Subgroups — C₂₃×#24913 #19172539

Order 5888.

1226 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#447	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2422	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2094	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2077	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2054	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1936	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1924	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#123	—	2	1	no	—
20	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
25	C₂₃×#447	—	2	4	no	—
26	C₂₃×#442	—	2	4	no	—
27	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
41	C₂₃×#397	—	2	1	no	—
42	C₂₃×#394	—	2	1	no	—
43	C₂₃×#390	C₂²	1	1	yes	characteristic
44	C₂₃×#390	C₂²	1	1	yes	characteristic
45	C₂₃×#390	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#386	—	2	1	no	—
48	C₂₃×#386	—	2	1	no	—
49	C₂₃×#385	—	2	1	no	—
50	C₂₃×#384	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#380	C₂²	1	1	yes	characteristic
52	C₂₃×#380	C₂²	1	1	yes	characteristic
53	C₂₃×#379	—	2	1	no	—
54	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
55	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
56	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#340	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	—	2	1	no	—
62	C₂²×D₄×C₂₃	—	2	2	no	—
63	C₂²×D₄×C₂₃	—	2	2	no	—
64	C₂²×D₄×C₂₃	—	2	2	no	—
65	C₂²×D₄×C₂₃	—	2	2	no	—
66	C₂²×D₄×C₂₃	—	2	1	no	—
67	C₂²×D₄×C₂₃	—	2	1	no	—
68	C₂²×D₄×C₂₃	—	4	1	no	—
69	C₂²×D₄×C₂₃	—	4	1	no	—
70	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₂₃	—	2	1	no	—
74	C₂³×C₄×C₂₃	—	2	1	no	—
75	C₂³×C₄×C₂₃	—	2	1	no	—
76	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂×D₈×C₂₃	—	2	2	no	—
78	C₂×D₈×C₂₃	—	2	2	no	—
79	C₂×D₈×C₂₃	—	2	2	no	—
80	C₂×D₈×C₂₃	—	2	2	no	—
81	C₂×D₈×C₂₃	—	4	1	no	—
82	C₂×D₈×C₂₃	D₄	1	4	yes	—
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	C₂₃×#123	—	4	4	no	—
88	C₂₃×#121	—	2	2	no	—
89	C₂₃×#121	—	4	1	no	—
90	C₄×D₄×C₂₃	—	2	2	no	—
91	C₄×D₄×C₂₃	—	2	2	no	—
92	C₄×D₄×C₂₃	—	2	2	no	—
93	C₄×D₄×C₂₃	—	4	1	no	—
94	C₄×D₄×C₂₃	—	4	1	no	—
95	C₄×D₄×C₂₃	—	4	1	no	—
96	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
97	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
98	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
99	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
117	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
121	C₂₃×#106	—	2	2	no	—
122	C₂₃×#106	—	4	1	no	—
123	C₂₃×C₄⋊C₈	—	4	1	no	—
124	C₂₃×#102	—	2	2	no	—
125	C₂₃×#102	—	2	2	no	—
