Subgroups — C₂₃×#17516 #19165142

Order 5888.

948 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3480	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1494	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1491	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1489	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1488	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1484	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1483	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1482	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1479	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1477	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#559	—	2	1	no	—
17	C₂₃×#559	C₄	1	1	yes	characteristic
18	C₂₃×#557	C₄	1	1	yes	characteristic
19	C₂₃×#556	—	2	1	no	—
20	C₂₃×#556	C₄	1	1	yes	characteristic
21	C₂₃×#553	—	2	1	no	—
22	C₂₃×#553	—	2	1	no	—
23	C₂₃×#553	C₄	1	1	yes	characteristic
24	C₂₃×#553	C₄	1	1	yes	characteristic
25	C₂₃×#550	C₄	1	1	yes	characteristic
26	C₂₃×#548	C₄	1	1	yes	characteristic
27	C₂₃×#548	C₄	1	1	yes	characteristic
28	C₂₃×#532	—	2	1	no	—
29	C₂₃×#532	C₂²	1	1	yes	characteristic
30	C₂₃×#529	—	2	1	no	—
31	C₂₃×#529	—	2	1	no	—
32	C₂₃×#529	C₂²	1	1	yes	characteristic
33	C₂₃×#529	C₂²	1	1	yes	characteristic
34	C₄×#41×C₂₃	—	2	1	no	—
35	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
36	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
37	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
39	C₂₃×#446	—	2	1	no	—
40	C₂₃×#436	—	2	1	no	—
41	C₂₃×#435	—	2	1	no	—
42	C₂₃×#435	—	2	1	no	—
43	C₂₃×#433	—	2	1	no	—
44	C₂₃×#433	—	2	1	no	—
45	C₂₃×#432	C₂²	1	1	yes	characteristic
46	C₂₃×#432	C₂²	1	1	yes	characteristic
47	C₂₃×#431	C₂²	1	1	yes	characteristic
48	C₂₃×#431	C₂²	1	1	yes	characteristic
49	C₂₃×#431	C₂²	1	1	yes	characteristic
50	C₂₃×#431	C₂²	1	1	yes	characteristic
51	C₂₃×#431	C₂²	1	1	yes	characteristic
52	C₂₃×#423	C₂²	1	1	yes	characteristic
53	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₂₃×#408	—	2	1	no	—
55	C₂₃×#405	—	2	1	no	—
56	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
57	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
59	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
60	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
61	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
62	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
67	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
72	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
73	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
74	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×#41×C₂₃	—	2	1	no	—
76	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
77	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
78	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
79	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
80	C₂×M₁₆×C₂₃	—	2	1	no	—
81	C₂×M₁₆×C₂₃	—	2	1	no	—
82	C₂×M₁₆×C₂₃	—	2	1	no	—
83	C₂²×C₈×C₂₃	—	2	1	no	—
84	C₂²×C₈×C₂₃	—	2	1	no	—
85	C₂₃×C₄⋊Q₈	—	2	1	no	—
86	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
87	C₂₃×#127	—	2	1	no	—
88	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
89	C₂₃×#126	—	2	1	no	—
90	C₂₃×#126	—	2	1	no	—
91	C₂₃×#126	—	2	1	no	—
92	C₂₃×#126	—	2	1	no	—
93	C₂₃×#126	—	2	1	no	—
94	C₂₃×#126	—	2	1	no	—
95	C₂₃×#125	—	2	1	no	—
96	C₂₃×#125	—	2	1	no	—
97	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
98	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
99	C₂₃×#124	—	2	1	no	—
100	C₂₃×#124	—	2	1	no	—
101	C₂₃×#124	—	2	1	no	—
102	C₂₃×#124	—	2	1	no	—
103	C₂₃×#124	—	2	1	no	—
104	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
