Subgroups — C₂₃×#34640 #19182266

Order 5888.

1646 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2655	C₂	1	2	yes	maximal, complemented
2	C₂₃×#2654	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2653	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2652	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2651	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2650	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2649	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2648	C₂	1	2	yes	maximal
9	C₂₃×#2402	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2401	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2398	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2396	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2395	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2392	C₂	1	1	yes	maximal, characteristic
15	C₂₃×#2298	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2290	C₂	1	2	yes	maximal, complemented
19	C₄×C₂₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
23	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#117	C₂²	1	2	yes	—
26	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#401	C₂²	1	2	yes	—
28	C₂₃×#400	C₂²	1	2	yes	—
29	C₂₃×#400	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	2	yes	—
35	C₂₃×#400	C₂²	1	2	yes	—
36	C₂₃×#399	C₂²	1	2	yes	—
37	C₂₃×#399	C₂²	1	1	yes	characteristic
38	C₂₃×#398	C₂²	1	2	yes	—
39	C₂₃×#398	C₂²	1	2	yes	—
40	C₂₃×#398	C₂²	1	1	yes	characteristic
41	C₂₃×#398	C₂²	1	2	yes	—
42	C₂₃×#398	C₂²	1	2	yes	—
43	C₂₃×#397	C₂²	1	2	yes	—
44	C₂₃×#397	C₂²	1	2	yes	—
45	C₂₃×#397	C₂²	1	2	yes	—
46	C₂₃×#397	C₂²	1	2	yes	—
47	C₂₃×#397	C₂²	1	2	yes	—
48	C₂₃×#397	C₂²	1	1	yes	characteristic
49	C₂₃×#397	C₂²	1	2	yes	—
50	C₂₃×#397	C₂²	1	2	yes	—
51	C₂₃×#396	C₂²	1	2	yes	—
52	C₂₃×#396	C₂²	1	2	yes	—
53	C₂₃×#396	C₂²	1	2	yes	—
54	C₂₃×#395	C₂²	1	1	yes	characteristic
55	C₂₃×#394	C₂²	1	2	yes	—
56	C₂₃×#394	C₂²	1	2	yes	—
57	C₂₃×#394	C₂²	1	2	yes	—
58	C₂₃×#394	C₂²	1	1	yes	characteristic
59	C₂₃×#394	C₂²	1	2	yes	—
60	C₂₃×#393	C₂²	1	1	yes	characteristic
61	C₂₃×#393	C₂²	1	2	yes	—
62	C₂₃×#392	C₂²	1	1	yes	characteristic
63	C₂₃×#391	C₂²	1	2	yes	—
64	C₂₃×#390	C₂²	1	2	yes	—
65	C₂₃×#389	C₂²	1	2	yes	—
66	C₂₃×#389	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×#387	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×#386	C₂²	1	2	yes	—
84	C₂₃×#386	C₂²	1	2	yes	—
85	C₂₃×#385	C₂²	1	2	yes	—
86	C₂₃×#385	C₂²	1	2	yes	—
87	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
88	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
89	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
93	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
95	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
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	C₂₃×#376	C₂²	1	1	yes	characteristic
103	C₂₃×#376	C₂²	1	1	yes	characteristic
104	C₂₃×#376	C₂²	1	2	yes	—
105	C₄³×C₂₃	C₂²	1	1	yes	characteristic
106	C₄³×C₂₃	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×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	C₄×Q₈×C₂₃	—	2	4	no	—
114	C₄×D₄×C₂₃	—	2	8	no	—
115	C₄×D₄×C₂₃	—	2	4	no	—
116	C₂₃×#117	—	2	4	no	—
117	C₂₃×#117	—	2	8	no	—
