Subgroups — C₂₃×#25104 #19172730

Order 5888.

1172 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#449	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2432	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2068	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×#2013	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1925	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1872	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×C₄⋊Q₈	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
27	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
28	C₂₃×#468	—	2	4	no	—
29	C₂₃×#463	—	2	4	no	—
30	C₂₃×#449	—	2	4	no	—
31	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂₃×#417	—	2	4	no	—
35	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#103	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
45	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂₃×#394	—	2	1	no	—
47	C₂₃×#394	—	2	1	no	—
48	C₂₃×#391	C₂²	1	1	yes	characteristic
49	C₂₃×#390	C₂²	1	1	yes	characteristic
50	C₂₃×#390	C₂²	1	1	yes	characteristic
51	C₂₃×#389	C₂²	1	1	yes	characteristic
52	C₂₃×#388	—	2	1	no	—
53	C₂₃×#386	—	2	1	no	—
54	C₂₃×#385	—	2	1	no	—
55	C₂₃×#385	—	2	1	no	—
56	C₂₃×#385	—	2	1	no	—
57	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
58	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
59	C₂₃×#340	C₂²	1	1	yes	characteristic
60	C₂₃×#340	C₂²	1	1	yes	characteristic
61	C₂₃×#336	C₂²	1	1	yes	characteristic
62	C₂₃×#336	C₂²	1	1	yes	characteristic
63	C₂×#41×C₂₃	—	2	2	no	—
64	C₂×#41×C₂₃	—	2	2	no	—
65	C₂×#41×C₂₃	—	2	2	no	—
66	C₂×#41×C₂₃	—	2	2	no	—
67	C₂×#41×C₂₃	—	4	1	no	—
68	C₂×#41×C₂₃	—	4	1	no	—
69	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₂₃	—	2	1	no	—
72	C₂²×D₄×C₂₃	—	2	1	no	—
73	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₂₃	—	2	1	no	—
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	—	2	2	no	—
82	C₂×SD₁₆×C₂₃	—	2	2	no	—
83	C₂×SD₁₆×C₂₃	—	4	1	no	—
84	C₂×SD₁₆×C₂₃	—	4	1	no	—
85	C₂×D₈×C₂₃	—	2	2	no	—
86	C₂×D₈×C₂₃	—	2	2	no	—
87	C₂×D₈×C₂₃	—	4	1	no	—
88	C₂×M₁₆×C₂₃	—	2	2	no	—
89	C₂×M₁₆×C₂₃	—	2	2	no	—
90	C₂×M₁₆×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×C₄⋊Q₈	—	2	2	no	—
96	C₂₃×C₄⋊Q₈	—	4	1	no	—
97	C₂₃×#124	—	2	2	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	—	2	1	no	—
111	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
112	C₂×C₄⋊C₄×C₂₃	—	4	1	no	—
113	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
128	C₂×C₄²×C₂₃	—	2	1	no	—
129	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
131	C₂₃×#107	—	2	2	no	—
132	C₂₃×C₄⋊C₈	—	2	2	no	—
133	C₂₃×C₄⋊C₈	—	4	1	no	—
134	C₂₃×#103	—	2	2	no	—
135	C₂₃×#103	—	2	2	no	—
136	C₂₃×#103	—	2	2	no	—
137	C₂₃×#103	—	2	2	no	—
138	C₂₃×#103	—	2	2	no	—
139	C₂₃×#103	—	4	1	no	—
140	C₂₃×#102	—	2	2	no	—