126	C₂₃×#102	—	2	2	no	—
127	C₂₃×#102	—	2	2	no	—
128	C₂₃×#102	—	2	2	no	—
129	C₂₃×#102	—	2	2	no	—
130	C₂₃×#102	—	4	1	no	—
131	C₂₃×#102	—	4	1	no	—
132	C₂₃×C₂²⋊C₈	—	2	2	no	—
133	C₂₃×C₂²⋊C₈	—	4	1	no	—
134	C₂₃×#97	—	2	2	no	—
135	C₂₃×#95	—	2	1	no	—
136	C₂₃×#95	—	2	1	no	—
137	C₂₃×#95	—	2	1	no	—
138	C₂₃×#95	D₄	1	1	yes	characteristic
139	C₂₃×#95	D₄	1	1	yes	characteristic
140	C₂⁴×C₂₃	—	2	1	no	—
141	C₂⁴×C₂₃	—	2	4	no	—
142	C₂⁴×C₂₃	—	2	1	no	—
143	C₂⁴×C₂₃	—	2	1	no	—
144	C₂⁴×C₂₃	—	4	2	no	—
145	C₂⁴×C₂₃	—	4	2	no	—
146	C₂⁴×C₂₃	—	4	2	no	—
147	C₂⁴×C₂₃	—	4	2	no	—
148	C₂⁴×C₂₃	—	8	1	no	—
149	C₂⁴×C₂₃	—	8	1	no	—
150	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
151	C₂×D₄×C₂₃	—	2	4	no	—
152	C₂×D₄×C₂₃	—	2	1	no	—
153	C₂×D₄×C₂₃	—	2	1	no	—
154	C₂×D₄×C₂₃	—	2	1	no	—
155	C₂×D₄×C₂₃	—	2	1	no	—
156	C₂×D₄×C₂₃	—	2	1	no	—
157	C₂×D₄×C₂₃	—	2	1	no	—
158	C₂×D₄×C₂₃	—	2	1	no	—
159	C₂×D₄×C₂₃	—	2	1	no	—
160	C₂×D₄×C₂₃	—	2	1	no	—
161	C₂×D₄×C₂₃	—	2	1	no	—
162	C₂×D₄×C₂₃	—	2	1	no	—
163	C₂×D₄×C₂₃	—	2	1	no	—
164	C₂×D₄×C₂₃	—	2	1	no	—
165	C₂×D₄×C₂₃	—	4	2	no	—
166	C₂×D₄×C₂₃	—	4	2	no	—
167	C₂×D₄×C₂₃	—	4	4	no	—
168	C₂×D₄×C₂₃	—	4	4	no	—
169	C₂×D₄×C₂₃	—	4	4	no	—
170	C₂×D₄×C₂₃	—	4	4	no	—
171	C₂×D₄×C₂₃	—	4	2	no	—
172	C₂×D₄×C₂₃	—	4	2	no	—
173	C₂×D₄×C₂₃	—	8	1	no	—
174	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
175	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
176	C₂×D₄×C₂₃	#41	1	2	yes	—
177	C₂×D₄×C₂₃	#41	1	2	yes	—
178	C₂×D₄×C₂₃	#41	1	2	yes	—
179	C₂²×C₄×C₂₃	—	2	1	no	—
180	C₂²×C₄×C₂₃	—	2	1	no	—
181	C₂²×C₄×C₂₃	—	2	1	no	—
182	C₂²×C₄×C₂₃	—	2	1	no	—
183	C₂²×C₄×C₂₃	—	2	1	no	—
184	C₂²×C₄×C₂₃	—	2	1	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	—	4	2	no	—
191	C₂²×C₄×C₂₃	—	4	2	no	—
192	C₂²×C₄×C₂₃	—	4	2	no	—
193	C₂²×C₄×C₂₃	—	4	2	no	—
194	C₂²×C₄×C₂₃	—	4	2	no	—
195	C₂²×C₄×C₂₃	—	4	2	no	—
196	C₂²×C₄×C₂₃	—	8	1	no	—
197	C₂²×C₄×C₂₃	—	8	1	no	—
198	C₂²×C₄×C₂₃	—	8	1	no	—
199	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
205	D₈×C₂₃	—	2	8	no	—
206	D₈×C₂₃	—	4	4	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	—	2	1	no	—
214	C₂×C₈×C₂₃	—	2	1	no	—
215	C₂×C₈×C₂₃	—	2	1	no	—
216	C₂×C₈×C₂₃	—	2	1	no	—
217	C₂×C₈×C₂₃	—	2	1	no	—
218	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
219	C₄⋊C₄×C₂₃	—	2	1	no	—
220	C₄⋊C₄×C₂₃	—	2	1	no	—
221	C₄⋊C₄×C₂₃	—	2	1	no	—
222	C₄⋊C₄×C₂₃	—	2	1	no	—
223	C₄⋊C₄×C₂₃	—	2	1	no	—
224	C₄⋊C₄×C₂₃	—	2	1	no	—
225	C₄⋊C₄×C₂₃	—	2	1	no	—
226	C₄⋊C₄×C₂₃	—	2	1	no	—
227	C₄⋊C₄×C₂₃	—	2	1	no	—
228	C₄⋊C₄×C₂₃	—	2	1	no	—
229	C₄⋊C₄×C₂₃	—	4	2	no	—
230	C₄⋊C₄×C₂₃	—	4	2	no	—
231	C₄⋊C₄×C₂₃	—	8	1	no	—
232	C₂²⋊C₄×C₂₃	—	2	2	no	—
