Subgroups — C₂₃×#60018 #19207644

Order 5888.

1824 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2750	C₂	1	2	yes	maximal, complemented
2	C₂₃×#2724	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2697	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2578	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2573	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2566	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2534	C₂	1	1	yes	maximal, characteristic
8	C₂₃×#2530	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2515	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2497	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2480	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2475	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2466	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2374	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2373	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2358	C₂	1	1	yes	maximal, characteristic
17	C₂₃×#2342	C₂	1	2	yes	maximal, complemented
18	C₄×C₂₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2290	C₂	1	2	yes	maximal, complemented
20	C₂×C₂₃×#126	C₂²	1	2	yes	—
21	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₂₃×#123	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#123	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#120	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#117	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#400	C₂²	1	2	yes	complemented
32	C₂₃×#400	C₂²	1	2	yes	complemented
33	C₂₃×#400	C₂²	1	2	yes	complemented
34	C₂₃×#400	C₂²	1	2	yes	complemented
35	C₂₃×#398	C₂²	1	2	yes	complemented
36	C₂₃×#397	C₂²	1	2	yes	—
37	C₂₃×#397	C₂²	1	2	yes	—
38	C₂₃×#397	C₂²	1	2	yes	—
39	C₂₃×#397	C₂²	1	2	yes	—
40	C₂₃×#397	C₂²	1	2	yes	complemented
41	C₂₃×#396	C₂²	1	2	yes	—
42	C₂₃×#396	C₂²	1	2	yes	—
43	C₂₃×#396	C₂²	1	2	yes	—
44	C₂₃×#396	C₂²	1	2	yes	complemented
45	C₂₃×#394	C₂²	1	2	yes	—
46	C₂₃×#394	C₂²	1	2	yes	—
47	C₂₃×#390	C₂²	1	1	yes	characteristic
48	C₂₃×#390	C₂²	1	1	yes	characteristic
49	C₂₃×#389	C₂²	1	2	yes	complemented
50	C₂₃×#389	C₂²	1	2	yes	complemented
51	C₂₃×#389	C₂²	1	2	yes	complemented
52	C₂₃×#388	C₂²	1	2	yes	—
53	C₂₃×#388	C₂²	1	2	yes	—
54	C₂₃×#388	C₂²	1	2	yes	—
55	C₂₃×#388	C₂²	1	2	yes	—
56	C₂₃×#388	C₂²	1	2	yes	—
57	C₂₃×#388	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	complemented
63	C₂₃×#387	C₂²	1	2	yes	complemented
64	C₂₃×#387	C₂²	1	2	yes	complemented
65	C₂₃×#387	C₂²	1	2	yes	complemented
66	C₂₃×#387	C₂²	1	2	yes	complemented
67	C₂₃×#387	C₂²	1	2	yes	complemented
68	C₂₃×#387	C₂²	1	2	yes	complemented
69	C₂₃×#387	C₂²	1	2	yes	complemented
70	C₂₃×#387	C₂²	1	2	yes	complemented
71	C₂₃×#387	C₂²	1	2	yes	complemented
72	C₂₃×#386	C₂²	1	2	yes	—
73	C₂₃×#386	C₂²	1	2	yes	—
74	C₂₃×#386	C₂²	1	2	yes	—
75	C₂₃×#386	C₂²	1	1	yes	characteristic
76	C₂₃×#385	C₂²	1	2	yes	—
77	C₂₃×#385	C₂²	1	2	yes	—
78	C₂₃×#385	C₂²	1	2	yes	—
79	C₂₃×#385	C₂²	1	2	yes	—
80	C₂₃×#385	C₂²	1	2	yes	—
81	C₂₃×#385	C₂²	1	1	yes	characteristic, complemented
82	C₂₃×#385	C₂²	1	2	yes	complemented
