Subgroups — C₂₃×#17506 #19165132

Order 5888.

890 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3461	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2965	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×#1493	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1491	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1489	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1488	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1487	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1485	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1483	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1482	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1481	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#544	C₄	1	1	yes	characteristic
17	C₂₃×#542	—	2	1	no	—
18	C₂₃×#542	C₄	1	1	yes	characteristic
19	C₂₃×#542	C₄	1	1	yes	characteristic
20	C₂₃×#541	—	2	1	no	—
21	C₂₃×#541	C₄	1	1	yes	characteristic
22	C₂₃×#541	C₄	1	1	yes	characteristic
23	C₂₃×#539	—	2	1	no	—
24	C₂₃×#539	—	2	1	no	—
25	C₂₃×#537	C₄	1	1	yes	characteristic
26	C₂₃×#536	C₄	1	1	yes	characteristic
27	C₂₃×#536	C₄	1	1	yes	characteristic
28	C₂₃×#533	—	2	1	no	—
29	C₂₃×#533	C₂²	1	1	yes	characteristic
30	C₂₃×#533	C₂²	1	1	yes	characteristic
31	C₂₃×#529	—	2	1	no	—
32	C₂₃×#529	—	2	1	no	—
33	C₂₃×#529	—	2	1	no	—
34	C₂₃×#529	C₂²	1	1	yes	characteristic
35	C₂₃×#529	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×#446	—	2	1	no	—
41	C₂₃×#436	—	2	1	no	—
42	C₂₃×#436	—	2	1	no	—
43	C₂₃×#435	—	2	1	no	—
44	C₂₃×#435	—	2	1	no	—
45	C₂₃×#435	—	2	1	no	—
46	C₂₃×#435	—	2	1	no	—
47	C₂₃×#432	C₂²	1	1	yes	characteristic
48	C₂₃×#432	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×#431	C₂²	1	1	yes	characteristic
53	C₂₃×#423	C₂²	1	1	yes	characteristic
54	C₂₃×#423	C₂²	1	1	yes	characteristic
55	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
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×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	C₂×C₄	1	1	yes	characteristic
76	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
77	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
78	C₂×M₁₆×C₂₃	—	2	1	no	—
79	C₂×M₁₆×C₂₃	—	2	1	no	—
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	C₂₃×C₄⋊Q₈	—	2	1	no	—
85	C₂₃×C₄⋊Q₈	—	2	1	no	—
86	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
87	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
88	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
89	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
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×#126	—	2	1	no	—
96	C₂₃×#126	—	2	1	no	—
97	C₂₃×#126	—	2	1	no	—
98	C₂₃×#125	—	2	1	no	—
99	C₂₃×#125	—	2	1	no	—
100	C₂₃×#125	—	2	1	no	—
101	C₂₃×#125	—	2	1	no	—
102	C₂₃×#125	—	2	1	no	—
103	C₂₃×#125	—	2	1	no	—
104	C₂₃×#125	—	2	1	no	—
105	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
106	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
107	C₂₃×#124	—	2	1	no	—
108	C₂₃×#124	—	2	1	no	—
109	C₂₃×#124	—	2	1	no	—
110	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
111	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
112	C₂₃×#123	—	2	1	no	—
113	C₂₃×#123	—	2	1	no	—
114	C₂₃×#123	—	2	1	no	—
115	C₂₃×#123	—	2	1	no	—
116	C₂₃×#123	—	2	1	no	—
117	C₂₃×#123	—	2	1	no	—
118	C₂₃×#123	—	2	1	no	—
119	C₂₃×#123	—	2	1	no	—
120	C₂₃×C₂²⋊Q₈	—	2	1	no	—
121	C₂₃×C₂²⋊Q₈	—	2	1	no	—
122	C₂₃×C₂²⋊Q₈	—	2	1	no	—
123	C₂₃×C₂²⋊Q₈	—	2	1	no	—
124	C₂₃×C₂²⋊Q₈	—	2	1	no	—
125	C₂₃×C₂²⋊Q₈	—	2	1	no	—
126	C₂₃×C₂²⋊Q₈	—	2	1	no	—
127	C₂₃×C₂²⋊Q₈	—	2	1	no	—
128	C₂₃×C₂²⋊Q₈	—	2	1	no	—
129	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