141	C₂₃×#102	—	2	2	no	—
142	C₂₃×#102	—	2	2	no	—
143	C₂₃×#102	D₄	1	4	yes	complemented
144	C₂₃×C₂²⋊C₈	—	2	2	no	—
145	C₂₃×#95	—	2	1	no	—
146	C₂₃×#95	—	2	1	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	C₂×D₄	1	1	yes	characteristic
154	#41×C₂₃	—	2	8	no	—
155	#41×C₂₃	—	4	4	no	—
156	#41×C₂₃	—	4	4	no	—
157	#41×C₂₃	—	4	4	no	—
158	C₂×Q₈×C₂₃	—	2	1	no	—
159	C₂×Q₈×C₂₃	—	2	1	no	—
160	C₂×Q₈×C₂₃	—	2	1	no	—
161	C₂×Q₈×C₂₃	—	2	1	no	—
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×Q₈×C₂₃	—	2	1	no	—
169	C₂×Q₈×C₂₃	#41	1	2	yes	—
170	C₂×D₄×C₂₃	—	2	4	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	—	4	2	no	—
182	C₂×D₄×C₂₃	—	4	2	no	—
183	C₂×D₄×C₂₃	—	4	2	no	—
184	C₂×D₄×C₂₃	—	4	2	no	—
185	C₂×D₄×C₂₃	—	4	2	no	—
186	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
187	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
198	C₂²×C₄×C₂₃	—	4	2	no	—
199	C₂²×C₄×C₂₃	—	4	2	no	—
200	C₂²×C₄×C₂₃	—	4	2	no	—
201	C₂²×C₄×C₂₃	—	4	2	no	—
202	C₂²×C₄×C₂₃	—	4	2	no	—
203	C₂²×C₄×C₂₃	—	4	2	no	—
204	C₂²×C₄×C₂₃	—	4	2	no	—
205	C₂²×C₄×C₂₃	—	8	1	no	—
206	C₂²×C₄×C₂₃	—	8	1	no	—
207	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
212	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₂₃	#41	1	2	yes	—
214	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
215	SD₁₆×C₂₃	—	4	4	no	—
216	SD₁₆×C₂₃	—	4	4	no	—
217	D₈×C₂₃	—	4	4	no	—
218	M₁₆×C₂₃	—	4	4	no	—
219	C₂×C₈×C₂₃	—	2	1	no	—
220	C₂×C₈×C₂₃	—	2	1	no	—
221	C₂×C₈×C₂₃	—	2	1	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	C₂×D₄	1	2	yes	—
231	C₄⋊C₄×C₂₃	—	2	1	no	—
232	C₄⋊C₄×C₂₃	—	2	1	no	—
233	C₄⋊C₄×C₂₃	—	2	1	no	—
234	C₄⋊C₄×C₂₃	—	2	1	no	—
235	C₄⋊C₄×C₂₃	—	2	1	no	—
236	C₄⋊C₄×C₂₃	—	2	1	no	—
237	C₄⋊C₄×C₂₃	—	4	2	no	—
238	C₄⋊C₄×C₂₃	—	4	2	no	—
239	C₄⋊C₄×C₂₃	—	4	2	no	—
240	C₄⋊C₄×C₂₃	—	4	2	no	—
241	C₄⋊C₄×C₂₃	—	4	2	no	—
242	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
243	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
244	C₂²⋊C₄×C₂₃	—	2	4	no	—
245	C₂²⋊C₄×C₂₃	—	2	2	no	—
246	C₂²⋊C₄×C₂₃	—	4	1	no	—
247	C₂²⋊C₄×C₂₃	—	4	2	no	—
248	C₂²⋊C₄×C₂₃	—	4	2	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	—	8	1	no	—
255	C₄²×C₂₃	—	2	1	no	—
256	C₄²×C₂₃	—	2	1	no	—
257	C₄²×C₂₃	—	2	1	no	—
258	C₄²×C₂₃	—	2	1	no	—
259	C₄²×C₂₃	—	4	2	no	—
260	#25104	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₂³×C₂₃	—	2	1	no	—
262	C₂³×C₂₃	—	2	1	no	—
263	C₂³×C₂₃	—	2	1	no	—
264	C₂³×C₂₃	—	2	1	no	—
265	C₂³×C₂₃	—	2	1	no	—
266	C₂³×C₂₃	—	2	1	no	—
267	C₂³×C₂₃	—	2	2	no	—
268	C₂³×C₂₃	—	2	2	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	—	4	1	no	—
281	C₂³×C₂₃	#121	1	2	yes	—
282	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
283	Q₈×C₂₃	—	2	2	no	—
284	Q₈×C₂₃	—	2	2	no	—
285	Q₈×C₂₃	—	4	1	no	—
286	Q₈×C₂₃	—	4	1	no	—
287	Q₈×C₂₃	—	4	1	no	—
288	Q₈×C₂₃	—	4	1	no	—
289	Q₈×C₂₃	—	4	1	no	—
