Subgroups — C₂₃×#22558 #19170184

Order 5888.

1100 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2280	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1924	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1818	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1779	C₂	1	1	yes	maximal, characteristic
13	C₂₃×#1752	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
21	C₂₃×#433	—	2	4	no	—
22	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₂₃×C₂²⋊C₈	—	2	4	no	—
27	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
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×#97	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
41	C₂₃×#381	C₄	1	1	yes	characteristic
42	C₂₃×#381	C₄	1	1	yes	characteristic
43	C₂₃×#380	C₄	1	1	yes	characteristic
44	C₂₃×#380	C₄	1	1	yes	characteristic
45	C₂₃×#380	C₄	1	1	yes	characteristic
46	C₂₃×#380	C₄	1	1	yes	characteristic
47	C₂₃×#379	C₄	1	1	yes	characteristic
48	C₂₃×#379	C₄	1	1	yes	characteristic
49	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
50	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
51	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
52	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
53	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
54	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
55	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
56	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
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	C₂⁵×C₂₃	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₂₃	—	2	2	no	—
63	C₂³×C₄×C₂₃	—	2	2	no	—
64	C₂³×C₄×C₂₃	—	2	2	no	—
65	C₂³×C₄×C₂₃	—	2	2	no	—
66	C₂³×C₄×C₂₃	—	4	1	no	—
67	C₂³×C₄×C₂₃	—	4	1	no	—
68	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₂₃	—	2	2	no	—
75	C₂²×C₈×C₂₃	—	2	2	no	—
76	C₂²×C₈×C₂₃	—	2	2	no	—
77	C₂²×C₈×C₂₃	—	2	2	no	—
78	C₂²×C₈×C₂₃	—	4	1	no	—
79	C₂²×C₈×C₂₃	—	4	1	no	—
80	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
88	C₂₃×#117	—	2	2	no	—
89	C₂₃×#117	—	2	2	no	—
90	C₂₃×#117	—	4	1	no	—
91	C₂₃×#117	—	4	1	no	—
92	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
112	C₂₃×C₄⋊C₈	—	2	2	no	—
113	C₂₃×C₄⋊C₈	—	2	2	no	—
114	C₂₃×C₄⋊C₈	—	4	1	no	—
115	C₂₃×C₄⋊C₈	—	4	1	no	—
116	C₂₃×C₂²⋊C₈	—	2	2	no	—
117	C₂₃×C₂²⋊C₈	—	2	2	no	—
118	C₂₃×C₂²⋊C₈	—	2	2	no	—
119	C₂₃×C₂²⋊C₈	—	2	2	no	—
120	C₂₃×C₂²⋊C₈	—	2	2	no	—
121	C₂₃×C₂²⋊C₈	—	2	2	no	—
122	C₂₃×C₂²⋊C₈	—	2	2	no	—
123	C₂₃×C₂²⋊C₈	—	4	1	no	—
124	C₂₃×C₂²⋊C₈	—	4	1	no	—
125	C₂₃×C₂²⋊C₈	D₄	1	4	yes	—
126	C₂₃×#97	—	2	2	no	—
127	C₂₃×#97	—	4	1	no	—
128	C₄×C₈×C₂₃	—	2	2	no	—
129	C₄×C₈×C₂₃	—	4	1	no	—
130	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
131	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
132	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
133	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
134	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
135	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
136	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
137	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
138	C₂⁴×C₂₃	—	2	2	no	—
139	C₂⁴×C₂₃	—	2	2	no	—
