Subgroups — C₂₃×#25156 #19172782

Order 5888.

1268 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×#461	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#450	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#450	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2429	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
7	C₂₃×#2065	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2013	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×#1880	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×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
28	C₂₃×#461	—	2	4	no	—
29	C₂₃×#450	—	2	4	no	—
30	C₂₃×#450	—	2	4	no	—
31	C₄×SD₁₆×C₂₃	—	2	4	no	—
32	C₂×C₂₃×#106	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×#103	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
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
42	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
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×#398	—	2	1	no	—
47	C₂₃×#396	—	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	—	2	1	no	—
52	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#388	—	2	1	no	—
54	C₂₃×#386	—	2	1	no	—
55	C₂₃×#386	—	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×Q₈×C₂₃	C₂³	1	1	yes	characteristic
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	2	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	C₂³×C₄×C₂₃	—	2	1	no	—
76	C₂³×C₄×C₂₃	—	2	1	no	—
77	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
78	C₂×SD₁₆×C₂₃	—	2	2	no	—
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	—	2	2	no	—
84	C₂×SD₁₆×C₂₃	—	2	2	no	—
85	C₂×SD₁₆×C₂₃	—	2	2	no	—
86	C₂×SD₁₆×C₂₃	—	2	2	no	—
87	C₂×SD₁₆×C₂₃	—	4	1	no	—
88	C₂×SD₁₆×C₂₃	—	4	1	no	—
89	C₂×SD₁₆×C₂₃	D₄	1	4	yes	—
90	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
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	C₂₃×C₄⋊Q₈	—	2	2	no	—
95	C₂₃×C₄⋊Q₈	—	4	1	no	—
96	C₂₃×C₂²⋊Q₈	—	2	2	no	—
97	C₂₃×C₂²⋊Q₈	—	2	2	no	—
98	C₂₃×C₂²⋊Q₈	—	4	1	no	—
99	C₂₃×C₂²⋊Q₈	—	4	1	no	—
100	C₄×Q₈×C₂₃	—	2	2	no	—
101	C₄×Q₈×C₂₃	—	4	1	no	—
102	C₄×D₄×C₂₃	—	2	2	no	—
103	C₄×D₄×C₂₃	—	2	2	no	—
104	C₄×D₄×C₂₃	—	4	1	no	—
105	C₄×D₄×C₂₃	—	4	1	no	—
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	1	no	—
110	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
111	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
112	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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×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	—	4	4	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×#106	—	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	—	2	2	no	—
136	C₂₃×#103	—	2	2	no	—
137	C₂₃×#103	—	4	1	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	—
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	—	4	2	no	—
155	C₂⁴×C₂₃	—	4	2	no	—
156	C₂⁴×C₂₃	—	4	2	no	—
157	C₂⁴×C₂₃	—	4	2	no	—
158	C₂⁴×C₂₃	—	8	1	no	—
159	C₂⁴×C₂₃	—	8	1	no	—
160	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
170	C₂×Q₈×C₂₃	—	2	1	no	—
171	C₂×Q₈×C₂₃	—	2	1	no	—
172	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
173	C₂×D₄×C₂₃	—	2	4	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	C₂×D₄	1	2	yes	—
