Subgroups — C₂₃×#60701 #19208327

Order 5888.

1976 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×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3185	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3182	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3181	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3172	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3170	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3167	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3056	C₂	1	4	yes	maximal, complemented
14	C₄×C₂₃×#137	C₂	1	4	yes	maximal, complemented
15	C₂×C₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#137	C₂²	1	4	yes	—
17	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
18	C₂₃×#533	—	2	1	no	—
19	C₂₃×#533	—	2	1	no	—
20	C₂₃×#533	—	2	1	no	—
21	C₂₃×#533	—	2	1	no	—
22	C₂₃×#533	C₂²	1	2	yes	—
23	C₂₃×#533	C₂²	1	1	yes	characteristic
24	C₂₃×#533	C₂²	1	2	yes	—
25	C₂₃×#533	C₂²	1	2	yes	—
26	C₂₃×#533	C₂²	1	2	yes	—
27	C₂₃×#533	C₂²	1	1	yes	characteristic
28	C₂₃×#533	C₂²	1	1	yes	characteristic
29	C₂₃×#532	C₂²	1	1	yes	characteristic
30	C₂₃×#532	C₂²	1	1	yes	characteristic
31	C₂₃×#532	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂₃×#529	—	2	1	no	—
35	C₂₃×#529	—	2	1	no	—
36	C₂₃×#529	—	2	1	no	—
37	C₂₃×#529	—	2	1	no	—
38	C₂₃×#529	C₂²	1	2	yes	—
39	C₂₃×#529	C₂²	1	2	yes	—
40	C₂×C₂₃×#125	—	2	1	no	—
41	C₂₃×#525	—	2	1	no	—
42	C₂₃×#525	—	2	1	no	—
43	C₂₃×#525	C₂²	1	2	yes	—
44	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
45	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
46	C₄×#41×C₂₃	—	2	1	no	—
47	C₄×#41×C₂₃	—	2	1	no	—
48	C₄×#41×C₂₃	C₂²	1	2	yes	—
49	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
50	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
51	C₂×C₂₃×#117	—	2	1	no	—
52	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
53	C₂₃×#501	C₂²	1	4	yes	complemented
54	C₂₃×#500	C₂²	1	2	yes	complemented
55	C₂₃×#498	C₂²	1	2	yes	complemented
56	C₂₃×#497	C₂²	1	4	yes	complemented
57	C₂₃×#494	C₂²	1	2	yes	complemented
58	C₂₃×#492	C₂²	1	2	yes	complemented
59	C₂₃×#491	C₂²	1	4	yes	complemented
60	C₂₃×#489	C₂²	1	4	yes	complemented
61	C₂₃×#487	C₂²	1	2	yes	complemented
62	C₂₃×#487	C₂²	1	2	yes	complemented
63	C₂₃×#487	C₂²	1	2	yes	complemented
64	C₂₃×#486	C₂²	1	2	yes	complemented
65	C₂₃×#470	C₂²	1	8	yes	—
66	C₂₃×#468	C₂²	1	8	yes	—
67	C₂₃×#467	C₂²	1	8	yes	—
68	C₂₃×#465	C₂²	1	8	yes	—
69	C₂₃×#441	C₂²	1	8	yes	complemented
70	C₂₃×#440	C₂²	1	8	yes	complemented
71	C₄×Q₁₆×C₂₃	C₂²	1	8	yes	complemented
72	C₄×SD₁₆×C₂₃	C₂²	1	8	yes	complemented
73	C₂₃×#428	C₂²	1	4	yes	—
74	C₂₃×#419	C₂²	1	4	yes	—
75	C₂₃×#417	C₂²	1	4	yes	—
76	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
77	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
78	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
79	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
80	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
81	C₂×C₂₃×#97	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	C₂₃×#137	—	2	16	no	—
92	C₂×Q₁₆×C₂₃	C₂³	1	8	yes	—