140	C₂⁴×C₂₃	—	2	2	no	—
141	C₂⁴×C₂₃	—	2	2	no	—
142	C₂⁴×C₂₃	—	2	2	no	—
143	C₂⁴×C₂₃	—	4	1	no	—
144	C₂⁴×C₂₃	—	4	1	no	—
145	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
146	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
147	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₂₃	—	2	1	no	—
149	C₂²×C₄×C₂₃	—	2	1	no	—
150	C₂²×C₄×C₂₃	—	2	1	no	—
151	C₂²×C₄×C₂₃	—	2	1	no	—
152	C₂²×C₄×C₂₃	—	2	1	no	—
153	C₂²×C₄×C₂₃	—	2	1	no	—
154	C₂²×C₄×C₂₃	—	2	1	no	—
155	C₂²×C₄×C₂₃	—	2	1	no	—
156	C₂²×C₄×C₂₃	—	2	2	no	—
157	C₂²×C₄×C₂₃	—	2	2	no	—
158	C₂²×C₄×C₂₃	—	2	2	no	—
159	C₂²×C₄×C₂₃	—	2	2	no	—
160	C₂²×C₄×C₂₃	—	2	2	no	—
161	C₂²×C₄×C₂₃	—	2	2	no	—
162	C₂²×C₄×C₂₃	—	2	1	no	—
163	C₂²×C₄×C₂₃	—	2	1	no	—
164	C₂²×C₄×C₂₃	—	2	1	no	—
165	C₂²×C₄×C₂₃	—	2	1	no	—
166	C₂²×C₄×C₂₃	—	2	1	no	—
167	C₂²×C₄×C₂₃	—	2	1	no	—
168	C₂²×C₄×C₂₃	—	4	1	no	—
169	C₂²×C₄×C₂₃	—	4	1	no	—
170	C₂²×C₄×C₂₃	—	4	1	no	—
171	C₂²×C₄×C₂₃	—	4	4	no	—
172	C₂²×C₄×C₂₃	—	4	4	no	—
173	C₂²×C₄×C₂₃	—	4	4	no	—
174	C₂²×C₄×C₂₃	—	4	4	no	—
175	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₂₃	#41	1	2	yes	—
188	C₂²×C₄×C₂₃	#41	1	2	yes	—
189	C₂²×C₄×C₂₃	#41	1	2	yes	—
190	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
191	C₂×C₈×C₂₃	—	2	1	no	—
192	C₂×C₈×C₂₃	—	2	1	no	—
193	C₂×C₈×C₂₃	—	2	1	no	—
194	C₂×C₈×C₂₃	—	2	1	no	—
195	C₂×C₈×C₂₃	—	2	1	no	—
196	C₂×C₈×C₂₃	—	2	1	no	—
197	C₂×C₈×C₂₃	—	2	1	no	—
198	C₂×C₈×C₂₃	—	2	1	no	—
199	C₂×C₈×C₂₃	—	2	1	no	—
200	C₂×C₈×C₂₃	—	2	1	no	—
201	C₂×C₈×C₂₃	—	2	1	no	—
202	C₂×C₈×C₂₃	—	2	1	no	—
203	C₂×C₈×C₂₃	—	2	1	no	—
204	C₂×C₈×C₂₃	—	2	1	no	—
205	C₂×C₈×C₂₃	—	2	1	no	—
206	C₂×C₈×C₂₃	—	2	1	no	—
207	C₂×C₈×C₂₃	—	2	1	no	—
208	C₂×C₈×C₂₃	—	2	1	no	—
209	C₂×C₈×C₂₃	—	2	1	no	—
210	C₂×C₈×C₂₃	—	2	1	no	—
211	C₂×C₈×C₂₃	—	2	1	no	—
212	C₂×C₈×C₂₃	—	2	1	no	—
213	C₂×C₈×C₂₃	—	4	4	no	—
214	C₂×C₈×C₂₃	—	4	4	no	—
215	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
216	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
217	C₄⋊C₄×C₂₃	—	2	2	no	—
218	C₄⋊C₄×C₂₃	—	2	2	no	—
219	C₄⋊C₄×C₂₃	—	4	1	no	—
220	C₄⋊C₄×C₂₃	—	4	1	no	—
221	C₂²⋊C₄×C₂₃	—	2	2	no	—
222	C₂²⋊C₄×C₂₃	—	2	2	no	—
223	C₂²⋊C₄×C₂₃	—	2	2	no	—
224	C₂²⋊C₄×C₂₃	—	2	2	no	—
225	C₂²⋊C₄×C₂₃	—	2	2	no	—
226	C₂²⋊C₄×C₂₃	—	2	2	no	—
227	C₂²⋊C₄×C₂₃	—	2	2	no	—
228	C₂²⋊C₄×C₂₃	—	2	2	no	—
229	C₂²⋊C₄×C₂₃	—	4	1	no	—
230	C₂²⋊C₄×C₂₃	—	4	1	no	—
231	C₂²⋊C₄×C₂₃	—	4	1	no	—
232	C₂²⋊C₄×C₂₃	—	4	1	no	—
233	C₄²×C₂₃	—	2	1	no	—
234	C₄²×C₂₃	—	2	1	no	—
235	C₄²×C₂₃	—	2	1	no	—
236	C₄²×C₂₃	—	2	1	no	—
237	C₄²×C₂₃	—	2	1	no	—
238	C₄²×C₂₃	—	2	1	no	—
239	C₄²×C₂₃	—	2	1	no	—
240	C₄²×C₂₃	—	2	1	no	—
241	#22558	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₂³×C₂₃	—	2	1	no	—
243	C₂³×C₂₃	—	2	1	no	—
244	C₂³×C₂₃	—	2	1	no	—
245	C₂³×C₂₃	—	2	1	no	—
246	C₂³×C₂₃	—	2	8	no	—
247	C₂³×C₂₃	—	2	1	no	—
248	C₂³×C₂₃	—	2	1	no	—
249	C₂³×C₂₃	—	2	1	no	—
250	C₂³×C₂₃	—	2	1	no	—
251	C₂³×C₂₃	—	2	1	no	—
252	C₂³×C₂₃	—	2	1	no	—
253	C₂³×C₂₃	—	2	1	no	—
254	C₂³×C₂₃	—	2	1	no	—
255	C₂³×C₂₃	—	2	1	no	—
256	C₂³×C₂₃	—	2	1	no	—
257	C₂³×C₂₃	—	2	1	no	—
258	C₂³×C₂₃	—	2	1	no	—
259	C₂³×C₂₃	—	4	4	no	—
260	C₂³×C₂₃	—	4	4	no	—
261	C₂³×C₂₃	—	4	4	no	—
262	C₂³×C₂₃	—	4	4	no	—
263	C₂³×C₂₃	—	4	4	no	—
