Subgroups — C₂₃×#25550 #19173176

Order 5888.

1242 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2416	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2025	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1874	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1874	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1853	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#553	—	2	4	no	—
19	C₂₃×#553	—	2	4	no	—
20	C₂×C₂₃×#126	—	2	1	no	—
21	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#123	—	2	1	no	—
23	C₂×C₂₃×#121	—	2	1	no	—
24	C₂×C₂₃×#121	—	2	1	no	—
25	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₂₃	—	2	1	no	—
30	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂₃×#482	—	2	4	no	—
36	C₂₃×#469	—	2	4	no	—
37	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#106	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
45	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₂₃×#396	—	2	1	no	—
50	C₂₃×#394	—	2	1	no	—
51	C₂₃×#390	C₂²	1	1	yes	characteristic
52	C₂₃×#389	C₂²	1	1	yes	characteristic
53	C₂₃×#386	—	2	1	no	—
54	C₂₃×#380	C₂²	1	1	yes	characteristic
55	C₂₃×#340	C₂²	1	1	yes	characteristic
56	C₂₃×#340	C₂²	1	1	yes	characteristic
57	C₂₃×#340	C₂²	1	1	yes	characteristic
58	C₂₃×#340	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	C₂²×D₄×C₂₃	—	2	1	no	—
64	C₂²×D₄×C₂₃	—	2	1	no	—
65	C₂²×D₄×C₂₃	—	2	1	no	—
66	C₂²×D₄×C₂₃	—	2	1	no	—
67	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
68	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₂₃	—	2	1	no	—
71	C₂³×C₄×C₂₃	—	2	1	no	—
72	C₂³×C₄×C₂₃	—	2	1	no	—
73	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂×D₈×C₂₃	—	2	2	no	—
76	C₂×D₈×C₂₃	—	2	2	no	—
77	C₂×D₈×C₂₃	—	4	1	no	—
78	C₂×M₁₆×C₂₃	—	2	2	no	—
79	C₂×M₁₆×C₂₃	—	2	2	no	—
80	C₂×M₁₆×C₂₃	—	4	1	no	—
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	C₂₃×#126	—	2	8	no	—
86	C₂₃×#125	—	2	2	no	—
87	C₂₃×#125	—	2	2	no	—
88	C₂₃×#123	—	2	8	no	—
89	C₂₃×#121	—	2	8	no	—
90	C₂₃×#121	—	2	2	no	—
91	C₂₃×#121	—	2	2	no	—
92	C₂₃×#121	—	2	2	no	—
93	C₂₃×#121	—	2	2	no	—
94	C₂₃×#121	—	2	2	no	—
95	C₂₃×#121	—	2	2	no	—
96	C₂₃×#121	—	4	1	no	—
97	C₂₃×#121	—	4	4	no	—
98	C₂₃×#121	D₄	1	4	yes	complemented
99	C₄×D₄×C₂₃	—	2	8	no	—
100	C₄×D₄×C₂₃	—	2	2	no	—
101	C₄×D₄×C₂₃	—	2	2	no	—
102	C₄×D₄×C₂₃	—	2	2	no	—
103	C₄×D₄×C₂₃	—	2	2	no	—
104	C₂₃×#117	—	2	2	no	—
105	C₂₃×#117	D₄	1	4	yes	complemented
106	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
107	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
108	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
109	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
110	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
111	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
112	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
113	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
114	C₂×C₄⋊C₄×C₂₃	—	4	1	no	—
115	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
131	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
132	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
133	C₂×C₄²×C₂₃	—	2	1	no	—
134	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