233	C₂²⋊C₄×C₂₃	—	2	2	no	—
234	C₂²⋊C₄×C₂₃	—	4	2	no	—
235	C₂²⋊C₄×C₂₃	—	4	2	no	—
236	C₂²⋊C₄×C₂₃	—	4	2	no	—
237	C₂²⋊C₄×C₂₃	—	4	2	no	—
238	C₂²⋊C₄×C₂₃	—	4	2	no	—
239	C₂²⋊C₄×C₂₃	—	4	2	no	—
240	C₂²⋊C₄×C₂₃	—	4	2	no	—
241	C₂²⋊C₄×C₂₃	—	4	2	no	—
242	C₂²⋊C₄×C₂₃	—	4	2	no	—
243	C₂²⋊C₄×C₂₃	—	4	2	no	—
244	C₂²⋊C₄×C₂₃	—	8	1	no	—
245	C₂²⋊C₄×C₂₃	—	8	1	no	—
246	C₄²×C₂₃	—	2	1	no	—
247	C₄²×C₂₃	—	2	1	no	—
248	C₄²×C₂₃	—	2	1	no	—
249	C₄²×C₂₃	—	2	1	no	—
250	#24913	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₂³×C₂₃	—	2	1	no	—
252	C₂³×C₂₃	—	2	2	no	—
253	C₂³×C₂₃	—	2	2	no	—
254	C₂³×C₂₃	—	2	1	no	—
255	C₂³×C₂₃	—	2	2	no	—
256	C₂³×C₂₃	—	2	1	no	—
257	C₂³×C₂₃	—	2	1	no	—
258	C₂³×C₂₃	—	2	1	no	—
259	C₂³×C₂₃	—	2	1	no	—
260	C₂³×C₂₃	—	2	2	no	—
261	C₂³×C₂₃	—	2	2	no	—
262	C₂³×C₂₃	—	4	8	no	—
263	C₂³×C₂₃	—	4	8	no	—
264	C₂³×C₂₃	—	4	1	no	—
265	C₂³×C₂₃	—	4	1	no	—
266	C₂³×C₂₃	—	4	1	no	—
267	C₂³×C₂₃	—	4	1	no	—
268	C₂³×C₂₃	—	4	1	no	—
269	C₂³×C₂₃	—	4	1	no	—
270	C₂³×C₂₃	—	4	1	no	—
271	C₂³×C₂₃	—	4	1	no	—
272	C₂³×C₂₃	—	4	1	no	—
273	C₂³×C₂₃	—	4	1	no	—
274	C₂³×C₂₃	—	4	1	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	—	8	4	no	—
281	C₂³×C₂₃	—	8	4	no	—
282	C₂³×C₂₃	—	8	4	no	—
283	C₂³×C₂₃	—	8	4	no	—
284	C₂³×C₂₃	—	8	4	no	—
285	C₂³×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
286	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
287	D₄×C₂₃	—	2	2	no	—
288	D₄×C₂₃	—	2	2	no	—
289	D₄×C₂₃	—	2	2	no	—
290	D₄×C₂₃	—	2	2	no	—
291	D₄×C₂₃	—	2	2	no	—
292	D₄×C₂₃	—	2	2	no	—
293	D₄×C₂₃	—	2	2	no	—
294	D₄×C₂₃	—	4	8	no	—
295	D₄×C₂₃	—	4	1	no	—
296	D₄×C₂₃	—	4	1	no	—
297	D₄×C₂₃	—	4	1	no	—
298	D₄×C₂₃	—	4	1	no	—
299	D₄×C₂₃	—	8	4	no	—
300	D₄×C₂₃	#123	1	4	yes	complemented
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	—	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	—	4	1	no	—
316	C₂×C₄×C₂₃	—	4	1	no	—
317	C₂×C₄×C₂₃	—	4	1	no	—
318	C₂×C₄×C₂₃	—	4	1	no	—
319	C₂×C₄×C₂₃	—	4	1	no	—
320	C₂×C₄×C₂₃	—	4	1	no	—
321	C₂×C₄×C₂₃	—	4	1	no	—
322	C₂×C₄×C₂₃	—	4	1	no	—
323	C₂×C₄×C₂₃	—	4	1	no	—
324	C₂×C₄×C₂₃	—	4	1	no	—
325	C₂×C₄×C₂₃	—	4	1	no	—
326	C₂×C₄×C₂₃	—	4	1	no	—
327	C₂×C₄×C₂₃	—	4	1	no	—
328	C₂×C₄×C₂₃	—	4	1	no	—
329	C₂×C₄×C₂₃	—	4	1	no	—
330	C₂×C₄×C₂₃	—	4	1	no	—
331	C₂×C₄×C₂₃	—	4	1	no	—
332	C₂×C₄×C₂₃	—	4	1	no	—
333	C₂×C₄×C₂₃	—	4	1	no	—
334	C₂×C₄×C₂₃	—	8	4	no	—
335	C₂×C₄×C₂₃	—	8	4	no	—
336	C₂×C₄×C₂₃	—	8	4	no	—
337	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
338	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
340	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
341	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
