Subgroups — C₂₃×#36605 #19184231

Order 5888.

1860 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#2850	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2850	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2594	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2579	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2573	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2570	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2545	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2525	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2514	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2512	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2510	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2481	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2447	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2446	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2373	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2356	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2353	C₂	1	2	yes	maximal, complemented
20	C₄×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂₃×#121	C₂	1	1	yes	maximal, characteristic
23	C₂×C₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#126	C₂²	1	2	yes	—
26	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
40	C₂₃×#401	C₂²	1	2	yes	—
41	C₂₃×#400	C₂²	1	2	yes	—
42	C₂₃×#400	C₂²	1	2	yes	—
43	C₂₃×#400	C₂²	1	2	yes	—
44	C₂₃×#398	C₂²	1	2	yes	—
45	C₂₃×#398	C₂²	1	2	yes	—
46	C₂₃×#397	C₂²	1	2	yes	—
47	C₂₃×#397	C₂²	1	2	yes	—
48	C₂₃×#397	C₂²	1	2	yes	—
49	C₂₃×#396	C₂²	1	2	yes	—
50	C₂₃×#396	C₂²	1	2	yes	—
51	C₂₃×#396	C₂²	1	2	yes	—
52	C₂₃×#391	C₂²	1	1	yes	characteristic
53	C₂₃×#391	C₂²	1	1	yes	characteristic
54	C₂₃×#391	C₂²	1	1	yes	characteristic
55	C₂₃×#391	C₂²	1	1	yes	characteristic
56	C₂₃×#391	C₂²	1	1	yes	characteristic
57	C₂₃×#391	C₂²	1	1	yes	characteristic
58	C₂₃×#390	C₂²	1	1	yes	characteristic
59	C₂₃×#390	C₂²	1	1	yes	characteristic
60	C₂₃×#390	C₂²	1	1	yes	characteristic
61	C₂₃×#389	C₂²	1	1	yes	characteristic
62	C₂₃×#389	C₂²	1	1	yes	characteristic
63	C₂₃×#389	C₂²	1	1	yes	characteristic
64	C₂₃×#389	C₂²	1	2	yes	—
65	C₂₃×#389	C₂²	1	2	yes	—
66	C₂₃×#388	C₂²	1	2	yes	—
67	C₂₃×#388	C₂²	1	2	yes	—
68	C₂₃×#388	C₂²	1	2	yes	—
69	C₂₃×#388	C₂²	1	2	yes	—
70	C₂₃×#388	C₂²	1	2	yes	—
71	C₂₃×#388	C₂²	1	2	yes	—
72	C₂₃×#388	C₂²	1	2	yes	—
73	C₂₃×#388	C₂²	1	2	yes	—
74	C₂₃×#388	C₂²	1	2	yes	—
75	C₂₃×#388	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×#387	C₂²	1	2	yes	—
85	C₂₃×#386	C₂²	1	2	yes	—
86	C₂₃×#386	C₂²	1	2	yes	—
87	C₂₃×#386	C₂²	1	2	yes	—
88	C₂₃×#386	C₂²	1	2	yes	—
89	C₂₃×#386	C₂²	1	2	yes	—
90	C₂₃×#385	C₂²	1	2	yes	—
91	C₂₃×#385	C₂²	1	2	yes	—
92	C₂₃×#385	C₂²	1	2	yes	—
93	C₂₃×#385	C₂²	1	2	yes	—
94	C₂₃×#384	C₂²	1	1	yes	characteristic
95	C₂₃×#383	C₂²	1	2	yes	—
96	C₂₃×#383	C₂²	1	2	yes	—
97	C₂₃×#382	C₂²	1	1	yes	characteristic
98	C₂₃×#382	C₂²	1	1	yes	characteristic
99	C₂₃×#381	C₂²	1	2	yes	—
100	C₂₃×#380	C₂²	1	2	yes	—
101	C₂₃×#380	C₂²	1	1	yes	characteristic
102	C₂₃×#380	C₂²	1	2	yes	—
103	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
120	C₂₃×#376	C₂²	1	2	yes	—
