Subgroups — C₂₃×#26784 #19174410

Order 5888.

966 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2491	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2067	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2057	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1999	C₂	1	1	yes	maximal, characteristic
9	C₂₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1925	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1925	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×#1852	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×#124	—	2	1	no	—
19	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₂₃	—	2	1	no	—
22	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
24	C₂₃×#480	—	2	4	no	—
25	C₂₃×#474	—	2	4	no	—
26	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
41	C₂₃×#394	—	2	1	no	—
42	C₂₃×#393	—	2	1	no	—
43	C₂₃×#390	C₂²	1	1	yes	characteristic
44	C₂₃×#390	C₂²	1	1	yes	characteristic
45	C₂₃×#390	C₂²	1	1	yes	characteristic
46	C₂₃×#389	C₂²	1	1	yes	characteristic
47	C₂₃×#388	—	2	1	no	—
48	C₂₃×#388	—	2	1	no	—
49	C₂₃×#386	—	2	1	no	—
50	C₂₃×#385	—	2	1	no	—
51	C₂₃×#380	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₂₃	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×#336	C₂²	1	1	yes	characteristic
60	C₂₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₂₃	—	2	1	no	—
62	C₂²×D₄×C₂₃	—	2	1	no	—
63	C₂²×D₄×C₂₃	—	2	1	no	—
64	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₂₃	—	2	1	no	—
67	C₂³×C₄×C₂₃	—	2	1	no	—
68	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
69	C₂×D₈×C₂₃	—	2	2	no	—
70	C₂×D₈×C₂₃	—	2	2	no	—
71	C₂×D₈×C₂₃	—	4	1	no	—
72	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
76	C₂₃×C₄⋊Q₈	—	2	2	no	—
77	C₂₃×C₄⋊Q₈	—	4	1	no	—
78	C₂₃×#124	—	4	4	no	—
79	C₂₃×#121	—	2	2	no	—
80	C₂₃×#121	—	2	2	no	—
81	C₂₃×#121	—	2	2	no	—
82	C₂₃×#121	—	4	1	no	—
83	C₄×D₄×C₂₃	—	2	2	no	—
84	C₄×D₄×C₂₃	—	4	1	no	—
85	C₄×D₄×C₂₃	—	4	4	no	—
86	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
87	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
88	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
89	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
90	C₂×C₄⋊C₄×C₂₃	—	4	1	no	—
91	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₂₃	C₂³	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×C₂²⋊C₄×C₂₃	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
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	D₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₂₃	—	2	1	no	—
110	C₂×C₄²×C₂₃	—	2	1	no	—
111	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
113	C₂₃×#107	—	2	2	no	—
114	C₂₃×#107	—	2	2	no	—
115	C₂₃×#107	—	2	2	no	—
116	C₂₃×#107	—	4	1	no	—
117	C₂₃×#107	D₄	1	4	yes	complemented
118	C₂₃×C₄⋊C₈	—	2	2	no	—
119	C₂₃×#102	—	2	2	no	—
120	C₂₃×#102	—	2	2	no	—
121	C₂₃×#102	—	2	2	no	—