342	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
343	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
344	C₈×C₂₃	—	2	2	no	—
345	C₈×C₂₃	—	4	1	no	—
346	C₈×C₂₃	—	4	1	no	—
347	C₈×C₂₃	—	4	1	no	—
348	C₂×#447	C₂×C₂₃	1	1	yes	characteristic
349	C₂×#442	C₂×C₂₃	1	1	yes	characteristic, complemented
350	#2422	C₂×C₂₃	1	1	yes	characteristic, complemented
351	D₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#2094	C₂×C₂₃	1	1	yes	characteristic, complemented
353	#2077	C₂×C₂₃	1	1	yes	characteristic, complemented
354	#2054	C₂×C₂₃	1	1	yes	characteristic, complemented
355	#2034	C₂×C₂₃	1	1	yes	characteristic, complemented
356	#1936	C₂×C₂₃	1	1	yes	characteristic, complemented
357	#1924	C₂×C₂₃	1	1	yes	characteristic, complemented
358	#1879	C₂×C₂₃	1	1	yes	characteristic, complemented
359	#1879	C₂×C₂₃	1	1	yes	characteristic, complemented
360	#1864	C₂×C₂₃	1	1	yes	characteristic, complemented
361	#1802	C₂×C₂₃	1	1	yes	characteristic, complemented
362	#1786	C₂×C₂₃	1	1	yes	characteristic, complemented
363	C₂²×C₂₃	—	2	2	no	—
364	C₂²×C₂₃	—	2	4	no	—
365	C₂²×C₂₃	—	2	2	no	—
366	C₂²×C₂₃	—	2	2	no	—
367	C₂²×C₂₃	—	4	2	no	—
368	C₂²×C₂₃	—	4	1	no	—
369	C₂²×C₂₃	—	4	2	no	—
370	C₂²×C₂₃	—	4	1	no	—
371	C₂²×C₂₃	—	4	2	no	—
372	C₂²×C₂₃	—	4	2	no	—
373	C₂²×C₂₃	—	4	1	no	—
374	C₂²×C₂₃	—	4	2	no	—
375	C₂²×C₂₃	—	4	2	no	—
376	C₂²×C₂₃	—	4	1	no	—
377	C₂²×C₂₃	—	4	2	no	—
378	C₂²×C₂₃	—	4	2	no	—
379	C₂²×C₂₃	—	4	2	no	—
380	C₂²×C₂₃	—	4	2	no	—
381	C₂²×C₂₃	—	4	2	no	—
382	C₂²×C₂₃	—	4	2	no	—
383	C₂²×C₂₃	—	8	16	no	—
384	C₂²×C₂₃	—	8	1	no	—
385	C₂²×C₂₃	—	8	1	no	—
386	C₂²×C₂₃	—	8	1	no	—
387	C₂²×C₂₃	—	8	1	no	—
388	C₂²×C₂₃	—	8	1	no	—
389	C₂²×C₂₃	—	8	1	no	—
390	C₂²×C₂₃	—	8	1	no	—
391	C₂²×C₂₃	—	8	1	no	—
392	C₂²×C₂₃	#525	1	1	yes	characteristic
393	C₂²×C₂₃	D₄²	1	1	yes	characteristic
394	C₂²×C₂₃	#546	1	1	yes	characteristic
395	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
396	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
397	C₂²×C₂₃	#576	1	1	yes	characteristic
398	C₂²×C₂₃	#577	1	1	yes	characteristic
399	C₄×C₂₃	—	2	2	no	—
400	C₄×C₂₃	—	4	1	no	—
401	C₄×C₂₃	—	4	1	no	—
402	C₄×C₂₃	—	4	1	no	—
403	C₄×C₂₃	—	4	1	no	—
404	C₄×C₂₃	—	8	1	no	—
405	C₄×C₂₃	—	8	1	no	—
406	C₄×C₂₃	—	8	1	no	—
407	C₄×C₂₃	—	8	1	no	—
408	C₄×C₂₃	—	8	1	no	—
409	C₄×C₂₃	C₂×#123	1	1	yes	characteristic
410	C₄×C₂₃	#538	1	1	yes	characteristic
411	C₄×C₂₃	#546	1	1	yes	characteristic
412	C₄×C₂₃	#551	1	1	yes	characteristic
413	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
414	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
415	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
416	C₂×#123	—	2	1	no	—