135	C₂₃×#107	—	2	2	no	—
136	C₂₃×#106	—	2	2	no	—
137	C₂₃×#106	—	2	2	no	—
138	C₂₃×#102	—	2	2	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	—	4	1	no	—
144	C₂₃×C₂²⋊C₈	—	2	2	no	—
145	C₂₃×C₂²⋊C₈	—	2	2	no	—
146	C₂₃×C₂²⋊C₈	—	4	1	no	—
147	C₂₃×#95	—	2	1	no	—
148	C₂₃×#95	—	2	1	no	—
149	C₂⁴×C₂₃	—	2	1	no	—
150	C₂⁴×C₂₃	—	2	1	no	—
151	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
152	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
153	C₂×D₄×C₂₃	—	2	4	no	—
154	C₂×D₄×C₂₃	—	2	2	no	—
155	C₂×D₄×C₂₃	—	2	2	no	—
156	C₂×D₄×C₂₃	—	2	4	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	—	2	1	no	—
166	C₂×D₄×C₂₃	—	2	1	no	—
167	C₂×D₄×C₂₃	—	2	1	no	—
168	C₂×D₄×C₂₃	—	4	1	no	—
169	C₂×D₄×C₂₃	—	4	2	no	—
170	C₂×D₄×C₂₃	—	4	2	no	—
171	C₂×D₄×C₂₃	—	4	2	no	—
172	C₂×D₄×C₂₃	—	4	2	no	—
173	C₂×D₄×C₂₃	—	4	2	no	—
174	C₂×D₄×C₂₃	—	4	2	no	—
175	C₂×D₄×C₂₃	—	4	2	no	—
176	C₂×D₄×C₂₃	—	8	1	no	—
177	C₂×D₄×C₂₃	—	8	1	no	—
178	C₂×D₄×C₂₃	—	8	1	no	—
179	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
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	4	no	—
189	C₂²×C₄×C₂₃	—	2	4	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	—	8	1	no	—
201	C₂²×C₄×C₂₃	—	8	1	no	—
202	C₂²×C₄×C₂₃	—	8	1	no	—
203	C₂²×C₄×C₂₃	—	8	1	no	—
204	C₂²×C₄×C₂₃	—	8	1	no	—
205	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
210	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
211	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
212	D₈×C₂₃	—	4	4	no	—
213	M₁₆×C₂₃	—	4	4	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	—	2	1	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	#41	1	2	yes	—
226	C₄⋊C₄×C₂₃	—	2	4	no	—
227	C₄⋊C₄×C₂₃	—	2	4	no	—
228	C₄⋊C₄×C₂₃	—	2	4	no	—
229	C₄⋊C₄×C₂₃	—	2	2	no	—
230	C₄⋊C₄×C₂₃	—	2	1	no	—
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	—	2	1	no	—
238	C₄⋊C₄×C₂₃	—	4	2	no	—
239	C₄⋊C₄×C₂₃	—	4	2	no	—
240	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
241	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
242	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
243	C₄⋊C₄×C₂₃	#41	1	2	yes	—
244	C₂²⋊C₄×C₂₃	—	2	4	no	—
245	C₂²⋊C₄×C₂₃	—	2	4	no	—
246	C₂²⋊C₄×C₂₃	—	2	4	no	—
247	C₂²⋊C₄×C₂₃	—	2	2	no	—
248	C₂²⋊C₄×C₂₃	—	2	4	no	—
249	C₂²⋊C₄×C₂₃	—	2	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	4	no	—
256	C₄²×C₂₃	—	2	1	no	—
257	C₄²×C₂₃	—	2	1	no	—
258	#25550	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₂³×C₂₃	—	2	1	no	—
260	C₂³×C₂₃	—	2	1	no	—
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	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	—	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	—	4	1	no	—
282	C₂³×C₂₃	—	4	1	no	—
283	C₂³×C₂₃	—	4	1	no	—
284	C₂³×C₂₃	—	4	1	no	—
285	C₂³×C₂₃	#120	1	2	yes	—
286	C₂³×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
287	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
288	D₄×C₂₃	—	2	2	no	—
289	D₄×C₂₃	—	2	2	no	—
290	D₄×C₂₃	—	4	4	no	—
291	D₄×C₂₃	—	4	8	no	—
292	D₄×C₂₃	—	4	1	no	—
293	D₄×C₂₃	—	4	1	no	—
294	D₄×C₂₃	—	4	1	no	—
295	D₄×C₂₃	—	4	1	no	—
296	D₄×C₂₃	—	4	1	no	—
297	D₄×C₂₃	—	4	1	no	—
298	D₄×C₂₃	—	8	4	no	—
299	D₄×C₂₃	—	8	4	no	—
300	D₄×C₂₃	—	8	4	no	—
301	C₂×C₄×C₂₃	—	2	1	no	—
