Subgroups — C₂₃×#36566 #19184192

Order 5888.

1790 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2864	C₂	1	2	yes	maximal, complemented
2	C₂₃×#2862	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2589	C₂	1	4	yes	maximal, complemented
4	C₂₃×#2581	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2580	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#2574	C₂	1	4	yes	maximal, complemented
7	C₂₃×#2465	C₂	1	4	yes	maximal, complemented
8	C₂₃×#2452	C₂	1	2	yes	maximal
9	C₂₃×#2451	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2368	C₂	1	4	yes	maximal, complemented
11	C₂₃×#2351	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2349	C₂	1	1	yes	maximal, characteristic
13	C₄×C₂₃×#124	C₂	1	1	yes	maximal, characteristic
14	C₄×C₂₃×#124	C₂	1	2	yes	maximal
15	C₄²×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
19	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
25	C₂₃×#400	C₂²	1	2	yes	—
26	C₂₃×#399	C₂²	1	2	yes	—
27	C₂₃×#398	C₂²	1	4	yes	—
28	C₂₃×#396	C₂²	1	4	yes	—
29	C₂₃×#395	C₂²	1	4	yes	—
30	C₂₃×#395	C₂²	1	2	yes	—
31	C₂₃×#393	C₂²	1	4	yes	—
32	C₂₃×#393	C₂²	1	2	yes	—
33	C₂₃×#391	C₂²	1	1	yes	characteristic
34	C₂₃×#391	C₂²	1	2	yes	—
35	C₂₃×#391	C₂²	1	4	yes	—
36	C₂₃×#391	C₂²	1	4	yes	—
37	C₂₃×#391	C₂²	1	4	yes	—
38	C₂₃×#390	C₂²	1	1	yes	characteristic
39	C₂₃×#390	C₂²	1	2	yes	—
40	C₂₃×#389	C₂²	1	2	yes	—
41	C₂₃×#389	C₂²	1	2	yes	—
42	C₂₃×#389	C₂²	1	2	yes	—
43	C₂₃×#389	C₂²	1	2	yes	—
44	C₂₃×#389	C₂²	1	4	yes	—
45	C₂₃×#388	C₂²	1	4	yes	—
46	C₂₃×#388	C₂²	1	4	yes	—
47	C₂₃×#388	C₂²	1	4	yes	—
48	C₂₃×#387	C₂²	1	4	yes	—
49	C₂₃×#387	C₂²	1	4	yes	—
50	C₂₃×#387	C₂²	1	4	yes	—
51	C₂₃×#387	C₂²	1	4	yes	—
52	C₂₃×#387	C₂²	1	4	yes	—
53	C₂₃×#387	C₂²	1	4	yes	—
54	C₂₃×#385	C₂²	1	4	yes	—
55	C₂₃×#385	C₂²	1	4	yes	—
56	C₂₃×#385	C₂²	1	4	yes	—
57	C₂₃×#382	C₂²	1	2	yes	—
58	C₂₃×#382	C₂²	1	1	yes	characteristic
59	C₂₃×#382	C₂²	1	2	yes	—
60	C₂₃×#382	C₂²	1	1	yes	characteristic
61	C₂₃×#382	C₂²	1	1	yes	characteristic
62	C₂₃×#380	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
64	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
65	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
67	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
69	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
70	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
71	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
72	C₂×C₂₃×#95	C₂²	1	2	yes	—
73	C₄³×C₂₃	C₂²	1	1	yes	characteristic
74	C₄³×C₂₃	C₂²	1	2	yes	—
75	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
77	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
78	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
80	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
81	C₂₃×C₄⋊Q₈	—	4	4	no	—
82	C₂₃×#124	Q₈	1	8	yes	complemented
83	C₂₃×C₂²⋊Q₈	—	2	16	no	—
84	C₄×Q₈×C₂₃	—	2	8	no	—
85	C₄×Q₈×C₂₃	—	2	4	no	—
86	C₄×Q₈×C₂₃	—	2	4	no	—
87	C₄×Q₈×C₂₃	—	4	4	no	—
88	C₄×D₄×C₂₃	—	2	4	no	—
89	C₄×D₄×C₂₃	—	4	4	no	—
90	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