264	C₂³×C₂₃	—	4	4	no	—
265	C₂³×C₂₃	#117	1	2	yes	—
266	C₂³×C₂₃	C₄×D₄	1	2	yes	—
267	C₂³×C₂₃	#131	1	2	yes	—
268	C₂³×C₂₃	#131	1	2	yes	—
269	C₂³×C₂₃	#131	1	2	yes	—
270	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
271	C₂×C₄×C₂₃	—	2	1	no	—
272	C₂×C₄×C₂₃	—	2	1	no	—
273	C₂×C₄×C₂₃	—	2	1	no	—
274	C₂×C₄×C₂₃	—	2	1	no	—
275	C₂×C₄×C₂₃	—	2	2	no	—
276	C₂×C₄×C₂₃	—	2	2	no	—
277	C₂×C₄×C₂₃	—	2	2	no	—
278	C₂×C₄×C₂₃	—	2	2	no	—
279	C₂×C₄×C₂₃	—	2	2	no	—
280	C₂×C₄×C₂₃	—	2	2	no	—
281	C₂×C₄×C₂₃	—	2	2	no	—
282	C₂×C₄×C₂₃	—	2	2	no	—
283	C₂×C₄×C₂₃	—	2	1	no	—
284	C₂×C₄×C₂₃	—	2	1	no	—
285	C₂×C₄×C₂₃	—	2	1	no	—
286	C₂×C₄×C₂₃	—	2	1	no	—
287	C₂×C₄×C₂₃	—	2	1	no	—
288	C₂×C₄×C₂₃	—	2	1	no	—
289	C₂×C₄×C₂₃	—	2	1	no	—
290	C₂×C₄×C₂₃	—	2	1	no	—
291	C₂×C₄×C₂₃	—	2	1	no	—
292	C₂×C₄×C₂₃	—	2	1	no	—
293	C₂×C₄×C₂₃	—	2	1	no	—
294	C₂×C₄×C₂₃	—	2	1	no	—
295	C₂×C₄×C₂₃	—	2	1	no	—
296	C₂×C₄×C₂₃	—	2	1	no	—
297	C₂×C₄×C₂₃	—	2	1	no	—
298	C₂×C₄×C₂₃	—	2	1	no	—
299	C₂×C₄×C₂₃	—	2	1	no	—
300	C₂×C₄×C₂₃	—	2	1	no	—
301	C₂×C₄×C₂₃	—	2	1	no	—
302	C₂×C₄×C₂₃	—	2	1	no	—
303	C₂×C₄×C₂₃	—	2	1	no	—
304	C₂×C₄×C₂₃	—	2	1	no	—
305	C₂×C₄×C₂₃	—	2	1	no	—
306	C₂×C₄×C₂₃	—	2	1	no	—
307	C₂×C₄×C₂₃	—	2	1	no	—
308	C₂×C₄×C₂₃	—	2	1	no	—
309	C₂×C₄×C₂₃	—	2	1	no	—
310	C₂×C₄×C₂₃	—	4	4	no	—
311	C₂×C₄×C₂₃	—	4	4	no	—
312	C₂×C₄×C₂₃	—	4	4	no	—
313	C₂×C₄×C₂₃	—	4	1	no	—
314	C₂×C₄×C₂₃	—	4	1	no	—
315	C₂×C₄×C₂₃	—	4	1	no	—
316	C₂×C₄×C₂₃	—	4	1	no	—
317	C₂×C₄×C₂₃	#117	1	2	yes	—
318	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
319	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
321	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
322	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
323	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
324	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
325	C₈×C₂₃	—	2	2	no	—
326	C₈×C₂₃	—	2	2	no	—
327	C₈×C₂₃	—	4	1	no	—
328	C₈×C₂₃	—	4	1	no	—
329	C₈×C₂₃	—	4	1	no	—
330	C₈×C₂₃	—	4	1	no	—
331	C₈×C₂₃	—	4	1	no	—
332	C₈×C₂₃	—	4	1	no	—
333	C₂×#433	C₂×C₂₃	1	1	yes	characteristic, complemented
334	C₂²×C₂²⋊C₈	C₂×C₂₃	1	1	yes	characteristic
335	#2280	C₂×C₂₃	1	1	yes	characteristic
336	#1924	C₂×C₂₃	1	1	yes	characteristic, complemented
337	#1924	C₂×C₂₃	1	1	yes	characteristic, complemented
338	#1923	C₂×C₂₃	1	1	yes	characteristic, complemented
339	#1923	C₂×C₂₃	1	1	yes	characteristic, complemented
340	#1850	C₂×C₂₃	1	1	yes	characteristic, complemented
341	#1850	C₂×C₂₃	1	1	yes	characteristic, complemented
342	#1818	C₂×C₂₃	1	1	yes	characteristic, complemented
343	#1798	C₂×C₂₃	1	1	yes	characteristic, complemented
344	#1779	C₂×C₂₃	1	1	yes	characteristic
345	#1752	C₂×C₂₃	1	1	yes	characteristic, complemented
346	C₈×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
347	#1750	C₂×C₂₃	1	1	yes	characteristic, complemented
348	C₂²×C₂₃	—	2	2	no	—
349	C₂²×C₂₃	—	2	2	no	—
350	C₂²×C₂₃	—	2	2	no	—
351	C₂²×C₂₃	—	2	2	no	—
352	C₂²×C₂₃	—	2	2	no	—
353	C₂²×C₂₃	—	2	2	no	—
354	C₂²×C₂₃	—	2	2	no	—
355	C₂²×C₂₃	—	2	2	no	—
356	C₂²×C₂₃	—	2	2	no	—
357	C₂²×C₂₃	—	2	2	no	—
358	C₂²×C₂₃	—	2	2	no	—
359	C₂²×C₂₃	—	2	2	no	—
360	C₂²×C₂₃	—	4	16	no	—
361	C₂²×C₂₃	—	4	1	no	—