130	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
131	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
132	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
133	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
134	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
135	C₂₃×#121	—	2	1	no	—
136	C₂₃×#121	—	2	1	no	—
137	C₂₃×#121	—	2	1	no	—
138	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
139	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
140	C₄×Q₈×C₂₃	—	2	1	no	—
141	C₄×Q₈×C₂₃	—	2	1	no	—
142	C₄×Q₈×C₂₃	—	2	1	no	—
143	C₄×Q₈×C₂₃	—	2	1	no	—
144	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
145	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
146	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
147	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
148	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
149	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
150	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
151	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
152	C₄×D₄×C₂₃	—	2	1	no	—
153	C₄×D₄×C₂₃	—	2	1	no	—
154	C₄×D₄×C₂₃	—	2	1	no	—
155	C₄×D₄×C₂₃	—	2	1	no	—
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	D₄	1	1	yes	characteristic
161	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
162	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
163	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
164	C₂₃×#117	—	2	1	no	—
165	C₂₃×#117	—	2	1	no	—
166	C₂₃×#117	—	2	1	no	—
167	C₂₃×#117	—	2	1	no	—
168	C₂₃×#117	—	2	1	no	—
169	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
170	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
171	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
172	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
174	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
175	C₂×C₄²×C₂₃	—	2	1	no	—
176	C₂×C₄²×C₂₃	—	2	1	no	—
177	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
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×#97	—	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	—	4	2	no	—
207	#41×C₂₃	—	4	2	no	—
208	C₂×Q₈×C₂₃	—	2	1	no	—
209	C₂×Q₈×C₂₃	—	2	1	no	—
210	C₂×Q₈×C₂₃	—	2	1	no	—
211	C₂×Q₈×C₂₃	—	4	2	no	—
212	C₂×Q₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
213	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
214	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
215	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
216	C₂×D₄×C₂₃	—	2	1	no	—
217	C₂×D₄×C₂₃	—	2	1	no	—
218	C₂×D₄×C₂₃	—	2	1	no	—
219	C₂×D₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
220	C₂×D₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
221	C₂×D₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
222	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
223	C₂²×C₄×C₂₃	—	2	1	no	—
224	C₂²×C₄×C₂₃	—	2	1	no	—
225	C₂²×C₄×C₂₃	—	2	1	no	—
226	C₂²×C₄×C₂₃	—	2	1	no	—
227	C₂²×C₄×C₂₃	—	2	1	no	—
228	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
229	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
230	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
231	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
237	M₁₆×C₂₃	—	4	2	no	—
238	M₁₆×C₂₃	—	4	2	no	—
239	M₁₆×C₂₃	—	8	1	no	—
240	M₁₆×C₂₃	—	8	1	no	—
241	C₂×C₈×C₂₃	—	2	1	no	—
242	C₂×C₈×C₂₃	—	2	1	no	—
243	C₂×C₈×C₂₃	—	2	1	no	—
244	C₂×C₈×C₂₃	—	2	1	no	—
245	C₂×C₈×C₂₃	—	2	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	—	4	2	no	—
250	C₂×C₈×C₂₃	—	8	1	no	—
251	C₄⋊C₄×C₂₃	—	2	1	no	—
252	C₄⋊C₄×C₂₃	—	2	1	no	—
253	C₄⋊C₄×C₂₃	—	2	1	no	—
254	C₄⋊C₄×C₂₃	—	2	1	no	—
255	C₄⋊C₄×C₂₃	—	2	1	no	—
256	C₄⋊C₄×C₂₃	—	2	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	C₂²⋊C₄	1	1	yes	characteristic