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	4	yes	—
100	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
105	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
106	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
112	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
113	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
114	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
116	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
117	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
118	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
119	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
120	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
121	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
122	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
123	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
125	C₂₃×#95	C₂³	1	1	yes	characteristic
126	C₂₃×#95	C₂³	1	2	yes	—
127	C₂₃×#95	C₂³	1	4	yes	—
128	C₂₃×#95	C₂³	1	4	yes	—
129	C₂₃×#95	C₂³	1	4	yes	—
130	C₂₃×#95	C₂³	1	4	yes	—
131	C₂₃×#95	C₂³	1	4	yes	—
132	C₂₃×#95	C₂³	1	4	yes	—
133	C₂₃×#95	C₂³	1	4	yes	—
134	C₂₃×#95	C₂³	1	1	yes	characteristic
135	C₂₃×#95	C₂³	1	2	yes	—
136	C₂₃×#95	C₂³	1	2	yes	—
137	C₂₃×#95	C₂³	1	2	yes	—
138	C₂₃×#95	C₂³	1	2	yes	—
139	C₂₃×#95	C₂³	1	4	yes	—
140	C₂₃×#95	C₂³	1	2	yes	—
141	C₂₃×#95	C₂³	1	4	yes	—
142	C₂₃×#95	C₂³	1	4	yes	—
143	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
144	C₂×Q₈×C₂₃	—	2	4	no	—
145	C₂×Q₈×C₂₃	—	2	2	no	—
146	C₂×Q₈×C₂₃	—	2	2	no	—
147	C₂×Q₈×C₂₃	—	2	8	no	—
148	C₂×Q₈×C₂₃	—	2	2	no	—
149	C₂×Q₈×C₂₃	—	4	4	no	—
150	C₂×Q₈×C₂₃	—	4	4	no	—
151	C₂×Q₈×C₂₃	C₂×Q₈	1	4	yes	—
152	C₂×D₄×C₂₃	—	2	2	no	—
153	C₂×D₄×C₂₃	—	2	2	no	—
154	C₂×D₄×C₂₃	C₂×Q₈	1	4	yes	—
155	C₂²×C₄×C₂₃	—	2	4	no	—
156	C₂²×C₄×C₂₃	—	2	8	no	—
157	C₂²×C₄×C₂₃	—	4	4	no	—
158	C₂²×C₄×C₂₃	—	4	4	no	—
159	C₂²×C₄×C₂₃	—	4	4	no	—
160	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
174	C₄⋊C₄×C₂₃	—	2	2	no	—
175	C₄⋊C₄×C₂₃	—	2	4	no	—
176	C₄⋊C₄×C₂₃	—	2	4	no	—
177	C₄⋊C₄×C₂₃	—	2	4	no	—
178	C₄⋊C₄×C₂₃	—	2	4	no	—
179	C₄⋊C₄×C₂₃	—	2	2	no	—
180	C₄⋊C₄×C₂₃	—	2	2	no	—
181	C₄⋊C₄×C₂₃	—	2	8	no	—
182	C₄⋊C₄×C₂₃	—	2	8	no	—
183	C₄⋊C₄×C₂₃	—	2	4	no	—
184	C₄⋊C₄×C₂₃	—	2	4	no	—
185	C₄⋊C₄×C₂₃	—	4	4	no	—
186	C₄⋊C₄×C₂₃	—	4	4	no	—
187	C₄⋊C₄×C₂₃	—	4	4	no	—
188	C₄⋊C₄×C₂₃	—	4	4	no	—
189	C₄⋊C₄×C₂₃	#41	1	8	yes	—
190	C₂²⋊C₄×C₂₃	—	2	4	no	—
191	C₂²⋊C₄×C₂₃	—	2	8	no	—
192	C₂²⋊C₄×C₂₃	—	2	8	no	—
193	C₂²⋊C₄×C₂₃	—	4	4	no	—
194	C₂²⋊C₄×C₂₃	—	4	4	no	—
195	C₂²⋊C₄×C₂₃	C₂×Q₈	1	16	yes	—
196	C₄²×C₂₃	—	2	4	no	—
197	C₄²×C₂₃	—	2	4	no	—
198	C₄²×C₂₃	—	2	4	no	—
199	C₄²×C₂₃	—	2	4	no	—
200	C₄²×C₂₃	—	2	4	no	—
201	C₄²×C₂₃	—	2	4	no	—
202	C₄²×C₂₃	—	2	2	no	—
203	C₄²×C₂₃	—	4	2	no	—
204	C₄²×C₂₃	—	4	2	no	—
205	C₄²×C₂₃	—	4	2	no	—
206	C₄²×C₂₃	—	4	4	no	—
207	C₄²×C₂₃	C₂×Q₈	1	4	yes	—
208	C₄²×C₂₃	#41	1	4	yes	—
209	#36566	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂³×C₂₃	—	2	4	no	—
211	C₂³×C₂₃	—	2	2	no	—
212	C₂³×C₂₃	—	2	2	no	—
213	C₂³×C₂₃	—	2	4	no	—
214	C₂³×C₂₃	C₂²×Q₈	1	4	yes	—
