Subgroups — C₂₃×#61933 #19209559

Order 5888.

1754 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3508	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3400	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3392	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3368	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3365	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3222	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3208	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3123	C₂	1	4	yes	maximal, complemented
10	C₂₃×#3107	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#564	—	2	2	no	—
13	C₂₃×#559	C₂²	1	4	yes	—
14	C₂₃×#557	—	2	2	no	—
15	C₂₃×#557	C₂²	1	4	yes	complemented
16	C₂₃×#557	C₂²	1	4	yes	complemented
17	C₂₃×#550	C₂²	1	4	yes	—
18	C₂₃×#546	—	2	4	no	—
19	C₂₃×#541	—	2	4	no	—
20	C₂₃×#541	C₂²	1	4	yes	—
21	C₂₃×#540	—	2	2	no	—
22	C₂₃×#535	C₂²	1	2	yes	—
23	C₂₃×#533	C₂²	1	2	yes	—
24	C₂₃×#533	C₂²	1	1	yes	characteristic
25	C₂₃×#532	—	2	2	no	—
26	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
27	C₂₃×#518	C₂²	1	2	yes	—
28	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#497	C₂²	1	4	yes	complemented
30	C₂₃×#492	C₂²	1	4	yes	—
31	C₂₃×#492	C₂²	1	4	yes	complemented
32	C₂₃×#490	C₂²	1	4	yes	complemented
33	C₂₃×#488	C₂²	1	4	yes	complemented
34	C₂₃×#486	C₂²	1	4	yes	—
35	C₂₃×#485	C₂²	1	4	yes	—
36	C₂₃×#478	C₂²	1	8	yes	complemented
37	C₂₃×#475	C₂²	1	2	yes	complemented
38	C₂₃×#474	C₂²	1	2	yes	complemented
39	C₂₃×#464	C₂²	1	8	yes	complemented
40	C₂₃×#462	C₂²	1	2	yes	complemented
41	C₂₃×#461	C₂²	1	2	yes	complemented
42	C₂₃×#461	C₂²	1	8	yes	complemented
43	C₂₃×#460	C₂²	1	4	yes	—
44	C₂₃×#460	C₂²	1	4	yes	—
45	C₂₃×#460	C₂²	1	8	yes	complemented
46	C₂₃×#452	C₂²	1	4	yes	—
47	C₂₃×#450	C₂²	1	8	yes	—
48	C₂₃×#446	C₂²	1	4	yes	complemented
49	C₈×Q₈×C₂₃	C₂²	1	4	yes	complemented
50	C₂₃×#440	C₂²	1	8	yes	complemented
51	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	complemented
52	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
53	C₄×SD₁₆×C₂₃	C₂²	1	8	yes	complemented
54	C₂₃×#433	C₂²	1	4	yes	—
55	C₂₃×#431	C₂²	1	2	yes	—
56	C₂×#41×C₂₃	—	2	4	no	—
57	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₂₃	—	2	2	no	—
59	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
60	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
61	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
62	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
63	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
64	C₂₃×C₄⋊Q₈	—	2	4	no	—
65	C₂₃×C₄⋊Q₈	D₄	1	2	yes	—
66	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
67	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
68	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₂₃×#127	—	2	1	no	—
70	C₂₃×#127	—	2	1	no	—
71	C₂₃×#127	C₂³	1	4	yes	—
72	C₂₃×#127	C₂³	1	4	yes	—
73	C₂₃×#126	—	2	8	no	—