105	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
106	C₂₃×#123	—	2	1	no	—
107	C₂₃×#123	—	2	1	no	—
108	C₂₃×#123	—	2	1	no	—
109	C₂₃×#123	—	2	1	no	—
110	C₂₃×#123	—	2	1	no	—
111	C₂₃×#123	—	2	1	no	—
112	C₂₃×C₂²⋊Q₈	—	2	1	no	—
113	C₂₃×C₂²⋊Q₈	—	2	1	no	—
114	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
115	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
116	C₂₃×#121	—	2	1	no	—
117	C₂₃×#121	—	2	1	no	—
118	C₂₃×#121	—	2	1	no	—
119	C₂₃×#121	—	2	1	no	—
120	C₂₃×#121	—	2	1	no	—
121	C₂₃×#121	—	2	1	no	—
122	C₂₃×#121	—	2	1	no	—
123	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
124	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
125	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
126	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
127	C₄×Q₈×C₂₃	—	2	1	no	—
128	C₄×Q₈×C₂₃	—	2	1	no	—
129	C₄×Q₈×C₂₃	—	2	1	no	—
130	C₄×Q₈×C₂₃	—	2	1	no	—
131	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
132	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
133	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
134	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
135	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
136	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
137	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
138	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
139	C₄×D₄×C₂₃	—	2	1	no	—
140	C₄×D₄×C₂₃	—	2	1	no	—
141	C₄×D₄×C₂₃	—	2	1	no	—
142	C₄×D₄×C₂₃	—	2	1	no	—
143	C₄×D₄×C₂₃	—	2	1	no	—
144	C₄×D₄×C₂₃	—	2	1	no	—
145	C₄×D₄×C₂₃	—	2	1	no	—
146	C₄×D₄×C₂₃	—	2	1	no	—
147	C₄×D₄×C₂₃	—	2	1	no	—
148	C₄×D₄×C₂₃	—	2	1	no	—
149	C₄×D₄×C₂₃	—	2	1	no	—
150	C₄×D₄×C₂₃	—	2	1	no	—
151	C₄×D₄×C₂₃	—	2	1	no	—
152	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
153	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
154	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
155	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
156	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
157	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
158	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
159	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
160	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
161	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
162	C₂₃×#117	—	2	1	no	—
163	C₂₃×#117	—	2	1	no	—
164	C₂₃×#117	—	2	1	no	—
165	C₂₃×#117	—	2	1	no	—
166	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
167	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
168	C₂₃×#117	D₄	1	1	yes	characteristic
169	C₂₃×#117	D₄	1	1	yes	characteristic
170	C₂₃×#117	D₄	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
172	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
173	C₂×C₄²×C₂₃	—	2	1	no	—
174	C₂×C₄²×C₂₃	—	2	1	no	—
175	C₂×C₄²×C₂₃	—	2	1	no	—
176	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
179	C₂₃×C₄⋊C₈	—	2	1	no	—
180	C₂₃×C₄⋊C₈	—	2	1	no	—
181	C₂₃×C₄⋊C₈	—	2	1	no	—
182	C₂₃×C₄⋊C₈	—	2	1	no	—
183	C₂₃×C₄⋊C₈	—	2	1	no	—
184	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
185	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
186	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
187	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
188	C₂₃×C₂²⋊C₈	—	2	1	no	—
189	C₂₃×C₂²⋊C₈	—	2	1	no	—
190	C₂₃×C₂²⋊C₈	—	2	1	no	—
191	C₂₃×C₂²⋊C₈	—	2	1	no	—
192	C₂₃×C₂²⋊C₈	—	2	1	no	—
193	C₂₃×C₂²⋊C₈	—	2	1	no	—
194	C₂₃×C₂²⋊C₈	—	2	1	no	—
195	C₂₃×#97	—	2	1	no	—
196	C₂₃×#97	—	2	1	no	—
197	C₂₃×#97	—	2	1	no	—
198	C₂₃×#97	—	2	1	no	—
199	C₄×C₈×C₂₃	—	2	1	no	—
200	C₄×C₈×C₂₃	—	2	1	no	—
201	C₄×C₈×C₂₃	—	2	1	no	—
202	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
