Subgroups — C₂₃×#22056 #19169682

Order 5888.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#447	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2324	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2309	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1972	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1936	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1934	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1926	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1925	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1875	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
23	C₂₃×#447	C₄	1	8	yes	complemented
24	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#390	—	2	1	no	—
39	C₂₃×#390	—	2	1	no	—
40	C₂₃×#390	—	2	1	no	—
41	C₂₃×#390	C₂²	1	1	yes	characteristic
42	C₂₃×#390	C₂²	1	1	yes	characteristic
43	C₂₃×#390	C₂²	1	1	yes	characteristic
44	C₂₃×#390	C₂²	1	1	yes	characteristic
45	C₂₃×#390	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#388	—	2	1	no	—
48	C₂₃×#386	—	2	1	no	—
49	C₂₃×#385	—	2	1	no	—
50	C₂₃×#380	C₂²	1	1	yes	characteristic
51	C₂₃×#379	—	2	1	no	—
52	C₂₃×#379	—	2	1	no	—
53	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
54	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
55	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
56	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
60	C₂⁵×C₂₃	—	2	1	no	—
61	C₂²×D₄×C₂₃	—	2	1	no	—
62	C₂²×D₄×C₂₃	—	2	1	no	—
63	C₂²×D₄×C₂₃	—	2	2	no	—
64	C₂²×D₄×C₂₃	—	4	1	no	—
65	C₂²×D₄×C₂₃	—	4	1	no	—
66	C₂²×D₄×C₂₃	—	4	1	no	—
67	C₂²×D₄×C₂₃	—	4	1	no	—
68	C₂²×D₄×C₂₃	C₂×C₄	1	4	yes	complemented
69	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₂₃	—	2	1	no	—
73	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
74	C₂×D₈×C₂₃	—	4	1	no	—
75	C₂×D₈×C₂₃	—	4	1	no	—
76	C₂×D₈×C₂₃	—	4	1	no	—
77	C₂×D₈×C₂₃	—	4	1	no	—
78	C₂×D₈×C₂₃	C₂×C₄	1	4	yes	—
79	C₂×D₈×C₂₃	C₂×C₄	1	4	yes	—
80	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
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	C₂₃×#121	—	2	2	no	—
85	C₂₃×#121	C₂×C₄	1	4	yes	—
86	C₄×D₄×C₂₃	—	4	1	no	—
87	C₄×D₄×C₂₃	—	4	1	no	—
88	C₂₃×#117	—	4	1	no	—
89	C₂₃×#117	—	4	1	no	—
90	C₂₃×#117	—	4	1	no	—
91	C₂₃×#117	—	4	1	no	—
92	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
93	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₂₃	—	2	1	no	—
117	C₂×C₄²×C₂₃	—	2	1	no	—
118	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
120	C₂₃×#107	—	4	1	no	—
121	C₂₃×#106	—	4	1	no	—
122	C₂₃×#102	—	4	1	no	—
123	C₂₃×#102	—	4	1	no	—
124	C₂₃×#102	—	4	1	no	—
125	C₂₃×#102	—	4	1	no	—
126	C₂₃×#102	—	4	1	no	—
127	C₂₃×#102	—	4	1	no	—
128	C₂₃×#102	C₂×C₄	1	4	yes	complemented
129	C₂₃×#102	C₂×C₄	1	4	yes	complemented
130	C₂₃×C₂²⋊C₈	—	2	2	no	—
131	C₂₃×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
132	C₂₃×#97	—	4	1	no	—
133	C₄×C₈×C₂₃	—	4	1	no	—
134	C₂₃×#95	—	2	1	no	—
135	C₂₃×#95	—	2	1	no	—
136	C₂₃×#95	—	2	1	no	—
137	C₂⁴×C₂₃	—	2	1	no	—
138	C₂⁴×C₂₃	—	2	1	no	—
139	C₂⁴×C₂₃	—	2	1	no	—
