Subgroups — C₂₃×#36722 #19184348

Order 5888.

2602 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2847	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2707	C₂	1	4	yes	maximal, complemented
6	C₂₃×#2705	C₂	1	4	yes	maximal, complemented
7	C₂₃×#2682	C₂	1	4	yes	maximal, complemented
8	C₂₃×#2681	C₂	1	4	yes	maximal, complemented
9	C₂₃×#2626	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2617	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2579	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2411	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2411	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2408	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2316	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#539	—	2	8	no	—
19	C₂×C₂₃×#126	C₂²	1	2	yes	complemented
20	C₂×C₂₃×#125	C₂²	1	2	yes	complemented
21	C₂×C₂₃×#123	—	2	8	no	—
22	C₂×C₂₃×#123	C₂²	1	4	yes	—
23	C₂×C₂₃×#123	C₂²	1	4	yes	—
24	C₂×C₂₃×#123	C₂²	1	2	yes	—
25	C₂×C₂₃×#123	C₂²	1	2	yes	complemented
26	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
29	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#121	C₂²	1	4	yes	—
31	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
32	C₂×C₂₃×#120	C₂²	1	2	yes	—
33	C₂×C₂₃×#120	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
35	C₂×C₂₃×#117	C₂²	1	2	yes	—
36	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
41	C₂₃×#399	C₂²	1	2	yes	complemented
42	C₂₃×#398	C₂²	1	4	yes	complemented
43	C₂₃×#397	C₂²	1	2	yes	complemented
44	C₂₃×#396	C₂²	1	4	yes	complemented
45	C₂₃×#396	C₂²	1	4	yes	complemented
46	C₂₃×#396	C₂²	1	4	yes	complemented
47	C₂₃×#396	C₂²	1	4	yes	complemented
48	C₂₃×#394	C₂²	1	4	yes	—
49	C₂₃×#394	C₂²	1	4	yes	complemented
50	C₂₃×#394	C₂²	1	4	yes	complemented
51	C₂₃×#394	C₂²	1	4	yes	complemented
52	C₂₃×#393	C₂²	1	2	yes	complemented
53	C₂₃×#392	C₂²	1	4	yes	—
54	C₂₃×#392	C₂²	1	2	yes	complemented
55	C₂₃×#390	C₂²	1	4	yes	—
56	C₂₃×#390	C₂²	1	4	yes	complemented
57	C₂₃×#390	C₂²	1	4	yes	complemented
58	C₂₃×#389	C₂²	1	4	yes	complemented
59	C₂₃×#389	C₂²	1	4	yes	complemented
60	C₂₃×#388	C₂²	1	4	yes	complemented
61	C₂₃×#388	C₂²	1	4	yes	complemented
62	C₂₃×#387	C₂²	1	4	yes	complemented
63	C₂₃×#386	C₂²	1	2	yes	—
64	C₂₃×#386	C₂²	1	2	yes	—
65	C₂₃×#386	C₂²	1	4	yes	complemented
66	C₂₃×#385	C₂²	1	2	yes	—
67	C₂₃×#385	C₂²	1	2	yes	—
68	C₂₃×#385	C₂²	1	4	yes	complemented
69	C₂₃×#385	C₂²	1	4	yes	complemented
70	C₂₃×#380	C₂²	1	2	yes	—
71	C₂₃×#380	C₂²	1	1	yes	characteristic
72	C₂₃×#380	C₂²	1	1	yes	characteristic
73	C₂₃×#380	C₂²	1	2	yes	complemented
74	C₂₃×#380	C₂²	1	2	yes	complemented
75	C₂₃×#379	C₂²	1	2	yes	—
76	C₂₃×#379	C₂²	1	2	yes	—
77	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
78	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₂₃	—	2	4	no	—
81	C₂²×D₄×C₂₃	—	4	4	no	—
82	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
83	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
