Subgroups — C₂₃×#25088 #19172714

Order 5888.

1310 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#447	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₂₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2435	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2065	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2054	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2042	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1983	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1926	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1872	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₂₃	—	2	1	no	—
26	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
28	C₂₃×#465	—	2	4	no	—
29	C₂₃×#463	—	2	4	no	—
30	C₂₃×#447	—	2	4	no	—
31	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₂₃×#102	—	2	4	no	—
38	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂₃×#394	—	2	1	no	—
47	C₂₃×#394	—	2	1	no	—
48	C₂₃×#390	C₂²	1	1	yes	characteristic
49	C₂₃×#390	C₂²	1	1	yes	characteristic
50	C₂₃×#390	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#388	—	2	1	no	—
53	C₂₃×#386	—	2	1	no	—
54	C₂₃×#385	—	2	1	no	—
55	C₂₃×#379	—	2	1	no	—
56	C₂₃×#379	—	2	1	no	—
57	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
59	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#340	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	—	2	1	no	—
64	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₂₃	—	2	2	no	—
66	C₂²×D₄×C₂₃	—	2	2	no	—
67	C₂²×D₄×C₂₃	—	2	1	no	—
68	C₂²×D₄×C₂₃	—	2	2	no	—
69	C₂²×D₄×C₂₃	—	2	1	no	—
70	C₂²×D₄×C₂₃	—	2	2	no	—
71	C₂²×D₄×C₂₃	—	4	1	no	—
72	C₂²×D₄×C₂₃	—	4	1	no	—
73	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₂₃	—	2	1	no	—
77	C₂³×C₄×C₂₃	—	2	1	no	—
78	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
79	C₂×SD₁₆×C₂₃	—	2	2	no	—
80	C₂×SD₁₆×C₂₃	—	2	2	no	—
81	C₂×SD₁₆×C₂₃	—	4	1	no	—
82	C₂×D₈×C₂₃	—	2	2	no	—
83	C₂×D₈×C₂₃	—	2	2	no	—
84	C₂×D₈×C₂₃	—	2	2	no	—
85	C₂×D₈×C₂₃	—	2	2	no	—
86	C₂×D₈×C₂₃	—	4	1	no	—
87	C₂×D₈×C₂₃	—	4	1	no	—
88	C₂²×C₈×C₂₃	—	2	2	no	—
89	C₂²×C₈×C₂₃	—	2	2	no	—
90	C₂²×C₈×C₂₃	—	4	1	no	—
91	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
95	C₂₃×#124	—	2	2	no	—
96	C₂₃×#124	—	2	2	no	—
97	C₂₃×#124	—	4	1	no	—
98	C₂₃×#124	—	4	1	no	—
99	C₂₃×C₂²⋊Q₈	—	2	2	no	—
100	C₂₃×C₂²⋊Q₈	—	2	2	no	—
101	C₂₃×#121	—	2	2	no	—
102	C₂₃×#121	D₄	1	4	yes	—
103	C₄×D₄×C₂₃	—	2	2	no	—
104	C₄×D₄×C₂₃	—	4	1	no	—
105	C₄×D₄×C₂₃	—	4	4	no	—
106	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
107	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
108	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
109	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
110	C₂×C₄⋊C₄×C₂₃	—	4	1	no	—
111	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
130	C₂×C₄²×C₂₃	—	2	1	no	—
131	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
133	C₂₃×#106	—	2	2	no	—
134	C₂₃×C₄⋊C₈	—	2	2	no	—
