Subgroups — C₂₃×#60947 #19208573

Order 5888.

1824 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3248	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3231	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3210	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3190	C₂	1	4	yes	maximal, complemented
11	C₂₃×#3170	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3167	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3108	C₂	1	4	yes	maximal, complemented
14	C₂₃×#3107	C₂	1	4	yes	maximal, complemented
15	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#533	—	2	1	no	—
17	C₂₃×#533	—	2	1	no	—
18	C₂₃×#533	—	2	1	no	—
19	C₂₃×#533	—	2	1	no	—
20	C₂₃×#533	C₂²	1	2	yes	—
21	C₂₃×#533	C₂²	1	1	yes	characteristic
22	C₂₃×#533	C₂²	1	2	yes	—
23	C₂₃×#533	C₂²	1	2	yes	—
24	C₂₃×#533	C₂²	1	2	yes	—
25	C₂₃×#533	C₂²	1	1	yes	characteristic
26	C₂₃×#533	C₂²	1	1	yes	characteristic
27	C₂₃×#532	C₂²	1	1	yes	characteristic
28	C₂₃×#532	C₂²	1	1	yes	characteristic
29	C₂₃×#532	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂₃×#529	—	2	1	no	—
33	C₂₃×#529	—	2	1	no	—
34	C₂₃×#529	—	2	1	no	—
35	C₂₃×#529	—	2	1	no	—
36	C₂₃×#529	C₂²	1	2	yes	—
37	C₂₃×#529	C₂²	1	2	yes	—
38	C₂×C₂₃×#125	—	2	1	no	—
39	C₂₃×#525	—	2	1	no	—
40	C₂₃×#525	—	2	1	no	—
41	C₂₃×#525	C₂²	1	2	yes	—
42	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
43	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
44	C₄×#41×C₂₃	—	2	1	no	—
45	C₄×#41×C₂₃	—	2	1	no	—
46	C₄×#41×C₂₃	C₂²	1	2	yes	—
47	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
48	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
49	C₂×C₂₃×#117	—	2	1	no	—
50	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
51	C₂₃×#500	C₂²	1	2	yes	complemented
52	C₂₃×#498	C₂²	1	2	yes	complemented
53	C₂₃×#494	C₂²	1	2	yes	complemented
54	C₂₃×#492	C₂²	1	2	yes	complemented
55	C₂₃×#487	C₂²	1	2	yes	complemented
56	C₂₃×#487	C₂²	1	2	yes	complemented
57	C₂₃×#487	C₂²	1	2	yes	complemented
58	C₂₃×#486	C₂²	1	2	yes	complemented
59	C₂₃×#485	C₂²	1	8	yes	—
60	C₂₃×#483	C₂²	1	4	yes	—
61	C₂₃×#480	C₂²	1	4	yes	—
62	C₂₃×#479	C₂²	1	8	yes	complemented
63	C₂₃×#475	C₂²	1	4	yes	complemented
64	C₂₃×#474	C₂²	1	4	yes	complemented
65	C₂₃×#467	C₂²	1	8	yes	—
66	C₂₃×#465	C₂²	1	8	yes	—
67	C₂₃×#464	C₂²	1	8	yes	complemented
68	C₂₃×#462	C₂²	1	4	yes	complemented
69	C₂₃×#461	C₂²	1	4	yes	complemented
70	C₂₃×#452	C₂²	1	8	yes	—
71	C₂₃×#451	C₂²	1	4	yes	—
72	C₂₃×#448	C₂²	1	4	yes	—
73	C₄×Q₁₆×C₂₃	C₂²	1	8	yes	complemented
74	C₄×SD₁₆×C₂₃	C₂²	1	8	yes	complemented
75	C₂₃×#431	C₂²	1	1	yes	characteristic
76	C₂₃×#431	C₂²	1	1	yes	characteristic
77	C₂₃×#431	C₂²	1	2	yes	—
78	C₂₃×#431	C₂²	1	2	yes	—
79	C₂₃×#431	C₂²	1	2	yes	—
80	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
81	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
82	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
83	C₂×#41×C₂₃	—	2	1	no	—
84	C₂×#41×C₂₃	—	2	1	no	—
85	C₂×#41×C₂₃	C₂³	1	2	yes	—
86	C₂²×Q₈×C₂₃	—	2	1	no	—
87	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
88	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
89	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
90	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