118	C₂₃×#117	—	2	4	no	—
119	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
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	1	yes	characteristic
127	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₂₃	C₂³	1	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×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₂₃	C₂³	1	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	2	yes	—
155	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
156	C₂×C₄²×C₂₃	—	2	4	no	—
157	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
158	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
164	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
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	2	yes	—
169	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
171	C₂₃×#95	C₂³	1	2	yes	—
172	C₂₃×#95	C₂³	1	2	yes	—
173	C₂₃×#95	C₂³	1	2	yes	—
174	C₂₃×#95	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	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	1	yes	characteristic
192	C₂₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
200	C₂₃×#95	C₂³	1	1	yes	characteristic
201	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
202	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
203	C₂×Q₈×C₂₃	—	2	2	no	—
204	C₂×Q₈×C₂₃	—	4	2	no	—
205	C₂×D₄×C₂₃	—	2	4	no	—
206	C₂×D₄×C₂₃	—	2	2	no	—
207	C₂×D₄×C₂₃	—	4	2	no	—
208	C₂×D₄×C₂₃	—	4	2	no	—
209	C₂×D₄×C₂₃	—	4	2	no	—
210	C₂²×C₄×C₂₃	—	2	2	no	—
211	C₂²×C₄×C₂₃	—	2	2	no	—
212	C₂²×C₄×C₂₃	—	2	4	no	—
213	C₂²×C₄×C₂₃	—	2	4	no	—
214	C₂²×C₄×C₂₃	—	2	4	no	—
215	C₂²×C₄×C₂₃	—	2	4	no	—
216	C₂²×C₄×C₂₃	—	4	2	no	—
217	C₂²×C₄×C₂₃	—	4	2	no	—
218	C₂²×C₄×C₂₃	#41	1	4	yes	—
219	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
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	2	yes	—
232	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
236	C₄⋊C₄×C₂₃	—	2	2	no	—
237	C₄⋊C₄×C₂₃	—	2	2	no	—
238	C₄⋊C₄×C₂₃	—	2	4	no	—
239	C₄⋊C₄×C₂₃	—	2	4	no	—
240	C₄⋊C₄×C₂₃	—	2	4	no	—
241	C₄⋊C₄×C₂₃	—	2	4	no	—
242	C₄⋊C₄×C₂₃	—	2	2	no	—
243	C₄⋊C₄×C₂₃	—	2	2	no	—
244	C₄⋊C₄×C₂₃	—	2	4	no	—
245	C₄⋊C₄×C₂₃	—	4	2	no	—
246	C₄⋊C₄×C₂₃	—	4	2	no	—
247	C₄⋊C₄×C₂₃	—	4	2	no	—
248	C₄⋊C₄×C₂₃	—	4	2	no	—
249	C₄⋊C₄×C₂₃	—	4	2	no	—
250	C₄⋊C₄×C₂₃	—	4	2	no	—
251	C₄⋊C₄×C₂₃	—	4	2	no	—
252	C₄⋊C₄×C₂₃	—	4	2	no	—
253	C₄⋊C₄×C₂₃	—	4	2	no	—
254	C₄⋊C₄×C₂₃	—	4	2	no	—
255	C₂²⋊C₄×C₂₃	—	2	4	no	—
256	C₂²⋊C₄×C₂₃	—	2	4	no	—
257	C₂²⋊C₄×C₂₃	—	2	4	no	—
258	C₂²⋊C₄×C₂₃	—	2	4	no	—
259	C₂²⋊C₄×C₂₃	—	2	2	no	—
260	C₂²⋊C₄×C₂₃	—	2	2	no	—
261	C₂²⋊C₄×C₂₃	—	2	4	no	—
262	C₂²⋊C₄×C₂₃	—	2	4	no	—
263	C₂²⋊C₄×C₂₃	—	4	2	no	—
264	C₂²⋊C₄×C₂₃	—	4	2	no	—
265	C₂²⋊C₄×C₂₃	—	4	2	no	—
266	C₂²⋊C₄×C₂₃	—	4	2	no	—
267	C₂²⋊C₄×C₂₃	—	4	2	no	—
268	C₂²⋊C₄×C₂₃	—	4	2	no	—
269	C₂²⋊C₄×C₂₃	—	4	2	no	—
270	C₂²⋊C₄×C₂₃	—	4	2	no	—
271	C₂²⋊C₄×C₂₃	—	4	2	no	—
272	C₂²⋊C₄×C₂₃	—	4	2	no	—
273	C₄²×C₂₃	—	2	4	no	—
274	C₄²×C₂₃	—	2	2	no	—
275	C₄²×C₂₃	—	2	2	no	—
276	C₄²×C₂₃	—	2	2	no	—
277	C₄²×C₂₃	—	2	2	no	—
278	C₄²×C₂₃	—	2	4	no	—
279	C₄²×C₂₃	—	2	4	no	—
280	C₄²×C₂₃	—	2	4	no	—
281	C₄²×C₂₃	—	4	2	no	—
282	C₄²×C₂₃	—	4	2	no	—
283	C₄²×C₂₃	—	4	2	no	—
284	C₄²×C₂₃	—	4	2	no	—
285	C₄²×C₂₃	#41	1	4	yes	—
286	C₄²×C₂₃	#41	1	4	yes	—
287	#34640	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₂³×C₂₃	—	2	1	no	—
