Subgroups — C₂₃×#36579 #19184205

Order 5888.

2388 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2850	C₂	1	2	yes	maximal
5	C₂₃×#2592	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2581	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2568	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2538	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2481	C₂	1	4	yes	maximal, complemented
10	C₂₃×#2469	C₂	1	4	yes	maximal, complemented
11	C₂₃×#2421	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2409	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2362	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2352	C₂	1	2	yes	maximal, complemented
16	C₄×C₂₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
17	C₄×C₂₃×#121	C₂	1	1	yes	maximal, characteristic
18	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₂₃×#556	—	2	8	no	—
20	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#126	C₂²	1	4	yes	—
22	C₂×C₂₃×#124	C₂²	1	2	yes	—
23	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₂₃	—	2	8	no	—
28	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#117	C₂²	1	2	yes	—
38	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
42	C₂₃×#400	C₂²	1	4	yes	—
43	C₂₃×#400	C₂²	1	4	yes	—
44	C₂₃×#397	C₂²	1	4	yes	—
45	C₂₃×#396	C₂²	1	4	yes	—
46	C₂₃×#395	C₂²	1	4	yes	—
47	C₂₃×#393	C₂²	1	4	yes	—
48	C₂₃×#391	C₂²	1	2	yes	—
49	C₂₃×#391	C₂²	1	2	yes	—
50	C₂₃×#391	C₂²	1	2	yes	—
51	C₂₃×#391	C₂²	1	2	yes	—
52	C₂₃×#391	C₂²	1	2	yes	—
53	C₂₃×#390	C₂²	1	2	yes	—
54	C₂₃×#390	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
59	C₂₃×#388	C₂²	1	4	yes	—
60	C₂₃×#388	C₂²	1	2	yes	—
61	C₂₃×#388	C₂²	1	4	yes	—
62	C₂₃×#388	C₂²	1	4	yes	—
63	C₂₃×#388	C₂²	1	4	yes	—
64	C₂₃×#387	C₂²	1	4	yes	—
65	C₂₃×#387	C₂²	1	4	yes	—
66	C₂₃×#387	C₂²	1	4	yes	—
67	C₂₃×#387	C₂²	1	4	yes	—
68	C₂₃×#386	C₂²	1	4	yes	—
69	C₂₃×#386	C₂²	1	2	yes	—
70	C₂₃×#386	C₂²	1	4	yes	—
71	C₂₃×#385	C₂²	1	4	yes	—
72	C₂₃×#384	C₂²	1	1	yes	characteristic
73	C₂₃×#382	C₂²	1	2	yes	—
74	C₂₃×#382	C₂²	1	2	yes	—
75	C₂₃×#380	C₂²	1	2	yes	—
76	C₂₃×#380	C₂²	1	2	yes	—
77	C₂₃×#380	C₂²	1	2	yes	—
78	C₂₃×#380	C₂²	1	1	yes	characteristic
79	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
80	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
81	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
82	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
84	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
85	C₂²×Q₈×C₂₃	—	2	4	no	—
86	C₂²×Q₈×C₂₃	—	2	4	no	—
87	C₂²×Q₈×C₂₃	—	2	4	no	—
88	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
89	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
90	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
93	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
95	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
96	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
97	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
100	C₂₃×C₄⋊Q₈	—	2	4	no	—
101	C₂₃×#126	—	2	16	no	—
102	C₂₃×#124	—	2	8	no	—
103	C₂₃×C₂²⋊Q₈	—	2	8	no	—
104	C₂₃×C₂²⋊Q₈	—	2	8	no	—
105	C₂₃×C₂²⋊Q₈	—	2	8	no	—
106	C₂₃×#121	—	2	4	no	—
107	C₄×Q₈×C₂₃	—	2	4	no	—