74	C₂₃×#125	—	2	4	no	—
75	C₂₃×#125	—	2	8	no	—
76	C₂₃×#125	—	2	8	no	—
77	C₂₃×#125	—	2	8	no	—
78	C₂₃×#125	—	2	2	no	—
79	C₂₃×#125	D₄	1	2	yes	—
80	C₂₃×#125	C₂³	1	4	yes	—
81	C₂₃×#124	—	2	4	no	—
82	C₂₃×#124	C₂³	1	4	yes	—
83	C₂₃×#123	—	2	8	no	—
84	C₂₃×C₂²⋊Q₈	—	2	2	no	—
85	C₂₃×C₂²⋊Q₈	D₄	1	4	yes	—
86	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
87	C₂₃×#121	—	2	4	no	—
88	C₂₃×#121	—	2	8	no	—
89	C₂₃×#121	—	2	4	no	—
90	C₂₃×#120	—	2	4	no	—
91	C₄×Q₈×C₂₃	—	2	4	no	—
92	C₄×Q₈×C₂₃	—	2	4	no	—
93	C₄×Q₈×C₂₃	—	2	2	no	—
94	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
95	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
96	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
97	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
98	C₄×D₄×C₂₃	—	2	2	no	—
99	C₄×D₄×C₂₃	—	2	4	no	—
100	C₄×D₄×C₂₃	—	2	4	no	—
101	C₄×D₄×C₂₃	C₂³	1	2	yes	—
102	C₄×D₄×C₂₃	C₂³	1	8	yes	—
103	C₂₃×#117	—	2	2	no	—
104	C₂₃×#117	—	2	1	no	—
105	C₂₃×#117	C₂³	1	1	yes	characteristic
106	C₂₃×#117	C₂³	1	2	yes	—
107	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
108	C₂×C₄²×C₂₃	—	2	1	no	—
109	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
110	C₂₃×#107	C₂³	1	4	yes	—
111	C₂₃×#106	C₂³	1	4	yes	—
112	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
113	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
114	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
115	C₂₃×#103	C₂³	1	4	yes	—
116	C₂₃×#103	C₂³	1	4	yes	—
117	C₂₃×#103	C₂³	1	4	yes	—
118	C₂₃×#102	C₂³	1	8	yes	—
119	C₂₃×#102	C₂³	1	4	yes	—
120	C₂₃×#102	C₂³	1	8	yes	—
121	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
122	C₂₃×#97	C₂³	1	4	yes	—
123	C₄×C₈×C₂₃	C₂³	1	4	yes	—
124	C₄×C₈×C₂₃	C₂³	1	4	yes	—
125	C₂⁴×C₂₃	—	2	2	no	—
126	#41×C₂₃	—	4	2	no	—
127	#41×C₂₃	—	8	8	no	—
128	C₂×Q₈×C₂₃	—	2	2	no	—
129	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
130	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
131	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
132	C₂×D₄×C₂₃	—	2	1	no	—
133	C₂×D₄×C₂₃	—	2	2	no	—
134	C₂×D₄×C₂₃	—	2	4	no	—
135	C₂×D₄×C₂₃	—	2	8	no	—
136	C₂×D₄×C₂₃	—	2	4	no	—
137	C₂×D₄×C₂₃	—	4	4	no	—
138	C₂×D₄×C₂₃	—	8	4	no	—
139	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
140	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
141	C₂²×C₄×C₂₃	—	2	1	no	—
142	C₂²×C₄×C₂₃	—	2	2	no	—
143	C₂²×C₄×C₂₃	—	2	8	no	—
144	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
146	Q₁₆×C₂₃	—	4	4	no	—
147	SD₁₆×C₂₃	—	4	8	no	—
148	SD₁₆×C₂₃	—	4	4	no	—
149	SD₁₆×C₂₃	—	4	8	no	—
150	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
151	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
152	C₄⋊C₄×C₂₃	—	2	2	no	—
153	C₄⋊C₄×C₂₃	—	2	2	no	—
154	C₄⋊C₄×C₂₃	—	2	2	no	—
155	C₄⋊C₄×C₂₃	—	2	2	no	—
156	C₄⋊C₄×C₂₃	—	2	4	no	—
157	C₄⋊C₄×C₂₃	—	2	8	no	—
158	C₄⋊C₄×C₂₃	—	2	8	no	—
159	C₄⋊C₄×C₂₃	—	2	4	no	—
160	C₄⋊C₄×C₂₃	—	2	8	no	—