275	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
276	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
277	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
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	C₂²⋊C₄×C₂₃	—	2	1	no	—
285	C₂²⋊C₄×C₂₃	—	2	1	no	—
286	C₂²⋊C₄×C₂₃	—	2	1	no	—
287	C₂²⋊C₄×C₂₃	—	2	1	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
300	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
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	C₄²×C₂₃	—	2	1	no	—
306	C₄²×C₂₃	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
313	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
314	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
315	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₂₃	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
322	#17506	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
323	C₂³×C₂₃	—	2	1	no	—
324	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
325	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
326	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
327	Q₈×C₂₃	—	2	2	no	—
328	Q₈×C₂₃	—	2	2	no	—
329	Q₈×C₂₃	—	2	2	no	—
330	Q₈×C₂₃	—	4	1	no	—
331	Q₈×C₂₃	—	4	2	no	—
332	Q₈×C₂₃	—	8	1	no	—
333	Q₈×C₂₃	—	8	1	no	—
334	D₄×C₂₃	—	2	2	no	—
335	D₄×C₂₃	—	4	1	no	—
336	D₄×C₂₃	—	4	1	no	—
337	D₄×C₂₃	—	4	1	no	—
338	D₄×C₂₃	—	4	2	no	—
339	D₄×C₂₃	—	8	1	no	—
340	D₄×C₂₃	—	8	1	no	—
341	C₂×C₄×C₂₃	—	2	2	no	—
342	C₂×C₄×C₂₃	—	2	2	no	—
343	C₂×C₄×C₂₃	—	2	2	no	—
344	C₂×C₄×C₂₃	—	2	1	no	—
345	C₂×C₄×C₂₃	—	2	1	no	—
346	C₂×C₄×C₂₃	—	2	1	no	—
347	C₂×C₄×C₂₃	—	2	1	no	—
348	C₂×C₄×C₂₃	—	2	1	no	—
349	C₂×C₄×C₂₃	—	2	1	no	—
350	C₂×C₄×C₂₃	—	2	1	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	—	4	1	no	—
358	C₂×C₄×C₂₃	—	4	1	no	—
359	C₂×C₄×C₂₃	—	4	1	no	—
360	C₂×C₄×C₂₃	—	4	2	no	—
361	C₂×C₄×C₂₃	—	4	2	no	—
362	C₂×C₄×C₂₃	—	4	1	no	—
363	C₂×C₄×C₂₃	—	4	1	no	—
364	C₂×C₄×C₂₃	—	8	1	no	—
365	C₂×C₄×C₂₃	—	8	1	no	—
366	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
367	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
368	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
369	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
370	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
371	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
372	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
373	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
374	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
375	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
376	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
378	C₈×C₂₃	—	2	2	no	—
379	C₈×C₂₃	—	4	1	no	—
380	C₈×C₂₃	—	4	1	no	—
381	C₈×C₂₃	—	4	1	no	—
382	C₈×C₂₃	—	4	1	no	—
383	C₈×C₂₃	—	4	1	no	—
384	C₈×C₂₃	—	4	1	no	—
385	C₈×C₂₃	—	4	1	no	—
386	#3461	C₂×C₂₃	1	1	yes	characteristic
387	#2989	C₂×C₂₃	1	1	yes	characteristic, complemented
388	#2965	C₂×C₂₃	1	1	yes	characteristic, complemented
389	#1497	C₂×C₂₃	1	1	yes	characteristic, complemented
390	#1495	C₂×C₂₃	1	1	yes	characteristic, complemented
391	#1494	C₂×C₂₃	1	1	yes	characteristic, complemented
392	#1493	C₂×C₂₃	1	1	yes	characteristic, complemented
393	#1491	C₂×C₂₃	1	1	yes	characteristic, complemented
394	#1489	C₂×C₂₃	1	1	yes	characteristic, complemented
395	#1488	C₂×C₂₃	1	1	yes	characteristic, complemented
396	#1487	C₂×C₂₃	1	1	yes	characteristic, complemented
397	#1485	C₂×C₂₃	1	1	yes	characteristic, complemented
398	#1483	C₂×C₂₃	1	1	yes	characteristic, complemented
399	#1482	C₂×C₂₃	1	1	yes	characteristic, complemented
400	#1481	C₂×C₂₃	1	1	yes	characteristic, complemented
401	C₂²×C₂₃	—	2	1	no	—