189	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
190	C₂×D₄×C₂₃	#41	1	2	yes	—
191	C₂×D₄×C₂₃	#41	1	2	yes	—
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	—	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	—	4	2	no	—
205	C₂²×C₄×C₂₃	—	4	2	no	—
206	C₂²×C₄×C₂₃	—	4	2	no	—
207	C₂²×C₄×C₂₃	—	4	2	no	—
208	C₂²×C₄×C₂₃	—	8	1	no	—
209	C₂²×C₄×C₂₃	—	8	1	no	—
210	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
216	SD₁₆×C₂₃	—	2	8	no	—
217	SD₁₆×C₂₃	—	4	4	no	—
218	SD₁₆×C₂₃	—	4	4	no	—
219	SD₁₆×C₂₃	—	4	4	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	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
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	—	2	1	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	—	4	2	no	—
243	C₄⋊C₄×C₂₃	—	4	2	no	—
244	C₄⋊C₄×C₂₃	—	4	2	no	—
245	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
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	C₂²⋊C₄×C₂₃	—	8	1	no	—
256	C₂²⋊C₄×C₂₃	SD₁₆	1	4	yes	complemented
257	C₄²×C₂₃	—	2	1	no	—
258	C₄²×C₂₃	—	2	1	no	—
259	C₄²×C₂₃	—	2	1	no	—
260	C₄²×C₂₃	—	2	1	no	—
261	C₄²×C₂₃	—	4	2	no	—
262	#25156	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₂³×C₂₃	—	2	1	no	—
264	C₂³×C₂₃	—	2	2	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	—	2	1	no	—
270	C₂³×C₂₃	—	2	1	no	—
271	C₂³×C₂₃	—	2	1	no	—
272	C₂³×C₂₃	—	2	2	no	—
273	C₂³×C₂₃	—	4	8	no	—
274	C₂³×C₂₃	—	4	8	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	—	8	4	no	—
286	C₂³×C₂₃	—	8	4	no	—
287	C₂³×C₂₃	—	8	4	no	—
288	C₂³×C₂₃	—	8	4	no	—
289	C₂³×C₂₃	—	8	4	no	—
290	C₂³×C₂₃	C₂×SD₁₆	1	2	yes	—
291	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
292	Q₈×C₂₃	—	2	2	no	—
293	Q₈×C₂₃	—	2	2	no	—
294	Q₈×C₂₃	—	4	1	no	—
295	Q₈×C₂₃	—	4	1	no	—
296	Q₈×C₂₃	—	4	1	no	—
297	Q₈×C₂₃	—	4	1	no	—
298	Q₈×C₂₃	—	4	1	no	—
299	Q₈×C₂₃	—	4	1	no	—
300	D₄×C₂₃	—	2	2	no	—
301	D₄×C₂₃	—	2	2	no	—
302	D₄×C₂₃	—	2	2	no	—
303	D₄×C₂₃	—	2	2	no	—
304	D₄×C₂₃	—	2	2	no	—
305	D₄×C₂₃	—	4	8	no	—
306	D₄×C₂₃	—	4	1	no	—
307	D₄×C₂₃	—	4	1	no	—
308	D₄×C₂₃	#121	1	4	yes	—
309	C₂×C₄×C₂₃	—	2	1	no	—
310	C₂×C₄×C₂₃	—	2	1	no	—
311	C₂×C₄×C₂₃	—	2	1	no	—
312	C₂×C₄×C₂₃	—	2	1	no	—
313	C₂×C₄×C₂₃	—	2	1	no	—
314	C₂×C₄×C₂₃	—	2	1	no	—
315	C₂×C₄×C₂₃	—	2	1	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	2	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	—	2	1	no	—
322	C₂×C₄×C₂₃	—	2	1	no	—
323	C₂×C₄×C₂₃	—	2	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	—	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	—	8	4	no	—
345	C₂×C₄×C₂₃	—	8	4	no	—
346	C₂×C₄×C₂₃	C₂×SD₁₆	1	2	yes	—
347	C₂×C₄×C₂₃	C₂×SD₁₆	1	2	yes	—
348	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
351	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
352	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
353	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
354	C₈×C₂₃	—	2	2	no	—
355	C₈×C₂₃	—	2	2	no	—
356	C₈×C₂₃	—	4	1	no	—
357	C₈×C₂₃	—	4	1	no	—
358	C₂×#461	C₂×C₂₃	1	1	yes	characteristic, complemented
359	C₂×#450	C₂×C₂₃	1	1	yes	characteristic
360	C₂×#450	C₂×C₂₃	1	1	yes	characteristic
361	C₂×C₄×SD₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
362	#2429	C₂×C₂₃	1	1	yes	characteristic, complemented
363	D₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic
364	#2065	C₂×C₂₃	1	1	yes	characteristic, complemented
365	#2035	C₂×C₂₃	1	1	yes	characteristic, complemented
366	#2035	C₂×C₂₃	1	1	yes	characteristic, complemented
367	#2013	C₂×C₂₃	1	1	yes	characteristic, complemented
368	#1968	C₂×C₂₃	1	1	yes	characteristic, complemented
369	#1923	C₂×C₂₃	1	1	yes	characteristic, complemented
370	#1880	C₂×C₂₃	1	1	yes	characteristic, complemented
371	#1877	C₂×C₂₃	1	1	yes	characteristic, complemented
372	#1864	C₂×C₂₃	1	1	yes	characteristic, complemented
373	C₂²×C₂₃	—	2	2	no	—
374	C₂²×C₂₃	—	2	4	no	—
375	C₂²×C₂₃	—	2	2	no	—
376	C₂²×C₂₃	—	2	2	no	—
377	C₂²×C₂₃	—	4	2	no	—
378	C₂²×C₂₃	—	4	1	no	—
379	C₂²×C₂₃	—	4	2	no	—
380	C₂²×C₂₃	—	4	1	no	—
381	C₂²×C₂₃	—	4	1	no	—
382	C₂²×C₂₃	—	4	2	no	—
383	C₂²×C₂₃	—	4	1	no	—
384	C₂²×C₂₃	—	4	2	no	—
385	C₂²×C₂₃	—	4	2	no	—
386	C₂²×C₂₃	—	4	2	no	—
387	C₂²×C₂₃	—	4	2	no	—
388	C₂²×C₂₃	—	4	2	no	—
389	C₂²×C₂₃	—	4	2	no	—
390	C₂²×C₂₃	—	8	16	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	#525	1	1	yes	characteristic
396	C₂²×C₂₃	D₄²	1	1	yes	characteristic
397	C₂²×C₂₃	D₄²	1	1	yes	characteristic
398	C₂²×C₂₃	C₂²×SD₁₆	1	1	yes	characteristic
399	C₂²×C₂₃	#575	1	1	yes	characteristic
400	C₂²×C₂₃	#577	1	1	yes	characteristic
401	C₂²×C₂₃	#577	1	1	yes	characteristic
402	C₄×C₂₃	—	2	2	no	—
403	C₄×C₂₃	—	2	2	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	1	no	—
409	C₄×C₂₃	—	8	1	no	—
410	C₄×C₂₃	—	8	1	no	—
411	C₄×C₂₃	—	8	1	no	—
412	C₄×C₂₃	—	8	1	no	—
413	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
414	C₄×C₂₃	#538	1	1	yes	characteristic
415	C₄×C₂₃	#546	1	1	yes	characteristic
416	C₄×C₂₃	#546	1	1	yes	characteristic
417	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
418	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
419	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
420	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
421	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
423	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
424	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
425	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
426	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
428	C₂²×C₂²⋊C₄	—	2	1	no	—
429	#461	—	2	4	no	—
430	#450	—	2	4	no	—
431	#450	—	2	4	no	—
432	C₄×SD₁₆	—	2	4	no	—
433	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
434	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
435	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
436	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
437	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
438	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
439	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
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×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
445	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
447	#398	—	2	1	no	—
448	#396	—	2	1	no	—
449	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
450	#390	C₂²×C₂₃	1	1	yes	characteristic
451	#390	C₂²×C₂₃	1	1	yes	characteristic
452	#389	—	2	1	no	—
453	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
454	#388	—	2	1	no	—
455	#386	—	2	1	no	—
456	#386	—	2	1	no	—
457	#380	C₂²×C₂₃	1	1	yes	characteristic
