Subgroups — C₂₃×#60030 #19207656

Order 5888.

1642 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2722	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2690	C₂	1	2	yes	maximal
3	C₂₃×#2677	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2611	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#2606	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2599	C₂	1	1	yes	maximal, characteristic
7	C₂₃×#2590	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2588	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2550	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2524	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2523	C₂	1	1	yes	maximal, characteristic
12	C₂₃×#2517	C₂	1	1	yes	maximal, characteristic
13	C₂₃×#2478	C₂	1	2	yes	maximal
14	C₂₃×#2462	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2373	C₂	1	2	yes	maximal
16	C₂₃×#2371	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2365	C₂	1	2	yes	maximal, complemented
18	C₄×C₂₃×C₂²⋊Q₈	C₂	1	2	yes	maximal
19	C₂₃×#2296	C₂	1	1	yes	maximal, characteristic
20	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₂₃×#126	C₂²	1	2	yes	—
22	C₂×C₂₃×#125	C₂²	1	2	yes	—
23	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
30	C₂₃×#400	C₂²	1	2	yes	—
31	C₂₃×#400	C₂²	1	2	yes	—
32	C₂₃×#400	C₂²	1	1	yes	characteristic
33	C₂₃×#399	C₂²	1	1	yes	characteristic
34	C₂₃×#398	C₂²	1	2	yes	—
35	C₂₃×#398	C₂²	1	2	yes	—
36	C₂₃×#398	C₂²	1	2	yes	—
37	C₂₃×#398	C₂²	1	2	yes	—
38	C₂₃×#398	C₂²	1	2	yes	—
39	C₂₃×#398	C₂²	1	2	yes	—
40	C₂₃×#398	C₂²	1	1	yes	characteristic
41	C₂₃×#398	C₂²	1	1	yes	characteristic
42	C₂₃×#397	C₂²	1	2	yes	—
43	C₂₃×#397	C₂²	1	2	yes	—
44	C₂₃×#397	C₂²	1	1	yes	characteristic
45	C₂₃×#397	C₂²	1	1	yes	characteristic
46	C₂₃×#395	C₂²	1	2	yes	—
47	C₂₃×#395	C₂²	1	2	yes	—
48	C₂₃×#395	C₂²	1	1	yes	characteristic
49	C₂₃×#393	C₂²	1	1	yes	characteristic
50	C₂₃×#391	C₂²	1	2	yes	—
51	C₂₃×#391	C₂²	1	2	yes	—
52	C₂₃×#391	C₂²	1	2	yes	—
53	C₂₃×#389	C₂²	1	2	yes	—
54	C₂₃×#389	C₂²	1	2	yes	—
55	C₂₃×#389	C₂²	1	2	yes	—
56	C₂₃×#389	C₂²	1	2	yes	—
57	C₂₃×#389	C₂²	1	2	yes	—
58	C₂₃×#389	C₂²	1	2	yes	—
59	C₂₃×#389	C₂²	1	2	yes	—
60	C₂₃×#389	C₂²	1	2	yes	—
61	C₂₃×#388	C₂²	1	2	yes	—
62	C₂₃×#388	C₂²	1	2	yes	—
63	C₂₃×#388	C₂²	1	2	yes	—
64	C₂₃×#387	C₂²	1	2	yes	—
65	C₂₃×#387	C₂²	1	2	yes	—
66	C₂₃×#387	C₂²	1	2	yes	—
67	C₂₃×#387	C₂²	1	2	yes	—
68	C₂₃×#387	C₂²	1	2	yes	—
69	C₂₃×#387	C₂²	1	2	yes	—
70	C₂₃×#387	C₂²	1	2	yes	—
71	C₂₃×#387	C₂²	1	2	yes	—
72	C₂₃×#387	C₂²	1	2	yes	—
73	C₂₃×#387	C₂²	1	2	yes	—
74	C₂₃×#387	C₂²	1	2	yes	—
75	C₂₃×#387	C₂²	1	2	yes	—
76	C₂₃×#387	C₂²	1	2	yes	—
77	C₂₃×#387	C₂²	1	2	yes	—
78	C₂₃×#387	C₂²	1	2	yes	—
79	C₂₃×#387	C₂²	1	2	yes	—
80	C₂₃×#387	C₂²	1	2	yes	—