135	C₂₃×C₄⋊C₈	—	4	1	no	—
136	C₂₃×#103	—	2	2	no	—
137	C₂₃×#103	—	2	2	no	—
138	C₂₃×#103	—	4	1	no	—
139	C₂₃×#102	—	2	2	no	—
140	C₂₃×#102	—	2	2	no	—
141	C₂₃×#102	—	2	2	no	—
142	C₂₃×#102	—	2	2	no	—
143	C₂₃×#102	—	2	2	no	—
144	C₂₃×#102	—	2	2	no	—
145	C₂₃×#102	D₄	1	4	yes	complemented
146	C₂₃×C₂²⋊C₈	—	2	2	no	—
147	C₂₃×#95	—	2	1	no	—
148	C₂₃×#95	—	2	1	no	—
149	C₂₃×#95	D₄	1	1	yes	characteristic
150	C₂₃×#95	D₄	1	1	yes	characteristic
151	C₂⁴×C₂₃	—	2	1	no	—
152	C₂⁴×C₂₃	—	2	1	no	—
153	C₂⁴×C₂₃	—	2	1	no	—
154	C₂⁴×C₂₃	—	4	2	no	—
155	C₂⁴×C₂₃	—	4	2	no	—
156	C₂⁴×C₂₃	—	4	2	no	—
157	C₂⁴×C₂₃	—	4	2	no	—
158	C₂⁴×C₂₃	—	4	2	no	—
159	C₂⁴×C₂₃	—	8	1	no	—
160	C₂⁴×C₂₃	—	8	1	no	—
161	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
162	C₂×Q₈×C₂₃	—	2	1	no	—
163	C₂×Q₈×C₂₃	—	2	1	no	—
164	C₂×Q₈×C₂₃	—	2	1	no	—
165	C₂×Q₈×C₂₃	—	2	1	no	—
166	C₂×Q₈×C₂₃	—	2	1	no	—
167	C₂×Q₈×C₂₃	—	2	1	no	—
168	C₂×D₄×C₂₃	—	2	8	no	—
169	C₂×D₄×C₂₃	—	2	4	no	—
170	C₂×D₄×C₂₃	—	2	1	no	—
171	C₂×D₄×C₂₃	—	2	1	no	—
172	C₂×D₄×C₂₃	—	2	1	no	—
173	C₂×D₄×C₂₃	—	2	1	no	—
174	C₂×D₄×C₂₃	—	2	1	no	—
175	C₂×D₄×C₂₃	—	2	1	no	—
176	C₂×D₄×C₂₃	—	2	1	no	—
177	C₂×D₄×C₂₃	—	2	1	no	—
178	C₂×D₄×C₂₃	—	2	1	no	—
179	C₂×D₄×C₂₃	—	2	1	no	—
180	C₂×D₄×C₂₃	—	2	1	no	—
181	C₂×D₄×C₂₃	—	2	1	no	—
182	C₂×D₄×C₂₃	—	2	1	no	—
183	C₂×D₄×C₂₃	—	2	1	no	—
184	C₂×D₄×C₂₃	—	2	1	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	2	no	—
189	C₂×D₄×C₂₃	—	4	4	no	—
190	C₂×D₄×C₂₃	—	4	2	no	—
191	C₂×D₄×C₂₃	—	4	2	no	—
192	C₂×D₄×C₂₃	—	4	2	no	—
193	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
194	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
195	C₂×D₄×C₂₃	#41	1	2	yes	—
196	C₂²×C₄×C₂₃	—	2	1	no	—
197	C₂²×C₄×C₂₃	—	2	1	no	—
198	C₂²×C₄×C₂₃	—	2	1	no	—
199	C₂²×C₄×C₂₃	—	2	1	no	—
200	C₂²×C₄×C₂₃	—	2	1	no	—
201	C₂²×C₄×C₂₃	—	2	1	no	—
202	C₂²×C₄×C₂₃	—	2	1	no	—
203	C₂²×C₄×C₂₃	—	2	1	no	—
204	C₂²×C₄×C₂₃	—	2	1	no	—
205	C₂²×C₄×C₂₃	—	4	2	no	—
206	C₂²×C₄×C₂₃	—	4	2	no	—
207	C₂²×C₄×C₂₃	—	4	2	no	—
208	C₂²×C₄×C₂₃	—	4	2	no	—
209	C₂²×C₄×C₂₃	—	8	1	no	—
210	C₂²×C₄×C₂₃	—	8	1	no	—
211	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
217	C₂²×C₄×C₂₃	#41	1	2	yes	—
218	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
219	SD₁₆×C₂₃	—	4	4	no	—
220	D₈×C₂₃	—	4	4	no	—
221	D₈×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	—	4	4	no	—
234	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
235	C₄⋊C₄×C₂₃	—	2	1	no	—
236	C₄⋊C₄×C₂₃	—	2	1	no	—
237	C₄⋊C₄×C₂₃	—	2	1	no	—
238	C₄⋊C₄×C₂₃	—	2	1	no	—
239	C₄⋊C₄×C₂₃	—	2	1	no	—
240	C₄⋊C₄×C₂₃	—	2	1	no	—
241	C₄⋊C₄×C₂₃	—	4	2	no	—
242	C₄⋊C₄×C₂₃	—	4	2	no	—
243	C₄⋊C₄×C₂₃	—	4	2	no	—
244	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
245	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
246	C₂²⋊C₄×C₂₃	—	2	2	no	—
247	C₂²⋊C₄×C₂₃	—	2	2	no	—
248	C₂²⋊C₄×C₂₃	—	2	4	no	—
249	C₂²⋊C₄×C₂₃	—	4	2	no	—
250	C₂²⋊C₄×C₂₃	—	4	2	no	—
251	C₂²⋊C₄×C₂₃	—	4	2	no	—
252	C₂²⋊C₄×C₂₃	—	4	2	no	—
253	C₂²⋊C₄×C₂₃	—	4	2	no	—