203	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
204	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
205	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
206	#41×C₂₃	—	2	2	no	—
207	#41×C₂₃	—	2	2	no	—
208	#41×C₂₃	—	4	1	no	—
209	#41×C₂₃	—	4	1	no	—
210	#41×C₂₃	—	4	1	no	—
211	#41×C₂₃	—	4	1	no	—
212	#41×C₂₃	—	4	2	no	—
213	#41×C₂₃	—	4	2	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	—	4	1	no	—
218	C₂×Q₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
219	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
220	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
221	C₂×D₄×C₂₃	—	2	1	no	—
222	C₂×D₄×C₂₃	—	2	1	no	—
223	C₂×D₄×C₂₃	—	2	1	no	—
224	C₂×D₄×C₂₃	—	2	1	no	—
225	C₂×D₄×C₂₃	—	2	1	no	—
226	C₂×D₄×C₂₃	—	2	1	no	—
227	C₂×D₄×C₂₃	—	2	1	no	—
228	C₂×D₄×C₂₃	—	2	1	no	—
229	C₂×D₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
230	C₂×D₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
231	C₂×D₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
232	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
233	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
234	C₂²×C₄×C₂₃	—	2	1	no	—
235	C₂²×C₄×C₂₃	—	2	1	no	—
236	C₂²×C₄×C₂₃	—	2	1	no	—
237	C₂²×C₄×C₂₃	—	2	1	no	—
238	C₂²×C₄×C₂₃	—	2	1	no	—
239	C₂²×C₄×C₂₃	—	2	1	no	—
240	C₂²×C₄×C₂₃	—	2	1	no	—
241	C₂²×C₄×C₂₃	—	2	1	no	—
242	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
243	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
244	C₂²×C₄×C₂₃	C₂²×C₄	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	M₁₆×C₂₃	—	4	2	no	—
252	M₁₆×C₂₃	—	4	2	no	—
253	M₁₆×C₂₃	—	4	2	no	—
254	C₂×C₈×C₂₃	—	2	1	no	—
255	C₂×C₈×C₂₃	—	2	1	no	—
256	C₂×C₈×C₂₃	—	2	1	no	—
257	C₂×C₈×C₂₃	—	2	1	no	—
258	C₂×C₈×C₂₃	—	2	1	no	—
259	C₂×C₈×C₂₃	—	2	1	no	—
260	C₂×C₈×C₂₃	—	2	1	no	—
261	C₂×C₈×C₂₃	—	2	1	no	—
262	C₂×C₈×C₂₃	—	4	2	no	—
263	C₂×C₈×C₂₃	—	4	2	no	—
264	C₄⋊C₄×C₂₃	—	2	1	no	—
265	C₄⋊C₄×C₂₃	—	2	1	no	—
266	C₄⋊C₄×C₂₃	—	2	1	no	—
267	C₄⋊C₄×C₂₃	—	2	1	no	—
268	C₄⋊C₄×C₂₃	—	2	1	no	—
269	C₄⋊C₄×C₂₃	—	2	1	no	—
270	C₄⋊C₄×C₂₃	—	2	1	no	—
271	C₄⋊C₄×C₂₃	—	2	1	no	—
272	C₄⋊C₄×C₂₃	—	2	1	no	—
273	C₄⋊C₄×C₂₃	—	2	1	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	C₂²⋊C₄	1	1	yes	characteristic
279	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
280	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
281	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
282	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
283	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
284	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
285	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
286	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
287	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
288	C₂²⋊C₄×C₂₃	—	2	1	no	—
289	C₂²⋊C₄×C₂₃	—	2	1	no	—
290	C₂²⋊C₄×C₂₃	—	2	1	no	—
291	C₂²⋊C₄×C₂₃	—	2	1	no	—
292	C₂²⋊C₄×C₂₃	—	2	1	no	—
293	C₂²⋊C₄×C₂₃	—	2	1	no	—
294	C₂²⋊C₄×C₂₃	—	2	1	no	—
295	C₂²⋊C₄×C₂₃	—	2	1	no	—
296	C₂²⋊C₄×C₂₃	—	2	1	no	—
297	C₂²⋊C₄×C₂₃	—	2	1	no	—
298	C₂²⋊C₄×C₂₃	—	2	1	no	—
299	C₂²⋊C₄×C₂₃	—	2	1	no	—
300	C₂²⋊C₄×C₂₃	—	2	1	no	—
301	C₂²⋊C₄×C₂₃	—	2	1	no	—
302	C₂²⋊C₄×C₂₃	—	2	1	no	—
303	C₂²⋊C₄×C₂₃	—	2	1	no	—
304	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
305	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
306	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
307	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
308	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
309	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
310	C₄²×C₂₃	—	2	1	no	—
311	C₄²×C₂₃	—	2	1	no	—
312	C₄²×C₂₃	—	2	1	no	—
313	C₄²×C₂₃	—	2	1	no	—
314	C₄²×C₂₃	—	2	1	no	—
315	C₄²×C₂₃	—	2	1	no	—
