Subgroups — C₂₃×#60892 #19208518

Order 5888.

1736 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3460	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3244	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3241	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3238	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3235	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3233	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3227	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3163	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3136	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3099	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3096	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	Q₈²×C₂₃	—	2	1	no	—
19	C₂₃×#557	—	2	1	no	—
20	C₂₃×#554	—	2	2	no	—
21	C₂₃×#554	—	2	1	no	—
22	D₄×Q₈×C₂₃	—	2	2	no	—
23	D₄×Q₈×C₂₃	—	2	1	no	—
24	C₂₃×#544	C₂²	1	1	yes	characteristic
25	C₂₃×#544	C₂²	1	2	yes	—
26	C₂₃×#544	C₂²	1	4	yes	complemented
27	C₂₃×#542	—	2	1	no	—
28	C₂₃×#542	C₂²	1	2	yes	—
29	C₂₃×#540	—	2	1	no	—
30	C₂₃×#540	C₂²	1	2	yes	—
31	C₂₃×#538	—	2	2	no	—
32	C₂₃×#537	C₂²	1	1	yes	characteristic
33	C₂₃×#535	C₂²	1	1	yes	characteristic
34	C₂₃×#535	C₂²	1	1	yes	characteristic
35	C₂₃×#533	C₂²	1	1	yes	characteristic
36	C₂₃×#533	C₂²	1	2	yes	complemented
37	C₂₃×#532	—	2	1	no	—
38	C₂₃×#532	C₂²	1	2	yes	—
39	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
41	C₂₃×#529	—	2	1	no	—
42	C₂₃×#529	C₂²	1	2	yes	—
43	C₂₃×#525	—	2	2	no	—
44	C₂₃×#520	C₂²	1	2	yes	—
45	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
46	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
48	C₂₃×#501	C₂²	1	4	yes	complemented
49	C₂₃×#501	C₂²	1	4	yes	complemented
50	C₂₃×#499	C₂²	1	4	yes	complemented
51	C₂₃×#498	C₂²	1	4	yes	complemented
52	C₂₃×#490	C₂²	1	4	yes	—
53	C₂₃×#489	C₂²	1	4	yes	—
54	C₂₃×#488	C₂²	1	4	yes	—
55	C₂₃×#486	C₂²	1	4	yes	—
56	C₂₃×#485	C₂²	1	4	yes	complemented
57	C₂₃×#483	C₂²	1	4	yes	complemented
58	C₂₃×#482	C₂²	1	4	yes	—
59	C₂₃×#482	C₂²	1	4	yes	—
60	C₂₃×#482	C₂²	1	4	yes	complemented
61	C₂₃×#481	C₂²	1	4	yes	—
62	C₂₃×#481	C₂²	1	4	yes	complemented
63	C₂₃×#480	C₂²	1	4	yes	—
64	C₂₃×#479	C₂²	1	2	yes	complemented
65	C₂₃×#478	C₂²	1	4	yes	—
66	C₂₃×#478	C₂²	1	2	yes	complemented
67	C₂₃×#477	C₂²	1	2	yes	complemented
68	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×#476	C₂²	1	2	yes	—
70	C₂₃×#476	C₂²	1	2	yes	—
71	C₂₃×#476	C₂²	1	2	yes	—
72	C₂₃×#476	C₂²	1	4	yes	—
73	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
74	C₂₃×#476	C₂²	1	2	yes	complemented
75	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
76	C₂₃×#475	C₂²	1	2	yes	complemented
77	C₂₃×#474	C₂²	1	2	yes	—
78	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
79	C₂₃×#474	C₂²	1	2	yes	complemented
80	C₂₃×#433	C₂²	1	4	yes	complemented
81	C₂₃×#432	C₂²	1	2	yes	complemented
82	C₂₃×#431	C₂²	1	2	yes	complemented
83	C₂₃×#428	C₂²	1	2	yes	—
84	C₂₃×#428	C₂²	1	2	yes	—
85	C₂₃×#427	C₂²	1	2	yes	—
86	C₂×C₂₃×#106	C₂²	1	2	yes	—
87	C₂₃×#423	C₂²	1	1	yes	characteristic
88	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
89	C₂₃×#418	C₂²	1	2	yes	—
90	C₂₃×#417	C₂²	1	2	yes	—
91	C₂₃×#416	C₂²	1	2	yes	—
92	C₂×C₂₃×#102	C₂²	1	2	yes	—
93	C₂₃×#408	C₂²	1	2	yes	—
94	C₂₃×#405	C₂²	1	2	yes	—
95	C₂×#41×C₂₃	—	2	2	no	—
96	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
97	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₂₃	—	2	1	no	—