289	C₂³×C₂₃	—	2	1	no	—
290	C₂³×C₂₃	—	2	2	no	—
291	C₂³×C₂₃	—	2	2	no	—
292	C₂³×C₂₃	—	2	2	no	—
293	C₂³×C₂₃	—	2	2	no	—
294	C₂³×C₂₃	—	2	2	no	—
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	C₂×#41	1	2	yes	—
300	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
301	Q₈×C₂₃	—	4	4	no	—
302	D₄×C₂₃	—	4	4	no	—
303	D₄×C₂₃	—	4	8	no	—
304	C₂×C₄×C₂₃	—	2	1	no	—
305	C₂×C₄×C₂₃	—	2	1	no	—
306	C₂×C₄×C₂₃	—	2	2	no	—
307	C₂×C₄×C₂₃	—	2	2	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	2	no	—
310	C₂×C₄×C₂₃	—	2	8	no	—
311	C₂×C₄×C₂₃	—	2	2	no	—
312	C₂×C₄×C₂₃	—	2	2	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	2	no	—
315	C₂×C₄×C₂₃	—	2	1	no	—
316	C₂×C₄×C₂₃	—	2	1	no	—
317	C₂×C₄×C₂₃	—	2	2	no	—
318	C₂×C₄×C₂₃	—	2	2	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	2	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	—	4	8	no	—
346	C₂×C₄×C₂₃	—	4	8	no	—
347	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
348	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
349	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
350	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
351	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
352	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
353	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
354	#2655	C₂×C₂₃	1	2	yes	complemented
355	#2654	C₂×C₂₃	1	2	yes	complemented
356	#2653	C₂×C₂₃	1	2	yes	complemented
357	#2652	C₂×C₂₃	1	2	yes	complemented
358	#2651	C₂×C₂₃	1	2	yes	complemented
359	#2650	C₂×C₂₃	1	2	yes	complemented
360	#2649	C₂×C₂₃	1	2	yes	complemented
361	#2648	C₂×C₂₃	1	2	yes	—
362	#2402	C₂×C₂₃	1	1	yes	characteristic, complemented
363	#2401	C₂×C₂₃	1	2	yes	complemented
364	#2398	C₂×C₂₃	1	1	yes	characteristic, complemented
365	#2396	C₂×C₂₃	1	1	yes	characteristic, complemented
366	#2395	C₂×C₂₃	1	2	yes	complemented
367	#2392	C₂×C₂₃	1	1	yes	characteristic
368	#2298	C₂×C₂₃	1	2	yes	complemented
369	#2295	C₂×C₂₃	1	1	yes	characteristic, complemented
370	#2293	C₂×C₂₃	1	1	yes	characteristic, complemented
371	#2290	C₂×C₂₃	1	2	yes	complemented
372	C₄×#117	C₂×C₂₃	1	1	yes	characteristic, complemented
373	C₂²×C₂₃	—	2	2	no	—
374	C₂²×C₂₃	—	2	4	no	—
375	C₂²×C₂₃	—	4	2	no	—
376	C₂²×C₂₃	—	4	1	no	—
377	C₂²×C₂₃	—	4	1	no	—
378	C₂²×C₂₃	—	4	2	no	—
379	C₂²×C₂₃	—	4	2	no	—
380	C₂²×C₂₃	—	4	2	no	—
381	C₂²×C₂₃	—	4	2	no	—
382	C₂²×C₂₃	—	4	2	no	—
383	C₂²×C₂₃	—	4	2	no	—
384	C₂²×C₂₃	—	4	2	no	—
385	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
386	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
387	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
388	C₂²×C₂₃	#585	1	2	yes	—
389	C₂²×C₂₃	#585	1	2	yes	—
390	C₄×C₂₃	—	2	2	no	—
391	C₄×C₂₃	—	2	4	no	—
392	C₄×C₂₃	—	2	2	no	—
393	C₄×C₂₃	—	2	2	no	—
394	C₄×C₂₃	—	4	2	no	—
395	C₄×C₂₃	—	4	1	no	—
396	C₄×C₂₃	—	4	1	no	—
397	C₄×C₂₃	—	4	2	no	—
398	C₄×C₂₃	—	4	2	no	—
399	C₄×C₂₃	—	4	2	no	—
400	C₄×C₂₃	—	4	2	no	—
401	C₄×C₂₃	—	4	2	no	—
402	C₄×C₂₃	—	4	2	no	—
403	C₄×C₂₃	—	4	2	no	—
404	C₄×C₂₃	—	4	2	no	—
405	C₄×C₂₃	—	4	2	no	—
406	C₄×C₂₃	#529	1	4	yes	—
407	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
408	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