121	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
122	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
126	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
135	C₂₃×C₄⋊Q₈	—	4	2	no	—
136	C₂₃×#126	—	2	8	no	—
137	C₂₃×#124	—	2	4	no	—
138	C₂₃×#124	—	4	2	no	—
139	C₂₃×C₂²⋊Q₈	—	2	4	no	—
140	C₂₃×C₂²⋊Q₈	—	2	4	no	—
141	C₂₃×#121	—	2	4	no	—
142	C₄×Q₈×C₂₃	—	2	4	no	—
143	C₄×Q₈×C₂₃	—	4	2	no	—
144	C₄×D₄×C₂₃	—	2	8	no	—
145	C₄×D₄×C₂₃	—	4	2	no	—
146	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
147	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
187	C₂×C₄²×C₂₃	—	2	4	no	—
188	C₂×C₄²×C₂₃	—	4	2	no	—
189	C₂×C₄²×C₂₃	—	4	2	no	—
190	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
191	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
192	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
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	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
201	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
207	C₂₃×#95	C₂³	1	1	yes	characteristic
208	C₂₃×#95	C₂³	1	1	yes	characteristic
209	C₂₃×#95	C₂³	1	1	yes	characteristic
210	C₂₃×#95	C₂³	1	1	yes	characteristic
211	C₂₃×#95	C₂³	1	1	yes	characteristic
212	C₂₃×#95	C₂³	1	1	yes	characteristic
213	C₂₃×#95	C₂³	1	1	yes	characteristic
214	C₂₃×#95	C₂³	1	1	yes	characteristic
215	C₂₃×#95	C₂³	1	2	yes	—
216	C₂₃×#95	C₂³	1	2	yes	—
217	C₂₃×#95	C₂³	1	2	yes	—
218	C₂₃×#95	C₂³	1	2	yes	—
219	C₂₃×#95	C₂³	1	2	yes	—
220	C₂₃×#95	C₂³	1	2	yes	—
221	C₂₃×#95	C₂³	1	2	yes	—
222	C₂₃×#95	C₂³	1	2	yes	—
223	C₂₃×#95	C₂³	1	2	yes	—
224	C₂₃×#95	C₂³	1	2	yes	—
225	C₂₃×#95	C₂³	1	2	yes	—
226	C₂₃×#95	C₂³	1	2	yes	—
227	C₂₃×#95	C₂³	1	2	yes	—
228	C₂₃×#95	C₂³	1	2	yes	—
229	C₂₃×#95	C₂³	1	2	yes	—
230	C₂₃×#95	C₂³	1	2	yes	—
231	C₂₃×#95	C₂³	1	2	yes	—
232	C₂₃×#95	C₂³	1	2	yes	—
233	C₂₃×#95	C₂³	1	2	yes	—
234	C₂₃×#95	C₂³	1	2	yes	—
235	C₂₃×#95	C₂³	1	2	yes	—
236	C₂₃×#95	C₂³	1	2	yes	—
237	C₂₃×#95	C₂³	1	2	yes	—
238	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
239	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₂₃	—	2	2	no	—
241	C₂×Q₈×C₂₃	—	2	2	no	—
242	C₂×Q₈×C₂₃	—	2	2	no	—
243	C₂×Q₈×C₂₃	—	2	2	no	—
244	C₂×Q₈×C₂₃	—	2	2	no	—
245	C₂×Q₈×C₂₃	—	2	2	no	—
246	C₂×D₄×C₂₃	—	2	4	no	—
247	C₂×D₄×C₂₃	—	2	4	no	—
248	C₂×D₄×C₂₃	—	2	4	no	—
249	C₂×D₄×C₂₃	—	2	2	no	—
250	C₂×D₄×C₂₃	—	2	2	no	—
251	C₂×D₄×C₂₃	—	2	2	no	—
252	C₂²×C₄×C₂₃	—	2	2	no	—
253	C₂²×C₄×C₂₃	—	2	2	no	—
254	C₂²×C₄×C₂₃	—	2	2	no	—
255	C₂²×C₄×C₂₃	—	2	2	no	—
256	C₂²×C₄×C₂₃	—	2	2	no	—
257	C₂²×C₄×C₂₃	—	2	2	no	—
258	C₂²×C₄×C₂₃	—	2	2	no	—
259	C₂²×C₄×C₂₃	—	2	2	no	—
260	C₂²×C₄×C₂₃	—	2	2	no	—
261	C₂²×C₄×C₂₃	—	2	2	no	—
262	C₂²×C₄×C₂₃	—	2	2	no	—
263	C₂²×C₄×C₂₃	—	2	2	no	—
264	C₂²×C₄×C₂₃	—	2	4	no	—
265	C₂²×C₄×C₂₃	—	4	1	no	—
266	C₂²×C₄×C₂₃	—	4	1	no	—
267	C₂²×C₄×C₂₃	—	4	1	no	—
268	C₂²×C₄×C₂₃	—	4	1	no	—
269	C₂²×C₄×C₂₃	—	4	1	no	—
270	C₂²×C₄×C₂₃	—	4	1	no	—
271	C₂²×C₄×C₂₃	—	4	1	no	—
272	C₂²×C₄×C₂₃	—	4	2	no	—
273	C₂²×C₄×C₂₃	—	4	2	no	—
274	C₂²×C₄×C₂₃	#41	1	4	yes	—
275	C₂²×C₄×C₂₃	#41	1	4	yes	—
276	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
297	C₄⋊C₄×C₂₃	—	2	2	no	—
298	C₄⋊C₄×C₂₃	—	2	2	no	—
299	C₄⋊C₄×C₂₃	—	2	2	no	—
