Subgroups — C₂₃×#25160 #19172786

Order 5888.

1316 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#447	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2427	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2067	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1968	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1864	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
18	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
28	C₂₃×#463	—	2	4	no	—
29	C₂₃×#450	—	2	4	no	—
30	C₂₃×#447	—	2	4	no	—
31	C₄×D₈×C₂₃	—	2	4	no	—
32	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₂₃×C₄⋊C₈	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	C₂²	1	1	yes	characteristic
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, complemented
42	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#397	—	2	1	no	—
47	C₂₃×#394	—	2	1	no	—
48	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#390	C₂²	1	1	yes	characteristic
50	C₂₃×#390	C₂²	1	1	yes	characteristic
51	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#386	—	2	1	no	—
53	C₂₃×#386	—	2	1	no	—
54	C₂₃×#386	—	2	1	no	—
55	C₂₃×#380	—	2	1	no	—
56	C₂₃×#380	C₂²	1	1	yes	characteristic
57	C₂₃×#379	—	2	1	no	—
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	2	no	—
68	C₂²×D₄×C₂₃	—	2	2	no	—
69	C₂²×D₄×C₂₃	—	2	1	no	—
70	C₂²×D₄×C₂₃	—	2	1	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	—	2	1	no	—
79	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
84	C₂×SD₁₆×C₂₃	—	2	2	no	—
85	C₂×SD₁₆×C₂₃	—	4	1	no	—
86	C₂×D₈×C₂₃	—	2	2	no	—
87	C₂×D₈×C₂₃	—	2	2	no	—
88	C₂×D₈×C₂₃	—	2	2	no	—
89	C₂×D₈×C₂₃	—	2	2	no	—
90	C₂×D₈×C₂₃	—	4	1	no	—
91	C₂×D₈×C₂₃	D₄	1	4	yes	—
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	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
96	C₂₃×#124	—	2	2	no	—
97	C₂₃×#124	—	4	1	no	—
98	C₂₃×C₂²⋊Q₈	—	2	2	no	—
99	C₂₃×C₂²⋊Q₈	—	4	1	no	—
100	C₂₃×#121	—	2	2	no	—
101	C₂₃×#121	—	4	1	no	—
102	C₄×D₄×C₂₃	—	2	2	no	—
103	C₄×D₄×C₂₃	—	2	2	no	—
104	C₄×D₄×C₂₃	—	2	2	no	—
105	C₄×D₄×C₂₃	—	4	1	no	—
106	C₄×D₄×C₂₃	—	4	1	no	—
107	C₄×D₄×C₂₃	—	4	1	no	—
108	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
109	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
110	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₂₃	—	2	1	no	—
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	—	4	4	no	—
127	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
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×#106	—	4	1	no	—
133	C₂₃×C₄⋊C₈	—	2	2	no	—
134	C₂₃×#103	—	2	2	no	—
135	C₂₃×#103	—	4	1	no	—
136	C₂₃×#102	—	2	2	no	—
137	C₂₃×#102	—	2	2	no	—
138	C₂₃×#102	—	2	2	no	—
139	C₂₃×#102	—	2	2	no	—
140	C₂₃×#102	—	2	2	no	—
141	C₂₃×#102	D₄	1	4	yes	complemented
142	C₂₃×C₂²⋊C₈	—	2	2	no	—
143	C₂₃×C₂²⋊C₈	—	2	2	no	—
144	C₄×C₈×C₂₃	—	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	4	no	—
153	C₂⁴×C₂₃	—	2	1	no	—
154	C₂⁴×C₂₃	—	2	1	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	4	no	—
169	C₂×D₄×C₂₃	—	2	1	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	—	4	2	no	—
183	C₂×D₄×C₂₃	—	4	2	no	—
184	C₂×D₄×C₂₃	—	4	4	no	—
185	C₂×D₄×C₂₃	—	4	4	no	—
186	C₂×D₄×C₂₃	—	4	4	no	—
187	C₂×D₄×C₂₃	—	4	4	no	—
188	C₂×D₄×C₂₃	—	4	2	no	—
189	C₂×D₄×C₂₃	—	4	2	no	—
190	C₂×D₄×C₂₃	—	8	1	no	—
191	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