409	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
410	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
411	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
412	C₂×#117	C₂²×C₂₃	1	2	yes	—
413	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
414	#401	C₂²×C₂₃	1	2	yes	—
415	#400	C₂²×C₂₃	1	2	yes	—
416	#400	C₂²×C₂₃	1	2	yes	—
417	#400	C₂²×C₂₃	1	2	yes	—
418	#400	C₂²×C₂₃	1	2	yes	—
419	#400	C₂²×C₂₃	1	2	yes	—
420	#400	C₂²×C₂₃	1	1	yes	characteristic
421	#400	C₂²×C₂₃	1	2	yes	—
422	#400	C₂²×C₂₃	1	2	yes	—
423	#399	C₂²×C₂₃	1	1	yes	characteristic
424	#399	C₂²×C₂₃	1	2	yes	—
425	#398	C₂²×C₂₃	1	1	yes	characteristic
426	#398	C₂²×C₂₃	1	2	yes	—
427	#398	C₂²×C₂₃	1	2	yes	—
428	#398	C₂²×C₂₃	1	2	yes	—
429	#398	C₂²×C₂₃	1	2	yes	—
430	#397	C₂²×C₂₃	1	1	yes	characteristic
431	#397	C₂²×C₂₃	1	2	yes	—
432	#397	C₂²×C₂₃	1	2	yes	—
433	#397	C₂²×C₂₃	1	2	yes	—
434	#397	C₂²×C₂₃	1	2	yes	—
435	#397	C₂²×C₂₃	1	2	yes	—
436	#397	C₂²×C₂₃	1	2	yes	—
437	#397	C₂²×C₂₃	1	2	yes	—
438	#396	C₂²×C₂₃	1	2	yes	—
439	#396	C₂²×C₂₃	1	2	yes	—
440	#396	C₂²×C₂₃	1	2	yes	—
441	#395	C₂²×C₂₃	1	1	yes	characteristic
442	#394	C₂²×C₂₃	1	2	yes	—
443	#394	C₂²×C₂₃	1	1	yes	characteristic
444	#394	C₂²×C₂₃	1	2	yes	—
445	#394	C₂²×C₂₃	1	2	yes	—
446	#394	C₂²×C₂₃	1	2	yes	—
447	#393	C₂²×C₂₃	1	2	yes	—
448	#393	C₂²×C₂₃	1	1	yes	characteristic
449	#392	C₂²×C₂₃	1	1	yes	characteristic
450	#391	C₂²×C₂₃	1	2	yes	—
451	#390	C₂²×C₂₃	1	2	yes	—
452	#389	C₂²×C₂₃	1	2	yes	—
453	#389	C₂²×C₂₃	1	2	yes	—
454	#388	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	#387	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	#386	C₂²×C₂₃	1	2	yes	—
471	#386	C₂²×C₂₃	1	2	yes	—
472	#385	C₂²×C₂₃	1	2	yes	—
473	#385	C₂²×C₂₃	1	2	yes	—
474	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
475	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
476	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
477	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
478	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
479	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
480	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
481	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
482	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
483	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
484	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
485	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
486	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
487	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
488	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
489	#376	C₂²×C₂₃	1	1	yes	characteristic
490	#376	C₂²×C₂₃	1	1	yes	characteristic
491	#376	C₂²×C₂₃	1	2	yes	—
492	C₄³	C₂²×C₂₃	1	1	yes	characteristic
493	C₄³	C₂²×C₂₃	1	1	yes	characteristic
494	C₂×C₂₃	—	4	2	no	—
495	C₂×C₂₃	—	8	2	no	—
496	C₂×C₂₃	C₂×#529	1	1	yes	characteristic
497	C₂×C₂₃	#3455	1	2	yes	—
498	C₂×C₂₃	#3455	1	1	yes	characteristic
499	C₂×C₂₃	#3455	1	1	yes	characteristic
500	C₂×C₂₃	#3455	1	2	yes	—
501	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
502	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
503	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
