Subgroups — C₂₃×#22848 #19170474

Order 5888.

1306 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#407	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₂₃×#120	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1924	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1753	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#120	C₄	1	1	yes	characteristic
23	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#436	—	2	4	no	—
27	C₂₃×#435	—	2	4	no	—
28	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#407	—	2	4	no	—
32	C₂×C₂₃×C₂²⋊C₈	—	2	4	no	—
33	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#386	C₄	1	1	yes	characteristic
48	C₂₃×#386	C₄	1	1	yes	characteristic
49	C₂₃×#386	C₄	1	1	yes	characteristic
50	C₂₃×#385	C₄	1	1	yes	characteristic
51	C₂₃×#385	C₄	1	1	yes	characteristic
52	C₂₃×#385	C₄	1	1	yes	characteristic
53	C₂₃×#379	C₄	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
57	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
63	C₂⁵×C₂₃	C₂×C₄	1	1	yes	characteristic
64	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
65	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
66	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
67	C₂³×C₄×C₂₃	—	2	2	no	—
68	C₂³×C₄×C₂₃	—	2	2	no	—
69	C₂³×C₄×C₂₃	—	2	2	no	—
70	C₂³×C₄×C₂₃	—	2	2	no	—
71	C₂³×C₄×C₂₃	—	4	1	no	—
72	C₂³×C₄×C₂₃	—	4	1	no	—
73	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
75	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
76	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
80	C₂×M₁₆×C₂₃	—	2	2	no	—
81	C₂×M₁₆×C₂₃	—	2	2	no	—
82	C₂×M₁₆×C₂₃	—	2	2	no	—
83	C₂×M₁₆×C₂₃	—	2	2	no	—
84	C₂×M₁₆×C₂₃	—	2	2	no	—
85	C₂×M₁₆×C₂₃	—	2	2	no	—
86	C₂×M₁₆×C₂₃	—	4	1	no	—
87	C₂×M₁₆×C₂₃	—	4	1	no	—
88	C₂×M₁₆×C₂₃	—	4	1	no	—
89	C₂²×C₈×C₂₃	—	2	2	no	—
90	C₂²×C₈×C₂₃	—	2	2	no	—
91	C₂²×C₈×C₂₃	—	2	2	no	—
92	C₂²×C₈×C₂₃	—	2	2	no	—
93	C₂²×C₈×C₂₃	—	4	1	no	—
94	C₂²×C₈×C₂₃	—	4	1	no	—
95	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
103	C₂₃×#120	—	2	4	no	—
104	C₄×D₄×C₂₃	—	2	2	no	—
105	C₄×D₄×C₂₃	—	2	2	no	—
106	C₄×D₄×C₂₃	—	2	2	no	—
107	C₄×D₄×C₂₃	—	2	2	no	—
108	C₄×D₄×C₂₃	—	4	1	no	—
109	C₄×D₄×C₂₃	—	4	1	no	—
110	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
113	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
125	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
128	C₂₃×C₄⋊C₈	—	2	2	no	—
129	C₂₃×C₄⋊C₈	—	2	2	no	—
130	C₂₃×C₄⋊C₈	—	4	1	no	—
131	C₂₃×C₂²⋊C₈	—	2	2	no	—
132	C₂₃×C₂²⋊C₈	—	2	2	no	—
133	C₂₃×C₂²⋊C₈	—	2	2	no	—
134	C₂₃×C₂²⋊C₈	—	2	2	no	—
135	C₂₃×C₂²⋊C₈	—	2	2	no	—
136	C₂₃×C₂²⋊C₈	—	2	2	no	—
137	C₂₃×C₂²⋊C₈	—	2	2	no	—
138	C₂₃×C₂²⋊C₈	—	2	2	no	—
139	C₂₃×C₂²⋊C₈	—	4	1	no	—
140	C₂₃×C₂²⋊C₈	D₄	1	4	yes	complemented
141	C₂₃×C₂²⋊C₈	D₄	1	4	yes	complemented
142	C₂₃×#97	—	2	2	no	—
143	C₄×C₈×C₂₃	—	2	2	no	—
144	C₄×C₈×C₂₃	—	4	1	no	—
145	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
146	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
147	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
148	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
149	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