192	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
193	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
194	C₂×D₄×C₂₃	#41	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	—	2	1	no	—
206	C₂²×C₄×C₂₃	—	2	1	no	—
207	C₂²×C₄×C₂₃	—	4	2	no	—
208	C₂²×C₄×C₂₃	—	4	2	no	—
209	C₂²×C₄×C₂₃	—	4	2	no	—
210	C₂²×C₄×C₂₃	—	4	2	no	—
211	C₂²×C₄×C₂₃	—	4	2	no	—
212	C₂²×C₄×C₂₃	—	4	2	no	—
213	C₂²×C₄×C₂₃	—	8	1	no	—
214	C₂²×C₄×C₂₃	—	8	1	no	—
215	C₂²×C₄×C₂₃	—	8	1	no	—
216	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
222	SD₁₆×C₂₃	—	4	4	no	—
223	SD₁₆×C₂₃	—	4	4	no	—
224	D₈×C₂₃	—	2	8	no	—
225	D₈×C₂₃	—	4	4	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	—	2	1	no	—
234	C₂×C₈×C₂₃	—	2	1	no	—
235	C₂×C₈×C₂₃	—	2	1	no	—
236	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
237	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
242	C₄⋊C₄×C₂₃	—	2	1	no	—
243	C₄⋊C₄×C₂₃	—	2	1	no	—
244	C₄⋊C₄×C₂₃	—	2	1	no	—
245	C₄⋊C₄×C₂₃	—	4	2	no	—
246	C₄⋊C₄×C₂₃	—	8	1	no	—
247	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
248	C₂²⋊C₄×C₂₃	—	2	2	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	—	4	2	no	—
255	C₂²⋊C₄×C₂₃	—	4	2	no	—
256	C₂²⋊C₄×C₂₃	—	4	2	no	—
257	C₂²⋊C₄×C₂₃	—	4	2	no	—
258	C₂²⋊C₄×C₂₃	—	4	2	no	—
259	C₂²⋊C₄×C₂₃	—	4	2	no	—
260	C₂²⋊C₄×C₂₃	—	8	1	no	—
261	C₂²⋊C₄×C₂₃	—	8	1	no	—
262	C₄²×C₂₃	—	2	1	no	—
263	C₄²×C₂₃	—	2	1	no	—
264	C₄²×C₂₃	—	2	1	no	—
265	C₄²×C₂₃	—	2	1	no	—
266	#25160	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂³×C₂₃	—	2	1	no	—
268	C₂³×C₂₃	—	2	2	no	—
269	C₂³×C₂₃	—	2	1	no	—
270	C₂³×C₂₃	—	2	2	no	—
271	C₂³×C₂₃	—	2	2	no	—
272	C₂³×C₂₃	—	2	1	no	—
273	C₂³×C₂₃	—	2	1	no	—
274	C₂³×C₂₃	—	2	1	no	—
275	C₂³×C₂₃	—	2	1	no	—
276	C₂³×C₂₃	—	2	2	no	—
277	C₂³×C₂₃	—	2	2	no	—
278	C₂³×C₂₃	—	4	8	no	—
279	C₂³×C₂₃	—	4	8	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	—	4	1	no	—
294	C₂³×C₂₃	—	4	1	no	—
295	C₂³×C₂₃	—	4	1	no	—
296	C₂³×C₂₃	—	8	4	no	—
297	C₂³×C₂₃	—	8	4	no	—
298	C₂³×C₂₃	—	8	4	no	—
299	C₂³×C₂₃	—	8	4	no	—
300	C₂³×C₂₃	—	8	4	no	—
301	C₂³×C₂₃	#135	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	—	2	2	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	—	8	4	no	—
320	D₄×C₂₃	#121	1	4	yes	—
321	C₂×C₄×C₂₃	—	2	1	no	—
322	C₂×C₄×C₂₃	—	2	1	no	—
323	C₂×C₄×C₂₃	—	2	1	no	—
324	C₂×C₄×C₂₃	—	2	1	no	—
325	C₂×C₄×C₂₃	—	2	1	no	—
326	C₂×C₄×C₂₃	—	2	1	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	1	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	—	4	1	no	—
337	C₂×C₄×C₂₃	—	4	1	no	—
338	C₂×C₄×C₂₃	—	4	1	no	—
339	C₂×C₄×C₂₃	—	4	1	no	—
340	C₂×C₄×C₂₃	—	4	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	—	8	4	no	—
357	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
358	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
361	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
362	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
364	C₈×C₂₃	—	2	2	no	—
365	C₈×C₂₃	—	2	2	no	—
366	C₈×C₂₃	—	4	1	no	—
367	C₈×C₂₃	—	4	1	no	—
368	C₂×#463	C₂×C₂₃	1	1	yes	characteristic, complemented
369	C₂×#450	C₂×C₂₃	1	1	yes	characteristic, complemented
370	C₂×#447	C₂×C₂₃	1	1	yes	characteristic
371	C₂×C₄×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
372	#2427	C₂×C₂₃	1	1	yes	characteristic, complemented
373	D₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
374	#2067	C₂×C₂₃	1	1	yes	characteristic, complemented