417	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
418	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
420	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
421	C₂²×C₂²⋊C₄	—	2	1	no	—
422	#447	—	2	4	no	—
423	#442	—	2	4	no	—
424	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
425	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
426	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
427	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
428	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
429	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
430	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
433	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
434	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
435	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
436	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
437	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
438	#397	—	2	1	no	—
439	#394	—	2	1	no	—
440	#390	C₂²×C₂₃	1	1	yes	characteristic
441	#390	C₂²×C₂₃	1	1	yes	characteristic
442	#390	C₂²×C₂₃	1	1	yes	characteristic, complemented
443	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
444	#386	—	2	1	no	—
445	#386	—	2	1	no	—
446	#385	—	2	1	no	—
447	#384	C₂²×C₂₃	1	1	yes	characteristic, complemented
448	#380	C₂²×C₂₃	1	1	yes	characteristic
449	#380	C₂²×C₂₃	1	1	yes	characteristic
450	#379	—	2	1	no	—
451	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
452	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
453	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
454	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
455	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
456	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
457	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
458	C₂×C₂₃	—	4	2	no	—
459	C₂×C₂₃	—	4	4	no	—
460	C₂×C₂₃	—	8	2	no	—
461	C₂×C₂₃	—	8	2	no	—
462	C₂×C₂₃	#2418	1	1	yes	characteristic
463	C₂×C₂₃	#3109	1	1	yes	characteristic
464	C₂×C₂₃	#3118	1	1	yes	characteristic
465	C₂×C₂₃	#3264	1	1	yes	characteristic
466	C₂×C₂₃	#3272	1	1	yes	characteristic
467	C₂×C₂₃	#3306	1	1	yes	characteristic
468	C₂×C₂₃	#3318	1	1	yes	characteristic
469	C₂⁵	—	2	1	no	—
470	C₂²×D₄	—	2	2	no	—
471	C₂²×D₄	—	2	2	no	—
472	C₂²×D₄	—	2	2	no	—
473	C₂²×D₄	—	2	2	no	—
474	C₂²×D₄	—	2	1	no	—
475	C₂²×D₄	—	2	1	no	—
476	C₂²×D₄	—	4	1	no	—
477	C₂²×D₄	—	4	1	no	—
478	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
479	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
480	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