83	C₂₃×#385	C₂²	1	2	yes	complemented
84	C₂₃×#384	C₂²	1	1	yes	characteristic, complemented
85	C₂₃×#383	C₂²	1	2	yes	complemented
86	C₂₃×#382	C₂²	1	1	yes	characteristic, complemented
87	C₂₃×#381	C₂²	1	2	yes	—
88	C₂₃×#381	C₂²	1	1	yes	characteristic
89	C₂₃×#381	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#380	C₂²	1	2	yes	—
91	C₂₃×#380	C₂²	1	2	yes	—
92	C₂₃×#380	C₂²	1	1	yes	characteristic
93	C₂₃×#379	C₂²	1	2	yes	—
94	C₂₃×#379	C₂²	1	1	yes	characteristic
95	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
96	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
97	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
98	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
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	2	yes	—
103	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
105	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
106	C₂₃×#376	C₂²	1	2	yes	complemented
107	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
109	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
111	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
113	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂₃×#126	—	2	8	no	—
118	C₂₃×#125	—	4	2	no	—
119	C₂₃×#123	—	2	4	no	—
120	C₂₃×#123	—	2	4	no	—
121	C₂₃×#120	—	2	4	no	—
122	C₄×D₄×C₂₃	—	2	8	no	—
123	C₄×D₄×C₂₃	—	4	2	no	—
124	C₂₃×#117	—	4	4	no	—
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	1	yes	characteristic
138	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₂₃	—	2	8	no	—
144	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
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	2	yes	—
148	C₂×C₂²⋊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	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
153	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
169	C₂×C₄²×C₂₃	—	4	2	no	—
170	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
172	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
173	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
175	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
176	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
178	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
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	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	C₂⁴×C₂₃	—	2	4	no	—
206	C₂⁴×C₂₃	—	2	2	no	—
207	C₂⁴×C₂₃	—	4	1	no	—
208	C₂⁴×C₂₃	—	4	2	no	—
209	C₂⁴×C₂₃	—	4	1	no	—
210	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
211	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
212	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
213	C₂×D₄×C₂₃	—	2	4	no	—
214	C₂×D₄×C₂₃	—	2	4	no	—
215	C₂×D₄×C₂₃	—	4	1	no	—
216	C₂×D₄×C₂₃	—	4	1	no	—
217	C₂×D₄×C₂₃	—	4	2	no	—
218	C₂×D₄×C₂₃	#41	1	4	yes	—
219	C₂²×C₄×C₂₃	—	2	4	no	—
220	C₂²×C₄×C₂₃	—	2	2	no	—
221	C₂²×C₄×C₂₃	—	2	2	no	—
222	C₂²×C₄×C₂₃	—	2	4	no	—
223	C₂²×C₄×C₂₃	—	2	4	no	—
224	C₂²×C₄×C₂₃	—	2	2	no	—
225	C₂²×C₄×C₂₃	—	2	4	no	—
226	C₂²×C₄×C₂₃	—	2	2	no	—
227	C₂²×C₄×C₂₃	—	4	1	no	—
228	C₂²×C₄×C₂₃	—	4	1	no	—
229	C₂²×C₄×C₂₃	—	4	2	no	—
230	C₂²×C₄×C₂₃	—	4	2	no	—