140	C₂⁴×C₂₃	—	2	4	no	—
141	C₂⁴×C₂₃	—	4	2	no	—
142	C₂⁴×C₂₃	—	4	2	no	—
143	C₂⁴×C₂₃	—	8	1	no	—
144	C₂⁴×C₂₃	—	8	1	no	—
145	C₂⁴×C₂₃	—	8	1	no	—
146	C₂⁴×C₂₃	—	8	1	no	—
147	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
148	C₂×D₄×C₂₃	—	2	4	no	—
149	C₂×D₄×C₂₃	—	2	4	no	—
150	C₂×D₄×C₂₃	—	2	1	no	—
151	C₂×D₄×C₂₃	—	2	1	no	—
152	C₂×D₄×C₂₃	—	2	1	no	—
153	C₂×D₄×C₂₃	—	2	1	no	—
154	C₂×D₄×C₂₃	—	2	1	no	—
155	C₂×D₄×C₂₃	—	2	1	no	—
156	C₂×D₄×C₂₃	—	2	1	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	—	4	4	no	—
166	C₂×D₄×C₂₃	—	4	4	no	—
167	C₂×D₄×C₂₃	—	4	2	no	—
168	C₂×D₄×C₂₃	—	4	2	no	—
169	C₂×D₄×C₂₃	—	4	4	no	—
170	C₂×D₄×C₂₃	—	4	4	no	—
171	C₂×D₄×C₂₃	—	8	1	no	—
172	C₂×D₄×C₂₃	—	8	1	no	—
173	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
174	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
175	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
176	C₂²×C₄×C₂₃	—	2	1	no	—
177	C₂²×C₄×C₂₃	—	2	1	no	—
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	1	no	—
183	C₂²×C₄×C₂₃	—	2	1	no	—
184	C₂²×C₄×C₂₃	—	2	1	no	—
185	C₂²×C₄×C₂₃	—	4	2	no	—
186	C₂²×C₄×C₂₃	—	8	1	no	—
187	C₂²×C₄×C₂₃	—	8	1	no	—
188	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
189	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₂₃	#41	1	2	yes	—
195	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
196	D₈×C₂₃	—	4	4	no	—
197	D₈×C₂₃	—	4	4	no	—
198	C₂×C₈×C₂₃	—	2	1	no	—
199	C₂×C₈×C₂₃	—	2	1	no	—
200	C₂×C₈×C₂₃	—	2	1	no	—
201	C₂×C₈×C₂₃	—	2	1	no	—
202	C₂×C₈×C₂₃	—	2	1	no	—
203	C₂×C₈×C₂₃	—	2	1	no	—
204	C₂×C₈×C₂₃	—	2	1	no	—
205	C₂×C₈×C₂₃	—	2	1	no	—
206	C₂×C₈×C₂₃	—	2	1	no	—
207	C₂×C₈×C₂₃	—	2	1	no	—
208	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
209	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
210	C₄⋊C₄×C₂₃	—	2	1	no	—
211	C₄⋊C₄×C₂₃	—	2	1	no	—
212	C₄⋊C₄×C₂₃	—	2	1	no	—
213	C₄⋊C₄×C₂₃	—	2	1	no	—
214	C₄⋊C₄×C₂₃	—	2	1	no	—
215	C₄⋊C₄×C₂₃	—	2	1	no	—
216	C₄⋊C₄×C₂₃	—	2	1	no	—
217	C₄⋊C₄×C₂₃	—	2	1	no	—
218	C₄⋊C₄×C₂₃	—	2	1	no	—
219	C₄⋊C₄×C₂₃	—	4	1	no	—
220	C₄⋊C₄×C₂₃	—	4	1	no	—
221	C₄⋊C₄×C₂₃	—	8	1	no	—
222	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
223	C₂²⋊C₄×C₂₃	—	2	4	no	—
224	C₂²⋊C₄×C₂₃	—	4	1	no	—
225	C₂²⋊C₄×C₂₃	—	4	1	no	—
226	C₂²⋊C₄×C₂₃	—	4	2	no	—
227	C₂²⋊C₄×C₂₃	—	4	2	no	—
228	C₂²⋊C₄×C₂₃	—	8	1	no	—
229	C₂²⋊C₄×C₂₃	—	8	1	no	—
230	C₂²⋊C₄×C₂₃	—	8	1	no	—
231	C₂²⋊C₄×C₂₃	—	8	1	no	—
232	C₂²⋊C₄×C₂₃	—	8	1	no	—
233	C₂²⋊C₄×C₂₃	—	8	1	no	—
234	C₂²⋊C₄×C₂₃	—	8	1	no	—
235	C₂²⋊C₄×C₂₃	—	8	1	no	—
236	C₂²⋊C₄×C₂₃	—	8	1	no	—
237	C₂²⋊C₄×C₂₃	—	8	1	no	—
238	C₂²⋊C₄×C₂₃	—	8	1	no	—
239	C₄²×C₂₃	—	2	1	no	—
240	C₄²×C₂₃	—	2	1	no	—
241	C₄²×C₂₃	—	2	1	no	—
242	C₄²×C₂₃	—	2	1	no	—
243	C₄²×C₂₃	—	4	2	no	—
244	C₄²×C₂₃	—	8	1	no	—
245	#22056	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
246	C₂³×C₂₃	—	2	1	no	—
247	C₂³×C₂₃	—	2	1	no	—
248	C₂³×C₂₃	—	2	1	no	—
249	C₂³×C₂₃	—	2	1	no	—
250	C₂³×C₂₃	—	2	1	no	—
251	C₂³×C₂₃	—	2	1	no	—
252	C₂³×C₂₃	—	2	2	no	—
253	C₂³×C₂₃	—	2	2	no	—
254	C₂³×C₂₃	—	2	2	no	—
255	C₂³×C₂₃	—	4	8	no	—
256	C₂³×C₂₃	—	4	1	no	—