254	C₂²⋊C₄×C₂₃	—	4	2	no	—
255	C₂²⋊C₄×C₂₃	—	4	2	no	—
256	C₂²⋊C₄×C₂₃	—	8	1	no	—
257	C₂²⋊C₄×C₂₃	—	8	1	no	—
258	C₂²⋊C₄×C₂₃	—	8	1	no	—
259	C₂²⋊C₄×C₂₃	—	8	1	no	—
260	C₂²⋊C₄×C₂₃	—	8	1	no	—
261	C₄²×C₂₃	—	2	1	no	—
262	C₄²×C₂₃	—	2	1	no	—
263	C₄²×C₂₃	—	2	1	no	—
264	C₄²×C₂₃	—	2	1	no	—
265	C₄²×C₂₃	—	4	2	no	—
266	#25088	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂³×C₂₃	—	2	1	no	—
268	C₂³×C₂₃	—	2	1	no	—
269	C₂³×C₂₃	—	2	1	no	—
270	C₂³×C₂₃	—	2	1	no	—
271	C₂³×C₂₃	—	2	2	no	—
272	C₂³×C₂₃	—	2	2	no	—
273	C₂³×C₂₃	—	2	2	no	—
274	C₂³×C₂₃	—	4	8	no	—
275	C₂³×C₂₃	—	4	1	no	—
276	C₂³×C₂₃	—	4	1	no	—
277	C₂³×C₂₃	—	4	1	no	—
278	C₂³×C₂₃	—	4	1	no	—
279	C₂³×C₂₃	—	4	1	no	—
280	C₂³×C₂₃	—	4	1	no	—
281	C₂³×C₂₃	—	4	1	no	—
282	C₂³×C₂₃	—	4	1	no	—
283	C₂³×C₂₃	—	4	1	no	—
284	C₂³×C₂₃	—	4	1	no	—
285	C₂³×C₂₃	—	4	1	no	—
286	C₂³×C₂₃	—	4	1	no	—
287	C₂³×C₂₃	—	4	1	no	—
288	C₂³×C₂₃	—	4	1	no	—
289	C₂³×C₂₃	—	4	1	no	—
290	C₂³×C₂₃	—	4	1	no	—
291	C₂³×C₂₃	—	4	1	no	—
292	C₂³×C₂₃	—	4	1	no	—
293	C₂³×C₂₃	—	8	4	no	—
294	C₂³×C₂₃	—	8	4	no	—
295	C₂³×C₂₃	—	8	4	no	—
296	C₂³×C₂₃	—	8	4	no	—
297	C₂³×C₂₃	—	8	4	no	—
298	C₂³×C₂₃	—	8	4	no	—
299	C₂³×C₂₃	#121	1	2	yes	—
300	C₂³×C₂₃	#135	1	2	yes	—
301	C₂³×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
302	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
303	Q₈×C₂₃	—	4	1	no	—
304	Q₈×C₂₃	—	4	1	no	—
305	Q₈×C₂₃	—	4	1	no	—
306	Q₈×C₂₃	—	4	1	no	—
307	D₄×C₂₃	—	2	2	no	—
308	D₄×C₂₃	—	2	2	no	—
309	D₄×C₂₃	—	2	2	no	—
310	D₄×C₂₃	—	2	2	no	—
311	D₄×C₂₃	—	2	2	no	—
312	D₄×C₂₃	—	2	2	no	—
313	D₄×C₂₃	—	4	8	no	—
314	D₄×C₂₃	—	4	8	no	—
315	D₄×C₂₃	—	4	1	no	—
316	D₄×C₂₃	—	4	1	no	—
317	D₄×C₂₃	—	4	1	no	—
318	D₄×C₂₃	—	4	1	no	—
319	D₄×C₂₃	—	4	1	no	—
320	D₄×C₂₃	—	4	1	no	—
321	C₂×C₄×C₂₃	—	2	1	no	—
322	C₂×C₄×C₂₃	—	2	1	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	1	no	—
329	C₂×C₄×C₂₃	—	2	1	no	—
330	C₂×C₄×C₂₃	—	2	2	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	—	4	1	no	—
342	C₂×C₄×C₂₃	—	4	1	no	—
343	C₂×C₄×C₂₃	—	4	1	no	—
344	C₂×C₄×C₂₃	—	4	1	no	—
345	C₂×C₄×C₂₃	—	4	1	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	—	8	4	no	—
355	C₂×C₄×C₂₃	—	8	4	no	—
356	C₂×C₄×C₂₃	#121	1	2	yes	—
357	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
360	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
361	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
363	C₈×C₂₃	—	2	2	no	—
364	C₈×C₂₃	—	4	1	no	—
365	C₈×C₂₃	—	4	1	no	—
366	C₈×C₂₃	—	4	1	no	—
367	C₂×#465	C₂×C₂₃	1	1	yes	characteristic, complemented
368	C₂×#463	C₂×C₂₃	1	1	yes	characteristic, complemented
369	C₂×#447	C₂×C₂₃	1	1	yes	characteristic
370	C₂²×#102	C₂×C₂₃	1	1	yes	characteristic, complemented
371	#2435	C₂×C₂₃	1	1	yes	characteristic, complemented
372	#2361	C₂×C₂₃	1	1	yes	characteristic, complemented
373	#2065	C₂×C₂₃	1	1	yes	characteristic, complemented
374	#2054	C₂×C₂₃	1	1	yes	characteristic, complemented
375	#2042	C₂×C₂₃	1	1	yes	characteristic, complemented