108	C₄×Q₈×C₂₃	—	2	4	no	—
109	C₄×Q₈×C₂₃	—	2	8	no	—
110	C₄×Q₈×C₂₃	—	2	8	no	—
111	C₄×Q₈×C₂₃	—	2	4	no	—
112	C₄×Q₈×C₂₃	—	2	8	no	—
113	C₄×Q₈×C₂₃	D₄	1	8	yes	complemented
114	C₄×D₄×C₂₃	—	2	8	no	—
115	C₄×D₄×C₂₃	—	2	4	no	—
116	C₂₃×#117	—	2	8	no	—
117	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
118	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
119	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	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	1	yes	characteristic
137	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
148	C₂×C₄²×C₂₃	—	2	4	no	—
149	C₂×C₄²×C₂₃	—	2	8	no	—
150	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
152	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
153	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
154	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
155	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
157	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
159	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
160	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
161	C₂₃×#95	C₂³	1	2	yes	—
162	C₂₃×#95	C₂³	1	4	yes	—
163	C₂₃×#95	C₂³	1	4	yes	—
164	C₂₃×#95	C₂³	1	2	yes	—
165	C₂₃×#95	C₂³	1	4	yes	—
166	C₂₃×#95	C₂³	1	4	yes	—
167	C₂₃×#95	C₂³	1	4	yes	—
168	C₂₃×#95	C₂³	1	2	yes	—
169	C₂₃×#95	C₂³	1	4	yes	—
170	C₂₃×#95	C₂³	1	4	yes	—
171	C₂₃×#95	C₂³	1	4	yes	—
172	C₂₃×#95	C₂³	1	4	yes	—
173	C₂₃×#95	C₂³	1	4	yes	—
174	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
175	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
176	C₂×Q₈×C₂₃	—	2	32	no	—
177	C₂×Q₈×C₂₃	—	2	4	no	—
178	C₂×Q₈×C₂₃	—	2	2	no	—
179	C₂×Q₈×C₂₃	—	2	4	no	—
180	C₂×Q₈×C₂₃	—	2	4	no	—
181	C₂×Q₈×C₂₃	—	2	4	no	—
182	C₂×Q₈×C₂₃	—	2	2	no	—
183	C₂×Q₈×C₂₃	—	2	2	no	—
184	C₂×Q₈×C₂₃	—	2	2	no	—
185	C₂×Q₈×C₂₃	—	2	4	no	—
186	C₂×Q₈×C₂₃	—	2	4	no	—
187	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
188	C₂×Q₈×C₂₃	#41	1	4	yes	—
189	C₂×D₄×C₂₃	—	2	4	no	—
190	C₂×D₄×C₂₃	—	2	4	no	—
191	C₂×D₄×C₂₃	—	2	4	no	—
192	C₂×D₄×C₂₃	—	2	2	no	—
193	C₂×D₄×C₂₃	—	2	2	no	—
194	C₂×D₄×C₂₃	—	2	2	no	—
195	C₂²×C₄×C₂₃	—	2	4	no	—
196	C₂²×C₄×C₂₃	—	2	2	no	—
197	C₂²×C₄×C₂₃	—	2	4	no	—
198	C₂²×C₄×C₂₃	—	2	2	no	—
199	C₂²×C₄×C₂₃	—	2	4	no	—
200	C₂²×C₄×C₂₃	—	2	2	no	—
201	C₂²×C₄×C₂₃	—	2	2	no	—
202	C₂²×C₄×C₂₃	—	2	4	no	—
203	C₂²×C₄×C₂₃	—	2	2	no	—
204	C₂²×C₄×C₂₃	—	2	4	no	—
205	C₂²×C₄×C₂₃	—	2	2	no	—
206	C₂²×C₄×C₂₃	—	2	4	no	—
207	C₂²×C₄×C₂₃	—	2	4	no	—
208	C₂²×C₄×C₂₃	—	2	4	no	—
209	C₂²×C₄×C₂₃	—	4	2	no	—
210	C₂²×C₄×C₂₃	—	4	1	no	—
211	C₂²×C₄×C₂₃	#41	1	4	yes	—
212	C₂²×C₄×C₂₃	#41	1	4	yes	—
213	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
226	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
228	C₄⋊C₄×C₂₃	—	2	4	no	—
229	C₄⋊C₄×C₂₃	—	2	4	no	—
230	C₄⋊C₄×C₂₃	—	2	4	no	—
231	C₄⋊C₄×C₂₃	—	2	4	no	—
232	C₄⋊C₄×C₂₃	—	2	2	no	—
233	C₄⋊C₄×C₂₃	—	2	4	no	—
234	C₄⋊C₄×C₂₃	—	2	2	no	—
235	C₄⋊C₄×C₂₃	—	2	8	no	—
236	C₄⋊C₄×C₂₃	—	2	4	no	—
237	C₄⋊C₄×C₂₃	—	2	4	no	—
238	C₄⋊C₄×C₂₃	—	2	2	no	—
239	C₄⋊C₄×C₂₃	—	2	4	no	—
240	C₄⋊C₄×C₂₃	—	2	4	no	—
241	C₄⋊C₄×C₂₃	—	2	8	no	—
242	C₄⋊C₄×C₂₃	—	2	8	no	—
243	C₄⋊C₄×C₂₃	—	2	2	no	—
244	C₄⋊C₄×C₂₃	—	4	2	no	—