257	C₂³×C₂₃	—	4	1	no	—
258	C₂³×C₂₃	—	4	1	no	—
259	C₂³×C₂₃	—	4	1	no	—
260	C₂³×C₂₃	—	4	1	no	—
261	C₂³×C₂₃	—	4	1	no	—
262	C₂³×C₂₃	—	4	1	no	—
263	C₂³×C₂₃	—	4	1	no	—
264	C₂³×C₂₃	—	4	1	no	—
265	C₂³×C₂₃	—	4	1	no	—
266	C₂³×C₂₃	—	4	1	no	—
267	C₂³×C₂₃	—	4	1	no	—
268	C₂³×C₂₃	—	4	1	no	—
269	C₂³×C₂₃	—	4	1	no	—
270	C₂³×C₂₃	—	4	1	no	—
271	C₂³×C₂₃	—	4	1	no	—
272	C₂³×C₂₃	—	4	1	no	—
273	C₂³×C₂₃	—	4	1	no	—
274	C₂³×C₂₃	—	8	4	no	—
275	C₂³×C₂₃	—	8	4	no	—
276	C₂³×C₂₃	—	8	4	no	—
277	C₂³×C₂₃	—	8	4	no	—
278	C₂³×C₂₃	—	8	4	no	—
279	C₂³×C₂₃	—	8	4	no	—
280	C₂³×C₂₃	C₄×D₄	1	2	yes	—
281	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
282	D₄×C₂₃	—	2	2	no	—
283	D₄×C₂₃	—	2	2	no	—
284	D₄×C₂₃	—	2	2	no	—
285	D₄×C₂₃	—	2	2	no	—
286	D₄×C₂₃	—	2	2	no	—
287	D₄×C₂₃	—	2	2	no	—
288	D₄×C₂₃	—	4	8	no	—
289	D₄×C₂₃	—	4	1	no	—
290	D₄×C₂₃	—	4	1	no	—
291	D₄×C₂₃	—	4	1	no	—
292	D₄×C₂₃	—	4	1	no	—
293	D₄×C₂₃	—	4	1	no	—
294	D₄×C₂₃	—	4	1	no	—
295	D₄×C₂₃	—	8	4	no	—
296	C₂×C₄×C₂₃	—	2	1	no	—
297	C₂×C₄×C₂₃	—	2	1	no	—
298	C₂×C₄×C₂₃	—	2	2	no	—
299	C₂×C₄×C₂₃	—	2	2	no	—
300	C₂×C₄×C₂₃	—	2	2	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	2	no	—
303	C₂×C₄×C₂₃	—	2	1	no	—
304	C₂×C₄×C₂₃	—	2	1	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	—	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	—	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	—	8	4	no	—
330	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
331	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
332	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
333	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
335	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
336	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
337	C₈×C₂₃	—	2	2	no	—
338	C₈×C₂₃	—	2	2	no	—
339	C₈×C₂₃	—	4	1	no	—
340	C₈×C₂₃	—	4	1	no	—
341	C₂×#447	C₂×C₂₃	1	1	yes	characteristic
342	#2324	C₂×C₂₃	1	1	yes	characteristic, complemented
343	#2309	C₂×C₂₃	1	1	yes	characteristic, complemented
344	#1972	C₂×C₂₃	1	1	yes	characteristic, complemented
345	#1970	C₂×C₂₃	1	1	yes	characteristic, complemented
346	#1936	C₂×C₂₃	1	1	yes	characteristic, complemented
347	#1934	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#1926	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#1925	C₂×C₂₃	1	1	yes	characteristic, complemented
350	#1879	C₂×C₂₃	1	1	yes	characteristic, complemented
351	#1879	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#1875	C₂×C₂₃	1	1	yes	characteristic, complemented
353	#1854	C₂×C₂₃	1	1	yes	characteristic, complemented
354	#1786	C₂×C₂₃	1	1	yes	characteristic, complemented
355	#1750	C₂×C₂₃	1	1	yes	characteristic, complemented
356	C₂²×C₂₃	—	2	2	no	—
357	C₂²×C₂₃	—	2	2	no	—
358	C₂²×C₂₃	—	2	2	no	—
359	C₂²×C₂₃	—	4	1	no	—
360	C₂²×C₂₃	—	4	1	no	—
361	C₂²×C₂₃	—	4	1	no	—
362	C₂²×C₂₃	—	4	1	no	—
363	C₂²×C₂₃	—	4	2	no	—
364	C₂²×C₂₃	—	4	2	no	—
365	C₂²×C₂₃	—	4	2	no	—
366	C₂²×C₂₃	—	4	2	no	—
367	C₂²×C₂₃	—	4	2	no	—
368	C₂²×C₂₃	—	4	2	no	—
369	C₂²×C₂₃	—	4	2	no	—
370	C₂²×C₂₃	—	4	2	no	—
371	C₂²×C₂₃	—	4	2	no	—