122	C₂₃×#102	—	2	2	no	—
123	C₂₃×#102	—	2	2	no	—
124	C₂₃×#102	—	2	2	no	—
125	C₂₃×C₂²⋊C₈	—	2	2	no	—
126	C₂₃×C₂²⋊C₈	—	2	2	no	—
127	C₄×C₈×C₂₃	—	2	2	no	—
128	C₂₃×#95	—	2	1	no	—
129	C₂₃×#95	—	2	1	no	—
130	C₂₃×#95	—	2	1	no	—
131	C₂₃×#95	—	2	1	no	—
132	C₂₃×#95	D₄	1	1	yes	characteristic
133	C₂₃×#95	D₄	1	1	yes	characteristic
134	C₂⁴×C₂₃	—	2	1	no	—
135	C₂⁴×C₂₃	—	2	1	no	—
136	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
137	C₂×Q₈×C₂₃	—	4	2	no	—
138	C₂×Q₈×C₂₃	—	4	2	no	—
139	C₂×Q₈×C₂₃	—	8	1	no	—
140	C₂×D₄×C₂₃	—	2	4	no	—
141	C₂×D₄×C₂₃	—	2	1	no	—
142	C₂×D₄×C₂₃	—	2	1	no	—
143	C₂×D₄×C₂₃	—	2	1	no	—
144	C₂×D₄×C₂₃	—	2	1	no	—
145	C₂×D₄×C₂₃	—	2	1	no	—
146	C₂×D₄×C₂₃	—	2	1	no	—
147	C₂×D₄×C₂₃	—	2	1	no	—
148	C₂×D₄×C₂₃	—	2	1	no	—
149	C₂×D₄×C₂₃	—	2	1	no	—
150	C₂×D₄×C₂₃	—	2	1	no	—
151	C₂×D₄×C₂₃	—	2	1	no	—
152	C₂×D₄×C₂₃	—	4	2	no	—
153	C₂×D₄×C₂₃	—	4	2	no	—
154	C₂×D₄×C₂₃	—	4	2	no	—
155	C₂×D₄×C₂₃	—	4	2	no	—
156	C₂×D₄×C₂₃	—	8	1	no	—
157	C₂×D₄×C₂₃	#41	1	2	yes	—
158	C₂²×C₄×C₂₃	—	2	1	no	—
159	C₂²×C₄×C₂₃	—	2	1	no	—
160	C₂²×C₄×C₂₃	—	2	1	no	—
161	C₂²×C₄×C₂₃	—	2	1	no	—
162	C₂²×C₄×C₂₃	—	2	1	no	—
163	C₂²×C₄×C₂₃	—	2	1	no	—
164	C₂²×C₄×C₂₃	—	2	1	no	—
165	C₂²×C₄×C₂₃	—	2	1	no	—
166	C₂²×C₄×C₂₃	—	2	1	no	—
167	C₂²×C₄×C₂₃	—	2	1	no	—
168	C₂²×C₄×C₂₃	—	2	1	no	—
169	C₂²×C₄×C₂₃	—	2	1	no	—
170	C₂²×C₄×C₂₃	—	4	2	no	—
171	C₂²×C₄×C₂₃	—	4	2	no	—
172	C₂²×C₄×C₂₃	—	4	2	no	—
173	C₂²×C₄×C₂₃	—	4	2	no	—
174	C₂²×C₄×C₂₃	—	8	1	no	—
175	C₂²×C₄×C₂₃	—	8	1	no	—
176	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
182	D₈×C₂₃	—	4	4	no	—
183	C₂×C₈×C₂₃	—	2	1	no	—
184	C₂×C₈×C₂₃	—	2	1	no	—
185	C₂×C₈×C₂₃	—	2	1	no	—
186	C₂×C₈×C₂₃	—	2	1	no	—
187	C₂×C₈×C₂₃	—	2	1	no	—
188	C₂×C₈×C₂₃	—	2	1	no	—
189	C₂×C₈×C₂₃	—	2	1	no	—
190	C₂×C₈×C₂₃	—	2	1	no	—
191	C₂×C₈×C₂₃	—	2	1	no	—
192	C₂×C₈×C₂₃	—	2	1	no	—
193	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
194	C₂×C₈×C₂₃	#41	1	2	yes	—
195	C₄⋊C₄×C₂₃	—	2	1	no	—
196	C₄⋊C₄×C₂₃	—	2	1	no	—
197	C₄⋊C₄×C₂₃	—	2	1	no	—
198	C₄⋊C₄×C₂₃	—	2	1	no	—
199	C₄⋊C₄×C₂₃	—	2	1	no	—
200	C₄⋊C₄×C₂₃	—	2	1	no	—
201	C₄⋊C₄×C₂₃	—	2	1	no	—
202	C₄⋊C₄×C₂₃	—	2	1	no	—
203	C₄⋊C₄×C₂₃	—	2	1	no	—
204	C₄⋊C₄×C₂₃	—	4	2	no	—
205	C₄⋊C₄×C₂₃	—	4	2	no	—
206	C₄⋊C₄×C₂₃	—	4	2	no	—
207	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
208	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
209	C₄⋊C₄×C₂₃	#41	1	2	yes	—
210	C₂²⋊C₄×C₂₃	—	2	4	no	—
211	C₂²⋊C₄×C₂₃	—	4	1	no	—
212	C₂²⋊C₄×C₂₃	—	4	2	no	—
213	C₂²⋊C₄×C₂₃	—	4	2	no	—
214	C₂²⋊C₄×C₂₃	—	4	2	no	—
215	C₂²⋊C₄×C₂₃	—	4	2	no	—
216	C₂²⋊C₄×C₂₃	—	4	2	no	—
217	C₂²⋊C₄×C₂₃	—	4	2	no	—
218	C₂²⋊C₄×C₂₃	—	4	2	no	—
219	C₂²⋊C₄×C₂₃	—	8	1	no	—
220	C₂²⋊C₄×C₂₃	—	8	1	no	—
221	C₂²⋊C₄×C₂₃	D₈	1	4	yes	complemented
222	C₄²×C₂₃	—	2	1	no	—
223	C₄²×C₂₃	—	2	1	no	—
224	C₄²×C₂₃	—	2	1	no	—
225	C₄²×C₂₃	—	2	1	no	—
226	C₄²×C₂₃	—	4	2	no	—
227	C₄²×C₂₃	—	4	2	no	—