231	C₂²×C₄×C₂₃	—	4	1	no	—
232	C₂²×C₄×C₂₃	—	4	1	no	—
233	C₂²×C₄×C₂₃	—	4	2	no	—
234	C₂²×C₄×C₂₃	—	4	2	no	—
235	C₂²×C₄×C₂₃	—	4	2	no	—
236	C₂²×C₄×C₂₃	—	4	1	no	—
237	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
253	C₄⋊C₄×C₂₃	—	2	4	no	—
254	C₄⋊C₄×C₂₃	—	2	4	no	—
255	C₄⋊C₄×C₂₃	—	2	4	no	—
256	C₄⋊C₄×C₂₃	—	2	4	no	—
257	C₄⋊C₄×C₂₃	—	2	4	no	—
258	C₄⋊C₄×C₂₃	—	2	4	no	—
259	C₄⋊C₄×C₂₃	—	2	4	no	—
260	C₄⋊C₄×C₂₃	—	4	2	no	—
261	C₄⋊C₄×C₂₃	—	4	2	no	—
262	C₄⋊C₄×C₂₃	—	4	2	no	—
263	C₄⋊C₄×C₂₃	—	4	2	no	—
264	C₄⋊C₄×C₂₃	—	4	2	no	—
265	C₄⋊C₄×C₂₃	—	4	2	no	—
266	C₄⋊C₄×C₂₃	—	4	2	no	—
267	C₄⋊C₄×C₂₃	—	4	1	no	—
268	C₄⋊C₄×C₂₃	—	4	1	no	—
269	C₄⋊C₄×C₂₃	—	4	1	no	—
270	C₄⋊C₄×C₂₃	—	4	2	no	—
271	C₂²⋊C₄×C₂₃	—	2	4	no	—
272	C₂²⋊C₄×C₂₃	—	2	2	no	—
273	C₂²⋊C₄×C₂₃	—	2	2	no	—
274	C₂²⋊C₄×C₂₃	—	2	2	no	—
275	C₂²⋊C₄×C₂₃	—	2	4	no	—
276	C₂²⋊C₄×C₂₃	—	2	4	no	—
277	C₂²⋊C₄×C₂₃	—	2	4	no	—
278	C₂²⋊C₄×C₂₃	—	2	4	no	—
279	C₂²⋊C₄×C₂₃	—	2	4	no	—
280	C₂²⋊C₄×C₂₃	—	2	4	no	—
281	C₂²⋊C₄×C₂₃	—	2	4	no	—
282	C₂²⋊C₄×C₂₃	—	2	4	no	—
283	C₂²⋊C₄×C₂₃	—	2	4	no	—
284	C₂²⋊C₄×C₂₃	—	4	2	no	—
285	C₂²⋊C₄×C₂₃	—	4	2	no	—
286	C₂²⋊C₄×C₂₃	—	4	2	no	—
287	C₂²⋊C₄×C₂₃	—	4	1	no	—
288	C₂²⋊C₄×C₂₃	—	4	2	no	—
289	C₂²⋊C₄×C₂₃	—	4	2	no	—
290	C₂²⋊C₄×C₂₃	—	4	2	no	—
291	C₂²⋊C₄×C₂₃	—	4	2	no	—
292	C₂²⋊C₄×C₂₃	—	4	1	no	—
293	C₂²⋊C₄×C₂₃	—	4	1	no	—
294	C₂²⋊C₄×C₂₃	#41	1	8	yes	—
295	C₄²×C₂₃	—	2	4	no	—
296	C₄²×C₂₃	—	2	4	no	—
297	C₄²×C₂₃	—	2	4	no	—
298	C₄²×C₂₃	—	2	2	no	—
299	C₄²×C₂₃	—	4	2	no	—
300	C₄²×C₂₃	—	4	1	no	—
301	C₄²×C₂₃	—	4	1	no	—
302	C₄²×C₂₃	—	4	2	no	—
303	C₄²×C₂₃	—	4	2	no	—
304	C₄²×C₂₃	—	4	2	no	—
305	#60018	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
306	C₂³×C₂₃	—	2	2	no	—
307	C₂³×C₂₃	—	2	2	no	—
308	C₂³×C₂₃	—	2	2	no	—
309	C₂³×C₂₃	—	2	2	no	—
310	C₂³×C₂₃	—	2	2	no	—
311	C₂³×C₂₃	—	2	1	no	—
312	C₂³×C₂₃	—	2	1	no	—
313	C₂³×C₂₃	—	2	2	no	—
314	C₂³×C₂₃	—	2	2	no	—
315	C₂³×C₂₃	—	2	1	no	—
316	C₂³×C₂₃	—	2	2	no	—
317	C₂³×C₂₃	—	2	2	no	—
318	C₂³×C₂₃	—	2	2	no	—
319	C₂³×C₂₃	—	2	1	no	—
320	C₂³×C₂₃	—	4	8	no	—
321	C₂³×C₂₃	—	4	4	no	—
322	C₂³×C₂₃	—	8	2	no	—
323	C₂³×C₂₃	—	8	4	no	—
324	C₂³×C₂₃	—	8	2	no	—
325	C₂³×C₂₃	C₂×#41	1	2	yes	—
326	C₂³×C₂₃	C₂×#41	1	4	yes	—
327	C₂³×C₂₃	C₂×#41	1	2	yes	—
328	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
329	D₄×C₂₃	—	4	4	no	—
330	D₄×C₂₃	—	4	8	no	—
331	C₂×C₄×C₂₃	—	2	2	no	—
332	C₂×C₄×C₂₃	—	2	2	no	—
333	C₂×C₄×C₂₃	—	2	1	no	—
334	C₂×C₄×C₂₃	—	2	1	no	—
335	C₂×C₄×C₂₃	—	2	2	no	—
336	C₂×C₄×C₂₃	—	2	2	no	—
337	C₂×C₄×C₂₃	—	2	2	no	—
338	C₂×C₄×C₂₃	—	2	2	no	—
339	C₂×C₄×C₂₃	—	2	2	no	—
340	C₂×C₄×C₂₃	—	2	2	no	—
341	C₂×C₄×C₂₃	—	2	2	no	—
342	C₂×C₄×C₂₃	—	2	2	no	—
343	C₂×C₄×C₂₃	—	2	2	no	—
344	C₂×C₄×C₂₃	—	2	2	no	—
345	C₂×C₄×C₂₃	—	2	2	no	—
346	C₂×C₄×C₂₃	—	2	2	no	—
347	C₂×C₄×C₂₃	—	2	2	no	—
348	C₂×C₄×C₂₃	—	2	2	no	—
349	C₂×C₄×C₂₃	—	2	2	no	—
350	C₂×C₄×C₂₃	—	2	2	no	—
351	C₂×C₄×C₂₃	—	2	2	no	—
352	C₂×C₄×C₂₃	—	2	1	no	—
353	C₂×C₄×C₂₃	—	2	1	no	—
354	C₂×C₄×C₂₃	—	2	2	no	—
355	C₂×C₄×C₂₃	—	2	2	no	—
356	C₂×C₄×C₂₃	—	2	1	no	—
357	C₂×C₄×C₂₃	—	2	2	no	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	2	2	no	—
360	C₂×C₄×C₂₃	—	2	2	no	—
361	C₂×C₄×C₂₃	—	2	2	no	—