481	C₂³×C₄	—	2	1	no	—
482	C₂³×C₄	—	2	1	no	—
483	C₂³×C₄	—	2	1	no	—
484	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
485	C₂×D₈	—	2	2	no	—
486	C₂×D₈	—	2	2	no	—
487	C₂×D₈	—	2	2	no	—
488	C₂×D₈	—	2	2	no	—
489	C₂×D₈	—	4	1	no	—
490	C₂×D₈	D₄×C₂₃	1	4	yes	—
491	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
495	#123	—	4	4	no	—
496	#121	—	2	2	no	—
497	#121	—	4	1	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	—	4	1	no	—
502	C₄×D₄	—	4	1	no	—
503	C₄×D₄	—	4	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	2	1	no	—
507	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	4	4	no	—
525	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
529	#106	—	2	2	no	—
530	#106	—	4	1	no	—
531	C₄⋊C₈	—	4	1	no	—
532	#102	—	2	2	no	—
533	#102	—	2	2	no	—
534	#102	—	2	2	no	—
535	#102	—	2	2	no	—
536	#102	—	2	2	no	—
537	#102	—	2	2	no	—
538	#102	—	4	1	no	—
539	#102	—	4	1	no	—
540	C₂²⋊C₈	—	2	2	no	—
541	C₂²⋊C₈	—	4	1	no	—
542	#97	—	2	2	no	—
543	#95	—	2	1	no	—
544	#95	—	2	1	no	—
545	#95	—	2	1	no	—
546	#95	D₄×C₂₃	1	1	yes	characteristic
547	#95	D₄×C₂₃	1	1	yes	characteristic
548	C₂₃	#24913	1	1	yes	characteristic, direct product factor, Sylow
549	C₂⁴	—	2	1	no	—
550	C₂⁴	—	2	4	no	—
551	C₂⁴	—	2	1	no	—
552	C₂⁴	—	2	1	no	—
553	C₂⁴	—	4	2	no	—
554	C₂⁴	—	4	2	no	—
555	C₂⁴	—	4	2	no	—
556	C₂⁴	—	4	2	no	—
557	C₂⁴	—	8	1	no	—
558	C₂⁴	—	8	1	no	—
559	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	4	2	no	—
575	C₂×D₄	—	4	2	no	—
576	C₂×D₄	—	4	4	no	—
577	C₂×D₄	—	4	4	no	—
578	C₂×D₄	—	4	4	no	—
579	C₂×D₄	—	4	4	no	—
580	C₂×D₄	—	4	2	no	—
581	C₂×D₄	—	4	2	no	—
582	C₂×D₄	—	8	1	no	—
583	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
584	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
585	C₂×D₄	#41×C₂₃	1	2	yes	—
586	C₂×D₄	#41×C₂₃	1	2	yes	—
587	C₂×D₄	#41×C₂₃	1	2	yes	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	4	2	no	—
600	C₂²×C₄	—	4	2	no	—
601	C₂²×C₄	—	4	2	no	—
602	C₂²×C₄	—	4	2	no	—
603	C₂²×C₄	—	4	2	no	—
604	C₂²×C₄	—	4	2	no	—
605	C₂²×C₄	—	8	1	no	—
606	C₂²×C₄	—	8	1	no	—
607	C₂²×C₄	—	8	1	no	—
608	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
609	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
610	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
611	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
614	D₈	—	2	8	no	—
615	D₈	—	4	4	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	4	2	no	—
639	C₄⋊C₄	—	4	2	no	—
640	C₄⋊C₄	—	8	1	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	4	2	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	—	4	2	no	—
651	C₂²⋊C₄	—	4	2	no	—
652	C₂²⋊C₄	—	4	2	no	—