362	C₂²×C₂₃	—	4	1	no	—
363	C₂²×C₂₃	—	4	1	no	—
364	C₂²×C₂₃	—	4	1	no	—
365	C₂²×C₂₃	—	4	1	no	—
366	C₂²×C₂₃	—	4	1	no	—
367	C₂²×C₂₃	—	4	1	no	—
368	C₂²×C₂₃	—	4	1	no	—
369	C₂²×C₂₃	#433	1	4	yes	complemented
370	C₂²×C₂₃	C₂×#117	1	1	yes	characteristic
371	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
372	C₂²×C₂₃	#518	1	1	yes	characteristic
373	C₂²×C₂₃	C₂×#131	1	1	yes	characteristic
374	C₂²×C₂₃	C₂×#131	1	1	yes	characteristic
375	C₂²×C₂₃	C₂×#131	1	1	yes	characteristic
376	C₂²×C₂₃	#568	1	1	yes	characteristic
377	C₄×C₂₃	—	2	2	no	—
378	C₄×C₂₃	—	2	2	no	—
379	C₄×C₂₃	—	4	1	no	—
380	C₄×C₂₃	—	4	1	no	—
381	C₄×C₂₃	—	4	1	no	—
382	C₄×C₂₃	—	4	1	no	—
383	C₄×C₂₃	—	4	1	no	—
384	C₄×C₂₃	—	4	1	no	—
385	C₄×C₂₃	—	4	1	no	—
386	C₄×C₂₃	—	4	1	no	—
387	C₄×C₂₃	—	4	1	no	—
388	C₄×C₂₃	#546	1	1	yes	characteristic
389	C₄×C₂₃	#546	1	1	yes	characteristic
390	C₄×C₂₃	#551	1	1	yes	characteristic
391	C₄×C₂₃	#551	1	1	yes	characteristic
392	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
393	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
394	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
395	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
396	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
397	#433	—	2	4	no	—
398	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
399	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
400	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
401	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
402	C₂×C₂²⋊C₈	—	2	4	no	—
403	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
404	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
405	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
406	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
407	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
408	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
409	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
410	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
411	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
412	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
413	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
414	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
415	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
416	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
417	#381	C₄×C₂₃	1	1	yes	characteristic
418	#381	C₄×C₂₃	1	1	yes	characteristic
419	#380	C₄×C₂₃	1	1	yes	characteristic
420	#380	C₄×C₂₃	1	1	yes	characteristic
421	#380	C₄×C₂₃	1	1	yes	characteristic
422	#380	C₄×C₂₃	1	1	yes	characteristic
423	#379	C₄×C₂₃	1	1	yes	characteristic
424	#379	C₄×C₂₃	1	1	yes	characteristic
425	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
426	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
427	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
428	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
429	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
430	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
431	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
432	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
