Subgroups — C₂₃×#59988 #19207614

Order 5888.

2024 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2804	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#2778	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2684	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2595	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2527	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2527	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2492	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2477	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2477	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2472	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2459	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2432	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2404	C₂	1	1	yes	maximal, characteristic
14	C₂₃×#2372	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2372	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2358	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2342	C₂	1	2	yes	maximal, complemented
18	C₂₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2290	C₂	1	2	yes	maximal, complemented
20	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#124	C₂²	1	2	yes	—
24	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₂₃×#120	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#120	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
29	C₂×C₂₃×#117	C₂²	1	2	yes	—
30	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
34	C₂₃×#401	C₂²	1	2	yes	complemented
35	C₂₃×#400	C₂²	1	2	yes	complemented
36	C₂₃×#400	C₂²	1	2	yes	complemented
37	C₂₃×#400	C₂²	1	2	yes	complemented
38	C₂₃×#397	C₂²	1	2	yes	—
39	C₂₃×#397	C₂²	1	2	yes	—
40	C₂₃×#397	C₂²	1	2	yes	complemented
41	C₂₃×#394	C₂²	1	2	yes	—
42	C₂₃×#394	C₂²	1	2	yes	—
43	C₂₃×#394	C₂²	1	2	yes	—
44	C₂₃×#394	C₂²	1	2	yes	complemented
45	C₂₃×#393	C₂²	1	2	yes	—
46	C₂₃×#393	C₂²	1	2	yes	—
47	C₂₃×#393	C₂²	1	2	yes	—
48	C₂₃×#393	C₂²	1	2	yes	complemented
49	C₂₃×#392	C₂²	1	2	yes	—
50	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#391	C₂²	1	2	yes	complemented
52	C₂₃×#391	C₂²	1	2	yes	complemented
53	C₂₃×#391	C₂²	1	2	yes	complemented
54	C₂₃×#391	C₂²	1	2	yes	complemented
55	C₂₃×#391	C₂²	1	2	yes	complemented
56	C₂₃×#390	C₂²	1	1	yes	characteristic
57	C₂₃×#390	C₂²	1	2	yes	—
58	C₂₃×#388	C₂²	1	2	yes	—
59	C₂₃×#388	C₂²	1	2	yes	—
60	C₂₃×#388	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×#388	C₂²	1	2	yes	—
65	C₂₃×#388	C₂²	1	2	yes	—
66	C₂₃×#388	C₂²	1	2	yes	complemented
67	C₂₃×#388	C₂²	1	2	yes	complemented
68	C₂₃×#388	C₂²	1	2	yes	complemented
69	C₂₃×#388	C₂²	1	2	yes	complemented
70	C₂₃×#387	C₂²	1	2	yes	complemented
71	C₂₃×#387	C₂²	1	2	yes	complemented
72	C₂₃×#387	C₂²	1	2	yes	complemented
73	C₂₃×#387	C₂²	1	2	yes	complemented
74	C₂₃×#387	C₂²	1	2	yes	complemented
75	C₂₃×#386	C₂²	1	2	yes	—
76	C₂₃×#386	C₂²	1	2	yes	—
77	C₂₃×#386	C₂²	1	1	yes	characteristic
78	C₂₃×#386	C₂²	1	1	yes	characteristic
79	C₂₃×#386	C₂²	1	2	yes	—
80	C₂₃×#386	C₂²	1	1	yes	characteristic
81	C₂₃×#386	C₂²	1	2	yes	—
82	C₂₃×#386	C₂²	1	2	yes	—
83	C₂₃×#386	C₂²	1	2	yes	—
84	C₂₃×#386	C₂²	1	1	yes	characteristic
85	C₂₃×#386	C₂²	1	1	yes	characteristic, complemented
86	C₂₃×#386	C₂²	1	1	yes	characteristic, complemented
87	C₂₃×#385	C₂²	1	2	yes	—
88	C₂₃×#385	C₂²	1	2	yes	—
89	C₂₃×#385	C₂²	1	2	yes	—
