Subgroups — C₂₃×#60954 #19208580

Order 5888.

1834 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×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3256	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3240	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3234	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3219	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3213	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3196	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3194	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3172	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3171	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3108	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3105	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3102	C₂	1	4	yes	maximal, complemented
17	C₂₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#533	C₂²	1	1	yes	characteristic
19	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
20	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
21	C₂₃×#532	C₂²	1	1	yes	characteristic
22	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
23	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
24	C₂₃×#529	—	2	1	no	—
25	C₂₃×#529	—	2	1	no	—
26	C₂₃×#529	—	2	1	no	—
27	C₂₃×#529	—	2	1	no	—
28	C₂₃×#529	—	2	1	no	—
29	C₂₃×#529	—	2	1	no	—
30	C₂₃×#529	—	2	1	no	—
31	C₂₃×#529	—	2	1	no	—
32	C₂₃×#529	C₂²	1	2	yes	—
33	C₂₃×#529	C₂²	1	2	yes	—
34	C₂₃×#529	C₂²	1	2	yes	—
35	C₂₃×#529	C₂²	1	2	yes	—
36	C₂₃×#529	C₂²	1	2	yes	—
37	C₂₃×#529	C₂²	1	2	yes	complemented
38	C₂×C₂₃×#126	—	2	1	no	—
39	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
41	C₂₃×#525	—	2	1	no	—
42	C₂₃×#525	—	2	1	no	—
43	C₂₃×#525	C₂²	1	2	yes	—
44	C₂×C₂₃×#123	—	2	1	no	—
45	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
47	C₄×#41×C₂₃	—	2	1	no	—
48	C₄×#41×C₂₃	—	2	1	no	—
49	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
50	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₂₃	—	2	1	no	—
52	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
53	C₂×C₂₃×#117	—	2	1	no	—
54	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
55	C₂₃×#501	C₂²	1	2	yes	complemented
56	C₂₃×#501	C₂²	1	2	yes	complemented
57	C₂₃×#497	C₂²	1	2	yes	complemented
58	C₂₃×#496	C₂²	1	2	yes	complemented
59	C₂₃×#491	C₂²	1	2	yes	complemented
60	C₂₃×#490	C₂²	1	2	yes	complemented
61	C₂₃×#489	C₂²	1	2	yes	complemented
62	C₂₃×#489	C₂²	1	2	yes	complemented
63	C₂₃×#485	C₂²	1	4	yes	complemented
64	C₂₃×#484	C₂²	1	2	yes	—
65	C₂₃×#483	C₂²	1	2	yes	—
66	C₂₃×#482	C₂²	1	4	yes	—
67	C₂₃×#481	C₂²	1	2	yes	—
68	C₂₃×#480	C₂²	1	2	yes	—
69	C₂₃×#479	C₂²	1	4	yes	complemented
70	C₂₃×#479	C₂²	1	4	yes	complemented
71	C₂₃×#478	C₂²	1	4	yes	complemented
72	C₂₃×#478	C₂²	1	4	yes	complemented
73	C₂₃×#470	C₂²	1	4	yes	complemented
74	C₂₃×#469	C₂²	1	4	yes	—
75	C₂₃×#468	C₂²	1	4	yes	—
76	C₂₃×#468	C₂²	1	4	yes	complemented
77	C₂₃×#464	C₂²	1	4	yes	complemented
78	C₂₃×#464	C₂²	1	4	yes	complemented
79	C₂₃×#463	C₂²	1	4	yes	complemented
80	C₂₃×#463	C₂²	1	4	yes	complemented
81	C₂₃×#452	C₂²	1	4	yes	complemented
82	C₂₃×#451	C₂²	1	2	yes	—
83	C₂₃×#450	C₂²	1	2	yes	—
84	C₂₃×#449	C₂²	1	4	yes	—
85	C₂₃×#448	C₂²	1	2	yes	—
86	C₂₃×#447	C₂²	1	2	yes	—
87	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	complemented
88	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
89	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
90	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
91	C₂₃×#432	C₂²	1	1	yes	characteristic
92	C₂₃×#432	C₂²	1	1	yes	characteristic
93	C₂₃×#432	C₂²	1	2	yes	complemented
94	C₂₃×#431	C₂²	1	2	yes	—
95	C₂₃×#431	C₂²	1	2	yes	complemented
96	C₂₃×#423	C₂²	1	2	yes	complemented
97	C₂₃×#407	C₂²	1	2	yes	—
98	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
99	C₂×#41×C₂₃	—	2	1	no	—
100	C₂×#41×C₂₃	—	2	1	no	—
101	C₂×#41×C₂₃	C₂³	1	2	yes	—
102	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₂₃	—	2	1	no	—
104	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₂₃	—	2	1	no	—