433	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
434	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
435	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
436	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
437	C₂×C₂₃	—	2	4	no	—
438	C₂×C₂₃	—	4	2	no	—
439	C₂×C₂₃	—	4	2	no	—
440	C₂×C₂₃	#2342	1	1	yes	characteristic
441	C₂×C₂₃	C₂×#433	1	1	yes	characteristic
442	C₂×C₂₃	#2924	1	1	yes	characteristic
443	C₂×C₂₃	#2929	1	1	yes	characteristic
444	C₂×C₂₃	#2933	1	1	yes	characteristic
445	C₂×C₂₃	#2976	1	1	yes	characteristic
446	C₂×C₂₃	#2977	1	1	yes	characteristic
447	C₂⁵	C₂×C₄×C₂₃	1	1	yes	characteristic
448	C₂³×C₄	—	2	2	no	—
449	C₂³×C₄	—	2	2	no	—
450	C₂³×C₄	—	2	2	no	—
451	C₂³×C₄	—	2	2	no	—
452	C₂³×C₄	—	4	1	no	—
453	C₂³×C₄	—	4	1	no	—
454	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
455	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
456	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
458	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
460	C₂²×C₈	—	2	2	no	—
461	C₂²×C₈	—	2	2	no	—
462	C₂²×C₈	—	2	2	no	—
463	C₂²×C₈	—	2	2	no	—
464	C₂²×C₈	—	4	1	no	—
465	C₂²×C₈	—	4	1	no	—
466	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
467	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
469	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
474	#117	—	2	2	no	—
475	#117	—	2	2	no	—
476	#117	—	4	1	no	—
477	#117	—	4	1	no	—
478	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
482	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
483	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
486	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
487	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
488	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
489	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
490	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
491	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
498	C₄⋊C₈	—	2	2	no	—
499	C₄⋊C₈	—	2	2	no	—
500	C₄⋊C₈	—	4	1	no	—
501	C₄⋊C₈	—	4	1	no	—
502	C₂²⋊C₈	—	2	2	no	—
503	C₂²⋊C₈	—	2	2	no	—
504	C₂²⋊C₈	—	2	2	no	—
505	C₂²⋊C₈	—	2	2	no	—
506	C₂²⋊C₈	—	2	2	no	—
507	C₂²⋊C₈	—	2	2	no	—
508	C₂²⋊C₈	—	2	2	no	—
509	C₂²⋊C₈	—	4	1	no	—
510	C₂²⋊C₈	—	4	1	no	—
511	C₂²⋊C₈	D₄×C₂₃	1	4	yes	—
512	#97	—	2	2	no	—
513	#97	—	4	1	no	—
514	C₄×C₈	—	2	2	no	—
515	C₄×C₈	—	4	1	no	—
516	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
517	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
518	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
519	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
520	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
521	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
522	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
523	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
524	C₂₃	#22558	1	1	yes	characteristic, direct product factor, Sylow
525	C₂⁴	—	2	2	no	—
526	C₂⁴	—	2	2	no	—
527	C₂⁴	—	2	2	no	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	—	2	2	no	—
530	C₂⁴	—	4	1	no	—
531	C₂⁴	—	4	1	no	—
532	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