372	C₂²×C₂₃	—	8	16	no	—
373	C₂²×C₂₃	—	8	1	no	—
374	C₂²×C₂₃	—	8	1	no	—
375	C₂²×C₂₃	—	8	1	no	—
376	C₂²×C₂₃	—	8	1	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	—	8	1	no	—
382	C₂²×C₂₃	—	8	1	no	—
383	C₂²×C₂₃	—	8	1	no	—
384	C₂²×C₂₃	—	8	1	no	—
385	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
386	C₂²×C₂₃	#534	1	1	yes	characteristic
387	C₂²×C₂₃	#535	1	1	yes	characteristic
388	C₂²×C₂₃	#576	1	1	yes	characteristic
389	C₂²×C₂₃	#576	1	1	yes	characteristic
390	C₂²×C₂₃	#576	1	1	yes	characteristic
391	C₂²×C₂₃	#577	1	1	yes	characteristic
392	C₄×C₂₃	—	2	2	no	—
393	C₄×C₂₃	—	4	1	no	—
394	C₄×C₂₃	—	4	1	no	—
395	C₄×C₂₃	—	4	1	no	—
396	C₄×C₂₃	—	4	1	no	—
397	C₄×C₂₃	—	4	2	no	—
398	C₄×C₂₃	—	8	1	no	—
399	C₄×C₂₃	—	8	1	no	—
400	C₄×C₂₃	—	8	1	no	—
401	C₄×C₂₃	—	8	1	no	—
402	C₄×C₂₃	#518	1	1	yes	characteristic
403	C₄×C₂₃	#518	1	1	yes	characteristic
404	C₄×C₂₃	#538	1	1	yes	characteristic
405	C₄×C₂₃	#538	1	1	yes	characteristic
406	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
407	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
408	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
409	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
410	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
411	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
412	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
413	#447	C₄×C₂₃	1	8	yes	complemented
414	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
415	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
416	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
418	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
419	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
420	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
421	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
423	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
424	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
425	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
426	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
427	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
428	#390	—	2	1	no	—
429	#390	—	2	1	no	—
430	#390	—	2	1	no	—
431	#390	C₂²×C₂₃	1	1	yes	characteristic
432	#390	C₂²×C₂₃	1	1	yes	characteristic
433	#390	C₂²×C₂₃	1	1	yes	characteristic
434	#390	C₂²×C₂₃	1	1	yes	characteristic
435	#390	C₂²×C₂₃	1	1	yes	characteristic, complemented
436	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
437	#388	—	2	1	no	—
438	#386	—	2	1	no	—
439	#385	—	2	1	no	—
440	#380	C₂²×C₂₃	1	1	yes	characteristic
441	#379	—	2	1	no	—
442	#379	—	2	1	no	—
443	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
444	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
445	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
446	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
447	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
448	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
449	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
450	C₂×C₂₃	—	4	2	no	—