300	C₄⋊C₄×C₂₃	—	2	2	no	—
301	C₄⋊C₄×C₂₃	—	2	2	no	—
302	C₄⋊C₄×C₂₃	—	2	2	no	—
303	C₄⋊C₄×C₂₃	—	2	2	no	—
304	C₄⋊C₄×C₂₃	—	2	4	no	—
305	C₄⋊C₄×C₂₃	—	2	2	no	—
306	C₄⋊C₄×C₂₃	—	2	4	no	—
307	C₄⋊C₄×C₂₃	—	2	2	no	—
308	C₄⋊C₄×C₂₃	—	2	2	no	—
309	C₄⋊C₄×C₂₃	—	2	2	no	—
310	C₄⋊C₄×C₂₃	—	2	4	no	—
311	C₄⋊C₄×C₂₃	—	2	4	no	—
312	C₄⋊C₄×C₂₃	—	2	4	no	—
313	C₄⋊C₄×C₂₃	—	2	4	no	—
314	C₄⋊C₄×C₂₃	—	2	2	no	—
315	C₄⋊C₄×C₂₃	—	4	2	no	—
316	C₄⋊C₄×C₂₃	—	4	2	no	—
317	C₄⋊C₄×C₂₃	—	4	2	no	—
318	C₄⋊C₄×C₂₃	—	4	2	no	—
319	C₄⋊C₄×C₂₃	—	4	2	no	—
320	C₄⋊C₄×C₂₃	#41	1	4	yes	—
321	C₂²⋊C₄×C₂₃	—	2	4	no	—
322	C₂²⋊C₄×C₂₃	—	2	4	no	—
323	C₂²⋊C₄×C₂₃	—	2	4	no	—
324	C₂²⋊C₄×C₂₃	—	2	4	no	—
325	C₂²⋊C₄×C₂₃	—	2	4	no	—
326	C₂²⋊C₄×C₂₃	—	2	4	no	—
327	C₂²⋊C₄×C₂₃	—	2	4	no	—
328	C₂²⋊C₄×C₂₃	—	2	4	no	—
329	C₂²⋊C₄×C₂₃	—	2	4	no	—
330	C₂²⋊C₄×C₂₃	—	2	4	no	—
331	C₂²⋊C₄×C₂₃	—	4	2	no	—
332	C₂²⋊C₄×C₂₃	—	4	2	no	—
333	C₂²⋊C₄×C₂₃	—	4	2	no	—
334	C₂²⋊C₄×C₂₃	—	4	2	no	—
335	C₂²⋊C₄×C₂₃	—	4	2	no	—
336	C₄²×C₂₃	—	2	2	no	—
337	C₄²×C₂₃	—	2	2	no	—
338	C₄²×C₂₃	—	2	2	no	—
339	C₄²×C₂₃	—	2	4	no	—
340	C₄²×C₂₃	—	2	4	no	—
341	C₄²×C₂₃	—	2	4	no	—
342	C₄²×C₂₃	—	2	2	no	—
343	C₄²×C₂₃	—	2	2	no	—
344	C₄²×C₂₃	—	2	2	no	—
345	C₄²×C₂₃	—	2	2	no	—
346	C₄²×C₂₃	—	4	1	no	—
347	C₄²×C₂₃	—	4	1	no	—
348	C₄²×C₂₃	—	4	1	no	—
349	C₄²×C₂₃	—	4	1	no	—
350	C₄²×C₂₃	—	4	2	no	—
351	C₄²×C₂₃	—	4	2	no	—
352	C₄²×C₂₃	#41	1	4	yes	—
353	#36605	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
354	C₂³×C₂₃	—	2	1	no	—
355	C₂³×C₂₃	—	2	1	no	—
356	C₂³×C₂₃	—	2	1	no	—
357	C₂³×C₂₃	—	2	1	no	—
358	C₂³×C₂₃	—	2	2	no	—
359	C₂³×C₂₃	—	2	2	no	—
360	C₂³×C₂₃	—	2	2	no	—
361	C₂³×C₂₃	—	2	2	no	—
362	C₂³×C₂₃	—	2	2	no	—
363	C₂³×C₂₃	—	2	2	no	—
364	C₂³×C₂₃	—	2	2	no	—
365	C₂³×C₂₃	C₂×#41	1	2	yes	—
366	C₂³×C₂₃	C₂×#41	1	2	yes	—
367	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
368	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
369	Q₈×C₂₃	—	4	4	no	—
370	Q₈×C₂₃	—	4	4	no	—
371	D₄×C₂₃	—	4	8	no	—
372	D₄×C₂₃	—	4	4	no	—
373	C₂×C₄×C₂₃	—	2	8	no	—
374	C₂×C₄×C₂₃	—	2	1	no	—
375	C₂×C₄×C₂₃	—	2	1	no	—
376	C₂×C₄×C₂₃	—	2	1	no	—
377	C₂×C₄×C₂₃	—	2	1	no	—
378	C₂×C₄×C₂₃	—	2	1	no	—
379	C₂×C₄×C₂₃	—	2	1	no	—
380	C₂×C₄×C₂₃	—	2	1	no	—
381	C₂×C₄×C₂₃	—	2	1	no	—
382	C₂×C₄×C₂₃	—	2	1	no	—
383	C₂×C₄×C₂₃	—	2	1	no	—
384	C₂×C₄×C₂₃	—	2	1	no	—
385	C₂×C₄×C₂₃	—	2	1	no	—
386	C₂×C₄×C₂₃	—	2	1	no	—
387	C₂×C₄×C₂₃	—	2	1	no	—
388	C₂×C₄×C₂₃	—	2	1	no	—
389	C₂×C₄×C₂₃	—	2	1	no	—
390	C₂×C₄×C₂₃	—	2	8	no	—
391	C₂×C₄×C₂₃	—	2	1	no	—
392	C₂×C₄×C₂₃	—	2	2	no	—
393	C₂×C₄×C₂₃	—	2	2	no	—
394	C₂×C₄×C₂₃	—	2	2	no	—
395	C₂×C₄×C₂₃	—	2	2	no	—
396	C₂×C₄×C₂₃	—	2	2	no	—
397	C₂×C₄×C₂₃	—	2	2	no	—
398	C₂×C₄×C₂₃	—	2	2	no	—
399	C₂×C₄×C₂₃	—	2	2	no	—
400	C₂×C₄×C₂₃	—	2	2	no	—
401	C₂×C₄×C₂₃	—	2	2	no	—
402	C₂×C₄×C₂₃	—	2	2	no	—
403	C₂×C₄×C₂₃	—	2	2	no	—
404	C₂×C₄×C₂₃	—	2	2	no	—
405	C₂×C₄×C₂₃	—	2	2	no	—
406	C₂×C₄×C₂₃	—	2	1	no	—
407	C₂×C₄×C₂₃	—	2	1	no	—
408	C₂×C₄×C₂₃	—	2	1	no	—
409	C₂×C₄×C₂₃	—	2	1	no	—
410	C₂×C₄×C₂₃	—	2	1	no	—
411	C₂×C₄×C₂₃	—	2	1	no	—
412	C₂×C₄×C₂₃	—	2	1	no	—
413	C₂×C₄×C₂₃	—	2	1	no	—
414	C₂×C₄×C₂₃	—	2	2	no	—
415	C₂×C₄×C₂₃	—	2	2	no	—
416	C₂×C₄×C₂₃	—	2	2	no	—
417	C₂×C₄×C₂₃	—	2	1	no	—
418	C₂×C₄×C₂₃	—	2	1	no	—
419	C₂×C₄×C₂₃	—	2	1	no	—