84	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
85	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
87	C₂³×C₄×C₂₃	—	2	4	no	—
88	C₂³×C₄×C₂₃	—	4	4	no	—
89	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
90	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
91	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
95	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
97	C₂₃×#126	—	2	8	no	—
98	C₂₃×#125	—	2	8	no	—
99	C₂₃×#123	—	2	8	no	—
100	C₂₃×#123	—	2	16	no	—
101	C₂₃×#123	—	2	16	no	—
102	C₂₃×#123	—	2	8	no	—
103	C₂₃×C₂²⋊Q₈	—	2	4	no	—
104	C₂₃×C₂²⋊Q₈	—	2	8	no	—
105	C₂₃×C₂²⋊Q₈	—	4	4	no	—
106	C₂₃×#121	—	2	4	no	—
107	C₂₃×#121	—	4	8	no	—
108	C₂₃×#121	—	4	4	no	—
109	C₂₃×#120	—	4	4	no	—
110	C₂₃×#120	—	4	4	no	—
111	C₄×D₄×C₂₃	—	2	8	no	—
112	C₂₃×#117	—	4	4	no	—
113	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
114	C₂×C₄⋊C₄×C₂₃	D₄	1	8	yes	complemented
115	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
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	4	yes	—
125	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
131	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
132	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
133	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
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	4	yes	—
146	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
152	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
153	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
154	C₂₃×#95	C₂³	1	2	yes	—
155	C₂₃×#95	C₂³	1	4	yes	—
156	C₂₃×#95	C₂³	1	2	yes	—
157	C₂₃×#95	C₂³	1	4	yes	—
158	C₂₃×#95	C₂³	1	4	yes	—
159	C₂₃×#95	C₂³	1	4	yes	—
160	C₂₃×#95	C₂³	1	4	yes	—
161	C₂⁴×C₂₃	—	2	2	no	—
162	C₂⁴×C₂₃	—	2	4	no	—
163	C₂⁴×C₂₃	—	2	2	no	—
164	C₂⁴×C₂₃	—	2	2	no	—
165	C₂⁴×C₂₃	—	2	2	no	—
166	C₂⁴×C₂₃	—	2	2	no	—
167	C₂⁴×C₂₃	—	2	2	no	—
168	C₂⁴×C₂₃	—	4	2	no	—
169	C₂⁴×C₂₃	—	4	2	no	—
170	C₂⁴×C₂₃	—	4	2	no	—
171	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
172	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
173	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
174	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
175	C₂×Q₈×C₂₃	—	2	2	no	—
176	C₂×Q₈×C₂₃	—	4	2	no	—
177	C₂×D₄×C₂₃	—	2	4	no	—
178	C₂×D₄×C₂₃	—	2	4	no	—
179	C₂×D₄×C₂₃	—	2	8	no	—
180	C₂×D₄×C₂₃	—	2	4	no	—
181	C₂×D₄×C₂₃	—	2	8	no	—
182	C₂×D₄×C₂₃	—	2	8	no	—
183	C₂×D₄×C₂₃	—	2	2	no	—
184	C₂×D₄×C₂₃	—	4	4	no	—
185	C₂×D₄×C₂₃	—	4	4	no	—
186	C₂×D₄×C₂₃	—	4	4	no	—
187	C₂×D₄×C₂₃	—	4	2	no	—
188	C₂×D₄×C₂₃	—	4	4	no	—
189	C₂×D₄×C₂₃	—	4	4	no	—
190	C₂×D₄×C₂₃	—	4	4	no	—
191	C₂×D₄×C₂₃	—	4	16	no	—
192	C₂²×C₄×C₂₃	—	2	2	no	—
193	C₂²×C₄×C₂₃	—	2	2	no	—
194	C₂²×C₄×C₂₃	—	2	2	no	—
195	C₂²×C₄×C₂₃	—	2	2	no	—
196	C₂²×C₄×C₂₃	—	2	4	no	—
197	C₂²×C₄×C₂₃	—	2	4	no	—
198	C₂²×C₄×C₂₃	—	2	4	no	—
199	C₂²×C₄×C₂₃	—	2	4	no	—
200	C₂²×C₄×C₂₃	—	2	4	no	—
201	C₂²×C₄×C₂₃	—	4	2	no	—
202	C₂²×C₄×C₂₃	—	4	2	no	—
203	C₂²×C₄×C₂₃	—	4	2	no	—
204	C₂²×C₄×C₂₃	—	4	2	no	—
205	C₂²×C₄×C₂₃	—	4	2	no	—