653	C₂²⋊C₄	—	8	1	no	—
654	C₂²⋊C₄	—	8	1	no	—
655	C₄²	—	2	1	no	—
656	C₄²	—	2	1	no	—
657	C₄²	—	2	1	no	—
658	C₄²	—	2	1	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	4	8	no	—
671	C₂³	—	4	8	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	1	no	—
678	C₂³	—	4	1	no	—
679	C₂³	—	4	1	no	—
680	C₂³	—	4	1	no	—
681	C₂³	—	4	1	no	—
682	C₂³	—	4	1	no	—
683	C₂³	—	4	1	no	—
684	C₂³	—	4	1	no	—
685	C₂³	—	4	1	no	—
686	C₂³	—	4	1	no	—
687	C₂³	—	4	1	no	—
688	C₂³	—	8	4	no	—
689	C₂³	—	8	4	no	—
690	C₂³	—	8	4	no	—
691	C₂³	—	8	4	no	—
692	C₂³	—	8	4	no	—
693	C₂³	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
694	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
695	D₄	—	2	2	no	—
696	D₄	—	2	2	no	—
697	D₄	—	2	2	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	2	no	—
700	D₄	—	2	2	no	—
701	D₄	—	2	2	no	—
702	D₄	—	4	8	no	—
703	D₄	—	4	1	no	—
704	D₄	—	4	1	no	—
705	D₄	—	4	1	no	—
706	D₄	—	4	1	no	—
707	D₄	—	8	4	no	—
708	D₄	C₂₃×#123	1	4	yes	complemented
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	8	4	no	—
743	C₂×C₄	—	8	4	no	—
744	C₂×C₄	—	8	4	no	—
745	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
746	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
747	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
748	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
749	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
750	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
751	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
752	C₈	—	2	2	no	—
753	C₈	—	4	1	no	—
754	C₈	—	4	1	no	—
755	C₈	—	4	1	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	8	16	no	—
777	C₂²	—	8	1	no	—
778	C₂²	—	8	1	no	—
779	C₂²	—	8	1	no	—
780	C₂²	—	8	1	no	—
781	C₂²	—	8	1	no	—
782	C₂²	—	8	1	no	—
783	C₂²	—	8	1	no	—
784	C₂²	—	8	1	no	—
785	C₂²	C₂₃×#525	1	1	yes	characteristic
786	C₂²	D₄²×C₂₃	1	1	yes	characteristic
787	C₂²	C₂₃×#546	1	1	yes	characteristic
788	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
789	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
790	C₂²	C₂₃×#576	1	1	yes	characteristic
791	C₂²	C₂₃×#577	1	1	yes	characteristic
792	C₄	—	2	2	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	1	no	—
795	C₄	—	4	1	no	—
796	C₄	—	4	1	no	—
797	C₄	—	8	1	no	—
798	C₄	—	8	1	no	—
799	C₄	—	8	1	no	—
800	C₄	—	8	1	no	—
801	C₄	—	8	1	no	—
802	C₄	C₂×C₂₃×#123	1	1	yes	characteristic
803	C₄	C₂₃×#538	1	1	yes	characteristic
804	C₄	C₂₃×#546	1	1	yes	characteristic
805	C₄	C₂₃×#551	1	1	yes	characteristic
806	C₂	—	4	2	no	—
807	C₂	—	4	4	no	—
808	C₂	—	8	2	no	—
809	C₂	—	8	2	no	—
810	C₂	C₂₃×#2418	1	1	yes	characteristic