228	#26784	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂³×C₂₃	—	2	1	no	—
230	C₂³×C₂₃	—	2	1	no	—
231	C₂³×C₂₃	—	2	1	no	—
232	C₂³×C₂₃	—	2	1	no	—
233	C₂³×C₂₃	—	2	1	no	—
234	C₂³×C₂₃	—	2	1	no	—
235	C₂³×C₂₃	—	2	2	no	—
236	C₂³×C₂₃	—	4	1	no	—
237	C₂³×C₂₃	—	4	1	no	—
238	C₂³×C₂₃	—	4	1	no	—
239	C₂³×C₂₃	—	4	1	no	—
240	C₂³×C₂₃	—	4	1	no	—
241	C₂³×C₂₃	—	4	1	no	—
242	C₂³×C₂₃	—	4	1	no	—
243	C₂³×C₂₃	—	4	1	no	—
244	C₂³×C₂₃	—	4	1	no	—
245	C₂³×C₂₃	—	4	1	no	—
246	C₂³×C₂₃	—	4	1	no	—
247	C₂³×C₂₃	—	4	1	no	—
248	C₂³×C₂₃	—	4	1	no	—
249	C₂³×C₂₃	C₂×D₈	1	2	yes	—
250	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
251	Q₈×C₂₃	—	8	4	no	—
252	D₄×C₂₃	—	2	2	no	—
253	D₄×C₂₃	—	2	2	no	—
254	D₄×C₂₃	—	4	8	no	—
255	D₄×C₂₃	—	4	1	no	—
256	D₄×C₂₃	—	4	1	no	—
257	D₄×C₂₃	—	4	1	no	—
258	D₄×C₂₃	—	4	1	no	—
259	D₄×C₂₃	—	4	1	no	—
260	D₄×C₂₃	—	4	1	no	—
261	D₄×C₂₃	—	8	4	no	—
262	C₂×C₄×C₂₃	—	2	1	no	—
263	C₂×C₄×C₂₃	—	2	1	no	—
264	C₂×C₄×C₂₃	—	2	1	no	—
265	C₂×C₄×C₂₃	—	2	1	no	—
266	C₂×C₄×C₂₃	—	2	1	no	—
267	C₂×C₄×C₂₃	—	2	2	no	—
268	C₂×C₄×C₂₃	—	2	1	no	—
269	C₂×C₄×C₂₃	—	2	1	no	—
270	C₂×C₄×C₂₃	—	2	2	no	—
271	C₂×C₄×C₂₃	—	2	2	no	—
272	C₂×C₄×C₂₃	—	2	1	no	—
273	C₂×C₄×C₂₃	—	2	1	no	—
274	C₂×C₄×C₂₃	—	2	1	no	—
275	C₂×C₄×C₂₃	—	2	1	no	—
276	C₂×C₄×C₂₃	—	2	1	no	—
277	C₂×C₄×C₂₃	—	2	1	no	—
278	C₂×C₄×C₂₃	—	4	1	no	—
279	C₂×C₄×C₂₃	—	4	1	no	—
280	C₂×C₄×C₂₃	—	4	1	no	—
281	C₂×C₄×C₂₃	—	4	1	no	—
282	C₂×C₄×C₂₃	—	4	1	no	—
283	C₂×C₄×C₂₃	—	4	1	no	—
284	C₂×C₄×C₂₃	—	4	1	no	—
285	C₂×C₄×C₂₃	—	4	1	no	—
286	C₂×C₄×C₂₃	—	4	1	no	—
287	C₂×C₄×C₂₃	—	4	1	no	—
288	C₂×C₄×C₂₃	—	4	1	no	—
289	C₂×C₄×C₂₃	—	4	1	no	—
290	C₂×C₄×C₂₃	—	4	1	no	—
291	C₂×C₄×C₂₃	—	4	1	no	—
292	C₂×C₄×C₂₃	—	4	1	no	—
293	C₂×C₄×C₂₃	—	4	1	no	—
294	C₂×C₄×C₂₃	—	4	1	no	—
295	C₂×C₄×C₂₃	—	4	1	no	—
296	C₂×C₄×C₂₃	—	4	1	no	—
297	C₂×C₄×C₂₃	—	8	4	no	—
298	C₂×C₄×C₂₃	—	8	4	no	—
299	C₂×C₄×C₂₃	C₂×D₈	1	2	yes	—
300	C₂×C₄×C₂₃	C₂×D₈	1	2	yes	—
301	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
303	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
304	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
305	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
306	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
307	C₈×C₂₃	—	2	2	no	—
308	C₈×C₂₃	—	2	2	no	—
309	C₈×C₂₃	—	4	1	no	—
310	C₈×C₂₃	—	4	1	no	—
311	C₂×#480	C₂×C₂₃	1	1	yes	characteristic, complemented
312	C₂×#474	C₂×C₂₃	1	1	yes	characteristic, complemented
313	#2491	C₂×C₂₃	1	1	yes	characteristic, complemented
314	#2361	C₂×C₂₃	1	1	yes	characteristic, complemented
315	#2067	C₂×C₂₃	1	1	yes	characteristic, complemented
316	#2057	C₂×C₂₃	1	1	yes	characteristic, complemented
317	#2033	C₂×C₂₃	1	1	yes	characteristic, complemented
318	#1999	C₂×C₂₃	1	1	yes	characteristic
319	#1970	C₂×C₂₃	1	1	yes	characteristic, complemented
320	#1925	C₂×C₂₃	1	1	yes	characteristic, complemented