206	C₂²×C₄×C₂₃	—	4	2	no	—
207	C₂²×C₄×C₂₃	—	4	4	no	—
208	C₂²×C₄×C₂₃	—	4	16	no	—
209	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
210	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
211	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
212	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
215	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
223	C₄⋊C₄×C₂₃	—	2	8	no	—
224	C₄⋊C₄×C₂₃	—	2	4	no	—
225	C₄⋊C₄×C₂₃	—	2	2	no	—
226	C₄⋊C₄×C₂₃	—	2	4	no	—
227	C₄⋊C₄×C₂₃	—	2	4	no	—
228	C₄⋊C₄×C₂₃	—	2	2	no	—
229	C₄⋊C₄×C₂₃	—	2	4	no	—
230	C₄⋊C₄×C₂₃	—	4	4	no	—
231	C₄⋊C₄×C₂₃	—	4	4	no	—
232	C₄⋊C₄×C₂₃	—	4	2	no	—
233	C₄⋊C₄×C₂₃	—	4	4	no	—
234	C₄⋊C₄×C₂₃	—	4	2	no	—
235	C₄⋊C₄×C₂₃	—	4	4	no	—
236	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
237	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
238	C₂²⋊C₄×C₂₃	—	2	4	no	—
239	C₂²⋊C₄×C₂₃	—	2	4	no	—
240	C₂²⋊C₄×C₂₃	—	2	4	no	—
241	C₂²⋊C₄×C₂₃	—	2	8	no	—
242	C₂²⋊C₄×C₂₃	—	2	8	no	—
243	C₂²⋊C₄×C₂₃	—	2	4	no	—
244	C₂²⋊C₄×C₂₃	—	2	4	no	—
245	C₂²⋊C₄×C₂₃	—	2	8	no	—
246	C₂²⋊C₄×C₂₃	—	2	4	no	—
247	C₂²⋊C₄×C₂₃	—	2	4	no	—
248	C₂²⋊C₄×C₂₃	—	2	4	no	—
249	C₂²⋊C₄×C₂₃	—	2	4	no	—
250	C₂²⋊C₄×C₂₃	—	4	4	no	—
251	C₂²⋊C₄×C₂₃	—	4	4	no	—
252	C₂²⋊C₄×C₂₃	—	4	4	no	—
253	C₂²⋊C₄×C₂₃	—	4	4	no	—
254	C₂²⋊C₄×C₂₃	—	4	4	no	—
255	C₂²⋊C₄×C₂₃	—	4	4	no	—
256	C₂²⋊C₄×C₂₃	—	4	4	no	—
257	C₄²×C₂₃	—	2	4	no	—
258	C₄²×C₂₃	—	4	4	no	—
259	#36722	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
260	C₂³×C₂₃	—	2	2	no	—
261	C₂³×C₂₃	—	2	2	no	—
262	C₂³×C₂₃	—	2	8	no	—
263	C₂³×C₂₃	—	2	2	no	—
264	C₂³×C₂₃	—	2	2	no	—
265	C₂³×C₂₃	—	2	2	no	—
266	C₂³×C₂₃	—	2	2	no	—
267	C₂³×C₂₃	—	2	2	no	—
268	C₂³×C₂₃	—	2	2	no	—
269	C₂³×C₂₃	—	2	2	no	—
270	C₂³×C₂₃	—	2	2	no	—
271	C₂³×C₂₃	—	2	2	no	—
272	C₂³×C₂₃	—	2	4	no	—
273	C₂³×C₂₃	—	2	4	no	—
274	C₂³×C₂₃	—	2	2	no	—
275	C₂³×C₂₃	—	2	2	no	—
276	C₂³×C₂₃	—	2	2	no	—
277	C₂³×C₂₃	—	2	4	no	—
278	C₂³×C₂₃	—	2	4	no	—
279	C₂³×C₂₃	—	4	8	no	—
280	C₂³×C₂₃	—	4	8	no	—
281	C₂³×C₂₃	—	4	4	no	—
282	C₂³×C₂₃	—	4	4	no	—
283	C₂³×C₂₃	—	4	4	no	—
284	C₂³×C₂₃	—	4	4	no	—
285	C₂³×C₂₃	—	4	4	no	—
286	C₂³×C₂₃	—	8	4	no	—
287	C₂³×C₂₃	—	8	4	no	—
288	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
289	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
290	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
291	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
292	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
293	Q₈×C₂₃	—	8	2	no	—
294	D₄×C₂₃	—	4	16	no	—
295	D₄×C₂₃	—	4	8	no	—
296	D₄×C₂₃	—	8	2	no	—
297	D₄×C₂₃	—	8	8	no	—
298	D₄×C₂₃	—	8	8	no	—
299	C₂×C₄×C₂₃	—	2	8	no	—
300	C₂×C₄×C₂₃	—	2	2	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	2	no	—
303	C₂×C₄×C₂₃	—	2	4	no	—
304	C₂×C₄×C₂₃	—	2	2	no	—
305	C₂×C₄×C₂₃	—	2	2	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	4	no	—
311	C₂×C₄×C₂₃	—	2	4	no	—
312	C₂×C₄×C₂₃	—	2	4	no	—
313	C₂×C₄×C₂₃	—	2	4	no	—
314	C₂×C₄×C₂₃	—	2	2	no	—
315	C₂×C₄×C₂₃	—	2	4	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	2	no	—