106	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
107	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
108	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
109	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
112	C₂×D₈×C₂₃	C₂³	1	4	yes	—
113	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
114	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₂₃×#127	C₂³	1	1	yes	characteristic
118	C₂₃×#126	—	2	2	no	—
119	C₂₃×#126	—	2	2	no	—
120	C₂₃×#126	—	2	2	no	—
121	C₂₃×#126	—	2	2	no	—
122	C₂₃×#126	—	2	2	no	—
123	C₂₃×#126	—	2	2	no	—
124	C₂₃×#125	—	2	1	no	—
125	C₂₃×#125	—	2	1	no	—
126	C₂₃×#125	—	2	1	no	—
127	C₂₃×#125	—	2	1	no	—
128	C₂₃×#125	C₂³	1	2	yes	—
129	C₂₃×#125	C₂³	1	2	yes	—
130	C₂₃×#125	C₂³	1	2	yes	—
131	C₂₃×#124	—	2	1	no	—
132	C₂₃×#124	—	2	1	no	—
133	C₂₃×#124	—	2	1	no	—
134	C₂₃×#124	—	2	1	no	—
135	C₂₃×#124	C₂³	1	2	yes	—
136	C₂₃×#124	C₂³	1	2	yes	—
137	C₂₃×#124	C₂³	1	2	yes	—
138	C₂₃×#123	—	2	2	no	—
139	C₂₃×#123	—	2	2	no	—
140	C₂₃×#123	—	2	2	no	—
141	C₂₃×#123	—	2	2	no	—
142	C₂₃×#123	—	2	2	no	—
143	C₂₃×#123	—	2	2	no	—
144	C₂₃×#123	—	2	2	no	—
145	C₂₃×C₂²⋊Q₈	—	2	1	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	1	no	—
150	C₂₃×C₂²⋊Q₈	—	2	1	no	—
151	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
155	C₂₃×#121	—	2	1	no	—
156	C₂₃×#121	—	2	1	no	—
157	C₂₃×#121	—	2	1	no	—
158	C₂₃×#121	—	2	1	no	—
159	C₂₃×#121	—	2	1	no	—
160	C₂₃×#121	—	2	1	no	—
161	C₂₃×#121	C₂³	1	2	yes	—
162	C₂₃×#121	C₂³	1	2	yes	—
163	C₂₃×#121	C₂³	1	2	yes	—
164	C₂₃×#121	C₂³	1	2	yes	—
165	C₂₃×#120	—	2	2	no	—
166	C₄×Q₈×C₂₃	—	2	1	no	—
167	C₄×Q₈×C₂₃	—	2	1	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	C₂³	1	2	yes	—
173	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
174	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
175	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
176	C₄×D₄×C₂₃	—	2	2	no	—
177	C₄×D₄×C₂₃	—	2	2	no	—
178	C₄×D₄×C₂₃	—	2	2	no	—
179	C₄×D₄×C₂₃	—	2	2	no	—
180	C₄×D₄×C₂₃	—	2	2	no	—
181	C₄×D₄×C₂₃	—	2	2	no	—
182	C₄×D₄×C₂₃	—	2	2	no	—
183	C₄×D₄×C₂₃	—	2	2	no	—
184	C₄×D₄×C₂₃	—	2	2	no	—
185	C₄×D₄×C₂₃	—	2	2	no	—
186	C₄×D₄×C₂₃	—	2	1	no	—
187	C₄×D₄×C₂₃	—	2	1	no	—
188	C₄×D₄×C₂₃	—	2	1	no	—
189	C₄×D₄×C₂₃	—	2	1	no	—
190	C₄×D₄×C₂₃	—	2	1	no	—
191	C₄×D₄×C₂₃	—	2	1	no	—
192	C₄×D₄×C₂₃	C₂³	1	2	yes	—
193	C₄×D₄×C₂₃	C₂³	1	2	yes	—
194	C₄×D₄×C₂₃	C₂³	1	2	yes	—
195	C₄×D₄×C₂₃	C₂³	1	2	yes	—
196	C₂₃×#117	—	2	1	no	—
197	C₂₃×#117	—	2	1	no	—
198	C₂₃×#117	—	2	2	no	—
199	C₂₃×#117	—	2	2	no	—
200	C₂₃×#117	—	2	2	no	—
201	C₂₃×#117	—	2	2	no	—
202	C₂₃×#117	—	2	2	no	—
203	C₂₃×#117	—	2	2	no	—
204	C₂₃×#117	—	2	2	no	—
205	C₂₃×#117	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
207	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
208	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
209	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
210	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
213	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
214	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
215	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
216	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
217	C₂×C₄²×C₂₃	—	2	1	no	—
218	C₂×C₄²×C₂₃	—	2	2	no	—
219	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
220	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
221	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
222	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
223	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
224	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
225	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
231	C₂₃×#107	C₂³	1	4	yes	—
232	C₂₃×#107	C₂³	1	4	yes	—
233	C₂₃×#106	C₂³	1	4	yes	—
234	C₂₃×#106	C₂³	1	4	yes	—
235	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
236	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
237	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
238	C₂₃×#103	C₂³	1	4	yes	—
239	C₂₃×#103	C₂³	1	4	yes	—
240	C₂₃×#103	C₂³	1	4	yes	—
241	C₂₃×#103	C₂³	1	4	yes	—
242	C₂₃×#102	C₂³	1	4	yes	—
