Subgroups — C₂₃×#59989 #19207615

Order 5888.

1750 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2807	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#2782	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2693	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2611	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2598	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#2587	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2533	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2517	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2509	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2505	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2475	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2470	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2470	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2455	C₂	1	1	yes	maximal, characteristic
15	C₂₃×#2359	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2359	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2346	C₂	1	2	yes	maximal, complemented
18	C₂₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2290	C₂	1	2	yes	maximal, complemented
20	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#123	C₂²	1	2	yes	—
22	C₂×C₂₃×#123	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#117	C₂²	1	2	yes	—
27	C₂×C₂₃×#117	C₂²	1	2	yes	—
28	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
30	C₂₃×#400	C₂²	1	2	yes	—
31	C₂₃×#400	C₂²	1	2	yes	—
32	C₂₃×#400	C₂²	1	2	yes	—
33	C₂₃×#400	C₂²	1	2	yes	—
34	C₂₃×#400	C₂²	1	1	yes	characteristic
35	C₂₃×#400	C₂²	1	2	yes	—
36	C₂₃×#400	C₂²	1	1	yes	characteristic
37	C₂₃×#400	C₂²	1	2	yes	—
38	C₂₃×#399	C₂²	1	1	yes	characteristic
39	C₂₃×#399	C₂²	1	1	yes	characteristic
40	C₂₃×#398	C₂²	1	2	yes	—
41	C₂₃×#398	C₂²	1	1	yes	characteristic
42	C₂₃×#397	C₂²	1	1	yes	characteristic
43	C₂₃×#397	C₂²	1	2	yes	—
44	C₂₃×#397	C₂²	1	2	yes	—
45	C₂₃×#396	C₂²	1	2	yes	—
46	C₂₃×#396	C₂²	1	2	yes	—
47	C₂₃×#394	C₂²	1	2	yes	—
48	C₂₃×#394	C₂²	1	1	yes	characteristic
49	C₂₃×#392	C₂²	1	1	yes	characteristic
50	C₂₃×#389	C₂²	1	2	yes	—
51	C₂₃×#389	C₂²	1	2	yes	—
52	C₂₃×#389	C₂²	1	2	yes	—
53	C₂₃×#389	C₂²	1	2	yes	—
54	C₂₃×#389	C₂²	1	2	yes	—
55	C₂₃×#389	C₂²	1	2	yes	—
56	C₂₃×#389	C₂²	1	2	yes	—
57	C₂₃×#389	C₂²	1	2	yes	—
58	C₂₃×#389	C₂²	1	2	yes	—
59	C₂₃×#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	—
67	C₂₃×#387	C₂²	1	2	yes	—
68	C₂₃×#387	C₂²	1	2	yes	—
69	C₂₃×#387	C₂²	1	2	yes	—
70	C₂₃×#387	C₂²	1	2	yes	—
71	C₂₃×#387	C₂²	1	2	yes	—
72	C₂₃×#387	C₂²	1	2	yes	—
73	C₂₃×#387	C₂²	1	2	yes	—
74	C₂₃×#387	C₂²	1	2	yes	—
75	C₂₃×#387	C₂²	1	2	yes	—
76	C₂₃×#386	C₂²	1	2	yes	—
77	C₂₃×#386	C₂²	1	2	yes	—
78	C₂₃×#386	C₂²	1	2	yes	—
79	C₂₃×#386	C₂²	1	2	yes	—
80	C₂₃×#385	C₂²	1	1	yes	characteristic
81	C₂₃×#385	C₂²	1	2	yes	—
82	C₂₃×#385	C₂²	1	1	yes	characteristic