318	C₂×C₄×C₂₃	—	2	2	no	—
319	C₂×C₄×C₂₃	—	2	4	no	—
320	C₂×C₄×C₂₃	—	2	4	no	—
321	C₂×C₄×C₂₃	—	2	4	no	—
322	C₂×C₄×C₂₃	—	2	4	no	—
323	C₂×C₄×C₂₃	—	4	4	no	—
324	C₂×C₄×C₂₃	—	4	4	no	—
325	C₂×C₄×C₂₃	—	4	8	no	—
326	C₂×C₄×C₂₃	—	4	8	no	—
327	C₂×C₄×C₂₃	—	4	4	no	—
328	C₂×C₄×C₂₃	—	4	4	no	—
329	C₂×C₄×C₂₃	—	8	4	no	—
330	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
331	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
332	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
334	C₂×#539	C₂×C₂₃	1	1	yes	characteristic, complemented
335	C₂²×#123	C₂×C₂₃	1	1	yes	characteristic, complemented
336	#2848	C₂×C₂₃	1	1	yes	characteristic, complemented
337	#2847	C₂×C₂₃	1	1	yes	characteristic, complemented
338	#2707	C₂×C₂₃	1	4	yes	complemented
339	#2705	C₂×C₂₃	1	4	yes	complemented
340	#2682	C₂×C₂₃	1	4	yes	complemented
341	#2681	C₂×C₂₃	1	4	yes	complemented
342	#2626	C₂×C₂₃	1	1	yes	characteristic, complemented
343	#2617	C₂×C₂₃	1	1	yes	characteristic, complemented
344	#2579	C₂×C₂₃	1	2	yes	complemented
345	#2411	C₂×C₂₃	1	2	yes	complemented
346	#2411	C₂×C₂₃	1	2	yes	complemented
347	#2408	C₂×C₂₃	1	2	yes	complemented
348	#2316	C₂×C₂₃	1	1	yes	characteristic, complemented
349	C₂²×C₂₃	—	2	2	no	—
350	C₂²×C₂₃	—	2	2	no	—
351	C₂²×C₂₃	—	2	4	no	—
352	C₂²×C₂₃	—	2	4	no	—
353	C₂²×C₂₃	—	2	4	no	—
354	C₂²×C₂₃	—	2	4	no	—
355	C₂²×C₂₃	—	2	4	no	—
356	C₂²×C₂₃	—	4	16	no	—
357	C₂²×C₂₃	—	4	2	no	—
358	C₂²×C₂₃	—	4	2	no	—
359	C₂²×C₂₃	—	4	2	no	—
360	C₂²×C₂₃	—	4	2	no	—
361	C₂²×C₂₃	—	4	2	no	—
362	C₂²×C₂₃	—	4	2	no	—
363	C₂²×C₂₃	—	4	2	no	—
364	C₂²×C₂₃	—	4	2	no	—
365	C₂²×C₂₃	—	4	2	no	—
366	C₂²×C₂₃	—	4	2	no	—
367	C₂²×C₂₃	—	4	4	no	—
368	C₂²×C₂₃	—	4	4	no	—
369	C₂²×C₂₃	—	4	4	no	—
370	C₂²×C₂₃	—	4	4	no	—
371	C₂²×C₂₃	—	8	8	no	—
372	C₂²×C₂₃	#537	1	4	yes	—
373	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
374	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
375	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
376	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
377	C₂²×C₂₃	#585	1	2	yes	—
378	C₄×C₂₃	—	2	4	no	—
379	C₄×C₂₃	—	2	2	no	—
380	C₄×C₂₃	—	2	2	no	—
381	C₄×C₂₃	—	2	4	no	—
382	C₄×C₂₃	—	4	2	no	—
383	C₄×C₂₃	—	4	2	no	—
384	C₄×C₂₃	—	4	2	no	—
385	C₄×C₂₃	—	4	2	no	—
386	C₄×C₂₃	—	4	2	no	—
387	C₄×C₂₃	—	4	4	no	—
388	C₄×C₂₃	—	4	4	no	—
389	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
390	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
391	#539	—	2	8	no	—
392	C₂×#126	C₂²×C₂₃	1	2	yes	complemented
393	C₂×#125	C₂²×C₂₃	1	2	yes	complemented
394	C₂×#123	—	2	8	no	—
395	C₂×#123	C₂²×C₂₃	1	4	yes	—
396	C₂×#123	C₂²×C₂₃	1	4	yes	—
397	C₂×#123	C₂²×C₂₃	1	2	yes	—
398	C₂×#123	C₂²×C₂₃	1	2	yes	complemented
399	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
400	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
401	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
402	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
403	C₂×#121	C₂²×C₂₃	1	4	yes	—