316	C₄²×C₂₃	—	2	1	no	—
317	C₄²×C₂₃	—	2	1	no	—
318	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
319	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
320	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
321	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
328	#17516	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂³×C₂₃	—	2	1	no	—
330	C₂³×C₂₃	—	2	1	no	—
331	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
332	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
333	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
334	Q₈×C₂₃	—	2	1	no	—
335	Q₈×C₂₃	—	2	1	no	—
336	Q₈×C₂₃	—	2	1	no	—
337	Q₈×C₂₃	—	4	1	no	—
338	Q₈×C₂₃	—	4	2	no	—
339	Q₈×C₂₃	—	4	2	no	—
340	Q₈×C₂₃	#131	1	2	yes	—
341	D₄×C₂₃	—	2	1	no	—
342	D₄×C₂₃	—	2	1	no	—
343	D₄×C₂₃	—	2	1	no	—
344	D₄×C₂₃	—	2	1	no	—
345	D₄×C₂₃	—	4	1	no	—
346	D₄×C₂₃	—	4	1	no	—
347	D₄×C₂₃	—	4	1	no	—
348	D₄×C₂₃	—	4	2	no	—
349	D₄×C₂₃	—	4	2	no	—
350	D₄×C₂₃	—	4	2	no	—
351	D₄×C₂₃	—	4	2	no	—
352	D₄×C₂₃	—	4	2	no	—
353	D₄×C₂₃	—	8	1	no	—
354	D₄×C₂₃	—	8	1	no	—
355	D₄×C₂₃	—	8	1	no	—
356	C₂×C₄×C₂₃	—	2	1	no	—
357	C₂×C₄×C₂₃	—	2	1	no	—
358	C₂×C₄×C₂₃	—	2	1	no	—
359	C₂×C₄×C₂₃	—	2	1	no	—
360	C₂×C₄×C₂₃	—	2	1	no	—
361	C₂×C₄×C₂₃	—	2	1	no	—
362	C₂×C₄×C₂₃	—	2	1	no	—
363	C₂×C₄×C₂₃	—	2	1	no	—
364	C₂×C₄×C₂₃	—	2	1	no	—
365	C₂×C₄×C₂₃	—	2	1	no	—
366	C₂×C₄×C₂₃	—	2	1	no	—
367	C₂×C₄×C₂₃	—	2	1	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	1	no	—
372	C₂×C₄×C₂₃	—	2	1	no	—
373	C₂×C₄×C₂₃	—	2	1	no	—
374	C₂×C₄×C₂₃	—	4	1	no	—
375	C₂×C₄×C₂₃	—	4	1	no	—
376	C₂×C₄×C₂₃	—	4	1	no	—
377	C₂×C₄×C₂₃	—	4	2	no	—
378	C₂×C₄×C₂₃	—	4	2	no	—
379	C₂×C₄×C₂₃	—	4	2	no	—
380	C₂×C₄×C₂₃	—	4	1	no	—
381	C₂×C₄×C₂₃	—	4	1	no	—
382	C₂×C₄×C₂₃	—	4	1	no	—
383	C₂×C₄×C₂₃	—	4	1	no	—
384	C₂×C₄×C₂₃	—	8	1	no	—
385	C₂×C₄×C₂₃	—	8	1	no	—
386	C₂×C₄×C₂₃	—	8	1	no	—
387	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
388	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
389	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
390	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
391	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
392	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
393	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
394	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
395	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
396	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
397	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
399	C₈×C₂₃	—	2	2	no	—
400	C₈×C₂₃	—	4	1	no	—
401	C₈×C₂₃	—	4	1	no	—
402	C₈×C₂₃	—	4	1	no	—
403	C₈×C₂₃	—	4	1	no	—
404	C₈×C₂₃	—	4	1	no	—
405	C₈×C₂₃	—	4	1	no	—
406	C₈×C₂₃	—	4	1	no	—
407	#3480	C₂×C₂₃	1	1	yes	characteristic
408	#2965	C₂×C₂₃	1	1	yes	characteristic, complemented
409	#2925	C₂×C₂₃	1	1	yes	characteristic, complemented
410	#1496	C₂×C₂₃	1	1	yes	characteristic, complemented
411	#1495	C₂×C₂₃	1	1	yes	characteristic, complemented
412	#1494	C₂×C₂₃	1	1	yes	characteristic, complemented
413	#1491	C₂×C₂₃	1	1	yes	characteristic, complemented
414	#1489	C₂×C₂₃	1	1	yes	characteristic, complemented
415	#1488	C₂×C₂₃	1	1	yes	characteristic, complemented
416	#1484	C₂×C₂₃	1	1	yes	characteristic, complemented
417	#1483	C₂×C₂₃	1	1	yes	characteristic, complemented
418	#1482	C₂×C₂₃	1	1	yes	characteristic, complemented
419	#1479	C₂×C₂₃	1	1	yes	characteristic, complemented
420	#1477	C₂×C₂₃	1	1	yes	characteristic, complemented
421	#1476	C₂×C₂₃	1	1	yes	characteristic, complemented
422	C₂²×C₂₃	—	2	1	no	—
423	C₂²×C₂₃	—	2	1	no	—
424	C₂²×C₂₃	—	2	1	no	—
425	C₂²×C₂₃	—	2	1	no	—
426	C₂²×C₂₃	—	2	1	no	—
427	C₂²×C₂₃	—	2	1	no	—
428	C₂²×C₂₃	—	2	1	no	—
429	C₂²×C₂₃	—	2	1	no	—