376	#2012	C₂×C₂₃	1	1	yes	characteristic, complemented
377	#1983	C₂×C₂₃	1	1	yes	characteristic, complemented
378	#1926	C₂×C₂₃	1	1	yes	characteristic, complemented
379	#1879	C₂×C₂₃	1	1	yes	characteristic, complemented
380	#1872	C₂×C₂₃	1	1	yes	characteristic, complemented
381	#1850	C₂×C₂₃	1	1	yes	characteristic, complemented
382	C₂²×C₂₃	—	2	2	no	—
383	C₂²×C₂₃	—	2	2	no	—
384	C₂²×C₂₃	—	2	2	no	—
385	C₂²×C₂₃	—	2	2	no	—
386	C₂²×C₂₃	—	2	2	no	—
387	C₂²×C₂₃	—	2	2	no	—
388	C₂²×C₂₃	—	4	2	no	—
389	C₂²×C₂₃	—	4	2	no	—
390	C₂²×C₂₃	—	4	2	no	—
391	C₂²×C₂₃	—	4	2	no	—
392	C₂²×C₂₃	—	4	2	no	—
393	C₂²×C₂₃	—	4	2	no	—
394	C₂²×C₂₃	—	4	2	no	—
395	C₂²×C₂₃	—	4	2	no	—
396	C₂²×C₂₃	—	4	2	no	—
397	C₂²×C₂₃	—	8	16	no	—
398	C₂²×C₂₃	—	8	1	no	—
399	C₂²×C₂₃	—	8	1	no	—
400	C₂²×C₂₃	—	8	1	no	—
401	C₂²×C₂₃	—	8	1	no	—
402	C₂²×C₂₃	—	8	1	no	—
403	C₂²×C₂₃	—	8	1	no	—
404	C₂²×C₂₃	—	8	1	no	—
405	C₂²×C₂₃	—	8	1	no	—
406	C₂²×C₂₃	—	8	1	no	—
407	C₂²×C₂₃	—	8	1	no	—
408	C₂²×C₂₃	—	8	1	no	—
409	C₂²×C₂₃	—	8	1	no	—
410	C₂²×C₂₃	#463	1	4	yes	complemented
411	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
412	C₂²×C₂₃	D₄²	1	1	yes	characteristic
413	C₂²×C₂₃	#546	1	1	yes	characteristic
414	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
415	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
416	C₂²×C₂₃	#576	1	1	yes	characteristic
417	C₂²×C₂₃	#577	1	1	yes	characteristic
418	C₄×C₂₃	—	2	2	no	—
419	C₄×C₂₃	—	4	1	no	—
420	C₄×C₂₃	—	4	2	no	—
421	C₄×C₂₃	—	4	1	no	—
422	C₄×C₂₃	—	4	2	no	—
423	C₄×C₂₃	—	4	1	no	—
424	C₄×C₂₃	—	4	1	no	—
425	C₄×C₂₃	—	8	1	no	—
426	C₄×C₂₃	—	8	1	no	—
427	C₄×C₂₃	—	8	1	no	—
428	C₄×C₂₃	#525	1	1	yes	characteristic
429	C₄×C₂₃	#538	1	1	yes	characteristic
430	C₄×C₂₃	D₄²	1	1	yes	characteristic
431	C₄×C₂₃	#546	1	1	yes	characteristic
432	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
433	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
434	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
435	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
436	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
437	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
438	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
439	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
440	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
441	C₂×C₄×D₄	—	2	1	no	—
442	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
443	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
444	#465	—	2	4	no	—
445	#463	—	2	4	no	—
446	#447	—	2	4	no	—
447	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
448	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
449	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
450	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
451	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
452	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
453	C₂×#102	—	2	4	no	—
454	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