245	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
246	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
247	C₂²⋊C₄×C₂₃	—	2	4	no	—
248	C₂²⋊C₄×C₂₃	—	2	8	no	—
249	C₂²⋊C₄×C₂₃	—	2	8	no	—
250	C₂²⋊C₄×C₂₃	—	2	4	no	—
251	C₂²⋊C₄×C₂₃	—	2	8	no	—
252	C₂²⋊C₄×C₂₃	—	2	4	no	—
253	C₂²⋊C₄×C₂₃	—	2	4	no	—
254	C₂²⋊C₄×C₂₃	—	2	8	no	—
255	C₂²⋊C₄×C₂₃	—	4	2	no	—
256	C₂²⋊C₄×C₂₃	—	4	4	no	—
257	C₄²×C₂₃	—	2	4	no	—
258	C₄²×C₂₃	—	2	2	no	—
259	C₄²×C₂₃	—	2	4	no	—
260	C₄²×C₂₃	—	2	2	no	—
261	C₄²×C₂₃	—	2	2	no	—
262	C₄²×C₂₃	—	2	4	no	—
263	C₄²×C₂₃	—	2	8	no	—
264	C₄²×C₂₃	—	2	4	no	—
265	C₄²×C₂₃	—	4	4	no	—
266	C₄²×C₂₃	C₂×D₄	1	4	yes	—
267	C₄²×C₂₃	C₂×D₄	1	8	yes	—
268	#36579	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₂³×C₂₃	—	2	1	no	—
270	C₂³×C₂₃	—	2	1	no	—
271	C₂³×C₂₃	—	2	1	no	—
272	C₂³×C₂₃	—	2	1	no	—
273	C₂³×C₂₃	—	2	2	no	—
274	C₂³×C₂₃	—	2	2	no	—
275	C₂³×C₂₃	—	2	2	no	—
276	C₂³×C₂₃	—	2	2	no	—
277	C₂³×C₂₃	—	2	2	no	—
278	C₂³×C₂₃	—	2	2	no	—
279	C₂³×C₂₃	—	2	2	no	—
280	C₂³×C₂₃	C₂×#41	1	2	yes	—
281	C₂³×C₂₃	C₂×#41	1	2	yes	—
282	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
283	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
284	Q₈×C₂₃	—	2	16	no	—
285	Q₈×C₂₃	—	2	8	no	—
286	Q₈×C₂₃	—	2	8	no	—
287	Q₈×C₂₃	—	4	8	no	—
288	D₄×C₂₃	—	4	8	no	—
289	D₄×C₂₃	—	4	4	no	—
290	C₂×C₄×C₂₃	—	2	16	no	—
291	C₂×C₄×C₂₃	—	2	1	no	—
292	C₂×C₄×C₂₃	—	2	2	no	—
293	C₂×C₄×C₂₃	—	2	1	no	—
294	C₂×C₄×C₂₃	—	2	2	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	1	no	—
299	C₂×C₄×C₂₃	—	2	2	no	—
300	C₂×C₄×C₂₃	—	2	1	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	1	no	—
303	C₂×C₄×C₂₃	—	2	8	no	—
304	C₂×C₄×C₂₃	—	2	8	no	—
305	C₂×C₄×C₂₃	—	2	2	no	—
306	C₂×C₄×C₂₃	—	2	2	no	—
307	C₂×C₄×C₂₃	—	2	1	no	—
308	C₂×C₄×C₂₃	—	2	4	no	—
309	C₂×C₄×C₂₃	—	2	2	no	—
310	C₂×C₄×C₂₃	—	2	2	no	—
311	C₂×C₄×C₂₃	—	2	4	no	—
312	C₂×C₄×C₂₃	—	2	4	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	2	no	—
315	C₂×C₄×C₂₃	—	2	4	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	1	no	—
320	C₂×C₄×C₂₃	—	2	2	no	—
321	C₂×C₄×C₂₃	—	2	4	no	—
322	C₂×C₄×C₂₃	—	2	2	no	—
323	C₂×C₄×C₂₃	—	2	4	no	—
324	C₂×C₄×C₂₃	—	2	1	no	—
325	C₂×C₄×C₂₃	—	2	2	no	—
326	C₂×C₄×C₂₃	—	4	8	no	—
327	C₂×C₄×C₂₃	—	4	4	no	—
328	C₂×C₄×C₂₃	—	4	8	no	—
329	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
330	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
332	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
335	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
336	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
337	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
338	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
339	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
340	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
341	C₂×#556	C₂×C₂₃	1	1	yes	characteristic, complemented
342	C₂²×C₄×Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
343	#2857	C₂×C₂₃	1	1	yes	characteristic, complemented
344	#2850	C₂×C₂₃	1	2	yes	—
345	#2592	C₂×C₂₃	1	2	yes	complemented
346	#2581	C₂×C₂₃	1	2	yes	complemented
347	#2568	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#2538	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#2481	C₂×C₂₃	1	4	yes	complemented