150	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
151	C₂⁴×C₂₃	—	2	2	no	—
152	C₂⁴×C₂₃	—	2	2	no	—
153	C₂⁴×C₂₃	—	2	2	no	—
154	C₂⁴×C₂₃	—	2	2	no	—
155	C₂⁴×C₂₃	—	2	2	no	—
156	C₂⁴×C₂₃	—	4	1	no	—
157	C₂⁴×C₂₃	—	4	1	no	—
158	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
159	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
160	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
161	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
162	C₂×D₄×C₂₃	—	2	2	no	—
163	C₂×D₄×C₂₃	—	2	2	no	—
164	C₂×D₄×C₂₃	—	2	2	no	—
165	C₂×D₄×C₂₃	—	2	2	no	—
166	C₂×D₄×C₂₃	—	2	2	no	—
167	C₂×D₄×C₂₃	—	2	2	no	—
168	C₂×D₄×C₂₃	—	2	2	no	—
169	C₂×D₄×C₂₃	—	4	1	no	—
170	C₂×D₄×C₂₃	—	4	1	no	—
171	C₂²×C₄×C₂₃	—	2	1	no	—
172	C₂²×C₄×C₂₃	—	2	1	no	—
173	C₂²×C₄×C₂₃	—	2	1	no	—
174	C₂²×C₄×C₂₃	—	2	1	no	—
175	C₂²×C₄×C₂₃	—	2	1	no	—
176	C₂²×C₄×C₂₃	—	2	1	no	—
177	C₂²×C₄×C₂₃	—	2	1	no	—
178	C₂²×C₄×C₂₃	—	2	1	no	—
179	C₂²×C₄×C₂₃	—	2	2	no	—
180	C₂²×C₄×C₂₃	—	2	2	no	—
181	C₂²×C₄×C₂₃	—	2	2	no	—
182	C₂²×C₄×C₂₃	—	2	2	no	—
183	C₂²×C₄×C₂₃	—	2	2	no	—
184	C₂²×C₄×C₂₃	—	2	2	no	—
185	C₂²×C₄×C₂₃	—	2	1	no	—
186	C₂²×C₄×C₂₃	—	2	1	no	—
187	C₂²×C₄×C₂₃	—	2	1	no	—
188	C₂²×C₄×C₂₃	—	2	1	no	—
189	C₂²×C₄×C₂₃	—	2	1	no	—
190	C₂²×C₄×C₂₃	—	2	1	no	—
191	C₂²×C₄×C₂₃	—	2	1	no	—
192	C₂²×C₄×C₂₃	—	2	1	no	—
193	C₂²×C₄×C₂₃	—	2	1	no	—
194	C₂²×C₄×C₂₃	—	2	1	no	—
195	C₂²×C₄×C₂₃	—	2	1	no	—
196	C₂²×C₄×C₂₃	—	2	1	no	—
197	C₂²×C₄×C₂₃	—	4	1	no	—
198	C₂²×C₄×C₂₃	—	4	1	no	—
199	C₂²×C₄×C₂₃	—	4	1	no	—
200	C₂²×C₄×C₂₃	—	4	4	no	—
201	C₂²×C₄×C₂₃	—	4	4	no	—
202	C₂²×C₄×C₂₃	—	4	4	no	—
203	C₂²×C₄×C₂₃	—	4	4	no	—
204	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
210	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
211	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
213	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
214	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
215	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
216	C₂²×C₄×C₂₃	#41	1	2	yes	—
217	C₂²×C₄×C₂₃	#41	1	2	yes	—
218	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
219	M₁₆×C₂₃	—	4	4	no	—
220	M₁₆×C₂₃	—	4	4	no	—
221	M₁₆×C₂₃	—	4	4	no	—
222	C₂×C₈×C₂₃	—	2	1	no	—
223	C₂×C₈×C₂₃	—	2	1	no	—
224	C₂×C₈×C₂₃	—	2	1	no	—
225	C₂×C₈×C₂₃	—	2	1	no	—
226	C₂×C₈×C₂₃	—	2	1	no	—
227	C₂×C₈×C₂₃	—	2	1	no	—
228	C₂×C₈×C₂₃	—	2	1	no	—
229	C₂×C₈×C₂₃	—	2	1	no	—
230	C₂×C₈×C₂₃	—	2	1	no	—
231	C₂×C₈×C₂₃	—	2	1	no	—
232	C₂×C₈×C₂₃	—	2	1	no	—
233	C₂×C₈×C₂₃	—	2	1	no	—
234	C₂×C₈×C₂₃	—	2	1	no	—
235	C₂×C₈×C₂₃	—	2	1	no	—
236	C₂×C₈×C₂₃	—	2	1	no	—
237	C₂×C₈×C₂₃	—	2	1	no	—
238	C₂×C₈×C₂₃	—	2	1	no	—
239	C₂×C₈×C₂₃	—	2	1	no	—
240	C₂×C₈×C₂₃	—	2	1	no	—
241	C₂×C₈×C₂₃	—	2	1	no	—
242	C₂×C₈×C₂₃	—	4	4	no	—
243	C₂×C₈×C₂₃	—	4	4	no	—
244	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
245	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
246	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
247	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
248	C₄⋊C₄×C₂₃	—	2	2	no	—
249	C₄⋊C₄×C₂₃	—	2	2	no	—
250	C₄⋊C₄×C₂₃	—	4	1	no	—
251	C₂²⋊C₄×C₂₃	—	2	2	no	—
252	C₂²⋊C₄×C₂₃	—	2	2	no	—
253	C₂²⋊C₄×C₂₃	—	2	2	no	—