451	C₂×C₂₃	—	8	2	no	—
452	C₂×C₂₃	—	8	2	no	—
453	C₂×C₂₃	—	8	2	no	—
454	C₂×C₂₃	#2321	1	1	yes	characteristic
455	C₂×C₂₃	#2946	1	1	yes	characteristic
456	C₂×C₂₃	#2948	1	1	yes	characteristic
457	C₂×C₂₃	#3198	1	1	yes	characteristic
458	C₂×C₂₃	#3199	1	1	yes	characteristic
459	C₂×C₂₃	#3220	1	1	yes	characteristic
460	C₂×C₂₃	#3224	1	1	yes	characteristic
461	C₂⁵	—	2	1	no	—
462	C₂²×D₄	—	2	1	no	—
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	—	2	2	no	—
465	C₂²×D₄	—	4	1	no	—
466	C₂²×D₄	—	4	1	no	—
467	C₂²×D₄	—	4	1	no	—
468	C₂²×D₄	—	4	1	no	—
469	C₂²×D₄	C₂×C₄×C₂₃	1	4	yes	complemented
470	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
471	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
472	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
473	C₂³×C₄	—	2	1	no	—
474	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
475	C₂×D₈	—	4	1	no	—
476	C₂×D₈	—	4	1	no	—
477	C₂×D₈	—	4	1	no	—
478	C₂×D₈	—	4	1	no	—
479	C₂×D₈	C₂×C₄×C₂₃	1	4	yes	—
480	C₂×D₈	C₂×C₄×C₂₃	1	4	yes	—
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	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
485	#121	—	2	2	no	—
486	#121	C₂×C₄×C₂₃	1	4	yes	—
487	C₄×D₄	—	4	1	no	—
488	C₄×D₄	—	4	1	no	—
489	#117	—	4	1	no	—
490	#117	—	4	1	no	—
491	#117	—	4	1	no	—
492	#117	—	4	1	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
495	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	—	2	1	no	—
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	—	2	1	no	—
519	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
520	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
521	#107	—	4	1	no	—
522	#106	—	4	1	no	—
523	#102	—	4	1	no	—
524	#102	—	4	1	no	—
525	#102	—	4	1	no	—
526	#102	—	4	1	no	—
527	#102	—	4	1	no	—
528	#102	—	4	1	no	—
529	#102	C₂×C₄×C₂₃	1	4	yes	complemented
530	#102	C₂×C₄×C₂₃	1	4	yes	complemented
531	C₂²⋊C₈	—	2	2	no	—
532	C₂²⋊C₈	C₂×C₄×C₂₃	1	4	yes	complemented
533	#97	—	4	1	no	—
534	C₄×C₈	—	4	1	no	—
535	#95	—	2	1	no	—
536	#95	—	2	1	no	—
537	#95	—	2	1	no	—
538	C₂₃	#22056	1	1	yes	characteristic, direct product factor, Sylow
539	C₂⁴	—	2	1	no	—
540	C₂⁴	—	2	1	no	—
541	C₂⁴	—	2	1	no	—
542	C₂⁴	—	2	4	no	—
543	C₂⁴	—	4	2	no	—
544	C₂⁴	—	4	2	no	—
545	C₂⁴	—	8	1	no	—
546	C₂⁴	—	8	1	no	—
547	C₂⁴	—	8	1	no	—
548	C₂⁴	—	8	1	no	—
549	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	4	4	no	—
568	C₂×D₄	—	4	4	no	—
569	C₂×D₄	—	4	2	no	—
570	C₂×D₄	—	4	2	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂×D₄	—	4	4	no	—
573	C₂×D₄	—	8	1	no	—
574	C₂×D₄	—	8	1	no	—
575	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
576	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
577	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	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	—	4	2	no	—
588	C₂²×C₄	—	8	1	no	—
589	C₂²×C₄	—	8	1	no	—
590	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
591	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
596	C₂²×C₄	#41×C₂₃	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