161	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
162	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
163	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
164	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
165	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
166	C₂²⋊C₄×C₂₃	—	2	1	no	—
167	C₂²⋊C₄×C₂₃	—	2	4	no	—
168	C₂²⋊C₄×C₂₃	—	2	8	no	—
169	C₂²⋊C₄×C₂₃	—	2	2	no	—
170	C₂²⋊C₄×C₂₃	—	2	8	no	—
171	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
172	C₄²×C₂₃	—	2	1	no	—
173	C₄²×C₂₃	—	2	2	no	—
174	C₄²×C₂₃	—	2	4	no	—
175	C₄²×C₂₃	—	2	8	no	—
176	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₂₃	C₂⁴	1	2	yes	—
179	C₄²×C₂₃	C₂⁴	1	4	yes	—
180	#61933	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂³×C₂₃	—	2	4	no	—
182	C₂³×C₂₃	—	2	1	no	—
183	C₂³×C₂₃	—	4	4	no	—
184	C₂³×C₂₃	—	8	4	no	—
185	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₂₃	—	2	8	no	—
187	Q₈×C₂₃	—	2	4	no	—
188	Q₈×C₂₃	—	2	4	no	—
189	Q₈×C₂₃	—	2	2	no	—
190	Q₈×C₂₃	—	4	4	no	—
191	D₄×C₂₃	—	2	8	no	—
192	D₄×C₂₃	—	2	2	no	—
193	D₄×C₂₃	—	4	4	no	—
194	D₄×C₂₃	—	4	2	no	—
195	D₄×C₂₃	—	4	8	no	—
196	D₄×C₂₃	—	8	4	no	—
197	D₄×C₂₃	—	8	8	no	—
198	C₂×C₄×C₂₃	—	2	4	no	—
199	C₂×C₄×C₂₃	—	2	2	no	—
200	C₂×C₄×C₂₃	—	2	4	no	—
201	C₂×C₄×C₂₃	—	2	4	no	—
202	C₂×C₄×C₂₃	—	2	1	no	—
203	C₂×C₄×C₂₃	—	2	2	no	—
204	C₂×C₄×C₂₃	—	4	2	no	—
205	C₂×C₄×C₂₃	—	4	4	no	—
206	C₂×C₄×C₂₃	—	8	8	no	—
207	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₂₃	C₂²×D₄	1	8	yes	—
209	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
210	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
212	C₈×C₂₃	—	2	4	no	—
213	C₈×C₂₃	—	2	4	no	—
214	#3556	C₂×C₂₃	1	1	yes	characteristic, complemented
215	#3508	C₂×C₂₃	1	1	yes	characteristic
216	#3400	C₂×C₂₃	1	4	yes	complemented
217	#3392	C₂×C₂₃	1	4	yes	complemented
218	#3368	C₂×C₂₃	1	4	yes	complemented
219	#3365	C₂×C₂₃	1	4	yes	complemented
220	#3222	C₂×C₂₃	1	4	yes	complemented
221	#3208	C₂×C₂₃	1	2	yes	complemented
222	#3123	C₂×C₂₃	1	4	yes	complemented
223	#3107	C₂×C₂₃	1	2	yes	complemented
224	#2986	C₂×C₂₃	1	1	yes	characteristic, complemented
225	C₂²×C₂₃	—	2	1	no	—
226	C₂²×C₂₃	—	2	2	no	—
227	C₂²×C₂₃	—	4	1	no	—
228	C₂²×C₂₃	—	4	4	no	—
229	C₂²×C₂₃	—	4	2	no	—
230	C₂²×C₂₃	—	4	8	no	—
231	C₂²×C₂₃	—	16	4	no	—
232	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
233	C₄×C₂₃	—	2	1	no	—
234	C₄×C₂₃	—	2	2	no	—
235	C₄×C₂₃	—	2	8	no	—
236	C₄×C₂₃	—	4	1	no	—
237	C₄×C₂₃	—	4	4	no	—
238	C₄×C₂₃	—	4	2	no	—
239	C₄×C₂₃	—	4	4	no	—
240	C₄×C₂₃	#577	1	4	yes	—
241	C₄×C₂₃	#585	1	2	yes	—
242	#564	—	2	2	no	—
243	#559	C₂²×C₂₃	1	4	yes	—
244	#557	—	2	2	no	—
245	#557	C₂²×C₂₃	1	4	yes	complemented
246	#557	C₂²×C₂₃	1	4	yes	complemented
247	#550	C₂²×C₂₃	1	4	yes	—
248	#546	—	2	4	no	—
249	#541	—	2	4	no	—
250	#541	C₂²×C₂₃	1	4	yes	—
251	#540	—	2	2	no	—
252	#535	C₂²×C₂₃	1	2	yes	—
253	#533	C₂²×C₂₃	1	2	yes	—