81	C₂₃×#387	C₂²	1	2	yes	—
82	C₂₃×#387	C₂²	1	2	yes	—
83	C₂₃×#387	C₂²	1	2	yes	—
84	C₂₃×#385	C₂²	1	1	yes	characteristic
85	C₂₃×#385	C₂²	1	1	yes	characteristic
86	C₂₃×#385	C₂²	1	2	yes	—
87	C₂₃×#385	C₂²	1	2	yes	—
88	C₂₃×#385	C₂²	1	1	yes	characteristic
89	C₂₃×#385	C₂²	1	1	yes	characteristic
90	C₂₃×#383	C₂²	1	2	yes	—
91	C₂₃×#383	C₂²	1	1	yes	characteristic
92	C₂₃×#382	C₂²	1	2	yes	—
93	C₂₃×#380	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
102	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
105	C₂₃×#376	C₂²	1	2	yes	—
106	C₂₃×#376	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
109	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
112	C₂₃×C₄⋊Q₈	—	2	8	no	—
113	C₂₃×#126	—	2	8	no	—
114	C₂₃×#125	—	2	8	no	—
115	C₂₃×#125	—	4	2	no	—
116	C₂₃×C₂²⋊Q₈	—	2	8	no	—
117	C₄×Q₈×C₂₃	—	4	4	no	—
118	C₄×Q₈×C₂₃	—	4	2	no	—
119	C₂₃×#117	—	2	4	no	—
120	C₂₃×#117	—	4	2	no	—
121	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₂₃	—	4	2	no	—
158	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
159	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
160	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
161	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
164	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
165	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
166	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
168	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
169	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
171	C₂₃×#95	C₂³	1	2	yes	—
172	C₂₃×#95	C₂³	1	2	yes	—
173	C₂₃×#95	C₂³	1	2	yes	—
174	C₂₃×#95	C₂³	1	1	yes	characteristic
175	C₂₃×#95	C₂³	1	1	yes	characteristic
176	C₂₃×#95	C₂³	1	2	yes	—
177	C₂₃×#95	C₂³	1	2	yes	—
178	C₂₃×#95	C₂³	1	2	yes	—
179	C₂₃×#95	C₂³	1	2	yes	—
180	C₂₃×#95	C₂³	1	2	yes	—
181	C₂₃×#95	C₂³	1	2	yes	—
182	C₂₃×#95	C₂³	1	2	yes	—
183	C₂₃×#95	C₂³	1	2	yes	—
184	C₂₃×#95	C₂³	1	2	yes	—
185	C₂₃×#95	C₂³	1	2	yes	—
186	C₂₃×#95	C₂³	1	2	yes	—
187	C₂₃×#95	C₂³	1	2	yes	—
188	C₂₃×#95	C₂³	1	2	yes	—
189	C₂₃×#95	C₂³	1	2	yes	—
190	C₂₃×#95	C₂³	1	2	yes	—
191	C₂₃×#95	C₂³	1	2	yes	—
192	C₂₃×#95	C₂³	1	1	yes	characteristic
193	C₂₃×#95	C₂³	1	2	yes	—
194	C₂₃×#95	C₂³	1	1	yes	characteristic
195	C₂₃×#95	C₂³	1	2	yes	—
196	C₂₃×#95	C₂³	1	2	yes	—
197	C₂₃×#95	C₂³	1	2	yes	—
198	C₂₃×#95	C₂³	1	2	yes	—
199	C₂₃×#95	C₂³	1	2	yes	—
200	C₂₃×#95	C₂³	1	2	yes	—
201	C₂₃×#95	C₂³	1	2	yes	—
202	C₂₃×#95	C₂³	1	2	yes	—
203	C₂₃×#95	C₂³	1	2	yes	—
204	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
205	C₂×Q₈×C₂₃	—	2	4	no	—
206	C₂×Q₈×C₂₃	—	2	4	no	—
207	C₂×Q₈×C₂₃	—	2	4	no	—
208	C₂×Q₈×C₂₃	—	4	2	no	—
209	C₂×Q₈×C₂₃	—	4	1	no	—
210	C₂²×C₄×C₂₃	—	2	2	no	—
211	C₂²×C₄×C₂₃	—	2	2	no	—
212	C₂²×C₄×C₂₃	—	2	2	no	—