375	#2036	C₂×C₂₃	1	1	yes	characteristic, complemented
376	#2034	C₂×C₂₃	1	1	yes	characteristic, complemented
377	#2012	C₂×C₂₃	1	1	yes	characteristic, complemented
378	#1968	C₂×C₂₃	1	1	yes	characteristic, complemented
379	#1923	C₂×C₂₃	1	1	yes	characteristic, complemented
380	#1879	C₂×C₂₃	1	1	yes	characteristic, complemented
381	#1877	C₂×C₂₃	1	1	yes	characteristic, complemented
382	#1864	C₂×C₂₃	1	1	yes	characteristic, complemented
383	C₂²×C₂₃	—	2	2	no	—
384	C₂²×C₂₃	—	2	4	no	—
385	C₂²×C₂₃	—	2	2	no	—
386	C₂²×C₂₃	—	2	2	no	—
387	C₂²×C₂₃	—	4	2	no	—
388	C₂²×C₂₃	—	4	1	no	—
389	C₂²×C₂₃	—	4	2	no	—
390	C₂²×C₂₃	—	4	1	no	—
391	C₂²×C₂₃	—	4	2	no	—
392	C₂²×C₂₃	—	4	1	no	—
393	C₂²×C₂₃	—	4	2	no	—
394	C₂²×C₂₃	—	4	1	no	—
395	C₂²×C₂₃	—	4	2	no	—
396	C₂²×C₂₃	—	4	2	no	—
397	C₂²×C₂₃	—	4	2	no	—
398	C₂²×C₂₃	—	4	2	no	—
399	C₂²×C₂₃	—	4	2	no	—
400	C₂²×C₂₃	—	4	2	no	—
401	C₂²×C₂₃	—	4	2	no	—
402	C₂²×C₂₃	—	4	2	no	—
403	C₂²×C₂₃	—	8	16	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	—	8	1	no	—
411	C₂²×C₂₃	—	8	1	no	—
412	C₂²×C₂₃	#525	1	1	yes	characteristic
413	C₂²×C₂₃	D₄²	1	1	yes	characteristic
414	C₂²×C₂₃	D₄²	1	1	yes	characteristic
415	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
416	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
417	C₂²×C₂₃	#576	1	1	yes	characteristic
418	C₂²×C₂₃	#577	1	1	yes	characteristic
419	C₄×C₂₃	—	2	2	no	—
420	C₄×C₂₃	—	4	1	no	—
421	C₄×C₂₃	—	4	2	no	—
422	C₄×C₂₃	—	4	1	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	—	8	1	no	—
429	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
430	C₄×C₂₃	#538	1	1	yes	characteristic
431	C₄×C₂₃	#546	1	1	yes	characteristic
432	C₄×C₂₃	#546	1	1	yes	characteristic
433	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
434	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
435	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
436	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
437	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
438	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic, complemented
439	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
440	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
441	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
442	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
443	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
444	C₂²×C₂²⋊C₄	—	2	1	no	—
445	#463	—	2	4	no	—
446	#450	—	2	4	no	—
447	#447	—	2	4	no	—
448	C₄×D₈	—	2	4	no	—
449	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
450	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
451	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
452	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
453	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
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, complemented
459	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
460	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
461	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
462	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
463	#397	—	2	1	no	—
464	#394	—	2	1	no	—
465	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
466	#390	C₂²×C₂₃	1	1	yes	characteristic
467	#390	C₂²×C₂₃	1	1	yes	characteristic
468	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
