Subgroups — C₂₃×#25547 #19173173

Order 5888.

1340 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#547	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2415	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2057	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2024	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1875	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1872	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	—	2	1	no	—
17	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂₃×#547	—	2	4	no	—
20	C₂₃×#547	—	2	4	no	—
21	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#123	—	2	1	no	—
23	C₂×C₂₃×#123	—	2	1	no	—
24	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×C₂²⋊Q₈	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	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂₃×#484	—	2	4	no	—
35	C₂₃×#468	—	2	4	no	—
36	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#107	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×#103	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	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂₃×#397	—	2	1	no	—
49	C₂₃×#394	—	2	1	no	—
50	C₂₃×#391	C₂²	1	1	yes	characteristic
51	C₂₃×#389	—	2	1	no	—
52	C₂₃×#389	C₂²	1	1	yes	characteristic
53	C₂₃×#388	—	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	C₂×#41×C₂₃	—	2	8	no	—
64	C₂×#41×C₂₃	—	4	4	no	—
65	C₂×#41×C₂₃	—	4	4	no	—
66	C₂²×Q₈×C₂₃	—	2	1	no	—
67	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₂₃	—	2	1	no	—
69	C₂²×D₄×C₂₃	—	2	1	no	—
70	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
71	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₂₃	—	2	1	no	—
73	C₂³×C₄×C₂₃	—	2	1	no	—
74	C₂³×C₄×C₂₃	—	2	1	no	—
75	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂×SD₁₆×C₂₃	—	2	2	no	—
78	C₂×SD₁₆×C₂₃	—	2	2	no	—
79	C₂×SD₁₆×C₂₃	—	4	1	no	—
80	C₂×M₁₆×C₂₃	—	2	2	no	—
81	C₂×M₁₆×C₂₃	—	2	2	no	—
82	C₂×M₁₆×C₂₃	—	4	1	no	—
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×C₄⋊Q₈	—	2	2	no	—
88	C₂₃×C₄⋊Q₈	—	2	2	no	—
89	C₂₃×#123	—	2	8	no	—
90	C₂₃×#123	—	2	8	no	—
91	C₂₃×C₂²⋊Q₈	—	2	8	no	—
92	C₂₃×C₂²⋊Q₈	—	2	2	no	—
93	C₂₃×C₂²⋊Q₈	—	2	2	no	—
94	C₂₃×C₂²⋊Q₈	—	2	2	no	—
95	C₂₃×C₂²⋊Q₈	—	4	1	no	—
96	C₂₃×#121	—	2	2	no	—
97	C₂₃×#121	—	2	2	no	—
98	C₂₃×#121	—	2	2	no	—
99	C₂₃×#121	D₄	1	4	yes	—
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	—	4	1	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	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	—	2	1	no	—
115	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₂₃	D₄	1	4	yes	—
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×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
132	C₂×C₄²×C₂₃	—	2	1	no	—
133	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
134	C₂₃×#107	—	2	2	no	—
135	C₂₃×#107	—	2	2	no	—
136	C₂₃×#107	—	2	2	no	—
137	C₂₃×#103	—	2	2	no	—
138	C₂₃×#103	—	2	2	no	—
139	C₂₃×#103	—	2	2	no	—
140	C₂₃×#102	—	2	2	no	—
141	C₂₃×#102	—	2	2	no	—
142	C₂₃×#102	—	4	1	no	—
143	C₂₃×C₂²⋊C₈	—	2	2	no	—
144	C₂₃×C₂²⋊C₈	—	2	2	no	—
145	C₂₃×C₂²⋊C₈	—	4	1	no	—
146	C₂₃×#95	—	2	1	no	—
147	C₂₃×#95	—	2	1	no	—
148	C₂₃×#95	—	2	1	no	—
149	C₂₃×#95	—	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	#41×C₂₃	—	4	32	no	—
154	C₂×Q₈×C₂₃	—	2	4	no	—
155	C₂×Q₈×C₂₃	—	2	1	no	—
156	C₂×Q₈×C₂₃	—	2	1	no	—
157	C₂×Q₈×C₂₃	—	2	1	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	—	4	2	no	—
162	C₂×Q₈×C₂₃	—	4	2	no	—
163	C₂×D₄×C₂₃	—	2	2	no	—
164	C₂×D₄×C₂₃	—	2	2	no	—
165	C₂×D₄×C₂₃	—	2	4	no	—
166	C₂×D₄×C₂₃	—	2	4	no	—
167	C₂×D₄×C₂₃	—	2	2	no	—
168	C₂×D₄×C₂₃	—	2	1	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	—	4	2	no	—
174	C₂×D₄×C₂₃	—	4	2	no	—
175	C₂×D₄×C₂₃	—	4	2	no	—
