Subgroups — D₂₃×#540 #15686751

Order 2944.

1260 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093023	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093022	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093021	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093020	C₂	1	2	yes	maximal, complemented
5	#13093019	C₂	1	4	yes	maximal, complemented
6	#13093018	C₂	1	2	yes	maximal, complemented
7	#13093017	C₂	1	4	yes	maximal, complemented
8	#127×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#125×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#123×D₂₃	C₂	1	4	yes	maximal, complemented
11	#121×D₂₃	C₂	1	4	yes	maximal, complemented
12	#121×D₂₃	C₂	1	2	yes	maximal, complemented
13	C₄×D₄×D₂₃	C₂	1	2	yes	maximal, complemented
14	#117×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×D₂₃	C₂²	1	2	yes	—
17	C₂×D₄×D₂₃	C₂²	1	4	yes	—
18	C₂×D₄×D₂₃	C₂²	1	4	yes	—
19	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄×D₂₃	C₂²	1	4	yes	—
21	C₂₃×#127	C₂²	1	1	yes	characteristic, complemented
22	C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
23	C₂₃×#123	C₂²	1	4	yes	complemented
24	C₂₃×#121	C₂²	1	4	yes	complemented
25	C₂₃×#121	C₂²	1	2	yes	complemented
26	C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
27	C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
28	#10625111	C₂²	1	4	yes	complemented
29	#10625111	C₂²	1	2	yes	complemented
30	#10625110	C₂²	1	4	yes	complemented
31	#10625110	C₂²	1	4	yes	complemented
32	#10625110	C₂²	1	4	yes	complemented
33	#10625109	C₂²	1	4	yes	complemented
34	#10625109	C₂²	1	2	yes	complemented
35	#10625106	C₂²	1	4	yes	complemented
36	D₄×Dic₂₃	C₂²	1	2	yes	complemented
37	#10625101	C₂²	1	4	yes	complemented
38	#10625101	C₂²	1	2	yes	complemented
39	#10625100	C₂²	1	4	yes	complemented
40	C₄×C₂²⋊D₂₃	C₂²	1	4	yes	complemented
41	#10625097	C₂²	1	1	yes	characteristic, complemented
42	#10625066	C₂²	1	2	yes	complemented
43	#10625066	C₂²	1	4	yes	complemented
44	#10625065	C₂²	1	4	yes	complemented
45	#10625065	C₂²	1	4	yes	complemented
46	#10625064	C₂²	1	2	yes	complemented
47	#10625063	C₂²	1	2	yes	complemented
48	C₄⋊C₄×D₂₃	C₂²	1	2	yes	—
49	C₄⋊C₄×D₂₃	C₂²	1	2	yes	—
50	C₄⋊C₄×D₂₃	C₂²	1	4	yes	—
51	#10625061	C₂²	1	2	yes	complemented
52	#10625060	C₂²	1	4	yes	complemented
53	#10625057	C₂²	1	4	yes	complemented
54	#10625055	C₂²	1	4	yes	complemented
55	#10625055	C₂²	1	4	yes	complemented
56	#10625055	C₂²	1	4	yes	complemented
57	#10625054	C₂²	1	4	yes	complemented
58	#10625054	C₂²	1	4	yes	complemented
59	(C₂²⋊D₂₃)⋊C₄	C₂²	1	4	yes	complemented
60	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
61	C₂²⋊C₄×D₂₃	C₂²	1	4	yes	—
62	C₂²⋊C₄×D₂₃	C₂²	1	4	yes	—
63	#10625048	C₂²	1	2	yes	complemented
64	#10625045	C₂²	1	1	yes	characteristic, complemented
65	C₄×D₉₂	C₂²	1	2	yes	complemented
66	#10625043	C₂²	1	1	yes	characteristic, complemented
67	#10625043	C₂²	1	1	yes	characteristic, complemented
68	C₄²×D₂₃	C₂²	1	1	yes	characteristic
69	C₄²×D₂₃	C₂²	1	1	yes	characteristic