350	#2469	C₂×C₂₃	1	4	yes	complemented
351	#2421	C₂×C₂₃	1	2	yes	complemented
352	#2409	C₂×C₂₃	1	2	yes	complemented
353	#2362	C₂×C₂₃	1	2	yes	complemented
354	#2355	C₂×C₂₃	1	1	yes	characteristic, complemented
355	#2352	C₂×C₂₃	1	2	yes	complemented
356	C₄×C₂²⋊Q₈	C₂×C₂₃	1	2	yes	complemented
357	C₄×#121	C₂×C₂₃	1	1	yes	characteristic
358	C₂²×C₂₃	—	2	2	no	—
359	C₂²×C₂₃	—	2	2	no	—
360	C₂²×C₂₃	—	2	2	no	—
361	C₂²×C₂₃	—	2	2	no	—
362	C₂²×C₂₃	—	2	2	no	—
363	C₂²×C₂₃	—	2	2	no	—
364	C₂²×C₂₃	—	4	2	no	—
365	C₂²×C₂₃	—	4	2	no	—
366	C₂²×C₂₃	—	4	2	no	—
367	C₂²×C₂₃	—	4	2	no	—
368	C₂²×C₂₃	—	4	2	no	—
369	C₂²×C₂₃	—	4	2	no	—
370	C₂²×C₂₃	—	4	2	no	—
371	C₂²×C₂₃	#556	1	4	yes	complemented
372	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
373	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
374	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
375	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
376	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
377	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
378	C₂²×C₂₃	#585	1	1	yes	characteristic
379	C₄×C₂₃	—	2	4	no	—
380	C₄×C₂₃	—	2	4	no	—
381	C₄×C₂₃	—	2	2	no	—
382	C₄×C₂₃	—	2	2	no	—
383	C₄×C₂₃	—	2	4	no	—
384	C₄×C₂₃	—	2	2	no	—
385	C₄×C₂₃	—	4	2	no	—
386	C₄×C₂₃	—	4	4	no	—
387	C₄×C₂₃	—	4	2	no	—
388	C₄×C₂₃	—	4	4	no	—
389	C₄×C₂₃	—	4	2	no	—
390	C₄×C₂₃	—	4	1	no	—
391	C₄×C₂₃	—	4	2	no	—
392	C₄×C₂₃	#525	1	4	yes	—
393	C₄×C₂₃	#548	1	4	yes	—
394	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
395	#556	—	2	8	no	—
396	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
397	C₂×#126	C₂²×C₂₃	1	4	yes	—
398	C₂×#124	C₂²×C₂₃	1	2	yes	—
399	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
400	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
401	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
402	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
403	C₂×C₄×Q₈	—	2	8	no	—
404	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
405	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
406	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
407	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
408	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
409	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
410	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
411	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
412	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
413	C₂×#117	C₂²×C₂₃	1	2	yes	—
414	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
415	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
416	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
417	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
418	#400	C₂²×C₂₃	1	4	yes	—
419	#400	C₂²×C₂₃	1	4	yes	—
420	#397	C₂²×C₂₃	1	4	yes	—
421	#396	C₂²×C₂₃	1	4	yes	—
422	#395	C₂²×C₂₃	1	4	yes	—
423	#393	C₂²×C₂₃	1	4	yes	—
424	#391	C₂²×C₂₃	1	2	yes	—
425	#391	C₂²×C₂₃	1	2	yes	—
426	#391	C₂²×C₂₃	1	2	yes	—
427	#391	C₂²×C₂₃	1	2	yes	—
428	#391	C₂²×C₂₃	1	2	yes	—
429	#390	C₂²×C₂₃	1	1	yes	characteristic
430	#390	C₂²×C₂₃	1	2	yes	—
431	#389	C₂²×C₂₃	1	1	yes	characteristic