404	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
405	C₂×#120	C₂²×C₂₃	1	2	yes	—
406	C₂×#120	C₂²×C₂₃	1	2	yes	—
407	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
408	C₂×#117	C₂²×C₂₃	1	2	yes	—
409	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
410	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
411	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
412	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
413	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
414	#399	C₂²×C₂₃	1	2	yes	complemented
415	#398	C₂²×C₂₃	1	4	yes	complemented
416	#397	C₂²×C₂₃	1	2	yes	complemented
417	#396	C₂²×C₂₃	1	4	yes	complemented
418	#396	C₂²×C₂₃	1	4	yes	complemented
419	#396	C₂²×C₂₃	1	4	yes	complemented
420	#396	C₂²×C₂₃	1	4	yes	complemented
421	#394	C₂²×C₂₃	1	4	yes	—
422	#394	C₂²×C₂₃	1	4	yes	complemented
423	#394	C₂²×C₂₃	1	4	yes	complemented
424	#394	C₂²×C₂₃	1	4	yes	complemented
425	#393	C₂²×C₂₃	1	2	yes	complemented
426	#392	C₂²×C₂₃	1	4	yes	—
427	#392	C₂²×C₂₃	1	2	yes	complemented
428	#390	C₂²×C₂₃	1	4	yes	—
429	#390	C₂²×C₂₃	1	4	yes	complemented
430	#390	C₂²×C₂₃	1	4	yes	complemented
431	#389	C₂²×C₂₃	1	4	yes	complemented
432	#389	C₂²×C₂₃	1	4	yes	complemented
433	#388	C₂²×C₂₃	1	4	yes	complemented
434	#388	C₂²×C₂₃	1	4	yes	complemented
435	#387	C₂²×C₂₃	1	4	yes	complemented
436	#386	C₂²×C₂₃	1	2	yes	—
437	#386	C₂²×C₂₃	1	2	yes	—
438	#386	C₂²×C₂₃	1	4	yes	complemented
439	#385	C₂²×C₂₃	1	2	yes	—
440	#385	C₂²×C₂₃	1	2	yes	—
441	#385	C₂²×C₂₃	1	4	yes	complemented
442	#385	C₂²×C₂₃	1	4	yes	complemented
443	#380	C₂²×C₂₃	1	2	yes	—
444	#380	C₂²×C₂₃	1	1	yes	characteristic
445	#380	C₂²×C₂₃	1	1	yes	characteristic
446	#380	C₂²×C₂₃	1	2	yes	complemented
447	#380	C₂²×C₂₃	1	2	yes	complemented
448	#379	C₂²×C₂₃	1	2	yes	—
449	#379	C₂²×C₂₃	1	2	yes	—
450	C₂×C₂₃	—	2	4	no	—
451	C₂×C₂₃	—	4	4	no	—
452	C₂×C₂₃	—	8	2	no	—
453	C₂×C₂₃	—	8	2	no	—
454	C₂×C₂₃	C₂×#537	1	1	yes	characteristic
455	C₂×C₂₃	#3484	1	1	yes	characteristic
456	C₂×C₂₃	#3487	1	1	yes	characteristic
457	C₂×C₂₃	#3534	1	2	yes	—
458	C₂×C₂₃	#3535	1	2	yes	—
459	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
460	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
461	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
462	C₂²×D₄	—	2	4	no	—
463	C₂²×D₄	—	4	4	no	—
464	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
465	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
466	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
467	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
468	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
469	C₂³×C₄	—	2	4	no	—
470	C₂³×C₄	—	4	4	no	—
471	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
472	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
473	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
476	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
477	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
479	#126	—	2	8	no	—
480	#125	—	2	8	no	—