243	C₂₃×#102	C₂³	1	4	yes	—
244	C₂₃×#102	C₂³	1	4	yes	—
245	C₂₃×#102	C₂³	1	4	yes	—
246	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
247	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
248	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
249	C₂₃×#97	C₂³	1	2	yes	—
250	C₂₃×#97	C₂³	1	2	yes	—
251	C₄×C₈×C₂₃	C₂³	1	4	yes	—
252	C₂⁴×C₂₃	—	2	1	no	—
253	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
254	#41×C₂₃	—	4	4	no	—
255	#41×C₂₃	—	4	4	no	—
256	#41×C₂₃	—	4	4	no	—
257	C₂×Q₈×C₂₃	—	2	1	no	—
258	C₂×Q₈×C₂₃	—	2	1	no	—
259	C₂×Q₈×C₂₃	—	2	1	no	—
260	C₂×Q₈×C₂₃	—	4	2	no	—
261	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
262	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
263	C₂×D₄×C₂₃	—	2	2	no	—
264	C₂×D₄×C₂₃	—	2	2	no	—
265	C₂×D₄×C₂₃	—	2	2	no	—
266	C₂×D₄×C₂₃	—	2	2	no	—
267	C₂×D₄×C₂₃	—	2	2	no	—
268	C₂×D₄×C₂₃	—	2	1	no	—
269	C₂×D₄×C₂₃	—	2	1	no	—
270	C₂×D₄×C₂₃	—	2	1	no	—
271	C₂×D₄×C₂₃	—	4	2	no	—
272	C₂×D₄×C₂₃	—	4	4	no	—
273	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
274	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₂₃	—	2	1	no	—
276	C₂²×C₄×C₂₃	—	2	1	no	—
277	C₂²×C₄×C₂₃	—	2	1	no	—
278	C₂²×C₄×C₂₃	—	2	2	no	—
279	C₂²×C₄×C₂₃	—	2	2	no	—
280	C₂²×C₄×C₂₃	—	2	2	no	—
281	C₂²×C₄×C₂₃	—	2	2	no	—
282	C₂²×C₄×C₂₃	—	2	2	no	—
283	C₂²×C₄×C₂₃	—	4	2	no	—
284	C₂²×C₄×C₂₃	—	4	2	no	—
285	C₂²×C₄×C₂₃	—	4	2	no	—
286	C₂²×C₄×C₂₃	—	4	4	no	—
287	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
305	Q₁₆×C₂₃	—	4	4	no	—
306	SD₁₆×C₂₃	—	4	4	no	—
307	SD₁₆×C₂₃	—	4	4	no	—
308	D₈×C₂₃	—	4	4	no	—
309	M₁₆×C₂₃	—	4	4	no	—
310	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
311	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
312	C₄⋊C₄×C₂₃	—	2	2	no	—
313	C₄⋊C₄×C₂₃	—	2	2	no	—
314	C₄⋊C₄×C₂₃	—	2	2	no	—
315	C₄⋊C₄×C₂₃	—	2	2	no	—
316	C₄⋊C₄×C₂₃	—	2	2	no	—
317	C₄⋊C₄×C₂₃	—	2	2	no	—
318	C₄⋊C₄×C₂₃	—	2	2	no	—
319	C₄⋊C₄×C₂₃	—	2	2	no	—
320	C₄⋊C₄×C₂₃	—	2	1	no	—
321	C₄⋊C₄×C₂₃	—	2	1	no	—
322	C₄⋊C₄×C₂₃	—	2	1	no	—
323	C₄⋊C₄×C₂₃	—	2	1	no	—
324	C₄⋊C₄×C₂₃	—	2	1	no	—
325	C₄⋊C₄×C₂₃	—	2	1	no	—
326	C₄⋊C₄×C₂₃	—	2	2	no	—
327	C₄⋊C₄×C₂₃	—	2	2	no	—
328	C₄⋊C₄×C₂₃	—	2	2	no	—
329	C₄⋊C₄×C₂₃	—	2	2	no	—
330	C₄⋊C₄×C₂₃	—	2	2	no	—
331	C₄⋊C₄×C₂₃	—	2	2	no	—
332	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
333	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
334	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
335	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
336	C₂²⋊C₄×C₂₃	—	2	2	no	—
337	C₂²⋊C₄×C₂₃	—	2	2	no	—
338	C₂²⋊C₄×C₂₃	—	2	2	no	—
339	C₂²⋊C₄×C₂₃	—	2	2	no	—
340	C₂²⋊C₄×C₂₃	—	2	2	no	—
341	C₂²⋊C₄×C₂₃	—	2	2	no	—
342	C₂²⋊C₄×C₂₃	—	2	2	no	—
343	C₂²⋊C₄×C₂₃	—	2	2	no	—
344	C₂²⋊C₄×C₂₃	—	2	2	no	—
345	C₂²⋊C₄×C₂₃	—	2	2	no	—
346	C₂²⋊C₄×C₂₃	—	2	2	no	—
347	C₂²⋊C₄×C₂₃	—	2	2	no	—
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	C₄²×C₂₃	—	2	2	no	—
356	C₄²×C₂₃	—	2	2	no	—
357	C₄²×C₂₃	—	2	2	no	—
358	C₄²×C₂₃	—	2	2	no	—
359	C₄²×C₂₃	—	2	2	no	—
360	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
361	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
362	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
363	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
364	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
365	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
366	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
367	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
368	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
369	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
370	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
371	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
374	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
375	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
376	#60954	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
377	C₂³×C₂₃	—	2	2	no	—
378	C₂³×C₂₃	—	2	2	no	—
379	C₂³×C₂₃	—	2	2	no	—
380	C₂³×C₂₃	—	4	1	no	—
381	C₂³×C₂₃	—	4	1	no	—
382	C₂³×C₂₃	—	4	2	no	—
383	C₂³×C₂₃	—	4	2	no	—
384	C₂³×C₂₃	—	4	2	no	—