254	#533	C₂²×C₂₃	1	1	yes	characteristic
255	#532	—	2	2	no	—
256	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
257	#518	C₂²×C₂₃	1	2	yes	—
258	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
259	#497	C₂²×C₂₃	1	4	yes	complemented
260	#492	C₂²×C₂₃	1	4	yes	—
261	#492	C₂²×C₂₃	1	4	yes	complemented
262	#490	C₂²×C₂₃	1	4	yes	complemented
263	#488	C₂²×C₂₃	1	4	yes	complemented
264	#486	C₂²×C₂₃	1	4	yes	—
265	#485	C₂²×C₂₃	1	4	yes	—
266	#478	C₂²×C₂₃	1	8	yes	complemented
267	#475	C₂²×C₂₃	1	2	yes	complemented
268	#474	C₂²×C₂₃	1	2	yes	complemented
269	#464	C₂²×C₂₃	1	8	yes	complemented
270	#462	C₂²×C₂₃	1	2	yes	complemented
271	#461	C₂²×C₂₃	1	2	yes	complemented
272	#461	C₂²×C₂₃	1	8	yes	complemented
273	#460	C₂²×C₂₃	1	4	yes	—
274	#460	C₂²×C₂₃	1	4	yes	—
275	#460	C₂²×C₂₃	1	8	yes	complemented
276	#452	C₂²×C₂₃	1	4	yes	—
277	#450	C₂²×C₂₃	1	8	yes	—
278	#446	C₂²×C₂₃	1	4	yes	complemented
279	C₈×Q₈	C₂²×C₂₃	1	4	yes	complemented
280	#440	C₂²×C₂₃	1	8	yes	complemented
281	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	complemented
282	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
283	C₄×SD₁₆	C₂²×C₂₃	1	8	yes	complemented
284	#433	C₂²×C₂₃	1	4	yes	—
285	#431	C₂²×C₂₃	1	2	yes	—
286	C₂×C₂₃	—	4	1	no	—
287	C₂×C₂₃	—	8	1	no	—
288	C₂×C₂₃	—	8	4	no	—
289	C₂×C₂₃	#3487	1	1	yes	characteristic
290	C₂×C₂₃	C₂×#577	1	2	yes	—
291	C₂×#41	—	2	4	no	—
292	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
295	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
296	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
297	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
298	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
299	C₄⋊Q₈	—	2	4	no	—
300	C₄⋊Q₈	D₄×C₂₃	1	2	yes	—
301	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
302	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
303	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
304	#127	—	2	1	no	—
305	#127	—	2	1	no	—
306	#127	C₂³×C₂₃	1	4	yes	—
307	#127	C₂³×C₂₃	1	4	yes	—
308	#126	—	2	8	no	—
309	#125	—	2	4	no	—
310	#125	—	2	8	no	—
311	#125	—	2	8	no	—
312	#125	—	2	8	no	—
313	#125	—	2	2	no	—
314	#125	D₄×C₂₃	1	2	yes	—
315	#125	C₂³×C₂₃	1	4	yes	—
316	#124	—	2	4	no	—
317	#124	C₂³×C₂₃	1	4	yes	—
318	#123	—	2	8	no	—
319	C₂²⋊Q₈	—	2	2	no	—
320	C₂²⋊Q₈	D₄×C₂₃	1	4	yes	—
321	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
322	#121	—	2	4	no	—
323	#121	—	2	4	no	—
324	#121	—	2	8	no	—
325	#120	—	2	4	no	—
326	C₄×Q₈	—	2	4	no	—
327	C₄×Q₈	—	2	4	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
330	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
331	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
332	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	2	4	no	—
335	C₄×D₄	—	2	4	no	—
336	C₄×D₄	C₂³×C₂₃	1	2	yes	—
337	C₄×D₄	C₂³×C₂₃	1	8	yes	—
338	#117	—	2	2	no	—
339	#117	—	2	1	no	—
340	#117	C₂³×C₂₃	1	1	yes	characteristic