70	#10625041	C₂²	1	1	yes	characteristic, complemented
71	C₂³×D₂₃	C₂³	1	1	yes	characteristic
72	C₂³×D₂₃	C₂³	1	4	yes	—
73	C₂×D₄×C₂₃	C₂³	1	2	yes	—
74	C₂×D₄×C₂₃	C₂³	1	4	yes	—
75	C₂×D₄×C₂₃	C₂³	1	4	yes	—
76	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
78	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
79	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
80	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
81	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
82	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
83	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
84	C₂²×Dic₂₃	C₂³	1	4	yes	—
85	D₄×D₂₃	—	2	8	no	—
86	D₄×D₂₃	—	4	8	no	—
87	D₄×D₂₃	—	4	8	no	—
88	C₂×D₉₂	C₂³	1	2	yes	—
89	C₂×D₉₂	C₂³	1	4	yes	—
90	C₂×D₉₂	C₂³	1	4	yes	—
91	C₂×C₄×D₂₃	—	2	4	no	—
92	C₂×C₄×D₂₃	—	4	8	no	—
93	C₂×C₄×D₂₃	C₂³	1	2	yes	—
94	C₂×C₄×D₂₃	C₂³	1	2	yes	—
95	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
96	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
97	C₂×C₄×D₂₃	C₂³	1	4	yes	—
98	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₂₃	C₂³	1	4	yes	—
100	C₂×C₄×D₂₃	C₂³	1	4	yes	—
101	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
102	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
103	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
104	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
105	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
106	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
107	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
108	C₄²×C₂₃	C₂³	1	1	yes	characteristic
109	C₄²×C₂₃	C₂³	1	1	yes	characteristic
110	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
111	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
112	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
113	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
114	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
115	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
116	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
117	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
118	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
119	C₄⋊Dic₂₃	C₂³	1	2	yes	—
120	C₄⋊Dic₂₃	C₂³	1	2	yes	—
121	C₄⋊Dic₂₃	C₂³	1	4	yes	—
122	Dic₂₃⋊C₄	C₂³	1	4	yes	—
123	Dic₂₃⋊C₄	C₂³	1	2	yes	—
124	Dic₂₃⋊C₄	C₂³	1	2	yes	—
125	Dic₂₃⋊C₄	C₂³	1	4	yes	—
126	Dic₂₃⋊C₄	C₂³	1	4	yes	—
127	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
128	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
129	C₄×Dic₂₃	C₂³	1	2	yes	—
130	C₄×Dic₂₃	C₂³	1	2	yes	—
131	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
132	C₂³×C₂₃	C₂⁴	1	4	yes	—
133	C₂²×D₂₃	—	2	2	no	—
134	C₂²×D₂₃	—	2	8	no	—
135	C₂²×D₂₃	—	2	8	no	—
136	C₂²×D₂₃	—	2	4	no	—
137	C₂²×D₂₃	—	2	8	no	—
138	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
139	C₂²×D₂₃	C₂⁴	1	4	yes	—
140	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
141	D₄×C₂₃	—	2	4	no	—
142	D₄×C₂₃	—	4	4	no	—
143	D₄×C₂₃	—	4	4	no	—