176	C₂×D₄×C₂₃	—	4	2	no	—
177	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₂₃	—	2	1	no	—
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	4	no	—
183	C₂²×C₄×C₂₃	—	2	4	no	—
184	C₂²×C₄×C₂₃	—	2	4	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	—	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	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
208	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
209	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
211	SD₁₆×C₂₃	—	4	4	no	—
212	M₁₆×C₂₃	—	4	4	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	—	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	#41	1	2	yes	complemented
225	C₄⋊C₄×C₂₃	—	2	4	no	—
226	C₄⋊C₄×C₂₃	—	2	4	no	—
227	C₄⋊C₄×C₂₃	—	2	4	no	—
228	C₄⋊C₄×C₂₃	—	2	2	no	—
229	C₄⋊C₄×C₂₃	—	2	1	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	—	4	2	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	complemented
244	C₂²⋊C₄×C₂₃	—	2	4	no	—
245	C₂²⋊C₄×C₂₃	—	2	4	no	—
246	C₂²⋊C₄×C₂₃	—	2	2	no	—
247	C₂²⋊C₄×C₂₃	—	2	4	no	—
248	C₂²⋊C₄×C₂₃	—	2	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	C₄²×C₂₃	—	2	1	no	—
254	C₄²×C₂₃	—	2	1	no	—
255	C₄²×C₂₃	—	4	2	no	—
256	#25547	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
257	C₂³×C₂₃	—	2	1	no	—
258	C₂³×C₂₃	—	2	1	no	—
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	2	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	#120	1	2	yes	—
277	C₂³×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
278	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
279	Q₈×C₂₃	—	4	8	no	—
280	Q₈×C₂₃	—	4	1	no	—
281	Q₈×C₂₃	—	4	1	no	—
282	Q₈×C₂₃	—	4	1	no	—
283	Q₈×C₂₃	—	4	1	no	—
284	D₄×C₂₃	—	2	8	no	—
285	D₄×C₂₃	—	2	2	no	—
286	D₄×C₂₃	—	2	2	no	—
287	D₄×C₂₃	—	4	8	no	—
288	D₄×C₂₃	—	4	8	no	—
289	D₄×C₂₃	—	4	1	no	—
290	D₄×C₂₃	—	4	1	no	—
291	C₂×C₄×C₂₃	—	2	1	no	—
292	C₂×C₄×C₂₃	—	2	1	no	—
293	C₂×C₄×C₂₃	—	2	1	no	—
294	C₂×C₄×C₂₃	—	2	1	no	—
295	C₂×C₄×C₂₃	—	2	2	no	—
296	C₂×C₄×C₂₃	—	2	2	no	—
297	C₂×C₄×C₂₃	—	2	2	no	—
298	C₂×C₄×C₂₃	—	2	2	no	—
299	C₂×C₄×C₂₃	—	2	1	no	—
300	C₂×C₄×C₂₃	—	2	1	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	2	no	—
303	C₂×C₄×C₂₃	—	2	2	no	—
304	C₂×C₄×C₂₃	—	2	2	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	—	4	8	no	—
310	C₂×C₄×C₂₃	—	4	8	no	—
311	C₂×C₄×C₂₃	—	4	8	no	—
312	C₂×C₄×C₂₃	—	4	1	no	—
313	C₂×C₄×C₂₃	—	4	1	no	—
314	C₂×C₄×C₂₃	—	4	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	#120	1	2	yes	—
334	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
335	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
338	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
339	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
340	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
341	C₈×C₂₃	—	2	2	no	—
342	C₈×C₂₃	—	4	1	no	—
343	C₈×C₂₃	—	4	1	no	—
344	C₈×C₂₃	—	4	1	no	—
345	C₂×#547	C₂×C₂₃	1	1	yes	characteristic
346	C₂×#484	C₂×C₂₃	1	1	yes	characteristic, complemented
347	C₂×#468	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#2415	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#2057	C₂×C₂₃	1	1	yes	characteristic, complemented
350	#2033	C₂×C₂₃	1	1	yes	characteristic, complemented
351	#2024	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#2000	C₂×C₂₃	1	1	yes	characteristic, complemented
353	#1877	C₂×C₂₃	1	1	yes	characteristic, complemented
354	#1875	C₂×C₂₃	1	1	yes	characteristic, complemented
355	#1872	C₂×C₂₃	1	1	yes	characteristic, complemented
356	#1870	C₂×C₂₃	1	1	yes	characteristic, complemented
357	#1862	C₂×C₂₃	1	1	yes	characteristic, complemented
358	#1852	C₂×C₂₃	1	1	yes	characteristic, complemented
359	#1736	C₂×C₂₃	1	1	yes	characteristic, complemented
360	C₂²×C₂₃	—	2	2	no	—