598	D₈	—	4	4	no	—
599	D₈	—	4	4	no	—
600	C₂×C₈	—	2	1	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
611	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	4	1	no	—
622	C₄⋊C₄	—	4	1	no	—
623	C₄⋊C₄	—	8	1	no	—
624	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	4	1	no	—
627	C₂²⋊C₄	—	4	1	no	—
628	C₂²⋊C₄	—	4	2	no	—
629	C₂²⋊C₄	—	4	2	no	—
630	C₂²⋊C₄	—	8	1	no	—
631	C₂²⋊C₄	—	8	1	no	—
632	C₂²⋊C₄	—	8	1	no	—
633	C₂²⋊C₄	—	8	1	no	—
634	C₂²⋊C₄	—	8	1	no	—
635	C₂²⋊C₄	—	8	1	no	—
636	C₂²⋊C₄	—	8	1	no	—
637	C₂²⋊C₄	—	8	1	no	—
638	C₂²⋊C₄	—	8	1	no	—
639	C₂²⋊C₄	—	8	1	no	—
640	C₂²⋊C₄	—	8	1	no	—
641	C₄²	—	2	1	no	—
642	C₄²	—	2	1	no	—
643	C₄²	—	2	1	no	—
644	C₄²	—	2	1	no	—
645	C₄²	—	4	2	no	—
646	C₄²	—	8	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	4	8	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	4	1	no	—
663	C₂³	—	4	1	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	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	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	8	4	no	—
676	C₂³	—	8	4	no	—
677	C₂³	—	8	4	no	—
678	C₂³	—	8	4	no	—
679	C₂³	—	8	4	no	—
680	C₂³	—	8	4	no	—
681	C₂³	C₄×D₄×C₂₃	1	2	yes	—
682	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
683	D₄	—	2	2	no	—
684	D₄	—	2	2	no	—
685	D₄	—	2	2	no	—
686	D₄	—	2	2	no	—
687	D₄	—	2	2	no	—
688	D₄	—	2	2	no	—
689	D₄	—	4	8	no	—
690	D₄	—	4	1	no	—
691	D₄	—	4	1	no	—
692	D₄	—	4	1	no	—
693	D₄	—	4	1	no	—
694	D₄	—	4	1	no	—
695	D₄	—	4	1	no	—
696	D₄	—	8	4	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	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	—	8	4	no	—
731	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
732	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
733	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
734	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
735	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
736	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
737	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
738	C₈	—	2	2	no	—
739	C₈	—	2	2	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	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	8	16	no	—
759	C₂²	—	8	1	no	—
760	C₂²	—	8	1	no	—
761	C₂²	—	8	1	no	—
762	C₂²	—	8	1	no	—
763	C₂²	—	8	1	no	—
764	C₂²	—	8	1	no	—
765	C₂²	—	8	1	no	—
766	C₂²	—	8	1	no	—
767	C₂²	—	8	1	no	—
768	C₂²	—	8	1	no	—
769	C₂²	—	8	1	no	—
770	C₂²	—	8	1	no	—
771	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
772	C₂²	C₂₃×#534	1	1	yes	characteristic
773	C₂²	C₂₃×#535	1	1	yes	characteristic
774	C₂²	C₂₃×#576	1	1	yes	characteristic
775	C₂²	C₂₃×#576	1	1	yes	characteristic
776	C₂²	C₂₃×#576	1	1	yes	characteristic
777	C₂²	C₂₃×#577	1	1	yes	characteristic
778	C₄	—	2	2	no	—
779	C₄	—	4	1	no	—
780	C₄	—	4	1	no	—
781	C₄	—	4	1	no	—
782	C₄	—	4	1	no	—
783	C₄	—	4	2	no	—
784	C₄	—	8	1	no	—
785	C₄	—	8	1	no	—
786	C₄	—	8	1	no	—
787	C₄	—	8	1	no	—
788	C₄	C₂₃×#518	1	1	yes	characteristic
789	C₄	C₂₃×#518	1	1	yes	characteristic
790	C₄	C₂₃×#538	1	1	yes	characteristic
791	C₄	C₂₃×#538	1	1	yes	characteristic