90	C₂₃×#385	C₂²	1	2	yes	complemented
91	C₂₃×#385	C₂²	1	2	yes	complemented
92	C₂₃×#381	C₂²	1	1	yes	characteristic
93	C₂₃×#381	C₂²	1	2	yes	—
94	C₂₃×#380	C₂²	1	2	yes	—
95	C₂₃×#379	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
97	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
105	C₂₃×#376	C₂²	1	2	yes	complemented
106	C₂₃×#376	C₂²	1	2	yes	complemented
107	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
108	C₂×#41×C₂₃	—	2	4	no	—
109	C₂×#41×C₂₃	—	4	2	no	—
110	C₂×#41×C₂₃	—	4	2	no	—
111	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
112	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
113	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
116	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
118	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
123	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
127	C₂₃×C₄⋊Q₈	—	4	2	no	—
128	C₂₃×#124	—	2	4	no	—
129	C₂₃×#124	—	2	8	no	—
130	C₂₃×C₂²⋊Q₈	—	4	4	no	—
131	C₂₃×C₂²⋊Q₈	—	4	2	no	—
132	C₂₃×#120	—	2	4	no	—
133	C₂₃×#120	—	4	2	no	—
134	C₄×D₄×C₂₃	—	2	8	no	—
135	C₂₃×#117	—	4	4	no	—
136	C₂₃×#117	—	4	2	no	—
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	2	yes	—
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
148	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
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	2	yes	—
154	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
159	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
175	C₂×C₄²×C₂₃	—	4	2	no	—
176	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
177	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
180	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
181	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
182	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
184	C₂×C₄²×C₂₃	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	2	yes	—
193	C₂₃×#95	C₂³	1	2	yes	—
194	C₂₃×#95	C₂³	1	2	yes	—
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	C₂₃×#95	C₂³	1	2	yes	—
205	C₂₃×#95	C₂³	1	2	yes	—
206	C₂₃×#95	C₂³	1	2	yes	—
207	C₂₃×#95	C₂³	1	2	yes	—
208	C₂₃×#95	C₂³	1	2	yes	—
209	C₂₃×#95	C₂³	1	2	yes	—
210	C₂⁴×C₂₃	—	2	4	no	—
211	C₂⁴×C₂₃	—	2	2	no	—
212	C₂⁴×C₂₃	—	4	1	no	—
213	C₂⁴×C₂₃	—	4	2	no	—
214	C₂⁴×C₂₃	—	4	1	no	—
215	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
216	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
217	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
218	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
219	#41×C₂₃	—	4	16	no	—
220	C₂×Q₈×C₂₃	—	2	2	no	—
221	C₂×Q₈×C₂₃	—	2	4	no	—
222	C₂×Q₈×C₂₃	—	2	2	no	—
223	C₂×Q₈×C₂₃	—	2	2	no	—
224	C₂×Q₈×C₂₃	—	4	1	no	—
225	C₂×Q₈×C₂₃	—	4	2	no	—
226	C₂×Q₈×C₂₃	—	4	1	no	—
227	C₂×Q₈×C₂₃	—	4	1	no	—
228	C₂×Q₈×C₂₃	—	4	2	no	—
229	C₂×D₄×C₂₃	—	2	4	no	—
230	C₂×D₄×C₂₃	—	2	4	no	—
231	C₂×D₄×C₂₃	—	2	2	no	—
232	C₂×D₄×C₂₃	—	2	2	no	—
233	C₂×D₄×C₂₃	—	2	4	no	—
234	C₂×D₄×C₂₃	—	2	2	no	—
235	C₂×D₄×C₂₃	—	4	2	no	—
236	C₂×D₄×C₂₃	—	4	1	no	—
237	C₂×D₄×C₂₃	—	4	1	no	—
238	C₂×D₄×C₂₃	—	4	1	no	—
239	C₂×D₄×C₂₃	—	4	1	no	—
240	C₂×D₄×C₂₃	—	4	1	no	—
241	C₂×D₄×C₂₃	—	4	2	no	—
242	C₂×D₄×C₂₃	—	4	2	no	—
243	C₂×D₄×C₂₃	#41	1	4	yes	—
244	C₂²×C₄×C₂₃	—	2	2	no	—
245	C₂²×C₄×C₂₃	—	2	2	no	—
246	C₂²×C₄×C₂₃	—	2	2	no	—
247	C₂²×C₄×C₂₃	—	2	4	no	—
248	C₂²×C₄×C₂₃	—	2	2	no	—
249	C₂²×C₄×C₂₃	—	2	4	no	—
250	C₂²×C₄×C₂₃	—	2	4	no	—
251	C₂²×C₄×C₂₃	—	2	2	no	—