361	C₂²×C₂₃	—	2	2	no	—
362	C₂²×C₂₃	—	2	2	no	—
363	C₂²×C₂₃	—	2	2	no	—
364	C₂²×C₂₃	—	2	2	no	—
365	C₂²×C₂₃	—	2	2	no	—
366	C₂²×C₂₃	—	4	1	no	—
367	C₂²×C₂₃	—	4	1	no	—
368	C₂²×C₂₃	—	4	1	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	1	no	—
374	C₂²×C₂₃	—	4	2	no	—
375	C₂²×C₂₃	—	4	2	no	—
376	C₂²×C₂₃	—	4	2	no	—
377	C₂²×C₂₃	—	8	1	no	—
378	C₂²×C₂₃	—	8	1	no	—
379	C₂²×C₂₃	—	8	1	no	—
380	C₂²×C₂₃	—	8	1	no	—
381	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
382	C₂²×C₂₃	#546	1	1	yes	characteristic
383	C₂²×C₂₃	#547	1	1	yes	characteristic
384	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
385	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
386	C₂²×C₂₃	#578	1	1	yes	characteristic
387	C₂²×C₂₃	#578	1	1	yes	characteristic
388	C₄×C₂₃	—	2	2	no	—
389	C₄×C₂₃	—	2	2	no	—
390	C₄×C₂₃	—	4	2	no	—
391	C₄×C₂₃	—	4	1	no	—
392	C₄×C₂₃	—	4	2	no	—
393	C₄×C₂₃	—	4	2	no	—
394	C₄×C₂₃	—	4	2	no	—
395	C₄×C₂₃	—	4	1	no	—
396	C₄×C₂₃	—	8	1	no	—
397	C₄×C₂₃	—	8	1	no	—
398	C₄×C₂₃	—	8	1	no	—
399	C₄×C₂₃	#532	1	1	yes	characteristic
400	C₄×C₂₃	#537	1	1	yes	characteristic
401	C₄×C₂₃	#546	1	1	yes	characteristic
402	C₄×C₂₃	#547	1	1	yes	characteristic
403	C₂²×#41	—	2	1	no	—
404	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
405	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
406	#547	—	2	4	no	—
407	#547	—	2	4	no	—
408	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
409	C₂×#123	—	2	1	no	—
410	C₂×#123	—	2	1	no	—
411	C₂×C₂²⋊Q₈	—	2	1	no	—
412	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
413	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
414	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
415	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
416	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
418	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
419	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
420	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
421	#484	—	2	4	no	—
422	#468	—	2	4	no	—
423	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
424	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
425	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
426	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
428	C₂×#103	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×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
433	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
434	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
435	#397	—	2	1	no	—
436	#394	—	2	1	no	—
437	#391	C₂²×C₂₃	1	1	yes	characteristic
438	#389	—	2	1	no	—
439	#389	C₂²×C₂₃	1	1	yes	characteristic
440	#388	—	2	1	no	—
441	#380	C₂²×C₂₃	1	1	yes	characteristic
442	#340	C₂²×C₂₃	1	1	yes	characteristic
443	#340	C₂²×C₂₃	1	1	yes	characteristic
444	#340	C₂²×C₂₃	1	1	yes	characteristic
445	#340	C₂²×C₂₃	1	1	yes	characteristic
446	#340	C₂²×C₂₃	1	1	yes	characteristic
447	#340	C₂²×C₂₃	1	1	yes	characteristic
448	#336	C₂²×C₂₃	1	1	yes	characteristic
449	#336	C₂²×C₂₃	1	1	yes	characteristic
450	C₂×C₂₃	—	4	2	no	—
451	C₂×C₂₃	—	4	2	no	—
452	C₂×C₂₃	—	8	2	no	—
453	C₂×C₂₃	#2430	1	1	yes	characteristic
454	C₂×C₂₃	#3003	1	1	yes	characteristic
455	C₂×C₂₃	#3011	1	1	yes	characteristic
456	C₂×C₂₃	#3308	1	1	yes	characteristic
457	C₂×C₂₃	#3330	1	1	yes	characteristic
458	C₂×C₂₃	#3343	1	1	yes	characteristic
459	C₂×C₂₃	#3353	1	1	yes	characteristic
460	C₂×#41	—	2	8	no	—
461	C₂×#41	—	4	4	no	—
462	C₂×#41	—	4	4	no	—
463	C₂²×Q₈	—	2	1	no	—
464	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
468	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
469	C₂³×C₄	—	2	1	no	—
470	C₂³×C₄	—	2	1	no	—
471	C₂³×C₄	—	2	1	no	—
472	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