341	#117	C₂³×C₂₃	1	2	yes	—
342	C₂×C₂²⋊C₄	—	2	4	no	—
343	C₂×C₄²	—	2	1	no	—
344	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
345	#107	C₂³×C₂₃	1	4	yes	—
346	#106	C₂³×C₂₃	1	4	yes	—
347	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
348	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
349	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
350	#103	C₂³×C₂₃	1	4	yes	—
351	#103	C₂³×C₂₃	1	4	yes	—
352	#103	C₂³×C₂₃	1	4	yes	—
353	#102	C₂³×C₂₃	1	8	yes	—
354	#102	C₂³×C₂₃	1	4	yes	—
355	#102	C₂³×C₂₃	1	8	yes	—
356	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
357	#97	C₂³×C₂₃	1	4	yes	—
358	C₄×C₈	C₂³×C₂₃	1	4	yes	—
359	C₄×C₈	C₂³×C₂₃	1	4	yes	—
360	C₂₃	#61933	1	1	yes	characteristic, direct product factor, Sylow
361	C₂⁴	—	2	2	no	—
362	#41	—	4	2	no	—
363	#41	—	8	8	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
366	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
367	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	8	no	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	4	4	no	—
374	C₂×D₄	—	8	4	no	—
375	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
376	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	8	no	—
380	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
382	Q₁₆	—	4	4	no	—
383	SD₁₆	—	4	8	no	—
384	SD₁₆	—	4	4	no	—
385	SD₁₆	—	4	8	no	—
386	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
387	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	8	no	—
394	C₄⋊C₄	—	2	8	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	8	no	—
397	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
398	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
399	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
400	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
401	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
402	C₂²⋊C₄	—	2	1	no	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	8	no	—
407	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
408	C₄²	—	2	1	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	4	no	—
411	C₄²	—	2	8	no	—
412	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
413	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
414	C₄²	C₂⁴×C₂₃	1	2	yes	—
415	C₄²	C₂⁴×C₂₃	1	4	yes	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	4	4	no	—
419	C₂³	—	8	4	no	—
420	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
421	Q₈	—	2	8	no	—
422	Q₈	—	2	4	no	—
423	Q₈	—	2	4	no	—
424	Q₈	—	2	2	no	—
425	Q₈	—	4	4	no	—
426	D₄	—	2	8	no	—
427	D₄	—	2	2	no	—
428	D₄	—	4	4	no	—
429	D₄	—	4	2	no	—
430	D₄	—	4	8	no	—
431	D₄	—	8	4	no	—
432	D₄	—	8	8	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	8	8	no	—
442	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
443	C₂×C₄	C₂²×D₄×C₂₃	1	8	yes	—
444	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