252	C₂²×C₄×C₂₃	—	2	2	no	—
253	C₂²×C₄×C₂₃	—	2	2	no	—
254	C₂²×C₄×C₂₃	—	2	4	no	—
255	C₂²×C₄×C₂₃	—	4	1	no	—
256	C₂²×C₄×C₂₃	—	4	1	no	—
257	C₂²×C₄×C₂₃	—	4	2	no	—
258	C₂²×C₄×C₂₃	—	4	2	no	—
259	C₂²×C₄×C₂₃	—	4	1	no	—
260	C₂²×C₄×C₂₃	—	4	1	no	—
261	C₂²×C₄×C₂₃	—	4	1	no	—
262	C₂²×C₄×C₂₃	—	4	2	no	—
263	C₂²×C₄×C₂₃	—	4	2	no	—
264	C₂²×C₄×C₂₃	—	4	2	no	—
265	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
280	C₄⋊C₄×C₂₃	—	2	4	no	—
281	C₄⋊C₄×C₂₃	—	2	4	no	—
282	C₄⋊C₄×C₂₃	—	2	4	no	—
283	C₄⋊C₄×C₂₃	—	2	4	no	—
284	C₄⋊C₄×C₂₃	—	4	2	no	—
285	C₄⋊C₄×C₂₃	—	4	2	no	—
286	C₄⋊C₄×C₂₃	—	4	2	no	—
287	C₄⋊C₄×C₂₃	—	4	1	no	—
288	C₄⋊C₄×C₂₃	—	4	2	no	—
289	C₄⋊C₄×C₂₃	—	4	2	no	—
290	C₂²⋊C₄×C₂₃	—	2	4	no	—
291	C₂²⋊C₄×C₂₃	—	2	2	no	—
292	C₂²⋊C₄×C₂₃	—	2	4	no	—
293	C₂²⋊C₄×C₂₃	—	2	4	no	—
294	C₂²⋊C₄×C₂₃	—	2	4	no	—
295	C₂²⋊C₄×C₂₃	—	2	4	no	—
296	C₂²⋊C₄×C₂₃	—	2	4	no	—
297	C₂²⋊C₄×C₂₃	—	2	4	no	—
298	C₂²⋊C₄×C₂₃	—	2	4	no	—
299	C₂²⋊C₄×C₂₃	—	2	4	no	—
300	C₂²⋊C₄×C₂₃	—	2	4	no	—
301	C₂²⋊C₄×C₂₃	—	2	4	no	—
302	C₂²⋊C₄×C₂₃	—	2	4	no	—
303	C₂²⋊C₄×C₂₃	—	4	2	no	—
304	C₂²⋊C₄×C₂₃	—	4	2	no	—
305	C₂²⋊C₄×C₂₃	—	4	2	no	—
306	C₂²⋊C₄×C₂₃	—	4	2	no	—
307	C₂²⋊C₄×C₂₃	—	4	2	no	—
308	C₂²⋊C₄×C₂₃	—	4	2	no	—
309	C₂²⋊C₄×C₂₃	—	4	2	no	—
310	C₂²⋊C₄×C₂₃	—	4	1	no	—
311	C₂²⋊C₄×C₂₃	—	4	1	no	—
312	C₂²⋊C₄×C₂₃	—	4	1	no	—
313	C₂²⋊C₄×C₂₃	—	4	2	no	—
314	C₂²⋊C₄×C₂₃	—	4	2	no	—
315	C₂²⋊C₄×C₂₃	#41	1	8	yes	complemented
316	C₄²×C₂₃	—	2	4	no	—
317	C₄²×C₂₃	—	2	2	no	—
318	C₄²×C₂₃	—	2	4	no	—
319	C₄²×C₂₃	—	2	4	no	—
320	C₄²×C₂₃	—	4	2	no	—
321	C₄²×C₂₃	—	4	2	no	—
322	C₄²×C₂₃	—	4	2	no	—
323	C₄²×C₂₃	—	4	2	no	—
324	C₄²×C₂₃	—	4	1	no	—
325	#59988	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	—	2	2	no	—
330	C₂³×C₂₃	—	2	2	no	—
331	C₂³×C₂₃	—	2	2	no	—
332	C₂³×C₂₃	—	2	1	no	—
333	C₂³×C₂₃	—	2	1	no	—
334	C₂³×C₂₃	—	2	1	no	—
335	C₂³×C₂₃	—	2	1	no	—
336	C₂³×C₂₃	—	2	2	no	—
337	C₂³×C₂₃	—	2	2	no	—
338	C₂³×C₂₃	—	2	2	no	—
339	C₂³×C₂₃	—	2	2	no	—
340	C₂³×C₂₃	—	2	2	no	—
341	C₂³×C₂₃	—	2	1	no	—
342	C₂³×C₂₃	—	2	1	no	—
343	C₂³×C₂₃	—	2	1	no	—
344	C₂³×C₂₃	—	2	2	no	—
345	C₂³×C₂₃	—	4	8	no	—
346	C₂³×C₂₃	—	4	4	no	—
347	C₂³×C₂₃	—	8	2	no	—
348	C₂³×C₂₃	—	8	4	no	—
349	C₂³×C₂₃	—	8	2	no	—
350	C₂³×C₂₃	C₂×#41	1	2	yes	—
351	C₂³×C₂₃	C₂×#41	1	4	yes	—
352	C₂³×C₂₃	C₂×#41	1	2	yes	—
353	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
354	Q₈×C₂₃	—	4	4	no	—
355	Q₈×C₂₃	—	8	2	no	—
356	Q₈×C₂₃	—	8	4	no	—
357	D₄×C₂₃	—	4	4	no	—
358	D₄×C₂₃	—	4	4	no	—
359	D₄×C₂₃	—	4	8	no	—
360	D₄×C₂₃	—	4	4	no	—
361	D₄×C₂₃	—	8	4	no	—
362	C₂×C₄×C₂₃	—	2	8	no	—
363	C₂×C₄×C₂₃	—	2	2	no	—
364	C₂×C₄×C₂₃	—	2	1	no	—
365	C₂×C₄×C₂₃	—	2	1	no	—
366	C₂×C₄×C₂₃	—	2	2	no	—
367	C₂×C₄×C₂₃	—	2	1	no	—
368	C₂×C₄×C₂₃	—	2	1	no	—
369	C₂×C₄×C₂₃	—	2	2	no	—
370	C₂×C₄×C₂₃	—	2	1	no	—
371	C₂×C₄×C₂₃	—	2	1	no	—
372	C₂×C₄×C₂₃	—	2	2	no	—
373	C₂×C₄×C₂₃	—	2	2	no	—
374	C₂×C₄×C₂₃	—	2	2	no	—
375	C₂×C₄×C₂₃	—	2	2	no	—
376	C₂×C₄×C₂₃	—	2	2	no	—
377	C₂×C₄×C₂₃	—	2	2	no	—
378	C₂×C₄×C₂₃	—	2	2	no	—
379	C₂×C₄×C₂₃	—	2	2	no	—
380	C₂×C₄×C₂₃	—	2	2	no	—
381	C₂×C₄×C₂₃	—	2	2	no	—
382	C₂×C₄×C₂₃	—	2	2	no	—
383	C₂×C₄×C₂₃	—	2	1	no	—
384	C₂×C₄×C₂₃	—	2	2	no	—
385	C₂×C₄×C₂₃	—	2	2	no	—
386	C₂×C₄×C₂₃	—	2	2	no	—
387	C₂×C₄×C₂₃	—	2	2	no	—
388	C₂×C₄×C₂₃	—	2	2	no	—
389	C₂×C₄×C₂₃	—	2	2	no	—
390	C₂×C₄×C₂₃	—	2	1	no	—
391	C₂×C₄×C₂₃	—	2	2	no	—
392	C₂×C₄×C₂₃	—	2	2	no	—
393	C₂×C₄×C₂₃	—	2	1	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	—	4	4	no	—
404	C₂×C₄×C₂₃	—	4	4	no	—