302	C₂×C₄×C₂₃	—	2	1	no	—
303	C₂×C₄×C₂₃	—	2	2	no	—
304	C₂×C₄×C₂₃	—	2	2	no	—
305	C₂×C₄×C₂₃	—	2	2	no	—
306	C₂×C₄×C₂₃	—	2	2	no	—
307	C₂×C₄×C₂₃	—	2	1	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	1	no	—
310	C₂×C₄×C₂₃	—	2	2	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	—	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	—	4	1	no	—
335	C₂×C₄×C₂₃	—	4	1	no	—
336	C₂×C₄×C₂₃	—	4	1	no	—
337	C₂×C₄×C₂₃	—	4	1	no	—
338	C₂×C₄×C₂₃	—	8	4	no	—
339	C₂×C₄×C₂₃	—	8	4	no	—
340	C₂×C₄×C₂₃	—	8	4	no	—
341	C₂×C₄×C₂₃	#120	1	2	yes	—
342	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
345	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
346	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
347	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
348	C₈×C₂₃	—	2	2	no	—
349	C₈×C₂₃	—	4	1	no	—
350	C₈×C₂₃	—	4	1	no	—
351	C₈×C₂₃	—	4	1	no	—
352	C₂×#553	C₂×C₂₃	1	1	yes	characteristic, complemented
353	C₂×#482	C₂×C₂₃	1	1	yes	characteristic, complemented
354	C₂×#469	C₂×C₂₃	1	1	yes	characteristic, complemented
355	#2416	C₂×C₂₃	1	1	yes	characteristic, complemented
356	#2059	C₂×C₂₃	1	1	yes	characteristic, complemented
357	#2033	C₂×C₂₃	1	1	yes	characteristic, complemented
358	#2025	C₂×C₂₃	1	1	yes	characteristic, complemented
359	#1999	C₂×C₂₃	1	1	yes	characteristic, complemented
360	#1879	C₂×C₂₃	1	1	yes	characteristic, complemented
361	#1874	C₂×C₂₃	1	1	yes	characteristic, complemented
362	#1874	C₂×C₂₃	1	1	yes	characteristic, complemented
363	#1870	C₂×C₂₃	1	1	yes	characteristic, complemented
364	#1864	C₂×C₂₃	1	1	yes	characteristic, complemented
365	#1853	C₂×C₂₃	1	1	yes	characteristic, complemented
366	#1736	C₂×C₂₃	1	1	yes	characteristic, complemented
367	C₂²×C₂₃	—	2	2	no	—
368	C₂²×C₂₃	—	2	2	no	—
369	C₂²×C₂₃	—	2	2	no	—
370	C₂²×C₂₃	—	2	2	no	—
371	C₂²×C₂₃	—	2	2	no	—
372	C₂²×C₂₃	—	2	2	no	—
373	C₂²×C₂₃	—	4	1	no	—
374	C₂²×C₂₃	—	4	1	no	—
375	C₂²×C₂₃	—	4	1	no	—
376	C₂²×C₂₃	—	4	1	no	—
377	C₂²×C₂₃	—	4	1	no	—
378	C₂²×C₂₃	—	4	1	no	—
379	C₂²×C₂₃	—	4	1	no	—
380	C₂²×C₂₃	—	4	1	no	—
381	C₂²×C₂₃	—	4	2	no	—
382	C₂²×C₂₃	—	4	2	no	—
383	C₂²×C₂₃	—	4	2	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	—	8	1	no	—
393	C₂²×C₂₃	—	8	1	no	—
394	C₂²×C₂₃	—	8	1	no	—
395	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
396	C₂²×C₂₃	#546	1	1	yes	characteristic
397	C₂²×C₂₃	#547	1	1	yes	characteristic
398	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
399	C₂²×C₂₃	#575	1	1	yes	characteristic
400	C₂²×C₂₃	#576	1	1	yes	characteristic
401	C₂²×C₂₃	#577	1	1	yes	characteristic
402	C₄×C₂₃	—	2	2	no	—
403	C₄×C₂₃	—	4	1	no	—
404	C₄×C₂₃	—	4	1	no	—
405	C₄×C₂₃	—	4	2	no	—
406	C₄×C₂₃	—	4	1	no	—
407	C₄×C₂₃	—	4	2	no	—
408	C₄×C₂₃	—	4	2	no	—
409	C₄×C₂₃	—	4	2	no	—
410	C₄×C₂₃	—	8	1	no	—
411	C₄×C₂₃	—	8	1	no	—
412	C₄×C₂₃	#532	1	1	yes	characteristic
413	C₄×C₂₃	#537	1	1	yes	characteristic
414	C₄×C₂₃	#546	1	1	yes	characteristic
415	C₄×C₂₃	#547	1	1	yes	characteristic
416	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
417	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
418	#553	—	2	4	no	—
419	#553	—	2	4	no	—
420	C₂×#126	—	2	1	no	—
421	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×#123	—	2	1	no	—