458	#379	—	2	1	no	—
459	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
460	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
461	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
462	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
463	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
464	C₂×C₂₃	—	4	2	no	—
465	C₂×C₂₃	—	4	4	no	—
466	C₂×C₂₃	—	8	2	no	—
467	C₂×C₂₃	#2424	1	1	yes	characteristic
468	C₂×C₂₃	#3101	1	1	yes	characteristic
469	C₂×C₂₃	#3123	1	1	yes	characteristic
470	C₂×C₂₃	#3267	1	1	yes	characteristic
471	C₂×C₂₃	#3275	1	1	yes	characteristic
472	C₂×C₂₃	D₄×SD₁₆	1	1	yes	characteristic
473	C₂×C₂₃	D₄×SD₁₆	1	1	yes	characteristic
474	C₂⁵	—	2	1	no	—
475	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
476	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
477	C₂²×D₄	—	2	2	no	—
478	C₂²×D₄	—	2	2	no	—
479	C₂²×D₄	—	2	2	no	—
480	C₂²×D₄	—	2	2	no	—
481	C₂²×D₄	—	2	1	no	—
482	C₂²×D₄	—	4	1	no	—
483	C₂²×D₄	—	4	1	no	—
484	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
485	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
486	C₂³×C₄	—	2	1	no	—
487	C₂³×C₄	—	2	1	no	—
488	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
489	C₂×SD₁₆	—	2	2	no	—
490	C₂×SD₁₆	—	2	2	no	—
491	C₂×SD₁₆	—	2	2	no	—
492	C₂×SD₁₆	—	2	2	no	—
493	C₂×SD₁₆	—	2	2	no	—
494	C₂×SD₁₆	—	2	2	no	—
495	C₂×SD₁₆	—	2	2	no	—
496	C₂×SD₁₆	—	2	2	no	—
497	C₂×SD₁₆	—	2	2	no	—
498	C₂×SD₁₆	—	4	1	no	—
499	C₂×SD₁₆	—	4	1	no	—
500	C₂×SD₁₆	D₄×C₂₃	1	4	yes	—
501	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
502	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
504	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
505	C₄⋊Q₈	—	2	2	no	—
506	C₄⋊Q₈	—	4	1	no	—
507	C₂²⋊Q₈	—	2	2	no	—
508	C₂²⋊Q₈	—	2	2	no	—
509	C₂²⋊Q₈	—	4	1	no	—
510	C₂²⋊Q₈	—	4	1	no	—
511	C₄×Q₈	—	2	2	no	—
512	C₄×Q₈	—	4	1	no	—
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	—	2	2	no	—
515	C₄×D₄	—	4	1	no	—
516	C₄×D₄	—	4	1	no	—
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	1	no	—
521	C₂×C₄⋊C₄	—	2	1	no	—
522	C₂×C₄⋊C₄	—	2	1	no	—
523	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	—	2	1	no	—
528	C₂×C₂²⋊C₄	—	2	1	no	—
529	C₂×C₂²⋊C₄	—	2	1	no	—
530	C₂×C₂²⋊C₄	—	2	1	no	—
531	C₂×C₂²⋊C₄	—	2	1	no	—
532	C₂×C₂²⋊C₄	—	2	1	no	—
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	—	4	4	no	—
537	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
539	C₂×C₄²	—	2	1	no	—
540	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
542	#106	—	2	2	no	—
543	#106	—	4	1	no	—
544	C₄⋊C₈	—	2	2	no	—
545	#103	—	2	2	no	—
546	#103	—	2	2	no	—
547	#103	—	2	2	no	—
548	#103	—	4	1	no	—
549	#102	—	2	2	no	—
550	#102	—	2	2	no	—
551	#102	—	2	2	no	—
552	#102	D₄×C₂₃	1	4	yes	—
553	C₂²⋊C₈	—	2	2	no	—
554	C₂²⋊C₈	—	2	2	no	—
555	C₄×C₈	—	2	2	no	—
556	#95	—	2	1	no	—
557	#95	—	2	1	no	—
558	#95	—	2	1	no	—
559	#95	—	2	1	no	—
560	#95	D₄×C₂₃	1	1	yes	characteristic
561	#95	D₄×C₂₃	1	1	yes	characteristic
562	C₂₃	#25156	1	1	yes	characteristic, direct product factor, Sylow
563	C₂⁴	—	2	1	no	—
564	C₂⁴	—	2	4	no	—
565	C₂⁴	—	2	1	no	—
566	C₂⁴	—	4	2	no	—
567	C₂⁴	—	4	2	no	—
568	C₂⁴	—	4	2	no	—
569	C₂⁴	—	4	2	no	—
570	C₂⁴	—	8	1	no	—
571	C₂⁴	—	8	1	no	—
572	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