481	#123	—	2	8	no	—
482	#123	—	2	16	no	—
483	#123	—	2	16	no	—
484	#123	—	2	8	no	—
485	C₂²⋊Q₈	—	2	4	no	—
486	C₂²⋊Q₈	—	2	8	no	—
487	C₂²⋊Q₈	—	4	4	no	—
488	#121	—	2	4	no	—
489	#121	—	4	8	no	—
490	#121	—	4	4	no	—
491	#120	—	4	4	no	—
492	#120	—	4	4	no	—
493	C₄×D₄	—	2	8	no	—
494	#117	—	4	4	no	—
495	C₂×C₄⋊C₄	—	2	4	no	—
496	C₂×C₄⋊C₄	D₄×C₂₃	1	8	yes	complemented
497	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
498	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
505	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
506	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
509	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
510	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
512	C₂×C₂²⋊C₄	—	2	4	no	—
513	C₂×C₂²⋊C₄	—	2	4	no	—
514	C₂×C₂²⋊C₄	—	2	4	no	—
515	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
534	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
535	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
536	#95	C₂³×C₂₃	1	2	yes	—
537	#95	C₂³×C₂₃	1	4	yes	—
538	#95	C₂³×C₂₃	1	2	yes	—
539	#95	C₂³×C₂₃	1	4	yes	—
540	#95	C₂³×C₂₃	1	4	yes	—
541	#95	C₂³×C₂₃	1	4	yes	—
542	#95	C₂³×C₂₃	1	4	yes	—
543	C₂₃	#36722	1	1	yes	characteristic, direct product factor, Sylow
544	C₂⁴	—	2	2	no	—
545	C₂⁴	—	2	4	no	—
546	C₂⁴	—	2	2	no	—
547	C₂⁴	—	2	2	no	—
548	C₂⁴	—	2	2	no	—
549	C₂⁴	—	2	2	no	—
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	4	2	no	—
552	C₂⁴	—	4	2	no	—
553	C₂⁴	—	4	2	no	—
554	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
555	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
556	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
557	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
558	C₂×Q₈	—	2	2	no	—
559	C₂×Q₈	—	4	2	no	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	8	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	8	no	—
565	C₂×D₄	—	2	8	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	4	4	no	—
568	C₂×D₄	—	4	4	no	—
569	C₂×D₄	—	4	4	no	—
570	C₂×D₄	—	4	2	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂×D₄	—	4	4	no	—
573	C₂×D₄	—	4	4	no	—
574	C₂×D₄	—	4	16	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	2	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	4	2	no	—
588	C₂²×C₄	—	4	2	no	—
589	C₂²×C₄	—	4	2	no	—
590	C₂²×C₄	—	4	4	no	—
591	C₂²×C₄	—	4	16	no	—
592	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
593	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
594	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
595	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
597	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
598	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
606	C₄⋊C₄	—	2	8	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	4	4	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₄⋊C₄	—	4	4	no	—
616	C₄⋊C₄	—	4	2	no	—
617	C₄⋊C₄	—	4	4	no	—
618	C₄⋊C₄	—	4	4	no	—
619	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