420	C₂×C₄×C₂₃	—	2	2	no	—
421	C₂×C₄×C₂₃	—	2	2	no	—
422	C₂×C₄×C₂₃	—	2	2	no	—
423	C₂×C₄×C₂₃	—	2	1	no	—
424	C₂×C₄×C₂₃	—	2	1	no	—
425	C₂×C₄×C₂₃	—	2	2	no	—
426	C₂×C₄×C₂₃	—	2	1	no	—
427	C₂×C₄×C₂₃	—	4	4	no	—
428	C₂×C₄×C₂₃	—	4	4	no	—
429	C₂×C₄×C₂₃	—	4	4	no	—
430	C₂×C₄×C₂₃	—	4	4	no	—
431	C₂×C₄×C₂₃	—	4	4	no	—
432	C₂×C₄×C₂₃	—	8	4	no	—
433	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
434	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
435	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
436	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
437	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
438	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
439	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
440	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
441	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
442	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
443	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
444	#2857	C₂×C₂₃	1	1	yes	characteristic, complemented
445	#2850	C₂×C₂₃	1	1	yes	characteristic
446	#2850	C₂×C₂₃	1	1	yes	characteristic
447	#2594	C₂×C₂₃	1	2	yes	complemented
448	#2579	C₂×C₂₃	1	2	yes	complemented
449	#2573	C₂×C₂₃	1	2	yes	complemented
450	#2570	C₂×C₂₃	1	1	yes	characteristic, complemented
451	#2545	C₂×C₂₃	1	1	yes	characteristic, complemented
452	#2525	C₂×C₂₃	1	2	yes	complemented
453	#2514	C₂×C₂₃	1	1	yes	characteristic, complemented
454	#2512	C₂×C₂₃	1	1	yes	characteristic, complemented
455	#2510	C₂×C₂₃	1	2	yes	complemented
456	#2481	C₂×C₂₃	1	2	yes	complemented
457	#2447	C₂×C₂₃	1	1	yes	characteristic, complemented
458	#2446	C₂×C₂₃	1	1	yes	characteristic, complemented
459	#2373	C₂×C₂₃	1	2	yes	complemented
460	#2367	C₂×C₂₃	1	1	yes	characteristic, complemented
461	#2356	C₂×C₂₃	1	1	yes	characteristic, complemented
462	#2353	C₂×C₂₃	1	2	yes	complemented
463	C₄×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
464	C₄×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
465	C₄×#121	C₂×C₂₃	1	1	yes	characteristic
466	C₂×C₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
467	C₂²×C₂₃	—	2	2	no	—
468	C₂²×C₂₃	—	2	2	no	—
469	C₂²×C₂₃	—	2	2	no	—
470	C₂²×C₂₃	—	2	2	no	—
471	C₂²×C₂₃	—	2	2	no	—
472	C₂²×C₂₃	—	2	2	no	—
473	C₂²×C₂₃	—	4	2	no	—
474	C₂²×C₂₃	—	4	2	no	—
475	C₂²×C₂₃	—	4	2	no	—
476	C₂²×C₂₃	—	4	2	no	—
477	C₂²×C₂₃	—	4	2	no	—
478	C₂²×C₂₃	—	4	2	no	—
479	C₂²×C₂₃	—	4	2	no	—
480	C₂²×C₂₃	#556	1	4	yes	—
481	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
482	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
483	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
484	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
485	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
486	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
487	C₂²×C₂₃	#585	1	1	yes	characteristic
488	C₄×C₂₃	—	2	2	no	—
489	C₄×C₂₃	—	2	2	no	—
490	C₄×C₂₃	—	2	2	no	—
491	C₄×C₂₃	—	2	2	no	—
492	C₄×C₂₃	—	2	2	no	—
493	C₄×C₂₃	—	2	2	no	—
494	C₄×C₂₃	—	2	2	no	—
495	C₄×C₂₃	—	2	2	no	—
496	C₄×C₂₃	—	4	2	no	—
497	C₄×C₂₃	—	4	2	no	—
498	C₄×C₂₃	—	4	2	no	—
499	C₄×C₂₃	—	4	2	no	—
500	C₄×C₂₃	—	4	2	no	—