93	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
94	C₂×M₁₆×C₂₃	—	2	8	no	—
95	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
96	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
97	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
98	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
99	C₂₃×C₄⋊Q₈	—	2	1	no	—
100	C₂₃×C₄⋊Q₈	—	2	1	no	—
101	C₂₃×C₄⋊Q₈	—	2	1	no	—
102	C₂₃×C₄⋊Q₈	—	2	1	no	—
103	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
104	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
106	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
107	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
108	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
109	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
110	C₂₃×#127	C₂³	1	1	yes	characteristic
111	C₂₃×#126	—	2	2	no	—
112	C₂₃×#126	—	2	2	no	—
113	C₂₃×#125	—	2	2	no	—
114	C₂₃×#125	—	2	2	no	—
115	C₂₃×#125	—	2	2	no	—
116	C₂₃×#125	—	2	2	no	—
117	C₂₃×#125	—	2	1	no	—
118	C₂₃×#125	—	2	1	no	—
119	C₂₃×#125	C₂³	1	2	yes	—
120	C₂₃×#124	—	2	1	no	—
121	C₂₃×#124	—	2	1	no	—
122	C₂₃×#124	C₂³	1	2	yes	—
123	C₂₃×#123	—	2	2	no	—
124	C₂₃×#123	—	2	2	no	—
125	C₂₃×#123	—	2	2	no	—
126	C₂₃×C₂²⋊Q₈	—	2	2	no	—
127	C₂₃×C₂²⋊Q₈	—	2	2	no	—
128	C₂₃×C₂²⋊Q₈	—	2	2	no	—
129	C₂₃×C₂²⋊Q₈	—	2	2	no	—
130	C₂₃×C₂²⋊Q₈	—	2	2	no	—
131	C₂₃×C₂²⋊Q₈	—	2	2	no	—
132	C₂₃×C₂²⋊Q₈	—	2	1	no	—
133	C₂₃×C₂²⋊Q₈	—	2	1	no	—
134	C₂₃×C₂²⋊Q₈	—	2	1	no	—
135	C₂₃×C₂²⋊Q₈	—	2	1	no	—
136	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
137	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
138	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
140	C₂₃×#121	—	2	1	no	—
141	C₂₃×#121	—	2	1	no	—
142	C₂₃×#121	—	2	1	no	—
143	C₂₃×#121	—	2	1	no	—
144	C₂₃×#121	C₂³	1	2	yes	—
145	C₂₃×#121	C₂³	1	2	yes	—
146	C₂₃×#120	—	2	2	no	—
147	C₄×Q₈×C₂₃	—	2	2	no	—
148	C₄×Q₈×C₂₃	—	2	2	no	—
149	C₄×Q₈×C₂₃	—	2	2	no	—
150	C₄×Q₈×C₂₃	—	2	2	no	—
151	C₄×Q₈×C₂₃	—	2	2	no	—
152	C₄×Q₈×C₂₃	—	2	2	no	—
153	C₄×Q₈×C₂₃	—	2	1	no	—
154	C₄×Q₈×C₂₃	—	2	1	no	—
155	C₄×Q₈×C₂₃	—	2	1	no	—
156	C₄×Q₈×C₂₃	—	2	1	no	—
157	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
158	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
160	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
161	C₄×D₄×C₂₃	—	2	2	no	—
162	C₄×D₄×C₂₃	—	2	2	no	—
163	C₄×D₄×C₂₃	—	2	2	no	—
164	C₄×D₄×C₂₃	—	2	2	no	—
165	C₄×D₄×C₂₃	—	2	2	no	—
166	C₄×D₄×C₂₃	—	2	2	no	—
167	C₄×D₄×C₂₃	—	2	1	no	—
168	C₄×D₄×C₂₃	—	2	1	no	—
169	C₄×D₄×C₂₃	—	2	1	no	—
170	C₄×D₄×C₂₃	—	2	1	no	—
171	C₄×D₄×C₂₃	C₂³	1	2	yes	—
172	C₄×D₄×C₂₃	C₂³	1	2	yes	—
173	C₂₃×#117	—	2	2	no	—
174	C₂₃×#117	—	2	2	no	—
175	C₂₃×#117	—	2	2	no	—
176	C₂₃×#117	—	2	2	no	—
177	C₂₃×#117	—	2	1	no	—
178	C₂₃×#117	—	2	1	no	—
179	C₂₃×#117	—	2	2	no	—
180	C₂₃×#117	—	2	2	no	—
181	C₂₃×#117	—	2	2	no	—
182	C₂₃×#117	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
184	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
185	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
186	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
187	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