290	Q₈×C₂₃	—	4	1	no	—
291	D₄×C₂₃	—	2	2	no	—
292	D₄×C₂₃	—	2	2	no	—
293	D₄×C₂₃	—	2	2	no	—
294	D₄×C₂₃	—	2	2	no	—
295	D₄×C₂₃	—	4	8	no	—
296	D₄×C₂₃	—	4	8	no	—
297	D₄×C₂₃	—	4	1	no	—
298	D₄×C₂₃	—	4	1	no	—
299	D₄×C₂₃	—	4	1	no	—
300	D₄×C₂₃	—	4	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	2	no	—
306	C₂×C₄×C₂₃	—	2	2	no	—
307	C₂×C₄×C₂₃	—	2	2	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	2	no	—
310	C₂×C₄×C₂₃	—	2	1	no	—
311	C₂×C₄×C₂₃	—	2	1	no	—
312	C₂×C₄×C₂₃	—	2	2	no	—
313	C₂×C₄×C₂₃	—	2	1	no	—
314	C₂×C₄×C₂₃	—	2	2	no	—
315	C₂×C₄×C₂₃	—	2	1	no	—
316	C₂×C₄×C₂₃	—	2	1	no	—
317	C₂×C₄×C₂₃	—	2	1	no	—
318	C₂×C₄×C₂₃	—	2	1	no	—
319	C₂×C₄×C₂₃	—	2	1	no	—
320	C₂×C₄×C₂₃	—	2	1	no	—
321	C₂×C₄×C₂₃	—	4	8	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	—	4	1	no	—
335	C₂×C₄×C₂₃	—	4	1	no	—
336	C₂×C₄×C₂₃	—	4	1	no	—
337	C₂×C₄×C₂₃	—	8	4	no	—
338	C₂×C₄×C₂₃	—	8	4	no	—
339	C₂×C₄×C₂₃	#121	1	2	yes	—
340	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
341	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
344	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
345	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
347	C₈×C₂₃	—	2	2	no	—
348	C₈×C₂₃	—	4	1	no	—
349	C₈×C₂₃	—	4	1	no	—
350	C₈×C₂₃	—	4	1	no	—
351	C₂×#468	C₂×C₂₃	1	1	yes	characteristic, complemented
352	C₂×#463	C₂×C₂₃	1	1	yes	characteristic, complemented
353	C₂×#449	C₂×C₂₃	1	1	yes	characteristic
354	C₂×#417	C₂×C₂₃	1	1	yes	characteristic, complemented
355	#2432	C₂×C₂₃	1	1	yes	characteristic, complemented
356	#2361	C₂×C₂₃	1	1	yes	characteristic, complemented
357	#2068	C₂×C₂₃	1	1	yes	characteristic, complemented
358	#2054	C₂×C₂₃	1	1	yes	characteristic, complemented
359	#2042	C₂×C₂₃	1	1	yes	characteristic, complemented
360	#2013	C₂×C₂₃	1	1	yes	characteristic, complemented
361	#1981	C₂×C₂₃	1	1	yes	characteristic, complemented
362	#1925	C₂×C₂₃	1	1	yes	characteristic, complemented
363	#1877	C₂×C₂₃	1	1	yes	characteristic, complemented
364	#1872	C₂×C₂₃	1	1	yes	characteristic, complemented
365	#1851	C₂×C₂₃	1	1	yes	characteristic, complemented
366	C₂²×C₂₃	—	2	2	no	—
367	C₂²×C₂₃	—	2	2	no	—
368	C₂²×C₂₃	—	2	2	no	—
369	C₂²×C₂₃	—	4	1	no	—
370	C₂²×C₂₃	—	4	1	no	—
371	C₂²×C₂₃	—	4	1	no	—
372	C₂²×C₂₃	—	4	1	no	—
373	C₂²×C₂₃	—	4	2	no	—
374	C₂²×C₂₃	—	4	2	no	—
375	C₂²×C₂₃	—	4	2	no	—
376	C₂²×C₂₃	—	4	2	no	—
377	C₂²×C₂₃	—	4	2	no	—
378	C₂²×C₂₃	—	4	2	no	—
379	C₂²×C₂₃	—	8	1	no	—
380	C₂²×C₂₃	—	8	1	no	—
381	C₂²×C₂₃	—	8	1	no	—
382	C₂²×C₂₃	—	8	1	no	—
383	C₂²×C₂₃	—	8	1	no	—
384	C₂²×C₂₃	—	8	1	no	—
385	C₂²×C₂₃	—	8	1	no	—
386	C₂²×C₂₃	—	8	1	no	—
387	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
388	C₂²×C₂₃	D₄²	1	1	yes	characteristic
389	C₂²×C₂₃	#546	1	1	yes	characteristic
390	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
391	C₂²×C₂₃	#575	1	1	yes	characteristic