213	C₂²×C₄×C₂₃	—	2	4	no	—
214	C₂²×C₄×C₂₃	—	2	4	no	—
215	C₂²×C₄×C₂₃	—	4	1	no	—
216	C₂²×C₄×C₂₃	—	4	1	no	—
217	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
235	C₄⋊C₄×C₂₃	—	2	4	no	—
236	C₄⋊C₄×C₂₃	—	2	4	no	—
237	C₄⋊C₄×C₂₃	—	2	4	no	—
238	C₄⋊C₄×C₂₃	—	2	4	no	—
239	C₄⋊C₄×C₂₃	—	2	4	no	—
240	C₄⋊C₄×C₂₃	—	2	4	no	—
241	C₄⋊C₄×C₂₃	—	2	4	no	—
242	C₄⋊C₄×C₂₃	—	2	4	no	—
243	C₄⋊C₄×C₂₃	—	2	4	no	—
244	C₄⋊C₄×C₂₃	—	2	4	no	—
245	C₄⋊C₄×C₂₃	—	2	4	no	—
246	C₄⋊C₄×C₂₃	—	2	4	no	—
247	C₄⋊C₄×C₂₃	—	2	4	no	—
248	C₄⋊C₄×C₂₃	—	2	4	no	—
249	C₄⋊C₄×C₂₃	—	2	4	no	—
250	C₄⋊C₄×C₂₃	—	2	4	no	—
251	C₄⋊C₄×C₂₃	—	2	4	no	—
252	C₄⋊C₄×C₂₃	—	2	4	no	—
253	C₄⋊C₄×C₂₃	—	2	4	no	—
254	C₄⋊C₄×C₂₃	—	2	4	no	—
255	C₄⋊C₄×C₂₃	—	4	1	no	—
256	C₄⋊C₄×C₂₃	—	4	1	no	—
257	C₄⋊C₄×C₂₃	—	4	2	no	—
258	C₄⋊C₄×C₂₃	—	4	1	no	—
259	C₄⋊C₄×C₂₃	—	4	1	no	—
260	C₄⋊C₄×C₂₃	—	4	2	no	—
261	C₄⋊C₄×C₂₃	—	4	1	no	—
262	C₄⋊C₄×C₂₃	#41	1	8	yes	—
263	C₂²⋊C₄×C₂₃	—	2	2	no	—
264	C₂²⋊C₄×C₂₃	—	2	4	no	—
265	C₂²⋊C₄×C₂₃	—	2	4	no	—
266	C₂²⋊C₄×C₂₃	—	2	4	no	—
267	C₂²⋊C₄×C₂₃	—	2	4	no	—
268	C₂²⋊C₄×C₂₃	—	4	1	no	—
269	C₂²⋊C₄×C₂₃	—	4	1	no	—
270	C₂²⋊C₄×C₂₃	#41	1	4	yes	—
271	C₄²×C₂₃	—	2	4	no	—
272	C₄²×C₂₃	—	2	4	no	—
273	C₄²×C₂₃	—	2	4	no	—
274	C₄²×C₂₃	—	2	4	no	—
275	C₄²×C₂₃	—	2	4	no	—
276	C₄²×C₂₃	—	2	2	no	—
277	C₄²×C₂₃	—	2	2	no	—
278	C₄²×C₂₃	—	2	4	no	—
279	C₄²×C₂₃	—	2	4	no	—
280	C₄²×C₂₃	—	4	2	no	—
281	C₄²×C₂₃	—	4	2	no	—
282	C₄²×C₂₃	—	4	2	no	—
283	C₄²×C₂₃	—	4	2	no	—
284	#60030	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
285	C₂³×C₂₃	—	2	2	no	—
286	C₂³×C₂₃	—	2	1	no	—
287	C₂³×C₂₃	—	2	2	no	—
288	C₂³×C₂₃	—	2	1	no	—
289	C₂³×C₂₃	C₂×#41	1	2	yes	—
290	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
291	Q₈×C₂₃	—	4	8	no	—
292	Q₈×C₂₃	—	4	4	no	—
293	C₂×C₄×C₂₃	—	2	8	no	—
294	C₂×C₄×C₂₃	—	2	1	no	—
295	C₂×C₄×C₂₃	—	2	2	no	—
296	C₂×C₄×C₂₃	—	2	2	no	—
297	C₂×C₄×C₂₃	—	2	1	no	—
298	C₂×C₄×C₂₃	—	2	2	no	—
299	C₂×C₄×C₂₃	—	2	2	no	—
300	C₂×C₄×C₂₃	—	2	2	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	1	no	—
303	C₂×C₄×C₂₃	—	2	2	no	—
304	C₂×C₄×C₂₃	—	2	2	no	—
305	C₂×C₄×C₂₃	—	2	2	no	—
306	C₂×C₄×C₂₃	—	2	1	no	—
307	C₂×C₄×C₂₃	—	2	2	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	2	no	—
310	C₂×C₄×C₂₃	—	2	2	no	—
311	C₂×C₄×C₂₃	—	2	2	no	—
312	C₂×C₄×C₂₃	—	2	2	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	2	no	—
315	C₂×C₄×C₂₃	—	2	2	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	2	no	—
318	C₂×C₄×C₂₃	—	2	2	no	—
319	C₂×C₄×C₂₃	—	2	2	no	—
320	C₂×C₄×C₂₃	—	2	2	no	—
321	C₂×C₄×C₂₃	—	2	1	no	—
322	C₂×C₄×C₂₃	—	2	1	no	—
323	C₂×C₄×C₂₃	—	2	1	no	—
324	C₂×C₄×C₂₃	—	2	1	no	—
325	C₂×C₄×C₂₃	—	2	2	no	—
326	C₂×C₄×C₂₃	—	2	2	no	—
327	C₂×C₄×C₂₃	—	2	2	no	—
328	C₂×C₄×C₂₃	—	2	2	no	—
329	C₂×C₄×C₂₃	—	2	2	no	—
