Subgroups — C₂₃×#17524 #19165150

Order 5888.

936 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3482	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1497	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×#1488	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1487	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1483	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1482	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1481	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	C₂×C₂₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#557	C₄	1	1	yes	characteristic
17	C₂₃×#556	—	2	1	no	—
18	C₂₃×#556	C₄	1	1	yes	characteristic
19	C₂₃×#552	—	2	1	no	—
20	C₂₃×#552	—	2	1	no	—
21	C₂₃×#552	C₄	1	1	yes	characteristic
22	C₂₃×#552	C₄	1	1	yes	characteristic
23	D₄×Q₈×C₂₃	C₄	1	1	yes	characteristic
24	C₂₃×#548	C₄	1	1	yes	characteristic
25	C₂₃×#548	C₄	1	1	yes	characteristic
26	C₂₃×#547	—	2	1	no	—
27	C₂₃×#547	C₄	1	1	yes	characteristic
28	C₂₃×#533	—	2	1	no	—
29	C₂₃×#533	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	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
39	C₂₃×#446	—	2	1	no	—
40	C₂₃×#435	—	2	1	no	—
41	C₂₃×#435	—	2	1	no	—
42	C₈×D₄×C₂₃	—	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×#424	—	2	1	no	—
53	C₂₃×#423	C₂²	1	1	yes	characteristic
54	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
55	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
56	C₂₃×#408	—	2	1	no	—
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×Q₈⋊C₈	C₂²	1	1	yes	characteristic
68	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
69	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
70	C₂₃×Q₈⋊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	D₄	1	1	yes	characteristic
78	C₂²×Q₈×C₂₃	C₂×C₄	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	C₂²×C₈×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	—	2	1	no	—
87	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
88	C₂₃×C₄⋊Q₈	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	—	2	1	no	—
98	C₂₃×#125	—	2	1	no	—
99	C₂₃×#125	—	2	1	no	—
100	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
101	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
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	—	2	1	no	—
115	C₂₃×C₂²⋊Q₈	—	2	1	no	—
116	C₂₃×C₂²⋊Q₈	—	2	1	no	—
117	C₂₃×C₂²⋊Q₈	—	2	1	no	—
118	C₂₃×C₂²⋊Q₈	—	2	1	no	—
119	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
120	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
121	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
122	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
123	C₂₃×#121	—	2	1	no	—
124	C₂₃×#121	—	2	1	no	—
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	—	2	1	no	—
132	C₄×Q₈×C₂₃	—	2	1	no	—
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	C₂×C₄	1	1	yes	characteristic
137	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
138	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
139	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
140	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
141	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
142	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
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	C₂×C₄	1	1	yes	characteristic
151	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
152	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
153	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
154	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
155	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
156	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
157	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
158	C₂₃×#117	—	2	1	no	—
159	C₂₃×#117	—	2	1	no	—
160	C₂₃×#117	—	2	1	no	—
161	C₂₃×#117	—	2	1	no	—
162	C₂₃×#117	—	2	1	no	—
163	C₂₃×#117	—	2	1	no	—
164	C₂₃×#117	—	2	1	no	—
165	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
166	C₂₃×#117	D₄	1	1	yes	characteristic
167	C₂₃×#117	D₄	1	1	yes	characteristic
168	C₂₃×#117	D₄	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