432	#389	C₂²×C₂₃	1	2	yes	—
433	#389	C₂²×C₂₃	1	2	yes	—
434	#389	C₂²×C₂₃	1	2	yes	—
435	#388	C₂²×C₂₃	1	4	yes	—
436	#388	C₂²×C₂₃	1	4	yes	—
437	#388	C₂²×C₂₃	1	4	yes	—
438	#388	C₂²×C₂₃	1	4	yes	—
439	#388	C₂²×C₂₃	1	2	yes	—
440	#387	C₂²×C₂₃	1	4	yes	—
441	#387	C₂²×C₂₃	1	4	yes	—
442	#387	C₂²×C₂₃	1	4	yes	—
443	#387	C₂²×C₂₃	1	4	yes	—
444	#386	C₂²×C₂₃	1	4	yes	—
445	#386	C₂²×C₂₃	1	4	yes	—
446	#386	C₂²×C₂₃	1	2	yes	—
447	#385	C₂²×C₂₃	1	4	yes	—
448	#384	C₂²×C₂₃	1	1	yes	characteristic
449	#382	C₂²×C₂₃	1	2	yes	—
450	#382	C₂²×C₂₃	1	2	yes	—
451	#380	C₂²×C₂₃	1	2	yes	—
452	#380	C₂²×C₂₃	1	2	yes	—
453	#380	C₂²×C₂₃	1	2	yes	—
454	#380	C₂²×C₂₃	1	1	yes	characteristic
455	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
456	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
457	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
458	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
459	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
460	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
461	C₂×C₂₃	—	2	4	no	—
462	C₂×C₂₃	—	8	2	no	—
463	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
464	C₂×C₂₃	C₂×#548	1	1	yes	characteristic
465	C₂×C₂₃	C₂×#556	1	1	yes	characteristic
466	C₂×C₂₃	#3480	1	1	yes	characteristic
467	C₂×C₂₃	#3489	1	1	yes	characteristic
468	C₂×C₂₃	#3507	1	1	yes	characteristic
469	C₂×C₂₃	#3523	1	1	yes	characteristic
470	C₂²×Q₈	—	2	4	no	—
471	C₂²×Q₈	—	2	4	no	—
472	C₂²×Q₈	—	2	4	no	—
473	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
474	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
475	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
476	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
477	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
478	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
479	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
480	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
481	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
482	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
483	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
485	C₄⋊Q₈	—	2	4	no	—
486	#126	—	2	16	no	—
487	#124	—	2	8	no	—
488	C₂²⋊Q₈	—	2	8	no	—
489	C₂²⋊Q₈	—	2	8	no	—
490	C₂²⋊Q₈	—	2	8	no	—
491	#121	—	2	4	no	—
492	C₄×Q₈	—	2	4	no	—
493	C₄×Q₈	—	2	4	no	—
494	C₄×Q₈	—	2	8	no	—
495	C₄×Q₈	—	2	4	no	—
496	C₄×Q₈	—	2	8	no	—
497	C₄×Q₈	—	2	8	no	—
498	C₄×Q₈	D₄×C₂₃	1	8	yes	complemented
499	C₄×D₄	—	2	8	no	—
500	C₄×D₄	—	2	4	no	—
501	#117	—	2	8	no	—
502	C₂×C₄⋊C₄	—	2	4	no	—
503	C₂×C₄⋊C₄	—	2	8	no	—
504	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
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	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
513	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
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	4	yes	—
517	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
518	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
533	C₂×C₄²	—	2	4	no	—
534	C₂×C₄²	—	2	8	no	—
535	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
536	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