455	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
456	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
457	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
458	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
459	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
460	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
461	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
462	#394	—	2	1	no	—
463	#394	—	2	1	no	—
464	#390	C₂²×C₂₃	1	1	yes	characteristic
465	#390	C₂²×C₂₃	1	1	yes	characteristic
466	#390	C₂²×C₂₃	1	1	yes	characteristic, complemented
467	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
468	#388	—	2	1	no	—
469	#386	—	2	1	no	—
470	#385	—	2	1	no	—
471	#379	—	2	1	no	—
472	#379	—	2	1	no	—
473	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
474	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
475	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
476	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
477	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
478	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
479	C₂×C₂₃	—	2	4	no	—
480	C₂×C₂₃	—	8	2	no	—
481	C₂×C₂₃	—	8	2	no	—
482	C₂×C₂₃	—	8	2	no	—
483	C₂×C₂₃	#2424	1	1	yes	characteristic
484	C₂×C₂₃	C₂×#463	1	1	yes	characteristic
485	C₂×C₂₃	#3045	1	1	yes	characteristic
486	C₂×C₂₃	#3264	1	1	yes	characteristic
487	C₂×C₂₃	#3282	1	1	yes	characteristic
488	C₂×C₂₃	#3297	1	1	yes	characteristic
489	C₂×C₂₃	#3306	1	1	yes	characteristic
490	C₂⁵	—	2	1	no	—
491	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
492	C₂²×D₄	—	2	2	no	—
493	C₂²×D₄	—	2	2	no	—
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	—	2	2	no	—
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	—	2	2	no	—
498	C₂²×D₄	—	4	1	no	—
499	C₂²×D₄	—	4	1	no	—
500	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
501	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
502	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
506	C₂×SD₁₆	—	2	2	no	—
507	C₂×SD₁₆	—	2	2	no	—
508	C₂×SD₁₆	—	4	1	no	—
509	C₂×D₈	—	2	2	no	—
510	C₂×D₈	—	2	2	no	—
511	C₂×D₈	—	2	2	no	—
512	C₂×D₈	—	2	2	no	—
513	C₂×D₈	—	4	1	no	—
514	C₂×D₈	—	4	1	no	—
515	C₂²×C₈	—	2	2	no	—
516	C₂²×C₈	—	2	2	no	—
517	C₂²×C₈	—	4	1	no	—
518	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
519	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
520	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
521	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
522	#124	—	2	2	no	—
523	#124	—	2	2	no	—
524	#124	—	4	1	no	—
525	#124	—	4	1	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	2	no	—
528	#121	—	2	2	no	—
529	#121	D₄×C₂₃	1	4	yes	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	4	1	no	—
532	C₄×D₄	—	4	4	no	—
533	C₂×C₄⋊C₄	—	2	2	no	—
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	—	4	1	no	—
538	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
542	C₂×C₂²⋊C₄	—	2	1	no	—