392	C₂²×C₂₃	#577	1	1	yes	characteristic
393	C₂²×C₂₃	#578	1	1	yes	characteristic
394	C₄×C₂₃	—	2	2	no	—
395	C₄×C₂₃	—	2	2	no	—
396	C₄×C₂₃	—	4	2	no	—
397	C₄×C₂₃	—	4	1	no	—
398	C₄×C₂₃	—	4	1	no	—
399	C₄×C₂₃	—	4	2	no	—
400	C₄×C₂₃	—	4	2	no	—
401	C₄×C₂₃	—	4	1	no	—
402	C₄×C₂₃	—	8	1	no	—
403	C₄×C₂₃	—	8	1	no	—
404	C₄×C₂₃	—	8	1	no	—
405	C₄×C₂₃	#525	1	1	yes	characteristic
406	C₄×C₂₃	#538	1	1	yes	characteristic
407	C₄×C₂₃	D₄²	1	1	yes	characteristic
408	C₄×C₂₃	#546	1	1	yes	characteristic
409	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
410	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
411	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
412	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
413	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
414	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
415	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
416	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
418	C₂×C₄×D₄	—	2	1	no	—
419	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
420	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
421	#468	—	2	4	no	—
422	#463	—	2	4	no	—
423	#449	—	2	4	no	—
424	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
425	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
426	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
427	#417	—	2	4	no	—
428	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
429	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
430	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
433	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
434	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
435	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
436	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
437	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
438	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
439	#394	—	2	1	no	—
440	#394	—	2	1	no	—
441	#391	C₂²×C₂₃	1	1	yes	characteristic
442	#390	C₂²×C₂₃	1	1	yes	characteristic
443	#390	C₂²×C₂₃	1	1	yes	characteristic
444	#389	C₂²×C₂₃	1	1	yes	characteristic
445	#388	—	2	1	no	—
446	#386	—	2	1	no	—
447	#385	—	2	1	no	—
448	#385	—	2	1	no	—
449	#385	—	2	1	no	—
450	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
451	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
452	#340	C₂²×C₂₃	1	1	yes	characteristic
453	#340	C₂²×C₂₃	1	1	yes	characteristic
454	#336	C₂²×C₂₃	1	1	yes	characteristic
455	#336	C₂²×C₂₃	1	1	yes	characteristic
456	C₂×C₂₃	—	4	2	no	—
457	C₂×C₂₃	—	8	2	no	—
458	C₂×C₂₃	—	8	2	no	—
459	C₂×C₂₃	#2424	1	1	yes	characteristic
460	C₂×C₂₃	#3036	1	1	yes	characteristic
461	C₂×C₂₃	#3046	1	1	yes	characteristic
462	C₂×C₂₃	#3269	1	1	yes	characteristic
463	C₂×C₂₃	#3272	1	1	yes	characteristic
