂₃	1	4	yes	—
489	#423	C₂²×C₂₃	1	2	yes	—
490	#423	C₂²×C₂₃	1	2	yes	—
491	#423	C₂²×C₂₃	1	2	yes	—
492	#423	C₂²×C₂₃	1	2	yes	—
493	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
494	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
495	#419	C₂²×C₂₃	1	4	yes	—
496	#417	C₂²×C₂₃	1	4	yes	—
497	C₂×C₂₃	—	2	2	no	—
498	C₂×C₂₃	—	2	2	no	—
499	C₂×C₂₃	—	4	1	no	—
500	C₂×C₂₃	—	8	2	no	—
501	C₂×C₂₃	C₂×#537	1	1	yes	characteristic
502	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
503	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
504	C₂×#41	—	2	1	no	—
505	C₂×#41	—	2	1	no	—
506	C₂×#41	C₂³×C₂₃	1	2	yes	—
507	C₂²×Q₈	—	2	1	no	—
508	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
509	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
510	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
512	#137	—	4	8	no	—
513	C₂×Q₁₆	C₂³×C₂₃	1	8	yes	—
514	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
515	C₂×M₁₆	—	4	4	no	—
516	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
517	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
518	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
519	C₄⋊Q₈	—	2	1	no	—
520	C₄⋊Q₈	—	2	1	no	—
521	C₄⋊Q₈	—	2	1	no	—
522	C₄⋊Q₈	—	2	1	no	—
523	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
524	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
525	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
526	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
527	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
528	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
529	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
530	#127	C₂³×C₂₃	1	1	yes	characteristic
531	#126	—	2	2	no	—
532	#126	—	2	2	no	—
533	#125	—	2	2	no	—
534	#125	—	2	2	no	—
535	#125	—	2	2	no	—
536	#125	—	2	2	no	—
537	#125	—	2	1	no	—
538	#125	—	2	1	no	—
539	#125	C₂³×C₂₃	1	2	yes	—
540	#124	—	2	1	no	—
541	#124	—	2	1	no	—
542	#124	C₂³×C₂₃	1	2	yes	—
543	#123	—	2	2	no	—
544	#123	—	2	2	no	—
545	#123	—	2	2	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	—	2	2	no	—
550	C₂²⋊Q₈	—	2	2	no	—
551	C₂²⋊Q₈	—	2	2	no	—
552	C₂²⋊Q₈	—	2	1	no	—
553	C₂²⋊Q₈	—	2	1	no	—
554	C₂²⋊Q₈	—	2	1	no	—
555	C₂²⋊Q₈	—	2	1	no	—
556	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
557	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
558	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
559	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
560	#121	—	2	1	no	—
561	#121	—	2	1	no	—
562	#121	—	2	1	no	—
563	#121	—	2	1	no	—
564	#121	C₂³×C₂₃	1	2	yes	—
565	#121	C₂³×C₂₃	1	2	yes	—
566	#120	—	2	2	no	—
567	C₄×Q₈	—	2	2	no	—
568	C₄×Q₈	—	2	2	no	—
569	C₄×Q₈	—	2	2	no	—
570	C₄×Q₈	—	2	2	no	—
571	C₄×Q₈	—	2	2	no	—
572	C₄×Q₈	—	2	2	no	—
573	C₄×Q₈	—	2	1	no	—
574	C₄×Q₈	—	2	1	no	—
575	C₄×Q₈	—	2	1	no	—
576	C₄×Q₈	—	2	1	no	—
577	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
578	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
579	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
580	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	—	2	2	no	—
584	C₄×D₄	—	2	2	no	—
585	C₄×D₄	—	2	2	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	1	no	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	C₂³×C₂₃	1	2	yes	—
592	C₄×D₄	C₂³×C₂₃	1	2	yes	—
593	#117	—	2	2	no	—
594	#117	—	2	2	no	—
595	#117	—	2	2	no	—
596	#117	—	2	2	no	—
597	#117	—	2	1	no	—
598	#117	—	2	1	no	—
599	#117	—	2	2	no	—
600	#117	—	2	2	no	—
601	#117	—	2	2	no	—
602	#117	C₂³×C₂₃	1	2	yes	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	2	no	—
607	C₂×C₄⋊C₄	—	2	2	no	—
608	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
609	C₂×C₂²⋊C₄	—	2	2	no	—