385	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
386	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
387	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
388	Q₈×C₂₃	—	2	4	no	—
389	Q₈×C₂₃	—	2	4	no	—
390	Q₈×C₂₃	—	4	2	no	—
391	Q₈×C₂₃	—	4	2	no	—
392	Q₈×C₂₃	—	4	2	no	—
393	D₄×C₂₃	—	2	4	no	—
394	D₄×C₂₃	—	2	4	no	—
395	D₄×C₂₃	—	4	2	no	—
396	D₄×C₂₃	—	4	2	no	—
397	D₄×C₂₃	—	4	2	no	—
398	D₄×C₂₃	—	4	4	no	—
399	D₄×C₂₃	—	4	4	no	—
400	D₄×C₂₃	—	4	4	no	—
401	D₄×C₂₃	—	4	4	no	—
402	D₄×C₂₃	—	4	4	no	—
403	C₂×C₄×C₂₃	—	2	2	no	—
404	C₂×C₄×C₂₃	—	2	2	no	—
405	C₂×C₄×C₂₃	—	2	2	no	—
406	C₂×C₄×C₂₃	—	2	2	no	—
407	C₂×C₄×C₂₃	—	2	2	no	—
408	C₂×C₄×C₂₃	—	2	2	no	—
409	C₂×C₄×C₂₃	—	2	2	no	—
410	C₂×C₄×C₂₃	—	2	2	no	—
411	C₂×C₄×C₂₃	—	2	2	no	—
412	C₂×C₄×C₂₃	—	2	2	no	—
413	C₂×C₄×C₂₃	—	2	2	no	—
414	C₂×C₄×C₂₃	—	2	2	no	—
415	C₂×C₄×C₂₃	—	2	2	no	—
416	C₂×C₄×C₂₃	—	2	2	no	—
417	C₂×C₄×C₂₃	—	4	1	no	—
418	C₂×C₄×C₂₃	—	4	1	no	—
419	C₂×C₄×C₂₃	—	4	1	no	—
420	C₂×C₄×C₂₃	—	4	1	no	—
421	C₂×C₄×C₂₃	—	4	1	no	—
422	C₂×C₄×C₂₃	—	4	1	no	—
423	C₂×C₄×C₂₃	—	4	1	no	—
424	C₂×C₄×C₂₃	—	4	1	no	—
425	C₂×C₄×C₂₃	—	4	1	no	—
426	C₂×C₄×C₂₃	—	4	1	no	—
427	C₂×C₄×C₂₃	—	4	4	no	—
428	C₂×C₄×C₂₃	—	4	4	no	—
429	C₂×C₄×C₂₃	—	4	4	no	—
430	C₂×C₄×C₂₃	—	4	2	no	—
431	C₂×C₄×C₂₃	—	4	2	no	—
432	C₂×C₄×C₂₃	—	4	2	no	—
433	C₂×C₄×C₂₃	—	4	4	no	—
434	C₂×C₄×C₂₃	—	4	4	no	—
435	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
444	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
447	C₈×C₂₃	—	2	4	no	—
448	C₈×C₂₃	—	2	4	no	—
449	#3444	C₂×C₂₃	1	1	yes	characteristic, complemented
450	C₂×#529	C₂×C₂₃	1	1	yes	characteristic, complemented
451	#3256	C₂×C₂₃	1	4	yes	complemented
452	#3240	C₂×C₂₃	1	2	yes	complemented
453	#3236	C₂×C₂₃	1	1	yes	characteristic, complemented
454	#3234	C₂×C₂₃	1	1	yes	characteristic, complemented
455	#3219	C₂×C₂₃	1	2	yes	complemented
456	#3215	C₂×C₂₃	1	1	yes	characteristic, complemented
457	#3213	C₂×C₂₃	1	1	yes	characteristic, complemented
458	#3196	C₂×C₂₃	1	2	yes	complemented
459	#3194	C₂×C₂₃	1	2	yes	complemented
460	#3172	C₂×C₂₃	1	2	yes	complemented
461	#3171	C₂×C₂₃	1	2	yes	complemented
462	#3108	C₂×C₂₃	1	2	yes	complemented
463	#3105	C₂×C₂₃	1	2	yes	complemented
464	#3102	C₂×C₂₃	1	4	yes	complemented
465	#2920	C₂×C₂₃	1	1	yes	characteristic, complemented
466	C₂²×C₂₃	—	2	1	no	—
467	C₂²×C₂₃	—	2	1	no	—
468	C₂²×C₂₃	—	2	1	no	—
469	C₂²×C₂₃	—	2	1	no	—
470	C₂²×C₂₃	—	2	1	no	—
471	C₂²×C₂₃	—	2	1	no	—
472	C₂²×C₂₃	—	2	1	no	—
473	C₂²×C₂₃	—	2	1	no	—
474	C₂²×C₂₃	—	4	4	no	—
475	C₂²×C₂₃	—	4	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	—	8	4	no	—
482	C₂²×C₂₃	#575	1	2	yes	—
483	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
484	C₄×C₂₃	—	2	1	no	—
485	C₄×C₂₃	—	2	1	no	—
486	C₄×C₂₃	—	2	1	no	—
487	C₄×C₂₃	—	2	1	no	—
488	C₄×C₂₃	—	2	1	no	—
489	C₄×C₂₃	—	2	1	no	—
490	C₄×C₂₃	—	2	1	no	—
491	C₄×C₂₃	—	2	1	no	—
492	C₄×C₂₃	—	2	1	no	—
493	C₄×C₂₃	—	2	1	no	—
494	C₄×C₂₃	—	4	2	no	—
495	C₄×C₂₃	—	4	2	no	—
496	C₄×C₂₃	—	4	2	no	—
497	C₄×C₂₃	—	4	2	no	—
498	C₄×C₂₃	—	4	2	no	—
499	C₄×C₂₃	—	4	2	no	—
500	C₄×C₂₃	#575	1	2	yes	—
501	C₄×C₂₃	#585	1	2	yes	—
502	#533	C₂²×C₂₃	1	1	yes	characteristic
503	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
504	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
505	#532	C₂²×C₂₃	1	1	yes	characteristic
506	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
507	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
508	#529	—	2	1	no	—
509	#529	—	2	1	no	—
510	#529	—	2	1	no	—
511	#529	—	2	1	no	—
512	#529	—	2	1	no	—
513	#529	—	2	1	no	—
514	#529	—	2	1	no	—
515	#529	—	2	1	no	—
516	#529	C₂²×C₂₃	1	2	yes	—
517	#529	C₂²×C₂₃	1	2	yes	—
518	#529	C₂²×C₂₃	1	2	yes	—
519	#529	C₂²×C₂₃	1	2	yes	—
520	#529	C₂²×C₂₃	1	2	yes	—
521	#529	C₂²×C₂₃	1	2	yes	complemented
522	C₂×#126	—	2	1	no	—
523	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
524	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
525	#525	—	2	1	no	—
526	#525	—	2	1	no	—
527	#525	C₂²×C₂₃	1	2	yes	—
528	C₂×#123	—	2	1	no	—
529	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