99	C₂²×Q₈×C₂₃	—	2	2	no	—
100	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₂₃	—	2	1	no	—
102	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
103	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
104	C₂₃×C₄⋊Q₈	—	2	2	no	—
105	C₂₃×C₄⋊Q₈	—	2	4	no	—
106	C₂₃×C₄⋊Q₈	—	2	1	no	—
107	C₂₃×C₄⋊Q₈	—	2	1	no	—
108	C₂₃×C₄⋊Q₈	—	2	2	no	—
109	C₂₃×C₄⋊Q₈	—	2	1	no	—
110	C₂₃×C₄⋊Q₈	—	2	2	no	—
111	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₂₃×#127	—	2	1	no	—
118	C₂₃×#127	C₂³	1	2	yes	—
119	C₂₃×#126	—	2	2	no	—
120	C₂₃×#126	—	2	2	no	—
121	C₂₃×#125	—	2	2	no	—
122	C₂₃×#125	—	2	4	no	—
123	C₂₃×#125	—	2	1	no	—
124	C₂₃×#125	C₂³	1	2	yes	—
125	C₂₃×#125	C₂³	1	4	yes	—
126	C₂₃×#125	C₂³	1	2	yes	—
127	C₂₃×#124	—	2	1	no	—
128	C₂₃×#124	—	2	2	no	—
129	C₂₃×#124	—	2	2	no	—
130	C₂₃×#124	C₂³	1	2	yes	—
131	C₂₃×#123	—	2	2	no	—
132	C₂₃×#123	—	2	2	no	—
133	C₂₃×#123	—	2	2	no	—
134	C₂₃×#123	—	2	2	no	—
135	C₂₃×C₂²⋊Q₈	—	2	1	no	—
136	C₂₃×C₂²⋊Q₈	—	2	1	no	—
137	C₂₃×C₂²⋊Q₈	—	2	2	no	—
138	C₂₃×C₂²⋊Q₈	—	2	1	no	—
139	C₂₃×C₂²⋊Q₈	—	2	2	no	—
140	C₂₃×C₂²⋊Q₈	—	2	2	no	—
141	C₂₃×C₂²⋊Q₈	—	2	4	no	—
142	C₂₃×C₂²⋊Q₈	—	2	4	no	—
143	C₂₃×C₂²⋊Q₈	—	2	4	no	—
144	C₂₃×C₂²⋊Q₈	—	2	2	no	—
145	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₂₃×#121	—	2	2	no	—
147	C₂₃×#121	—	2	1	no	—
148	C₂₃×#121	—	2	2	no	—
149	C₂₃×#121	—	2	1	no	—
150	C₂₃×#121	—	2	1	no	—
151	C₂₃×#121	—	2	2	no	—
152	C₂₃×#121	—	2	2	no	—
153	C₂₃×#121	C₂³	1	2	yes	—
154	C₂₃×#121	C₂³	1	2	yes	—
155	C₂₃×#121	C₂³	1	2	yes	—
156	C₂₃×#120	—	2	2	no	—
157	C₂₃×#120	—	2	2	no	—
158	C₄×Q₈×C₂₃	—	2	2	no	—
159	C₄×Q₈×C₂₃	—	2	1	no	—
160	C₄×Q₈×C₂₃	—	2	2	no	—
161	C₄×Q₈×C₂₃	—	2	1	no	—
162	C₄×Q₈×C₂₃	—	2	2	no	—
163	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
164	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
165	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₂₃	—	2	4	no	—
168	C₄×D₄×C₂₃	—	2	2	no	—
169	C₄×D₄×C₂₃	—	2	1	no	—
170	C₄×D₄×C₂₃	—	2	1	no	—
171	C₄×D₄×C₂₃	—	2	2	no	—
172	C₄×D₄×C₂₃	—	2	1	no	—
173	C₄×D₄×C₂₃	—	2	1	no	—
174	C₄×D₄×C₂₃	—	2	2	no	—
175	C₄×D₄×C₂₃	D₄	1	2	yes	—
176	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
177	C₄×D₄×C₂₃	D₄	1	2	yes	—
178	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
179	C₄×D₄×C₂₃	C₂³	1	2	yes	—
180	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₂₃	C₂³	1	2	yes	—
183	C₂₃×#117	—	2	1	no	—
184	C₂₃×#117	—	2	2	no	—
185	C₂₃×#117	C₂³	1	2	yes	—
186	C₂₃×#117	C₂³	1	1	yes	characteristic
187	C₂₃×#117	C₂³	1	4	yes	—
188	C₂₃×#117	C₂³	1	1	yes	characteristic
189	C₂₃×#117	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
191	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
192	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
195	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
196	C₂×C₄²×C₂₃	—	2	1	no	—
197	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
199	C₂₃×#107	C₂³	1	2	yes	—
200	C₂₃×#107	C₂³	1	2	yes	—
201	C₂₃×#107	C₂³	1	4	yes	—
202	C₂₃×#107	C₂³	1	4	yes	—
203	C₂₃×#106	C₂³	1	4	yes	—
204	C₂₃×#106	C₂³	1	4	yes	—
205	C₂₃×#106	C₂³	1	2	yes	—
206	C₂₃×#106	C₂³	1	2	yes	—
207	C₂₃×#106	C₂³	1	4	yes	—
208	C₂₃×#106	C₂³	1	4	yes	—
209	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
210	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
211	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
212	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₂₃×#103	C₂³	1	2	yes	—
215	C₂₃×#103	C₂³	1	2	yes	—
216	C₂₃×#103	C₂³	1	4	yes	—