362	C₂×C₄×C₂₃	—	2	2	no	—
363	C₂×C₄×C₂₃	—	2	2	no	—
364	C₂×C₄×C₂₃	—	2	2	no	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	2	2	no	—
367	C₂×C₄×C₂₃	—	2	2	no	—
368	C₂×C₄×C₂₃	—	2	2	no	—
369	C₂×C₄×C₂₃	—	2	2	no	—
370	C₂×C₄×C₂₃	—	2	2	no	—
371	C₂×C₄×C₂₃	—	4	4	no	—
372	C₂×C₄×C₂₃	—	4	8	no	—
373	C₂×C₄×C₂₃	—	4	4	no	—
374	C₂×C₄×C₂₃	—	4	4	no	—
375	C₂×C₄×C₂₃	—	8	4	no	—
376	C₂×C₄×C₂₃	—	8	2	no	—
377	C₂×C₄×C₂₃	—	8	2	no	—
378	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
379	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
380	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
381	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
382	#2750	C₂×C₂₃	1	2	yes	complemented
383	#2724	C₂×C₂₃	1	1	yes	characteristic, complemented
384	#2697	C₂×C₂₃	1	1	yes	characteristic
385	#2578	C₂×C₂₃	1	2	yes	complemented
386	#2573	C₂×C₂₃	1	2	yes	complemented
387	#2566	C₂×C₂₃	1	1	yes	characteristic, complemented
388	#2534	C₂×C₂₃	1	1	yes	characteristic
389	#2530	C₂×C₂₃	1	2	yes	complemented
390	#2515	C₂×C₂₃	1	2	yes	complemented
391	#2497	C₂×C₂₃	1	2	yes	complemented
392	#2480	C₂×C₂₃	1	2	yes	complemented
393	#2475	C₂×C₂₃	1	2	yes	complemented
394	#2466	C₂×C₂₃	1	2	yes	complemented
395	#2374	C₂×C₂₃	1	1	yes	characteristic, complemented
396	#2373	C₂×C₂₃	1	2	yes	complemented
397	#2358	C₂×C₂₃	1	1	yes	characteristic
398	#2342	C₂×C₂₃	1	2	yes	complemented
399	C₄×#123	C₂×C₂₃	1	1	yes	characteristic, complemented
400	#2290	C₂×C₂₃	1	2	yes	complemented
401	C₂²×C₂₃	—	2	4	no	—
402	C₂²×C₂₃	—	2	4	no	—
403	C₂²×C₂₃	—	2	4	no	—
404	C₂²×C₂₃	—	2	4	no	—
405	C₂²×C₂₃	—	2	2	no	—
406	C₂²×C₂₃	—	2	2	no	—
407	C₂²×C₂₃	—	2	4	no	—
408	C₂²×C₂₃	—	4	2	no	—
409	C₂²×C₂₃	—	4	1	no	—
410	C₂²×C₂₃	—	4	1	no	—
411	C₂²×C₂₃	—	4	2	no	—
412	C₂²×C₂₃	—	4	2	no	—
413	C₂²×C₂₃	—	4	2	no	—
414	C₂²×C₂₃	—	4	2	no	—
415	C₂²×C₂₃	—	4	1	no	—
416	C₂²×C₂₃	—	4	1	no	—
417	C₂²×C₂₃	—	4	2	no	—
418	C₂²×C₂₃	—	8	8	no	—
419	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
420	C₂²×C₂₃	C₂²×#41	1	2	yes	—
421	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
422	C₂²×C₂₃	#585	1	2	yes	—
423	C₂²×C₂₃	#585	1	1	yes	characteristic
424	C₄×C₂₃	—	2	4	no	—
425	C₄×C₂₃	—	2	2	no	—
426	C₄×C₂₃	—	2	4	no	—
427	C₄×C₂₃	—	2	2	no	—
428	C₄×C₂₃	—	4	2	no	—
429	C₄×C₂₃	—	4	2	no	—
430	C₄×C₂₃	—	4	2	no	—
431	C₄×C₂₃	—	4	1	no	—
432	C₄×C₂₃	—	4	2	no	—
433	C₄×C₂₃	—	4	2	no	—
434	C₄×C₂₃	—	4	2	no	—
435	C₄×C₂₃	—	4	2	no	—
436	C₄×C₂₃	—	4	2	no	—
437	C₄×C₂₃	—	4	2	no	—
438	C₄×C₂₃	—	4	1	no	—
439	C₄×C₂₃	—	4	1	no	—
440	C₂×#126	C₂²×C₂₃	1	2	yes	—
441	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic, complemented
442	C₂×#123	C₂²×C₂₃	1	1	yes	characteristic
443	C₂×#123	C₂²×C₂₃	1	1	yes	characteristic
444	C₂×#120	C₂²×C₂₃	1	1	yes	characteristic
445	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
446	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
447	C₂×#117	C₂²×C₂₃	1	2	yes	—
448	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
449	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
450	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
451	#400	C₂²×C₂₃	1	2	yes	complemented