188	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
190	C₂×C₄²×C₂₃	—	2	2	no	—
191	C₂×C₄²×C₂₃	—	2	2	no	—
192	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
194	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
195	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
196	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
197	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
198	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
204	C₂₃×#107	C₂³	1	8	yes	—
205	C₂₃×#106	C₂³	1	8	yes	—
206	C₂₃×#103	C₂³	1	8	yes	—
207	C₂₃×#103	C₂³	1	8	yes	—
208	C₂₃×#103	C₂³	1	8	yes	—
209	C₂₃×#102	C₂³	1	8	yes	—
210	C₂₃×#97	C₂³	1	4	yes	—
211	C₂₃×#97	C₂³	1	2	yes	—
212	C₂₃×#97	C₂³	1	2	yes	—
213	C₄×C₈×C₂₃	C₂³	1	4	yes	—
214	C₄×C₈×C₂₃	C₂³	1	2	yes	—
215	C₄×C₈×C₂₃	C₂³	1	2	yes	—
216	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
217	#41×C₂₃	—	2	8	no	—
218	#41×C₂₃	—	4	4	no	—
219	#41×C₂₃	—	4	4	no	—
220	C₂×Q₈×C₂₃	—	2	1	no	—
221	C₂×Q₈×C₂₃	—	2	1	no	—
222	C₂×Q₈×C₂₃	—	2	2	no	—
223	C₂×Q₈×C₂₃	—	2	2	no	—
224	C₂×Q₈×C₂₃	—	2	2	no	—
225	C₂×Q₈×C₂₃	—	2	8	no	—
226	C₂×Q₈×C₂₃	—	4	4	no	—
227	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
228	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
229	C₂×D₄×C₂₃	—	2	2	no	—
230	C₂×D₄×C₂₃	—	2	2	no	—
231	C₂×D₄×C₂₃	—	2	2	no	—
232	C₂×D₄×C₂₃	—	2	1	no	—
233	C₂×D₄×C₂₃	—	2	1	no	—
234	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₂₃	—	2	4	no	—
236	C₂²×C₄×C₂₃	—	2	4	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	—	2	2	no	—
241	C₂²×C₄×C₂₃	—	2	2	no	—
242	C₂²×C₄×C₂₃	—	4	2	no	—
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	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
261	Q₁₆×C₂₃	—	2	16	no	—
262	SD₁₆×C₂₃	—	2	16	no	—
263	M₁₆×C₂₃	—	2	4	no	—
264	M₁₆×C₂₃	—	2	8	no	—
265	M₁₆×C₂₃	#41	1	8	yes	complemented
266	C₂×C₈×C₂₃	—	2	8	no	—
267	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
268	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
269	C₄⋊C₄×C₂₃	—	2	2	no	—
270	C₄⋊C₄×C₂₃	—	2	2	no	—
271	C₄⋊C₄×C₂₃	—	2	2	no	—
272	C₄⋊C₄×C₂₃	—	2	2	no	—
273	C₄⋊C₄×C₂₃	—	2	2	no	—
274	C₄⋊C₄×C₂₃	—	2	2	no	—
275	C₄⋊C₄×C₂₃	—	2	4	no	—
276	C₄⋊C₄×C₂₃	—	2	4	no	—
277	C₄⋊C₄×C₂₃	—	2	4	no	—
278	C₄⋊C₄×C₂₃	—	2	4	no	—
279	C₄⋊C₄×C₂₃	—	2	2	no	—
280	C₄⋊C₄×C₂₃	—	2	1	no	—
281	C₄⋊C₄×C₂₃	—	2	1	no	—
282	C₄⋊C₄×C₂₃	—	2	1	no	—
283	C₄⋊C₄×C₂₃	—	2	1	no	—
284	C₄⋊C₄×C₂₃	—	2	2	no	—
285	C₄⋊C₄×C₂₃	—	2	2	no	—
286	C₄⋊C₄×C₂₃	—	2	2	no	—
287	C₄⋊C₄×C₂₃	—	2	2	no	—
288	C₄⋊C₄×C₂₃	—	2	2	no	—
289	C₄⋊C₄×C₂₃	—	2	2	no	—
290	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
291	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
292	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
293	C₂²⋊C₄×C₂₃	—	2	4	no	—
294	C₂²⋊C₄×C₂₃	—	2	4	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	C₂²⋊C₄×C₂₃	—	2	2	no	—
300	C₂²⋊C₄×C₂₃	—	2	2	no	—
301	C₂²⋊C₄×C₂₃	—	2	2	no	—
302	C₂²⋊C₄×C₂₃	—	2	2	no	—
303	C₂²⋊C₄×C₂₃	—	2	2	no	—
304	C₄²×C₂₃	—	2	2	no	—
305	C₄²×C₂₃	—	2	4	no	—
306	C₄²×C₂₃	—	2	2	no	—
307	C₄²×C₂₃	—	2	2	no	—
308	C₄²×C₂₃	—	2	4	no	—
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	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	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