530	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
531	C₄×#41	—	2	1	no	—
532	C₄×#41	—	2	1	no	—
533	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
534	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
535	C₂×C₄×D₄	—	2	1	no	—
536	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
537	C₂×#117	—	2	1	no	—
538	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
539	#501	C₂²×C₂₃	1	2	yes	complemented
540	#501	C₂²×C₂₃	1	2	yes	complemented
541	#497	C₂²×C₂₃	1	2	yes	complemented
542	#496	C₂²×C₂₃	1	2	yes	complemented
543	#491	C₂²×C₂₃	1	2	yes	complemented
544	#490	C₂²×C₂₃	1	2	yes	complemented
545	#489	C₂²×C₂₃	1	2	yes	complemented
546	#489	C₂²×C₂₃	1	2	yes	complemented
547	#485	C₂²×C₂₃	1	4	yes	complemented
548	#484	C₂²×C₂₃	1	2	yes	—
549	#483	C₂²×C₂₃	1	2	yes	—
550	#482	C₂²×C₂₃	1	4	yes	—
551	#481	C₂²×C₂₃	1	2	yes	—
552	#480	C₂²×C₂₃	1	2	yes	—
553	#479	C₂²×C₂₃	1	4	yes	complemented
554	#479	C₂²×C₂₃	1	4	yes	complemented
555	#478	C₂²×C₂₃	1	4	yes	complemented
556	#478	C₂²×C₂₃	1	4	yes	complemented
557	#470	C₂²×C₂₃	1	4	yes	complemented
558	#469	C₂²×C₂₃	1	4	yes	—
559	#468	C₂²×C₂₃	1	4	yes	—
560	#468	C₂²×C₂₃	1	4	yes	complemented
561	#464	C₂²×C₂₃	1	4	yes	complemented
562	#464	C₂²×C₂₃	1	4	yes	complemented
563	#463	C₂²×C₂₃	1	4	yes	complemented
564	#463	C₂²×C₂₃	1	4	yes	complemented
565	#452	C₂²×C₂₃	1	4	yes	complemented
566	#451	C₂²×C₂₃	1	2	yes	—
567	#450	C₂²×C₂₃	1	2	yes	—
568	#449	C₂²×C₂₃	1	4	yes	—
569	#448	C₂²×C₂₃	1	2	yes	—
570	#447	C₂²×C₂₃	1	2	yes	—
571	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	complemented
572	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
573	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
574	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
575	#432	C₂²×C₂₃	1	1	yes	characteristic
576	#432	C₂²×C₂₃	1	1	yes	characteristic
577	#432	C₂²×C₂₃	1	2	yes	complemented
578	#431	C₂²×C₂₃	1	2	yes	—
579	#431	C₂²×C₂₃	1	2	yes	complemented
580	#423	C₂²×C₂₃	1	2	yes	complemented
581	#407	C₂²×C₂₃	1	2	yes	—
582	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
583	C₂×C₂₃	—	2	2	no	—
584	C₂×C₂₃	—	4	1	no	—
585	C₂×C₂₃	—	4	1	no	—
586	C₂×C₂₃	—	8	2	no	—
587	C₂×C₂₃	—	8	2	no	—
588	C₂×C₂₃	#3449	1	1	yes	characteristic
589	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
590	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
591	C₂×#41	—	2	1	no	—
592	C₂×#41	—	2	1	no	—
593	C₂×#41	C₂³×C₂₃	1	2	yes	—
594	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
595	C₂²×D₄	—	2	1	no	—
596	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
597	C₂³×C₄	—	2	1	no	—
598	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
599	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
600	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
601	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
602	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
603	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
604	C₂×D₈	C₂³×C₂₃	1	4	yes	—
605	C₂×M₁₆	C₂³×C₂₃	1	4	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	1	yes	characteristic
609	#127	C₂³×C₂₃	1	1	yes	characteristic
610	#126	—	2	2	no	—
611	#126	—	2	2	no	—
612	#126	—	2	2	no	—
613	#126	—	2	2	no	—
614	#126	—	2	2	no	—
615	#126	—	2	2	no	—
616	#125	—	2	1	no	—
617	#125	—	2	1	no	—
618	#125	—	2	1	no	—
619	#125	—	2	1	no	—
620	#125	C₂³×C₂₃	1	2	yes	—
621	#125	C₂³×C₂₃	1	2	yes	—
622	#125	C₂³×C₂₃	1	2	yes	—
623	#124	—	2	1	no	—
624	#124	—	2	1	no	—
625	#124	—	2	1	no	—
626	#124	—	2	1	no	—
627	#124	C₂³×C₂₃	1	2	yes	—
628	#124	C₂³×C₂₃	1	2	yes	—
629	#124	C₂³×C₂₃	1	2	yes	—
630	#123	—	2	2	no	—
631	#123	—	2	2	no	—
632	#123	—	2	2	no	—
633	#123	—	2	2	no	—
634	#123	—	2	2	no	—
635	#123	—	2	2	no	—
636	#123	—	2	2	no	—
637	C₂²⋊Q₈	—	2	1	no	—
638	C₂²⋊Q₈	—	2	1	no	—
639	C₂²⋊Q₈	—	2	1	no	—
640	C₂²⋊Q₈	—	2	1	no	—
641	C₂²⋊Q₈	—	2	1	no	—
642	C₂²⋊Q₈	—	2	1	no	—
643	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
644	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
645	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