423	C₂×#121	—	2	1	no	—
424	C₂×#121	—	2	1	no	—
425	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
426	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
428	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
429	C₂×C₄×D₄	—	2	1	no	—
430	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
433	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
434	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
435	#482	—	2	4	no	—
436	#469	—	2	4	no	—
437	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
438	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
439	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
440	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
441	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
442	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
443	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
444	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
445	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
447	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
448	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
449	#396	—	2	1	no	—
450	#394	—	2	1	no	—
451	#390	C₂²×C₂₃	1	1	yes	characteristic
452	#389	C₂²×C₂₃	1	1	yes	characteristic
453	#386	—	2	1	no	—
454	#380	C₂²×C₂₃	1	1	yes	characteristic
455	#340	C₂²×C₂₃	1	1	yes	characteristic
456	#340	C₂²×C₂₃	1	1	yes	characteristic
457	#340	C₂²×C₂₃	1	1	yes	characteristic
458	#340	C₂²×C₂₃	1	1	yes	characteristic
459	#340	C₂²×C₂₃	1	1	yes	characteristic
460	#340	C₂²×C₂₃	1	1	yes	characteristic
461	#336	C₂²×C₂₃	1	1	yes	characteristic
462	#336	C₂²×C₂₃	1	1	yes	characteristic
463	C₂×C₂₃	—	4	2	no	—
464	C₂×C₂₃	—	4	2	no	—
465	C₂×C₂₃	—	8	2	no	—
466	C₂×C₂₃	—	16	1	no	—
467	C₂×C₂₃	#2430	1	1	yes	characteristic
468	C₂×C₂₃	#3006	1	1	yes	characteristic
469	C₂×C₂₃	#3012	1	1	yes	characteristic
470	C₂×C₂₃	#3318	1	1	yes	characteristic
471	C₂×C₂₃	#3326	1	1	yes	characteristic
472	C₂×C₂₃	#3345	1	1	yes	characteristic
473	C₂×C₂₃	#3355	1	1	yes	characteristic
474	C₂²×D₄	—	2	1	no	—
475	C₂²×D₄	—	2	1	no	—
476	C₂²×D₄	—	2	1	no	—
477	C₂²×D₄	—	2	1	no	—
478	C₂²×D₄	D₄×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	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
486	C₂×D₈	—	2	2	no	—
487	C₂×D₈	—	2	2	no	—
488	C₂×D₈	—	4	1	no	—
489	C₂×M₁₆	—	2	2	no	—
490	C₂×M₁₆	—	2	2	no	—
491	C₂×M₁₆	—	4	1	no	—
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	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
496	#126	—	2	8	no	—
497	#125	—	2	2	no	—
498	#125	—	2	2	no	—
499	#123	—	2	8	no	—
500	#121	—	2	8	no	—
501	#121	—	2	2	no	—
502	#121	—	2	2	no	—
503	#121	—	2	2	no	—
504	#121	—	2	2	no	—
505	#121	—	2	2	no	—
506	#121	—	2	2	no	—
507	#121	—	4	1	no	—
508	#121	—	4	4	no	—
509	#121	D₄×C₂₃	1	4	yes	complemented
510	C₄×D₄	—	2	8	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	—	2	2	no	—
515	#117	—	2	2	no	—
516	#117	D₄×C₂₃	1	4	yes	complemented
517	C₂×C₄⋊C₄	—	2	1	no	—
518	C₂×C₄⋊C₄	—	2	1	no	—
519	C₂×C₄⋊C₄	—	2	1	no	—
520	C₂×C₄⋊C₄	—	2	2	no	—
521	C₂×C₄⋊C₄	—	2	2	no	—
522	C₂×C₄⋊C₄	—	2	2	no	—
523	C₂×C₄⋊C₄	—	2	1	no	—
524	C₂×C₄⋊C₄	—	2	1	no	—
525	C₂×C₄⋊C₄	—	4	1	no	—