330	C₂×C₄×C₂₃	—	2	2	no	—
331	C₂×C₄×C₂₃	—	2	2	no	—
332	C₂×C₄×C₂₃	—	2	2	no	—
333	C₂×C₄×C₂₃	—	2	2	no	—
334	C₂×C₄×C₂₃	—	2	2	no	—
335	C₂×C₄×C₂₃	—	2	2	no	—
336	C₂×C₄×C₂₃	—	2	2	no	—
337	C₂×C₄×C₂₃	—	4	4	no	—
338	C₂×C₄×C₂₃	—	4	4	no	—
339	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
340	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
341	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
342	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
343	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
344	C₂×C₄×C₂₃	2₋¹⁺⁴	1	4	yes	—
345	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
346	#2722	C₂×C₂₃	1	1	yes	characteristic
347	#2690	C₂×C₂₃	1	2	yes	—
348	#2677	C₂×C₂₃	1	1	yes	characteristic
349	#2611	C₂×C₂₃	1	1	yes	characteristic
350	#2606	C₂×C₂₃	1	2	yes	complemented
351	#2599	C₂×C₂₃	1	1	yes	characteristic
352	#2590	C₂×C₂₃	1	2	yes	complemented
353	#2588	C₂×C₂₃	1	2	yes	complemented
354	#2550	C₂×C₂₃	1	2	yes	complemented
355	#2524	C₂×C₂₃	1	2	yes	complemented
356	#2523	C₂×C₂₃	1	1	yes	characteristic
357	#2517	C₂×C₂₃	1	1	yes	characteristic
358	#2478	C₂×C₂₃	1	2	yes	—
359	#2462	C₂×C₂₃	1	2	yes	complemented
360	#2373	C₂×C₂₃	1	2	yes	—
361	#2371	C₂×C₂₃	1	2	yes	complemented
362	#2365	C₂×C₂₃	1	2	yes	complemented
363	C₄×C₂²⋊Q₈	C₂×C₂₃	1	2	yes	—
364	#2296	C₂×C₂₃	1	1	yes	characteristic
365	C₂²×C₂₃	—	2	4	no	—
366	C₂²×C₂₃	—	2	2	no	—
367	C₂²×C₂₃	—	4	1	no	—
368	C₂²×C₂₃	—	4	2	no	—
369	C₂²×C₂₃	—	4	1	no	—
370	C₂²×C₂₃	C₂²×#41	1	2	yes	—
371	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
372	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
373	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
374	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
375	C₄×C₂₃	—	2	4	no	—
376	C₄×C₂₃	—	2	4	no	—
377	C₄×C₂₃	—	2	4	no	—
378	C₄×C₂₃	—	2	2	no	—
379	C₄×C₂₃	—	2	2	no	—
380	C₄×C₂₃	—	2	4	no	—
381	C₄×C₂₃	—	2	4	no	—
382	C₄×C₂₃	—	4	1	no	—
383	C₄×C₂₃	—	4	2	no	—
384	C₄×C₂₃	—	4	1	no	—
385	C₄×C₂₃	—	4	2	no	—
386	C₄×C₂₃	—	4	2	no	—
387	C₄×C₂₃	—	4	2	no	—
388	C₄×C₂₃	—	4	2	no	—
389	C₄×C₂₃	—	4	2	no	—
390	C₄×C₂₃	—	4	2	no	—
391	C₄×C₂₃	—	4	1	no	—
392	C₄×C₂₃	—	4	1	no	—
393	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
394	C₂×#126	C₂²×C₂₃	1	2	yes	—
395	C₂×#125	C₂²×C₂₃	1	2	yes	—
396	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
397	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
398	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
399	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
400	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
401	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
402	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
403	#400	C₂²×C₂₃	1	1	yes	characteristic