217	C₂₃×#102	C₂³	1	4	yes	—
218	C₂₃×#102	C₂³	1	4	yes	—
219	C₂₃×#102	C₂³	1	2	yes	—
220	C₂₃×#102	C₂³	1	2	yes	—
221	C₂₃×#102	C₂³	1	4	yes	—
222	C₂₃×#102	C₂³	1	4	yes	—
223	C₂₃×#102	C₂³	1	4	yes	—
224	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
225	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₂₃×#97	C₂³	1	4	yes	—
227	C₄×C₈×C₂₃	C₂³	1	4	yes	—
228	C₂⁴×C₂₃	—	2	1	no	—
229	#41×C₂₃	—	2	2	no	—
230	#41×C₂₃	—	2	2	no	—
231	#41×C₂₃	—	2	2	no	—
232	#41×C₂₃	—	2	2	no	—
233	#41×C₂₃	—	8	4	no	—
234	C₂×Q₈×C₂₃	—	2	1	no	—
235	C₂×Q₈×C₂₃	—	2	1	no	—
236	C₂×Q₈×C₂₃	—	2	2	no	—
237	C₂×Q₈×C₂₃	—	2	2	no	—
238	C₂×Q₈×C₂₃	—	2	2	no	—
239	C₂×Q₈×C₂₃	—	2	4	no	—
240	C₂×Q₈×C₂₃	—	8	2	no	—
241	C₂×Q₈×C₂₃	—	8	4	no	—
242	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
244	C₂×D₄×C₂₃	—	2	1	no	—
245	C₂×D₄×C₂₃	—	2	2	no	—
246	C₂×D₄×C₂₃	—	2	2	no	—
247	C₂×D₄×C₂₃	—	2	2	no	—
248	C₂×D₄×C₂₃	—	2	1	no	—
249	C₂×D₄×C₂₃	—	2	2	no	—
250	C₂×D₄×C₂₃	—	2	2	no	—
251	C₂×D₄×C₂₃	—	2	2	no	—
252	C₂×D₄×C₂₃	—	2	2	no	—
253	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
254	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
255	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
256	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₂₃	—	2	1	no	—
258	C₂²×C₄×C₂₃	—	2	4	no	—
259	C₂²×C₄×C₂₃	—	2	2	no	—
260	C₂²×C₄×C₂₃	—	2	1	no	—
261	C₂²×C₄×C₂₃	—	2	1	no	—
262	C₂²×C₄×C₂₃	—	2	2	no	—
263	C₂²×C₄×C₂₃	—	2	1	no	—
264	C₂²×C₄×C₂₃	—	2	2	no	—
265	C₂²×C₄×C₂₃	—	8	2	no	—
266	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
272	M₁₆×C₂₃	—	2	4	no	—
273	C₂×C₈×C₂₃	—	2	4	no	—
274	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
275	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
276	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₂₃	—	2	2	no	—
278	C₄⋊C₄×C₂₃	—	2	1	no	—
279	C₄⋊C₄×C₂₃	—	2	2	no	—
280	C₄⋊C₄×C₂₃	—	2	4	no	—
281	C₄⋊C₄×C₂₃	—	2	1	no	—
282	C₄⋊C₄×C₂₃	—	2	4	no	—
283	C₄⋊C₄×C₂₃	—	2	2	no	—
284	C₄⋊C₄×C₂₃	—	2	1	no	—
285	C₄⋊C₄×C₂₃	—	2	1	no	—
286	C₄⋊C₄×C₂₃	—	2	2	no	—
287	C₄⋊C₄×C₂₃	—	2	2	no	—
288	C₄⋊C₄×C₂₃	—	2	2	no	—
289	C₄⋊C₄×C₂₃	—	2	2	no	—
290	C₄⋊C₄×C₂₃	—	2	1	no	—
291	C₄⋊C₄×C₂₃	—	2	2	no	—
292	C₄⋊C₄×C₂₃	—	2	4	no	—
293	C₄⋊C₄×C₂₃	—	2	2	no	—
294	C₄⋊C₄×C₂₃	—	2	4	no	—
295	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
296	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
300	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
305	C₂²⋊C₄×C₂₃	—	2	1	no	—
306	C₂²⋊C₄×C₂₃	—	2	4	no	—
307	C₂²⋊C₄×C₂₃	—	2	2	no	—
308	C₂²⋊C₄×C₂₃	—	2	2	no	—
309	C₂²⋊C₄×C₂₃	—	2	2	no	—
310	C₂²⋊C₄×C₂₃	—	2	2	no	—
311	C₂²⋊C₄×C₂₃	—	2	1	no	—
312	C₂²⋊C₄×C₂₃	—	2	1	no	—
313	C₂²⋊C₄×C₂₃	—	2	2	no	—
314	C₂²⋊C₄×C₂₃	—	2	2	no	—
315	C₂²⋊C₄×C₂₃	—	2	2	no	—
316	C₂²⋊C₄×C₂₃	—	2	2	no	—
317	C₂²⋊C₄×C₂₃	—	2	2	no	—
318	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
319	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
320	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
321	C₄²×C₂₃	—	2	1	no	—
322	C₄²×C₂₃	—	2	1	no	—
323	C₄²×C₂₃	—	2	1	no	—
324	C₄²×C₂₃	—	2	4	no	—
325	C₄²×C₂₃	—	2	2	no	—
326	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₂₃	C₂×D₄	1	2	yes	—
328	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₂₃	C₂×D₄	1	2	yes	—
330	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
331	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
332	C₄²×C₂₃	C₂⁴	1	2	yes	—
333	#60892	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
334	C₂³×C₂₃	—	2	2	no	—