170	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
171	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
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	—	2	1	no	—
185	C₂₃×C₄⋊C₈	—	2	1	no	—
186	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
187	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
188	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
189	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×C₂²⋊C₈	—	2	1	no	—
196	C₂₃×C₂²⋊C₈	—	2	1	no	—
197	C₂₃×#97	—	2	1	no	—
198	C₂₃×#97	—	2	1	no	—
199	C₂₃×#97	—	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	—	4	2	no	—
208	#41×C₂₃	—	4	1	no	—
209	#41×C₂₃	—	4	4	no	—
210	C₂×Q₈×C₂₃	—	2	1	no	—
211	C₂×Q₈×C₂₃	—	2	1	no	—
212	C₂×Q₈×C₂₃	—	2	1	no	—
213	C₂×Q₈×C₂₃	—	2	2	no	—
214	C₂×Q₈×C₂₃	—	2	2	no	—
215	C₂×Q₈×C₂₃	—	4	1	no	—
216	C₂×Q₈×C₂₃	—	4	1	no	—
217	C₂×Q₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
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	C₂²⋊C₄	1	1	yes	characteristic
225	C₂×D₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
226	C₂×D₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
227	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
228	C₂²×C₄×C₂₃	—	2	1	no	—
229	C₂²×C₄×C₂₃	—	2	1	no	—
230	C₂²×C₄×C₂₃	—	2	1	no	—
231	C₂²×C₄×C₂₃	—	2	1	no	—
232	C₂²×C₄×C₂₃	—	2	1	no	—
233	C₂²×C₄×C₂₃	—	2	1	no	—
234	C₂²×C₄×C₂₃	—	2	1	no	—
235	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
236	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
237	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
238	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
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	M₁₆×C₂₃	—	4	2	no	—
245	M₁₆×C₂₃	—	8	1	no	—
246	C₂×C₈×C₂₃	—	2	1	no	—
247	C₂×C₈×C₂₃	—	2	1	no	—
248	C₂×C₈×C₂₃	—	2	1	no	—
249	C₂×C₈×C₂₃	—	2	1	no	—
250	C₂×C₈×C₂₃	—	2	1	no	—
251	C₂×C₈×C₂₃	—	2	1	no	—
252	C₂×C₈×C₂₃	—	2	1	no	—
253	C₂×C₈×C₂₃	—	2	1	no	—
254	C₂×C₈×C₂₃	—	4	2	no	—
255	C₂×C₈×C₂₃	—	8	1	no	—
256	C₂×C₈×C₂₃	—	8	1	no	—
257	C₄⋊C₄×C₂₃	—	2	1	no	—
258	C₄⋊C₄×C₂₃	—	2	1	no	—
259	C₄⋊C₄×C₂₃	—	2	1	no	—
260	C₄⋊C₄×C₂₃	—	2	1	no	—
261	C₄⋊C₄×C₂₃	—	2	1	no	—
262	C₄⋊C₄×C₂₃	—	2	1	no	—
263	C₄⋊C₄×C₂₃	—	2	1	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	C₂²⋊C₄	1	1	yes	characteristic
302	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
303	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
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	C₄²×C₂₃	—	2	1	no	—
308	C₄²×C₂₃	—	2	1	no	—
309	C₄²×C₂₃	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
317	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
318	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
319	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₂₃	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
326	#17524	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
327	C₂³×C₂₃	—	2	1	no	—
328	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
329	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
330	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
331	Q₈×C₂₃	—	2	1	no	—
332	Q₈×C₂₃	—	2	1	no	—
333	Q₈×C₂₃	—	2	1	no	—
334	Q₈×C₂₃	—	2	1	no	—
335	Q₈×C₂₃	—	2	1	no	—
336	Q₈×C₂₃	—	4	1	no	—
337	Q₈×C₂₃	—	4	2	no	—
338	Q₈×C₂₃	—	4	2	no	—
339	Q₈×C₂₃	—	4	2	no	—
340	Q₈×C₂₃	#131	1	2	yes	—
341	D₄×C₂₃	—	2	2	no	—
342	D₄×C₂₃	—	2	2	no	—
343	D₄×C₂₃	—	2	1	no	—
344	D₄×C₂₃	—	2	1	no	—
345	D₄×C₂₃	—	4	1	no	—
346	D₄×C₂₃	—	4	2	no	—
347	D₄×C₂₃	—	4	2	no	—
348	D₄×C₂₃	—	4	2	no	—
349	C₂×C₄×C₂₃	—	2	1	no	—
350	C₂×C₄×C₂₃	—	2	2	no	—
351	C₂×C₄×C₂₃	—	2	1	no	—
352	C₂×C₄×C₂₃	—	2	1	no	—
353	C₂×C₄×C₂₃	—	2	1	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	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	—	4	1	no	—
370	C₂×C₄×C₂₃	—	4	1	no	—
371	C₂×C₄×C₂₃	—	4	2	no	—
372	C₂×C₄×C₂₃	—	4	2	no	—
373	C₂×C₄×C₂₃	—	4	2	no	—
374	C₂×C₄×C₂₃	—	4	2	no	—
375	C₂×C₄×C₂₃	—	4	2	no	—
376	C₂×C₄×C₂₃	—	4	2	no	—
377	C₂×C₄×C₂₃	—	4	1	no	—
378	C₂×C₄×C₂₃	—	4	1	no	—
379	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
380	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