464	C₂×C₂₃	#3308	1	1	yes	characteristic
465	C₂×C₂₃	#3326	1	1	yes	characteristic
466	C₂×#41	—	2	2	no	—
467	C₂×#41	—	2	2	no	—
468	C₂×#41	—	2	2	no	—
469	C₂×#41	—	2	2	no	—
470	C₂×#41	—	4	1	no	—
471	C₂×#41	—	4	1	no	—
472	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
473	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
474	C₂²×D₄	—	2	1	no	—
475	C₂²×D₄	—	2	1	no	—
476	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
477	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
478	C₂³×C₄	—	2	1	no	—
479	C₂³×C₄	—	2	1	no	—
480	C₂³×C₄	—	2	1	no	—
481	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
482	C₂×SD₁₆	—	2	2	no	—
483	C₂×SD₁₆	—	2	2	no	—
484	C₂×SD₁₆	—	2	2	no	—
485	C₂×SD₁₆	—	2	2	no	—
486	C₂×SD₁₆	—	4	1	no	—
487	C₂×SD₁₆	—	4	1	no	—
488	C₂×D₈	—	2	2	no	—
489	C₂×D₈	—	2	2	no	—
490	C₂×D₈	—	4	1	no	—
491	C₂×M₁₆	—	2	2	no	—
492	C₂×M₁₆	—	2	2	no	—
493	C₂×M₁₆	—	4	1	no	—
494	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
496	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
497	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
498	C₄⋊Q₈	—	2	2	no	—
499	C₄⋊Q₈	—	4	1	no	—
500	#124	—	2	2	no	—
501	#124	—	4	1	no	—
502	C₂²⋊Q₈	—	2	2	no	—
503	C₂²⋊Q₈	—	2	2	no	—
504	#121	—	2	2	no	—
505	#121	D₄×C₂₃	1	4	yes	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	4	1	no	—
508	C₄×D₄	—	4	4	no	—
509	C₂×C₄⋊C₄	—	2	2	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	—	2	1	no	—
513	C₂×C₄⋊C₄	—	2	1	no	—
514	C₂×C₄⋊C₄	—	2	1	no	—
515	C₂×C₄⋊C₄	—	4	1	no	—
516	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
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	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	—	2	1	no	—
528	C₂×C₂²⋊C₄	—	2	1	no	—
529	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
531	C₂×C₄²	—	2	1	no	—
532	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
534	#107	—	2	2	no	—
535	C₄⋊C₈	—	2	2	no	—
536	C₄⋊C₈	—	4	1	no	—
537	#103	—	2	2	no	—
538	#103	—	2	2	no	—
539	#103	—	2	2	no	—
540	#103	—	2	2	no	—
541	#103	—	2	2	no	—
542	#103	—	4	1	no	—
543	#102	—	2	2	no	—
544	#102	—	2	2	no	—
545	#102	—	2	2	no	—
546	#102	D₄×C₂₃	1	4	yes	complemented
547	C₂²⋊C₈	—	2	2	no	—
548	#95	—	2	1	no	—
549	#95	—	2	1	no	—
550	#95	—	2	1	no	—
551	#95	—	2	1	no	—
552	#95	D₄×C₂₃	1	1	yes	characteristic
553	#95	D₄×C₂₃	1	1	yes	characteristic
554	C₂₃	#25104	1	1	yes	characteristic, direct product factor, Sylow
555	C₂⁴	—	2	1	no	—
556	C₂⁴	—	2	1	no	—
557	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
558	#41	—	2	8	no	—
559	#41	—	4	4	no	—
560	#41	—	4	4	no	—
561	#41	—	4	4	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	1	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	—	2	1	no	—
571	C₂×Q₈	—	2	1	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×Q₈	#41×C₂₃	1	2	yes	—