254	C₂²⋊C₄×C₂₃	—	2	2	no	—
255	C₂²⋊C₄×C₂₃	—	2	2	no	—
256	C₂²⋊C₄×C₂₃	—	2	2	no	—
257	C₂²⋊C₄×C₂₃	—	2	2	no	—
258	C₂²⋊C₄×C₂₃	—	2	2	no	—
259	C₂²⋊C₄×C₂₃	—	4	1	no	—
260	C₂²⋊C₄×C₂₃	—	4	1	no	—
261	C₂²⋊C₄×C₂₃	—	4	1	no	—
262	C₂²⋊C₄×C₂₃	M₁₆	1	4	yes	complemented
263	C₄²×C₂₃	—	2	1	no	—
264	C₄²×C₂₃	—	2	1	no	—
265	C₄²×C₂₃	—	2	1	no	—
266	C₄²×C₂₃	—	2	1	no	—
267	C₄²×C₂₃	—	2	1	no	—
268	C₄²×C₂₃	—	2	1	no	—
269	#22848	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
270	C₂³×C₂₃	—	2	1	no	—
271	C₂³×C₂₃	—	2	1	no	—
272	C₂³×C₂₃	—	2	1	no	—
273	C₂³×C₂₃	—	2	1	no	—
274	C₂³×C₂₃	—	2	8	no	—
275	C₂³×C₂₃	—	2	1	no	—
276	C₂³×C₂₃	—	2	1	no	—
277	C₂³×C₂₃	—	2	1	no	—
278	C₂³×C₂₃	—	2	1	no	—
279	C₂³×C₂₃	—	2	1	no	—
280	C₂³×C₂₃	—	2	1	no	—
281	C₂³×C₂₃	—	2	1	no	—
282	C₂³×C₂₃	—	2	1	no	—
283	C₂³×C₂₃	—	2	1	no	—
284	C₂³×C₂₃	—	2	1	no	—
285	C₂³×C₂₃	—	2	1	no	—
286	C₂³×C₂₃	—	2	1	no	—
287	C₂³×C₂₃	—	2	1	no	—
288	C₂³×C₂₃	—	2	1	no	—
289	C₂³×C₂₃	—	2	1	no	—
290	C₂³×C₂₃	—	2	1	no	—
291	C₂³×C₂₃	—	2	1	no	—
292	C₂³×C₂₃	—	2	1	no	—
293	C₂³×C₂₃	—	2	1	no	—
294	C₂³×C₂₃	—	4	4	no	—
295	C₂³×C₂₃	—	4	4	no	—
296	C₂³×C₂₃	—	4	4	no	—
297	C₂³×C₂₃	—	4	4	no	—
298	C₂³×C₂₃	—	4	4	no	—
299	C₂³×C₂₃	—	4	4	no	—
300	C₂³×C₂₃	C₄×D₄	1	2	yes	—
301	C₂³×C₂₃	C₄×D₄	1	2	yes	—
302	C₂³×C₂₃	C₂×M₁₆	1	2	yes	—
303	C₂³×C₂₃	#131	1	2	yes	—
304	C₂³×C₂₃	#131	1	2	yes	—
305	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
306	D₄×C₂₃	—	4	4	no	—
307	D₄×C₂₃	—	4	4	no	—
308	D₄×C₂₃	—	4	4	no	—
309	C₂×C₄×C₂₃	—	2	1	no	—
310	C₂×C₄×C₂₃	—	2	1	no	—
311	C₂×C₄×C₂₃	—	2	1	no	—
312	C₂×C₄×C₂₃	—	2	1	no	—
313	C₂×C₄×C₂₃	—	2	1	no	—
314	C₂×C₄×C₂₃	—	2	1	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	1	no	—
326	C₂×C₄×C₂₃	—	2	1	no	—
327	C₂×C₄×C₂₃	—	2	1	no	—
328	C₂×C₄×C₂₃	—	2	1	no	—
329	C₂×C₄×C₂₃	—	2	1	no	—
330	C₂×C₄×C₂₃	—	2	1	no	—
331	C₂×C₄×C₂₃	—	2	1	no	—
332	C₂×C₄×C₂₃	—	2	1	no	—
333	C₂×C₄×C₂₃	—	2	1	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	1	no	—
339	C₂×C₄×C₂₃	—	2	1	no	—
340	C₂×C₄×C₂₃	—	2	1	no	—
341	C₂×C₄×C₂₃	—	2	1	no	—
342	C₂×C₄×C₂₃	—	2	1	no	—
343	C₂×C₄×C₂₃	—	4	4	no	—
344	C₂×C₄×C₂₃	—	4	4	no	—
345	C₂×C₄×C₂₃	—	4	4	no	—
346	C₂×C₄×C₂₃	—	4	1	no	—
347	C₂×C₄×C₂₃	—	4	1	no	—
348	C₂×C₄×C₂₃	—	4	1	no	—
349	C₂×C₄×C₂₃	—	4	1	no	—
350	C₂×C₄×C₂₃	—	4	1	no	—
351	C₂×C₄×C₂₃	—	4	1	no	—
352	C₂×C₄×C₂₃	—	4	1	no	—
353	C₂×C₄×C₂₃	—	4	1	no	—
354	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
355	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
356	C₂×C₄×C₂₃	C₂×M₁₆	1	2	yes	—
357	C₂×C₄×C₂₃	C₂×M₁₆	1	2	yes	—
358	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
361	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
362	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
364	C₈×C₂₃	—	2	2	no	—
365	C₈×C₂₃	—	2	2	no	—
366	C₈×C₂₃	—	2	2	no	—
367	C₈×C₂₃	—	2	2	no	—
368	C₈×C₂₃	—	4	1	no	—
369	C₈×C₂₃	—	4	1	no	—
370	C₈×C₂₃	—	4	1	no	—
371	C₈×C₂₃	—	4	1	no	—
372	C₂×#436	C₂×C₂₃	1	1	yes	characteristic, complemented
373	C₂×#435	C₂×C₂₃	1	1	yes	characteristic, complemented
374	C₂×#407	C₂×C₂₃	1	1	yes	characteristic, complemented
375	C₂²×C₂²⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
376	C₄×#120	C₂×C₂₃	1	1	yes	characteristic