321	#1925	C₂×C₂₃	1	1	yes	characteristic, complemented
322	#1923	C₂×C₂₃	1	1	yes	characteristic, complemented
323	#1879	C₂×C₂₃	1	1	yes	characteristic, complemented
324	#1852	C₂×C₂₃	1	1	yes	characteristic, complemented
325	C₄×#107	C₂×C₂₃	1	1	yes	characteristic, complemented
326	C₂²×C₂₃	—	2	2	no	—
327	C₂²×C₂₃	—	2	2	no	—
328	C₂²×C₂₃	—	2	2	no	—
329	C₂²×C₂₃	—	4	1	no	—
330	C₂²×C₂₃	—	4	1	no	—
331	C₂²×C₂₃	—	4	1	no	—
332	C₂²×C₂₃	—	4	1	no	—
333	C₂²×C₂₃	—	4	2	no	—
334	C₂²×C₂₃	—	4	2	no	—
335	C₂²×C₂₃	—	4	2	no	—
336	C₂²×C₂₃	—	8	1	no	—
337	C₂²×C₂₃	—	8	1	no	—
338	C₂²×C₂₃	—	8	1	no	—
339	C₂²×C₂₃	—	8	1	no	—
340	C₂²×C₂₃	—	8	1	no	—
341	C₂²×C₂₃	—	8	1	no	—
342	C₂²×C₂₃	—	8	1	no	—
343	C₂²×C₂₃	—	8	1	no	—
344	C₂²×C₂₃	—	8	1	no	—
345	C₂²×C₂₃	—	8	1	no	—
346	C₂²×C₂₃	—	8	1	no	—
347	C₂²×C₂₃	#525	1	1	yes	characteristic
348	C₂²×C₂₃	D₄²	1	1	yes	characteristic
349	C₂²×C₂₃	#547	1	1	yes	characteristic
350	C₂²×C₂₃	C₂²×D₈	1	1	yes	characteristic
351	C₂²×C₂₃	#575	1	1	yes	characteristic
352	C₂²×C₂₃	#576	1	1	yes	characteristic
353	C₂²×C₂₃	#578	1	1	yes	characteristic
354	C₄×C₂₃	—	2	2	no	—
355	C₄×C₂₃	—	2	2	no	—
356	C₄×C₂₃	—	4	1	no	—
357	C₄×C₂₃	—	4	2	no	—
358	C₄×C₂₃	—	4	1	no	—
359	C₄×C₂₃	—	4	1	no	—
360	C₄×C₂₃	—	4	2	no	—
361	C₄×C₂₃	—	4	2	no	—
362	C₄×C₂₃	—	8	1	no	—
363	C₄×C₂₃	—	8	1	no	—
364	C₄×C₂₃	—	8	1	no	—
365	C₄×C₂₃	#532	1	1	yes	characteristic
366	C₄×C₂₃	#542	1	1	yes	characteristic
367	C₄×C₂₃	#548	1	1	yes	characteristic
368	C₄×C₂₃	#551	1	1	yes	characteristic
369	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
370	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
371	C₂×#124	—	2	1	no	—
372	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
373	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
374	C₂×C₄×D₄	—	2	1	no	—
375	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
376	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
377	#480	—	2	4	no	—
378	#474	—	2	4	no	—
379	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
380	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
381	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
382	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
383	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
384	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
385	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
386	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
387	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
388	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
389	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
390	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
391	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
392	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
393	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
394	#394	—	2	1	no	—
395	#393	—	2	1	no	—