381	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
382	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
383	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
384	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
385	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
386	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
387	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
388	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
389	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
391	C₈×C₂₃	—	4	1	no	—
392	C₈×C₂₃	—	4	1	no	—
393	C₈×C₂₃	—	4	1	no	—
394	C₈×C₂₃	—	4	1	no	—
395	C₈×C₂₃	—	4	1	no	—
396	C₈×C₂₃	—	4	1	no	—
397	C₈×C₂₃	—	4	1	no	—
398	C₈×C₂₃	—	4	1	no	—
399	#3482	C₂×C₂₃	1	1	yes	characteristic
400	#2990	C₂×C₂₃	1	1	yes	characteristic, complemented
401	#2922	C₂×C₂₃	1	1	yes	characteristic, complemented
402	#1497	C₂×C₂₃	1	1	yes	characteristic, complemented
403	#1495	C₂×C₂₃	1	1	yes	characteristic, complemented
404	#1494	C₂×C₂₃	1	1	yes	characteristic, complemented
405	#1491	C₂×C₂₃	1	1	yes	characteristic, complemented
406	#1488	C₂×C₂₃	1	1	yes	characteristic, complemented
407	#1487	C₂×C₂₃	1	1	yes	characteristic, complemented
408	#1483	C₂×C₂₃	1	1	yes	characteristic, complemented
409	#1482	C₂×C₂₃	1	1	yes	characteristic, complemented
410	#1481	C₂×C₂₃	1	1	yes	characteristic, complemented
411	#1479	C₂×C₂₃	1	1	yes	characteristic, complemented
412	#1477	C₂×C₂₃	1	1	yes	characteristic, complemented
413	C₂×Q₈⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
414	C₂²×C₂₃	—	2	1	no	—
415	C₂²×C₂₃	—	2	1	no	—
416	C₂²×C₂₃	—	2	1	no	—
417	C₂²×C₂₃	—	2	1	no	—
418	C₂²×C₂₃	—	2	1	no	—
419	C₂²×C₂₃	—	2	1	no	—
420	C₂²×C₂₃	—	2	1	no	—
421	C₂²×C₂₃	—	2	1	no	—
422	C₂²×C₂₃	—	4	1	no	—
423	C₂²×C₂₃	—	4	1	no	—
424	C₂²×C₂₃	—	4	1	no	—
425	C₂²×C₂₃	#421	1	2	yes	—
426	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
427	C₄×C₂₃	—	2	1	no	—
428	C₄×C₂₃	—	2	1	no	—
429	C₄×C₂₃	—	2	1	no	—
430	C₄×C₂₃	—	2	2	no	—
431	C₄×C₂₃	—	2	1	no	—
432	C₄×C₂₃	—	2	1	no	—
433	C₄×C₂₃	—	2	1	no	—
434	C₄×C₂₃	—	2	1	no	—
435	C₄×C₂₃	—	2	1	no	—
436	C₄×C₂₃	—	2	1	no	—
437	C₄×C₂₃	—	2	1	no	—
438	C₄×C₂₃	—	4	1	no	—
439	C₄×C₂₃	—	4	1	no	—
440	C₄×C₂₃	—	4	1	no	—
441	C₄×C₂₃	—	4	1	no	—
442	C₄×C₂₃	—	4	1	no	—
443	C₄×C₂₃	—	4	1	no	—
444	C₄×C₂₃	C₂×#131	1	1	yes	characteristic
445	C₄×C₂₃	#568	1	1	yes	characteristic
446	C₄×C₂₃	#577	1	1	yes	characteristic
447	C₄×C₂₃	#578	1	1	yes	characteristic
448	#557	C₄×C₂₃	1	1	yes	characteristic
449	#556	—	2	1	no	—
450	#556	C₄×C₂₃	1	1	yes	characteristic
451	#552	—	2	1	no	—
452	#552	—	2	1	no	—
453	#552	C₄×C₂₃	1	1	yes	characteristic
454	#552	C₄×C₂₃	1	1	yes	characteristic
455	D₄×Q₈	C₄×C₂₃	1	1	yes	characteristic
456	#548	C₄×C₂₃	1	1	yes	characteristic
457	#548	C₄×C₂₃	1	1	yes	characteristic
458	#547	—	2	1	no	—
459	#547	C₄×C₂₃	1	1	yes	characteristic
460	#533	—	2	1	no	—
461	#533	C₂²×C₂₃	1	1	yes	characteristic
462	#529	—	2	1	no	—
463	#529	—	2	1	no	—
464	#529	C₂²×C₂₃	1	1	yes	characteristic
465	#529	C₂²×C₂₃	1	1	yes	characteristic
466	C₄×#41	—	2	1	no	—
467	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
468	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
469	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
470	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
471	#446	—	2	1	no	—
472	#435	—	2	1	no	—
473	#435	—	2	1	no	—
474	C₈×D₄	—	2	1	no	—
475	#433	—	2	1	no	—
476	#433	—	2	1	no	—
477	#432	C₂²×C₂₃	1	1	yes	characteristic
478	#432	C₂²×C₂₃	1	1	yes	characteristic
479	#431	C₂²×C₂₃	1	1	yes	characteristic
480	#431	C₂²×C₂₃	1	1	yes	characteristic
481	#431	C₂²×C₂₃	1	1	yes	characteristic
482	#431	C₂²×C₂₃	1	1	yes	characteristic
483	#431	C₂²×C₂₃	1	1	yes	characteristic
484	#424	—	2	1	no	—
485	#423	C₂²×C₂₃	1	1	yes	characteristic
486	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
487	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
488	#408	—	2	1	no	—
489	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
490	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
491	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
492	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