91	C₂×Q₁₆×C₂₃	C₂³	1	8	yes	—
92	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
93	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
94	C₂₃×C₄⋊Q₈	—	2	1	no	—
95	C₂₃×C₄⋊Q₈	—	2	1	no	—
96	C₂₃×C₄⋊Q₈	—	2	1	no	—
97	C₂₃×C₄⋊Q₈	—	2	1	no	—
98	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
100	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
101	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
102	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
103	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₂₃×#127	C₂³	1	1	yes	characteristic
106	C₂₃×#126	—	2	2	no	—
107	C₂₃×#126	—	2	2	no	—
108	C₂₃×#125	—	2	2	no	—
109	C₂₃×#125	—	2	2	no	—
110	C₂₃×#125	—	2	2	no	—
111	C₂₃×#125	—	2	2	no	—
112	C₂₃×#125	—	2	1	no	—
113	C₂₃×#125	—	2	1	no	—
114	C₂₃×#125	C₂³	1	2	yes	—
115	C₂₃×#124	—	2	1	no	—
116	C₂₃×#124	—	2	1	no	—
117	C₂₃×#124	C₂³	1	2	yes	—
118	C₂₃×#123	—	2	2	no	—
119	C₂₃×#123	—	2	2	no	—
120	C₂₃×#123	—	2	2	no	—
121	C₂₃×C₂²⋊Q₈	—	2	2	no	—
122	C₂₃×C₂²⋊Q₈	—	2	2	no	—
123	C₂₃×C₂²⋊Q₈	—	2	2	no	—
124	C₂₃×C₂²⋊Q₈	—	2	2	no	—
125	C₂₃×C₂²⋊Q₈	—	2	2	no	—
126	C₂₃×C₂²⋊Q₈	—	2	2	no	—
127	C₂₃×C₂²⋊Q₈	—	2	1	no	—
128	C₂₃×C₂²⋊Q₈	—	2	1	no	—
129	C₂₃×C₂²⋊Q₈	—	2	1	no	—
130	C₂₃×C₂²⋊Q₈	—	2	1	no	—
131	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
132	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
133	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₂₃×#121	—	2	1	no	—
136	C₂₃×#121	—	2	1	no	—
137	C₂₃×#121	—	2	1	no	—
138	C₂₃×#121	—	2	1	no	—
139	C₂₃×#121	C₂³	1	2	yes	—
140	C₂₃×#121	C₂³	1	2	yes	—
141	C₂₃×#120	—	2	2	no	—
142	C₄×Q₈×C₂₃	—	2	2	no	—
143	C₄×Q₈×C₂₃	—	2	2	no	—
144	C₄×Q₈×C₂₃	—	2	2	no	—
145	C₄×Q₈×C₂₃	—	2	2	no	—
146	C₄×Q₈×C₂₃	—	2	2	no	—
147	C₄×Q₈×C₂₃	—	2	2	no	—
148	C₄×Q₈×C₂₃	—	2	1	no	—
149	C₄×Q₈×C₂₃	—	2	1	no	—
150	C₄×Q₈×C₂₃	—	2	1	no	—
151	C₄×Q₈×C₂₃	—	2	1	no	—
152	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
153	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
154	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
155	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
156	C₄×D₄×C₂₃	—	2	2	no	—
157	C₄×D₄×C₂₃	—	2	2	no	—
158	C₄×D₄×C₂₃	—	2	2	no	—
159	C₄×D₄×C₂₃	—	2	2	no	—
160	C₄×D₄×C₂₃	—	2	2	no	—
161	C₄×D₄×C₂₃	—	2	2	no	—
162	C₄×D₄×C₂₃	—	2	1	no	—
163	C₄×D₄×C₂₃	—	2	1	no	—
164	C₄×D₄×C₂₃	—	2	1	no	—
165	C₄×D₄×C₂₃	—	2	1	no	—
166	C₄×D₄×C₂₃	C₂³	1	2	yes	—
167	C₄×D₄×C₂₃	C₂³	1	2	yes	—
168	C₂₃×#117	—	2	2	no	—
169	C₂₃×#117	—	2	2	no	—
170	C₂₃×#117	—	2	2	no	—
171	C₂₃×#117	—	2	2	no	—
172	C₂₃×#117	—	2	1	no	—
173	C₂₃×#117	—	2	1	no	—
174	C₂₃×#117	—	2	2	no	—
175	C₂₃×#117	—	2	2	no	—
176	C₂₃×#117	—	2	2	no	—
177	C₂₃×#117	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
179	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
180	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
181	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
182	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
183	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
185	C₂×C₄²×C₂₃	—	2	2	no	—
186	C₂×C₄²×C₂₃	—	2	2	no	—
187	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
199	C₂₃×#107	C₂³	1	8	yes	—
200	C₂₃×#106	C₂³	1	8	yes	—
201	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