404	#400	C₂²×C₂₃	1	2	yes	—
405	#400	C₂²×C₂₃	1	2	yes	—
406	#399	C₂²×C₂₃	1	1	yes	characteristic
407	#398	C₂²×C₂₃	1	2	yes	—
408	#398	C₂²×C₂₃	1	1	yes	characteristic
409	#398	C₂²×C₂₃	1	2	yes	—
410	#398	C₂²×C₂₃	1	2	yes	—
411	#398	C₂²×C₂₃	1	1	yes	characteristic
412	#398	C₂²×C₂₃	1	2	yes	—
413	#398	C₂²×C₂₃	1	2	yes	—
414	#398	C₂²×C₂₃	1	2	yes	—
415	#397	C₂²×C₂₃	1	1	yes	characteristic
416	#397	C₂²×C₂₃	1	1	yes	characteristic
417	#397	C₂²×C₂₃	1	2	yes	—
418	#397	C₂²×C₂₃	1	2	yes	—
419	#395	C₂²×C₂₃	1	2	yes	—
420	#395	C₂²×C₂₃	1	1	yes	characteristic
421	#395	C₂²×C₂₃	1	2	yes	—
422	#393	C₂²×C₂₃	1	1	yes	characteristic
423	#391	C₂²×C₂₃	1	2	yes	—
424	#391	C₂²×C₂₃	1	2	yes	—
425	#391	C₂²×C₂₃	1	2	yes	—
426	#389	C₂²×C₂₃	1	2	yes	—
427	#389	C₂²×C₂₃	1	2	yes	—
428	#389	C₂²×C₂₃	1	2	yes	—
429	#389	C₂²×C₂₃	1	2	yes	—
430	#389	C₂²×C₂₃	1	2	yes	—
431	#389	C₂²×C₂₃	1	2	yes	—
432	#389	C₂²×C₂₃	1	2	yes	—
433	#389	C₂²×C₂₃	1	2	yes	—
434	#388	C₂²×C₂₃	1	2	yes	—
435	#388	C₂²×C₂₃	1	2	yes	—
436	#388	C₂²×C₂₃	1	2	yes	—
437	#387	C₂²×C₂₃	1	2	yes	—
438	#387	C₂²×C₂₃	1	2	yes	—
439	#387	C₂²×C₂₃	1	2	yes	—
440	#387	C₂²×C₂₃	1	2	yes	—
441	#387	C₂²×C₂₃	1	2	yes	—
442	#387	C₂²×C₂₃	1	2	yes	—
443	#387	C₂²×C₂₃	1	2	yes	—
444	#387	C₂²×C₂₃	1	2	yes	—
445	#387	C₂²×C₂₃	1	2	yes	—
446	#387	C₂²×C₂₃	1	2	yes	—
447	#387	C₂²×C₂₃	1	2	yes	—
448	#387	C₂²×C₂₃	1	2	yes	—
449	#387	C₂²×C₂₃	1	2	yes	—
450	#387	C₂²×C₂₃	1	2	yes	—
451	#387	C₂²×C₂₃	1	2	yes	—
452	#387	C₂²×C₂₃	1	2	yes	—
453	#387	C₂²×C₂₃	1	2	yes	—
454	#387	C₂²×C₂₃	1	2	yes	—
455	#387	C₂²×C₂₃	1	2	yes	—
456	#387	C₂²×C₂₃	1	2	yes	—
457	#385	C₂²×C₂₃	1	2	yes	—
458	#385	C₂²×C₂₃	1	2	yes	—
459	#385	C₂²×C₂₃	1	1	yes	characteristic
460	#385	C₂²×C₂₃	1	1	yes	characteristic
461	#385	C₂²×C₂₃	1	1	yes	characteristic
462	#385	C₂²×C₂₃	1	1	yes	characteristic
463	#383	C₂²×C₂₃	1	1	yes	characteristic
464	#383	C₂²×C₂₃	1	2	yes	—
465	#382	C₂²×C₂₃	1	2	yes	—
466	#380	C₂²×C₂₃	1	2	yes	—
467	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
468	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
469	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
470	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
471	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
472	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
473	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
474	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
475	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
476	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
477	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
478	#376	C₂²×C₂₃	1	2	yes	—
479	#376	C₂²×C₂₃	1	1	yes	characteristic
480	C₂×C₂₃	—	4	2	no	—
481	C₂×C₂₃	#3481	1	1	yes	characteristic
482	C₂×C₂₃	#3482	1	2	yes	—