323	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
324	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
325	#60701	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
326	C₂³×C₂₃	—	2	2	no	—
327	C₂³×C₂₃	—	2	2	no	—
328	C₂³×C₂₃	—	2	2	no	—
329	C₂³×C₂₃	—	4	1	no	—
330	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
331	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
332	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
333	Q₈×C₂₃	—	2	8	no	—
334	Q₈×C₂₃	—	2	4	no	—
335	Q₈×C₂₃	—	4	4	no	—
336	Q₈×C₂₃	—	4	4	no	—
337	Q₈×C₂₃	—	4	2	no	—
338	Q₈×C₂₃	—	4	4	no	—
339	Q₈×C₂₃	—	4	2	no	—
340	D₄×C₂₃	—	2	4	no	—
341	D₄×C₂₃	—	4	4	no	—
342	D₄×C₂₃	—	4	4	no	—
343	D₄×C₂₃	—	4	4	no	—
344	D₄×C₂₃	—	4	2	no	—
345	D₄×C₂₃	—	4	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	2	no	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	2	2	no	—
360	C₂×C₄×C₂₃	—	2	2	no	—
361	C₂×C₄×C₂₃	—	2	2	no	—
362	C₂×C₄×C₂₃	—	2	4	no	—
363	C₂×C₄×C₂₃	—	2	4	no	—
364	C₂×C₄×C₂₃	—	4	1	no	—
365	C₂×C₄×C₂₃	—	4	1	no	—
366	C₂×C₄×C₂₃	—	4	1	no	—
367	C₂×C₄×C₂₃	—	4	4	no	—
368	C₂×C₄×C₂₃	—	4	4	no	—
369	C₂×C₄×C₂₃	—	4	4	no	—
370	C₂×C₄×C₂₃	—	4	4	no	—
371	C₂×C₄×C₂₃	—	4	4	no	—
372	C₂×C₄×C₂₃	#137	1	4	yes	complemented
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	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
385	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
386	C₈×C₂₃	—	2	4	no	—
387	C₈×C₂₃	C₂×#41	1	8	yes	—
388	#3444	C₂×C₂₃	1	1	yes	characteristic
389	C₂×#533	C₂×C₂₃	1	1	yes	characteristic, complemented
390	#3185	C₂×C₂₃	1	2	yes	complemented
391	#3182	C₂×C₂₃	1	2	yes	complemented
392	#3181	C₂×C₂₃	1	4	yes	complemented
393	#3172	C₂×C₂₃	1	4	yes	complemented
394	#3170	C₂×C₂₃	1	2	yes	complemented
395	#3167	C₂×C₂₃	1	2	yes	complemented
396	#3165	C₂×C₂₃	1	1	yes	characteristic, complemented
397	#3152	C₂×C₂₃	1	1	yes	characteristic, complemented
398	#3141	C₂×C₂₃	1	1	yes	characteristic, complemented
399	#3139	C₂×C₂₃	1	1	yes	characteristic, complemented
400	#3056	C₂×C₂₃	1	4	yes	complemented
401	C₄×#137	C₂×C₂₃	1	4	yes	complemented
402	C₂×C₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
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	4	no	—
411	C₂²×C₂₃	—	4	2	no	—
412	C₂²×C₂₃	—	4	2	no	—
413	C₂²×C₂₃	—	4	2	no	—
414	C₂²×C₂₃	#532	1	2	yes	—
415	C₂²×C₂₃	C₂×#137	1	2	yes	—
416	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
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	2	no	—
425	C₄×C₂₃	—	4	4	no	—
426	C₄×C₂₃	—	4	2	no	—
427	C₄×C₂₃	—	4	2	no	—
428	C₄×C₂₃	—	4	4	no	—
429	C₄×C₂₃	#532	1	2	yes	—
430	C₄×C₂₃	C₂×#137	1	2	yes	—
431	C₄×C₂₃	C₂×#137	1	2	yes	—
432	C₄×C₂₃	#575	1	2	yes	—
433	C₄×C₂₃	C₂²×#41	1	2	yes	—
434	C₂×#137	C₂²×C₂₃	1	4	yes	—
435	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
436	#533	—	2	1	no	—
437	#533	—	2	1	no	—
438	#533	—	2	1	no	—
439	#533	—	2	1	no	—
440	#533	C₂²×C₂₃	1	2	yes	—
441	#533	C₂²×C₂₃	1	1	yes	characteristic
442	#533	C₂²×C₂₃	1	2	yes	—
443	#533	C₂²×C₂₃	1	2	yes	—
444	#533	C₂²×C₂₃	1	2	yes	—