402	C₂²×C₂₃	—	2	1	no	—
403	C₂²×C₂₃	—	2	1	no	—
404	C₂²×C₂₃	—	2	1	no	—
405	C₂²×C₂₃	—	2	1	no	—
406	C₂²×C₂₃	—	2	1	no	—
407	C₂²×C₂₃	—	2	1	no	—
408	C₂²×C₂₃	—	2	1	no	—
409	C₂²×C₂₃	—	2	1	no	—
410	C₂²×C₂₃	—	4	1	no	—
411	C₂²×C₂₃	—	4	1	no	—
412	C₂²×C₂₃	—	4	1	no	—
413	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
414	C₄×C₂₃	—	2	1	no	—
415	C₄×C₂₃	—	2	1	no	—
416	C₄×C₂₃	—	2	1	no	—
417	C₄×C₂₃	—	2	1	no	—
418	C₄×C₂₃	—	2	1	no	—
419	C₄×C₂₃	—	2	1	no	—
420	C₄×C₂₃	—	2	1	no	—
421	C₄×C₂₃	—	2	1	no	—
422	C₄×C₂₃	—	2	1	no	—
423	C₄×C₂₃	—	2	1	no	—
424	C₄×C₂₃	—	4	1	no	—
425	C₄×C₂₃	—	4	1	no	—
426	C₄×C₂₃	—	4	1	no	—
427	C₄×C₂₃	—	4	1	no	—
428	C₄×C₂₃	—	4	1	no	—
429	C₄×C₂₃	—	4	1	no	—
430	C₄×C₂₃	—	4	1	no	—
431	C₄×C₂₃	#568	1	2	yes	—
432	C₄×C₂₃	#577	1	1	yes	characteristic
433	C₄×C₂₃	#578	1	1	yes	characteristic
434	#544	C₄×C₂₃	1	1	yes	characteristic
435	#542	—	2	1	no	—
436	#542	C₄×C₂₃	1	1	yes	characteristic
437	#542	C₄×C₂₃	1	1	yes	characteristic
438	#541	—	2	1	no	—
439	#541	C₄×C₂₃	1	1	yes	characteristic
440	#541	C₄×C₂₃	1	1	yes	characteristic
441	#539	—	2	1	no	—
442	#539	—	2	1	no	—
443	#537	C₄×C₂₃	1	1	yes	characteristic
444	#536	C₄×C₂₃	1	1	yes	characteristic
445	#536	C₄×C₂₃	1	1	yes	characteristic
446	#533	—	2	1	no	—
447	#533	C₂²×C₂₃	1	1	yes	characteristic
448	#533	C₂²×C₂₃	1	1	yes	characteristic
449	#529	—	2	1	no	—
450	#529	—	2	1	no	—
451	#529	—	2	1	no	—
452	#529	C₂²×C₂₃	1	1	yes	characteristic
453	#529	C₂²×C₂₃	1	1	yes	characteristic
454	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
455	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
456	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
457	#446	—	2	1	no	—
458	#446	—	2	1	no	—
459	#436	—	2	1	no	—
460	#436	—	2	1	no	—
461	#435	—	2	1	no	—
462	#435	—	2	1	no	—
463	#435	—	2	1	no	—
464	#435	—	2	1	no	—
465	#432	C₂²×C₂₃	1	1	yes	characteristic
466	#432	C₂²×C₂₃	1	1	yes	characteristic
467	#431	C₂²×C₂₃	1	1	yes	characteristic
468	#431	C₂²×C₂₃	1	1	yes	characteristic
469	#431	C₂²×C₂₃	1	1	yes	characteristic
470	#431	C₂²×C₂₃	1	1	yes	characteristic
471	#423	C₂²×C₂₃	1	1	yes	characteristic
472	#423	C₂²×C₂₃	1	1	yes	characteristic
473	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
474	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
475	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
476	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
477	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
478	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
479	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
480	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
481	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
482	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
483	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
484	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
485	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
486	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
487	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
488	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
489	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
490	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
491	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
492	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
493	C₂×C₂₃	—	4	1	no	—
494	C₂×C₂₃	—	4	1	no	—
495	C₂×C₂₃	—	4	1	no	—
496	C₂×C₂₃	—	8	1	no	—
497	C₂×C₂₃	#2879	1	1	yes	characteristic
498	C₂×C₂₃	#2898	1	1	yes	characteristic
499	C₂×C₂₃	#2901	1	1	yes	characteristic
500	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
501	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