610	C₂×C₄²	—	2	2	no	—
611	C₂×C₄²	—	2	2	no	—
612	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
613	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
614	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
615	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
616	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
617	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
624	#107	C₂³×C₂₃	1	8	yes	—
625	#106	C₂³×C₂₃	1	8	yes	—
626	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
627	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
628	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
629	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
630	#103	C₂³×C₂₃	1	8	yes	—
631	#103	C₂³×C₂₃	1	8	yes	—
632	#103	C₂³×C₂₃	1	8	yes	—
633	#102	C₂³×C₂₃	1	8	yes	—
634	C₂₃	#60918	1	1	yes	characteristic, direct product factor, Sylow
635	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
636	#41	—	2	4	no	—
637	#41	—	2	4	no	—
638	#41	—	4	4	no	—
639	#41	—	4	4	no	—
640	C₂×Q₈	—	2	1	no	—
641	C₂×Q₈	—	2	1	no	—
642	C₂×Q₈	—	2	2	no	—
643	C₂×Q₈	—	2	2	no	—
644	C₂×Q₈	—	2	2	no	—
645	C₂×Q₈	—	2	4	no	—
646	C₂×Q₈	—	2	4	no	—
647	C₂×Q₈	—	4	4	no	—
648	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
649	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
656	C₂²×C₄	—	2	4	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
669	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
670	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
671	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
672	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
673	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
676	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
677	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
683	Q₁₆	—	4	8	no	—
684	SD₁₆	—	4	8	no	—
685	M₁₆	—	2	8	no	—
686	M₁₆	—	4	4	no	—
687	C₂×C₈	—	4	4	no	—
688	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
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	C₂⁴×C₂₃	1	4	yes	—
711	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
712	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₄²	—	2	2	no	—
725	C₄²	—	2	2	no	—
726	C₄²	—	2	4	no	—
727	C₄²	—	2	4	no	—
728	C₄²	—	2	2	no	—
729	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
730	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
731	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
732	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
733	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
734	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
735	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
736	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
737	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
738	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
739	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
740	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
741	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
742	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
743	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
744	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	4	1	no	—
749	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
750	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
751	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
752	Q₈	—	2	4	no	—
753	Q₈	—	2	2	no	—
754	Q₈	—	2	4	no	—
755	Q₈	—	2	2	no	—
756	Q₈	—	4	4	no	—
757	Q₈	—	4	2	no	—
758	Q₈	—	4	2	no	—
759	Q₈	—	4	4	no	—
760	Q₈	—	4	4	no	—
761	D₄	—	2	2	no	—
762	D₄	—	2	2	no	—
763	D₄	—	4	2	no	—
764	D₄	—	4	4	no	—