430	C₂²×C₂₃	—	2	1	no	—
431	C₂²×C₂₃	—	4	1	no	—
432	C₂²×C₂₃	—	4	1	no	—
433	C₂²×C₂₃	—	4	1	no	—
434	C₂²×C₂₃	—	4	1	no	—
435	C₂²×C₂₃	—	4	1	no	—
436	C₂²×C₂₃	—	4	1	no	—
437	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
438	C₄×C₂₃	—	2	1	no	—
439	C₄×C₂₃	—	2	1	no	—
440	C₄×C₂₃	—	2	1	no	—
441	C₄×C₂₃	—	2	2	no	—
442	C₄×C₂₃	—	2	1	no	—
443	C₄×C₂₃	—	2	1	no	—
444	C₄×C₂₃	—	2	1	no	—
445	C₄×C₂₃	—	2	1	no	—
446	C₄×C₂₃	—	2	1	no	—
447	C₄×C₂₃	—	2	1	no	—
448	C₄×C₂₃	—	2	1	no	—
449	C₄×C₂₃	—	4	1	no	—
450	C₄×C₂₃	—	4	1	no	—
451	C₄×C₂₃	—	4	1	no	—
452	C₄×C₂₃	—	4	1	no	—
453	C₄×C₂₃	—	4	1	no	—
454	C₄×C₂₃	C₂×#131	1	1	yes	characteristic
455	C₄×C₂₃	#568	1	1	yes	characteristic
456	C₄×C₂₃	#575	1	1	yes	characteristic
457	C₄×C₂₃	#575	1	1	yes	characteristic
458	#559	—	2	1	no	—
459	#559	C₄×C₂₃	1	1	yes	characteristic
460	#557	C₄×C₂₃	1	1	yes	characteristic
461	#556	—	2	1	no	—
462	#556	C₄×C₂₃	1	1	yes	characteristic
463	#553	—	2	1	no	—
464	#553	—	2	1	no	—
465	#553	C₄×C₂₃	1	1	yes	characteristic
466	#553	C₄×C₂₃	1	1	yes	characteristic
467	#550	C₄×C₂₃	1	1	yes	characteristic
468	#548	C₄×C₂₃	1	1	yes	characteristic
469	#548	C₄×C₂₃	1	1	yes	characteristic
470	#532	—	2	1	no	—
471	#532	C₂²×C₂₃	1	1	yes	characteristic
472	#529	—	2	1	no	—
473	#529	—	2	1	no	—
474	#529	C₂²×C₂₃	1	1	yes	characteristic
475	#529	C₂²×C₂₃	1	1	yes	characteristic
476	C₄×#41	—	2	1	no	—
477	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
478	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
479	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
480	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
481	#446	—	2	1	no	—
482	#436	—	2	1	no	—
483	#435	—	2	1	no	—
484	#435	—	2	1	no	—
485	#433	—	2	1	no	—
486	#433	—	2	1	no	—
487	#432	C₂²×C₂₃	1	1	yes	characteristic
488	#432	C₂²×C₂₃	1	1	yes	characteristic
489	#431	C₂²×C₂₃	1	1	yes	characteristic
490	#431	C₂²×C₂₃	1	1	yes	characteristic
491	#431	C₂²×C₂₃	1	1	yes	characteristic
492	#431	C₂²×C₂₃	1	1	yes	characteristic
493	#431	C₂²×C₂₃	1	1	yes	characteristic
494	#423	C₂²×C₂₃	1	1	yes	characteristic
495	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
496	#408	—	2	1	no	—
497	#405	—	2	1	no	—
498	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
499	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
500	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
501	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
502	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
503	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
504	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
505	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
506	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
507	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
508	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
509	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
510	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
511	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
512	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
513	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
514	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
515	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
516	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
517	C₂×C₂₃	—	4	1	no	—
518	C₂×C₂₃	—	4	1	no	—
519	C₂×C₂₃	—	4	1	no	—
520	C₂×C₂₃	—	8	1	no	—
521	C₂×C₂₃	—	8	1	no	—
522	C₂×C₂₃	#2880	1	1	yes	characteristic
523	C₂×C₂₃	#2896	1	1	yes	characteristic
524	C₂×C₂₃	#2901	1	1	yes	characteristic
525	C₂×#41	—	2	1	no	—
526	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
527	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