396	#390	C₂²×C₂₃	1	1	yes	characteristic
397	#390	C₂²×C₂₃	1	1	yes	characteristic
398	#390	C₂²×C₂₃	1	1	yes	characteristic
399	#389	C₂²×C₂₃	1	1	yes	characteristic
400	#388	—	2	1	no	—
401	#388	—	2	1	no	—
402	#386	—	2	1	no	—
403	#385	—	2	1	no	—
404	#380	C₂²×C₂₃	1	1	yes	characteristic
405	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
406	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
407	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
408	#340	C₂²×C₂₃	1	1	yes	characteristic
409	#340	C₂²×C₂₃	1	1	yes	characteristic
410	#340	C₂²×C₂₃	1	1	yes	characteristic
411	#340	C₂²×C₂₃	1	1	yes	characteristic
412	#336	C₂²×C₂₃	1	1	yes	characteristic
413	#336	C₂²×C₂₃	1	1	yes	characteristic
414	C₂×C₂₃	—	4	2	no	—
415	C₂×C₂₃	—	8	2	no	—
416	C₂×C₂₃	—	16	1	no	—
417	C₂×C₂₃	#2461	1	1	yes	characteristic
418	C₂×C₂₃	#3100	1	1	yes	characteristic
419	C₂×C₂₃	#3124	1	1	yes	characteristic
420	C₂×C₂₃	#3277	1	1	yes	characteristic
421	C₂×C₂₃	D₄×D₈	1	1	yes	characteristic
422	C₂×C₂₃	#3334	1	1	yes	characteristic
423	C₂×C₂₃	#3347	1	1	yes	characteristic
424	C₂²×Q₈	—	2	1	no	—
425	C₂²×D₄	—	2	1	no	—
426	C₂²×D₄	—	2	1	no	—
427	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
428	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
429	C₂³×C₄	—	2	1	no	—
430	C₂³×C₄	—	2	1	no	—
431	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
432	C₂×D₈	—	2	2	no	—
433	C₂×D₈	—	2	2	no	—
434	C₂×D₈	—	4	1	no	—
435	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
436	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
437	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
438	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
439	C₄⋊Q₈	—	2	2	no	—
440	C₄⋊Q₈	—	4	1	no	—
441	#124	—	4	4	no	—
442	#121	—	2	2	no	—
443	#121	—	2	2	no	—
444	#121	—	2	2	no	—
445	#121	—	4	1	no	—
446	C₄×D₄	—	2	2	no	—
447	C₄×D₄	—	4	1	no	—
448	C₄×D₄	—	4	4	no	—
449	C₂×C₄⋊C₄	—	2	2	no	—
450	C₂×C₄⋊C₄	—	2	1	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	—	4	1	no	—
454	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₂²⋊C₄	—	2	1	no	—
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
471	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
472	C₂×C₄²	—	2	1	no	—
473	C₂×C₄²	—	2	1	no	—
474	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
475	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
476	#107	—	2	2	no	—
477	#107	—	2	2	no	—
478	#107	—	2	2	no	—
479	#107	—	4	1	no	—
480	#107	D₄×C₂₃	1	4	yes	complemented
481	C₄⋊C₈	—	2	2	no	—
482	#102	—	2	2	no	—
483	#102	—	2	2	no	—
484	#102	—	2	2	no	—
485	#102	—	2	2	no	—
486	#102	—	2	2	no	—
487	#102	—	2	2	no	—
488	C₂²⋊C₈	—	2	2	no	—
489	C₂²⋊C₈	—	2	2	no	—
490	C₄×C₈	—	2	2	no	—
491	#95	—	2	1	no	—
492	#95	—	2	1	no	—
493	#95	—	2	1	no	—
494	#95	—	2	1	no	—
495	#95	D₄×C₂₃	1	1	yes	characteristic
496	#95	D₄×C₂₃	1	1	yes	characteristic