573	C₂×Q₈	—	2	1	no	—
574	C₂×Q₈	—	2	1	no	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	4	2	no	—
595	C₂×D₄	—	4	2	no	—
596	C₂×D₄	—	4	4	no	—
597	C₂×D₄	—	4	4	no	—
598	C₂×D₄	—	4	4	no	—
599	C₂×D₄	—	4	4	no	—
600	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
601	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
602	C₂×D₄	#41×C₂₃	1	2	yes	—
603	C₂×D₄	#41×C₂₃	1	2	yes	—
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	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	4	2	no	—
617	C₂²×C₄	—	4	2	no	—
618	C₂²×C₄	—	4	2	no	—
619	C₂²×C₄	—	4	2	no	—
620	C₂²×C₄	—	8	1	no	—
621	C₂²×C₄	—	8	1	no	—
622	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
626	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
628	SD₁₆	—	2	8	no	—
629	SD₁₆	—	4	4	no	—
630	SD₁₆	—	4	4	no	—
631	SD₁₆	—	4	4	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	—	2	1	no	—
638	C₂×C₈	—	2	1	no	—
639	C₂×C₈	—	2	1	no	—
640	C₂×C₈	—	2	1	no	—
641	C₂×C₈	—	2	1	no	—
642	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
643	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
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	—	2	1	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	2	no	—
653	C₄⋊C₄	—	4	2	no	—
654	C₄⋊C₄	—	4	2	no	—
655	C₄⋊C₄	—	4	2	no	—
656	C₄⋊C₄	—	4	2	no	—
657	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
658	C₂²⋊C₄	—	4	1	no	—
659	C₂²⋊C₄	—	4	2	no	—
660	C₂²⋊C₄	—	4	2	no	—
661	C₂²⋊C₄	—	4	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	C₂²⋊C₄	—	8	1	no	—
668	C₂²⋊C₄	SD₁₆×C₂₃	1	4	yes	complemented
669	C₄²	—	2	1	no	—
670	C₄²	—	2	1	no	—
671	C₄²	—	2	1	no	—
672	C₄²	—	2	1	no	—
673	C₄²	—	4	2	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	4	8	no	—
685	C₂³	—	4	8	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	—	8	4	no	—
697	C₂³	—	8	4	no	—
698	C₂³	—	8	4	no	—
699	C₂³	—	8	4	no	—
700	C₂³	—	8	4	no	—
701	C₂³	C₂×SD₁₆×C₂₃	1	2	yes	—
702	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
703	Q₈	—	2	2	no	—
704	Q₈	—	2	2	no	—
705	Q₈	—	4	1	no	—
706	Q₈	—	4	1	no	—
707	Q₈	—	4	1	no	—
708	Q₈	—	4	1	no	—
709	Q₈	—	4	1	no	—
710	Q₈	—	4	1	no	—
711	D₄	—	2	2	no	—
712	D₄	—	2	2	no	—
713	D₄	—	2	2	no	—
714	D₄	—	2	2	no	—
715	D₄	—	2	2	no	—
716	D₄	—	4	8	no	—
717	D₄	—	4	1	no	—
718	D₄	—	4	1	no	—
719	D₄	C₂₃×#121	1	4	yes	—
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	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	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	—	4	1	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	8	4	no	—
756	C₂×C₄	—	8	4	no	—
757	C₂×C₄	C₂×SD₁₆×C₂₃	1	2	yes	—
758	C₂×C₄	C₂×SD₁₆×C₂₃	1	2	yes	—
759	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
760	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
761	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
762	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
763	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
764	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
765	C₈	—	2	2	no	—
766	C₈	—	2	2	no	—
767	C₈	—	4	1	no	—
768	C₈	—	4	1	no	—
769	C₂²	—	2	4	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	8	16	no	—
787	C₂²	—	8	1	no	—
788	C₂²	—	8	1	no	—
789	C₂²	—	8	1	no	—
790	C₂²	—	8	1	no	—