528	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
529	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
530	C₂×M₁₆	—	2	1	no	—
531	C₂×M₁₆	—	2	1	no	—
532	C₂×M₁₆	—	2	1	no	—
533	C₂²×C₈	—	2	1	no	—
534	C₂²×C₈	—	2	1	no	—
535	C₄⋊Q₈	—	2	1	no	—
536	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
537	#127	—	2	1	no	—
538	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
539	#126	—	2	1	no	—
540	#126	—	2	1	no	—
541	#126	—	2	1	no	—
542	#126	—	2	1	no	—
543	#126	—	2	1	no	—
544	#126	—	2	1	no	—
545	#125	—	2	1	no	—
546	#125	—	2	1	no	—
547	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
548	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
549	#124	—	2	1	no	—
550	#124	—	2	1	no	—
551	#124	—	2	1	no	—
552	#124	—	2	1	no	—
553	#124	—	2	1	no	—
554	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
555	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
556	#123	—	2	1	no	—
557	#123	—	2	1	no	—
558	#123	—	2	1	no	—
559	#123	—	2	1	no	—
560	#123	—	2	1	no	—
561	#123	—	2	1	no	—
562	C₂²⋊Q₈	—	2	1	no	—
563	C₂²⋊Q₈	—	2	1	no	—
564	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
565	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
566	#121	—	2	1	no	—
567	#121	—	2	1	no	—
568	#121	—	2	1	no	—
569	#121	—	2	1	no	—
570	#121	—	2	1	no	—
571	#121	—	2	1	no	—
572	#121	—	2	1	no	—
573	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
574	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
575	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
576	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
577	C₄×Q₈	—	2	1	no	—
578	C₄×Q₈	—	2	1	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
582	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
583	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
584	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
585	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
586	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
587	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
588	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	1	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
603	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
604	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
605	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
606	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
607	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
608	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
609	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
610	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
611	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
612	#117	—	2	1	no	—
613	#117	—	2	1	no	—
614	#117	—	2	1	no	—
615	#117	—	2	1	no	—
616	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
617	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
618	#117	D₄×C₂₃	1	1	yes	characteristic
619	#117	D₄×C₂₃	1	1	yes	characteristic
620	#117	D₄×C₂₃	1	1	yes	characteristic
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
623	C₂×C₄²	—	2	1	no	—
624	C₂×C₄²	—	2	1	no	—
625	C₂×C₄²	—	2	1	no	—
626	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
629	C₄⋊C₈	—	2	1	no	—
630	C₄⋊C₈	—	2	1	no	—
631	C₄⋊C₈	—	2	1	no	—
632	C₄⋊C₈	—	2	1	no	—
633	C₄⋊C₈	—	2	1	no	—
634	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
635	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
636	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
637	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
638	C₂²⋊C₈	—	2	1	no	—
639	C₂²⋊C₈	—	2	1	no	—
640	C₂²⋊C₈	—	2	1	no	—
641	C₂²⋊C₈	—	2	1	no	—
642	C₂²⋊C₈	—	2	1	no	—
643	C₂²⋊C₈	—	2	1	no	—