501	C₄×C₂₃	—	4	2	no	—
502	C₄×C₂₃	—	4	1	no	—
503	C₄×C₂₃	—	4	1	no	—
504	C₄×C₂₃	—	4	1	no	—
505	C₄×C₂₃	—	4	2	no	—
506	C₄×C₂₃	—	4	1	no	—
507	C₄×C₂₃	—	4	1	no	—
508	C₄×C₂₃	#553	1	4	yes	—
509	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
510	C₂×#126	C₂²×C₂₃	1	2	yes	—
511	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
512	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
513	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
514	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
515	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
516	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
517	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
518	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
519	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
520	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
521	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
522	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
523	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
524	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
525	#401	C₂²×C₂₃	1	2	yes	—
526	#400	C₂²×C₂₃	1	2	yes	—
527	#400	C₂²×C₂₃	1	2	yes	—
528	#400	C₂²×C₂₃	1	2	yes	—
529	#398	C₂²×C₂₃	1	2	yes	—
530	#398	C₂²×C₂₃	1	2	yes	—
531	#397	C₂²×C₂₃	1	2	yes	—
532	#397	C₂²×C₂₃	1	2	yes	—
533	#397	C₂²×C₂₃	1	2	yes	—
534	#396	C₂²×C₂₃	1	2	yes	—
535	#396	C₂²×C₂₃	1	2	yes	—
536	#396	C₂²×C₂₃	1	2	yes	—
537	#391	C₂²×C₂₃	1	1	yes	characteristic
538	#391	C₂²×C₂₃	1	1	yes	characteristic
539	#391	C₂²×C₂₃	1	1	yes	characteristic
540	#391	C₂²×C₂₃	1	1	yes	characteristic
541	#391	C₂²×C₂₃	1	1	yes	characteristic
542	#391	C₂²×C₂₃	1	1	yes	characteristic
543	#390	C₂²×C₂₃	1	1	yes	characteristic
544	#390	C₂²×C₂₃	1	1	yes	characteristic
545	#390	C₂²×C₂₃	1	1	yes	characteristic
546	#389	C₂²×C₂₃	1	1	yes	characteristic
547	#389	C₂²×C₂₃	1	1	yes	characteristic
548	#389	C₂²×C₂₃	1	2	yes	—
549	#389	C₂²×C₂₃	1	2	yes	—
550	#389	C₂²×C₂₃	1	1	yes	characteristic
551	#388	C₂²×C₂₃	1	2	yes	—
552	#388	C₂²×C₂₃	1	2	yes	—
553	#388	C₂²×C₂₃	1	2	yes	—
554	#388	C₂²×C₂₃	1	2	yes	—
555	#388	C₂²×C₂₃	1	2	yes	—
556	#388	C₂²×C₂₃	1	2	yes	—
557	#388	C₂²×C₂₃	1	2	yes	—
558	#388	C₂²×C₂₃	1	2	yes	—
559	#388	C₂²×C₂₃	1	2	yes	—
560	#388	C₂²×C₂₃	1	2	yes	—
561	#387	C₂²×C₂₃	1	2	yes	—
562	#387	C₂²×C₂₃	1	2	yes	—
563	#387	C₂²×C₂₃	1	2	yes	—
564	#387	C₂²×C₂₃	1	2	yes	—
565	#387	C₂²×C₂₃	1	2	yes	—
566	#387	C₂²×C₂₃	1	2	yes	—
567	#387	C₂²×C₂₃	1	2	yes	—
568	#387	C₂²×C₂₃	1	2	yes	—
569	#387	C₂²×C₂₃	1	2	yes	—
570	#386	C₂²×C₂₃	1	2	yes	—
571	#386	C₂²×C₂₃	1	2	yes	—
572	#386	C₂²×C₂₃	1	2	yes	—
573	#386	C₂²×C₂₃	1	2	yes	—
574	#386	C₂²×C₂₃	1	2	yes	—
575	#385	C₂²×C₂₃	1	2	yes	—
576	#385	C₂²×C₂₃	1	2	yes	—
577	#385	C₂²×C₂₃	1	2	yes	—
578	#385	C₂²×C₂₃	1	2	yes	—
579	#384	C₂²×C₂₃	1	1	yes	characteristic
580	#383	C₂²×C₂₃	1	2	yes	—
581	#383	C₂²×C₂₃	1	2	yes	—
582	#382	C₂²×C₂₃	1	1	yes	characteristic
583	#382	C₂²×C₂₃	1	1	yes	characteristic
584	#381	C₂²×C₂₃	1	2	yes	—
585	#380	C₂²×C₂₃	1	2	yes	—
586	#380	C₂²×C₂₃	1	2	yes	—
587	#380	C₂²×C₂₃	1	1	yes	characteristic
588	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