335	C₂³×C₂₃	—	2	1	no	—
336	C₂³×C₂₃	—	4	2	no	—
337	C₂³×C₂₃	—	8	1	no	—
338	C₂³×C₂₃	—	8	1	no	—
339	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
340	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
341	Q₈×C₂₃	—	2	2	no	—
342	Q₈×C₂₃	—	2	1	no	—
343	Q₈×C₂₃	—	2	1	no	—
344	Q₈×C₂₃	—	4	2	no	—
345	Q₈×C₂₃	—	4	4	no	—
346	Q₈×C₂₃	—	4	2	no	—
347	Q₈×C₂₃	—	8	2	no	—
348	Q₈×C₂₃	—	8	4	no	—
349	Q₈×C₂₃	—	8	2	no	—
350	D₄×C₂₃	—	2	4	no	—
351	D₄×C₂₃	—	2	2	no	—
352	D₄×C₂₃	—	2	2	no	—
353	D₄×C₂₃	—	2	2	no	—
354	D₄×C₂₃	—	2	1	no	—
355	D₄×C₂₃	—	2	1	no	—
356	D₄×C₂₃	—	4	2	no	—
357	D₄×C₂₃	—	4	2	no	—
358	D₄×C₂₃	—	8	2	no	—
359	D₄×C₂₃	—	8	2	no	—
360	D₄×C₂₃	—	8	2	no	—
361	D₄×C₂₃	—	8	2	no	—
362	D₄×C₂₃	—	8	2	no	—
363	C₂×C₄×C₂₃	—	2	2	no	—
364	C₂×C₄×C₂₃	—	2	4	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	1	no	—
370	C₂×C₄×C₂₃	—	2	1	no	—
371	C₂×C₄×C₂₃	—	2	4	no	—
372	C₂×C₄×C₂₃	—	2	2	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	—	8	1	no	—
380	C₂×C₄×C₂₃	—	8	2	no	—
381	C₂×C₄×C₂₃	—	8	1	no	—
382	C₂×C₄×C₂₃	—	8	2	no	—
383	C₂×C₄×C₂₃	—	8	4	no	—
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	1	yes	characteristic
388	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
393	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
394	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
395	C₈×C₂₃	—	2	2	no	—
396	C₈×C₂₃	—	2	2	no	—
397	C₈×C₂₃	—	2	4	no	—
398	#3503	C₂×C₂₃	1	1	yes	characteristic, complemented
399	#3460	C₂×C₂₃	1	1	yes	characteristic
400	#3244	C₂×C₂₃	1	4	yes	complemented
401	#3241	C₂×C₂₃	1	4	yes	complemented
402	#3238	C₂×C₂₃	1	2	yes	complemented
403	#3235	C₂×C₂₃	1	2	yes	complemented
404	#3233	C₂×C₂₃	1	2	yes	complemented
405	#3227	C₂×C₂₃	1	2	yes	complemented
406	#3163	C₂×C₂₃	1	2	yes	complemented
407	#3136	C₂×C₂₃	1	2	yes	complemented
408	#3099	C₂×C₂₃	1	2	yes	complemented
409	#3096	C₂×C₂₃	1	2	yes	complemented
410	#3079	C₂×C₂₃	1	1	yes	characteristic, complemented
411	#3077	C₂×C₂₃	1	1	yes	characteristic, complemented
412	#3076	C₂×C₂₃	1	1	yes	characteristic, complemented
413	C₂×#476	C₂×C₂₃	1	1	yes	characteristic, complemented
414	#2925	C₂×C₂₃	1	1	yes	characteristic, complemented
415	C₂²×C₂₃	—	2	1	no	—
416	C₂²×C₂₃	—	2	1	no	—
417	C₂²×C₂₃	—	2	2	no	—
418	C₂²×C₂₃	—	2	2	no	—
419	C₂²×C₂₃	—	2	2	no	—
420	C₂²×C₂₃	—	4	1	no	—
421	C₂²×C₂₃	—	4	2	no	—
422	C₂²×C₂₃	—	4	1	no	—
423	C₂²×C₂₃	—	4	2	no	—
424	C₂²×C₂₃	—	4	2	no	—
425	C₂²×C₂₃	—	4	1	no	—
426	C₂²×C₂₃	—	8	4	no	—
427	C₂²×C₂₃	#536	1	2	yes	—
428	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
429	C₄×C₂₃	—	2	1	no	—
430	C₄×C₂₃	—	2	1	no	—
431	C₄×C₂₃	—	2	2	no	—
432	C₄×C₂₃	—	2	2	no	—
433	C₄×C₂₃	—	2	1	no	—
434	C₄×C₂₃	—	2	2	no	—
435	C₄×C₂₃	—	4	4	no	—
436	C₄×C₂₃	—	4	2	no	—
437	C₄×C₂₃	—	4	1	no	—
438	C₄×C₂₃	—	4	1	no	—
439	C₄×C₂₃	—	4	2	no	—
440	C₄×C₂₃	—	4	1	no	—
441	C₄×C₂₃	—	4	2	no	—
442	C₄×C₂₃	#536	1	2	yes	—
443	C₄×C₂₃	#577	1	2	yes	—
444	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
445	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
446	Q₈²	—	2	1	no	—
447	#557	—	2	1	no	—
448	#554	—	2	2	no	—
449	#554	—	2	1	no	—
450	D₄×Q₈	—	2	2	no	—
451	D₄×Q₈	—	2	1	no	—
452	#544	C₂²×C₂₃	1	2	yes	—
453	#544	C₂²×C₂₃	1	1	yes	characteristic
454	#544	C₂²×C₂₃	1	4	yes	complemented
455	#542	—	2	1	no	—
456	#542	C₂²×C₂₃	1	2	yes	—
457	#540	—	2	1	no	—
458	#540	C₂²×C₂₃	1	2	yes	—
459	#538	—	2	2	no	—
460	#537	C₂²×C₂₃	1	1	yes	characteristic
461	#535	C₂²×C₂₃	1	1	yes	characteristic