543	C₂×C₂²⋊C₄	—	2	1	no	—
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
557	C₂×C₄²	—	2	1	no	—
558	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
560	#106	—	2	2	no	—
561	C₄⋊C₈	—	2	2	no	—
562	C₄⋊C₈	—	4	1	no	—
563	#103	—	2	2	no	—
564	#103	—	2	2	no	—
565	#103	—	4	1	no	—
566	#102	—	2	2	no	—
567	#102	—	2	2	no	—
568	#102	—	2	2	no	—
569	#102	—	2	2	no	—
570	#102	—	2	2	no	—
571	#102	—	2	2	no	—
572	#102	D₄×C₂₃	1	4	yes	complemented
573	C₂²⋊C₈	—	2	2	no	—
574	#95	—	2	1	no	—
575	#95	—	2	1	no	—
576	#95	D₄×C₂₃	1	1	yes	characteristic
577	#95	D₄×C₂₃	1	1	yes	characteristic
578	C₂₃	#25088	1	1	yes	characteristic, direct product factor, Sylow
579	C₂⁴	—	2	1	no	—
580	C₂⁴	—	2	1	no	—
581	C₂⁴	—	2	1	no	—
582	C₂⁴	—	4	2	no	—
583	C₂⁴	—	4	2	no	—
584	C₂⁴	—	4	2	no	—
585	C₂⁴	—	4	2	no	—
586	C₂⁴	—	4	2	no	—
587	C₂⁴	—	8	1	no	—
588	C₂⁴	—	8	1	no	—
589	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	—	2	1	no	—
592	C₂×Q₈	—	2	1	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×D₄	—	2	8	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	2	1	no	—
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	4	4	no	—
614	C₂×D₄	—	4	4	no	—
615	C₂×D₄	—	4	2	no	—
616	C₂×D₄	—	4	2	no	—
617	C₂×D₄	—	4	4	no	—
618	C₂×D₄	—	4	2	no	—
619	C₂×D₄	—	4	2	no	—
620	C₂×D₄	—	4	2	no	—
621	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
622	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
623	C₂×D₄	#41×C₂₃	1	2	yes	—
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	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	4	2	no	—
634	C₂²×C₄	—	4	2	no	—
635	C₂²×C₄	—	4	2	no	—
636	C₂²×C₄	—	4	2	no	—
637	C₂²×C₄	—	8	1	no	—
638	C₂²×C₄	—	8	1	no	—
639	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
640	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
642	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
644	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
645	C₂²×C₄	#41×C₂₃	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
647	SD₁₆	—	4	4	no	—
648	D₈	—	4	4	no	—
649	D₈	—	4	4	no	—
650	C₂×C₈	—	2	1	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	1	no	—
654	C₂×C₈	—	2	1	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	—	4	4	no	—
662	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	4	2	no	—
670	C₄⋊C₄	—	4	2	no	—
671	C₄⋊C₄	—	4	2	no	—
672	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
673	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	2	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	4	2	no	—
678	C₂²⋊C₄	—	4	2	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	4	2	no	—
683	C₂²⋊C₄	—	4	2	no	—
684	C₂²⋊C₄	—	8	1	no	—
685	C₂²⋊C₄	—	8	1	no	—
686	C₂²⋊C₄	—	8	1	no	—
687	C₂²⋊C₄	—	8	1	no	—
688	C₂²⋊C₄	—	8	1	no	—
689	C₄²	—	2	1	no	—
690	C₄²	—	2	1	no	—
691	C₄²	—	2	1	no	—
692	C₄²	—	2	1	no	—
693	C₄²	—	4	2	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	4	8	no	—
702	C₂³	—	4	1	no	—
703	C₂³	—	4	1	no	—