445	#533	C₂²×C₂₃	1	1	yes	characteristic
446	#533	C₂²×C₂₃	1	1	yes	characteristic
447	#532	C₂²×C₂₃	1	1	yes	characteristic
448	#532	C₂²×C₂₃	1	1	yes	characteristic
449	#532	C₂²×C₂₃	1	1	yes	characteristic
450	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
451	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
452	#529	—	2	1	no	—
453	#529	—	2	1	no	—
454	#529	—	2	1	no	—
455	#529	—	2	1	no	—
456	#529	C₂²×C₂₃	1	2	yes	—
457	#529	C₂²×C₂₃	1	2	yes	—
458	C₂×#125	—	2	1	no	—
459	#525	—	2	1	no	—
460	#525	—	2	1	no	—
461	#525	C₂²×C₂₃	1	2	yes	—
462	C₂×C₂²⋊Q₈	—	2	1	no	—
463	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
464	C₄×#41	—	2	1	no	—
465	C₄×#41	—	2	1	no	—
466	C₄×#41	C₂²×C₂₃	1	2	yes	—
467	C₂×C₄×Q₈	—	2	1	no	—
468	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
469	C₂×#117	—	2	1	no	—
470	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
471	#501	C₂²×C₂₃	1	4	yes	complemented
472	#500	C₂²×C₂₃	1	2	yes	complemented
473	#498	C₂²×C₂₃	1	2	yes	complemented
474	#497	C₂²×C₂₃	1	4	yes	complemented
475	#494	C₂²×C₂₃	1	2	yes	complemented
476	#492	C₂²×C₂₃	1	2	yes	complemented
477	#491	C₂²×C₂₃	1	4	yes	complemented
478	#489	C₂²×C₂₃	1	4	yes	complemented
479	#487	C₂²×C₂₃	1	2	yes	complemented
480	#487	C₂²×C₂₃	1	2	yes	complemented
481	#487	C₂²×C₂₃	1	2	yes	complemented
482	#486	C₂²×C₂₃	1	2	yes	complemented
483	#470	C₂²×C₂₃	1	8	yes	—
484	#468	C₂²×C₂₃	1	8	yes	—
485	#467	C₂²×C₂₃	1	8	yes	—
486	#465	C₂²×C₂₃	1	8	yes	—
487	#441	C₂²×C₂₃	1	8	yes	complemented
488	#440	C₂²×C₂₃	1	8	yes	complemented
489	C₄×Q₁₆	C₂²×C₂₃	1	8	yes	complemented
490	C₄×SD₁₆	C₂²×C₂₃	1	8	yes	complemented
491	#428	C₂²×C₂₃	1	4	yes	—
492	#419	C₂²×C₂₃	1	4	yes	—
493	#417	C₂²×C₂₃	1	4	yes	—
494	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
495	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
496	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
497	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
498	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
499	C₂×#97	C₂²×C₂₃	1	2	yes	—
500	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
501	C₂×C₂₃	—	2	2	no	—
502	C₂×C₂₃	—	2	2	no	—
503	C₂×C₂₃	—	4	1	no	—
504	C₂×C₂₃	—	8	2	no	—
505	C₂×C₂₃	C₂×#532	1	1	yes	characteristic
506	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
507	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
508	C₂×#41	—	2	1	no	—
509	C₂×#41	—	2	1	no	—
510	C₂×#41	C₂³×C₂₃	1	2	yes	—
511	C₂²×Q₈	—	2	1	no	—
512	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
513	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
514	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
516	#137	—	2	16	no	—
517	C₂×Q₁₆	C₂³×C₂₃	1	8	yes	—
518	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
519	C₂×M₁₆	—	2	8	no	—
520	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
521	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
522	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
523	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
524	C₄⋊Q₈	—	2	1	no	—
525	C₄⋊Q₈	—	2	1	no	—
526	C₄⋊Q₈	—	2	1	no	—
527	C₄⋊Q₈	—	2	1	no	—