646	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
647	#121	—	2	1	no	—
648	#121	—	2	1	no	—
649	#121	—	2	1	no	—
650	#121	—	2	1	no	—
651	#121	—	2	1	no	—
652	#121	—	2	1	no	—
653	#121	C₂³×C₂₃	1	2	yes	—
654	#121	C₂³×C₂₃	1	2	yes	—
655	#121	C₂³×C₂₃	1	2	yes	—
656	#121	C₂³×C₂₃	1	2	yes	—
657	#120	—	2	2	no	—
658	C₄×Q₈	—	2	1	no	—
659	C₄×Q₈	—	2	1	no	—
660	C₄×Q₈	—	2	1	no	—
661	C₄×Q₈	—	2	1	no	—
662	C₄×Q₈	—	2	1	no	—
663	C₄×Q₈	—	2	1	no	—
664	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
665	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
666	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
667	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	1	no	—
679	C₄×D₄	—	2	1	no	—
680	C₄×D₄	—	2	1	no	—
681	C₄×D₄	—	2	1	no	—
682	C₄×D₄	—	2	1	no	—
683	C₄×D₄	—	2	1	no	—
684	C₄×D₄	C₂³×C₂₃	1	2	yes	—
685	C₄×D₄	C₂³×C₂₃	1	2	yes	—
686	C₄×D₄	C₂³×C₂₃	1	2	yes	—
687	C₄×D₄	C₂³×C₂₃	1	2	yes	—
688	#117	—	2	1	no	—
689	#117	—	2	1	no	—
690	#117	—	2	2	no	—
691	#117	—	2	2	no	—
692	#117	—	2	2	no	—
693	#117	—	2	2	no	—
694	#117	—	2	2	no	—
695	#117	—	2	2	no	—
696	#117	—	2	2	no	—
697	#117	C₂³×C₂₃	1	2	yes	—
698	C₂×C₄⋊C₄	—	2	1	no	—
699	C₂×C₄⋊C₄	—	2	1	no	—
700	C₂×C₄⋊C₄	—	2	1	no	—
701	C₂×C₄⋊C₄	—	2	1	no	—
702	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
703	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
704	C₂×C₂²⋊C₄	—	2	1	no	—
705	C₂×C₂²⋊C₄	—	2	1	no	—
706	C₂×C₂²⋊C₄	—	2	1	no	—
707	C₂×C₂²⋊C₄	—	2	1	no	—
708	C₂×C₂²⋊C₄	—	2	1	no	—
709	C₂×C₄²	—	2	1	no	—
710	C₂×C₄²	—	2	2	no	—
711	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
712	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
713	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
714	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
715	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
716	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
717	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
718	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
719	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
720	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
721	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
722	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
723	#107	C₂³×C₂₃	1	4	yes	—
724	#107	C₂³×C₂₃	1	4	yes	—
725	#106	C₂³×C₂₃	1	4	yes	—
726	#106	C₂³×C₂₃	1	4	yes	—
727	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
728	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
729	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
730	#103	C₂³×C₂₃	1	4	yes	—
731	#103	C₂³×C₂₃	1	4	yes	—
732	#103	C₂³×C₂₃	1	4	yes	—
733	#103	C₂³×C₂₃	1	4	yes	—
734	#102	C₂³×C₂₃	1	4	yes	—
735	#102	C₂³×C₂₃	1	4	yes	—
736	#102	C₂³×C₂₃	1	4	yes	—
737	#102	C₂³×C₂₃	1	4	yes	—
738	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
739	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
740	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
741	#97	C₂³×C₂₃	1	2	yes	—
742	#97	C₂³×C₂₃	1	2	yes	—
743	C₄×C₈	C₂³×C₂₃	1	4	yes	—
744	C₂₃	#60954	1	1	yes	characteristic, direct product factor, Sylow
745	C₂⁴	—	2	1	no	—
746	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
747	#41	—	4	4	no	—
748	#41	—	4	4	no	—
749	#41	—	4	4	no	—
750	C₂×Q₈	—	2	1	no	—
751	C₂×Q₈	—	2	1	no	—
752	C₂×Q₈	—	2	1	no	—
753	C₂×Q₈	—	4	2	no	—
754	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
755	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	1	no	—
762	C₂×D₄	—	2	1	no	—
763	C₂×D₄	—	2	1	no	—
764	C₂×D₄	—	4	2	no	—
765	C₂×D₄	—	4	4	no	—
766	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
767	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	1	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	4	2	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	—	4	4	no	—
780	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
781	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
782	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
783	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
784	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