537	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
539	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
540	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
542	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
543	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
544	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
546	#95	C₂³×C₂₃	1	2	yes	—
547	#95	C₂³×C₂₃	1	4	yes	—
548	#95	C₂³×C₂₃	1	4	yes	—
549	#95	C₂³×C₂₃	1	2	yes	—
550	#95	C₂³×C₂₃	1	4	yes	—
551	#95	C₂³×C₂₃	1	4	yes	—
552	#95	C₂³×C₂₃	1	4	yes	—
553	#95	C₂³×C₂₃	1	2	yes	—
554	#95	C₂³×C₂₃	1	4	yes	—
555	#95	C₂³×C₂₃	1	4	yes	—
556	#95	C₂³×C₂₃	1	4	yes	—
557	#95	C₂³×C₂₃	1	4	yes	—
558	#95	C₂³×C₂₃	1	4	yes	—
559	C₂₃	#36579	1	1	yes	characteristic, direct product factor, Sylow
560	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
561	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
562	C₂×Q₈	—	2	32	no	—
563	C₂×Q₈	—	2	4	no	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	2	4	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	4	no	—
568	C₂×Q₈	—	2	2	no	—
569	C₂×Q₈	—	2	2	no	—
570	C₂×Q₈	—	2	2	no	—
571	C₂×Q₈	—	2	4	no	—
572	C₂×Q₈	—	2	4	no	—
573	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
574	C₂×Q₈	#41×C₂₃	1	4	yes	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	4	2	no	—
596	C₂²×C₄	—	4	1	no	—
597	C₂²×C₄	#41×C₂₃	1	4	yes	—
598	C₂²×C₄	#41×C₂₃	1	4	yes	—
599	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
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	4	yes	—
604	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
605	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	8	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	8	no	—
628	C₄⋊C₄	—	2	8	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	4	2	no	—
631	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
632	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	8	no	—
635	C₂²⋊C₄	—	2	8	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	8	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	8	no	—
641	C₂²⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	4	4	no	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	2	no	—
645	C₄²	—	2	4	no	—
646	C₄²	—	2	2	no	—
647	C₄²	—	2	2	no	—
648	C₄²	—	2	4	no	—
649	C₄²	—	2	8	no	—
650	C₄²	—	2	4	no	—
651	C₄²	—	4	4	no	—
652	C₄²	C₂×D₄×C₂₃	1	4	yes	—
653	C₄²	C₂×D₄×C₂₃	1	8	yes	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	C₂×#41×C₂₃	1	2	yes	—
666	C₂³	C₂×#41×C₂₃	1	2	yes	—
667	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
668	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
669	Q₈	—	2	16	no	—
670	Q₈	—	2	8	no	—
671	Q₈	—	2	8	no	—
672	Q₈	—	4	8	no	—
673	D₄	—	4	8	no	—
674	D₄	—	4	4	no	—
675	C₂×C₄	—	2	16	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	8	no	—
689	C₂×C₄	—	2	8	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	4	8	no	—
712	C₂×C₄	—	4	4	no	—
713	C₂×C₄	—	4	8	no	—
714	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
715	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
716	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
717	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