792	C₂	—	4	2	no	—
793	C₂	—	8	2	no	—
794	C₂	—	8	2	no	—
795	C₂	—	8	2	no	—
796	C₂	C₂₃×#2321	1	1	yes	characteristic
797	C₂	C₂₃×#2946	1	1	yes	characteristic
798	C₂	C₂₃×#2948	1	1	yes	characteristic
799	C₂	C₂₃×#3198	1	1	yes	characteristic
800	C₂	C₂₃×#3199	1	1	yes	characteristic
801	C₂	C₂₃×#3220	1	1	yes	characteristic
802	C₂	C₂₃×#3224	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#447	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2324	C₂	semidirect
3. C₂₃×#2309	C₂	semidirect
4. C₂₃×#1972	C₂	semidirect
5. C₂₃×#1970	C₂	semidirect
6. C₂₃×#1936	C₂	semidirect
7. C₂₃×#1934	C₂	semidirect
8. C₂₃×#1926	C₂	semidirect
9. C₂₃×#1925	C₂	semidirect
10. C₂₃×#1879	C₂	semidirect
11. C₂₃×#1879	C₂	semidirect
12. C₂₃×#1875	C₂	semidirect
13. C₂₃×#1854	C₂	semidirect
14. C₂₃×#1786	C₂	semidirect
15. C₂₃×#1750	C₂	semidirect
20. C₂×C₄×D₄×C₂₃	C₂²	semidirect
23. C₂₃×#447	C₄	semidirect
24. C₂×C₂₃×#107	C₂²	semidirect
25. C₂×C₂₃×#106	C₂²	semidirect
32. C₂×C₂₃×#102	C₂²	semidirect
33. C₂×C₂₃×#102	C₂²	semidirect
36. C₂×C₂₃×#97	C₂²	semidirect
37. C₂×C₄×C₈×C₂₃	C₂²	semidirect
45. C₂₃×#390	C₂²	semidirect
46. C₂₃×#389	C₂²	semidirect
53. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
54. C₂₃×#340	C₂²	semidirect
55. C₂₃×#340	C₂²	semidirect
56. C₂₃×#340	C₂²	semidirect
57. C₂₃×#340	C₂²	semidirect
58. C₂₃×#336	C₂²	semidirect
59. C₂₃×#336	C₂²	semidirect
68. C₂²×D₄×C₂₃	C₂×C₄	semidirect
128. C₂₃×#102	C₂×C₄	semidirect
129. C₂₃×#102	C₂×C₄	semidirect
131. C₂₃×C₂²⋊C₈	C₂×C₄	semidirect
245. #22056	C₂₃	direct (N × H)
342. #2324	C₂×C₂₃	semidirect
343. #2309	C₂×C₂₃	semidirect
344. #1972	C₂×C₂₃	semidirect
345. #1970	C₂×C₂₃	semidirect
346. #1936	C₂×C₂₃	semidirect
347. #1934	C₂×C₂₃	semidirect
348. #1926	C₂×C₂₃	semidirect
349. #1925	C₂×C₂₃	semidirect
350. #1879	C₂×C₂₃	semidirect
351. #1879	C₂×C₂₃	semidirect
352. #1875	C₂×C₂₃	semidirect
353. #1854	C₂×C₂₃	semidirect
354. #1786	C₂×C₂₃	semidirect
355. #1750	C₂×C₂₃	semidirect
410. C₂×C₄×D₄	C₂²×C₂₃	semidirect
413. #447	C₄×C₂₃	semidirect
414. C₂×#107	C₂²×C₂₃	semidirect
415. C₂×#106	C₂²×C₂₃	semidirect
422. C₂×#102	C₂²×C₂₃	semidirect
423. C₂×#102	C₂²×C₂₃	semidirect
426. C₂×#97	C₂²×C₂₃	semidirect
427. C₂×C₄×C₈	C₂²×C₂₃	semidirect
435. #390	C₂²×C₂₃	semidirect
436. #389	C₂²×C₂₃	semidirect
443. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
444. #340	C₂²×C₂₃	semidirect
445. #340	C₂²×C₂₃	semidirect
446. #340	C₂²×C₂₃	semidirect
447. #340	C₂²×C₂₃	semidirect
448. #336	C₂²×C₂₃	semidirect
449. #336	C₂²×C₂₃	semidirect
469. C₂²×D₄	C₂×C₄×C₂₃	semidirect
529. #102	C₂×C₄×C₂₃	semidirect
530. #102	C₂×C₄×C₂₃	semidirect
532. C₂²⋊C₈	C₂×C₄×C₂₃	semidirect
538. C₂₃	#22056	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×#447	2
C₂₃×#2324	2
C₂₃×#2309	2
C₂₃×#1972	2
C₂₃×#1970	2
C₂₃×#1936	2
C₂₃×#1934	2
C₂₃×#1926	2
C₂₃×#1925	2
C₂₃×#1879	2
C₂₃×#1875	2
C₂₃×#1854	2
C₂₃×#1786	2
C₂₃×#1750	2
#22056	23

Subgroups — C23×#22056 #19169682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#22056 #19169682