202	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
203	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
204	C₂₃×#103	C₂³	1	8	yes	—
205	C₂₃×#103	C₂³	1	8	yes	—
206	C₂₃×#103	C₂³	1	8	yes	—
207	C₂₃×#102	C₂³	1	8	yes	—
208	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
209	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
210	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
211	C₄×C₈×C₂₃	C₂³	1	4	yes	—
212	C₄×C₈×C₂₃	C₂³	1	2	yes	—
213	C₄×C₈×C₂₃	C₂³	1	2	yes	—
214	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
215	#41×C₂₃	—	4	4	no	—
216	#41×C₂₃	—	4	4	no	—
217	#41×C₂₃	—	4	4	no	—
218	C₂×Q₈×C₂₃	—	2	1	no	—
219	C₂×Q₈×C₂₃	—	2	1	no	—
220	C₂×Q₈×C₂₃	—	2	2	no	—
221	C₂×Q₈×C₂₃	—	2	2	no	—
222	C₂×Q₈×C₂₃	—	2	2	no	—
223	C₂×Q₈×C₂₃	—	4	4	no	—
224	C₂×Q₈×C₂₃	—	4	4	no	—
225	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
226	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
227	C₂×D₄×C₂₃	—	2	2	no	—
228	C₂×D₄×C₂₃	—	2	2	no	—
229	C₂×D₄×C₂₃	—	2	2	no	—
230	C₂×D₄×C₂₃	—	2	1	no	—
231	C₂×D₄×C₂₃	—	2	1	no	—
232	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₂₃	—	2	4	no	—
234	C₂²×C₄×C₂₃	—	2	4	no	—
235	C₂²×C₄×C₂₃	—	2	2	no	—
236	C₂²×C₄×C₂₃	—	2	2	no	—
237	C₂²×C₄×C₂₃	—	2	2	no	—
238	C₂²×C₄×C₂₃	—	2	2	no	—
239	C₂²×C₄×C₂₃	—	2	2	no	—
240	C₂²×C₄×C₂₃	—	4	2	no	—
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	C₂²×C₄×C₂₃	C₂×D₄	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	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
259	Q₁₆×C₂₃	—	4	8	no	—
260	SD₁₆×C₂₃	—	4	8	no	—
261	C₂×C₈×C₂₃	—	4	4	no	—
262	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
263	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
264	C₄⋊C₄×C₂₃	—	2	2	no	—
265	C₄⋊C₄×C₂₃	—	2	2	no	—
266	C₄⋊C₄×C₂₃	—	2	2	no	—
267	C₄⋊C₄×C₂₃	—	2	2	no	—
268	C₄⋊C₄×C₂₃	—	2	2	no	—
269	C₄⋊C₄×C₂₃	—	2	2	no	—
270	C₄⋊C₄×C₂₃	—	2	4	no	—
271	C₄⋊C₄×C₂₃	—	2	4	no	—
272	C₄⋊C₄×C₂₃	—	2	4	no	—
273	C₄⋊C₄×C₂₃	—	2	4	no	—
274	C₄⋊C₄×C₂₃	—	2	2	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	—	2	1	no	—
279	C₄⋊C₄×C₂₃	—	2	2	no	—
280	C₄⋊C₄×C₂₃	—	2	2	no	—
281	C₄⋊C₄×C₂₃	—	2	2	no	—
282	C₄⋊C₄×C₂₃	—	2	2	no	—
283	C₄⋊C₄×C₂₃	—	2	2	no	—
284	C₄⋊C₄×C₂₃	—	2	2	no	—
285	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
286	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
288	C₂²⋊C₄×C₂₃	—	2	4	no	—
289	C₂²⋊C₄×C₂₃	—	2	4	no	—
290	C₂²⋊C₄×C₂₃	—	2	2	no	—
291	C₂²⋊C₄×C₂₃	—	2	2	no	—
292	C₂²⋊C₄×C₂₃	—	2	2	no	—
293	C₂²⋊C₄×C₂₃	—	2	2	no	—
294	C₂²⋊C₄×C₂₃	—	2	2	no	—
295	C₂²⋊C₄×C₂₃	—	2	2	no	—
296	C₂²⋊C₄×C₂₃	—	2	2	no	—
297	C₂²⋊C₄×C₂₃	—	2	2	no	—
298	C₂²⋊C₄×C₂₃	—	2	2	no	—
299	C₄²×C₂₃	—	2	2	no	—
300	C₄²×C₂₃	—	2	4	no	—
301	C₄²×C₂₃	—	2	2	no	—
302	C₄²×C₂₃	—	2	2	no	—
303	C₄²×C₂₃	—	2	4	no	—
304	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
317	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
318	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
319	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
320	#60947	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
321	C₂³×C₂₃	—	2	2	no	—
322	C₂³×C₂₃	—	2	2	no	—
323	C₂³×C₂₃	—	2	2	no	—
324	C₂³×C₂₃	—	4	1	no	—
325	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
326	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