405	C₂×C₄×C₂₃	—	4	8	no	—
406	C₂×C₄×C₂₃	—	4	4	no	—
407	C₂×C₄×C₂₃	—	4	4	no	—
408	C₂×C₄×C₂₃	—	8	4	no	—
409	C₂×C₄×C₂₃	—	8	2	no	—
410	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
411	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
412	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
413	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
414	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
415	#2804	C₂×C₂₃	1	1	yes	characteristic, complemented
416	#2778	C₂×C₂₃	1	2	yes	complemented
417	#2684	C₂×C₂₃	1	1	yes	characteristic, complemented
418	#2595	C₂×C₂₃	1	2	yes	complemented
419	#2527	C₂×C₂₃	1	2	yes	complemented
420	#2527	C₂×C₂₃	1	2	yes	complemented
421	#2492	C₂×C₂₃	1	2	yes	complemented
422	#2477	C₂×C₂₃	1	2	yes	complemented
423	#2477	C₂×C₂₃	1	2	yes	complemented
424	#2472	C₂×C₂₃	1	2	yes	complemented
425	#2459	C₂×C₂₃	1	2	yes	complemented
426	#2432	C₂×C₂₃	1	1	yes	characteristic, complemented
427	#2404	C₂×C₂₃	1	1	yes	characteristic
428	#2372	C₂×C₂₃	1	1	yes	characteristic, complemented
429	#2372	C₂×C₂₃	1	2	yes	complemented
430	#2358	C₂×C₂₃	1	1	yes	characteristic, complemented
431	#2342	C₂×C₂₃	1	2	yes	complemented
432	#2297	C₂×C₂₃	1	1	yes	characteristic, complemented
433	#2290	C₂×C₂₃	1	2	yes	complemented
434	C₂²×C₂₃	—	2	4	no	—
435	C₂²×C₂₃	—	2	4	no	—
436	C₂²×C₂₃	—	2	4	no	—
437	C₂²×C₂₃	—	2	4	no	—
438	C₂²×C₂₃	—	2	2	no	—
439	C₂²×C₂₃	—	2	2	no	—
440	C₂²×C₂₃	—	2	4	no	—
441	C₂²×C₂₃	—	4	2	no	—
442	C₂²×C₂₃	—	4	1	no	—
443	C₂²×C₂₃	—	4	1	no	—
444	C₂²×C₂₃	—	4	2	no	—
445	C₂²×C₂₃	—	4	2	no	—
446	C₂²×C₂₃	—	4	2	no	—
447	C₂²×C₂₃	—	4	2	no	—
448	C₂²×C₂₃	—	4	1	no	—
449	C₂²×C₂₃	—	4	1	no	—
450	C₂²×C₂₃	—	4	2	no	—
451	C₂²×C₂₃	—	4	2	no	—
452	C₂²×C₂₃	—	4	1	no	—
453	C₂²×C₂₃	—	4	1	no	—
454	C₂²×C₂₃	—	4	2	no	—
455	C₂²×C₂₃	—	4	1	no	—
456	C₂²×C₂₃	—	8	8	no	—
457	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
458	C₂²×C₂₃	C₂²×#41	1	2	yes	—
459	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
460	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
461	C₂²×C₂₃	#585	1	2	yes	—
462	C₄×C₂₃	—	2	4	no	—
463	C₄×C₂₃	—	2	2	no	—
464	C₄×C₂₃	—	2	2	no	—
465	C₄×C₂₃	—	2	2	no	—
466	C₄×C₂₃	—	2	4	no	—
467	C₄×C₂₃	—	4	2	no	—
468	C₄×C₂₃	—	4	2	no	—
469	C₄×C₂₃	—	4	2	no	—
470	C₄×C₂₃	—	4	1	no	—
471	C₄×C₂₃	—	4	2	no	—
472	C₄×C₂₃	—	4	2	no	—
473	C₄×C₂₃	—	4	2	no	—
474	C₄×C₂₃	—	4	2	no	—
475	C₄×C₂₃	—	4	2	no	—
476	C₄×C₂₃	—	4	2	no	—
477	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
478	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
479	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
480	C₂×#124	C₂²×C₂₃	1	2	yes	—
481	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
482	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
483	C₂×#120	C₂²×C₂₃	1	1	yes	characteristic
484	C₂×#120	C₂²×C₂₃	1	1	yes	characteristic
485	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
486	C₂×#117	C₂²×C₂₃	1	2	yes	—
487	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic, complemented
488	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
489	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
490	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
491	#401	C₂²×C₂₃	1	2	yes	complemented
492	#400	C₂²×C₂₃	1	2	yes	complemented
493	#400	C₂²×C₂₃	1	2	yes	complemented
494	#400	C₂²×C₂₃	1	2	yes	complemented
495	#397	C₂²×C₂₃	1	2	yes	—
496	#397	C₂²×C₂₃	1	2	yes	—