462	#535	C₂²×C₂₃	1	1	yes	characteristic
463	#533	C₂²×C₂₃	1	1	yes	characteristic
464	#533	C₂²×C₂₃	1	2	yes	complemented
465	#532	—	2	1	no	—
466	#532	C₂²×C₂₃	1	2	yes	—
467	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
468	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
469	#529	—	2	1	no	—
470	#529	C₂²×C₂₃	1	2	yes	—
471	#525	—	2	2	no	—
472	#520	C₂²×C₂₃	1	2	yes	—
473	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
474	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
475	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
476	#501	C₂²×C₂₃	1	4	yes	complemented
477	#501	C₂²×C₂₃	1	4	yes	complemented
478	#499	C₂²×C₂₃	1	4	yes	complemented
479	#498	C₂²×C₂₃	1	4	yes	complemented
480	#490	C₂²×C₂₃	1	4	yes	—
481	#489	C₂²×C₂₃	1	4	yes	—
482	#488	C₂²×C₂₃	1	4	yes	—
483	#486	C₂²×C₂₃	1	4	yes	—
484	#485	C₂²×C₂₃	1	4	yes	complemented
485	#483	C₂²×C₂₃	1	4	yes	complemented
486	#482	C₂²×C₂₃	1	4	yes	—
487	#482	C₂²×C₂₃	1	4	yes	—
488	#482	C₂²×C₂₃	1	4	yes	complemented
489	#481	C₂²×C₂₃	1	4	yes	—
490	#481	C₂²×C₂₃	1	4	yes	complemented
491	#480	C₂²×C₂₃	1	4	yes	—
492	#479	C₂²×C₂₃	1	2	yes	complemented
493	#478	C₂²×C₂₃	1	4	yes	—
494	#478	C₂²×C₂₃	1	2	yes	complemented
495	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
496	#477	C₂²×C₂₃	1	2	yes	complemented
497	#476	C₂²×C₂₃	1	2	yes	—
498	#476	C₂²×C₂₃	1	2	yes	—
499	#476	C₂²×C₂₃	1	2	yes	—
500	#476	C₂²×C₂₃	1	4	yes	—
501	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
502	#476	C₂²×C₂₃	1	2	yes	complemented
503	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
504	#475	C₂²×C₂₃	1	2	yes	complemented
505	#474	C₂²×C₂₃	1	2	yes	—
506	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
507	#474	C₂²×C₂₃	1	2	yes	complemented
508	#433	C₂²×C₂₃	1	4	yes	complemented
509	#432	C₂²×C₂₃	1	2	yes	complemented
510	#431	C₂²×C₂₃	1	2	yes	complemented
511	#428	C₂²×C₂₃	1	2	yes	—
512	#428	C₂²×C₂₃	1	2	yes	—
513	#427	C₂²×C₂₃	1	2	yes	—
514	C₂×#106	C₂²×C₂₃	1	2	yes	—
515	#423	C₂²×C₂₃	1	1	yes	characteristic
516	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
517	#418	C₂²×C₂₃	1	2	yes	—
518	#417	C₂²×C₂₃	1	2	yes	—
519	#416	C₂²×C₂₃	1	2	yes	—
520	C₂×#102	C₂²×C₂₃	1	2	yes	—
521	#408	C₂²×C₂₃	1	2	yes	—
522	#405	C₂²×C₂₃	1	2	yes	—
523	C₂×C₂₃	—	2	2	no	—
524	C₂×C₂₃	—	4	2	no	—
525	C₂×C₂₃	—	8	1	no	—
526	C₂×C₂₃	—	8	2	no	—
527	C₂×C₂₃	C₂×#536	1	1	yes	characteristic
528	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
529	C₂×C₂₃	#3585	1	1	yes	characteristic
530	C₂×#41	—	2	2	no	—
531	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
532	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
533	C₂²×Q₈	—	2	1	no	—
534	C₂²×Q₈	—	2	2	no	—
535	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
536	C₂³×C₄	—	2	1	no	—
537	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
538	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
539	C₄⋊Q₈	—	2	1	no	—
540	C₄⋊Q₈	—	2	2	no	—
541	C₄⋊Q₈	—	2	4	no	—
542	C₄⋊Q₈	—	2	1	no	—
543	C₄⋊Q₈	—	2	1	no	—
544	C₄⋊Q₈	—	2	2	no	—
545	C₄⋊Q₈	—	2	2	no	—
546	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
547	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
548	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
549	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
550	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
551	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
552	#127	—	2	1	no	—
553	#127	C₂³×C₂₃	1	2	yes	—
554	#126	—	2	2	no	—