327	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
328	Q₈×C₂₃	—	2	8	no	—
329	Q₈×C₂₃	—	2	4	no	—
330	Q₈×C₂₃	—	4	4	no	—
331	Q₈×C₂₃	—	4	4	no	—
332	Q₈×C₂₃	—	4	4	no	—
333	Q₈×C₂₃	—	4	2	no	—
334	Q₈×C₂₃	—	4	2	no	—
335	D₄×C₂₃	—	2	4	no	—
336	D₄×C₂₃	—	4	4	no	—
337	D₄×C₂₃	—	4	4	no	—
338	D₄×C₂₃	—	4	4	no	—
339	D₄×C₂₃	—	4	2	no	—
340	D₄×C₂₃	—	4	2	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	2	no	—
345	C₂×C₄×C₂₃	—	2	2	no	—
346	C₂×C₄×C₂₃	—	2	2	no	—
347	C₂×C₄×C₂₃	—	2	2	no	—
348	C₂×C₄×C₂₃	—	2	2	no	—
349	C₂×C₄×C₂₃	—	2	2	no	—
350	C₂×C₄×C₂₃	—	2	2	no	—
351	C₂×C₄×C₂₃	—	2	2	no	—
352	C₂×C₄×C₂₃	—	2	2	no	—
353	C₂×C₄×C₂₃	—	2	2	no	—
354	C₂×C₄×C₂₃	—	2	2	no	—
355	C₂×C₄×C₂₃	—	2	2	no	—
356	C₂×C₄×C₂₃	—	2	2	no	—
357	C₂×C₄×C₂₃	—	2	4	no	—
358	C₂×C₄×C₂₃	—	2	4	no	—
359	C₂×C₄×C₂₃	—	4	1	no	—
360	C₂×C₄×C₂₃	—	4	1	no	—
361	C₂×C₄×C₂₃	—	4	1	no	—
362	C₂×C₄×C₂₃	—	4	4	no	—
363	C₂×C₄×C₂₃	—	4	4	no	—
364	C₂×C₄×C₂₃	—	4	4	no	—
365	C₂×C₄×C₂₃	—	4	4	no	—
366	C₂×C₄×C₂₃	—	4	4	no	—
367	C₂×C₄×C₂₃	#135	1	4	yes	—
368	C₂×C₄×C₂₃	#137	1	4	yes	—
369	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₂₃	C₂²×D₄	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	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
381	C₈×C₂₃	—	2	4	no	—
382	C₈×C₂₃	—	2	4	no	—
383	#3444	C₂×C₂₃	1	1	yes	characteristic
384	C₂×#533	C₂×C₂₃	1	1	yes	characteristic, complemented
385	#3248	C₂×C₂₃	1	4	yes	complemented
386	#3231	C₂×C₂₃	1	2	yes	complemented
387	#3229	C₂×C₂₃	1	1	yes	characteristic, complemented
388	#3226	C₂×C₂₃	1	1	yes	characteristic, complemented
389	#3210	C₂×C₂₃	1	2	yes	complemented
390	#3209	C₂×C₂₃	1	1	yes	characteristic, complemented
391	#3206	C₂×C₂₃	1	1	yes	characteristic, complemented
392	#3190	C₂×C₂₃	1	4	yes	complemented
393	#3170	C₂×C₂₃	1	2	yes	complemented
394	#3167	C₂×C₂₃	1	2	yes	complemented
395	#3108	C₂×C₂₃	1	4	yes	complemented
396	#3107	C₂×C₂₃	1	4	yes	complemented
397	C₂×#431	C₂×C₂₃	1	1	yes	characteristic, complemented
398	C₂²×C₂₃	—	2	1	no	—
399	C₂²×C₂₃	—	2	1	no	—
400	C₂²×C₂₃	—	2	1	no	—
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	—	4	4	no	—
406	C₂²×C₂₃	—	4	2	no	—
407	C₂²×C₂₃	—	4	2	no	—
408	C₂²×C₂₃	—	4	2	no	—
409	C₂²×C₂₃	C₂×#135	1	2	yes	—
410	C₂²×C₂₃	C₂×#137	1	2	yes	—
411	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
412	C₄×C₂₃	—	2	1	no	—
413	C₄×C₂₃	—	2	1	no	—
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	—	4	2	no	—
420	C₄×C₂₃	—	4	4	no	—
421	C₄×C₂₃	—	4	2	no	—
422	C₄×C₂₃	—	4	4	no	—
423	C₄×C₂₃	—	4	2	no	—
424	C₄×C₂₃	C₂×#135	1	2	yes	—
425	C₄×C₂₃	C₂×#135	1	2	yes	—
426	C₄×C₂₃	C₂×#137	1	2	yes	—
427	C₄×C₂₃	C₂×#137	1	2	yes	—
428	C₄×C₂₃	#585	1	2	yes	—
429	#533	—	2	1	no	—
430	#533	—	2	1	no	—
431	#533	—	2	1	no	—
432	#533	—	2	1	no	—
433	#533	C₂²×C₂₃	1	2	yes	—
434	#533	C₂²×C₂₃	1	2	yes	—
435	#533	C₂²×C₂₃	1	1	yes	characteristic
436	#533	C₂²×C₂₃	1	2	yes	—
437	#533	C₂²×C₂₃	1	2	yes	—
438	#533	C₂²×C₂₃	1	1	yes	characteristic
439	#533	C₂²×C₂₃	1	1	yes	characteristic
440	#532	C₂²×C₂₃	1	1	yes	characteristic
441	#532	C₂²×C₂₃	1	1	yes	characteristic
442	#532	C₂²×C₂₃	1	1	yes	characteristic
443	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
444	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