497	#397	C₂²×C₂₃	1	2	yes	complemented
498	#394	C₂²×C₂₃	1	2	yes	—
499	#394	C₂²×C₂₃	1	2	yes	—
500	#394	C₂²×C₂₃	1	2	yes	—
501	#394	C₂²×C₂₃	1	2	yes	complemented
502	#393	C₂²×C₂₃	1	2	yes	—
503	#393	C₂²×C₂₃	1	2	yes	—
504	#393	C₂²×C₂₃	1	2	yes	—
505	#393	C₂²×C₂₃	1	2	yes	complemented
506	#392	C₂²×C₂₃	1	2	yes	—
507	#391	C₂²×C₂₃	1	2	yes	complemented
508	#391	C₂²×C₂₃	1	2	yes	complemented
509	#391	C₂²×C₂₃	1	2	yes	complemented
510	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
511	#391	C₂²×C₂₃	1	2	yes	complemented
512	#391	C₂²×C₂₃	1	2	yes	complemented
513	#390	C₂²×C₂₃	1	2	yes	—
514	#390	C₂²×C₂₃	1	1	yes	characteristic
515	#388	C₂²×C₂₃	1	2	yes	—
516	#388	C₂²×C₂₃	1	2	yes	—
517	#388	C₂²×C₂₃	1	2	yes	—
518	#388	C₂²×C₂₃	1	2	yes	—
519	#388	C₂²×C₂₃	1	2	yes	—
520	#388	C₂²×C₂₃	1	2	yes	—
521	#388	C₂²×C₂₃	1	2	yes	—
522	#388	C₂²×C₂₃	1	2	yes	—
523	#388	C₂²×C₂₃	1	2	yes	complemented
524	#388	C₂²×C₂₃	1	2	yes	complemented
525	#388	C₂²×C₂₃	1	2	yes	complemented
526	#388	C₂²×C₂₃	1	2	yes	complemented
527	#387	C₂²×C₂₃	1	2	yes	complemented
528	#387	C₂²×C₂₃	1	2	yes	complemented
529	#387	C₂²×C₂₃	1	2	yes	complemented
530	#387	C₂²×C₂₃	1	2	yes	complemented
531	#387	C₂²×C₂₃	1	2	yes	complemented
532	#386	C₂²×C₂₃	1	1	yes	characteristic
533	#386	C₂²×C₂₃	1	1	yes	characteristic
534	#386	C₂²×C₂₃	1	2	yes	—
535	#386	C₂²×C₂₃	1	2	yes	—
536	#386	C₂²×C₂₃	1	1	yes	characteristic
537	#386	C₂²×C₂₃	1	2	yes	—
538	#386	C₂²×C₂₃	1	2	yes	—
539	#386	C₂²×C₂₃	1	2	yes	—
540	#386	C₂²×C₂₃	1	1	yes	characteristic
541	#386	C₂²×C₂₃	1	2	yes	—
542	#386	C₂²×C₂₃	1	1	yes	characteristic, complemented
543	#386	C₂²×C₂₃	1	1	yes	characteristic, complemented
544	#385	C₂²×C₂₃	1	2	yes	—
545	#385	C₂²×C₂₃	1	2	yes	—
546	#385	C₂²×C₂₃	1	2	yes	—
547	#385	C₂²×C₂₃	1	2	yes	complemented
548	#385	C₂²×C₂₃	1	2	yes	complemented
549	#381	C₂²×C₂₃	1	2	yes	—
550	#381	C₂²×C₂₃	1	1	yes	characteristic
551	#380	C₂²×C₂₃	1	2	yes	—
552	#379	C₂²×C₂₃	1	2	yes	—
553	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
554	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
555	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
556	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
557	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
558	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
559	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
560	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
561	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
562	#376	C₂²×C₂₃	1	2	yes	complemented
563	#376	C₂²×C₂₃	1	2	yes	complemented
564	C₂×C₂₃	—	4	2	no	—
565	C₂×C₂₃	—	4	4	no	—
566	C₂×C₂₃	—	4	2	no	—
567	C₂×C₂₃	—	8	1	no	—
568	C₂×C₂₃	#3475	1	2	yes	—
569	C₂×C₂₃	#3481	1	1	yes	characteristic
570	C₂×C₂₃	#3490	1	1	yes	characteristic
571	C₂×C₂₃	#3514	1	2	yes	—
572	C₂×C₂₃	#3540	1	1	yes	characteristic
573	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
574	C₂×#41	—	2	4	no	—
575	C₂×#41	—	4	2	no	—
576	C₂×#41	—	4	2	no	—
577	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
578	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
579	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
580	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
581	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
582	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
583	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