526	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	—	2	1	no	—
534	C₂×C₂²⋊C₄	—	2	1	no	—
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₂²⋊C₄	—	2	1	no	—
537	C₂×C₂²⋊C₄	—	2	1	no	—
538	C₂×C₂²⋊C₄	—	2	1	no	—
539	C₂×C₂²⋊C₄	—	2	1	no	—
540	C₂×C₂²⋊C₄	—	2	1	no	—
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
543	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
544	C₂×C₄²	—	2	1	no	—
545	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
546	#107	—	2	2	no	—
547	#106	—	2	2	no	—
548	#106	—	2	2	no	—
549	#102	—	2	2	no	—
550	#102	—	2	2	no	—
551	#102	—	2	2	no	—
552	#102	—	2	2	no	—
553	#102	—	2	2	no	—
554	#102	—	4	1	no	—
555	C₂²⋊C₈	—	2	2	no	—
556	C₂²⋊C₈	—	2	2	no	—
557	C₂²⋊C₈	—	4	1	no	—
558	#95	—	2	1	no	—
559	#95	—	2	1	no	—
560	C₂₃	#25550	1	1	yes	characteristic, direct product factor, Sylow
561	C₂⁴	—	2	1	no	—
562	C₂⁴	—	2	1	no	—
563	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
564	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	4	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	—	2	1	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	—	4	1	no	—
581	C₂×D₄	—	4	2	no	—
582	C₂×D₄	—	4	2	no	—
583	C₂×D₄	—	4	2	no	—
584	C₂×D₄	—	4	2	no	—
585	C₂×D₄	—	4	2	no	—
586	C₂×D₄	—	4	2	no	—
587	C₂×D₄	—	4	2	no	—
588	C₂×D₄	—	8	1	no	—
589	C₂×D₄	—	8	1	no	—
590	C₂×D₄	—	8	1	no	—
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	4	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	4	2	no	—
611	C₂²×C₄	—	4	2	no	—
612	C₂²×C₄	—	8	1	no	—
613	C₂²×C₄	—	8	1	no	—
614	C₂²×C₄	—	8	1	no	—
615	C₂²×C₄	—	8	1	no	—
616	C₂²×C₄	—	8	1	no	—
617	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
622	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
624	D₈	—	4	4	no	—
625	M₁₆	—	4	4	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	—	2	1	no	—
635	C₂×C₈	—	2	1	no	—
636	C₂×C₈	—	2	1	no	—
637	C₂×C₈	#41×C₂₃	1	2	yes	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	—	4	2	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
653	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
654	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
655	C₄⋊C₄	#41×C₂₃	1	2	yes	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₂²⋊C₄	—	4	2	no	—
666	C₂²⋊C₄	—	8	1	no	—
667	C₄²	—	2	4	no	—
668	C₄²	—	2	1	no	—
669	C₄²	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	2	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	—	4	1	no	—
689	C₂³	—	4	1	no	—
690	C₂³	—	4	1	no	—
691	C₂³	—	4	1	no	—
692	C₂³	—	4	1	no	—
693	C₂³	—	4	1	no	—
694	C₂³	—	4	1	no	—
695	C₂³	—	4	1	no	—
696	C₂³	C₂₃×#120	1	2	yes	—
697	C₂³	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
698	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
699	D₄	—	2	2	no	—
700	D₄	—	2	2	no	—
701	D₄	—	4	4	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	—	4	1	no	—
708	D₄	—	4	1	no	—
709	D₄	—	8	4	no	—
710	D₄	—	8	4	no	—
711	D₄	—	8	4	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	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	—	2	1	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	2	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	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	8	4	no	—