215	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
216	Q₈×C₂₃	—	2	8	no	—
217	Q₈×C₂₃	—	2	8	no	—
218	Q₈×C₂₃	—	8	8	no	—
219	D₄×C₂₃	—	2	8	no	—
220	C₂×C₄×C₂₃	—	2	2	no	—
221	C₂×C₄×C₂₃	—	2	2	no	—
222	C₂×C₄×C₂₃	—	2	2	no	—
223	C₂×C₄×C₂₃	—	2	2	no	—
224	C₂×C₄×C₂₃	—	2	2	no	—
225	C₂×C₄×C₂₃	—	2	2	no	—
226	C₂×C₄×C₂₃	—	2	2	no	—
227	C₂×C₄×C₂₃	—	2	2	no	—
228	C₂×C₄×C₂₃	—	2	2	no	—
229	C₂×C₄×C₂₃	—	2	2	no	—
230	C₂×C₄×C₂₃	—	2	2	no	—
231	C₂×C₄×C₂₃	—	2	2	no	—
232	C₂×C₄×C₂₃	—	2	2	no	—
233	C₂×C₄×C₂₃	—	2	2	no	—
234	C₂×C₄×C₂₃	—	2	2	no	—
235	C₂×C₄×C₂₃	—	2	4	no	—
236	C₂×C₄×C₂₃	—	2	2	no	—
237	C₂×C₄×C₂₃	—	2	4	no	—
238	C₂×C₄×C₂₃	—	2	4	no	—
239	C₂×C₄×C₂₃	—	2	2	no	—
240	C₂×C₄×C₂₃	—	2	4	no	—
241	C₂×C₄×C₂₃	—	2	4	no	—
242	C₂×C₄×C₂₃	—	2	2	no	—
243	C₂×C₄×C₂₃	—	2	2	no	—
244	C₂×C₄×C₂₃	—	2	2	no	—
245	C₂×C₄×C₂₃	—	2	4	no	—
246	C₂×C₄×C₂₃	—	2	4	no	—
247	C₂×C₄×C₂₃	—	2	4	no	—
248	C₂×C₄×C₂₃	—	8	4	no	—
249	C₂×C₄×C₂₃	—	8	8	no	—
250	C₂×C₄×C₂₃	C₂²×Q₈	1	4	yes	—
251	C₂×C₄×C₂₃	C₂²×Q₈	1	4	yes	—
252	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
253	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
254	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
255	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
256	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
257	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
258	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
259	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
260	#2864	C₂×C₂₃	1	2	yes	complemented
261	#2862	C₂×C₂₃	1	1	yes	characteristic, complemented
262	#2589	C₂×C₂₃	1	4	yes	complemented
263	#2581	C₂×C₂₃	1	1	yes	characteristic, complemented
264	#2580	C₂×C₂₃	1	1	yes	characteristic
265	#2574	C₂×C₂₃	1	4	yes	complemented
266	#2465	C₂×C₂₃	1	4	yes	complemented
267	#2452	C₂×C₂₃	1	2	yes	—
268	#2451	C₂×C₂₃	1	2	yes	complemented
269	#2368	C₂×C₂₃	1	4	yes	complemented
270	#2351	C₂×C₂₃	1	1	yes	characteristic, complemented
271	#2349	C₂×C₂₃	1	1	yes	characteristic
272	C₄×#124	C₂×C₂₃	1	1	yes	characteristic
273	C₄×#124	C₂×C₂₃	1	2	yes	—
274	C₄²×Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
275	C₂²×C₂₃	—	2	4	no	—
276	C₂²×C₂₃	—	2	8	no	—
277	C₂²×C₂₃	—	4	2	no	—
278	C₂²×C₂₃	—	4	2	no	—
279	C₂²×C₂₃	—	4	4	no	—
280	C₂²×C₂₃	C₂³×Q₈	1	1	yes	characteristic
281	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
282	C₂²×C₂₃	C₂²×#41	1	2	yes	—
283	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
284	C₂²×C₂₃	#585	1	2	yes	—
285	C₄×C₂₃	—	2	4	no	—
286	C₄×C₂₃	—	2	2	no	—
287	C₄×C₂₃	—	2	4	no	—
288	C₄×C₂₃	—	2	4	no	—
289	C₄×C₂₃	—	2	2	no	—
290	C₄×C₂₃	—	2	4	no	—
291	C₄×C₂₃	—	2	4	no	—
292	C₄×C₂₃	—	4	2	no	—
293	C₄×C₂₃	—	4	2	no	—
294	C₄×C₂₃	—	4	2	no	—
295	C₄×C₂₃	—	4	2	no	—
296	C₄×C₂₃	—	4	4	no	—
297	C₄×C₂₃	—	4	4	no	—
298	C₄×C₂₃	#554	1	4	yes	—
299	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
300	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
301	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
302	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