811	C₂	C₂₃×#3109	1	1	yes	characteristic
812	C₂	C₂₃×#3118	1	1	yes	characteristic
813	C₂	C₂₃×#3264	1	1	yes	characteristic
814	C₂	C₂₃×#3272	1	1	yes	characteristic
815	C₂	C₂₃×#3306	1	1	yes	characteristic
816	C₂	C₂₃×#3318	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
2. C₂×C₂₃×#442	C₂	semidirect
3. C₂₃×#2422	C₂	semidirect
4. D₄×C₂²⋊C₄×C₂₃	C₂	semidirect
5. C₂₃×#2094	C₂	semidirect
6. C₂₃×#2077	C₂	semidirect
7. C₂₃×#2054	C₂	semidirect
8. C₂₃×#2034	C₂	semidirect
9. C₂₃×#1936	C₂	semidirect
10. C₂₃×#1924	C₂	semidirect
11. C₂₃×#1879	C₂	semidirect
12. C₂₃×#1879	C₂	semidirect
13. C₂₃×#1864	C₂	semidirect
14. C₂₃×#1802	C₂	semidirect
15. C₂₃×#1786	C₂	semidirect
23. C₂×C₄×D₄×C₂₃	C₂²	semidirect
27. C₂×C₂₃×#106	C₂²	semidirect
28. C₂×C₂₃×#106	C₂²	semidirect
29. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
36. C₂×C₂₃×#102	C₂²	semidirect
37. C₂×C₂₃×#102	C₂²	semidirect
40. C₂×C₂₃×#97	C₂²	semidirect
45. C₂₃×#390	C₂²	semidirect
46. C₂₃×#389	C₂²	semidirect
50. C₂₃×#384	C₂²	semidirect
55. C₂₃×#340	C₂²	semidirect
56. C₂₃×#340	C₂²	semidirect
57. C₂₃×#340	C₂²	semidirect
58. C₂₃×#340	C₂²	semidirect
59. C₂₃×#336	C₂²	semidirect
60. C₂₃×#336	C₂²	semidirect
250. #24913	C₂₃	direct (N × H)
300. D₄×C₂₃	#123	semidirect
349. C₂×#442	C₂×C₂₃	semidirect
350. #2422	C₂×C₂₃	semidirect
351. D₄×C₂²⋊C₄	C₂×C₂₃	semidirect
352. #2094	C₂×C₂₃	semidirect
353. #2077	C₂×C₂₃	semidirect
354. #2054	C₂×C₂₃	semidirect
355. #2034	C₂×C₂₃	semidirect
356. #1936	C₂×C₂₃	semidirect
357. #1924	C₂×C₂₃	semidirect
358. #1879	C₂×C₂₃	semidirect
359. #1879	C₂×C₂₃	semidirect
360. #1864	C₂×C₂₃	semidirect
361. #1802	C₂×C₂₃	semidirect
362. #1786	C₂×C₂₃	semidirect
420. C₂×C₄×D₄	C₂²×C₂₃	semidirect
424. C₂×#106	C₂²×C₂₃	semidirect
425. C₂×#106	C₂²×C₂₃	semidirect
426. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
433. C₂×#102	C₂²×C₂₃	semidirect
434. C₂×#102	C₂²×C₂₃	semidirect
437. C₂×#97	C₂²×C₂₃	semidirect
442. #390	C₂²×C₂₃	semidirect
443. #389	C₂²×C₂₃	semidirect
447. #384	C₂²×C₂₃	semidirect
452. #340	C₂²×C₂₃	semidirect
453. #340	C₂²×C₂₃	semidirect
454. #340	C₂²×C₂₃	semidirect
455. #340	C₂²×C₂₃	semidirect
456. #336	C₂²×C₂₃	semidirect
457. #336	C₂²×C₂₃	semidirect
548. C₂₃	#24913	direct (N × H)
708. D₄	C₂₃×#123	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#447	2
C₂×C₂₃×#442	2
C₂₃×#2422	2
D₄×C₂²⋊C₄×C₂₃	2
C₂₃×#2094	2
C₂₃×#2077	2
C₂₃×#2054	2
C₂₃×#2034	2
C₂₃×#1936	2
C₂₃×#1924	2
C₂₃×#1879	2
C₂₃×#1864	2
C₂₃×#1802	2
C₂₃×#1786	2
#24913	23

Subgroups — C23×#24913 #19172539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#24913 #19172539