483	C₂×C₂₃	#3492	1	1	yes	characteristic
484	C₂×C₂₃	#3509	1	2	yes	—
485	C₂×C₂₃	#3538	1	1	yes	characteristic
486	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
487	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
491	C₄⋊Q₈	—	2	8	no	—
492	#126	—	2	8	no	—
493	#125	—	2	8	no	—
494	#125	—	4	2	no	—
495	C₂²⋊Q₈	—	2	8	no	—
496	C₄×Q₈	—	4	4	no	—
497	C₄×Q₈	—	4	2	no	—
498	#117	—	2	4	no	—
499	#117	—	4	2	no	—
500	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
536	C₂×C₄²	—	4	2	no	—
537	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
540	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
541	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
542	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
543	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
544	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
545	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
546	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
547	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
548	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
549	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
550	#95	C₂³×C₂₃	1	2	yes	—
551	#95	C₂³×C₂₃	1	2	yes	—
552	#95	C₂³×C₂₃	1	2	yes	—
553	#95	C₂³×C₂₃	1	1	yes	characteristic
554	#95	C₂³×C₂₃	1	1	yes	characteristic
555	#95	C₂³×C₂₃	1	2	yes	—
556	#95	C₂³×C₂₃	1	2	yes	—
557	#95	C₂³×C₂₃	1	2	yes	—
558	#95	C₂³×C₂₃	1	2	yes	—
559	#95	C₂³×C₂₃	1	2	yes	—
560	#95	C₂³×C₂₃	1	2	yes	—
561	#95	C₂³×C₂₃	1	2	yes	—
562	#95	C₂³×C₂₃	1	2	yes	—
563	#95	C₂³×C₂₃	1	2	yes	—
564	#95	C₂³×C₂₃	1	2	yes	—
565	#95	C₂³×C₂₃	1	2	yes	—
566	#95	C₂³×C₂₃	1	2	yes	—
567	#95	C₂³×C₂₃	1	2	yes	—
568	#95	C₂³×C₂₃	1	2	yes	—
569	#95	C₂³×C₂₃	1	2	yes	—
570	#95	C₂³×C₂₃	1	2	yes	—
571	#95	C₂³×C₂₃	1	1	yes	characteristic
572	#95	C₂³×C₂₃	1	2	yes	—
573	#95	C₂³×C₂₃	1	1	yes	characteristic
574	#95	C₂³×C₂₃	1	2	yes	—
575	#95	C₂³×C₂₃	1	2	yes	—
576	#95	C₂³×C₂₃	1	2	yes	—
577	#95	C₂³×C₂₃	1	2	yes	—
578	#95	C₂³×C₂₃	1	2	yes	—
579	#95	C₂³×C₂₃	1	2	yes	—
580	#95	C₂³×C₂₃	1	2	yes	—
581	#95	C₂³×C₂₃	1	2	yes	—
582	#95	C₂³×C₂₃	1	2	yes	—
583	C₂₃	#60030	1	1	yes	characteristic, direct product factor, Sylow
584	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
585	C₂×Q₈	—	2	4	no	—
586	C₂×Q₈	—	2	4	no	—
587	C₂×Q₈	—	2	4	no	—
588	C₂×Q₈	—	4	2	no	—
589	C₂×Q₈	—	4	1	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	4	1	no	—
596	C₂²×C₄	—	4	1	no	—
597	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	4	1	no	—
636	C₄⋊C₄	—	4	1	no	—
637	C₄⋊C₄	—	4	2	no	—
638	C₄⋊C₄	—	4	1	no	—
639	C₄⋊C₄	—	4	1	no	—
640	C₄⋊C₄	—	4	2	no	—
641	C₄⋊C₄	—	4	1	no	—
642	C₄⋊C₄	#41×C₂₃	1	8	yes	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	4	1	no	—