469	#386	—	2	1	no	—
470	#386	—	2	1	no	—
471	#386	—	2	1	no	—
472	#380	—	2	1	no	—
473	#380	C₂²×C₂₃	1	1	yes	characteristic
474	#379	—	2	1	no	—
475	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
476	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
477	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
478	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
479	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
480	C₂×C₂₃	—	4	2	no	—
481	C₂×C₂₃	—	4	4	no	—
482	C₂×C₂₃	—	8	2	no	—
483	C₂×C₂₃	—	8	2	no	—
484	C₂×C₂₃	#2424	1	1	yes	characteristic
485	C₂×C₂₃	#3105	1	1	yes	characteristic
486	C₂×C₂₃	#3118	1	1	yes	characteristic
487	C₂×C₂₃	#3264	1	1	yes	characteristic
488	C₂×C₂₃	#3272	1	1	yes	characteristic
489	C₂×C₂₃	#3280	1	1	yes	characteristic
490	C₂×C₂₃	#3282	1	1	yes	characteristic
491	C₂⁵	—	2	1	no	—
492	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
493	C₂²×D₄	—	2	2	no	—
494	C₂²×D₄	—	2	2	no	—
495	C₂²×D₄	—	2	2	no	—
496	C₂²×D₄	—	2	2	no	—
497	C₂²×D₄	—	2	1	no	—
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	—	4	1	no	—
500	C₂²×D₄	—	4	1	no	—
501	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
502	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
503	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	—	2	1	no	—
506	C₂³×C₄	—	2	1	no	—
507	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
508	C₂×SD₁₆	—	2	2	no	—
509	C₂×SD₁₆	—	2	2	no	—
510	C₂×SD₁₆	—	2	2	no	—
511	C₂×SD₁₆	—	2	2	no	—
512	C₂×SD₁₆	—	2	2	no	—
513	C₂×SD₁₆	—	4	1	no	—
514	C₂×D₈	—	2	2	no	—
515	C₂×D₈	—	2	2	no	—
516	C₂×D₈	—	2	2	no	—
517	C₂×D₈	—	2	2	no	—
518	C₂×D₈	—	4	1	no	—
519	C₂×D₈	D₄×C₂₃	1	4	yes	—
520	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
521	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
522	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
523	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
524	#124	—	2	2	no	—
525	#124	—	4	1	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	4	1	no	—
528	#121	—	2	2	no	—
529	#121	—	4	1	no	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	2	no	—
533	C₄×D₄	—	4	1	no	—
534	C₄×D₄	—	4	1	no	—
535	C₄×D₄	—	4	1	no	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	—	2	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	—	4	4	no	—
555	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
557	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
558	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
559	#107	—	2	2	no	—
560	#106	—	4	1	no	—
561	C₄⋊C₈	—	2	2	no	—
562	#103	—	2	2	no	—
563	#103	—	4	1	no	—
564	#102	—	2	2	no	—
565	#102	—	2	2	no	—
566	#102	—	2	2	no	—
567	#102	—	2	2	no	—
568	#102	—	2	2	no	—
569	#102	D₄×C₂₃	1	4	yes	complemented
570	C₂²⋊C₈	—	2	2	no	—
571	C₂²⋊C₈	—	2	2	no	—
572	C₄×C₈	—	2	2	no	—
573	#95	—	2	1	no	—
574	#95	—	2	1	no	—
575	#95	—	2	1	no	—
576	#95	—	2	1	no	—
577	#95	D₄×C₂₃	1	1	yes	characteristic
578	#95	D₄×C₂₃	1	1	yes	characteristic
579	C₂₃	#25160	1	1	yes	characteristic, direct product factor, Sylow
580	C₂⁴	—	2	1	no	—
581	C₂⁴	—	2	4	no	—
582	C₂⁴	—	2	1	no	—
583	C₂⁴	—	2	1	no	—
584	C₂⁴	—	4	2	no	—
585	C₂⁴	—	4	2	no	—
586	C₂⁴	—	4	2	no	—
587	C₂⁴	—	4	2	no	—
588	C₂⁴	—	8	1	no	—
589	C₂⁴	—	8	1	no	—
590	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