505	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
507	C₄×Q₈	—	2	4	no	—
508	C₄×D₄	—	2	8	no	—
509	C₄×D₄	—	2	4	no	—
510	#117	—	2	4	no	—
511	#117	—	2	8	no	—
512	#117	—	2	4	no	—
513	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
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×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
550	C₂×C₄²	—	2	4	no	—
551	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
552	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
555	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
556	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
557	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
558	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
559	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
560	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
561	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
562	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
563	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
564	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
565	#95	C₂³×C₂₃	1	2	yes	—
566	#95	C₂³×C₂₃	1	2	yes	—
567	#95	C₂³×C₂₃	1	2	yes	—
568	#95	C₂³×C₂₃	1	2	yes	—
569	#95	C₂³×C₂₃	1	2	yes	—
570	#95	C₂³×C₂₃	1	2	yes	—
571	#95	C₂³×C₂₃	1	2	yes	—
572	#95	C₂³×C₂₃	1	2	yes	—
573	#95	C₂³×C₂₃	1	2	yes	—
574	#95	C₂³×C₂₃	1	2	yes	—
575	#95	C₂³×C₂₃	1	2	yes	—
576	#95	C₂³×C₂₃	1	2	yes	—
577	#95	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	2	yes	—
584	#95	C₂³×C₂₃	1	2	yes	—
585	#95	C₂³×C₂₃	1	1	yes	characteristic
586	#95	C₂³×C₂₃	1	1	yes	characteristic
587	#95	C₂³×C₂₃	1	2	yes	—
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	1	yes	characteristic
594	#95	C₂³×C₂₃	1	1	yes	characteristic
595	C₂₃	#34640	1	1	yes	characteristic, direct product factor, Sylow
596	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
597	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
598	C₂×Q₈	—	2	2	no	—
599	C₂×Q₈	—	4	2	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	4	2	no	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	—	4	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	4	2	no	—
612	C₂²×C₄	—	4	2	no	—
613	C₂²×C₄	#41×C₂₃	1	4	yes	—
614	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
621	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
628	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
629	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
630	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	4	2	no	—
641	C₄⋊C₄	—	4	2	no	—
642	C₄⋊C₄	—	4	2	no	—
643	C₄⋊C₄	—	4	2	no	—
644	C₄⋊C₄	—	4	2	no	—
645	C₄⋊C₄	—	4	2	no	—
646	C₄⋊C₄	—	4	2	no	—
647	C₄⋊C₄	—	4	2	no	—
648	C₄⋊C₄	—	4	2	no	—
649	C₄⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	4	2	no	—
659	C₂²⋊C₄	—	4	2	no	—
660	C₂²⋊C₄	—	4	2	no	—
661	C₂²⋊C₄	—	4	2	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₂²⋊C₄	—	4	2	no	—
666	C₂²⋊C₄	—	4	2	no	—
667	C₂²⋊C₄	—	4	2	no	—
668	C₄²	—	2	4	no	—
669	C₄²	—	2	2	no	—
670	C₄²	—	2	2	no	—
671	C₄²	—	2	2	no	—
672	C₄²	—	2	2	no	—
673	C₄²	—	2	4	no	—
674	C₄²	—	2	4	no	—
675	C₄²	—	2	4	no	—
676	C₄²	—	4	2	no	—
677	C₄²	—	4	2	no	—
678	C₄²	—	4	2	no	—
679	C₄²	—	4	2	no	—
680	C₄²	#41×C₂₃	1	4	yes	—