574	C₂×D₄	—	2	4	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	4	2	no	—
586	C₂×D₄	—	4	2	no	—
587	C₂×D₄	—	4	2	no	—
588	C₂×D₄	—	4	2	no	—
589	C₂×D₄	—	4	2	no	—
590	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
591	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
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	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	4	2	no	—
603	C₂²×C₄	—	4	2	no	—
604	C₂²×C₄	—	4	2	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	—	4	2	no	—
607	C₂²×C₄	—	4	2	no	—
608	C₂²×C₄	—	4	2	no	—
609	C₂²×C₄	—	8	1	no	—
610	C₂²×C₄	—	8	1	no	—
611	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
613	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
614	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
616	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
617	C₂²×C₄	#41×C₂₃	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
619	SD₁₆	—	4	4	no	—
620	SD₁₆	—	4	4	no	—
621	D₈	—	4	4	no	—
622	M₁₆	—	4	4	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	—	2	1	no	—
628	C₂×C₈	—	2	1	no	—
629	C₂×C₈	—	2	1	no	—
630	C₂×C₈	—	2	1	no	—
631	C₂×C₈	—	2	1	no	—
632	C₂×C₈	—	2	1	no	—
633	C₂×C₈	—	2	1	no	—
634	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	4	2	no	—
642	C₄⋊C₄	—	4	2	no	—
643	C₄⋊C₄	—	4	2	no	—
644	C₄⋊C₄	—	4	2	no	—
645	C₄⋊C₄	—	4	2	no	—
646	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
647	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	4	1	no	—
651	C₂²⋊C₄	—	4	2	no	—
652	C₂²⋊C₄	—	4	2	no	—
653	C₂²⋊C₄	—	4	2	no	—
654	C₂²⋊C₄	—	4	2	no	—
655	C₂²⋊C₄	—	4	2	no	—
656	C₂²⋊C₄	—	4	2	no	—
657	C₂²⋊C₄	—	4	2	no	—
658	C₂²⋊C₄	—	8	1	no	—
659	C₄²	—	2	1	no	—
660	C₄²	—	2	1	no	—
661	C₄²	—	2	1	no	—
662	C₄²	—	2	1	no	—
663	C₄²	—	4	2	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	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	C₂₃×#121	1	2	yes	—
685	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
686	Q₈	—	2	2	no	—
687	Q₈	—	2	2	no	—
688	Q₈	—	4	1	no	—
689	Q₈	—	4	1	no	—
690	Q₈	—	4	1	no	—
691	Q₈	—	4	1	no	—
692	Q₈	—	4	1	no	—
693	Q₈	—	4	1	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	2	no	—
697	D₄	—	2	2	no	—
698	D₄	—	4	8	no	—
699	D₄	—	4	8	no	—
700	D₄	—	4	1	no	—
701	D₄	—	4	1	no	—
702	D₄	—	4	1	no	—
703	D₄	—	4	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	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	2	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	4	8	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	—	8	4	no	—
741	C₂×C₄	—	8	4	no	—
742	C₂×C₄	C₂₃×#121	1	2	yes	—
743	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
744	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
746	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
747	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
748	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