644	C₂²⋊C₈	—	2	1	no	—
645	#97	—	2	1	no	—
646	#97	—	2	1	no	—
647	#97	—	2	1	no	—
648	#97	—	2	1	no	—
649	C₄×C₈	—	2	1	no	—
650	C₄×C₈	—	2	1	no	—
651	C₄×C₈	—	2	1	no	—
652	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
653	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
654	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
655	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
656	C₂₃	#17516	1	1	yes	characteristic, direct product factor, Sylow
657	#41	—	2	2	no	—
658	#41	—	2	2	no	—
659	#41	—	4	1	no	—
660	#41	—	4	1	no	—
661	#41	—	4	1	no	—
662	#41	—	4	1	no	—
663	#41	—	4	2	no	—
664	#41	—	4	2	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	2	no	—
668	C₂×Q₈	—	4	1	no	—
669	C₂×Q₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
670	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
671	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
681	C₂×D₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
682	C₂×D₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
683	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
684	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
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	—	2	1	no	—
690	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
694	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
695	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
696	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
699	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
700	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
701	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
702	M₁₆	—	4	2	no	—
703	M₁₆	—	4	2	no	—
704	M₁₆	—	4	2	no	—
705	C₂×C₈	—	2	1	no	—
706	C₂×C₈	—	2	1	no	—
707	C₂×C₈	—	2	1	no	—
708	C₂×C₈	—	2	1	no	—
709	C₂×C₈	—	2	1	no	—
710	C₂×C₈	—	2	1	no	—
711	C₂×C₈	—	2	1	no	—
712	C₂×C₈	—	2	1	no	—
713	C₂×C₈	—	4	2	no	—
714	C₂×C₈	—	4	2	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
730	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
731	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
732	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
733	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
734	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
735	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
736	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
737	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
738	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	1	no	—
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	1	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
756	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
757	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
758	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
759	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
760	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
761	C₄²	—	2	1	no	—
762	C₄²	—	2	1	no	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	1	no	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	1	no	—
767	C₄²	—	2	1	no	—
768	C₄²	—	2	1	no	—
769	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
770	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
771	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
772	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
773	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
774	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
775	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
776	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
777	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
778	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