502	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
503	C₂×M₁₆	—	2	1	no	—
504	C₂×M₁₆	—	2	1	no	—
505	C₂×M₁₆	—	2	1	no	—
506	C₂×M₁₆	—	2	1	no	—
507	C₂²×C₈	—	2	1	no	—
508	C₂²×C₈	—	2	1	no	—
509	C₄⋊Q₈	—	2	1	no	—
510	C₄⋊Q₈	—	2	1	no	—
511	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
512	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
513	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
514	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
515	#126	—	2	1	no	—
516	#126	—	2	1	no	—
517	#126	—	2	1	no	—
518	#126	—	2	1	no	—
519	#126	—	2	1	no	—
520	#126	—	2	1	no	—
521	#126	—	2	1	no	—
522	#126	—	2	1	no	—
523	#125	—	2	1	no	—
524	#125	—	2	1	no	—
525	#125	—	2	1	no	—
526	#125	—	2	1	no	—
527	#125	—	2	1	no	—
528	#125	—	2	1	no	—
529	#125	—	2	1	no	—
530	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
531	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
532	#124	—	2	1	no	—
533	#124	—	2	1	no	—
534	#124	—	2	1	no	—
535	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
536	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
537	#123	—	2	1	no	—
538	#123	—	2	1	no	—
539	#123	—	2	1	no	—
540	#123	—	2	1	no	—
541	#123	—	2	1	no	—
542	#123	—	2	1	no	—
543	#123	—	2	1	no	—
544	#123	—	2	1	no	—
545	C₂²⋊Q₈	—	2	1	no	—
546	C₂²⋊Q₈	—	2	1	no	—
547	C₂²⋊Q₈	—	2	1	no	—
548	C₂²⋊Q₈	—	2	1	no	—
549	C₂²⋊Q₈	—	2	1	no	—
550	C₂²⋊Q₈	—	2	1	no	—
551	C₂²⋊Q₈	—	2	1	no	—
552	C₂²⋊Q₈	—	2	1	no	—
553	C₂²⋊Q₈	—	2	1	no	—
554	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
555	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
556	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
557	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
558	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
559	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
560	#121	—	2	1	no	—
561	#121	—	2	1	no	—
562	#121	—	2	1	no	—
563	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
564	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
565	C₄×Q₈	—	2	1	no	—
566	C₄×Q₈	—	2	1	no	—
567	C₄×Q₈	—	2	1	no	—
568	C₄×Q₈	—	2	1	no	—
569	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
570	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
571	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
572	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
573	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
574	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
575	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
576	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
577	C₄×D₄	—	2	1	no	—
578	C₄×D₄	—	2	1	no	—
579	C₄×D₄	—	2	1	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
582	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
583	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
584	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
585	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
586	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
587	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
588	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
589	#117	—	2	1	no	—
590	#117	—	2	1	no	—
591	#117	—	2	1	no	—
592	#117	—	2	1	no	—
593	#117	—	2	1	no	—
594	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
595	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
596	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
597	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
600	C₂×C₄²	—	2	1	no	—
601	C₂×C₄²	—	2	1	no	—
602	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
605	C₄⋊C₈	—	2	1	no	—
606	C₄⋊C₈	—	2	1	no	—
607	C₄⋊C₈	—	2	1	no	—
608	C₄⋊C₈	—	2	1	no	—
609	C₄⋊C₈	—	2	1	no	—