528	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
529	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
530	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
531	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
532	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
533	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
534	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
535	#127	C₂³×C₂₃	1	1	yes	characteristic
536	#126	—	2	2	no	—
537	#126	—	2	2	no	—
538	#125	—	2	2	no	—
539	#125	—	2	2	no	—
540	#125	—	2	2	no	—
541	#125	—	2	2	no	—
542	#125	—	2	1	no	—
543	#125	—	2	1	no	—
544	#125	C₂³×C₂₃	1	2	yes	—
545	#124	—	2	1	no	—
546	#124	—	2	1	no	—
547	#124	C₂³×C₂₃	1	2	yes	—
548	#123	—	2	2	no	—
549	#123	—	2	2	no	—
550	#123	—	2	2	no	—
551	C₂²⋊Q₈	—	2	2	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	—	2	2	no	—
554	C₂²⋊Q₈	—	2	2	no	—
555	C₂²⋊Q₈	—	2	2	no	—
556	C₂²⋊Q₈	—	2	2	no	—
557	C₂²⋊Q₈	—	2	1	no	—
558	C₂²⋊Q₈	—	2	1	no	—
559	C₂²⋊Q₈	—	2	1	no	—
560	C₂²⋊Q₈	—	2	1	no	—
561	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
562	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
563	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
564	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
565	#121	—	2	1	no	—
566	#121	—	2	1	no	—
567	#121	—	2	1	no	—
568	#121	—	2	1	no	—
569	#121	C₂³×C₂₃	1	2	yes	—
570	#121	C₂³×C₂₃	1	2	yes	—
571	#120	—	2	2	no	—
572	C₄×Q₈	—	2	2	no	—
573	C₄×Q₈	—	2	2	no	—
574	C₄×Q₈	—	2	2	no	—
575	C₄×Q₈	—	2	2	no	—
576	C₄×Q₈	—	2	2	no	—
577	C₄×Q₈	—	2	2	no	—
578	C₄×Q₈	—	2	1	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×Q₈	—	2	1	no	—
582	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
583	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
584	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
585	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	—	2	2	no	—
590	C₄×D₄	—	2	2	no	—
591	C₄×D₄	—	2	2	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	C₂³×C₂₃	1	2	yes	—
597	C₄×D₄	C₂³×C₂₃	1	2	yes	—
598	#117	—	2	2	no	—
599	#117	—	2	2	no	—
600	#117	—	2	2	no	—
601	#117	—	2	2	no	—
602	#117	—	2	1	no	—
603	#117	—	2	1	no	—
604	#117	—	2	2	no	—
605	#117	—	2	2	no	—
606	#117	—	2	2	no	—
607	#117	C₂³×C₂₃	1	2	yes	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	2	no	—
612	C₂×C₄⋊C₄	—	2	2	no	—
613	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
614	C₂×C₂²⋊C₄	—	2	2	no	—
615	C₂×C₄²	—	2	2	no	—
616	C₂×C₄²	—	2	2	no	—
617	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
618	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
619	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
620	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
621	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
622	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
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	#107	C₂³×C₂₃	1	8	yes	—
630	#106	C₂³×C₂₃	1	8	yes	—
631	#103	C₂³×C₂₃	1	8	yes	—
632	#103	C₂³×C₂₃	1	8	yes	—
633	#103	C₂³×C₂₃	1	8	yes	—
634	#102	C₂³×C₂₃	1	8	yes	—
635	#97	C₂³×C₂₃	1	4	yes	—
636	#97	C₂³×C₂₃	1	2	yes	—
637	#97	C₂³×C₂₃	1	2	yes	—