779	C₂³	—	2	1	no	—
780	C₂³	—	2	1	no	—
781	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
782	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
783	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
784	Q₈	—	2	1	no	—
785	Q₈	—	2	1	no	—
786	Q₈	—	2	1	no	—
787	Q₈	—	4	1	no	—
788	Q₈	—	4	2	no	—
789	Q₈	—	4	2	no	—
790	Q₈	C₂₃×#131	1	2	yes	—
791	D₄	—	2	1	no	—
792	D₄	—	2	1	no	—
793	D₄	—	2	1	no	—
794	D₄	—	2	1	no	—
795	D₄	—	4	1	no	—
796	D₄	—	4	1	no	—
797	D₄	—	4	1	no	—
798	D₄	—	4	2	no	—
799	D₄	—	4	2	no	—
800	D₄	—	4	2	no	—
801	D₄	—	4	2	no	—
802	D₄	—	4	2	no	—
803	D₄	—	8	1	no	—
804	D₄	—	8	1	no	—
805	D₄	—	8	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	8	1	no	—
835	C₂×C₄	—	8	1	no	—
836	C₂×C₄	—	8	1	no	—
837	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
838	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
839	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
840	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
841	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
842	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
843	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
844	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
845	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
846	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
847	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
849	C₈	—	2	2	no	—
850	C₈	—	4	1	no	—
851	C₈	—	4	1	no	—
852	C₈	—	4	1	no	—
853	C₈	—	4	1	no	—
854	C₈	—	4	1	no	—
855	C₈	—	4	1	no	—
856	C₈	—	4	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	1	no	—
865	C₂²	—	2	1	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	2	no	—
877	C₄	—	2	1	no	—
878	C₄	—	2	1	no	—
879	C₄	—	2	1	no	—
880	C₄	—	2	1	no	—
881	C₄	—	2	1	no	—
882	C₄	—	2	1	no	—
883	C₄	—	2	1	no	—
884	C₄	—	4	1	no	—
885	C₄	—	4	1	no	—
886	C₄	—	4	1	no	—
887	C₄	—	4	1	no	—
888	C₄	—	4	1	no	—
889	C₄	C₂×C₂₃×#131	1	1	yes	characteristic
890	C₄	C₂₃×#568	1	1	yes	characteristic
891	C₄	C₂₃×#575	1	1	yes	characteristic
892	C₄	C₂₃×#575	1	1	yes	characteristic
893	C₂	—	4	1	no	—
894	C₂	—	4	1	no	—
895	C₂	—	4	1	no	—
896	C₂	—	8	1	no	—
897	C₂	—	8	1	no	—
898	C₂	C₂₃×#2880	1	1	yes	characteristic
899	C₂	C₂₃×#2896	1	1	yes	characteristic
900	C₂	C₂₃×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₄²	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂²×C₂²⋊C₄
prime radical	C₂₃×#3480	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2965	C₂	semidirect
3. C₂₃×#2925	C₂	semidirect
4. C₂₃×#1496	C₂	semidirect
5. C₂₃×#1495	C₂	semidirect
6. C₂₃×#1494	C₂	semidirect
7. C₂₃×#1491	C₂	semidirect
8. C₂₃×#1489	C₂	semidirect
9. C₂₃×#1488	C₂	semidirect
10. C₂₃×#1484	C₂	semidirect
11. C₂₃×#1483	C₂	semidirect
12. C₂₃×#1482	C₂	semidirect
13. C₂₃×#1479	C₂	semidirect
14. C₂₃×#1477	C₂	semidirect
15. C₂₃×#1476	C₂	semidirect
328. #17516	C₂₃	direct (N × H)
408. #2965	C₂×C₂₃	semidirect
409. #2925	C₂×C₂₃	semidirect
410. #1496	C₂×C₂₃	semidirect
411. #1495	C₂×C₂₃	semidirect
412. #1494	C₂×C₂₃	semidirect
413. #1491	C₂×C₂₃	semidirect
414. #1489	C₂×C₂₃	semidirect
415. #1488	C₂×C₂₃	semidirect
416. #1484	C₂×C₂₃	semidirect
417. #1483	C₂×C₂₃	semidirect
418. #1482	C₂×C₂₃	semidirect
419. #1479	C₂×C₂₃	semidirect
420. #1477	C₂×C₂₃	semidirect
421. #1476	C₂×C₂₃	semidirect
656. C₂₃	#17516	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×#3480	2
C₂₃×#2965	2
C₂₃×#2925	2
C₂₃×#1496	2
C₂₃×#1495	2
C₂₃×#1494	2
C₂₃×#1491	2
C₂₃×#1489	2
C₂₃×#1488	2
C₂₃×#1484	2
C₂₃×#1483	2
C₂₃×#1482	2
C₂₃×#1479	2
C₂₃×#1477	2
C₂₃×#1476	2
#17516	23

Subgroups — C23×#17516 #19165142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#17516 #19165142