474	C₂×SD₁₆	—	2	2	no	—
475	C₂×SD₁₆	—	2	2	no	—
476	C₂×SD₁₆	—	4	1	no	—
477	C₂×M₁₆	—	2	2	no	—
478	C₂×M₁₆	—	2	2	no	—
479	C₂×M₁₆	—	4	1	no	—
480	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
481	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
482	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
483	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
484	C₄⋊Q₈	—	2	2	no	—
485	C₄⋊Q₈	—	2	2	no	—
486	#123	—	2	8	no	—
487	#123	—	2	8	no	—
488	C₂²⋊Q₈	—	2	8	no	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	2	no	—
492	C₂²⋊Q₈	—	4	1	no	—
493	#121	—	2	2	no	—
494	#121	—	2	2	no	—
495	#121	—	2	2	no	—
496	#121	D₄×C₂₃	1	4	yes	—
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	—	2	2	no	—
501	#117	—	2	2	no	—
502	#117	—	4	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	2	no	—
506	C₂×C₄⋊C₄	—	2	1	no	—
507	C₂×C₄⋊C₄	—	2	2	no	—
508	C₂×C₄⋊C₄	—	2	2	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
513	C₂×C₄⋊C₄	D₄×C₂₃	1	4	yes	—
514	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
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	D₄×C₂₃	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
529	C₂×C₄²	—	2	1	no	—
530	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
531	#107	—	2	2	no	—
532	#107	—	2	2	no	—
533	#107	—	2	2	no	—
534	#103	—	2	2	no	—
535	#103	—	2	2	no	—
536	#103	—	2	2	no	—
537	#102	—	2	2	no	—
538	#102	—	2	2	no	—
539	#102	—	4	1	no	—
540	C₂²⋊C₈	—	2	2	no	—
541	C₂²⋊C₈	—	2	2	no	—
542	C₂²⋊C₈	—	4	1	no	—
543	#95	—	2	1	no	—
544	#95	—	2	1	no	—
545	#95	—	2	1	no	—
546	#95	—	2	1	no	—
547	C₂₃	#25547	1	1	yes	characteristic, direct product factor, Sylow
548	C₂⁴	—	2	1	no	—
549	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
550	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
551	#41	—	4	32	no	—
552	C₂×Q₈	—	2	4	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	4	2	no	—
560	C₂×Q₈	—	4	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	2	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	—	4	2	no	—
572	C₂×D₄	—	4	2	no	—
573	C₂×D₄	—	4	2	no	—
574	C₂×D₄	—	4	2	no	—
575	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
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	—	4	2	no	—
597	C₂²×C₄	—	4	2	no	—
598	C₂²×C₄	—	4	2	no	—
599	C₂²×C₄	—	4	2	no	—
600	C₂²×C₄	—	4	2	no	—
601	C₂²×C₄	—	4	2	no	—
602	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
603	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
604	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
605	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
606	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
607	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
609	SD₁₆	—	4	4	no	—
610	M₁₆	—	4	4	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	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	#41×C₂₃	1	2	yes	complemented
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	1	no	—
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	—	4	2	no	—
636	C₄⋊C₄	—	4	2	no	—
637	C₄⋊C₄	—	4	2	no	—
638	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
639	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
640	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
641	C₄⋊C₄	#41×C₂₃	1	2	yes	complemented
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	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	C₄²	—	2	1	no	—
652	C₄²	—	2	1	no	—
653	C₄²	—	4	2	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	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	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	C₂₃×#120	1	2	yes	—
674	C₂³	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