620	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	8	no	—
625	C₂²⋊C₄	—	2	8	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	8	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	4	4	no	—
634	C₂²⋊C₄	—	4	4	no	—
635	C₂²⋊C₄	—	4	4	no	—
636	C₂²⋊C₄	—	4	4	no	—
637	C₂²⋊C₄	—	4	4	no	—
638	C₂²⋊C₄	—	4	4	no	—
639	C₂²⋊C₄	—	4	4	no	—
640	C₄²	—	2	4	no	—
641	C₄²	—	4	4	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	8	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	4	no	—
655	C₂³	—	2	4	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	4	no	—
660	C₂³	—	2	4	no	—
661	C₂³	—	4	8	no	—
662	C₂³	—	4	8	no	—
663	C₂³	—	4	4	no	—
664	C₂³	—	4	4	no	—
665	C₂³	—	4	4	no	—
666	C₂³	—	4	4	no	—
667	C₂³	—	4	4	no	—
668	C₂³	—	8	4	no	—
669	C₂³	—	8	4	no	—
670	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
671	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
672	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
673	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
674	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
675	Q₈	—	8	2	no	—
676	D₄	—	4	16	no	—
677	D₄	—	4	8	no	—
678	D₄	—	8	2	no	—
679	D₄	—	8	8	no	—
680	D₄	—	8	8	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	8	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	4	4	no	—
706	C₂×C₄	—	4	4	no	—
707	C₂×C₄	—	4	8	no	—
708	C₂×C₄	—	4	8	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	8	4	no	—
712	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
713	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
714	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
715	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	4	no	—
719	C₂²	—	2	4	no	—
720	C₂²	—	2	4	no	—
721	C₂²	—	2	4	no	—
722	C₂²	—	2	4	no	—
723	C₂²	—	4	16	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	4	no	—
735	C₂²	—	4	4	no	—
736	C₂²	—	4	4	no	—
737	C₂²	—	4	4	no	—
738	C₂²	—	8	8	no	—
739	C₂²	C₂₃×#537	1	4	yes	—
740	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
741	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
742	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
743	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
744	C₂²	C₂₃×#585	1	2	yes	—
745	C₄	—	2	4	no	—
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	4	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	4	no	—
755	C₄	—	4	4	no	—
756	C₂	—	2	4	no	—
757	C₂	—	4	4	no	—
758	C₂	—	8	2	no	—
759	C₂	—	8	2	no	—
760	C₂	C₂×C₂₃×#537	1	1	yes	characteristic
761	C₂	C₂₃×#3484	1	1	yes	characteristic
762	C₂	C₂₃×#3487	1	1	yes	characteristic
763	C₂	C₂₃×#3534	1	2	yes	—
764	C₂	C₂₃×#3535	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
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. C₂×C₂₃×#539	C₂	semidirect
2. C₂²×C₂₃×#123	C₂	semidirect
3. C₂₃×#2848	C₂	semidirect
4. C₂₃×#2847	C₂	semidirect
5. C₂₃×#2707	C₂	semidirect
6. C₂₃×#2705	C₂	semidirect
7. C₂₃×#2682	C₂	semidirect
8. C₂₃×#2681	C₂	semidirect
9. C₂₃×#2626	C₂	semidirect