704	C₂³	—	4	1	no	—
705	C₂³	—	4	1	no	—
706	C₂³	—	4	1	no	—
707	C₂³	—	4	1	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	4	1	no	—
710	C₂³	—	4	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	4	1	no	—
716	C₂³	—	4	1	no	—
717	C₂³	—	4	1	no	—
718	C₂³	—	4	1	no	—
719	C₂³	—	4	1	no	—
720	C₂³	—	8	4	no	—
721	C₂³	—	8	4	no	—
722	C₂³	—	8	4	no	—
723	C₂³	—	8	4	no	—
724	C₂³	—	8	4	no	—
725	C₂³	—	8	4	no	—
726	C₂³	C₂₃×#121	1	2	yes	—
727	C₂³	C₂₃×#135	1	2	yes	—
728	C₂³	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
729	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
730	Q₈	—	4	1	no	—
731	Q₈	—	4	1	no	—
732	Q₈	—	4	1	no	—
733	Q₈	—	4	1	no	—
734	D₄	—	2	2	no	—
735	D₄	—	2	2	no	—
736	D₄	—	2	2	no	—
737	D₄	—	2	2	no	—
738	D₄	—	2	2	no	—
739	D₄	—	2	2	no	—
740	D₄	—	4	8	no	—
741	D₄	—	4	8	no	—
742	D₄	—	4	1	no	—
743	D₄	—	4	1	no	—
744	D₄	—	4	1	no	—
745	D₄	—	4	1	no	—
746	D₄	—	4	1	no	—
747	D₄	—	4	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	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	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	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	2	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	4	1	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	8	4	no	—
782	C₂×C₄	—	8	4	no	—
783	C₂×C₄	C₂₃×#121	1	2	yes	—
784	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
785	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
786	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
787	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
788	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
789	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
790	C₈	—	2	2	no	—
791	C₈	—	4	1	no	—
792	C₈	—	4	1	no	—
793	C₈	—	4	1	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	2	2	no	—
796	C₂²	—	2	2	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	8	16	no	—
810	C₂²	—	8	1	no	—
811	C₂²	—	8	1	no	—
812	C₂²	—	8	1	no	—
813	C₂²	—	8	1	no	—
814	C₂²	—	8	1	no	—
815	C₂²	—	8	1	no	—
816	C₂²	—	8	1	no	—
817	C₂²	—	8	1	no	—
818	C₂²	—	8	1	no	—
819	C₂²	—	8	1	no	—
820	C₂²	—	8	1	no	—
821	C₂²	—	8	1	no	—
822	C₂²	C₂₃×#463	1	4	yes	complemented
823	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
824	C₂²	D₄²×C₂₃	1	1	yes	characteristic
825	C₂²	C₂₃×#546	1	1	yes	characteristic
826	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
827	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
828	C₂²	C₂₃×#576	1	1	yes	characteristic
829	C₂²	C₂₃×#577	1	1	yes	characteristic
830	C₄	—	2	2	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	1	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	8	1	no	—
838	C₄	—	8	1	no	—
839	C₄	—	8	1	no	—
840	C₄	C₂₃×#525	1	1	yes	characteristic
841	C₄	C₂₃×#538	1	1	yes	characteristic
842	C₄	D₄²×C₂₃	1	1	yes	characteristic
843	C₄	C₂₃×#546	1	1	yes	characteristic
844	C₂	—	2	4	no	—
845	C₂	—	8	2	no	—
846	C₂	—	8	2	no	—
847	C₂	—	8	2	no	—