533	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
534	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	4	1	no	—
556	C₂²×C₄	—	4	1	no	—
557	C₂²×C₄	—	4	1	no	—
558	C₂²×C₄	—	4	4	no	—
559	C₂²×C₄	—	4	4	no	—
560	C₂²×C₄	—	4	4	no	—
561	C₂²×C₄	—	4	4	no	—
562	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
563	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
564	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
565	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
566	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
567	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
568	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
569	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
570	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
571	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
572	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
574	C₂²×C₄	#41×C₂₃	1	2	yes	—
575	C₂²×C₄	#41×C₂₃	1	2	yes	—
576	C₂²×C₄	#41×C₂₃	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	4	4	no	—
601	C₂×C₈	—	4	4	no	—
602	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
603	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	4	1	no	—
607	C₄⋊C₄	—	4	1	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	2	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	—	4	1	no	—
617	C₂²⋊C₄	—	4	1	no	—
618	C₂²⋊C₄	—	4	1	no	—
619	C₂²⋊C₄	—	4	1	no	—
620	C₄²	—	2	1	no	—
621	C₄²	—	2	1	no	—
622	C₄²	—	2	1	no	—
623	C₄²	—	2	1	no	—
624	C₄²	—	2	1	no	—
625	C₄²	—	2	1	no	—
626	C₄²	—	2	1	no	—
627	C₄²	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	1	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	8	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	4	4	no	—
646	C₂³	—	4	4	no	—
647	C₂³	—	4	4	no	—
648	C₂³	—	4	4	no	—
649	C₂³	—	4	4	no	—
650	C₂³	—	4	4	no	—
651	C₂³	C₂₃×#117	1	2	yes	—
652	C₂³	C₄×D₄×C₂₃	1	2	yes	—
653	C₂³	C₂₃×#131	1	2	yes	—
654	C₂³	C₂₃×#131	1	2	yes	—
655	C₂³	C₂₃×#131	1	2	yes	—
656	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	C₂₃×#117	1	2	yes	—
704	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
705	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
706	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
707	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
708	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
709	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
710	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
711	C₈	—	2	2	no	—
712	C₈	—	2	2	no	—
713	C₈	—	4	1	no	—
714	C₈	—	4	1	no	—
715	C₈	—	4	1	no	—
716	C₈	—	4	1	no	—
717	C₈	—	4	1	no	—
718	C₈	—	4	1	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	2	2	no	—
731	C₂²	—	4	16	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	1	no	—
740	C₂²	C₂₃×#433	1	4	yes	complemented
741	C₂²	C₂×C₂₃×#117	1	1	yes	characteristic
742	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
743	C₂²	C₂₃×#518	1	1	yes	characteristic
744	C₂²	C₂×C₂₃×#131	1	1	yes	characteristic
745	C₂²	C₂×C₂₃×#131	1	1	yes	characteristic
746	C₂²	C₂×C₂₃×#131	1	1	yes	characteristic