589	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
590	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
591	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
592	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
593	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
594	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
595	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
596	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
597	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
598	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
599	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
600	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
601	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
602	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
603	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
604	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
605	#376	C₂²×C₂₃	1	2	yes	—
606	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
607	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
608	C₂×C₂₃	—	2	4	no	—
609	C₂×C₂₃	—	8	2	no	—
610	C₂×C₂₃	#3444	1	1	yes	characteristic
611	C₂×C₂₃	C₂×#553	1	1	yes	characteristic
612	C₂×C₂₃	C₂×#556	1	1	yes	characteristic
613	C₂×C₂₃	#3480	1	1	yes	characteristic
614	C₂×C₂₃	#3495	1	1	yes	characteristic
615	C₂×C₂₃	#3505	1	1	yes	characteristic
616	C₂×C₂₃	#3520	1	1	yes	characteristic
617	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
618	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
619	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
620	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
621	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
622	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
623	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
624	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
626	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
627	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
628	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
629	C₄⋊Q₈	—	4	2	no	—
630	#126	—	2	8	no	—
631	#124	—	2	4	no	—
632	#124	—	4	2	no	—
633	C₂²⋊Q₈	—	2	4	no	—
634	C₂²⋊Q₈	—	2	4	no	—
635	#121	—	2	4	no	—
636	C₄×Q₈	—	2	4	no	—
637	C₄×Q₈	—	4	2	no	—
638	C₄×D₄	—	2	8	no	—
639	C₄×D₄	—	4	2	no	—
640	C₂×C₄⋊C₄	—	2	4	no	—
641	C₂×C₄⋊C₄	—	2	4	no	—
642	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
666	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
681	C₂×C₄²	—	2	4	no	—
682	C₂×C₄²	—	4	2	no	—
683	C₂×C₄²	—	4	2	no	—
684	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
685	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
687	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
688	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
690	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
695	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
696	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
701	#95	C₂³×C₂₃	1	1	yes	characteristic
702	#95	C₂³×C₂₃	1	1	yes	characteristic
703	#95	C₂³×C₂₃	1	1	yes	characteristic
704	#95	C₂³×C₂₃	1	1	yes	characteristic