785	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
786	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
787	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
788	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
789	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
790	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
791	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
792	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
793	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
794	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
798	Q₁₆	—	4	4	no	—
799	SD₁₆	—	4	4	no	—
800	SD₁₆	—	4	4	no	—
801	D₈	—	4	4	no	—
802	M₁₆	—	4	4	no	—
803	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
804	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	1	no	—
814	C₄⋊C₄	—	2	1	no	—
815	C₄⋊C₄	—	2	1	no	—
816	C₄⋊C₄	—	2	1	no	—
817	C₄⋊C₄	—	2	1	no	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
827	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
828	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
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	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
854	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
855	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
856	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
857	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
858	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
859	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
860	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
861	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
862	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
863	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
864	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
865	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
866	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
867	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
868	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
869	C₂³	—	2	2	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	4	1	no	—
873	C₂³	—	4	1	no	—
874	C₂³	—	4	2	no	—
875	C₂³	—	4	2	no	—
876	C₂³	—	4	2	no	—
877	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
878	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
879	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
880	Q₈	—	2	4	no	—
881	Q₈	—	2	4	no	—
882	Q₈	—	4	2	no	—
883	Q₈	—	4	2	no	—
884	Q₈	—	4	2	no	—
885	D₄	—	2	4	no	—
886	D₄	—	2	4	no	—
887	D₄	—	4	2	no	—
888	D₄	—	4	2	no	—
889	D₄	—	4	2	no	—
890	D₄	—	4	4	no	—
891	D₄	—	4	4	no	—
892	D₄	—	4	4	no	—
893	D₄	—	4	4	no	—
894	D₄	—	4	4	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	4	1	no	—
911	C₂×C₄	—	4	1	no	—
912	C₂×C₄	—	4	1	no	—
913	C₂×C₄	—	4	1	no	—
914	C₂×C₄	—	4	1	no	—
915	C₂×C₄	—	4	1	no	—
916	C₂×C₄	—	4	1	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	4	4	no	—
920	C₂×C₄	—	4	4	no	—
921	C₂×C₄	—	4	4	no	—
922	C₂×C₄	—	4	2	no	—
923	C₂×C₄	—	4	2	no	—
924	C₂×C₄	—	4	2	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	4	no	—
927	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
928	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
929	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
930	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
931	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
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	1	yes	characteristic
936	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
937	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
938	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
939	C₈	—	2	4	no	—
940	C₈	—	2	4	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	1	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	1	no	—
948	C₂²	—	2	1	no	—
949	C₂²	—	4	4	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	—	8	4	no	—
957	C₂²	C₂₃×#575	1	2	yes	—
958	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
959	C₄	—	2	1	no	—