555	#126	—	2	2	no	—
556	#125	—	2	1	no	—
557	#125	—	2	2	no	—
558	#125	—	2	4	no	—
559	#125	C₂³×C₂₃	1	2	yes	—
560	#125	C₂³×C₂₃	1	2	yes	—
561	#125	C₂³×C₂₃	1	4	yes	—
562	#124	—	2	1	no	—
563	#124	—	2	2	no	—
564	#124	—	2	2	no	—
565	#124	C₂³×C₂₃	1	2	yes	—
566	#123	—	2	2	no	—
567	#123	—	2	2	no	—
568	#123	—	2	2	no	—
569	#123	—	2	2	no	—
570	C₂²⋊Q₈	—	2	1	no	—
571	C₂²⋊Q₈	—	2	1	no	—
572	C₂²⋊Q₈	—	2	1	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	4	no	—
578	C₂²⋊Q₈	—	2	4	no	—
579	C₂²⋊Q₈	—	2	4	no	—
580	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
581	#121	—	2	2	no	—
582	#121	—	2	1	no	—
583	#121	—	2	2	no	—
584	#121	—	2	1	no	—
585	#121	—	2	1	no	—
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	C₂³×C₂₃	1	2	yes	—
589	#121	C₂³×C₂₃	1	2	yes	—
590	#121	C₂³×C₂₃	1	2	yes	—
591	#120	—	2	2	no	—
592	#120	—	2	2	no	—
593	C₄×Q₈	—	2	2	no	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	—	2	2	no	—
597	C₄×Q₈	—	2	2	no	—
598	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
599	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
602	C₄×D₄	—	2	4	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	D₄×C₂₃	1	2	yes	—
611	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
612	C₄×D₄	D₄×C₂₃	1	2	yes	—
613	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
614	C₄×D₄	C₂³×C₂₃	1	2	yes	—
615	C₄×D₄	C₂³×C₂₃	1	2	yes	—
616	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
617	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
618	#117	—	2	1	no	—
619	#117	—	2	2	no	—
620	#117	C₂³×C₂₃	1	1	yes	characteristic
621	#117	C₂³×C₂₃	1	2	yes	—
622	#117	C₂³×C₂₃	1	4	yes	—
623	#117	C₂³×C₂₃	1	1	yes	characteristic
624	#117	C₂³×C₂₃	1	2	yes	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	—	2	2	no	—
627	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
630	C₂×C₂²⋊C₄	—	2	1	no	—
631	C₂×C₄²	—	2	1	no	—
632	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
633	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
634	#107	C₂³×C₂₃	1	2	yes	—
635	#107	C₂³×C₂₃	1	2	yes	—
636	#107	C₂³×C₂₃	1	4	yes	—
637	#107	C₂³×C₂₃	1	4	yes	—
638	#106	C₂³×C₂₃	1	4	yes	—
639	#106	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	#106	C₂³×C₂₃	1	4	yes	—
644	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
645	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
646	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
647	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
648	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
649	#103	C₂³×C₂₃	1	2	yes	—
650	#103	C₂³×C₂₃	1	2	yes	—
651	#103	C₂³×C₂₃	1	4	yes	—
652	#102	C₂³×C₂₃	1	4	yes	—
653	#102	C₂³×C₂₃	1	4	yes	—
654	#102	C₂³×C₂₃	1	2	yes	—
655	#102	C₂³×C₂₃	1	2	yes	—
656	#102	C₂³×C₂₃	1	4	yes	—
657	#102	C₂³×C₂₃	1	4	yes	—
658	#102	C₂³×C₂₃	1	4	yes	—
659	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
660	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
661	#97	C₂³×C₂₃	1	4	yes	—
662	C₄×C₈	C₂³×C₂₃	1	4	yes	—
663	C₂₃	#60892	1	1	yes	characteristic, direct product factor, Sylow
664	C₂⁴	—	2	1	no	—
665	#41	—	2	2	no	—
666	#41	—	2	2	no	—
667	#41	—	2	2	no	—
668	#41	—	2	2	no	—
669	#41	—	8	4	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	4	no	—
676	C₂×Q₈	—	8	2	no	—
677	C₂×Q₈	—	8	4	no	—
678	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
679	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
690	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