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×Q₈	—	2	1	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	—	4	2	no	—
612	C₂×D₄	—	4	2	no	—
613	C₂×D₄	—	4	4	no	—
614	C₂×D₄	—	4	4	no	—
615	C₂×D₄	—	4	4	no	—
616	C₂×D₄	—	4	4	no	—
617	C₂×D₄	—	4	2	no	—
618	C₂×D₄	—	4	2	no	—
619	C₂×D₄	—	8	1	no	—
620	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
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	C₂×D₄	#41×C₂₃	1	2	yes	—
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	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	4	2	no	—
637	C₂²×C₄	—	4	2	no	—
638	C₂²×C₄	—	4	2	no	—
639	C₂²×C₄	—	4	2	no	—
640	C₂²×C₄	—	4	2	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	—	8	1	no	—
643	C₂²×C₄	—	8	1	no	—
644	C₂²×C₄	—	8	1	no	—
645	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
649	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
651	SD₁₆	—	4	4	no	—
652	SD₁₆	—	4	4	no	—
653	D₈	—	2	8	no	—
654	D₈	—	4	4	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	—	2	1	no	—
662	C₂×C₈	—	2	1	no	—
663	C₂×C₈	—	2	1	no	—
664	C₂×C₈	—	2	1	no	—
665	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
666	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	4	2	no	—
675	C₄⋊C₄	—	8	1	no	—
676	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	2	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	—	4	2	no	—
685	C₂²⋊C₄	—	4	2	no	—
686	C₂²⋊C₄	—	4	2	no	—
687	C₂²⋊C₄	—	4	2	no	—
688	C₂²⋊C₄	—	4	2	no	—
689	C₂²⋊C₄	—	8	1	no	—
690	C₂²⋊C₄	—	8	1	no	—
691	C₄²	—	2	1	no	—
692	C₄²	—	2	1	no	—
693	C₄²	—	2	1	no	—
694	C₄²	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	4	8	no	—
707	C₂³	—	4	8	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	—	4	1	no	—
721	C₂³	—	4	1	no	—
722	C₂³	—	4	1	no	—
723	C₂³	—	4	1	no	—
724	C₂³	—	8	4	no	—
725	C₂³	—	8	4	no	—
726	C₂³	—	8	4	no	—
727	C₂³	—	8	4	no	—
728	C₂³	—	8	4	no	—
729	C₂³	C₂₃×#135	1	2	yes	—
730	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
731	Q₈	—	4	1	no	—
732	Q₈	—	4	1	no	—
733	Q₈	—	4	1	no	—
734	Q₈	—	4	1	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	—	2	2	no	—
741	D₄	—	2	2	no	—
742	D₄	—	4	8	no	—
743	D₄	—	4	1	no	—
744	D₄	—	4	1	no	—
745	D₄	—	4	1	no	—
746	D₄	—	4	1	no	—
747	D₄	—	8	4	no	—
748	D₄	C₂₃×#121	1	4	yes	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	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	2	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	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	—	4	1	no	—
782	C₂×C₄	—	8	4	no	—
783	C₂×C₄	—	8	4	no	—
784	C₂×C₄	—	8	4	no	—
785	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
786	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
787	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
788	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
789	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
790	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
791	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
792	C₈	—	2	2	no	—
793	C₈	—	2	2	no	—
794	C₈	—	4	1	no	—
795	C₈	—	4	1	no	—
796	C₂²	—	2	4	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	1	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	8	16	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	—	8	1	no	—
823	C₂²	—	8	1	no	—
824	C₂²	—	8	1	no	—
825	C₂²	C₂₃×#525	1	1	yes	characteristic
826	C₂²	D₄²×C₂₃	1	1	yes	characteristic