848	C₂	C₂₃×#2424	1	1	yes	characteristic
849	C₂	C₂×C₂₃×#463	1	1	yes	characteristic
850	C₂	C₂₃×#3045	1	1	yes	characteristic
851	C₂	C₂₃×#3264	1	1	yes	characteristic
852	C₂	C₂₃×#3282	1	1	yes	characteristic
853	C₂	C₂₃×#3297	1	1	yes	characteristic
854	C₂	C₂₃×#3306	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#447	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₄×C₂²⋊C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#465	C₂	semidirect
2. C₂×C₂₃×#463	C₂	semidirect
4. C₂²×C₂₃×#102	C₂	semidirect
5. C₂₃×#2435	C₂	semidirect
6. C₂₃×#2361	C₂	semidirect
7. C₂₃×#2065	C₂	semidirect
8. C₂₃×#2054	C₂	semidirect
9. C₂₃×#2042	C₂	semidirect
10. C₂₃×#2012	C₂	semidirect
11. C₂₃×#1983	C₂	semidirect
12. C₂₃×#1926	C₂	semidirect
13. C₂₃×#1879	C₂	semidirect
14. C₂₃×#1872	C₂	semidirect
15. C₂₃×#1850	C₂	semidirect
17. C₂²×SD₁₆×C₂₃	C₂²	semidirect
26. C₂×C₄×D₄×C₂₃	C₂²	semidirect
31. C₂×C₂₃×#106	C₂²	semidirect
32. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
33. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
34. C₂×C₂₃×#103	C₂²	semidirect
35. C₂×C₂₃×#103	C₂²	semidirect
36. C₂×C₂₃×#103	C₂²	semidirect
44. C₂×C₂₃×#102	C₂²	semidirect
50. C₂₃×#390	C₂²	semidirect
51. C₂₃×#389	C₂²	semidirect
57. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
59. C₂₃×#340	C₂²	semidirect
60. C₂₃×#340	C₂²	semidirect
61. C₂₃×#336	C₂²	semidirect
62. C₂₃×#336	C₂²	semidirect
145. C₂₃×#102	D₄	semidirect
266. #25088	C₂₃	direct (N × H)
367. C₂×#465	C₂×C₂₃	semidirect
368. C₂×#463	C₂×C₂₃	semidirect
370. C₂²×#102	C₂×C₂₃	semidirect
371. #2435	C₂×C₂₃	semidirect
372. #2361	C₂×C₂₃	semidirect
373. #2065	C₂×C₂₃	semidirect
374. #2054	C₂×C₂₃	semidirect
375. #2042	C₂×C₂₃	semidirect
376. #2012	C₂×C₂₃	semidirect
377. #1983	C₂×C₂₃	semidirect
378. #1926	C₂×C₂₃	semidirect
379. #1879	C₂×C₂₃	semidirect
380. #1872	C₂×C₂₃	semidirect
381. #1850	C₂×C₂₃	semidirect
410. C₂²×C₂₃	#463	semidirect
433. C₂²×SD₁₆	C₂²×C₂₃	semidirect
442. C₂×C₄×D₄	C₂²×C₂₃	semidirect
447. C₂×#106	C₂²×C₂₃	semidirect
448. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
449. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
450. C₂×#103	C₂²×C₂₃	semidirect
451. C₂×#103	C₂²×C₂₃	semidirect
452. C₂×#103	C₂²×C₂₃	semidirect
460. C₂×#102	C₂²×C₂₃	semidirect
466. #390	C₂²×C₂₃	semidirect
467. #389	C₂²×C₂₃	semidirect
473. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
475. #340	C₂²×C₂₃	semidirect
476. #340	C₂²×C₂₃	semidirect
477. #336	C₂²×C₂₃	semidirect
478. #336	C₂²×C₂₃	semidirect
572. #102	D₄×C₂₃	semidirect
578. C₂₃	#25088	direct (N × H)
822. C₂²	C₂₃×#463	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#465	2
C₂×C₂₃×#463	2
C₂×C₂₃×#447	2
C₂²×C₂₃×#102	2
C₂₃×#2435	2
C₂₃×#2361	2
C₂₃×#2065	2
C₂₃×#2054	2
C₂₃×#2042	2
C₂₃×#2012	2
C₂₃×#1983	2
C₂₃×#1926	2
C₂₃×#1879	2
C₂₃×#1872	2
C₂₃×#1850	2
#25088	23

Subgroups — C23×#25088 #19172714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25088 #19172714