303	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
304	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
305	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
306	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
307	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
308	#400	C₂²×C₂₃	1	2	yes	—
309	#399	C₂²×C₂₃	1	2	yes	—
310	#398	C₂²×C₂₃	1	4	yes	—
311	#396	C₂²×C₂₃	1	4	yes	—
312	#395	C₂²×C₂₃	1	4	yes	—
313	#395	C₂²×C₂₃	1	2	yes	—
314	#393	C₂²×C₂₃	1	4	yes	—
315	#393	C₂²×C₂₃	1	2	yes	—
316	#391	C₂²×C₂₃	1	4	yes	—
317	#391	C₂²×C₂₃	1	2	yes	—
318	#391	C₂²×C₂₃	1	4	yes	—
319	#391	C₂²×C₂₃	1	4	yes	—
320	#391	C₂²×C₂₃	1	1	yes	characteristic
321	#390	C₂²×C₂₃	1	2	yes	—
322	#390	C₂²×C₂₃	1	1	yes	characteristic
323	#389	C₂²×C₂₃	1	2	yes	—
324	#389	C₂²×C₂₃	1	2	yes	—
325	#389	C₂²×C₂₃	1	4	yes	—
326	#389	C₂²×C₂₃	1	2	yes	—
327	#389	C₂²×C₂₃	1	2	yes	—
328	#388	C₂²×C₂₃	1	4	yes	—
329	#388	C₂²×C₂₃	1	4	yes	—
330	#388	C₂²×C₂₃	1	4	yes	—
331	#387	C₂²×C₂₃	1	4	yes	—
332	#387	C₂²×C₂₃	1	4	yes	—
333	#387	C₂²×C₂₃	1	4	yes	—
334	#387	C₂²×C₂₃	1	4	yes	—
335	#387	C₂²×C₂₃	1	4	yes	—
336	#387	C₂²×C₂₃	1	4	yes	—
337	#385	C₂²×C₂₃	1	4	yes	—
338	#385	C₂²×C₂₃	1	4	yes	—
339	#385	C₂²×C₂₃	1	4	yes	—
340	#382	C₂²×C₂₃	1	2	yes	—
341	#382	C₂²×C₂₃	1	1	yes	characteristic
342	#382	C₂²×C₂₃	1	1	yes	characteristic
343	#382	C₂²×C₂₃	1	2	yes	—
344	#382	C₂²×C₂₃	1	1	yes	characteristic
345	#380	C₂²×C₂₃	1	2	yes	—
346	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
347	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
348	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
349	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
350	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
351	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
352	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
353	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
354	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
355	C₂×#95	C₂²×C₂₃	1	2	yes	—
356	C₄³	C₂²×C₂₃	1	1	yes	characteristic
357	C₄³	C₂²×C₂₃	1	2	yes	—
358	C₂×C₂₃	—	4	4	no	—
359	C₂×C₂₃	#3444	1	1	yes	characteristic
360	C₂×C₂₃	C₂×#554	1	1	yes	characteristic
361	C₂×C₂₃	Q₈×#41	1	2	yes	—
362	C₂×C₂₃	#3510	1	1	yes	characteristic
363	C₂×C₂₃	#3514	1	2	yes	—
364	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
365	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
366	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
367	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
368	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
369	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
370	C₄⋊Q₈	—	4	4	no	—
371	#124	Q₈×C₂₃	1	8	yes	complemented
372	C₂²⋊Q₈	—	2	16	no	—
373	C₄×Q₈	—	2	8	no	—
374	C₄×Q₈	—	2	4	no	—
375	C₄×Q₈	—	2	4	no	—
376	C₄×Q₈	—	4	4	no	—
377	C₄×D₄	—	2	4	no	—
378	C₄×D₄	—	4	4	no	—
379	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
380	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
382	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
388	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