960	C₄	—	2	1	no	—
961	C₄	—	2	1	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	1	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	1	no	—
966	C₄	—	2	1	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	1	no	—
969	C₄	—	4	2	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×#575	1	2	yes	—
976	C₄	C₂₃×#585	1	2	yes	—
977	C₂	—	2	2	no	—
978	C₂	—	4	1	no	—
979	C₂	—	4	1	no	—
980	C₂	—	8	2	no	—
981	C₂	—	8	2	no	—
982	C₂	C₂₃×#3449	1	1	yes	characteristic
983	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
984	C₂	C₂×C₂₃×#575	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3444	C₂	semidirect
2. C₂×C₂₃×#529	C₂	semidirect
3. C₂₃×#3256	C₂	semidirect
4. C₂₃×#3240	C₂	semidirect
5. C₂₃×#3236	C₂	semidirect
6. C₂₃×#3234	C₂	semidirect
7. C₂₃×#3219	C₂	semidirect
8. C₂₃×#3215	C₂	semidirect
9. C₂₃×#3213	C₂	semidirect
10. C₂₃×#3196	C₂	semidirect
11. C₂₃×#3194	C₂	semidirect
12. C₂₃×#3172	C₂	semidirect
13. C₂₃×#3171	C₂	semidirect
14. C₂₃×#3108	C₂	semidirect
15. C₂₃×#3105	C₂	semidirect
16. C₂₃×#3102	C₂	semidirect
17. C₂₃×#2920	C₂	semidirect
19. C₂₃×#533	C₂²	semidirect
20. C₂₃×#533	C₂²	semidirect
22. C₂₃×#532	C₂²	semidirect
23. C₂₃×#532	C₂²	semidirect
37. C₂₃×#529	C₂²	semidirect
49. C₄×#41×C₂₃	C₂²	semidirect
55. C₂₃×#501	C₂²	semidirect
56. C₂₃×#501	C₂²	semidirect
57. C₂₃×#497	C₂²	semidirect
58. C₂₃×#496	C₂²	semidirect
59. C₂₃×#491	C₂²	semidirect
60. C₂₃×#490	C₂²	semidirect
61. C₂₃×#489	C₂²	semidirect
62. C₂₃×#489	C₂²	semidirect
63. C₂₃×#485	C₂²	semidirect
69. C₂₃×#479	C₂²	semidirect
70. C₂₃×#479	C₂²	semidirect
71. C₂₃×#478	C₂²	semidirect
72. C₂₃×#478	C₂²	semidirect
73. C₂₃×#470	C₂²	semidirect
76. C₂₃×#468	C₂²	semidirect
77. C₂₃×#464	C₂²	semidirect
78. C₂₃×#464	C₂²	semidirect
79. C₂₃×#463	C₂²	semidirect
80. C₂₃×#463	C₂²	semidirect
81. C₂₃×#452	C₂²	semidirect
87. C₄×Q₁₆×C₂₃	C₂²	semidirect
88. C₄×SD₁₆×C₂₃	C₂²	semidirect
89. C₄×SD₁₆×C₂₃	C₂²	semidirect
90. C₄×D₈×C₂₃	C₂²	semidirect
93. C₂₃×#432	C₂²	semidirect
95. C₂₃×#431	C₂²	semidirect
96. C₂₃×#423	C₂²	semidirect
98. C₄×M₁₆×C₂₃	C₂²	semidirect
376. #60954	C₂₃	direct (N × H)
449. #3444	C₂×C₂₃	semidirect
450. C₂×#529	C₂×C₂₃	semidirect
451. #3256	C₂×C₂₃	semidirect
452. #3240	C₂×C₂₃	semidirect
453. #3236	C₂×C₂₃	semidirect
454. #3234	C₂×C₂₃	semidirect
455. #3219	C₂×C₂₃	semidirect
456. #3215	C₂×C₂₃	semidirect
457. #3213	C₂×C₂₃	semidirect
458. #3196	C₂×C₂₃	semidirect
459. #3194	C₂×C₂₃	semidirect
460. #3172	C₂×C₂₃	semidirect
461. #3171	C₂×C₂₃	semidirect
462. #3108	C₂×C₂₃	semidirect
463. #3105	C₂×C₂₃	semidirect
464. #3102	C₂×C₂₃	semidirect
465. #2920	C₂×C₂₃	semidirect
503. #533	C₂²×C₂₃	semidirect
504. #533	C₂²×C₂₃	semidirect
506. #532	C₂²×C₂₃	semidirect
507. #532	C₂²×C₂₃	semidirect
521. #529	C₂²×C₂₃	semidirect
533. C₄×#41	C₂²×C₂₃	semidirect
539. #501	C₂²×C₂₃	semidirect
540. #501	C₂²×C₂₃	semidirect
541. #497	C₂²×C₂₃	semidirect
542. #496	C₂²×C₂₃	semidirect
543. #491	C₂²×C₂₃	semidirect
544. #490	C₂²×C₂₃	semidirect
545. #489	C₂²×C₂₃	semidirect
546. #489	C₂²×C₂₃	semidirect
547. #485	C₂²×C₂₃	semidirect
553. #479	C₂²×C₂₃	semidirect
554. #479	C₂²×C₂₃	semidirect
555. #478	C₂²×C₂₃	semidirect
556. #478	C₂²×C₂₃	semidirect
557. #470	C₂²×C₂₃	semidirect
560. #468	C₂²×C₂₃	semidirect
561. #464	C₂²×C₂₃	semidirect
562. #464	C₂²×C₂₃	semidirect
563. #463	C₂²×C₂₃	semidirect
564. #463	C₂²×C₂₃	semidirect
565. #452	C₂²×C₂₃	semidirect
571. C₄×Q₁₆	C₂²×C₂₃	semidirect
572. C₄×SD₁₆	C₂²×C₂₃	semidirect
573. C₄×SD₁₆	C₂²×C₂₃	semidirect
574. C₄×D₈	C₂²×C₂₃	semidirect
577. #432	C₂²×C₂₃	semidirect
579. #431	C₂²×C₂₃	semidirect
580. #423	C₂²×C₂₃	semidirect
582. C₄×M₁₆	C₂²×C₂₃	semidirect
744. C₂₃	#60954	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×#3444	2
C₂×C₂₃×#529	2
C₂₃×#3256	2
C₂₃×#3240	2
C₂₃×#3236	2
C₂₃×#3234	2
C₂₃×#3219	2
C₂₃×#3215	2
C₂₃×#3213	2
C₂₃×#3196	2
C₂₃×#3194	2
C₂₃×#3172	2
C₂₃×#3171	2
C₂₃×#3108	2
C₂₃×#3105	2
C₂₃×#3102	2
C₂₃×#2920	2
#60954	23

Subgroups — C23×#60954 #19208580

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60954 #19208580