719	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
720	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
721	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
722	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
723	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
724	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
725	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	2	2	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	C₂₃×#556	1	4	yes	complemented
740	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
741	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
742	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
743	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
744	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
745	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
746	C₂²	C₂₃×#585	1	1	yes	characteristic
747	C₄	—	2	4	no	—
748	C₄	—	2	4	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	4	no	—
752	C₄	—	2	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	4	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	4	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	1	no	—
759	C₄	—	4	2	no	—
760	C₄	C₂₃×#525	1	4	yes	—
761	C₄	C₂₃×#548	1	4	yes	—
762	C₂	—	2	4	no	—
763	C₂	—	8	2	no	—
764	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
765	C₂	C₂×C₂₃×#548	1	1	yes	characteristic
766	C₂	C₂×C₂₃×#556	1	1	yes	characteristic
767	C₂	C₂₃×#3480	1	1	yes	characteristic
768	C₂	C₂₃×#3489	1	1	yes	characteristic
769	C₂	C₂₃×#3507	1	1	yes	characteristic
770	C₂	C₂₃×#3523	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#121	C₂²
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
1. C₂×C₂₃×#556	C₂	semidirect
2. C₂²×C₄×Q₈×C₂₃	C₂	semidirect
3. C₂₃×#2857	C₂	semidirect
5. C₂₃×#2592	C₂	semidirect
6. C₂₃×#2581	C₂	semidirect
7. C₂₃×#2568	C₂	semidirect
8. C₂₃×#2538	C₂	semidirect
9. C₂₃×#2481	C₂	semidirect
10. C₂₃×#2469	C₂	semidirect
11. C₂₃×#2421	C₂	semidirect
12. C₂₃×#2409	C₂	semidirect
13. C₂₃×#2362	C₂	semidirect
14. C₂₃×#2355	C₂	semidirect
15. C₂₃×#2352	C₂	semidirect
16. C₄×C₂₃×C₂²⋊Q₈	C₂	semidirect
113. C₄×Q₈×C₂₃	D₄	semidirect
268. #36579	C₂₃	direct (N × H)
341. C₂×#556	C₂×C₂₃	semidirect
342. C₂²×C₄×Q₈	C₂×C₂₃	semidirect
343. #2857	C₂×C₂₃	semidirect
345. #2592	C₂×C₂₃	semidirect
346. #2581	C₂×C₂₃	semidirect
347. #2568	C₂×C₂₃	semidirect
348. #2538	C₂×C₂₃	semidirect
349. #2481	C₂×C₂₃	semidirect
350. #2469	C₂×C₂₃	semidirect
351. #2421	C₂×C₂₃	semidirect
352. #2409	C₂×C₂₃	semidirect
353. #2362	C₂×C₂₃	semidirect
354. #2355	C₂×C₂₃	semidirect
355. #2352	C₂×C₂₃	semidirect
356. C₄×C₂²⋊Q₈	C₂×C₂₃	semidirect
371. C₂²×C₂₃	#556	semidirect
498. C₄×Q₈	D₄×C₂₃	semidirect
559. C₂₃	#36579	direct (N × H)
739. C₂²	C₂₃×#556	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#556	2
C₂²×C₄×Q₈×C₂₃	2
C₂₃×#2857	2
C₂₃×#2850	2
C₂₃×#2592	2
C₂₃×#2581	2
C₂₃×#2568	2
C₂₃×#2538	2
C₂₃×#2481	2
C₂₃×#2469	2
C₂₃×#2421	2
C₂₃×#2409	2
C₂₃×#2362	2
C₂₃×#2355	2
C₂₃×#2352	2
C₄×C₂₃×C₂²⋊Q₈	2
C₄×C₂₃×#121	2
#36579	23

Subgroups — C23×#36579 #19184205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36579 #19184205