747	C₂²	C₂₃×#568	1	1	yes	characteristic
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	4	1	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	1	no	—
757	C₄	—	4	1	no	—
758	C₄	—	4	1	no	—
759	C₄	C₂₃×#546	1	1	yes	characteristic
760	C₄	C₂₃×#546	1	1	yes	characteristic
761	C₄	C₂₃×#551	1	1	yes	characteristic
762	C₄	C₂₃×#551	1	1	yes	characteristic
763	C₂	—	2	4	no	—
764	C₂	—	4	2	no	—
765	C₂	—	4	2	no	—
766	C₂	C₂₃×#2342	1	1	yes	characteristic
767	C₂	C₂×C₂₃×#433	1	1	yes	characteristic
768	C₂	C₂₃×#2924	1	1	yes	characteristic
769	C₂	C₂₃×#2929	1	1	yes	characteristic
770	C₂	C₂₃×#2933	1	1	yes	characteristic
771	C₂	C₂₃×#2976	1	1	yes	characteristic
772	C₂	C₂₃×#2977	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	C₂⁵×C₂₃	C₂×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×#433	C₂	semidirect
4. C₂₃×#1924	C₂	semidirect
5. C₂₃×#1924	C₂	semidirect
6. C₂₃×#1923	C₂	semidirect
7. C₂₃×#1923	C₂	semidirect
8. C₂₃×#1850	C₂	semidirect
9. C₂₃×#1850	C₂	semidirect
10. C₂₃×#1818	C₂	semidirect
11. C₂₃×#1798	C₂	semidirect
13. C₂₃×#1752	C₂	semidirect
14. C₈×C₂²⋊C₄×C₂₃	C₂	semidirect
15. C₂₃×#1750	C₂	semidirect
22. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
23. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
24. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
25. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
37. C₂×C₂₃×#97	C₂²	semidirect
38. C₂×C₂₃×#97	C₂²	semidirect
39. C₂×C₄×C₈×C₂₃	C₂²	semidirect
40. C₂×C₄×C₈×C₂₃	C₂²	semidirect
53. C₂₃×#336	C₂²	semidirect
54. C₂₃×#336	C₂²	semidirect
55. C₂₃×#336	C₂²	semidirect
56. C₂₃×#336	C₂²	semidirect
57. C₂₃×#336	C₂²	semidirect
58. C₂₃×#336	C₂²	semidirect
59. C₂₃×#336	C₂²	semidirect
60. C₂₃×#336	C₂²	semidirect
241. #22558	C₂₃	direct (N × H)
333. C₂×#433	C₂×C₂₃	semidirect
336. #1924	C₂×C₂₃	semidirect
337. #1924	C₂×C₂₃	semidirect
338. #1923	C₂×C₂₃	semidirect
339. #1923	C₂×C₂₃	semidirect
340. #1850	C₂×C₂₃	semidirect
341. #1850	C₂×C₂₃	semidirect
342. #1818	C₂×C₂₃	semidirect
343. #1798	C₂×C₂₃	semidirect
345. #1752	C₂×C₂₃	semidirect
346. C₈×C₂²⋊C₄	C₂×C₂₃	semidirect
347. #1750	C₂×C₂₃	semidirect
369. C₂²×C₂₃	#433	semidirect
398. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
399. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
400. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
401. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
413. C₂×#97	C₂²×C₂₃	semidirect
414. C₂×#97	C₂²×C₂₃	semidirect
415. C₂×C₄×C₈	C₂²×C₂₃	semidirect
416. C₂×C₄×C₈	C₂²×C₂₃	semidirect
429. #336	C₂²×C₂₃	semidirect
430. #336	C₂²×C₂₃	semidirect
431. #336	C₂²×C₂₃	semidirect
432. #336	C₂²×C₂₃	semidirect
433. #336	C₂²×C₂₃	semidirect
434. #336	C₂²×C₂₃	semidirect
435. #336	C₂²×C₂₃	semidirect
436. #336	C₂²×C₂₃	semidirect
524. C₂₃	#22558	direct (N × H)
740. C₂²	C₂₃×#433	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#433	2
C₂²×C₂₃×C₂²⋊C₈	2
C₂₃×#2280	2
C₂₃×#1924	2
C₂₃×#1923	2
C₂₃×#1850	2
C₂₃×#1818	2
C₂₃×#1798	2
C₂₃×#1779	2
C₂₃×#1752	2
C₈×C₂²⋊C₄×C₂₃	2
C₂₃×#1750	2
#22558	23

Subgroups — C23×#22558 #19170184

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#22558 #19170184