638	C₄×C₈	C₂³×C₂₃	1	4	yes	—
639	C₄×C₈	C₂³×C₂₃	1	2	yes	—
640	C₄×C₈	C₂³×C₂₃	1	2	yes	—
641	C₂₃	#60701	1	1	yes	characteristic, direct product factor, Sylow
642	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
643	#41	—	2	8	no	—
644	#41	—	4	4	no	—
645	#41	—	4	4	no	—
646	C₂×Q₈	—	2	1	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	2	2	no	—
649	C₂×Q₈	—	2	2	no	—
650	C₂×Q₈	—	2	2	no	—
651	C₂×Q₈	—	2	8	no	—
652	C₂×Q₈	—	4	4	no	—
653	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
654	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	—	2	1	no	—
660	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	4	2	no	—
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	C₂×D₄×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	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
687	Q₁₆	—	2	16	no	—
688	SD₁₆	—	2	16	no	—
689	M₁₆	—	2	4	no	—
690	M₁₆	—	2	8	no	—
691	M₁₆	#41×C₂₃	1	8	yes	complemented
692	C₂×C₈	—	2	8	no	—
693	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
694	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	2	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	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
717	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
718	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₄²	—	2	2	no	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	4	no	—
733	C₄²	—	2	4	no	—
734	C₄²	—	2	2	no	—
735	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
736	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
737	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
738	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
739	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
740	C₄²	C₂×D₄×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	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
749	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
750	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	4	1	no	—
755	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
756	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
757	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
758	Q₈	—	2	8	no	—
759	Q₈	—	2	4	no	—
760	Q₈	—	4	4	no	—
761	Q₈	—	4	2	no	—
762	Q₈	—	4	4	no	—
763	Q₈	—	4	2	no	—
764	Q₈	—	4	4	no	—
765	D₄	—	2	4	no	—
766	D₄	—	4	4	no	—
767	D₄	—	4	4	no	—
768	D₄	—	4	4	no	—
769	D₄	—	4	2	no	—
770	D₄	—	4	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	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	2	4	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	4	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	—	4	4	no	—
797	C₂×C₄	C₂₃×#137	1	4	yes	complemented
798	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
799	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
800	C₂×C₄	C₂²×D₄×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	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
806	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
808	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
809	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