83	C₂₃×#385	C₂²	1	2	yes	—
84	C₂₃×#385	C₂²	1	2	yes	—
85	C₂₃×#385	C₂²	1	2	yes	—
86	C₂₃×#385	C₂²	1	2	yes	—
87	C₂₃×#385	C₂²	1	2	yes	—
88	C₂₃×#385	C₂²	1	1	yes	characteristic
89	C₂₃×#385	C₂²	1	2	yes	—
90	C₂₃×#385	C₂²	1	2	yes	—
91	C₂₃×#385	C₂²	1	1	yes	characteristic
92	C₂₃×#383	C₂²	1	1	yes	characteristic
93	C₂₃×#382	C₂²	1	2	yes	—
94	C₂₃×#382	C₂²	1	2	yes	—
95	C₂₃×#380	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
100	C₄×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	C₂₃×#376	C₂²	1	2	yes	—
105	C₂₃×#376	C₂²	1	1	yes	characteristic
106	C₂×C₂₃×#95	C₂²	1	2	yes	—
107	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
108	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
111	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
112	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
114	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
115	C₂₃×#125	—	4	2	no	—
116	C₂₃×#123	—	2	8	no	—
117	C₂₃×#123	—	2	8	no	—
118	C₄×D₄×C₂₃	—	2	8	no	—
119	C₄×D₄×C₂₃	—	4	2	no	—
120	C₂₃×#117	—	2	8	no	—
121	C₂₃×#117	—	2	4	no	—
122	C₂₃×#117	—	4	2	no	—
123	C₂₃×#117	—	4	4	no	—
124	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	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	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	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
164	C₂×C₄²×C₂₃	—	4	2	no	—
165	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
166	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
167	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
168	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
173	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
174	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
175	C₂₃×#95	C₂³	1	2	yes	—
176	C₂₃×#95	C₂³	1	2	yes	—
177	C₂₃×#95	C₂³	1	2	yes	—
178	C₂₃×#95	C₂³	1	2	yes	—
179	C₂₃×#95	C₂³	1	2	yes	—
180	C₂₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
198	C₂₃×#95	C₂³	1	1	yes	characteristic
199	C₂₃×#95	C₂³	1	2	yes	—
200	C₂₃×#95	C₂³	1	2	yes	—
201	C₂₃×#95	C₂³	1	2	yes	—
202	C₂₃×#95	C₂³	1	2	yes	—
203	C₂₃×#95	C₂³	1	2	yes	—
204	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
205	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
206	C₂×D₄×C₂₃	—	2	4	no	—
207	C₂×D₄×C₂₃	—	2	4	no	—
208	C₂×D₄×C₂₃	—	2	4	no	—
209	C₂×D₄×C₂₃	—	4	1	no	—
210	C₂×D₄×C₂₃	—	4	2	no	—
211	C₂²×C₄×C₂₃	—	2	2	no	—
212	C₂²×C₄×C₂₃	—	2	2	no	—
213	C₂²×C₄×C₂₃	—	2	2	no	—
214	C₂²×C₄×C₂₃	—	2	4	no	—
215	C₂²×C₄×C₂₃	—	2	4	no	—
216	C₂²×C₄×C₂₃	—	2	4	no	—
217	C₂²×C₄×C₂₃	—	2	4	no	—
218	C₂²×C₄×C₂₃	—	2	4	no	—
219	C₂²×C₄×C₂₃	—	4	1	no	—
220	C₂²×C₄×C₂₃	—	4	1	no	—
221	C₂²×C₄×C₂₃	—	4	2	no	—
222	C₂²×C₄×C₂₃	—	4	2	no	—
223	C₂²×C₄×C₂₃	—	4	2	no	—
224	C₂²×C₄×C₂₃	—	4	2	no	—
225	C₂²×C₄×C₂₃	—	4	2	no	—
226	C₂²×C₄×C₂₃	—	4	2	no	—
227	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
244	C₄⋊C₄×C₂₃	—	2	4	no	—
245	C₄⋊C₄×C₂₃	—	2	4	no	—