377	#1954	C₂×C₂₃	1	1	yes	characteristic, complemented
378	#1924	C₂×C₂₃	1	1	yes	characteristic, complemented
379	#1923	C₂×C₂₃	1	1	yes	characteristic, complemented
380	#1870	C₂×C₂₃	1	1	yes	characteristic, complemented
381	#1870	C₂×C₂₃	1	1	yes	characteristic, complemented
382	#1869	C₂×C₂₃	1	1	yes	characteristic, complemented
383	#1851	C₂×C₂₃	1	1	yes	characteristic, complemented
384	#1850	C₂×C₂₃	1	1	yes	characteristic, complemented
385	#1753	C₂×C₂₃	1	1	yes	characteristic, complemented
386	C₈×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
387	C₂²×C₂₃	—	2	2	no	—
388	C₂²×C₂₃	—	2	2	no	—
389	C₂²×C₂₃	—	2	2	no	—
390	C₂²×C₂₃	—	2	2	no	—
391	C₂²×C₂₃	—	2	2	no	—
392	C₂²×C₂₃	—	2	2	no	—
393	C₂²×C₂₃	—	2	2	no	—
394	C₂²×C₂₃	—	2	2	no	—
395	C₂²×C₂₃	—	2	2	no	—
396	C₂²×C₂₃	—	2	2	no	—
397	C₂²×C₂₃	—	2	2	no	—
398	C₂²×C₂₃	—	2	2	no	—
399	C₂²×C₂₃	—	4	16	no	—
400	C₂²×C₂₃	—	4	1	no	—
401	C₂²×C₂₃	—	4	1	no	—
402	C₂²×C₂₃	—	4	1	no	—
403	C₂²×C₂₃	—	4	1	no	—
404	C₂²×C₂₃	—	4	1	no	—
405	C₂²×C₂₃	—	4	1	no	—
406	C₂²×C₂₃	—	4	1	no	—
407	C₂²×C₂₃	—	4	1	no	—
408	C₂²×C₂₃	—	4	1	no	—
409	C₂²×C₂₃	—	4	1	no	—
410	C₂²×C₂₃	—	4	1	no	—
411	C₂²×C₂₃	—	4	1	no	—
412	C₂²×C₂₃	—	4	1	no	—
413	C₂²×C₂₃	—	4	1	no	—
414	C₂²×C₂₃	—	4	1	no	—
415	C₂²×C₂₃	#436	1	4	yes	complemented
416	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
417	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
418	C₂²×C₂₃	#518	1	1	yes	characteristic
419	C₂²×C₂₃	C₂²×M₁₆	1	1	yes	characteristic
420	C₂²×C₂₃	C₂×#131	1	1	yes	characteristic
421	C₂²×C₂₃	C₂×#131	1	1	yes	characteristic
422	C₂²×C₂₃	#568	1	1	yes	characteristic
423	C₄×C₂₃	—	2	2	no	—
424	C₄×C₂₃	—	2	2	no	—
425	C₄×C₂₃	—	2	2	no	—
426	C₄×C₂₃	—	2	2	no	—
427	C₄×C₂₃	—	4	1	no	—
428	C₄×C₂₃	—	4	1	no	—
429	C₄×C₂₃	—	4	1	no	—
430	C₄×C₂₃	—	4	1	no	—
431	C₄×C₂₃	—	4	1	no	—
432	C₄×C₂₃	—	4	1	no	—
433	C₄×C₂₃	D₄²	1	1	yes	characteristic
434	C₄×C₂₃	#546	1	1	yes	characteristic
435	C₄×C₂₃	#546	1	1	yes	characteristic
436	C₄×C₂₃	#551	1	1	yes	characteristic
437	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
438	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
439	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
440	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
441	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
442	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
443	C₂×#120	C₄×C₂₃	1	1	yes	characteristic
444	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
445	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
447	#436	—	2	4	no	—
448	#435	—	2	4	no	—
449	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
450	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
451	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
452	#407	—	2	4	no	—
453	C₂×C₂²⋊C₈	—	2	4	no	—
454	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
455	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
456	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
457	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
458	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