749	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
750	C₈	—	2	2	no	—
751	C₈	—	4	1	no	—
752	C₈	—	4	1	no	—
753	C₈	—	4	1	no	—
754	C₂²	—	2	2	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	8	1	no	—
768	C₂²	—	8	1	no	—
769	C₂²	—	8	1	no	—
770	C₂²	—	8	1	no	—
771	C₂²	—	8	1	no	—
772	C₂²	—	8	1	no	—
773	C₂²	—	8	1	no	—
774	C₂²	—	8	1	no	—
775	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
776	C₂²	D₄²×C₂₃	1	1	yes	characteristic
777	C₂²	C₂₃×#546	1	1	yes	characteristic
778	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
779	C₂²	C₂₃×#575	1	1	yes	characteristic
780	C₂²	C₂₃×#577	1	1	yes	characteristic
781	C₂²	C₂₃×#578	1	1	yes	characteristic
782	C₄	—	2	2	no	—
783	C₄	—	2	2	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	1	no	—
786	C₄	—	4	1	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	1	no	—
790	C₄	—	8	1	no	—
791	C₄	—	8	1	no	—
792	C₄	—	8	1	no	—
793	C₄	C₂₃×#525	1	1	yes	characteristic
794	C₄	C₂₃×#538	1	1	yes	characteristic
795	C₄	D₄²×C₂₃	1	1	yes	characteristic
796	C₄	C₂₃×#546	1	1	yes	characteristic
797	C₂	—	4	2	no	—
798	C₂	—	8	2	no	—
799	C₂	—	8	2	no	—
800	C₂	C₂₃×#2424	1	1	yes	characteristic
801	C₂	C₂₃×#3036	1	1	yes	characteristic
802	C₂	C₂₃×#3046	1	1	yes	characteristic
803	C₂	C₂₃×#3269	1	1	yes	characteristic
804	C₂	C₂₃×#3272	1	1	yes	characteristic
805	C₂	C₂₃×#3308	1	1	yes	characteristic
806	C₂	C₂₃×#3326	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#449	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×#468	C₂	semidirect
2. C₂×C₂₃×#463	C₂	semidirect
4. C₂×C₂₃×#417	C₂	semidirect
5. C₂₃×#2432	C₂	semidirect
6. C₂₃×#2361	C₂	semidirect
7. C₂₃×#2068	C₂	semidirect
8. C₂₃×#2054	C₂	semidirect
9. C₂₃×#2042	C₂	semidirect
10. C₂₃×#2013	C₂	semidirect
11. C₂₃×#1981	C₂	semidirect
12. C₂₃×#1925	C₂	semidirect
13. C₂₃×#1877	C₂	semidirect
14. C₂₃×#1872	C₂	semidirect
15. C₂₃×#1851	C₂	semidirect
143. C₂₃×#102	D₄	semidirect
260. #25104	C₂₃	direct (N × H)
351. C₂×#468	C₂×C₂₃	semidirect
352. C₂×#463	C₂×C₂₃	semidirect
354. C₂×#417	C₂×C₂₃	semidirect
355. #2432	C₂×C₂₃	semidirect
356. #2361	C₂×C₂₃	semidirect
357. #2068	C₂×C₂₃	semidirect
358. #2054	C₂×C₂₃	semidirect
359. #2042	C₂×C₂₃	semidirect
360. #2013	C₂×C₂₃	semidirect
361. #1981	C₂×C₂₃	semidirect
362. #1925	C₂×C₂₃	semidirect
363. #1877	C₂×C₂₃	semidirect
364. #1872	C₂×C₂₃	semidirect
365. #1851	C₂×C₂₃	semidirect
546. #102	D₄×C₂₃	semidirect
554. C₂₃	#25104	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#468	2
C₂×C₂₃×#463	2
C₂×C₂₃×#449	2
C₂×C₂₃×#417	2
C₂₃×#2432	2
C₂₃×#2361	2
C₂₃×#2068	2
C₂₃×#2054	2
C₂₃×#2042	2
C₂₃×#2013	2
C₂₃×#1981	2
C₂₃×#1925	2
C₂₃×#1877	2
C₂₃×#1872	2
C₂₃×#1851	2
#25104	23

Subgroups — C23×#25104 #19172730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25104 #19172730