246	C₄⋊C₄×C₂₃	—	2	4	no	—
247	C₄⋊C₄×C₂₃	—	2	4	no	—
248	C₄⋊C₄×C₂₃	—	2	4	no	—
249	C₄⋊C₄×C₂₃	—	2	4	no	—
250	C₄⋊C₄×C₂₃	—	2	4	no	—
251	C₄⋊C₄×C₂₃	—	2	4	no	—
252	C₄⋊C₄×C₂₃	—	2	4	no	—
253	C₄⋊C₄×C₂₃	—	2	4	no	—
254	C₄⋊C₄×C₂₃	—	4	2	no	—
255	C₄⋊C₄×C₂₃	—	4	2	no	—
256	C₄⋊C₄×C₂₃	—	4	2	no	—
257	C₄⋊C₄×C₂₃	—	4	2	no	—
258	C₄⋊C₄×C₂₃	—	4	2	no	—
259	C₄⋊C₄×C₂₃	—	4	2	no	—
260	C₄⋊C₄×C₂₃	—	4	1	no	—
261	C₄⋊C₄×C₂₃	—	4	1	no	—
262	C₄⋊C₄×C₂₃	—	4	2	no	—
263	C₄⋊C₄×C₂₃	—	4	1	no	—
264	C₄⋊C₄×C₂₃	—	4	1	no	—
265	C₄⋊C₄×C₂₃	—	4	2	no	—
266	C₄⋊C₄×C₂₃	—	4	1	no	—
267	C₂²⋊C₄×C₂₃	—	2	2	no	—
268	C₂²⋊C₄×C₂₃	—	2	4	no	—
269	C₂²⋊C₄×C₂₃	—	2	4	no	—
270	C₂²⋊C₄×C₂₃	—	2	4	no	—
271	C₂²⋊C₄×C₂₃	—	2	4	no	—
272	C₂²⋊C₄×C₂₃	—	2	4	no	—
273	C₂²⋊C₄×C₂₃	—	2	4	no	—
274	C₂²⋊C₄×C₂₃	—	2	4	no	—
275	C₂²⋊C₄×C₂₃	—	2	4	no	—
276	C₂²⋊C₄×C₂₃	—	4	2	no	—
277	C₂²⋊C₄×C₂₃	—	4	2	no	—
278	C₂²⋊C₄×C₂₃	—	4	2	no	—
279	C₂²⋊C₄×C₂₃	—	4	2	no	—
280	C₂²⋊C₄×C₂₃	—	4	1	no	—
281	C₂²⋊C₄×C₂₃	—	4	1	no	—
282	C₂²⋊C₄×C₂₃	#41	1	8	yes	—
283	C₂²⋊C₄×C₂₃	#41	1	4	yes	—
284	C₄²×C₂₃	—	2	4	no	—
285	C₄²×C₂₃	—	2	4	no	—
286	C₄²×C₂₃	—	2	4	no	—
287	C₄²×C₂₃	—	2	4	no	—
288	C₄²×C₂₃	—	2	4	no	—
289	C₄²×C₂₃	—	2	2	no	—
290	C₄²×C₂₃	—	2	2	no	—
291	C₄²×C₂₃	—	4	2	no	—
292	C₄²×C₂₃	—	4	2	no	—
293	C₄²×C₂₃	—	4	2	no	—
294	#59989	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₂³×C₂₃	—	2	2	no	—
296	C₂³×C₂₃	—	2	2	no	—
297	C₂³×C₂₃	—	2	2	no	—
298	C₂³×C₂₃	—	2	2	no	—
299	C₂³×C₂₃	—	2	1	no	—
300	C₂³×C₂₃	—	2	2	no	—
301	C₂³×C₂₃	—	2	1	no	—
302	C₂³×C₂₃	—	2	2	no	—
303	C₂³×C₂₃	—	2	2	no	—
304	C₂³×C₂₃	—	2	2	no	—
305	C₂³×C₂₃	C₂×#41	1	2	yes	—
306	C₂³×C₂₃	C₂×#41	1	4	yes	—
307	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
308	D₄×C₂₃	—	4	8	no	—
309	D₄×C₂₃	—	4	4	no	—
310	C₂×C₄×C₂₃	—	2	8	no	—
311	C₂×C₄×C₂₃	—	2	1	no	—
312	C₂×C₄×C₂₃	—	2	2	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	1	no	—
315	C₂×C₄×C₂₃	—	2	2	no	—
316	C₂×C₄×C₂₃	—	2	1	no	—
317	C₂×C₄×C₂₃	—	2	2	no	—
318	C₂×C₄×C₂₃	—	2	1	no	—
319	C₂×C₄×C₂₃	—	2	2	no	—
320	C₂×C₄×C₂₃	—	2	2	no	—
321	C₂×C₄×C₂₃	—	2	2	no	—
322	C₂×C₄×C₂₃	—	2	2	no	—
323	C₂×C₄×C₂₃	—	2	2	no	—
324	C₂×C₄×C₂₃	—	2	2	no	—
325	C₂×C₄×C₂₃	—	2	2	no	—
326	C₂×C₄×C₂₃	—	2	2	no	—
327	C₂×C₄×C₂₃	—	2	2	no	—
328	C₂×C₄×C₂₃	—	2	2	no	—
329	C₂×C₄×C₂₃	—	2	2	no	—
330	C₂×C₄×C₂₃	—	2	2	no	—
331	C₂×C₄×C₂₃	—	2	2	no	—
332	C₂×C₄×C₂₃	—	2	2	no	—
333	C₂×C₄×C₂₃	—	2	2	no	—
334	C₂×C₄×C₂₃	—	2	1	no	—
335	C₂×C₄×C₂₃	—	2	1	no	—
336	C₂×C₄×C₂₃	—	2	1	no	—
337	C₂×C₄×C₂₃	—	2	1	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	2	no	—
353	C₂×C₄×C₂₃	—	4	4	no	—
354	C₂×C₄×C₂₃	—	4	8	no	—
355	C₂×C₄×C₂₃	—	4	8	no	—
356	C₂×C₄×C₂₃	—	4	4	no	—
357	C₂×C₄×C₂₃	—	8	4	no	—
358	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
359	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
360	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
361	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