445	#529	—	2	1	no	—
446	#529	—	2	1	no	—
447	#529	—	2	1	no	—
448	#529	—	2	1	no	—
449	#529	C₂²×C₂₃	1	2	yes	—
450	#529	C₂²×C₂₃	1	2	yes	—
451	C₂×#125	—	2	1	no	—
452	#525	—	2	1	no	—
453	#525	—	2	1	no	—
454	#525	C₂²×C₂₃	1	2	yes	—
455	C₂×C₂²⋊Q₈	—	2	1	no	—
456	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
457	C₄×#41	—	2	1	no	—
458	C₄×#41	—	2	1	no	—
459	C₄×#41	C₂²×C₂₃	1	2	yes	—
460	C₂×C₄×Q₈	—	2	1	no	—
461	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
462	C₂×#117	—	2	1	no	—
463	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
464	#500	C₂²×C₂₃	1	2	yes	complemented
465	#498	C₂²×C₂₃	1	2	yes	complemented
466	#494	C₂²×C₂₃	1	2	yes	complemented
467	#492	C₂²×C₂₃	1	2	yes	complemented
468	#487	C₂²×C₂₃	1	2	yes	complemented
469	#487	C₂²×C₂₃	1	2	yes	complemented
470	#487	C₂²×C₂₃	1	2	yes	complemented
471	#486	C₂²×C₂₃	1	2	yes	complemented
472	#485	C₂²×C₂₃	1	8	yes	—
473	#483	C₂²×C₂₃	1	4	yes	—
474	#480	C₂²×C₂₃	1	4	yes	—
475	#479	C₂²×C₂₃	1	8	yes	complemented
476	#475	C₂²×C₂₃	1	4	yes	complemented
477	#474	C₂²×C₂₃	1	4	yes	complemented
478	#467	C₂²×C₂₃	1	8	yes	—
479	#465	C₂²×C₂₃	1	8	yes	—
480	#464	C₂²×C₂₃	1	8	yes	complemented
481	#462	C₂²×C₂₃	1	4	yes	complemented
482	#461	C₂²×C₂₃	1	4	yes	complemented
483	#452	C₂²×C₂₃	1	8	yes	—
484	#451	C₂²×C₂₃	1	4	yes	—
485	#448	C₂²×C₂₃	1	4	yes	—
486	C₄×Q₁₆	C₂²×C₂₃	1	8	yes	complemented
487	C₄×SD₁₆	C₂²×C₂₃	1	8	yes	complemented
488	#431	C₂²×C₂₃	1	2	yes	—
489	#431	C₂²×C₂₃	1	2	yes	—
490	#431	C₂²×C₂₃	1	1	yes	characteristic
491	#431	C₂²×C₂₃	1	1	yes	characteristic
492	#431	C₂²×C₂₃	1	2	yes	—
493	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
494	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
495	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
496	C₂×C₂₃	—	2	2	no	—
497	C₂×C₂₃	—	2	2	no	—
498	C₂×C₂₃	—	4	1	no	—
499	C₂×C₂₃	—	8	2	no	—
500	C₂×C₂₃	#3449	1	1	yes	characteristic
501	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
502	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
503	C₂×#41	—	2	1	no	—
504	C₂×#41	—	2	1	no	—
505	C₂×#41	C₂³×C₂₃	1	2	yes	—
506	C₂²×Q₈	—	2	1	no	—
507	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
508	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
509	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
511	C₂×Q₁₆	C₂³×C₂₃	1	8	yes	—
512	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
513	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
514	C₄⋊Q₈	—	2	1	no	—
515	C₄⋊Q₈	—	2	1	no	—
516	C₄⋊Q₈	—	2	1	no	—
517	C₄⋊Q₈	—	2	1	no	—
518	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
519	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
520	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
521	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
522	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
523	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
524	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
525	#127	C₂³×C₂₃	1	1	yes	characteristic
526	#126	—	2	2	no	—
527	#126	—	2	2	no	—
528	#125	—	2	2	no	—
529	#125	—	2	2	no	—
530	#125	—	2	2	no	—
531	#125	—	2	2	no	—
532	#125	—	2	1	no	—
533	#125	—	2	1	no	—
534	#125	C₂³×C₂₃	1	2	yes	—
535	#124	—	2	1	no	—
536	#124	—	2	1	no	—