765	D₄	—	4	4	no	—
766	D₄	—	4	4	no	—
767	D₄	—	4	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	4	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	4	no	—
792	C₂×C₄	—	4	4	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	C₂₃×#137	1	4	yes	complemented
797	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
799	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
800	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
801	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
806	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
808	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
809	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
810	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
811	C₈	—	2	8	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	4	4	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	C₂₃×#537	1	2	yes	—
824	C₂²	C₂×C₂₃×#137	1	2	yes	—
825	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
826	C₄	—	2	1	no	—
827	C₄	—	2	1	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	4	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	4	no	—
838	C₄	C₂₃×#537	1	2	yes	—
839	C₄	C₂×C₂₃×#137	1	2	yes	—
840	C₄	C₂×C₂₃×#137	1	2	yes	—
841	C₄	C₂₃×#575	1	2	yes	—
842	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
843	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
844	C₂	—	2	2	no	—
845	C₂	—	2	2	no	—
846	C₂	—	4	1	no	—
847	C₂	—	8	2	no	—
848	C₂	C₂×C₂₃×#537	1	1	yes	characteristic
849	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic
850	C₂	C₂×C₂₃×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#533	C₂	semidirect
3. C₂₃×#3255	C₂	semidirect
4. C₂₃×#3254	C₂	semidirect
5. C₂₃×#3252	C₂	semidirect
6. C₂₃×#3249	C₂	semidirect
7. C₂₃×#3248	C₂	semidirect
8. C₂₃×#3246	C₂	semidirect
9. C₂₃×#3079	C₂	semidirect
10. C₂₃×#3078	C₂	semidirect
11. C₂₃×#3056	C₂	semidirect
12. C₂₃×#3039	C₂	semidirect
13. C₂₃×#3037	C₂	semidirect
14. C₂×C₂₃×#423	C₂	semidirect
52. C₂₃×#479	C₂²	semidirect
53. C₂₃×#477	C₂²	semidirect
54. C₂₃×#477	C₂²	semidirect
55. C₂₃×#476	C₂²	semidirect
56. C₂₃×#475	C₂²	semidirect
57. C₂₃×#475	C₂²	semidirect
58. C₂₃×#474	C₂²	semidirect
63. C₂₃×#464	C₂²	semidirect
64. C₂₃×#462	C₂²	semidirect
65. C₂₃×#462	C₂²	semidirect
66. C₂₃×#462	C₂²	semidirect
67. C₂₃×#461	C₂²	semidirect
68. C₂₃×#461	C₂²	semidirect
69. C₂₃×#460	C₂²	semidirect
319. #60918	C₂₃	direct (N × H)
371. C₂×C₄×C₂₃	#137	semidirect
388. C₂×#533	C₂×C₂₃	semidirect
389. #3255	C₂×C₂₃	semidirect
390. #3254	C₂×C₂₃	semidirect
391. #3252	C₂×C₂₃	semidirect
392. #3249	C₂×C₂₃	semidirect
393. #3248	C₂×C₂₃	semidirect
394. #3246	C₂×C₂₃	semidirect
395. #3079	C₂×C₂₃	semidirect
396. #3078	C₂×C₂₃	semidirect
397. #3056	C₂×C₂₃	semidirect
398. #3039	C₂×C₂₃	semidirect
399. #3037	C₂×C₂₃	semidirect
400. C₂×#423	C₂×C₂₃	semidirect
470. #479	C₂²×C₂₃	semidirect
471. #477	C₂²×C₂₃	semidirect
472. #477	C₂²×C₂₃	semidirect
473. #476	C₂²×C₂₃	semidirect
474. #475	C₂²×C₂₃	semidirect
475. #475	C₂²×C₂₃	semidirect
476. #474	C₂²×C₂₃	semidirect
481. #464	C₂²×C₂₃	semidirect
482. #462	C₂²×C₂₃	semidirect
483. #462	C₂²×C₂₃	semidirect
484. #462	C₂²×C₂₃	semidirect
485. #461	C₂²×C₂₃	semidirect
486. #461	C₂²×C₂₃	semidirect
487. #460	C₂²×C₂₃	semidirect
634. C₂₃	#60918	direct (N × H)
796. C₂×C₄	C₂₃×#137	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3444	2
C₂×C₂₃×#533	2
C₂₃×#3255	2
C₂₃×#3254	2
C₂₃×#3252	2
C₂₃×#3249	2
C₂₃×#3248	2
C₂₃×#3246	2
C₂₃×#3079	2
C₂₃×#3078	2
C₂₃×#3056	2
C₂₃×#3039	2
C₂₃×#3037	2
C₂×C₂₃×#423	2
#60918	23

Subgroups — C23×#60918 #19208544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60918 #19208544