610	C₄⋊C₈	—	2	1	no	—
611	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
612	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
613	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
614	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
615	C₂²⋊C₈	—	2	1	no	—
616	C₂²⋊C₈	—	2	1	no	—
617	C₂²⋊C₈	—	2	1	no	—
618	C₂²⋊C₈	—	2	1	no	—
619	C₂²⋊C₈	—	2	1	no	—
620	C₂²⋊C₈	—	2	1	no	—
621	#97	—	2	1	no	—
622	#97	—	2	1	no	—
623	#97	—	2	1	no	—
624	#97	—	2	1	no	—
625	C₄×C₈	—	2	1	no	—
626	C₄×C₈	—	2	1	no	—
627	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
628	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
629	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
630	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
631	C₂₃	#17506	1	1	yes	characteristic, direct product factor, Sylow
632	#41	—	4	2	no	—
633	#41	—	4	2	no	—
634	C₂×Q₈	—	2	1	no	—
635	C₂×Q₈	—	2	1	no	—
636	C₂×Q₈	—	2	1	no	—
637	C₂×Q₈	—	4	2	no	—
638	C₂×Q₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
639	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
640	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
641	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
646	C₂×D₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
647	C₂×D₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
648	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
655	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
656	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
660	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
661	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
662	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
663	M₁₆	—	4	2	no	—
664	M₁₆	—	4	2	no	—
665	M₁₆	—	8	1	no	—
666	M₁₆	—	8	1	no	—
667	C₂×C₈	—	2	1	no	—
668	C₂×C₈	—	2	1	no	—
669	C₂×C₈	—	2	1	no	—
670	C₂×C₈	—	2	1	no	—
671	C₂×C₈	—	2	1	no	—
672	C₂×C₈	—	2	1	no	—
673	C₂×C₈	—	2	1	no	—
674	C₂×C₈	—	2	1	no	—
675	C₂×C₈	—	4	2	no	—
676	C₂×C₈	—	8	1	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
701	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
702	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
703	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
704	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
705	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
706	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
707	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
708	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
709	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
710	C₂²⋊C₄	—	2	1	no	—
711	C₂²⋊C₄	—	2	1	no	—
712	C₂²⋊C₄	—	2	1	no	—
713	C₂²⋊C₄	—	2	1	no	—
714	C₂²⋊C₄	—	2	1	no	—
715	C₂²⋊C₄	—	2	1	no	—
716	C₂²⋊C₄	—	2	1	no	—
717	C₂²⋊C₄	—	2	1	no	—
718	C₂²⋊C₄	—	2	1	no	—
719	C₂²⋊C₄	—	2	1	no	—
720	C₂²⋊C₄	—	2	1	no	—
721	C₂²⋊C₄	—	2	1	no	—
722	C₂²⋊C₄	—	2	1	no	—
723	C₂²⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	—	2	1	no	—
725	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
726	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
727	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
728	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
729	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
730	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
731	C₄²	—	2	1	no	—
732	C₄²	—	2	1	no	—
733	C₄²	—	2	1	no	—
734	C₄²	—	2	1	no	—
735	C₄²	—	2	1	no	—
736	C₄²	—	2	1	no	—
737	C₄²	—	2	1	no	—
738	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
739	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
740	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
741	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