537	#124	C₂³×C₂₃	1	2	yes	—
538	#123	—	2	2	no	—
539	#123	—	2	2	no	—
540	#123	—	2	2	no	—
541	C₂²⋊Q₈	—	2	2	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	2	2	no	—
545	C₂²⋊Q₈	—	2	2	no	—
546	C₂²⋊Q₈	—	2	2	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	C₂³×C₂₃	1	4	yes	—
552	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
553	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
554	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
555	#121	—	2	1	no	—
556	#121	—	2	1	no	—
557	#121	—	2	1	no	—
558	#121	—	2	1	no	—
559	#121	C₂³×C₂₃	1	2	yes	—
560	#121	C₂³×C₂₃	1	2	yes	—
561	#120	—	2	2	no	—
562	C₄×Q₈	—	2	2	no	—
563	C₄×Q₈	—	2	2	no	—
564	C₄×Q₈	—	2	2	no	—
565	C₄×Q₈	—	2	2	no	—
566	C₄×Q₈	—	2	2	no	—
567	C₄×Q₈	—	2	2	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	C₂³×C₂₃	1	4	yes	—
573	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
574	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
575	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	2	no	—
581	C₄×D₄	—	2	2	no	—
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	C₂³×C₂₃	1	2	yes	—
587	C₄×D₄	C₂³×C₂₃	1	2	yes	—
588	#117	—	2	2	no	—
589	#117	—	2	2	no	—
590	#117	—	2	2	no	—
591	#117	—	2	2	no	—
592	#117	—	2	1	no	—
593	#117	—	2	1	no	—
594	#117	—	2	2	no	—
595	#117	—	2	2	no	—
596	#117	—	2	2	no	—
597	#117	C₂³×C₂₃	1	2	yes	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	—	2	2	no	—
602	C₂×C₄⋊C₄	—	2	2	no	—
603	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
604	C₂×C₂²⋊C₄	—	2	2	no	—
605	C₂×C₄²	—	2	2	no	—
606	C₂×C₄²	—	2	2	no	—
607	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
608	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
609	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
610	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
611	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
612	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
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	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
619	#107	C₂³×C₂₃	1	8	yes	—
620	#106	C₂³×C₂₃	1	8	yes	—
621	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
622	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
623	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
624	#103	C₂³×C₂₃	1	8	yes	—
625	#103	C₂³×C₂₃	1	8	yes	—
626	#103	C₂³×C₂₃	1	8	yes	—
627	#102	C₂³×C₂₃	1	8	yes	—
628	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
629	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
630	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
631	C₄×C₈	C₂³×C₂₃	1	4	yes	—
632	C₄×C₈	C₂³×C₂₃	1	2	yes	—
633	C₄×C₈	C₂³×C₂₃	1	2	yes	—
634	C₂₃	#60947	1	1	yes	characteristic, direct product factor, Sylow
635	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
636	#41	—	4	4	no	—
637	#41	—	4	4	no	—
638	#41	—	4	4	no	—
639	C₂×Q₈	—	2	1	no	—
640	C₂×Q₈	—	2	1	no	—
641	C₂×Q₈	—	2	2	no	—
642	C₂×Q₈	—	2	2	no	—
643	C₂×Q₈	—	2	2	no	—
644	C₂×Q₈	—	4	4	no	—
645	C₂×Q₈	—	4	4	no	—
646	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
647	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
663	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
664	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