827	C₂²	D₄²×C₂₃	1	1	yes	characteristic
828	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
829	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
830	C₂²	C₂₃×#576	1	1	yes	characteristic
831	C₂²	C₂₃×#577	1	1	yes	characteristic
832	C₄	—	2	2	no	—
833	C₄	—	4	1	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	1	no	—
838	C₄	—	8	1	no	—
839	C₄	—	8	1	no	—
840	C₄	—	8	1	no	—
841	C₄	—	8	1	no	—
842	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
843	C₄	C₂₃×#538	1	1	yes	characteristic
844	C₄	C₂₃×#546	1	1	yes	characteristic
845	C₄	C₂₃×#546	1	1	yes	characteristic
846	C₂	—	4	2	no	—
847	C₂	—	4	4	no	—
848	C₂	—	8	2	no	—
849	C₂	—	8	2	no	—
850	C₂	C₂₃×#2424	1	1	yes	characteristic
851	C₂	C₂₃×#3105	1	1	yes	characteristic
852	C₂	C₂₃×#3118	1	1	yes	characteristic
853	C₂	C₂₃×#3264	1	1	yes	characteristic
854	C₂	C₂₃×#3272	1	1	yes	characteristic
855	C₂	C₂₃×#3280	1	1	yes	characteristic
856	C₂	C₂₃×#3282	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×#463	C₂	semidirect
2. C₂×C₂₃×#450	C₂	semidirect
4. C₂×C₄×D₈×C₂₃	C₂	semidirect
5. C₂₃×#2427	C₂	semidirect
6. D₄×C₂²⋊C₄×C₂₃	C₂	semidirect
7. C₂₃×#2067	C₂	semidirect
8. C₂₃×#2036	C₂	semidirect
9. C₂₃×#2034	C₂	semidirect
10. C₂₃×#2012	C₂	semidirect
11. C₂₃×#1968	C₂	semidirect
12. C₂₃×#1923	C₂	semidirect
13. C₂₃×#1879	C₂	semidirect
14. C₂₃×#1877	C₂	semidirect
15. C₂₃×#1864	C₂	semidirect
21. C₂×C₂₃×#124	C₂²	semidirect
26. C₂×C₄×D₄×C₂₃	C₂²	semidirect
32. C₂×C₂₃×#107	C₂²	semidirect
33. C₂×C₂₃×#106	C₂²	semidirect
34. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
35. C₂×C₂₃×#103	C₂²	semidirect
36. C₂×C₂₃×#103	C₂²	semidirect
41. C₂×C₂₃×#102	C₂²	semidirect
42. C₂×C₂₃×#102	C₂²	semidirect
45. C₂×C₄×C₈×C₂₃	C₂²	semidirect
48. C₂₃×#391	C₂²	semidirect
51. C₂₃×#389	C₂²	semidirect
59. C₂₃×#340	C₂²	semidirect
60. C₂₃×#340	C₂²	semidirect
61. C₂₃×#336	C₂²	semidirect
62. C₂₃×#336	C₂²	semidirect
141. C₂₃×#102	D₄	semidirect
266. #25160	C₂₃	direct (N × H)
368. C₂×#463	C₂×C₂₃	semidirect
369. C₂×#450	C₂×C₂₃	semidirect
371. C₂×C₄×D₈	C₂×C₂₃	semidirect
372. #2427	C₂×C₂₃	semidirect
373. D₄×C₂²⋊C₄	C₂×C₂₃	semidirect
374. #2067	C₂×C₂₃	semidirect
375. #2036	C₂×C₂₃	semidirect
376. #2034	C₂×C₂₃	semidirect
377. #2012	C₂×C₂₃	semidirect
378. #1968	C₂×C₂₃	semidirect
379. #1923	C₂×C₂₃	semidirect
380. #1879	C₂×C₂₃	semidirect
381. #1877	C₂×C₂₃	semidirect
382. #1864	C₂×C₂₃	semidirect
438. C₂×#124	C₂²×C₂₃	semidirect
443. C₂×C₄×D₄	C₂²×C₂₃	semidirect
449. C₂×#107	C₂²×C₂₃	semidirect
450. C₂×#106	C₂²×C₂₃	semidirect
451. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
452. C₂×#103	C₂²×C₂₃	semidirect
453. C₂×#103	C₂²×C₂₃	semidirect
458. C₂×#102	C₂²×C₂₃	semidirect
459. C₂×#102	C₂²×C₂₃	semidirect
462. C₂×C₄×C₈	C₂²×C₂₃	semidirect
465. #391	C₂²×C₂₃	semidirect
468. #389	C₂²×C₂₃	semidirect
476. #340	C₂²×C₂₃	semidirect
477. #340	C₂²×C₂₃	semidirect
478. #336	C₂²×C₂₃	semidirect
479. #336	C₂²×C₂₃	semidirect
569. #102	D₄×C₂₃	semidirect
579. C₂₃	#25160	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×#463	2
C₂×C₂₃×#450	2
C₂×C₂₃×#447	2
C₂×C₄×D₈×C₂₃	2
C₂₃×#2427	2
D₄×C₂²⋊C₄×C₂₃	2
C₂₃×#2067	2
C₂₃×#2036	2
C₂₃×#2034	2
C₂₃×#2012	2
C₂₃×#1968	2
C₂₃×#1923	2
C₂₃×#1879	2
C₂₃×#1877	2
C₂₃×#1864	2
#25160	23

Subgroups — C23×#25160 #19172786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25160 #19172786