362	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
363	#2807	C₂×C₂₃	1	1	yes	characteristic, complemented
364	#2782	C₂×C₂₃	1	2	yes	complemented
365	#2693	C₂×C₂₃	1	1	yes	characteristic
366	#2611	C₂×C₂₃	1	1	yes	characteristic, complemented
367	#2598	C₂×C₂₃	1	1	yes	characteristic
368	#2587	C₂×C₂₃	1	2	yes	complemented
369	#2533	C₂×C₂₃	1	2	yes	complemented
370	#2517	C₂×C₂₃	1	1	yes	characteristic, complemented
371	#2509	C₂×C₂₃	1	2	yes	complemented
372	#2505	C₂×C₂₃	1	2	yes	complemented
373	#2475	C₂×C₂₃	1	2	yes	complemented
374	#2470	C₂×C₂₃	1	2	yes	complemented
375	#2470	C₂×C₂₃	1	2	yes	complemented
376	#2455	C₂×C₂₃	1	1	yes	characteristic
377	#2359	C₂×C₂₃	1	2	yes	complemented
378	#2359	C₂×C₂₃	1	2	yes	complemented
379	#2346	C₂×C₂₃	1	2	yes	complemented
380	#2296	C₂×C₂₃	1	1	yes	characteristic, complemented
381	#2290	C₂×C₂₃	1	2	yes	complemented
382	C₂²×C₂₃	—	2	4	no	—
383	C₂²×C₂₃	—	2	4	no	—
384	C₂²×C₂₃	—	2	4	no	—
385	C₂²×C₂₃	—	2	2	no	—
386	C₂²×C₂₃	—	2	4	no	—
387	C₂²×C₂₃	—	4	2	no	—
388	C₂²×C₂₃	—	4	1	no	—
389	C₂²×C₂₃	—	4	2	no	—
390	C₂²×C₂₃	—	4	2	no	—
391	C₂²×C₂₃	—	4	2	no	—
392	C₂²×C₂₃	—	4	1	no	—
393	C₂²×C₂₃	—	4	2	no	—
394	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
395	C₂²×C₂₃	C₂²×#41	1	2	yes	—
396	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
397	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
398	C₂²×C₂₃	#585	1	2	yes	—
399	C₄×C₂₃	—	2	4	no	—
400	C₄×C₂₃	—	2	4	no	—
401	C₄×C₂₃	—	2	2	no	—
402	C₄×C₂₃	—	2	2	no	—
403	C₄×C₂₃	—	2	4	no	—
404	C₄×C₂₃	—	4	2	no	—
405	C₄×C₂₃	—	4	2	no	—
406	C₄×C₂₃	—	4	2	no	—
407	C₄×C₂₃	—	4	1	no	—
408	C₄×C₂₃	—	4	2	no	—
409	C₄×C₂₃	—	4	1	no	—
410	C₄×C₂₃	—	4	2	no	—
411	C₄×C₂₃	—	4	2	no	—
412	C₄×C₂₃	—	4	1	no	—
413	C₄×C₂₃	—	4	2	no	—
414	C₄×C₂₃	—	4	2	no	—
415	C₄×C₂₃	—	4	1	no	—
416	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×#123	C₂²×C₂₃	1	2	yes	—
418	C₂×#123	C₂²×C₂₃	1	2	yes	—
419	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
420	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
421	C₂×#117	C₂²×C₂₃	1	2	yes	—
422	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
424	C₂×#117	C₂²×C₂₃	1	2	yes	—
425	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
426	#400	C₂²×C₂₃	1	2	yes	—
427	#400	C₂²×C₂₃	1	1	yes	characteristic
428	#400	C₂²×C₂₃	1	1	yes	characteristic
429	#400	C₂²×C₂₃	1	2	yes	—
430	#400	C₂²×C₂₃	1	2	yes	—
431	#400	C₂²×C₂₃	1	2	yes	—
432	#400	C₂²×C₂₃	1	2	yes	—
433	#400	C₂²×C₂₃	1	2	yes	—
434	#399	C₂²×C₂₃	1	1	yes	characteristic
435	#399	C₂²×C₂₃	1	1	yes	characteristic
436	#398	C₂²×C₂₃	1	1	yes	characteristic
437	#398	C₂²×C₂₃	1	2	yes	—
438	#397	C₂²×C₂₃	1	1	yes	characteristic
439	#397	C₂²×C₂₃	1	2	yes	—
440	#397	C₂²×C₂₃	1	2	yes	—
441	#396	C₂²×C₂₃	1	2	yes	—
442	#396	C₂²×C₂₃	1	2	yes	—
443	#394	C₂²×C₂₃	1	1	yes	characteristic
444	#394	C₂²×C₂₃	1	2	yes	—
445	#392	C₂²×C₂₃	1	1	yes	characteristic