389	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
390	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
392	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
393	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
394	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
401	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
402	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
403	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
404	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
405	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
406	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
407	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
408	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
409	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
410	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
411	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
412	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
414	#95	C₂³×C₂₃	1	1	yes	characteristic
415	#95	C₂³×C₂₃	1	2	yes	—
416	#95	C₂³×C₂₃	1	4	yes	—
417	#95	C₂³×C₂₃	1	4	yes	—
418	#95	C₂³×C₂₃	1	4	yes	—
419	#95	C₂³×C₂₃	1	4	yes	—
420	#95	C₂³×C₂₃	1	4	yes	—
421	#95	C₂³×C₂₃	1	4	yes	—
422	#95	C₂³×C₂₃	1	4	yes	—
423	#95	C₂³×C₂₃	1	1	yes	characteristic
424	#95	C₂³×C₂₃	1	2	yes	—
425	#95	C₂³×C₂₃	1	2	yes	—
426	#95	C₂³×C₂₃	1	2	yes	—
427	#95	C₂³×C₂₃	1	2	yes	—
428	#95	C₂³×C₂₃	1	4	yes	—
429	#95	C₂³×C₂₃	1	2	yes	—
430	#95	C₂³×C₂₃	1	4	yes	—
431	#95	C₂³×C₂₃	1	4	yes	—
432	C₂₃	#36566	1	1	yes	characteristic, direct product factor, Sylow
433	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
434	C₂×Q₈	—	2	4	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	2	8	no	—
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	—	4	4	no	—
440	C₂×Q₈	—	4	4	no	—
441	C₂×Q₈	C₂×Q₈×C₂₃	1	4	yes	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	C₂×Q₈×C₂₃	1	4	yes	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	2	8	no	—
447	C₂²×C₄	—	4	4	no	—
448	C₂²×C₄	—	4	4	no	—
449	C₂²×C₄	—	4	4	no	—
450	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
452	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
453	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
454	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
456	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
457	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
458	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
459	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
461	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
462	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
463	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	8	no	—
472	C₄⋊C₄	—	2	8	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	4	4	no	—
476	C₄⋊C₄	—	4	4	no	—
477	C₄⋊C₄	—	4	4	no	—
478	C₄⋊C₄	—	4	4	no	—
479	C₄⋊C₄	#41×C₂₃	1	8	yes	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	8	no	—
482	C₂²⋊C₄	—	2	8	no	—
483	C₂²⋊C₄	—	4	4	no	—