459	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
460	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
461	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
462	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
463	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
464	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
465	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
466	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
467	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
468	#386	C₄×C₂₃	1	1	yes	characteristic
469	#386	C₄×C₂₃	1	1	yes	characteristic
470	#386	C₄×C₂₃	1	1	yes	characteristic
471	#385	C₄×C₂₃	1	1	yes	characteristic
472	#385	C₄×C₂₃	1	1	yes	characteristic
473	#385	C₄×C₂₃	1	1	yes	characteristic
474	#379	C₄×C₂₃	1	1	yes	characteristic
475	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
476	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
477	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
478	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
479	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
480	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
481	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
482	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
483	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
484	C₂×C₂₃	—	2	4	no	—
485	C₂×C₂₃	—	4	2	no	—
486	C₂×C₂₃	—	4	2	no	—
487	C₂×C₂₃	—	8	1	no	—
488	C₂×C₂₃	#2358	1	1	yes	characteristic
489	C₂×C₂₃	C₂×#436	1	1	yes	characteristic
490	C₂×C₂₃	#2929	1	1	yes	characteristic
491	C₂×C₂₃	#2933	1	1	yes	characteristic
492	C₂×C₂₃	D₄×M₁₆	1	1	yes	characteristic
493	C₂×C₂₃	#2974	1	1	yes	characteristic
494	C₂×C₂₃	#2976	1	1	yes	characteristic
495	C₂⁵	C₂×C₄×C₂₃	1	1	yes	characteristic
496	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
497	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
498	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
499	C₂³×C₄	—	2	2	no	—
500	C₂³×C₄	—	2	2	no	—
501	C₂³×C₄	—	2	2	no	—
502	C₂³×C₄	—	2	2	no	—
503	C₂³×C₄	—	4	1	no	—
504	C₂³×C₄	—	4	1	no	—
505	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
506	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
507	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
508	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
512	C₂×M₁₆	—	2	2	no	—
513	C₂×M₁₆	—	2	2	no	—
514	C₂×M₁₆	—	2	2	no	—
515	C₂×M₁₆	—	2	2	no	—
516	C₂×M₁₆	—	2	2	no	—
517	C₂×M₁₆	—	2	2	no	—
518	C₂×M₁₆	—	4	1	no	—
519	C₂×M₁₆	—	4	1	no	—
520	C₂×M₁₆	—	4	1	no	—
521	C₂²×C₈	—	2	2	no	—
522	C₂²×C₈	—	2	2	no	—
523	C₂²×C₈	—	2	2	no	—
524	C₂²×C₈	—	2	2	no	—
525	C₂²×C₈	—	4	1	no	—
526	C₂²×C₈	—	4	1	no	—
527	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
528	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
529	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
530	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
531	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
532	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
533	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
534	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