452	#400	C₂²×C₂₃	1	2	yes	complemented
453	#400	C₂²×C₂₃	1	2	yes	complemented
454	#400	C₂²×C₂₃	1	2	yes	complemented
455	#398	C₂²×C₂₃	1	2	yes	complemented
456	#397	C₂²×C₂₃	1	2	yes	—
457	#397	C₂²×C₂₃	1	2	yes	—
458	#397	C₂²×C₂₃	1	2	yes	—
459	#397	C₂²×C₂₃	1	2	yes	—
460	#397	C₂²×C₂₃	1	2	yes	complemented
461	#396	C₂²×C₂₃	1	2	yes	—
462	#396	C₂²×C₂₃	1	2	yes	—
463	#396	C₂²×C₂₃	1	2	yes	—
464	#396	C₂²×C₂₃	1	2	yes	complemented
465	#394	C₂²×C₂₃	1	2	yes	—
466	#394	C₂²×C₂₃	1	2	yes	—
467	#390	C₂²×C₂₃	1	1	yes	characteristic
468	#390	C₂²×C₂₃	1	1	yes	characteristic
469	#389	C₂²×C₂₃	1	2	yes	complemented
470	#389	C₂²×C₂₃	1	2	yes	complemented
471	#389	C₂²×C₂₃	1	2	yes	complemented
472	#388	C₂²×C₂₃	1	2	yes	—
473	#388	C₂²×C₂₃	1	2	yes	—
474	#388	C₂²×C₂₃	1	2	yes	—
475	#388	C₂²×C₂₃	1	2	yes	—
476	#388	C₂²×C₂₃	1	2	yes	—
477	#388	C₂²×C₂₃	1	2	yes	—
478	#388	C₂²×C₂₃	1	2	yes	—
479	#388	C₂²×C₂₃	1	2	yes	—
480	#388	C₂²×C₂₃	1	2	yes	—
481	#388	C₂²×C₂₃	1	2	yes	—
482	#388	C₂²×C₂₃	1	2	yes	complemented
483	#387	C₂²×C₂₃	1	2	yes	complemented
484	#387	C₂²×C₂₃	1	2	yes	complemented
485	#387	C₂²×C₂₃	1	2	yes	complemented
486	#387	C₂²×C₂₃	1	2	yes	complemented
487	#387	C₂²×C₂₃	1	2	yes	complemented
488	#387	C₂²×C₂₃	1	2	yes	complemented
489	#387	C₂²×C₂₃	1	2	yes	complemented
490	#387	C₂²×C₂₃	1	2	yes	complemented
491	#387	C₂²×C₂₃	1	2	yes	complemented
492	#386	C₂²×C₂₃	1	2	yes	—
493	#386	C₂²×C₂₃	1	2	yes	—
494	#386	C₂²×C₂₃	1	1	yes	characteristic
495	#386	C₂²×C₂₃	1	2	yes	—
496	#385	C₂²×C₂₃	1	2	yes	—
497	#385	C₂²×C₂₃	1	2	yes	—
498	#385	C₂²×C₂₃	1	2	yes	—
499	#385	C₂²×C₂₃	1	2	yes	—
500	#385	C₂²×C₂₃	1	2	yes	—
501	#385	C₂²×C₂₃	1	2	yes	complemented
502	#385	C₂²×C₂₃	1	1	yes	characteristic, complemented
503	#385	C₂²×C₂₃	1	2	yes	complemented
504	#384	C₂²×C₂₃	1	1	yes	characteristic, complemented
505	#383	C₂²×C₂₃	1	2	yes	complemented
506	#382	C₂²×C₂₃	1	1	yes	characteristic, complemented
507	#381	C₂²×C₂₃	1	1	yes	characteristic
508	#381	C₂²×C₂₃	1	2	yes	—
509	#381	C₂²×C₂₃	1	1	yes	characteristic, complemented
510	#380	C₂²×C₂₃	1	2	yes	—
511	#380	C₂²×C₂₃	1	2	yes	—
512	#380	C₂²×C₂₃	1	1	yes	characteristic
513	#379	C₂²×C₂₃	1	2	yes	—
514	#379	C₂²×C₂₃	1	1	yes	characteristic
515	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
516	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
517	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
518	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
519	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
520	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
521	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
522	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
523	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
524	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
525	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
526	#376	C₂²×C₂₃	1	2	yes	complemented
527	C₂×C₂₃	—	4	2	no	—
528	C₂×C₂₃	—	4	4	no	—
529	C₂×C₂₃	—	4	2	no	—
530	C₂×C₂₃	#3475	1	2	yes	—
531	C₂×C₂₃	#3481	1	1	yes	characteristic
532	C₂×C₂₃	#3505	1	1	yes	characteristic
533	C₂×C₂₃	#3521	1	2	yes	—