791	C₂²	C₂₃×#525	1	1	yes	characteristic
792	C₂²	D₄²×C₂₃	1	1	yes	characteristic
793	C₂²	D₄²×C₂₃	1	1	yes	characteristic
794	C₂²	C₂²×SD₁₆×C₂₃	1	1	yes	characteristic
795	C₂²	C₂₃×#575	1	1	yes	characteristic
796	C₂²	C₂₃×#577	1	1	yes	characteristic
797	C₂²	C₂₃×#577	1	1	yes	characteristic
798	C₄	—	2	2	no	—
799	C₄	—	2	2	no	—
800	C₄	—	4	1	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	1	no	—
805	C₄	—	8	1	no	—
806	C₄	—	8	1	no	—
807	C₄	—	8	1	no	—
808	C₄	—	8	1	no	—
809	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
810	C₄	C₂₃×#538	1	1	yes	characteristic
811	C₄	C₂₃×#546	1	1	yes	characteristic
812	C₄	C₂₃×#546	1	1	yes	characteristic
813	C₂	—	4	2	no	—
814	C₂	—	4	4	no	—
815	C₂	—	8	2	no	—
816	C₂	C₂₃×#2424	1	1	yes	characteristic
817	C₂	C₂₃×#3101	1	1	yes	characteristic
818	C₂	C₂₃×#3123	1	1	yes	characteristic
819	C₂	C₂₃×#3267	1	1	yes	characteristic
820	C₂	C₂₃×#3275	1	1	yes	characteristic
821	C₂	D₄×SD₁₆×C₂₃	1	1	yes	characteristic
822	C₂	D₄×SD₁₆×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂³×D₄×C₂₃	C₂²
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×#461	C₂	semidirect
4. C₂×C₄×SD₁₆×C₂₃	C₂	semidirect
5. C₂₃×#2429	C₂	semidirect
7. C₂₃×#2065	C₂	semidirect
8. C₂₃×#2035	C₂	semidirect
9. C₂₃×#2035	C₂	semidirect
10. C₂₃×#2013	C₂	semidirect
11. C₂₃×#1968	C₂	semidirect
12. C₂₃×#1923	C₂	semidirect
13. C₂₃×#1880	C₂	semidirect
14. C₂₃×#1877	C₂	semidirect
15. C₂₃×#1864	C₂	semidirect
21. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
32. C₂×C₂₃×#106	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
37. C₂×C₂₃×#103	C₂²	semidirect
38. C₂×C₂₃×#103	C₂²	semidirect
45. C₂×C₄×C₈×C₂₃	C₂²	semidirect
48. C₂₃×#391	C₂²	semidirect
52. C₂₃×#389	C₂²	semidirect
59. C₂₃×#340	C₂²	semidirect
60. C₂₃×#340	C₂²	semidirect
61. C₂₃×#336	C₂²	semidirect
62. C₂₃×#336	C₂²	semidirect
256. C₂²⋊C₄×C₂₃	SD₁₆	semidirect
262. #25156	C₂₃	direct (N × H)
358. C₂×#461	C₂×C₂₃	semidirect
361. C₂×C₄×SD₁₆	C₂×C₂₃	semidirect
362. #2429	C₂×C₂₃	semidirect
364. #2065	C₂×C₂₃	semidirect
365. #2035	C₂×C₂₃	semidirect
366. #2035	C₂×C₂₃	semidirect
367. #2013	C₂×C₂₃	semidirect
368. #1968	C₂×C₂₃	semidirect
369. #1923	C₂×C₂₃	semidirect
370. #1880	C₂×C₂₃	semidirect
371. #1877	C₂×C₂₃	semidirect
372. #1864	C₂×C₂₃	semidirect
422. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
425. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
433. C₂×#106	C₂²×C₂₃	semidirect
434. C₂×#106	C₂²×C₂₃	semidirect
435. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
436. C₂×#103	C₂²×C₂₃	semidirect
437. C₂×#103	C₂²×C₂₃	semidirect
438. C₂×#103	C₂²×C₂₃	semidirect
439. C₂×#103	C₂²×C₂₃	semidirect
446. C₂×C₄×C₈	C₂²×C₂₃	semidirect
449. #391	C₂²×C₂₃	semidirect
453. #389	C₂²×C₂₃	semidirect
460. #340	C₂²×C₂₃	semidirect
461. #340	C₂²×C₂₃	semidirect
462. #336	C₂²×C₂₃	semidirect
463. #336	C₂²×C₂₃	semidirect
562. C₂₃	#25156	direct (N × H)
668. C₂²⋊C₄	SD₁₆×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×#461	2
C₂×C₂₃×#450	2
C₂×C₄×SD₁₆×C₂₃	2
C₂₃×#2429	2
D₄×C₂²⋊C₄×C₂₃	2
C₂₃×#2065	2
C₂₃×#2035	2
C₂₃×#2013	2
C₂₃×#1968	2
C₂₃×#1923	2
C₂₃×#1880	2
C₂₃×#1877	2
C₂₃×#1864	2
#25156	23

Subgroups — C23×#25156 #19172782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25156 #19172782