535	#120	—	2	4	no	—
536	C₄×D₄	—	2	2	no	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	4	1	no	—
541	C₄×D₄	—	4	1	no	—
542	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
545	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
547	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
551	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
552	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
554	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
555	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
557	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
558	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
560	C₄⋊C₈	—	2	2	no	—
561	C₄⋊C₈	—	2	2	no	—
562	C₄⋊C₈	—	4	1	no	—
563	C₂²⋊C₈	—	2	2	no	—
564	C₂²⋊C₈	—	2	2	no	—
565	C₂²⋊C₈	—	2	2	no	—
566	C₂²⋊C₈	—	2	2	no	—
567	C₂²⋊C₈	—	2	2	no	—
568	C₂²⋊C₈	—	2	2	no	—
569	C₂²⋊C₈	—	2	2	no	—
570	C₂²⋊C₈	—	2	2	no	—
571	C₂²⋊C₈	—	4	1	no	—
572	C₂²⋊C₈	D₄×C₂₃	1	4	yes	complemented
573	C₂²⋊C₈	D₄×C₂₃	1	4	yes	complemented
574	#97	—	2	2	no	—
575	C₄×C₈	—	2	2	no	—
576	C₄×C₈	—	4	1	no	—
577	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
578	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
579	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
580	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
581	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
582	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
583	C₂₃	#22848	1	1	yes	characteristic, direct product factor, Sylow
584	C₂⁴	—	2	2	no	—
585	C₂⁴	—	2	2	no	—
586	C₂⁴	—	2	2	no	—
587	C₂⁴	—	2	2	no	—
588	C₂⁴	—	2	2	no	—
589	C₂⁴	—	4	1	no	—
590	C₂⁴	—	4	1	no	—
591	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
592	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
593	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
594	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	4	1	no	—
603	C₂×D₄	—	4	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	4	1	no	—
631	C₂²×C₄	—	4	1	no	—
632	C₂²×C₄	—	4	1	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	C₂²×C₄×C₂₃	1	1	yes	characteristic
638	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
639	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
640	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
641	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
642	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
643	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
644	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
645	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
646	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
648	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
649	C₂²×C₄	#41×C₂₃	1	2	yes	—
650	C₂²×C₄	#41×C₂₃	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
652	M₁₆	—	4	4	no	—
653	M₁₆	—	4	4	no	—
654	M₁₆	—	4	4	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	—	2	1	no	—
659	C₂×C₈	—	2	1	no	—
660	C₂×C₈	—	2	1	no	—
661	C₂×C₈	—	2	1	no	—
662	C₂×C₈	—	2	1	no	—
663	C₂×C₈	—	2	1	no	—
664	C₂×C₈	—	2	1	no	—
665	C₂×C₈	—	2	1	no	—
666	C₂×C₈	—	2	1	no	—