446	#389	C₂²×C₂₃	1	2	yes	—
447	#389	C₂²×C₂₃	1	2	yes	—
448	#389	C₂²×C₂₃	1	2	yes	—
449	#389	C₂²×C₂₃	1	2	yes	—
450	#389	C₂²×C₂₃	1	2	yes	—
451	#389	C₂²×C₂₃	1	2	yes	—
452	#389	C₂²×C₂₃	1	2	yes	—
453	#389	C₂²×C₂₃	1	2	yes	—
454	#389	C₂²×C₂₃	1	2	yes	—
455	#388	C₂²×C₂₃	1	2	yes	—
456	#388	C₂²×C₂₃	1	2	yes	—
457	#388	C₂²×C₂₃	1	2	yes	—
458	#388	C₂²×C₂₃	1	2	yes	—
459	#388	C₂²×C₂₃	1	2	yes	—
460	#388	C₂²×C₂₃	1	2	yes	—
461	#388	C₂²×C₂₃	1	2	yes	—
462	#388	C₂²×C₂₃	1	2	yes	—
463	#387	C₂²×C₂₃	1	2	yes	—
464	#387	C₂²×C₂₃	1	2	yes	—
465	#387	C₂²×C₂₃	1	2	yes	—
466	#387	C₂²×C₂₃	1	2	yes	—
467	#387	C₂²×C₂₃	1	2	yes	—
468	#387	C₂²×C₂₃	1	2	yes	—
469	#387	C₂²×C₂₃	1	2	yes	—
470	#387	C₂²×C₂₃	1	2	yes	—
471	#387	C₂²×C₂₃	1	2	yes	—
472	#386	C₂²×C₂₃	1	2	yes	—
473	#386	C₂²×C₂₃	1	2	yes	—
474	#386	C₂²×C₂₃	1	2	yes	—
475	#386	C₂²×C₂₃	1	2	yes	—
476	#385	C₂²×C₂₃	1	2	yes	—
477	#385	C₂²×C₂₃	1	2	yes	—
478	#385	C₂²×C₂₃	1	2	yes	—
479	#385	C₂²×C₂₃	1	1	yes	characteristic
480	#385	C₂²×C₂₃	1	2	yes	—
481	#385	C₂²×C₂₃	1	2	yes	—
482	#385	C₂²×C₂₃	1	1	yes	characteristic
483	#385	C₂²×C₂₃	1	2	yes	—
484	#385	C₂²×C₂₃	1	1	yes	characteristic
485	#385	C₂²×C₂₃	1	2	yes	—
486	#385	C₂²×C₂₃	1	1	yes	characteristic
487	#385	C₂²×C₂₃	1	2	yes	—
488	#383	C₂²×C₂₃	1	1	yes	characteristic
489	#382	C₂²×C₂₃	1	2	yes	—
490	#382	C₂²×C₂₃	1	2	yes	—
491	#380	C₂²×C₂₃	1	2	yes	—
492	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
493	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
494	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
495	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
496	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
497	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
498	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
499	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
500	#376	C₂²×C₂₃	1	1	yes	characteristic
501	#376	C₂²×C₂₃	1	2	yes	—
502	C₂×#95	C₂²×C₂₃	1	2	yes	—
503	C₂×C₂₃	—	4	4	no	—
504	C₂×C₂₃	—	4	2	no	—
505	C₂×C₂₃	#3475	1	2	yes	—
506	C₂×C₂₃	#3481	1	1	yes	characteristic
507	C₂×C₂₃	#3492	1	1	yes	characteristic
508	C₂×C₂₃	#3515	1	2	yes	—
509	C₂×C₂₃	#3540	1	1	yes	characteristic
510	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
511	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
512	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
514	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
515	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
517	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
518	#125	—	4	2	no	—
519	#123	—	2	8	no	—
520	#123	—	2	8	no	—
521	C₄×D₄	—	2	8	no	—
522	C₄×D₄	—	4	2	no	—
523	#117	—	2	8	no	—
524	#117	—	2	4	no	—
525	#117	—	4	2	no	—
526	#117	—	4	4	no	—
527	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
552	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
560	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