484	C₂²⋊C₄	—	4	4	no	—
485	C₂²⋊C₄	C₂×Q₈×C₂₃	1	16	yes	—
486	C₄²	—	2	4	no	—
487	C₄²	—	2	4	no	—
488	C₄²	—	2	4	no	—
489	C₄²	—	2	4	no	—
490	C₄²	—	2	4	no	—
491	C₄²	—	2	4	no	—
492	C₄²	—	2	2	no	—
493	C₄²	—	4	4	no	—
494	C₄²	—	4	2	no	—
495	C₄²	—	4	2	no	—
496	C₄²	—	4	2	no	—
497	C₄²	C₂×Q₈×C₂₃	1	4	yes	—
498	C₄²	#41×C₂₃	1	4	yes	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	2	4	no	—
503	C₂³	C₂²×Q₈×C₂₃	1	4	yes	—
504	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
505	Q₈	—	2	8	no	—
506	Q₈	—	2	8	no	—
507	Q₈	—	8	8	no	—
508	D₄	—	2	8	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	8	4	no	—
538	C₂×C₄	—	8	8	no	—
539	C₂×C₄	C₂²×Q₈×C₂₃	1	4	yes	—
540	C₂×C₄	C₂²×Q₈×C₂₃	1	4	yes	—
541	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
542	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
543	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
544	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
545	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
546	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
547	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
548	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	8	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	4	no	—
554	C₂²	C₂³×Q₈×C₂₃	1	1	yes	characteristic
555	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
556	C₂²	C₂²×#41×C₂₃	1	2	yes	—
557	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
558	C₂²	C₂₃×#585	1	2	yes	—
559	C₄	—	2	4	no	—
560	C₄	—	2	2	no	—
561	C₄	—	2	4	no	—
562	C₄	—	2	4	no	—
563	C₄	—	2	2	no	—
564	C₄	—	2	4	no	—
565	C₄	—	2	4	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	4	no	—
570	C₄	—	4	4	no	—
571	C₄	—	4	2	no	—
572	C₄	C₂₃×#554	1	4	yes	—
573	C₂	—	4	4	no	—
574	C₂	C₂₃×#3444	1	1	yes	characteristic
575	C₂	C₂×C₂₃×#554	1	1	yes	characteristic
576	C₂	Q₈×#41×C₂₃	1	2	yes	—
577	C₂	C₂₃×#3510	1	1	yes	characteristic
578	C₂	C₂₃×#3514	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂²×D₄×C₂₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#2864	C₂	semidirect
2. C₂₃×#2862	C₂	semidirect
3. C₂₃×#2589	C₂	semidirect
4. C₂₃×#2581	C₂	semidirect
6. C₂₃×#2574	C₂	semidirect
7. C₂₃×#2465	C₂	semidirect
9. C₂₃×#2451	C₂	semidirect
10. C₂₃×#2368	C₂	semidirect
11. C₂₃×#2351	C₂	semidirect
15. C₄²×Q₈×C₂₃	C₂	semidirect
82. C₂₃×#124	Q₈	semidirect
209. #36566	C₂₃	direct (N × H)
260. #2864	C₂×C₂₃	semidirect
261. #2862	C₂×C₂₃	semidirect
262. #2589	C₂×C₂₃	semidirect
263. #2581	C₂×C₂₃	semidirect
265. #2574	C₂×C₂₃	semidirect
266. #2465	C₂×C₂₃	semidirect
268. #2451	C₂×C₂₃	semidirect
269. #2368	C₂×C₂₃	semidirect
270. #2351	C₂×C₂₃	semidirect
274. C₄²×Q₈	C₂×C₂₃	semidirect
371. #124	Q₈×C₂₃	semidirect
432. C₂₃	#36566	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#2864	2
C₂₃×#2862	2
C₂₃×#2589	2
C₂₃×#2581	2
C₂₃×#2580	2
C₂₃×#2574	2
C₂₃×#2465	2
C₂₃×#2452	2
C₂₃×#2451	2
C₂₃×#2368	2
C₂₃×#2351	2
C₂₃×#2349	2
C₄×C₂₃×#124	2
C₄²×Q₈×C₂₃	2
#36566	23

Subgroups — C23×#36566 #19184192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36566 #19184192