584	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
585	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
586	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
587	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
588	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
589	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
590	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
591	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
592	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
593	C₄⋊Q₈	—	4	2	no	—
594	#124	—	2	4	no	—
595	#124	—	2	8	no	—
596	C₂²⋊Q₈	—	4	4	no	—
597	C₂²⋊Q₈	—	4	2	no	—
598	#120	—	2	4	no	—
599	#120	—	4	2	no	—
600	C₄×D₄	—	2	8	no	—
601	#117	—	4	4	no	—
602	#117	—	4	2	no	—
603	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
613	C₂×C₂²⋊C₄	—	2	8	no	—
614	C₂×C₂²⋊C₄	—	4	2	no	—
615	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
623	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
633	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
641	C₂×C₄²	—	4	2	no	—
642	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
643	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
644	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
645	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
647	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
648	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
650	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
651	#95	C₂³×C₂₃	1	2	yes	—
652	#95	C₂³×C₂₃	1	2	yes	—
653	#95	C₂³×C₂₃	1	2	yes	—
654	#95	C₂³×C₂₃	1	2	yes	—
655	#95	C₂³×C₂₃	1	2	yes	—
656	#95	C₂³×C₂₃	1	2	yes	—
657	#95	C₂³×C₂₃	1	2	yes	—
658	#95	C₂³×C₂₃	1	2	yes	—
659	#95	C₂³×C₂₃	1	2	yes	—
660	#95	C₂³×C₂₃	1	2	yes	—
661	#95	C₂³×C₂₃	1	2	yes	—
662	#95	C₂³×C₂₃	1	2	yes	—
663	#95	C₂³×C₂₃	1	2	yes	—
664	#95	C₂³×C₂₃	1	2	yes	—
665	#95	C₂³×C₂₃	1	2	yes	—
666	#95	C₂³×C₂₃	1	2	yes	—
667	#95	C₂³×C₂₃	1	2	yes	—
668	#95	C₂³×C₂₃	1	2	yes	—
669	#95	C₂³×C₂₃	1	2	yes	—
670	#95	C₂³×C₂₃	1	2	yes	—
671	#95	C₂³×C₂₃	1	2	yes	—
672	#95	C₂³×C₂₃	1	2	yes	—
673	#95	C₂³×C₂₃	1	2	yes	—
674	#95	C₂³×C₂₃	1	2	yes	—
675	#95	C₂³×C₂₃	1	2	yes	—
676	C₂₃	#59988	1	1	yes	characteristic, direct product factor, Sylow
677	C₂⁴	—	2	4	no	—
678	C₂⁴	—	2	2	no	—
679	C₂⁴	—	4	1	no	—
680	C₂⁴	—	4	2	no	—
681	C₂⁴	—	4	1	no	—
682	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
683	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
684	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
685	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
686	#41	—	4	16	no	—
687	C₂×Q₈	—	2	2	no	—
688	C₂×Q₈	—	2	4	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	2	2	no	—
691	C₂×Q₈	—	4	1	no	—
692	C₂×Q₈	—	4	2	no	—
693	C₂×Q₈	—	4	1	no	—
694	C₂×Q₈	—	4	1	no	—
695	C₂×Q₈	—	4	2	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	4	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	4	1	no	—
703	C₂×D₄	—	4	1	no	—
704	C₂×D₄	—	4	1	no	—
705	C₂×D₄	—	4	1	no	—
706	C₂×D₄	—	4	1	no	—
707	C₂×D₄	—	4	2	no	—
708	C₂×D₄	—	4	2	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	#41×C₂₃	1	4	yes	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	4	no	—
722	C₂²×C₄	—	4	1	no	—
723	C₂²×C₄	—	4	1	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	1	no	—
726	C₂²×C₄	—	4	1	no	—
727	C₂²×C₄	—	4	2	no	—
728	C₂²×C₄	—	4	1	no	—
729	C₂²×C₄	—	4	2	no	—
730	C₂²×C₄	—	4	2	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	4	2	no	—