497	C₂₃	#26784	1	1	yes	characteristic, direct product factor, Sylow
498	C₂⁴	—	2	1	no	—
499	C₂⁴	—	2	1	no	—
500	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
501	C₂×Q₈	—	4	2	no	—
502	C₂×Q₈	—	4	2	no	—
503	C₂×Q₈	—	8	1	no	—
504	C₂×D₄	—	2	4	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	4	2	no	—
517	C₂×D₄	—	4	2	no	—
518	C₂×D₄	—	4	2	no	—
519	C₂×D₄	—	4	2	no	—
520	C₂×D₄	—	8	1	no	—
521	C₂×D₄	#41×C₂₃	1	2	yes	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	4	2	no	—
535	C₂²×C₄	—	4	2	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	—	4	2	no	—
538	C₂²×C₄	—	8	1	no	—
539	C₂²×C₄	—	8	1	no	—
540	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
541	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
542	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
543	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
544	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
545	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
546	D₈	—	4	4	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
558	C₂×C₈	#41×C₂₃	1	2	yes	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	4	2	no	—
569	C₄⋊C₄	—	4	2	no	—
570	C₄⋊C₄	—	4	2	no	—
571	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
572	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
573	C₄⋊C₄	#41×C₂₃	1	2	yes	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	4	1	no	—
576	C₂²⋊C₄	—	4	2	no	—
577	C₂²⋊C₄	—	4	2	no	—
578	C₂²⋊C₄	—	4	2	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	—	4	2	no	—
581	C₂²⋊C₄	—	4	2	no	—
582	C₂²⋊C₄	—	4	2	no	—
583	C₂²⋊C₄	—	8	1	no	—
584	C₂²⋊C₄	—	8	1	no	—
585	C₂²⋊C₄	D₈×C₂₃	1	4	yes	complemented
586	C₄²	—	2	1	no	—
587	C₄²	—	2	1	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	2	1	no	—
590	C₄²	—	4	2	no	—
591	C₄²	—	4	2	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	4	1	no	—
600	C₂³	—	4	1	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	—	4	1	no	—
610	C₂³	—	4	1	no	—
611	C₂³	—	4	1	no	—
612	C₂³	C₂×D₈×C₂₃	1	2	yes	—
613	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
614	Q₈	—	8	4	no	—
615	D₄	—	2	2	no	—
616	D₄	—	2	2	no	—
617	D₄	—	4	8	no	—
618	D₄	—	4	1	no	—
619	D₄	—	4	1	no	—
620	D₄	—	4	1	no	—
621	D₄	—	4	1	no	—
622	D₄	—	4	1	no	—
623	D₄	—	4	1	no	—
624	D₄	—	8	4	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	8	4	no	—
661	C₂×C₄	—	8	4	no	—
662	C₂×C₄	C₂×D₈×C₂₃	1	2	yes	—
663	C₂×C₄	C₂×D₈×C₂₃	1	2	yes	—
664	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
665	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
666	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
667	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
668	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
669	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
670	C₈	—	2	2	no	—
671	C₈	—	2	2	no	—
672	C₈	—	4	1	no	—