10. C₂₃×#2617	C₂	semidirect
11. C₂₃×#2579	C₂	semidirect
12. C₂₃×#2411	C₂	semidirect
13. C₂₃×#2411	C₂	semidirect
14. C₂₃×#2408	C₂	semidirect
15. C₂₃×#2316	C₂	semidirect
19. C₂×C₂₃×#126	C₂²	semidirect
20. C₂×C₂₃×#125	C₂²	semidirect
25. C₂×C₂₃×#123	C₂²	semidirect
27. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
28. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₂₃×#121	C₂²	semidirect
41. C₂₃×#399	C₂²	semidirect
42. C₂₃×#398	C₂²	semidirect
43. C₂₃×#397	C₂²	semidirect
44. C₂₃×#396	C₂²	semidirect
45. C₂₃×#396	C₂²	semidirect
46. C₂₃×#396	C₂²	semidirect
47. C₂₃×#396	C₂²	semidirect
49. C₂₃×#394	C₂²	semidirect
50. C₂₃×#394	C₂²	semidirect
51. C₂₃×#394	C₂²	semidirect
52. C₂₃×#393	C₂²	semidirect
54. C₂₃×#392	C₂²	semidirect
56. C₂₃×#390	C₂²	semidirect
57. C₂₃×#390	C₂²	semidirect
58. C₂₃×#389	C₂²	semidirect
59. C₂₃×#389	C₂²	semidirect
60. C₂₃×#388	C₂²	semidirect
61. C₂₃×#388	C₂²	semidirect
62. C₂₃×#387	C₂²	semidirect
65. C₂₃×#386	C₂²	semidirect
68. C₂₃×#385	C₂²	semidirect
69. C₂₃×#385	C₂²	semidirect
73. C₂₃×#380	C₂²	semidirect
74. C₂₃×#380	C₂²	semidirect
114. C₂×C₄⋊C₄×C₂₃	D₄	semidirect
259. #36722	C₂₃	direct (N × H)
334. C₂×#539	C₂×C₂₃	semidirect
335. C₂²×#123	C₂×C₂₃	semidirect
336. #2848	C₂×C₂₃	semidirect
337. #2847	C₂×C₂₃	semidirect
338. #2707	C₂×C₂₃	semidirect
339. #2705	C₂×C₂₃	semidirect
340. #2682	C₂×C₂₃	semidirect
341. #2681	C₂×C₂₃	semidirect
342. #2626	C₂×C₂₃	semidirect
343. #2617	C₂×C₂₃	semidirect
344. #2579	C₂×C₂₃	semidirect
345. #2411	C₂×C₂₃	semidirect
346. #2411	C₂×C₂₃	semidirect
347. #2408	C₂×C₂₃	semidirect
348. #2316	C₂×C₂₃	semidirect
392. C₂×#126	C₂²×C₂₃	semidirect
393. C₂×#125	C₂²×C₂₃	semidirect
398. C₂×#123	C₂²×C₂₃	semidirect
400. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
401. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
404. C₂×#121	C₂²×C₂₃	semidirect
414. #399	C₂²×C₂₃	semidirect
415. #398	C₂²×C₂₃	semidirect
416. #397	C₂²×C₂₃	semidirect
417. #396	C₂²×C₂₃	semidirect
418. #396	C₂²×C₂₃	semidirect
419. #396	C₂²×C₂₃	semidirect
420. #396	C₂²×C₂₃	semidirect
422. #394	C₂²×C₂₃	semidirect
423. #394	C₂²×C₂₃	semidirect
424. #394	C₂²×C₂₃	semidirect
425. #393	C₂²×C₂₃	semidirect
427. #392	C₂²×C₂₃	semidirect
429. #390	C₂²×C₂₃	semidirect
430. #390	C₂²×C₂₃	semidirect
431. #389	C₂²×C₂₃	semidirect
432. #389	C₂²×C₂₃	semidirect
433. #388	C₂²×C₂₃	semidirect
434. #388	C₂²×C₂₃	semidirect
435. #387	C₂²×C₂₃	semidirect
438. #386	C₂²×C₂₃	semidirect
441. #385	C₂²×C₂₃	semidirect
442. #385	C₂²×C₂₃	semidirect
446. #380	C₂²×C₂₃	semidirect
447. #380	C₂²×C₂₃	semidirect
496. C₂×C₄⋊C₄	D₄×C₂₃	semidirect
543. C₂₃	#36722	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#539	2
C₂²×C₂₃×#123	2
C₂₃×#2848	2
C₂₃×#2847	2
C₂₃×#2707	2
C₂₃×#2705	2
C₂₃×#2682	2
C₂₃×#2681	2
C₂₃×#2626	2
C₂₃×#2617	2
C₂₃×#2579	2
C₂₃×#2411	2
C₂₃×#2408	2
C₂₃×#2316	2
#36722	23

Subgroups — C23×#36722 #19184348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36722 #19184348