665	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
669	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
670	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
671	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
672	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
673	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
676	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
679	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
680	Q₁₆	—	4	8	no	—
681	SD₁₆	—	4	8	no	—
682	C₂×C₈	—	4	4	no	—
683	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
684	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	2	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	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
707	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
708	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₄²	—	2	2	no	—
721	C₄²	—	2	2	no	—
722	C₄²	—	2	4	no	—
723	C₄²	—	2	4	no	—
724	C₄²	—	2	2	no	—
725	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
726	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
727	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
728	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
729	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
730	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
731	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
732	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
733	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
734	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
735	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
736	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
737	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
738	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
739	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
740	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	4	1	no	—
745	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
746	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
747	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
748	Q₈	—	2	8	no	—
749	Q₈	—	2	4	no	—
750	Q₈	—	4	4	no	—
751	Q₈	—	4	4	no	—
752	Q₈	—	4	4	no	—
753	Q₈	—	4	2	no	—
754	Q₈	—	4	2	no	—
755	D₄	—	2	4	no	—
756	D₄	—	4	4	no	—
757	D₄	—	4	4	no	—
758	D₄	—	4	4	no	—
759	D₄	—	4	2	no	—
760	D₄	—	4	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	4	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	4	no	—
783	C₂×C₄	—	4	4	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	4	4	no	—
786	C₂×C₄	—	4	4	no	—
787	C₂×C₄	C₂₃×#135	1	4	yes	—
788	C₂×C₄	C₂₃×#137	1	4	yes	—
789	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
790	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
793	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
794	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
795	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
796	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
797	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
799	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
800	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
801	C₈	—	2	4	no	—