667	C₂×C₈	—	2	1	no	—
668	C₂×C₈	—	2	1	no	—
669	C₂×C₈	—	2	1	no	—
670	C₂×C₈	—	2	1	no	—
671	C₂×C₈	—	2	1	no	—
672	C₂×C₈	—	2	1	no	—
673	C₂×C₈	—	2	1	no	—
674	C₂×C₈	—	2	1	no	—
675	C₂×C₈	—	4	4	no	—
676	C₂×C₈	—	4	4	no	—
677	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
678	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
679	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
680	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	4	1	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	4	1	no	—
693	C₂²⋊C₄	—	4	1	no	—
694	C₂²⋊C₄	—	4	1	no	—
695	C₂²⋊C₄	M₁₆×C₂₃	1	4	yes	complemented
696	C₄²	—	2	1	no	—
697	C₄²	—	2	1	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	2	1	no	—
700	C₄²	—	2	1	no	—
701	C₄²	—	2	1	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	8	no	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	1	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	4	4	no	—
727	C₂³	—	4	4	no	—
728	C₂³	—	4	4	no	—
729	C₂³	—	4	4	no	—
730	C₂³	—	4	4	no	—
731	C₂³	—	4	4	no	—
732	C₂³	C₄×D₄×C₂₃	1	2	yes	—
733	C₂³	C₄×D₄×C₂₃	1	2	yes	—
734	C₂³	C₂×M₁₆×C₂₃	1	2	yes	—
735	C₂³	C₂₃×#131	1	2	yes	—
736	C₂³	C₂₃×#131	1	2	yes	—
737	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
738	D₄	—	4	4	no	—
739	D₄	—	4	4	no	—
740	D₄	—	4	4	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	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	—	2	2	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
787	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
788	C₂×C₄	C₂×M₁₆×C₂₃	1	2	yes	—
789	C₂×C₄	C₂×M₁₆×C₂₃	1	2	yes	—
790	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
792	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
793	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
794	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
795	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
796	C₈	—	2	2	no	—
797	C₈	—	2	2	no	—
798	C₈	—	2	2	no	—
799	C₈	—	2	2	no	—
800	C₈	—	4	1	no	—
801	C₈	—	4	1	no	—
802	C₈	—	4	1	no	—
803	C₈	—	4	1	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	2	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	4	16	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	1	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	C₂₃×#436	1	4	yes	complemented
833	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
834	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
835	C₂²	C₂₃×#518	1	1	yes	characteristic
836	C₂²	C₂²×M₁₆×C₂₃	1	1	yes	characteristic
837	C₂²	C₂×C₂₃×#131	1	1	yes	characteristic
838	C₂²	C₂×C₂₃×#131	1	1	yes	characteristic
839	C₂²	C₂₃×#568	1	1	yes	characteristic
840	C₄	—	2	2	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	1	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	1	no	—
850	C₄	D₄²×C₂₃	1	1	yes	characteristic
851	C₄	C₂₃×#546	1	1	yes	characteristic
852	C₄	C₂₃×#546	1	1	yes	characteristic
853	C₄	C₂₃×#551	1	1	yes	characteristic
854	C₂	—	2	4	no	—
855	C₂	—	4	2	no	—
856	C₂	—	4	2	no	—
857	C₂	—	8	1	no	—
858	C₂	C₂₃×#2358	1	1	yes	characteristic
859	C₂	C₂×C₂₃×#436	1	1	yes	characteristic
860	C₂	C₂₃×#2929	1	1	yes	characteristic