534	C₂×C₂₃	#3533	1	1	yes	characteristic
535	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
536	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
537	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
539	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
543	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
544	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
545	#126	—	2	8	no	—
546	#125	—	4	2	no	—
547	#123	—	2	4	no	—
548	#123	—	2	4	no	—
549	#120	—	2	4	no	—
550	C₄×D₄	—	2	8	no	—
551	C₄×D₄	—	4	2	no	—
552	#117	—	4	4	no	—
553	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
571	C₂×C₂²⋊C₄	—	2	8	no	—
572	C₂×C₂²⋊C₄	—	4	2	no	—
573	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
580	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
583	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
584	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
589	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
590	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
594	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
597	C₂×C₄²	—	4	2	no	—
598	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
599	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
601	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
602	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
603	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
604	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
605	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
607	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
608	#95	C₂³×C₂₃	1	2	yes	—
609	#95	C₂³×C₂₃	1	2	yes	—
610	#95	C₂³×C₂₃	1	2	yes	—
611	#95	C₂³×C₂₃	1	2	yes	—
612	#95	C₂³×C₂₃	1	2	yes	—
613	#95	C₂³×C₂₃	1	2	yes	—
614	#95	C₂³×C₂₃	1	2	yes	—
615	#95	C₂³×C₂₃	1	2	yes	—
616	#95	C₂³×C₂₃	1	2	yes	—
617	#95	C₂³×C₂₃	1	2	yes	—
618	#95	C₂³×C₂₃	1	2	yes	—
619	#95	C₂³×C₂₃	1	2	yes	—
620	#95	C₂³×C₂₃	1	2	yes	—
621	#95	C₂³×C₂₃	1	2	yes	—
622	#95	C₂³×C₂₃	1	2	yes	—
623	#95	C₂³×C₂₃	1	2	yes	—
624	#95	C₂³×C₂₃	1	2	yes	—
625	#95	C₂³×C₂₃	1	2	yes	—
626	#95	C₂³×C₂₃	1	2	yes	—
627	#95	C₂³×C₂₃	1	2	yes	—
628	#95	C₂³×C₂₃	1	2	yes	—
629	#95	C₂³×C₂₃	1	2	yes	—
630	#95	C₂³×C₂₃	1	2	yes	—
631	#95	C₂³×C₂₃	1	2	yes	—
632	#95	C₂³×C₂₃	1	2	yes	—
633	C₂₃	#60018	1	1	yes	characteristic, direct product factor, Sylow
634	C₂⁴	—	2	4	no	—
635	C₂⁴	—	2	2	no	—
636	C₂⁴	—	4	1	no	—
637	C₂⁴	—	4	2	no	—
638	C₂⁴	—	4	1	no	—
639	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
640	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
641	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	4	1	no	—
645	C₂×D₄	—	4	1	no	—
646	C₂×D₄	—	4	2	no	—
647	C₂×D₄	#41×C₂₃	1	4	yes	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	4	1	no	—
657	C₂²×C₄	—	4	1	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	1	no	—
661	C₂²×C₄	—	4	1	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	—	4	1	no	—
666	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	4	2	no	—
690	C₄⋊C₄	—	4	1	no	—
691	C₄⋊C₄	—	4	1	no	—
692	C₄⋊C₄	—	4	1	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₄⋊C₄	—	4	2	no	—