561	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
567	C₂×C₄²	—	4	2	no	—
568	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
569	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
570	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
571	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
572	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
573	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
574	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
575	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
576	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
577	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
578	#95	C₂³×C₂₃	1	2	yes	—
579	#95	C₂³×C₂₃	1	2	yes	—
580	#95	C₂³×C₂₃	1	2	yes	—
581	#95	C₂³×C₂₃	1	2	yes	—
582	#95	C₂³×C₂₃	1	2	yes	—
583	#95	C₂³×C₂₃	1	1	yes	characteristic
584	#95	C₂³×C₂₃	1	2	yes	—
585	#95	C₂³×C₂₃	1	2	yes	—
586	#95	C₂³×C₂₃	1	2	yes	—
587	#95	C₂³×C₂₃	1	1	yes	characteristic
588	#95	C₂³×C₂₃	1	2	yes	—
589	#95	C₂³×C₂₃	1	2	yes	—
590	#95	C₂³×C₂₃	1	2	yes	—
591	#95	C₂³×C₂₃	1	2	yes	—
592	#95	C₂³×C₂₃	1	2	yes	—
593	#95	C₂³×C₂₃	1	2	yes	—
594	#95	C₂³×C₂₃	1	2	yes	—
595	#95	C₂³×C₂₃	1	2	yes	—
596	#95	C₂³×C₂₃	1	2	yes	—
597	#95	C₂³×C₂₃	1	2	yes	—
598	#95	C₂³×C₂₃	1	2	yes	—
599	#95	C₂³×C₂₃	1	2	yes	—
600	#95	C₂³×C₂₃	1	1	yes	characteristic
601	#95	C₂³×C₂₃	1	1	yes	characteristic
602	#95	C₂³×C₂₃	1	2	yes	—
603	#95	C₂³×C₂₃	1	2	yes	—
604	#95	C₂³×C₂₃	1	2	yes	—
605	#95	C₂³×C₂₃	1	2	yes	—
606	#95	C₂³×C₂₃	1	2	yes	—
607	C₂₃	#59989	1	1	yes	characteristic, direct product factor, Sylow
608	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
609	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	4	1	no	—
614	C₂×D₄	—	4	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	4	1	no	—
624	C₂²×C₄	—	4	1	no	—
625	C₂²×C₄	—	4	2	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	—	4	2	no	—
629	C₂²×C₄	—	4	2	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
642	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	4	1	no	—
659	C₄⋊C₄	—	4	1	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	—	4	1	no	—
662	C₄⋊C₄	—	4	1	no	—
663	C₄⋊C₄	—	4	2	no	—
664	C₄⋊C₄	—	4	1	no	—
665	C₄⋊C₄	—	4	2	no	—
666	C₄⋊C₄	—	4	2	no	—
667	C₄⋊C₄	—	4	2	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₄⋊C₄	—	4	2	no	—
670	C₄⋊C₄	—	4	2	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	4	1	no	—
682	C₂²⋊C₄	—	4	1	no	—
683	C₂²⋊C₄	—	4	2	no	—
684	C₂²⋊C₄	—	4	2	no	—
685	C₂²⋊C₄	—	4	2	no	—
686	C₂²⋊C₄	#41×C₂₃	1	8	yes	—
687	C₂²⋊C₄	#41×C₂₃	1	4	yes	—
688	C₄²	—	2	4	no	—
689	C₄²	—	2	4	no	—
690	C₄²	—	2	4	no	—
691	C₄²	—	2	4	no	—
692	C₄²	—	2	4	no	—
693	C₄²	—	2	2	no	—
694	C₄²	—	2	2	no	—
695	C₄²	—	4	2	no	—
696	C₄²	—	4	2	no	—
697	C₄²	—	4	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	C₂×#41×C₂₃	1	2	yes	—
709	C₂³	C₂×#41×C₂₃	1	4	yes	—