691	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
692	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	8	2	no	—
702	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
703	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
704	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
705	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
708	M₁₆	—	2	4	no	—
709	C₂×C₈	—	2	4	no	—
710	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
711	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
712	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	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	1	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	2	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	4	yes	—
736	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
739	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
740	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	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	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
755	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
756	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
757	C₄²	—	2	1	no	—
758	C₄²	—	2	1	no	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	4	no	—
761	C₄²	—	2	2	no	—
762	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
763	C₄²	C₂×D₄×C₂₃	1	2	yes	—
764	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
765	C₄²	C₂×D₄×C₂₃	1	2	yes	—
766	C₄²	C₂⁴×C₂₃	1	2	yes	—
767	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
768	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
769	C₂³	—	2	2	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	4	2	no	—
772	C₂³	—	8	1	no	—
773	C₂³	—	8	1	no	—
774	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
775	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
776	Q₈	—	2	2	no	—
777	Q₈	—	2	1	no	—
778	Q₈	—	2	1	no	—
779	Q₈	—	4	2	no	—
780	Q₈	—	4	4	no	—
781	Q₈	—	4	2	no	—
782	Q₈	—	8	2	no	—
783	Q₈	—	8	4	no	—
784	Q₈	—	8	2	no	—
785	D₄	—	2	4	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	2	no	—
788	D₄	—	2	1	no	—
789	D₄	—	2	1	no	—
790	D₄	—	2	2	no	—
791	D₄	—	4	2	no	—
792	D₄	—	4	2	no	—
793	D₄	—	8	2	no	—
794	D₄	—	8	2	no	—
795	D₄	—	8	2	no	—
796	D₄	—	8	2	no	—
797	D₄	—	8	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	4	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	4	1	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	4	no	—
812	C₂×C₄	—	4	2	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	8	2	no	—
815	C₂×C₄	—	8	1	no	—
816	C₂×C₄	—	8	1	no	—
817	C₂×C₄	—	8	2	no	—
818	C₂×C₄	—	8	4	no	—
819	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
821	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
822	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
823	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
825	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
826	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
827	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
828	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
829	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
830	C₈	—	2	2	no	—
831	C₈	—	2	2	no	—
832	C₈	—	2	4	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	8	4	no	—
845	C₂²	C₂₃×#536	1	2	yes	—
846	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
847	C₄	—	2	2	no	—
848	C₄	—	2	1	no	—
849	C₄	—	2	2	no	—
850	C₄	—	2	1	no	—
851	C₄	—	2	1	no	—