681	C₄²	#41×C₂₃	1	4	yes	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	1	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	C₂×#41×C₂₃	1	2	yes	—
694	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
695	Q₈	—	4	4	no	—
696	D₄	—	4	4	no	—
697	D₄	—	4	8	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	8	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	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	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	4	8	no	—
740	C₂×C₄	—	4	8	no	—
741	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
742	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
743	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
744	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
745	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
746	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
747	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
748	C₂²	—	2	2	no	—
749	C₂²	—	2	4	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
761	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
762	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
763	C₂²	C₂₃×#585	1	2	yes	—
764	C₂²	C₂₃×#585	1	2	yes	—
765	C₄	—	2	2	no	—
766	C₄	—	2	4	no	—
767	C₄	—	2	2	no	—
768	C₄	—	2	2	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	1	no	—
774	C₄	—	4	1	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	C₂₃×#529	1	4	yes	—
782	C₂	—	4	2	no	—
783	C₂	—	8	2	no	—
784	C₂	C₂×C₂₃×#529	1	1	yes	characteristic
785	C₂	C₂₃×#3455	1	2	yes	—
786	C₂	C₂₃×#3455	1	1	yes	characteristic
787	C₂	C₂₃×#3455	1	1	yes	characteristic
788	C₂	C₂₃×#3455	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
socle	C₂³×C₂₃	C₂⁵
prime radical	C₂₃×#392	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂₃×#2655	C₂	semidirect
2. C₂₃×#2654	C₂	semidirect
3. C₂₃×#2653	C₂	semidirect
4. C₂₃×#2652	C₂	semidirect
5. C₂₃×#2651	C₂	semidirect
6. C₂₃×#2650	C₂	semidirect
7. C₂₃×#2649	C₂	semidirect
9. C₂₃×#2402	C₂	semidirect
10. C₂₃×#2401	C₂	semidirect
11. C₂₃×#2398	C₂	semidirect
12. C₂₃×#2396	C₂	semidirect
13. C₂₃×#2395	C₂	semidirect
15. C₂₃×#2298	C₂	semidirect
16. C₂₃×#2295	C₂	semidirect
17. C₂₃×#2293	C₂	semidirect
18. C₂₃×#2290	C₂	semidirect
19. C₄×C₂₃×#117	C₂	semidirect
287. #34640	C₂₃	direct (N × H)
354. #2655	C₂×C₂₃	semidirect
355. #2654	C₂×C₂₃	semidirect
356. #2653	C₂×C₂₃	semidirect
357. #2652	C₂×C₂₃	semidirect
358. #2651	C₂×C₂₃	semidirect
359. #2650	C₂×C₂₃	semidirect
360. #2649	C₂×C₂₃	semidirect
362. #2402	C₂×C₂₃	semidirect
363. #2401	C₂×C₂₃	semidirect
364. #2398	C₂×C₂₃	semidirect
365. #2396	C₂×C₂₃	semidirect
366. #2395	C₂×C₂₃	semidirect
368. #2298	C₂×C₂₃	semidirect
369. #2295	C₂×C₂₃	semidirect
370. #2293	C₂×C₂₃	semidirect
371. #2290	C₂×C₂₃	semidirect
372. C₄×#117	C₂×C₂₃	semidirect
595. C₂₃	#34640	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×#2655	2
C₂₃×#2654	2
C₂₃×#2653	2
C₂₃×#2652	2
C₂₃×#2651	2
C₂₃×#2650	2
C₂₃×#2649	2
C₂₃×#2648	2
C₂₃×#2402	2
C₂₃×#2401	2
C₂₃×#2398	2
C₂₃×#2396	2
C₂₃×#2395	2
C₂₃×#2392	2
C₂₃×#2298	2
C₂₃×#2295	2
C₂₃×#2293	2
C₂₃×#2290	2
C₄×C₂₃×#117	2
#34640	23

Subgroups — C23×#34640 #19182266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34640 #19182266