493	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
494	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
495	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
496	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
497	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
498	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
499	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
500	Q₈⋊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	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
504	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
505	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
506	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
507	C₂×C₂₃	—	2	2	no	—
508	C₂×C₂₃	—	4	1	no	—
509	C₂×C₂₃	—	4	1	no	—
510	C₂×C₂₃	—	8	1	no	—
511	C₂×C₂₃	#2880	1	1	yes	characteristic
512	C₂×C₂₃	#2898	1	1	yes	characteristic
513	C₂×C₂₃	C₂×#421	1	1	yes	characteristic
514	C₂×#41	—	2	1	no	—
515	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
516	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
517	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
518	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
519	C₂×M₁₆	—	2	1	no	—
520	C₂×M₁₆	—	2	1	no	—
521	C₂²×C₈	—	2	1	no	—
522	C₂²×C₈	—	2	1	no	—
523	C₂²×C₈	—	2	1	no	—
524	C₄⋊Q₈	—	2	1	no	—
525	C₄⋊Q₈	—	2	1	no	—
526	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
527	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
528	#126	—	2	1	no	—
529	#126	—	2	1	no	—
530	#126	—	2	1	no	—
531	#126	—	2	1	no	—
532	#126	—	2	1	no	—
533	#126	—	2	1	no	—
534	#125	—	2	1	no	—
535	#125	—	2	1	no	—
536	#125	—	2	1	no	—
537	#125	—	2	1	no	—
538	#125	—	2	1	no	—
539	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
540	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
541	#124	—	2	1	no	—
542	#124	—	2	1	no	—
543	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
544	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
545	#123	—	2	1	no	—
546	#123	—	2	1	no	—
547	#123	—	2	1	no	—
548	#123	—	2	1	no	—
549	#123	—	2	1	no	—
550	#123	—	2	1	no	—
551	C₂²⋊Q₈	—	2	1	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	—	2	1	no	—
557	C₂²⋊Q₈	—	2	1	no	—
558	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
559	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
560	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
561	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
562	#121	—	2	1	no	—
563	#121	—	2	1	no	—
564	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
565	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
566	C₄×Q₈	—	2	1	no	—
567	C₄×Q₈	—	2	1	no	—
568	C₄×Q₈	—	2	1	no	—
569	C₄×Q₈	—	2	1	no	—
570	C₄×Q₈	—	2	1	no	—
571	C₄×Q₈	—	2	1	no	—
572	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
573	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
574	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
575	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
576	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
577	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
578	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
579	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
580	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
581	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
582	C₄×D₄	—	2	1	no	—
583	C₄×D₄	—	2	1	no	—
584	C₄×D₄	—	2	1	no	—
585	C₄×D₄	—	2	1	no	—
586	C₄×D₄	—	2	1	no	—
587	C₄×D₄	—	2	1	no	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
590	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
591	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
592	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
593	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
594	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
595	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
596	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
597	#117	—	2	1	no	—
598	#117	—	2	1	no	—
599	#117	—	2	1	no	—
600	#117	—	2	1	no	—
601	#117	—	2	1	no	—
602	#117	—	2	1	no	—
603	#117	—	2	1	no	—