750	C₂×C₄	—	8	4	no	—
751	C₂×C₄	—	8	4	no	—
752	C₂×C₄	C₂₃×#120	1	2	yes	—
753	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
754	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
755	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
756	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
757	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
758	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
759	C₈	—	2	2	no	—
760	C₈	—	4	1	no	—
761	C₈	—	4	1	no	—
762	C₈	—	4	1	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	1	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	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	—	8	1	no	—
786	C₂²	—	8	1	no	—
787	C₂²	—	8	1	no	—
788	C₂²	—	8	1	no	—
789	C₂²	—	8	1	no	—
790	C₂²	—	8	1	no	—
791	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
792	C₂²	C₂₃×#546	1	1	yes	characteristic
793	C₂²	C₂₃×#547	1	1	yes	characteristic
794	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
795	C₂²	C₂₃×#575	1	1	yes	characteristic
796	C₂²	C₂₃×#576	1	1	yes	characteristic
797	C₂²	C₂₃×#577	1	1	yes	characteristic
798	C₄	—	2	2	no	—
799	C₄	—	4	1	no	—
800	C₄	—	4	1	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	2	no	—
806	C₄	—	8	1	no	—
807	C₄	—	8	1	no	—
808	C₄	C₂₃×#532	1	1	yes	characteristic
809	C₄	C₂₃×#537	1	1	yes	characteristic
810	C₄	C₂₃×#546	1	1	yes	characteristic
811	C₄	C₂₃×#547	1	1	yes	characteristic
812	C₂	—	4	2	no	—
813	C₂	—	4	2	no	—
814	C₂	—	8	2	no	—
815	C₂	—	16	1	no	—
816	C₂	C₂₃×#2430	1	1	yes	characteristic
817	C₂	C₂₃×#3006	1	1	yes	characteristic
818	C₂	C₂₃×#3012	1	1	yes	characteristic
819	C₂	C₂₃×#3318	1	1	yes	characteristic
820	C₂	C₂₃×#3326	1	1	yes	characteristic
821	C₂	C₂₃×#3345	1	1	yes	characteristic
822	C₂	C₂₃×#3355	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#553	C₂	semidirect
2. C₂×C₂₃×#482	C₂	semidirect
3. C₂×C₂₃×#469	C₂	semidirect
4. C₂₃×#2416	C₂	semidirect
5. C₂₃×#2059	C₂	semidirect
6. C₂₃×#2033	C₂	semidirect
7. C₂₃×#2025	C₂	semidirect
8. C₂₃×#1999	C₂	semidirect
9. C₂₃×#1879	C₂	semidirect
10. C₂₃×#1874	C₂	semidirect
11. C₂₃×#1874	C₂	semidirect
12. C₂₃×#1870	C₂	semidirect
13. C₂₃×#1864	C₂	semidirect
14. C₂₃×#1853	C₂	semidirect
15. C₂₃×#1736	C₂	semidirect
98. C₂₃×#121	D₄	semidirect
105. C₂₃×#117	D₄	semidirect
258. #25550	C₂₃	direct (N × H)
352. C₂×#553	C₂×C₂₃	semidirect
353. C₂×#482	C₂×C₂₃	semidirect
354. C₂×#469	C₂×C₂₃	semidirect
355. #2416	C₂×C₂₃	semidirect
356. #2059	C₂×C₂₃	semidirect
357. #2033	C₂×C₂₃	semidirect
358. #2025	C₂×C₂₃	semidirect
359. #1999	C₂×C₂₃	semidirect
360. #1879	C₂×C₂₃	semidirect
361. #1874	C₂×C₂₃	semidirect
362. #1874	C₂×C₂₃	semidirect
363. #1870	C₂×C₂₃	semidirect
364. #1864	C₂×C₂₃	semidirect
365. #1853	C₂×C₂₃	semidirect
366. #1736	C₂×C₂₃	semidirect
509. #121	D₄×C₂₃	semidirect
516. #117	D₄×C₂₃	semidirect
560. C₂₃	#25550	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×#553	2
C₂×C₂₃×#482	2
C₂×C₂₃×#469	2
C₂₃×#2416	2
C₂₃×#2059	2
C₂₃×#2033	2
C₂₃×#2025	2
C₂₃×#1999	2
C₂₃×#1879	2
C₂₃×#1874	2
C₂₃×#1870	2
C₂₃×#1864	2
C₂₃×#1853	2
C₂₃×#1736	2
#25550	23

Subgroups — C23×#25550 #19173176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25550 #19173176