695	C₄⋊C₄	—	4	2	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	4	2	no	—
714	C₂²⋊C₄	—	4	2	no	—
715	C₂²⋊C₄	—	4	1	no	—
716	C₂²⋊C₄	—	4	1	no	—
717	C₂²⋊C₄	—	4	2	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	1	no	—
720	C₂²⋊C₄	—	4	2	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	#41×C₂₃	1	8	yes	—
724	C₄²	—	2	4	no	—
725	C₄²	—	2	4	no	—
726	C₄²	—	2	4	no	—
727	C₄²	—	2	2	no	—
728	C₄²	—	4	2	no	—
729	C₄²	—	4	2	no	—
730	C₄²	—	4	1	no	—
731	C₄²	—	4	1	no	—
732	C₄²	—	4	2	no	—
733	C₄²	—	4	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	2	1	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	1	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	1	no	—
748	C₂³	—	4	8	no	—
749	C₂³	—	4	4	no	—
750	C₂³	—	8	2	no	—
751	C₂³	—	8	4	no	—
752	C₂³	—	8	2	no	—
753	C₂³	C₂×#41×C₂₃	1	2	yes	—
754	C₂³	C₂×#41×C₂₃	1	4	yes	—
755	C₂³	C₂×#41×C₂₃	1	2	yes	—
756	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
757	D₄	—	4	4	no	—
758	D₄	—	4	8	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	4	4	no	—
800	C₂×C₄	—	4	8	no	—
801	C₂×C₄	—	4	4	no	—
802	C₂×C₄	—	4	4	no	—
803	C₂×C₄	—	8	4	no	—
804	C₂×C₄	—	8	2	no	—
805	C₂×C₄	—	8	2	no	—
806	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
807	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
808	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
809	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
810	C₂²	—	2	4	no	—
811	C₂²	—	2	4	no	—
812	C₂²	—	2	4	no	—
813	C₂²	—	2	4	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	4	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	1	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	8	8	no	—
828	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
829	C₂²	C₂²×#41×C₂₃	1	2	yes	—
830	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
831	C₂²	C₂₃×#585	1	2	yes	—
832	C₂²	C₂₃×#585	1	1	yes	characteristic
833	C₄	—	2	4	no	—
834	C₄	—	2	2	no	—
835	C₄	—	2	4	no	—
836	C₄	—	2	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	2	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	2	no	—
849	C₂	—	4	4	no	—
850	C₂	—	4	2	no	—
851	C₂	—	4	2	no	—
852	C₂	C₂₃×#3475	1	2	yes	—
853	C₂	C₂₃×#3481	1	1	yes	characteristic
854	C₂	C₂₃×#3505	1	1	yes	characteristic
855	C₂	C₂₃×#3521	1	2	yes	—
856	C₂	C₂₃×#3533	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#120	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×#2750	C₂	semidirect
2. C₂₃×#2724	C₂	semidirect
4. C₂₃×#2578	C₂	semidirect
5. C₂₃×#2573	C₂	semidirect
6. C₂₃×#2566	C₂	semidirect
8. C₂₃×#2530	C₂	semidirect
9. C₂₃×#2515	C₂	semidirect
10. C₂₃×#2497	C₂	semidirect
11. C₂₃×#2480	C₂	semidirect
12. C₂₃×#2475	C₂	semidirect
13. C₂₃×#2466	C₂	semidirect
14. C₂₃×#2374	C₂	semidirect
15. C₂₃×#2373	C₂	semidirect
17. C₂₃×#2342	C₂	semidirect
18. C₄×C₂₃×#123	C₂	semidirect
19. C₂₃×#2290	C₂	semidirect
21. C₂×C₂₃×#125	C₂²	semidirect
30. C₂²×C₄²×C₂₃	C₂²	semidirect
31. C₂₃×#400	C₂²	semidirect
32. C₂₃×#400	C₂²	semidirect
33. C₂₃×#400	C₂²	semidirect
34. C₂₃×#400	C₂²	semidirect
35. C₂₃×#398	C₂²	semidirect