604	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
605	#117	D₄×C₂₃	1	1	yes	characteristic
606	#117	D₄×C₂₃	1	1	yes	characteristic
607	#117	D₄×C₂₃	1	1	yes	characteristic
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
612	C₂×C₄²	—	2	1	no	—
613	C₂×C₄²	—	2	1	no	—
614	C₂×C₄²	—	2	1	no	—
615	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
618	C₄⋊C₈	—	2	1	no	—
619	C₄⋊C₈	—	2	1	no	—
620	C₄⋊C₈	—	2	1	no	—
621	C₄⋊C₈	—	2	1	no	—
622	C₄⋊C₈	—	2	1	no	—
623	C₄⋊C₈	—	2	1	no	—
624	C₄⋊C₈	—	2	1	no	—
625	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
626	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
627	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
628	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
629	C₂²⋊C₈	—	2	1	no	—
630	C₂²⋊C₈	—	2	1	no	—
631	C₂²⋊C₈	—	2	1	no	—
632	C₂²⋊C₈	—	2	1	no	—
633	C₂²⋊C₈	—	2	1	no	—
634	C₂²⋊C₈	—	2	1	no	—
635	C₂²⋊C₈	—	2	1	no	—
636	#97	—	2	1	no	—
637	#97	—	2	1	no	—
638	#97	—	2	1	no	—
639	C₄×C₈	—	2	1	no	—
640	C₄×C₈	—	2	1	no	—
641	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
642	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
643	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
644	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
645	C₂₃	#17524	1	1	yes	characteristic, direct product factor, Sylow
646	#41	—	2	2	no	—
647	#41	—	4	2	no	—
648	#41	—	4	1	no	—
649	#41	—	4	4	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	1	no	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	4	1	no	—
656	C₂×Q₈	—	4	1	no	—
657	C₂×Q₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
658	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
659	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
660	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
665	C₂×D₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
666	C₂×D₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
667	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
676	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
677	C₂²×C₄	C₂²×C₄×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	C₂×D₄×C₂₃	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
683	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
684	M₁₆	—	4	2	no	—
685	M₁₆	—	8	1	no	—
686	C₂×C₈	—	2	1	no	—
687	C₂×C₈	—	2	1	no	—
688	C₂×C₈	—	2	1	no	—
689	C₂×C₈	—	2	1	no	—
690	C₂×C₈	—	2	1	no	—
691	C₂×C₈	—	2	1	no	—
692	C₂×C₈	—	2	1	no	—
693	C₂×C₈	—	2	1	no	—
694	C₂×C₈	—	4	2	no	—
695	C₂×C₈	—	8	1	no	—
696	C₂×C₈	—	8	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	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	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
719	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
720	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
721	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
722	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
723	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
724	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
725	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
726	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
727	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	1	no	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	2	1	no	—
737	C₂²⋊C₄	—	2	1	no	—
738	C₂²⋊C₄	—	2	1	no	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
742	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
743	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
744	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
745	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
746	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
747	C₄²	—	2	1	no	—
748	C₄²	—	2	1	no	—
749	C₄²	—	2	1	no	—
750	C₄²	—	2	1	no	—
751	C₄²	—	2	1	no	—
752	C₄²	—	2	1	no	—
753	C₄²	—	2	1	no	—
754	C₄²	—	2	1	no	—
755	C₄²	—	2	1	no	—
756	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
757	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
758	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
759	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