810	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
811	C₈	—	2	4	no	—
812	C₈	C₂×#41×C₂₃	1	8	yes	—
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	4	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	C₂₃×#532	1	2	yes	—
825	C₂²	C₂×C₂₃×#137	1	2	yes	—
826	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
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	2	no	—
835	C₄	—	4	4	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	4	no	—
839	C₄	C₂₃×#532	1	2	yes	—
840	C₄	C₂×C₂₃×#137	1	2	yes	—
841	C₄	C₂×C₂₃×#137	1	2	yes	—
842	C₄	C₂₃×#575	1	2	yes	—
843	C₄	C₂²×#41×C₂₃	1	2	yes	—
844	C₂	—	2	2	no	—
845	C₂	—	2	2	no	—
846	C₂	—	4	1	no	—
847	C₂	—	8	2	no	—
848	C₂	C₂×C₂₃×#532	1	1	yes	characteristic
849	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic
850	C₂	C₂×C₂₃×#575	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×#3185	C₂	semidirect
4. C₂₃×#3182	C₂	semidirect
5. C₂₃×#3181	C₂	semidirect
6. C₂₃×#3172	C₂	semidirect
7. C₂₃×#3170	C₂	semidirect
8. C₂₃×#3167	C₂	semidirect
9. C₂₃×#3165	C₂	semidirect
10. C₂₃×#3152	C₂	semidirect
11. C₂₃×#3141	C₂	semidirect
12. C₂₃×#3139	C₂	semidirect
13. C₂₃×#3056	C₂	semidirect
14. C₄×C₂₃×#137	C₂	semidirect
15. C₂×C₄×M₁₆×C₂₃	C₂	semidirect
53. C₂₃×#501	C₂²	semidirect
54. C₂₃×#500	C₂²	semidirect
55. C₂₃×#498	C₂²	semidirect
56. C₂₃×#497	C₂²	semidirect
57. C₂₃×#494	C₂²	semidirect
58. C₂₃×#492	C₂²	semidirect
59. C₂₃×#491	C₂²	semidirect
60. C₂₃×#489	C₂²	semidirect
61. C₂₃×#487	C₂²	semidirect
62. C₂₃×#487	C₂²	semidirect
63. C₂₃×#487	C₂²	semidirect
64. C₂₃×#486	C₂²	semidirect
69. C₂₃×#441	C₂²	semidirect
70. C₂₃×#440	C₂²	semidirect
71. C₄×Q₁₆×C₂₃	C₂²	semidirect
72. C₄×SD₁₆×C₂₃	C₂²	semidirect
265. M₁₆×C₂₃	#41	semidirect
325. #60701	C₂₃	direct (N × H)
372. C₂×C₄×C₂₃	#137	semidirect
389. C₂×#533	C₂×C₂₃	semidirect
390. #3185	C₂×C₂₃	semidirect
391. #3182	C₂×C₂₃	semidirect
392. #3181	C₂×C₂₃	semidirect
393. #3172	C₂×C₂₃	semidirect
394. #3170	C₂×C₂₃	semidirect
395. #3167	C₂×C₂₃	semidirect
396. #3165	C₂×C₂₃	semidirect
397. #3152	C₂×C₂₃	semidirect
398. #3141	C₂×C₂₃	semidirect
399. #3139	C₂×C₂₃	semidirect
400. #3056	C₂×C₂₃	semidirect
401. C₄×#137	C₂×C₂₃	semidirect
402. C₂×C₄×M₁₆	C₂×C₂₃	semidirect
471. #501	C₂²×C₂₃	semidirect
472. #500	C₂²×C₂₃	semidirect
473. #498	C₂²×C₂₃	semidirect
474. #497	C₂²×C₂₃	semidirect
475. #494	C₂²×C₂₃	semidirect
476. #492	C₂²×C₂₃	semidirect
477. #491	C₂²×C₂₃	semidirect
478. #489	C₂²×C₂₃	semidirect
479. #487	C₂²×C₂₃	semidirect
480. #487	C₂²×C₂₃	semidirect
481. #487	C₂²×C₂₃	semidirect
482. #486	C₂²×C₂₃	semidirect
487. #441	C₂²×C₂₃	semidirect
488. #440	C₂²×C₂₃	semidirect
489. C₄×Q₁₆	C₂²×C₂₃	semidirect
490. C₄×SD₁₆	C₂²×C₂₃	semidirect
641. C₂₃	#60701	direct (N × H)
691. M₁₆	#41×C₂₃	semidirect
797. C₂×C₄	C₂₃×#137	semidirect

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×#3185	2
C₂₃×#3182	2
C₂₃×#3181	2
C₂₃×#3172	2
C₂₃×#3170	2
C₂₃×#3167	2
C₂₃×#3165	2
C₂₃×#3152	2
C₂₃×#3141	2
C₂₃×#3139	2
C₂₃×#3056	2
C₄×C₂₃×#137	2
C₂×C₄×M₁₆×C₂₃	2
#60701	23

Subgroups — C23×#60701 #19208327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60701 #19208327