675	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
676	Q₈	—	4	8	no	—
677	Q₈	—	4	1	no	—
678	Q₈	—	4	1	no	—
679	Q₈	—	4	1	no	—
680	Q₈	—	4	1	no	—
681	D₄	—	2	8	no	—
682	D₄	—	2	2	no	—
683	D₄	—	2	2	no	—
684	D₄	—	4	8	no	—
685	D₄	—	4	8	no	—
686	D₄	—	4	1	no	—
687	D₄	—	4	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	4	8	no	—
707	C₂×C₄	—	4	8	no	—
708	C₂×C₄	—	4	8	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	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	C₂₃×#120	1	2	yes	—
731	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
732	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
733	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
734	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
735	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
736	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
737	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
738	C₈	—	2	2	no	—
739	C₈	—	4	1	no	—
740	C₈	—	4	1	no	—
741	C₈	—	4	1	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	1	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	1	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	8	1	no	—
760	C₂²	—	8	1	no	—
761	C₂²	—	8	1	no	—
762	C₂²	—	8	1	no	—
763	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
764	C₂²	C₂₃×#546	1	1	yes	characteristic
765	C₂²	C₂₃×#547	1	1	yes	characteristic
766	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
767	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
768	C₂²	C₂₃×#578	1	1	yes	characteristic
769	C₂²	C₂₃×#578	1	1	yes	characteristic
770	C₄	—	2	2	no	—
771	C₄	—	2	2	no	—
772	C₄	—	4	1	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	1	no	—
777	C₄	—	4	2	no	—
778	C₄	—	8	1	no	—
779	C₄	—	8	1	no	—
780	C₄	—	8	1	no	—
781	C₄	C₂₃×#532	1	1	yes	characteristic
782	C₄	C₂₃×#537	1	1	yes	characteristic
783	C₄	C₂₃×#546	1	1	yes	characteristic
784	C₄	C₂₃×#547	1	1	yes	characteristic
785	C₂	—	4	2	no	—
786	C₂	—	4	2	no	—
787	C₂	—	8	2	no	—
788	C₂	C₂₃×#2430	1	1	yes	characteristic
789	C₂	C₂₃×#3003	1	1	yes	characteristic
790	C₂	C₂₃×#3011	1	1	yes	characteristic
791	C₂	C₂₃×#3308	1	1	yes	characteristic
792	C₂	C₂₃×#3330	1	1	yes	characteristic
793	C₂	C₂₃×#3343	1	1	yes	characteristic
794	C₂	C₂₃×#3353	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#547	C₂
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
2. C₂×C₂₃×#484	C₂	semidirect
3. C₂×C₂₃×#468	C₂	semidirect
4. C₂₃×#2415	C₂	semidirect
5. C₂₃×#2057	C₂	semidirect
6. C₂₃×#2033	C₂	semidirect
7. C₂₃×#2024	C₂	semidirect
8. C₂₃×#2000	C₂	semidirect
9. C₂₃×#1877	C₂	semidirect
10. C₂₃×#1875	C₂	semidirect
11. C₂₃×#1872	C₂	semidirect
12. C₂₃×#1870	C₂	semidirect
13. C₂₃×#1862	C₂	semidirect
14. C₂₃×#1852	C₂	semidirect
15. C₂₃×#1736	C₂	semidirect
224. C₂×C₈×C₂₃	#41	semidirect
243. C₄⋊C₄×C₂₃	#41	semidirect
256. #25547	C₂₃	direct (N × H)
346. C₂×#484	C₂×C₂₃	semidirect
347. C₂×#468	C₂×C₂₃	semidirect
348. #2415	C₂×C₂₃	semidirect
349. #2057	C₂×C₂₃	semidirect
350. #2033	C₂×C₂₃	semidirect
351. #2024	C₂×C₂₃	semidirect
352. #2000	C₂×C₂₃	semidirect
353. #1877	C₂×C₂₃	semidirect
354. #1875	C₂×C₂₃	semidirect
355. #1872	C₂×C₂₃	semidirect
356. #1870	C₂×C₂₃	semidirect
357. #1862	C₂×C₂₃	semidirect
358. #1852	C₂×C₂₃	semidirect
359. #1736	C₂×C₂₃	semidirect
547. C₂₃	#25547	direct (N × H)
622. C₂×C₈	#41×C₂₃	semidirect
641. C₄⋊C₄	#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#547	2
C₂×C₂₃×#484	2
C₂×C₂₃×#468	2
C₂₃×#2415	2
C₂₃×#2057	2
C₂₃×#2033	2
C₂₃×#2024	2
C₂₃×#2000	2
C₂₃×#1877	2
C₂₃×#1875	2
C₂₃×#1872	2
C₂₃×#1870	2
C₂₃×#1862	2
C₂₃×#1852	2
C₂₃×#1736	2
#25547	23

Subgroups — C23×#25547 #19173173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25547 #19173173