705	#95	C₂³×C₂₃	1	1	yes	characteristic
706	#95	C₂³×C₂₃	1	1	yes	characteristic
707	#95	C₂³×C₂₃	1	1	yes	characteristic
708	#95	C₂³×C₂₃	1	1	yes	characteristic
709	#95	C₂³×C₂₃	1	2	yes	—
710	#95	C₂³×C₂₃	1	2	yes	—
711	#95	C₂³×C₂₃	1	2	yes	—
712	#95	C₂³×C₂₃	1	2	yes	—
713	#95	C₂³×C₂₃	1	2	yes	—
714	#95	C₂³×C₂₃	1	2	yes	—
715	#95	C₂³×C₂₃	1	2	yes	—
716	#95	C₂³×C₂₃	1	2	yes	—
717	#95	C₂³×C₂₃	1	2	yes	—
718	#95	C₂³×C₂₃	1	2	yes	—
719	#95	C₂³×C₂₃	1	2	yes	—
720	#95	C₂³×C₂₃	1	2	yes	—
721	#95	C₂³×C₂₃	1	2	yes	—
722	#95	C₂³×C₂₃	1	2	yes	—
723	#95	C₂³×C₂₃	1	2	yes	—
724	#95	C₂³×C₂₃	1	2	yes	—
725	#95	C₂³×C₂₃	1	2	yes	—
726	#95	C₂³×C₂₃	1	2	yes	—
727	#95	C₂³×C₂₃	1	2	yes	—
728	#95	C₂³×C₂₃	1	2	yes	—
729	#95	C₂³×C₂₃	1	2	yes	—
730	#95	C₂³×C₂₃	1	2	yes	—
731	#95	C₂³×C₂₃	1	2	yes	—
732	C₂₃	#36605	1	1	yes	characteristic, direct product factor, Sylow
733	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
734	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
735	C₂×Q₈	—	2	2	no	—
736	C₂×Q₈	—	2	2	no	—
737	C₂×Q₈	—	2	2	no	—
738	C₂×Q₈	—	2	2	no	—
739	C₂×Q₈	—	2	2	no	—
740	C₂×Q₈	—	2	2	no	—
741	C₂×D₄	—	2	4	no	—
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	4	no	—
760	C₂²×C₄	—	4	1	no	—
761	C₂²×C₄	—	4	1	no	—
762	C₂²×C₄	—	4	1	no	—
763	C₂²×C₄	—	4	1	no	—
764	C₂²×C₄	—	4	1	no	—
765	C₂²×C₄	—	4	1	no	—
766	C₂²×C₄	—	4	1	no	—
767	C₂²×C₄	—	4	2	no	—
768	C₂²×C₄	—	4	2	no	—
769	C₂²×C₄	#41×C₂₃	1	4	yes	—
770	C₂²×C₄	#41×C₂₃	1	4	yes	—
771	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	4	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	4	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	4	no	—
806	C₄⋊C₄	—	2	4	no	—
807	C₄⋊C₄	—	2	4	no	—
808	C₄⋊C₄	—	2	4	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	4	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	2	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	#41×C₂₃	1	4	yes	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	—	2	4	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	4	2	no	—
827	C₂²⋊C₄	—	4	2	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	4	no	—
835	C₄²	—	2	4	no	—
836	C₄²	—	2	4	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	4	1	no	—
842	C₄²	—	4	1	no	—
843	C₄²	—	4	1	no	—
844	C₄²	—	4	1	no	—
845	C₄²	—	4	2	no	—
846	C₄²	—	4	2	no	—
847	C₄²	#41×C₂₃	1	4	yes	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	C₂×#41×C₂₃	1	2	yes	—
860	C₂³	C₂×#41×C₂₃	1	2	yes	—
861	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
862	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
863	Q₈	—	4	4	no	—
864	Q₈	—	4	4	no	—
865	D₄	—	4	8	no	—
866	D₄	—	4	4	no	—
867	C₂×C₄	—	2	8	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	8	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	4	4	no	—
922	C₂×C₄	—	4	4	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	4	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	8	4	no	—
927	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
928	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
929	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
930	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
931	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