752	C₄⋊C₄	—	4	1	no	—
753	C₄⋊C₄	—	4	2	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₄⋊C₄	—	4	2	no	—
756	C₄⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	4	2	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	—	4	1	no	—
773	C₂²⋊C₄	—	4	1	no	—
774	C₂²⋊C₄	—	4	1	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₂²⋊C₄	—	4	2	no	—
779	C₂²⋊C₄	—	4	2	no	—
780	C₂²⋊C₄	—	4	2	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	#41×C₂₃	1	8	yes	complemented
783	C₄²	—	2	4	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	4	no	—
786	C₄²	—	2	4	no	—
787	C₄²	—	4	2	no	—
788	C₄²	—	4	2	no	—
789	C₄²	—	4	2	no	—
790	C₄²	—	4	1	no	—
791	C₄²	—	4	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	1	no	—
799	C₂³	—	2	1	no	—
800	C₂³	—	2	1	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	1	no	—
808	C₂³	—	2	1	no	—
809	C₂³	—	2	1	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	4	8	no	—
812	C₂³	—	4	4	no	—
813	C₂³	—	8	2	no	—
814	C₂³	—	8	4	no	—
815	C₂³	—	8	2	no	—
816	C₂³	C₂×#41×C₂₃	1	2	yes	—
817	C₂³	C₂×#41×C₂₃	1	4	yes	—
818	C₂³	C₂×#41×C₂₃	1	2	yes	—
819	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
820	Q₈	—	4	4	no	—
821	Q₈	—	8	2	no	—
822	Q₈	—	8	4	no	—
823	D₄	—	4	4	no	—
824	D₄	—	4	4	no	—
825	D₄	—	4	8	no	—
826	D₄	—	4	4	no	—
827	D₄	—	8	4	no	—
828	C₂×C₄	—	2	8	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	4	4	no	—
871	C₂×C₄	—	4	4	no	—
872	C₂×C₄	—	4	8	no	—
873	C₂×C₄	—	4	4	no	—
874	C₂×C₄	—	8	4	no	—
875	C₂×C₄	—	8	2	no	—
876	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
877	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
878	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
879	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
880	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
881	C₂²	—	2	4	no	—
882	C₂²	—	2	4	no	—
883	C₂²	—	2	4	no	—
884	C₂²	—	2	4	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	4	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	1	no	—
890	C₂²	—	4	1	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	1	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	8	8	no	—
904	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
905	C₂²	C₂²×#41×C₂₃	1	2	yes	—
906	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
907	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
908	C₂²	C₂₃×#585	1	2	yes	—
909	C₄	—	2	4	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	2	4	no	—
914	C₄	—	4	2	no	—
915	C₄	—	4	2	no	—
916	C₄	—	4	2	no	—
917	C₄	—	4	1	no	—
918	C₄	—	4	2	no	—
919	C₄	—	4	2	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	2	no	—
924	C₂	—	4	4	no	—
925	C₂	—	4	2	no	—
926	C₂	—	4	2	no	—
927	C₂	—	8	1	no	—
928	C₂	C₂₃×#3475	1	2	yes	—
929	C₂	C₂₃×#3481	1	1	yes	characteristic
930	C₂	C₂₃×#3490	1	1	yes	characteristic
931	C₂	C₂₃×#3514	1	2	yes	—
932	C₂	C₂₃×#3540	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂₃×#2404	C₂
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×#2804	C₂	semidirect
2. C₂₃×#2778	C₂	semidirect
3. C₂₃×#2684	C₂	semidirect
4. C₂₃×#2595	C₂	semidirect
5. C₂₃×#2527	C₂	semidirect
6. C₂₃×#2527	C₂	semidirect
7. C₂₃×#2492	C₂	semidirect
8. C₂₃×#2477	C₂	semidirect
9. C₂₃×#2477	C₂	semidirect
10. C₂₃×#2472	C₂	semidirect
11. C₂₃×#2459	C₂	semidirect
12. C₂₃×#2432	C₂	semidirect
14. C₂₃×#2372	C₂	semidirect
15. C₂₃×#2372	C₂	semidirect