852	C₄	—	2	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	4	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	1	no	—
860	C₄	C₂₃×#536	1	2	yes	—
861	C₄	C₂₃×#577	1	2	yes	—
862	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
863	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
864	C₂	—	2	2	no	—
865	C₂	—	4	2	no	—
866	C₂	—	8	2	no	—
867	C₂	—	8	1	no	—
868	C₂	C₂×C₂₃×#536	1	1	yes	characteristic
869	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
870	C₂	C₂₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3460	C₂
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×#3503	C₂	semidirect
3. C₂₃×#3244	C₂	semidirect
4. C₂₃×#3241	C₂	semidirect
5. C₂₃×#3238	C₂	semidirect
6. C₂₃×#3235	C₂	semidirect
7. C₂₃×#3233	C₂	semidirect
8. C₂₃×#3227	C₂	semidirect
9. C₂₃×#3163	C₂	semidirect
10. C₂₃×#3136	C₂	semidirect
11. C₂₃×#3099	C₂	semidirect
12. C₂₃×#3096	C₂	semidirect
13. C₂₃×#3079	C₂	semidirect
14. C₂₃×#3077	C₂	semidirect
15. C₂₃×#3076	C₂	semidirect
16. C₂×C₂₃×#476	C₂	semidirect
17. C₂₃×#2925	C₂	semidirect
26. C₂₃×#544	C₂²	semidirect
36. C₂₃×#533	C₂²	semidirect
40. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
48. C₂₃×#501	C₂²	semidirect
49. C₂₃×#501	C₂²	semidirect
50. C₂₃×#499	C₂²	semidirect
51. C₂₃×#498	C₂²	semidirect
56. C₂₃×#485	C₂²	semidirect
57. C₂₃×#483	C₂²	semidirect
60. C₂₃×#482	C₂²	semidirect
62. C₂₃×#481	C₂²	semidirect
64. C₂₃×#479	C₂²	semidirect
66. C₂₃×#478	C₂²	semidirect
67. C₂₃×#477	C₂²	semidirect
68. C₂₃×#477	C₂²	semidirect
73. C₂₃×#476	C₂²	semidirect
74. C₂₃×#476	C₂²	semidirect
75. C₂₃×#475	C₂²	semidirect
76. C₂₃×#475	C₂²	semidirect
78. C₂₃×#474	C₂²	semidirect
79. C₂₃×#474	C₂²	semidirect
80. C₂₃×#433	C₂²	semidirect
81. C₂₃×#432	C₂²	semidirect
82. C₂₃×#431	C₂²	semidirect
333. #60892	C₂₃	direct (N × H)
398. #3503	C₂×C₂₃	semidirect
400. #3244	C₂×C₂₃	semidirect
401. #3241	C₂×C₂₃	semidirect
402. #3238	C₂×C₂₃	semidirect
403. #3235	C₂×C₂₃	semidirect
404. #3233	C₂×C₂₃	semidirect
405. #3227	C₂×C₂₃	semidirect
406. #3163	C₂×C₂₃	semidirect
407. #3136	C₂×C₂₃	semidirect
408. #3099	C₂×C₂₃	semidirect
409. #3096	C₂×C₂₃	semidirect
410. #3079	C₂×C₂₃	semidirect
411. #3077	C₂×C₂₃	semidirect
412. #3076	C₂×C₂₃	semidirect
413. C₂×#476	C₂×C₂₃	semidirect
414. #2925	C₂×C₂₃	semidirect
454. #544	C₂²×C₂₃	semidirect
464. #533	C₂²×C₂₃	semidirect
468. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
476. #501	C₂²×C₂₃	semidirect
477. #501	C₂²×C₂₃	semidirect
478. #499	C₂²×C₂₃	semidirect
479. #498	C₂²×C₂₃	semidirect
484. #485	C₂²×C₂₃	semidirect
485. #483	C₂²×C₂₃	semidirect
488. #482	C₂²×C₂₃	semidirect
490. #481	C₂²×C₂₃	semidirect
492. #479	C₂²×C₂₃	semidirect
494. #478	C₂²×C₂₃	semidirect
495. #477	C₂²×C₂₃	semidirect
496. #477	C₂²×C₂₃	semidirect
501. #476	C₂²×C₂₃	semidirect
502. #476	C₂²×C₂₃	semidirect
503. #475	C₂²×C₂₃	semidirect
504. #475	C₂²×C₂₃	semidirect
506. #474	C₂²×C₂₃	semidirect
507. #474	C₂²×C₂₃	semidirect
508. #433	C₂²×C₂₃	semidirect
509. #432	C₂²×C₂₃	semidirect
510. #431	C₂²×C₂₃	semidirect
663. C₂₃	#60892	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×#3503	2
C₂₃×#3460	2
C₂₃×#3244	2
C₂₃×#3241	2
C₂₃×#3238	2
C₂₃×#3235	2
C₂₃×#3233	2
C₂₃×#3227	2
C₂₃×#3163	2
C₂₃×#3136	2
C₂₃×#3099	2
C₂₃×#3096	2
C₂₃×#3079	2
C₂₃×#3077	2
C₂₃×#3076	2
C₂×C₂₃×#476	2
C₂₃×#2925	2
#60892	23

Subgroups — C23×#60892 #19208518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60892 #19208518