649	C₂²⋊C₄	—	4	1	no	—
650	C₂²⋊C₄	#41×C₂₃	1	4	yes	—
651	C₄²	—	2	4	no	—
652	C₄²	—	2	4	no	—
653	C₄²	—	2	4	no	—
654	C₄²	—	2	4	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	4	no	—
660	C₄²	—	4	2	no	—
661	C₄²	—	4	2	no	—
662	C₄²	—	4	2	no	—
663	C₄²	—	4	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	1	no	—
668	C₂³	C₂×#41×C₂₃	1	2	yes	—
669	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
670	Q₈	—	4	8	no	—
671	Q₈	—	4	4	no	—
672	C₂×C₄	—	2	8	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
719	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
720	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
721	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
722	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
723	C₂×C₄	C₂₃×2₋¹⁺⁴	1	4	yes	—
724	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
725	C₂²	—	2	4	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	1	no	—
730	C₂²	C₂²×#41×C₂₃	1	2	yes	—
731	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
732	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
733	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
734	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
735	C₄	—	2	4	no	—
736	C₄	—	2	4	no	—
737	C₄	—	2	4	no	—
738	C₄	—	2	2	no	—
739	C₄	—	2	2	no	—
740	C₄	—	2	4	no	—
741	C₄	—	2	4	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	1	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	2	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	1	no	—
753	C₂	—	4	2	no	—
754	C₂	C₂₃×#3481	1	1	yes	characteristic
755	C₂	C₂₃×#3482	1	2	yes	—
756	C₂	C₂₃×#3492	1	1	yes	characteristic
757	C₂	C₂₃×#3509	1	2	yes	—
758	C₂	C₂₃×#3538	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂⁴×C₂₃	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₂₃×#2606	C₂	semidirect
7. C₂₃×#2590	C₂	semidirect
8. C₂₃×#2588	C₂	semidirect
9. C₂₃×#2550	C₂	semidirect
10. C₂₃×#2524	C₂	semidirect
14. C₂₃×#2462	C₂	semidirect
16. C₂₃×#2371	C₂	semidirect
17. C₂₃×#2365	C₂	semidirect
284. #60030	C₂₃	direct (N × H)
350. #2606	C₂×C₂₃	semidirect
352. #2590	C₂×C₂₃	semidirect
353. #2588	C₂×C₂₃	semidirect
354. #2550	C₂×C₂₃	semidirect
355. #2524	C₂×C₂₃	semidirect
359. #2462	C₂×C₂₃	semidirect
361. #2371	C₂×C₂₃	semidirect
362. #2365	C₂×C₂₃	semidirect
583. C₂₃	#60030	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×#2722	2
C₂₃×#2690	2
C₂₃×#2677	2
C₂₃×#2611	2
C₂₃×#2606	2
C₂₃×#2599	2
C₂₃×#2590	2
C₂₃×#2588	2
C₂₃×#2550	2
C₂₃×#2524	2
C₂₃×#2523	2
C₂₃×#2517	2
C₂₃×#2478	2
C₂₃×#2462	2
C₂₃×#2373	2
C₂₃×#2371	2
C₂₃×#2365	2
C₄×C₂₃×C₂²⋊Q₈	2
C₂₃×#2296	2
#60030	23

Subgroups — C23×#60030 #19207656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60030 #19207656