742	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
743	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
744	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
745	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
746	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
747	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
748	C₂³	—	2	1	no	—
749	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
750	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
751	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
752	Q₈	—	2	2	no	—
753	Q₈	—	2	2	no	—
754	Q₈	—	2	2	no	—
755	Q₈	—	4	1	no	—
756	Q₈	—	4	2	no	—
757	Q₈	—	8	1	no	—
758	Q₈	—	8	1	no	—
759	D₄	—	2	2	no	—
760	D₄	—	4	1	no	—
761	D₄	—	4	1	no	—
762	D₄	—	4	1	no	—
763	D₄	—	4	2	no	—
764	D₄	—	8	1	no	—
765	D₄	—	8	1	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	2	no	—
786	C₂×C₄	—	4	2	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	8	1	no	—
790	C₂×C₄	—	8	1	no	—
791	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
792	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
793	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
794	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
795	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
796	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
797	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
798	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
799	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
800	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
801	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
803	C₈	—	2	2	no	—
804	C₈	—	4	1	no	—
805	C₈	—	4	1	no	—
806	C₈	—	4	1	no	—
807	C₈	—	4	1	no	—
808	C₈	—	4	1	no	—
809	C₈	—	4	1	no	—
810	C₈	—	4	1	no	—
811	C₂²	—	2	1	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
824	C₄	—	2	1	no	—
825	C₄	—	2	1	no	—
826	C₄	—	2	1	no	—
827	C₄	—	2	1	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	1	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	1	no	—
840	C₄	—	4	1	no	—
841	C₄	C₂₃×#568	1	2	yes	—
842	C₄	C₂₃×#577	1	1	yes	characteristic
843	C₄	C₂₃×#578	1	1	yes	characteristic
844	C₂	—	4	1	no	—
845	C₂	—	4	1	no	—
846	C₂	—	4	1	no	—
847	C₂	—	8	1	no	—
848	C₂	C₂₃×#2879	1	1	yes	characteristic
849	C₂	C₂₃×#2898	1	1	yes	characteristic
850	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×#537	C₄
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×#2989	C₂	semidirect
3. C₂₃×#2965	C₂	semidirect
4. C₂₃×#1497	C₂	semidirect
5. C₂₃×#1495	C₂	semidirect
6. C₂₃×#1494	C₂	semidirect
7. C₂₃×#1493	C₂	semidirect
8. C₂₃×#1491	C₂	semidirect
9. C₂₃×#1489	C₂	semidirect
10. C₂₃×#1488	C₂	semidirect
11. C₂₃×#1487	C₂	semidirect
12. C₂₃×#1485	C₂	semidirect
13. C₂₃×#1483	C₂	semidirect
14. C₂₃×#1482	C₂	semidirect
15. C₂₃×#1481	C₂	semidirect
322. #17506	C₂₃	direct (N × H)
387. #2989	C₂×C₂₃	semidirect
388. #2965	C₂×C₂₃	semidirect
389. #1497	C₂×C₂₃	semidirect
390. #1495	C₂×C₂₃	semidirect
391. #1494	C₂×C₂₃	semidirect
392. #1493	C₂×C₂₃	semidirect
393. #1491	C₂×C₂₃	semidirect
394. #1489	C₂×C₂₃	semidirect
395. #1488	C₂×C₂₃	semidirect
396. #1487	C₂×C₂₃	semidirect
397. #1485	C₂×C₂₃	semidirect
398. #1483	C₂×C₂₃	semidirect
399. #1482	C₂×C₂₃	semidirect
400. #1481	C₂×C₂₃	semidirect
631. C₂₃	#17506	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×#3461	2
C₂₃×#2989	2
C₂₃×#2965	2
C₂₃×#1497	2
C₂₃×#1495	2
C₂₃×#1494	2
C₂₃×#1493	2
C₂₃×#1491	2
C₂₃×#1489	2
C₂₃×#1488	2
C₂₃×#1487	2
C₂₃×#1485	2
C₂₃×#1483	2
C₂₃×#1482	2
C₂₃×#1481	2
#17506	23

Subgroups — C23×#17506 #19165132

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#17506 #19165132