16. C₂₃×#2358	C₂	semidirect
17. C₂₃×#2342	C₂	semidirect
18. C₂₃×#2297	C₂	semidirect
19. C₂₃×#2290	C₂	semidirect
21. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
30. C₂×C₂₃×#117	C₂²	semidirect
33. C₂²×C₄²×C₂₃	C₂²	semidirect
34. C₂₃×#401	C₂²	semidirect
35. C₂₃×#400	C₂²	semidirect
36. C₂₃×#400	C₂²	semidirect
37. C₂₃×#400	C₂²	semidirect
40. C₂₃×#397	C₂²	semidirect
44. C₂₃×#394	C₂²	semidirect
48. C₂₃×#393	C₂²	semidirect
50. C₂₃×#391	C₂²	semidirect
51. C₂₃×#391	C₂²	semidirect
52. C₂₃×#391	C₂²	semidirect
53. C₂₃×#391	C₂²	semidirect
54. C₂₃×#391	C₂²	semidirect
55. C₂₃×#391	C₂²	semidirect
66. C₂₃×#388	C₂²	semidirect
67. C₂₃×#388	C₂²	semidirect
68. C₂₃×#388	C₂²	semidirect
69. C₂₃×#388	C₂²	semidirect
70. C₂₃×#387	C₂²	semidirect
71. C₂₃×#387	C₂²	semidirect
72. C₂₃×#387	C₂²	semidirect
73. C₂₃×#387	C₂²	semidirect
74. C₂₃×#387	C₂²	semidirect
85. C₂₃×#386	C₂²	semidirect
86. C₂₃×#386	C₂²	semidirect
90. C₂₃×#385	C₂²	semidirect
91. C₂₃×#385	C₂²	semidirect
96. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
105. C₂₃×#376	C₂²	semidirect
106. C₂₃×#376	C₂²	semidirect
315. C₂²⋊C₄×C₂₃	#41	semidirect
325. #59988	C₂₃	direct (N × H)
415. #2804	C₂×C₂₃	semidirect
416. #2778	C₂×C₂₃	semidirect
417. #2684	C₂×C₂₃	semidirect
418. #2595	C₂×C₂₃	semidirect
419. #2527	C₂×C₂₃	semidirect
420. #2527	C₂×C₂₃	semidirect
421. #2492	C₂×C₂₃	semidirect
422. #2477	C₂×C₂₃	semidirect
423. #2477	C₂×C₂₃	semidirect
424. #2472	C₂×C₂₃	semidirect
425. #2459	C₂×C₂₃	semidirect
426. #2432	C₂×C₂₃	semidirect
428. #2372	C₂×C₂₃	semidirect
429. #2372	C₂×C₂₃	semidirect
430. #2358	C₂×C₂₃	semidirect
431. #2342	C₂×C₂₃	semidirect
432. #2297	C₂×C₂₃	semidirect
433. #2290	C₂×C₂₃	semidirect
478. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
482. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
487. C₂×#117	C₂²×C₂₃	semidirect
490. C₂²×C₄²	C₂²×C₂₃	semidirect
491. #401	C₂²×C₂₃	semidirect
492. #400	C₂²×C₂₃	semidirect
493. #400	C₂²×C₂₃	semidirect
494. #400	C₂²×C₂₃	semidirect
497. #397	C₂²×C₂₃	semidirect
501. #394	C₂²×C₂₃	semidirect
505. #393	C₂²×C₂₃	semidirect
507. #391	C₂²×C₂₃	semidirect
508. #391	C₂²×C₂₃	semidirect
509. #391	C₂²×C₂₃	semidirect
510. #391	C₂²×C₂₃	semidirect
511. #391	C₂²×C₂₃	semidirect
512. #391	C₂²×C₂₃	semidirect
523. #388	C₂²×C₂₃	semidirect
524. #388	C₂²×C₂₃	semidirect
525. #388	C₂²×C₂₃	semidirect
526. #388	C₂²×C₂₃	semidirect
527. #387	C₂²×C₂₃	semidirect
528. #387	C₂²×C₂₃	semidirect
529. #387	C₂²×C₂₃	semidirect
530. #387	C₂²×C₂₃	semidirect
531. #387	C₂²×C₂₃	semidirect
542. #386	C₂²×C₂₃	semidirect
543. #386	C₂²×C₂₃	semidirect
547. #385	C₂²×C₂₃	semidirect
548. #385	C₂²×C₂₃	semidirect
553. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
559. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
560. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
561. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
562. #376	C₂²×C₂₃	semidirect
563. #376	C₂²×C₂₃	semidirect
676. C₂₃	#59988	direct (N × H)
782. C₂²⋊C₄	#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#2804	2
C₂₃×#2778	2
C₂₃×#2684	2
C₂₃×#2595	2
C₂₃×#2527	2
C₂₃×#2492	2
C₂₃×#2477	2
C₂₃×#2472	2
C₂₃×#2459	2
C₂₃×#2432	2
C₂₃×#2404	2
C₂₃×#2372	2
C₂₃×#2358	2
C₂₃×#2342	2
C₂₃×#2297	2
C₂₃×#2290	2
#59988	23

Subgroups — C23×#59988 #19207614

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#59988 #19207614