710	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
711	D₄	—	4	8	no	—
712	D₄	—	4	4	no	—
713	C₂×C₄	—	2	8	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	—	4	8	no	—
758	C₂×C₄	—	4	8	no	—
759	C₂×C₄	—	4	4	no	—
760	C₂×C₄	—	8	4	no	—
761	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
762	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
763	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
764	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
765	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
766	C₂²	—	2	4	no	—
767	C₂²	—	2	4	no	—
768	C₂²	—	2	4	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	4	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	2	no	—
778	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
779	C₂²	C₂²×#41×C₂₃	1	2	yes	—
780	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
781	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
782	C₂²	C₂₃×#585	1	2	yes	—
783	C₄	—	2	4	no	—
784	C₄	—	2	4	no	—
785	C₄	—	2	2	no	—
786	C₄	—	2	2	no	—
787	C₄	—	2	4	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	1	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	1	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	1	no	—
800	C₂	—	4	4	no	—
801	C₂	—	4	2	no	—
802	C₂	C₂₃×#3475	1	2	yes	—
803	C₂	C₂₃×#3481	1	1	yes	characteristic
804	C₂	C₂₃×#3492	1	1	yes	characteristic
805	C₂	C₂₃×#3515	1	2	yes	—
806	C₂	C₂₃×#3540	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂₃×#392	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×#2807	C₂	semidirect
2. C₂₃×#2782	C₂	semidirect
4. C₂₃×#2611	C₂	semidirect
6. C₂₃×#2587	C₂	semidirect
7. C₂₃×#2533	C₂	semidirect
8. C₂₃×#2517	C₂	semidirect
9. C₂₃×#2509	C₂	semidirect
10. C₂₃×#2505	C₂	semidirect
11. C₂₃×#2475	C₂	semidirect
12. C₂₃×#2470	C₂	semidirect
13. C₂₃×#2470	C₂	semidirect
15. C₂₃×#2359	C₂	semidirect
16. C₂₃×#2359	C₂	semidirect
17. C₂₃×#2346	C₂	semidirect
18. C₂₃×#2296	C₂	semidirect
19. C₂₃×#2290	C₂	semidirect
294. #59989	C₂₃	direct (N × H)
363. #2807	C₂×C₂₃	semidirect
364. #2782	C₂×C₂₃	semidirect
366. #2611	C₂×C₂₃	semidirect
368. #2587	C₂×C₂₃	semidirect
369. #2533	C₂×C₂₃	semidirect
370. #2517	C₂×C₂₃	semidirect
371. #2509	C₂×C₂₃	semidirect
372. #2505	C₂×C₂₃	semidirect
373. #2475	C₂×C₂₃	semidirect
374. #2470	C₂×C₂₃	semidirect
375. #2470	C₂×C₂₃	semidirect
377. #2359	C₂×C₂₃	semidirect
378. #2359	C₂×C₂₃	semidirect
379. #2346	C₂×C₂₃	semidirect
380. #2296	C₂×C₂₃	semidirect
381. #2290	C₂×C₂₃	semidirect
607. C₂₃	#59989	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×#2807	2
C₂₃×#2782	2
C₂₃×#2693	2
C₂₃×#2611	2
C₂₃×#2598	2
C₂₃×#2587	2
C₂₃×#2533	2
C₂₃×#2517	2
C₂₃×#2509	2
C₂₃×#2505	2
C₂₃×#2475	2
C₂₃×#2470	2
C₂₃×#2455	2
C₂₃×#2359	2
C₂₃×#2346	2
C₂₃×#2296	2
C₂₃×#2290	2
#59989	23

Subgroups — C23×#59989 #19207615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#59989 #19207615