861	C₂	C₂₃×#2933	1	1	yes	characteristic
862	C₂	D₄×M₁₆×C₂₃	1	1	yes	characteristic
863	C₂	C₂₃×#2974	1	1	yes	characteristic
864	C₂	C₂₃×#2976	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂³×C₂₃	C₂³×C₄
prime radical	C₂×C₂₃×#120	C₄
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. C₂×C₂₃×#436	C₂	semidirect
2. C₂×C₂₃×#435	C₂	semidirect
3. C₂×C₂₃×#407	C₂	semidirect
4. C₂²×C₂₃×C₂²⋊C₈	C₂	semidirect
6. C₂₃×#1954	C₂	semidirect
7. C₂₃×#1924	C₂	semidirect
8. C₂₃×#1923	C₂	semidirect
9. C₂₃×#1870	C₂	semidirect
10. C₂₃×#1870	C₂	semidirect
11. C₂₃×#1869	C₂	semidirect
12. C₂₃×#1851	C₂	semidirect
13. C₂₃×#1850	C₂	semidirect
14. C₂₃×#1753	C₂	semidirect
15. C₈×C₂²⋊C₄×C₂₃	C₂	semidirect
19. C₂²×M₁₆×C₂₃	C₂²	semidirect
28. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
29. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
30. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
41. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
42. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
43. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
44. C₂×C₂₃×#97	C₂²	semidirect
45. C₂×C₄×C₈×C₂₃	C₂²	semidirect
46. C₂×C₄×C₈×C₂₃	C₂²	semidirect
57. C₂₃×#336	C₂²	semidirect
58. C₂₃×#336	C₂²	semidirect
59. C₂₃×#336	C₂²	semidirect
60. C₂₃×#336	C₂²	semidirect
61. C₂₃×#336	C₂²	semidirect
62. C₂₃×#336	C₂²	semidirect
140. C₂₃×C₂²⋊C₈	D₄	semidirect
141. C₂₃×C₂²⋊C₈	D₄	semidirect
262. C₂²⋊C₄×C₂₃	M₁₆	semidirect
269. #22848	C₂₃	direct (N × H)
372. C₂×#436	C₂×C₂₃	semidirect
373. C₂×#435	C₂×C₂₃	semidirect
374. C₂×#407	C₂×C₂₃	semidirect
375. C₂²×C₂²⋊C₈	C₂×C₂₃	semidirect
377. #1954	C₂×C₂₃	semidirect
378. #1924	C₂×C₂₃	semidirect
379. #1923	C₂×C₂₃	semidirect
380. #1870	C₂×C₂₃	semidirect
381. #1870	C₂×C₂₃	semidirect
382. #1869	C₂×C₂₃	semidirect
383. #1851	C₂×C₂₃	semidirect
384. #1850	C₂×C₂₃	semidirect
385. #1753	C₂×C₂₃	semidirect
386. C₈×C₂²⋊C₄	C₂×C₂₃	semidirect
415. C₂²×C₂₃	#436	semidirect
440. C₂²×M₁₆	C₂²×C₂₃	semidirect
449. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
450. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
451. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
462. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
463. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
464. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
465. C₂×#97	C₂²×C₂₃	semidirect
466. C₂×C₄×C₈	C₂²×C₂₃	semidirect
467. C₂×C₄×C₈	C₂²×C₂₃	semidirect
478. #336	C₂²×C₂₃	semidirect
479. #336	C₂²×C₂₃	semidirect
480. #336	C₂²×C₂₃	semidirect
481. #336	C₂²×C₂₃	semidirect
482. #336	C₂²×C₂₃	semidirect
483. #336	C₂²×C₂₃	semidirect
572. C₂²⋊C₈	D₄×C₂₃	semidirect
573. C₂²⋊C₈	D₄×C₂₃	semidirect
583. C₂₃	#22848	direct (N × H)
695. C₂²⋊C₄	M₁₆×C₂₃	semidirect
832. C₂²	C₂₃×#436	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#436	2
C₂×C₂₃×#435	2
C₂×C₂₃×#407	2
C₂²×C₂₃×C₂²⋊C₈	2
C₄×C₂₃×#120	2
C₂₃×#1954	2
C₂₃×#1924	2
C₂₃×#1923	2
C₂₃×#1870	2
C₂₃×#1869	2
C₂₃×#1851	2
C₂₃×#1850	2
C₂₃×#1753	2
C₈×C₂²⋊C₄×C₂₃	2
#22848	23

Subgroups — C23×#22848 #19170474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#22848 #19170474