673	C₈	—	4	1	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	4	1	no	—
678	C₂²	—	4	1	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	2	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	8	1	no	—
685	C₂²	—	8	1	no	—
686	C₂²	—	8	1	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	8	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	—	8	1	no	—
692	C₂²	—	8	1	no	—
693	C₂²	—	8	1	no	—
694	C₂²	—	8	1	no	—
695	C₂²	C₂₃×#525	1	1	yes	characteristic
696	C₂²	D₄²×C₂₃	1	1	yes	characteristic
697	C₂²	C₂₃×#547	1	1	yes	characteristic
698	C₂²	C₂²×D₈×C₂₃	1	1	yes	characteristic
699	C₂²	C₂₃×#575	1	1	yes	characteristic
700	C₂²	C₂₃×#576	1	1	yes	characteristic
701	C₂²	C₂₃×#578	1	1	yes	characteristic
702	C₄	—	2	2	no	—
703	C₄	—	2	2	no	—
704	C₄	—	4	1	no	—
705	C₄	—	4	1	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	2	no	—
710	C₄	—	8	1	no	—
711	C₄	—	8	1	no	—
712	C₄	—	8	1	no	—
713	C₄	C₂₃×#532	1	1	yes	characteristic
714	C₄	C₂₃×#542	1	1	yes	characteristic
715	C₄	C₂₃×#548	1	1	yes	characteristic
716	C₄	C₂₃×#551	1	1	yes	characteristic
717	C₂	—	4	2	no	—
718	C₂	—	8	2	no	—
719	C₂	—	16	1	no	—
720	C₂	C₂₃×#2461	1	1	yes	characteristic
721	C₂	C₂₃×#3100	1	1	yes	characteristic
722	C₂	C₂₃×#3124	1	1	yes	characteristic
723	C₂	C₂₃×#3277	1	1	yes	characteristic
724	C₂	D₄×D₈×C₂₃	1	1	yes	characteristic
725	C₂	C₂₃×#3334	1	1	yes	characteristic
726	C₂	C₂₃×#3347	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂₃×#1999	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×#480	C₂	semidirect
2. C₂×C₂₃×#474	C₂	semidirect
3. C₂₃×#2491	C₂	semidirect
4. C₂₃×#2361	C₂	semidirect
5. C₂₃×#2067	C₂	semidirect
6. C₂₃×#2057	C₂	semidirect
7. C₂₃×#2033	C₂	semidirect
9. C₂₃×#1970	C₂	semidirect
10. C₂₃×#1925	C₂	semidirect
11. C₂₃×#1925	C₂	semidirect
12. C₂₃×#1923	C₂	semidirect
13. C₂₃×#1879	C₂	semidirect
14. C₂₃×#1852	C₂	semidirect
15. C₄×C₂₃×#107	C₂	semidirect
117. C₂₃×#107	D₄	semidirect
221. C₂²⋊C₄×C₂₃	D₈	semidirect
228. #26784	C₂₃	direct (N × H)
311. C₂×#480	C₂×C₂₃	semidirect
312. C₂×#474	C₂×C₂₃	semidirect
313. #2491	C₂×C₂₃	semidirect
314. #2361	C₂×C₂₃	semidirect
315. #2067	C₂×C₂₃	semidirect
316. #2057	C₂×C₂₃	semidirect
317. #2033	C₂×C₂₃	semidirect
319. #1970	C₂×C₂₃	semidirect
320. #1925	C₂×C₂₃	semidirect
321. #1925	C₂×C₂₃	semidirect
322. #1923	C₂×C₂₃	semidirect
323. #1879	C₂×C₂₃	semidirect
324. #1852	C₂×C₂₃	semidirect
325. C₄×#107	C₂×C₂₃	semidirect
480. #107	D₄×C₂₃	semidirect
497. C₂₃	#26784	direct (N × H)
585. C₂²⋊C₄	D₈×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×#480	2
C₂×C₂₃×#474	2
C₂₃×#2491	2
C₂₃×#2361	2
C₂₃×#2067	2
C₂₃×#2057	2
C₂₃×#2033	2
C₂₃×#1999	2
C₂₃×#1970	2
C₂₃×#1925	2
C₂₃×#1923	2
C₂₃×#1879	2
C₂₃×#1852	2
C₄×C₂₃×#107	2
#26784	23

Subgroups — C23×#26784 #19174410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#26784 #19174410