932	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
933	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
934	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
935	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
936	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
937	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	C₂₃×#556	1	4	yes	—
952	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
953	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
954	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
955	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
956	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
957	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
958	C₂²	C₂₃×#585	1	1	yes	characteristic
959	C₄	—	2	2	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	2	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	2	no	—
966	C₄	—	2	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	1	no	—
974	C₄	—	4	1	no	—
975	C₄	—	4	1	no	—
976	C₄	—	4	2	no	—
977	C₄	—	4	1	no	—
978	C₄	—	4	1	no	—
979	C₄	C₂₃×#553	1	4	yes	—
980	C₂	—	2	4	no	—
981	C₂	—	8	2	no	—
982	C₂	C₂₃×#3444	1	1	yes	characteristic
983	C₂	C₂×C₂₃×#553	1	1	yes	characteristic
984	C₂	C₂×C₂₃×#556	1	1	yes	characteristic
985	C₂	C₂₃×#3480	1	1	yes	characteristic
986	C₂	C₂₃×#3495	1	1	yes	characteristic
987	C₂	C₂₃×#3505	1	1	yes	characteristic
988	C₂	C₂₃×#3520	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. C₂₃×#2857	C₂	semidirect
4. C₂₃×#2594	C₂	semidirect
5. C₂₃×#2579	C₂	semidirect
6. C₂₃×#2573	C₂	semidirect
7. C₂₃×#2570	C₂	semidirect
8. C₂₃×#2545	C₂	semidirect
9. C₂₃×#2525	C₂	semidirect
10. C₂₃×#2514	C₂	semidirect
11. C₂₃×#2512	C₂	semidirect
12. C₂₃×#2510	C₂	semidirect
13. C₂₃×#2481	C₂	semidirect
14. C₂₃×#2447	C₂	semidirect
15. C₂₃×#2446	C₂	semidirect
16. C₂₃×#2373	C₂	semidirect
17. C₂₃×#2367	C₂	semidirect
18. C₂₃×#2356	C₂	semidirect
19. C₂₃×#2353	C₂	semidirect
20. C₄×C₂₃×C₂²⋊Q₈	C₂	semidirect
21. C₄×C₂₃×C₂²⋊Q₈	C₂	semidirect
23. C₂×C₄×C₄⋊C₄×C₂₃	C₂	semidirect
353. #36605	C₂₃	direct (N × H)
444. #2857	C₂×C₂₃	semidirect
447. #2594	C₂×C₂₃	semidirect
448. #2579	C₂×C₂₃	semidirect
449. #2573	C₂×C₂₃	semidirect
450. #2570	C₂×C₂₃	semidirect
451. #2545	C₂×C₂₃	semidirect
452. #2525	C₂×C₂₃	semidirect
453. #2514	C₂×C₂₃	semidirect
454. #2512	C₂×C₂₃	semidirect
455. #2510	C₂×C₂₃	semidirect
456. #2481	C₂×C₂₃	semidirect
457. #2447	C₂×C₂₃	semidirect
458. #2446	C₂×C₂₃	semidirect
459. #2373	C₂×C₂₃	semidirect
460. #2367	C₂×C₂₃	semidirect
461. #2356	C₂×C₂₃	semidirect
462. #2353	C₂×C₂₃	semidirect
463. C₄×C₂²⋊Q₈	C₂×C₂₃	semidirect
464. C₄×C₂²⋊Q₈	C₂×C₂₃	semidirect
466. C₂×C₄×C₄⋊C₄	C₂×C₂₃	semidirect
732. C₂₃	#36605	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×#2857	2
C₂₃×#2850	2
C₂₃×#2594	2
C₂₃×#2579	2
C₂₃×#2573	2
C₂₃×#2570	2
C₂₃×#2545	2
C₂₃×#2525	2
C₂₃×#2514	2
C₂₃×#2512	2
C₂₃×#2510	2
C₂₃×#2481	2
C₂₃×#2447	2
C₂₃×#2446	2
C₂₃×#2373	2
C₂₃×#2367	2
C₂₃×#2356	2
C₂₃×#2353	2
C₄×C₂₃×C₂²⋊Q₈	2
C₄×C₂₃×#121	2
C₂×C₄×C₄⋊C₄×C₂₃	2
#36605	23

Subgroups — C23×#36605 #19184231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36605 #19184231