760	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
761	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
762	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
763	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
764	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
765	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
766	C₂³	—	2	1	no	—
767	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
768	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
769	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
770	Q₈	—	2	1	no	—
771	Q₈	—	2	1	no	—
772	Q₈	—	2	1	no	—
773	Q₈	—	2	1	no	—
774	Q₈	—	2	1	no	—
775	Q₈	—	4	1	no	—
776	Q₈	—	4	2	no	—
777	Q₈	—	4	2	no	—
778	Q₈	—	4	2	no	—
779	Q₈	C₂₃×#131	1	2	yes	—
780	D₄	—	2	2	no	—
781	D₄	—	2	2	no	—
782	D₄	—	2	1	no	—
783	D₄	—	2	1	no	—
784	D₄	—	4	1	no	—
785	D₄	—	4	2	no	—
786	D₄	—	4	2	no	—
787	D₄	—	4	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	1	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	4	2	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	1	no	—
817	C₂×C₄	—	4	1	no	—
818	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
819	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
820	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
821	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
822	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
823	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
824	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
825	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
826	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
827	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
829	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
830	C₈	—	4	1	no	—
831	C₈	—	4	1	no	—
832	C₈	—	4	1	no	—
833	C₈	—	4	1	no	—
834	C₈	—	4	1	no	—
835	C₈	—	4	1	no	—
836	C₈	—	4	1	no	—
837	C₈	—	4	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	1	no	—
843	C₂²	—	2	1	no	—
844	C₂²	—	2	1	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	1	no	—
849	C₂²	C₂₃×#421	1	2	yes	—
850	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
851	C₄	—	2	1	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	1	no	—
854	C₄	—	2	2	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	1	no	—
859	C₄	—	2	1	no	—
860	C₄	—	2	1	no	—
861	C₄	—	2	1	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	1	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	1	no	—
868	C₄	C₂×C₂₃×#131	1	1	yes	characteristic
869	C₄	C₂₃×#568	1	1	yes	characteristic
870	C₄	C₂₃×#577	1	1	yes	characteristic
871	C₄	C₂₃×#578	1	1	yes	characteristic
872	C₂	—	2	2	no	—
873	C₂	—	4	1	no	—
874	C₂	—	4	1	no	—
875	C₂	—	8	1	no	—
876	C₂	C₂₃×#2880	1	1	yes	characteristic
877	C₂	C₂₃×#2898	1	1	yes	characteristic
878	C₂	C₂×C₂₃×#421	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×#3482	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×#2990	C₂	semidirect
3. C₂₃×#2922	C₂	semidirect
4. C₂₃×#1497	C₂	semidirect
5. C₂₃×#1495	C₂	semidirect
6. C₂₃×#1494	C₂	semidirect
7. C₂₃×#1491	C₂	semidirect
8. C₂₃×#1488	C₂	semidirect
9. C₂₃×#1487	C₂	semidirect
10. C₂₃×#1483	C₂	semidirect
11. C₂₃×#1482	C₂	semidirect
12. C₂₃×#1481	C₂	semidirect
13. C₂₃×#1479	C₂	semidirect
14. C₂₃×#1477	C₂	semidirect
15. C₂×C₂₃×Q₈⋊C₈	C₂	semidirect
326. #17524	C₂₃	direct (N × H)
400. #2990	C₂×C₂₃	semidirect
401. #2922	C₂×C₂₃	semidirect
402. #1497	C₂×C₂₃	semidirect
403. #1495	C₂×C₂₃	semidirect
404. #1494	C₂×C₂₃	semidirect
405. #1491	C₂×C₂₃	semidirect
406. #1488	C₂×C₂₃	semidirect
407. #1487	C₂×C₂₃	semidirect
408. #1483	C₂×C₂₃	semidirect
409. #1482	C₂×C₂₃	semidirect
410. #1481	C₂×C₂₃	semidirect
411. #1479	C₂×C₂₃	semidirect
412. #1477	C₂×C₂₃	semidirect
413. C₂×Q₈⋊C₈	C₂×C₂₃	semidirect
645. C₂₃	#17524	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×#3482	2
C₂₃×#2990	2
C₂₃×#2922	2
C₂₃×#1497	2
C₂₃×#1495	2
C₂₃×#1494	2
C₂₃×#1491	2
C₂₃×#1488	2
C₂₃×#1487	2
C₂₃×#1483	2
C₂₃×#1482	2
C₂₃×#1481	2
C₂₃×#1479	2
C₂₃×#1477	2
C₂×C₂₃×Q₈⋊C₈	2
#17524	23

Subgroups — C23×#17524 #19165150

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#17524 #19165150