445	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
446	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
447	C₈	—	2	4	no	—
448	C₈	—	2	4	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	4	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	8	no	—
455	C₂²	—	16	4	no	—
456	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
457	C₄	—	2	1	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	8	no	—
460	C₄	—	4	1	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	4	no	—
464	C₄	C₂₃×#577	1	4	yes	—
465	C₄	C₂₃×#585	1	2	yes	—
466	C₂	—	4	1	no	—
467	C₂	—	8	4	no	—
468	C₂	—	8	1	no	—
469	C₂	C₂₃×#3487	1	1	yes	characteristic
470	C₂	C₂×C₂₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3508	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3556	C₂	semidirect
3. C₂₃×#3400	C₂	semidirect
4. C₂₃×#3392	C₂	semidirect
5. C₂₃×#3368	C₂	semidirect
6. C₂₃×#3365	C₂	semidirect
7. C₂₃×#3222	C₂	semidirect
8. C₂₃×#3208	C₂	semidirect
9. C₂₃×#3123	C₂	semidirect
10. C₂₃×#3107	C₂	semidirect
11. C₂₃×#2986	C₂	semidirect
15. C₂₃×#557	C₂²	semidirect
16. C₂₃×#557	C₂²	semidirect
29. C₂₃×#497	C₂²	semidirect
31. C₂₃×#492	C₂²	semidirect
32. C₂₃×#490	C₂²	semidirect
33. C₂₃×#488	C₂²	semidirect
36. C₂₃×#478	C₂²	semidirect
37. C₂₃×#475	C₂²	semidirect
38. C₂₃×#474	C₂²	semidirect
39. C₂₃×#464	C₂²	semidirect
40. C₂₃×#462	C₂²	semidirect
41. C₂₃×#461	C₂²	semidirect
42. C₂₃×#461	C₂²	semidirect
45. C₂₃×#460	C₂²	semidirect
48. C₂₃×#446	C₂²	semidirect
49. C₈×Q₈×C₂₃	C₂²	semidirect
50. C₂₃×#440	C₂²	semidirect
51. C₄×Q₁₆×C₂₃	C₂²	semidirect
52. C₄×SD₁₆×C₂₃	C₂²	semidirect
53. C₄×SD₁₆×C₂₃	C₂²	semidirect
180. #61933	C₂₃	direct (N × H)
214. #3556	C₂×C₂₃	semidirect
216. #3400	C₂×C₂₃	semidirect
217. #3392	C₂×C₂₃	semidirect
218. #3368	C₂×C₂₃	semidirect
219. #3365	C₂×C₂₃	semidirect
220. #3222	C₂×C₂₃	semidirect
221. #3208	C₂×C₂₃	semidirect
222. #3123	C₂×C₂₃	semidirect
223. #3107	C₂×C₂₃	semidirect
224. #2986	C₂×C₂₃	semidirect
245. #557	C₂²×C₂₃	semidirect
246. #557	C₂²×C₂₃	semidirect
259. #497	C₂²×C₂₃	semidirect
261. #492	C₂²×C₂₃	semidirect
262. #490	C₂²×C₂₃	semidirect
263. #488	C₂²×C₂₃	semidirect
266. #478	C₂²×C₂₃	semidirect
267. #475	C₂²×C₂₃	semidirect
268. #474	C₂²×C₂₃	semidirect
269. #464	C₂²×C₂₃	semidirect
270. #462	C₂²×C₂₃	semidirect
271. #461	C₂²×C₂₃	semidirect
272. #461	C₂²×C₂₃	semidirect
275. #460	C₂²×C₂₃	semidirect
278. #446	C₂²×C₂₃	semidirect
279. C₈×Q₈	C₂²×C₂₃	semidirect
280. #440	C₂²×C₂₃	semidirect
281. C₄×Q₁₆	C₂²×C₂₃	semidirect
282. C₄×SD₁₆	C₂²×C₂₃	semidirect
283. C₄×SD₁₆	C₂²×C₂₃	semidirect
360. C₂₃	#61933	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×#3556	2
C₂₃×#3508	2
C₂₃×#3400	2
C₂₃×#3392	2
C₂₃×#3368	2
C₂₃×#3365	2
C₂₃×#3222	2
C₂₃×#3208	2
C₂₃×#3123	2
C₂₃×#3107	2
C₂₃×#2986	2
#61933	23

Subgroups — C23×#61933 #19209559

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61933 #19209559