40. C₂₃×#397	C₂²	semidirect
44. C₂₃×#396	C₂²	semidirect
49. C₂₃×#389	C₂²	semidirect
50. C₂₃×#389	C₂²	semidirect
51. C₂₃×#389	C₂²	semidirect
62. C₂₃×#388	C₂²	semidirect
63. C₂₃×#387	C₂²	semidirect
64. C₂₃×#387	C₂²	semidirect
65. C₂₃×#387	C₂²	semidirect
66. C₂₃×#387	C₂²	semidirect
67. C₂₃×#387	C₂²	semidirect
68. C₂₃×#387	C₂²	semidirect
69. C₂₃×#387	C₂²	semidirect
70. C₂₃×#387	C₂²	semidirect
71. C₂₃×#387	C₂²	semidirect
81. C₂₃×#385	C₂²	semidirect
82. C₂₃×#385	C₂²	semidirect
83. C₂₃×#385	C₂²	semidirect
84. C₂₃×#384	C₂²	semidirect
85. C₂₃×#383	C₂²	semidirect
86. C₂₃×#382	C₂²	semidirect
89. C₂₃×#381	C₂²	semidirect
95. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
96. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
97. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
98. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
106. C₂₃×#376	C₂²	semidirect
305. #60018	C₂₃	direct (N × H)
382. #2750	C₂×C₂₃	semidirect
383. #2724	C₂×C₂₃	semidirect
385. #2578	C₂×C₂₃	semidirect
386. #2573	C₂×C₂₃	semidirect
387. #2566	C₂×C₂₃	semidirect
389. #2530	C₂×C₂₃	semidirect
390. #2515	C₂×C₂₃	semidirect
391. #2497	C₂×C₂₃	semidirect
392. #2480	C₂×C₂₃	semidirect
393. #2475	C₂×C₂₃	semidirect
394. #2466	C₂×C₂₃	semidirect
395. #2374	C₂×C₂₃	semidirect
396. #2373	C₂×C₂₃	semidirect
398. #2342	C₂×C₂₃	semidirect
399. C₄×#123	C₂×C₂₃	semidirect
400. #2290	C₂×C₂₃	semidirect
441. C₂×#125	C₂²×C₂₃	semidirect
450. C₂²×C₄²	C₂²×C₂₃	semidirect
451. #400	C₂²×C₂₃	semidirect
452. #400	C₂²×C₂₃	semidirect
453. #400	C₂²×C₂₃	semidirect
454. #400	C₂²×C₂₃	semidirect
455. #398	C₂²×C₂₃	semidirect
460. #397	C₂²×C₂₃	semidirect
464. #396	C₂²×C₂₃	semidirect
469. #389	C₂²×C₂₃	semidirect
470. #389	C₂²×C₂₃	semidirect
471. #389	C₂²×C₂₃	semidirect
482. #388	C₂²×C₂₃	semidirect
483. #387	C₂²×C₂₃	semidirect
484. #387	C₂²×C₂₃	semidirect
485. #387	C₂²×C₂₃	semidirect
486. #387	C₂²×C₂₃	semidirect
487. #387	C₂²×C₂₃	semidirect
488. #387	C₂²×C₂₃	semidirect
489. #387	C₂²×C₂₃	semidirect
490. #387	C₂²×C₂₃	semidirect
491. #387	C₂²×C₂₃	semidirect
501. #385	C₂²×C₂₃	semidirect
502. #385	C₂²×C₂₃	semidirect
503. #385	C₂²×C₂₃	semidirect
504. #384	C₂²×C₂₃	semidirect
505. #383	C₂²×C₂₃	semidirect
506. #382	C₂²×C₂₃	semidirect
509. #381	C₂²×C₂₃	semidirect
515. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
516. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
517. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
518. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
524. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
525. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
526. #376	C₂²×C₂₃	semidirect
633. C₂₃	#60018	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×#2750	2
C₂₃×#2724	2
C₂₃×#2697	2
C₂₃×#2578	2
C₂₃×#2573	2
C₂₃×#2566	2
C₂₃×#2534	2
C₂₃×#2530	2
C₂₃×#2515	2
C₂₃×#2497	2
C₂₃×#2480	2
C₂₃×#2475	2
C₂₃×#2466	2
C₂₃×#2374	2
C₂₃×#2373	2
C₂₃×#2358	2
C₂₃×#2342	2
C₄×C₂₃×#123	2
C₂₃×#2290	2
#60018	23

Subgroups — C23×#60018 #19207644

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60018 #19207644