802	C₈	—	2	4	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	2	1	no	—
808	C₂²	—	2	1	no	—
809	C₂²	—	2	1	no	—
810	C₂²	—	4	4	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	C₂×C₂₃×#135	1	2	yes	—
815	C₂²	C₂×C₂₃×#137	1	2	yes	—
816	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
817	C₄	—	2	1	no	—
818	C₄	—	2	1	no	—
819	C₄	—	2	1	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	1	no	—
822	C₄	—	2	1	no	—
823	C₄	—	2	1	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	4	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	4	no	—
828	C₄	—	4	2	no	—
829	C₄	C₂×C₂₃×#135	1	2	yes	—
830	C₄	C₂×C₂₃×#135	1	2	yes	—
831	C₄	C₂×C₂₃×#137	1	2	yes	—
832	C₄	C₂×C₂₃×#137	1	2	yes	—
833	C₄	C₂₃×#585	1	2	yes	—
834	C₂	—	2	2	no	—
835	C₂	—	2	2	no	—
836	C₂	—	4	1	no	—
837	C₂	—	8	2	no	—
838	C₂	C₂₃×#3449	1	1	yes	characteristic
839	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic
840	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂³×D₄
prime radical	C₂₃×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#533	C₂	semidirect
3. C₂₃×#3248	C₂	semidirect
4. C₂₃×#3231	C₂	semidirect
5. C₂₃×#3229	C₂	semidirect
6. C₂₃×#3226	C₂	semidirect
7. C₂₃×#3210	C₂	semidirect
8. C₂₃×#3209	C₂	semidirect
9. C₂₃×#3206	C₂	semidirect
10. C₂₃×#3190	C₂	semidirect
11. C₂₃×#3170	C₂	semidirect
12. C₂₃×#3167	C₂	semidirect
13. C₂₃×#3108	C₂	semidirect
14. C₂₃×#3107	C₂	semidirect
15. C₂×C₂₃×#431	C₂	semidirect
51. C₂₃×#500	C₂²	semidirect
52. C₂₃×#498	C₂²	semidirect
53. C₂₃×#494	C₂²	semidirect
54. C₂₃×#492	C₂²	semidirect
55. C₂₃×#487	C₂²	semidirect
56. C₂₃×#487	C₂²	semidirect
57. C₂₃×#487	C₂²	semidirect
58. C₂₃×#486	C₂²	semidirect
62. C₂₃×#479	C₂²	semidirect
63. C₂₃×#475	C₂²	semidirect
64. C₂₃×#474	C₂²	semidirect
67. C₂₃×#464	C₂²	semidirect
68. C₂₃×#462	C₂²	semidirect
69. C₂₃×#461	C₂²	semidirect
73. C₄×Q₁₆×C₂₃	C₂²	semidirect
74. C₄×SD₁₆×C₂₃	C₂²	semidirect
320. #60947	C₂₃	direct (N × H)
384. C₂×#533	C₂×C₂₃	semidirect
385. #3248	C₂×C₂₃	semidirect
386. #3231	C₂×C₂₃	semidirect
387. #3229	C₂×C₂₃	semidirect
388. #3226	C₂×C₂₃	semidirect
389. #3210	C₂×C₂₃	semidirect
390. #3209	C₂×C₂₃	semidirect
391. #3206	C₂×C₂₃	semidirect
392. #3190	C₂×C₂₃	semidirect
393. #3170	C₂×C₂₃	semidirect
394. #3167	C₂×C₂₃	semidirect
395. #3108	C₂×C₂₃	semidirect
396. #3107	C₂×C₂₃	semidirect
397. C₂×#431	C₂×C₂₃	semidirect
464. #500	C₂²×C₂₃	semidirect
465. #498	C₂²×C₂₃	semidirect
466. #494	C₂²×C₂₃	semidirect
467. #492	C₂²×C₂₃	semidirect
468. #487	C₂²×C₂₃	semidirect
469. #487	C₂²×C₂₃	semidirect
470. #487	C₂²×C₂₃	semidirect
471. #486	C₂²×C₂₃	semidirect
475. #479	C₂²×C₂₃	semidirect
476. #475	C₂²×C₂₃	semidirect
477. #474	C₂²×C₂₃	semidirect
480. #464	C₂²×C₂₃	semidirect
481. #462	C₂²×C₂₃	semidirect
482. #461	C₂²×C₂₃	semidirect
486. C₄×Q₁₆	C₂²×C₂₃	semidirect
487. C₄×SD₁₆	C₂²×C₂₃	semidirect
634. C₂₃	#60947	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3444	2
C₂×C₂₃×#533	2
C₂₃×#3248	2
C₂₃×#3231	2
C₂₃×#3229	2
C₂₃×#3226	2
C₂₃×#3210	2
C₂₃×#3209	2
C₂₃×#3206	2
C₂₃×#3190	2
C₂₃×#3170	2
C₂₃×#3167	2
C₂₃×#3108	2
C₂₃×#3107	2
C₂×C₂₃×#431	2
#60947	23

Subgroups — C23×#60947 #19208573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60947 #19208573