144	C₂×C₄×C₂₃	—	2	2	no	—
145	C₂×C₄×C₂₃	—	4	4	no	—
146	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
147	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
148	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
149	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
150	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
151	C₂²⋊D₂₃	—	2	8	no	—
152	C₂²⋊D₂₃	—	4	4	no	—
153	C₂²⋊D₂₃	—	4	4	no	—
154	C₂²⋊D₂₃	—	4	4	no	—
155	C₂²⋊D₂₃	—	4	4	no	—
156	C₂×Dic₂₃	—	2	2	no	—
157	C₂×Dic₂₃	—	4	4	no	—
158	C₂×Dic₂₃	C₂⁴	1	2	yes	—
159	C₂×Dic₂₃	C₂⁴	1	2	yes	—
160	C₂×Dic₂₃	C₂⁴	1	4	yes	—
161	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
162	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
163	D₉₂	—	2	4	no	—
164	D₉₂	—	4	4	no	—
165	D₉₂	—	4	4	no	—
166	C₄×D₂₃	—	2	2	no	—
167	C₄×D₂₃	—	2	4	no	—
168	C₄×D₂₃	—	2	8	no	—
169	C₄×D₂₃	—	2	4	no	—
170	C₄×D₂₃	—	2	2	no	—
171	C₄×D₂₃	—	2	2	no	—
172	C₄×D₂₃	—	4	4	no	—
173	C₄×D₂₃	—	4	4	no	—
174	C₄×D₂₃	#41	1	4	yes	—
175	C₂×#540	—	23	1	no	maximal, Sylow
176	C₂²×C₂₃	—	2	1	no	—
177	C₂²×C₂₃	—	2	4	no	—
178	C₂²×C₂₃	—	2	4	no	—
179	C₂²×C₂₃	—	2	2	no	—
180	C₂²×C₂₃	—	2	4	no	—
181	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
182	C₂×D₂₃	—	2	1	no	—
183	C₂×D₂₃	—	2	4	no	—
184	C₂×D₂₃	—	2	4	no	—
185	C₂×D₂₃	—	2	2	no	—
186	C₂×D₂₃	—	2	4	no	—
187	C₂×D₂₃	—	4	4	no	—
188	C₂×D₂₃	—	4	16	no	—
189	C₂×D₂₃	C₂×#41	1	2	yes	—
190	C₂×D₂₃	H(5,𝔽₂)	1	4	yes	—
191	C₄×C₂₃	—	2	1	no	—
192	C₄×C₂₃	—	2	2	no	—
193	C₄×C₂₃	—	2	4	no	—
194	C₄×C₂₃	—	2	2	no	—
195	C₄×C₂₃	C₂×#41	1	2	yes	—
196	Dic₂₃	—	2	1	no	—
197	Dic₂₃	—	2	2	no	—
198	Dic₂₃	—	2	4	no	—
199	Dic₂₃	—	2	2	no	—
200	Dic₂₃	C₂×#41	1	2	yes	—
201	#540	—	23	1	no	—
202	#540	—	23	1	no	—
203	#540	—	23	4	no	—
204	#540	—	23	4	no	—
205	#540	—	23	2	no	—
206	#540	—	23	2	no	—
207	#540	—	23	1	no	—
208	#540	D₂₃	1	1	yes	characteristic, direct product factor
209	C₂×#127	—	23	1	no	—
210	C₂×#125	—	23	1	no	—
211	C₂×#123	—	23	4	no	—
212	C₂×#121	—	23	4	no	—
213	C₂×#121	—	23	2	no	—
214	C₂×C₄×D₄	—	23	2	no	—
215	C₂×#117	—	23	1	no	—
216	C₂×C₂₃	—	4	1	no	—
217	C₂×C₂₃	—	4	4	no	—
218	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
219	C₂×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
220	D₂₃	—	4	1	no	—
221	D₂₃	—	4	4	no	—
222	D₂₃	#540	1	4	yes	direct product factor
223	C₂²×D₄	—	23	2	no	—
224	C₂²×D₄	—	23	4	no	—
225	C₂²×D₄	—	23	4	no	—
226	C₂³×C₄	—	23	1	no	—
227	C₂³×C₄	—	23	4	no	—
228	#127	—	23	4	no	—
229	#127	—	23	2	no	—
230	#127	—	23	1	no	—
231	#127	C₂×D₂₃	1	1	yes	characteristic, complemented
232	#125	—	23	4	no	—
233	#125	—	23	2	no	—
234	#125	—	23	1	no	—
235	#125	C₂×D₂₃	1	1	yes	characteristic, complemented
236	#123	—	23	4	no	—
237	#123	—	23	4	no	—
238	#123	—	23	4	no	—
239	#123	—	23	4	no	—
240	#123	—	23	4	no	—
241	#123	—	23	4	no	—
242	#123	—	23	4	no	—
243	#123	C₂×D₂₃	1	4	yes	complemented
244	#121	—	23	4	no	—
245	#121	—	23	2	no	—
246	#121	—	23	4	no	—
247	#121	—	23	4	no	—
248	#121	—	23	4	no	—
249	#121	—	23	4	no	—
250	#121	—	23	2	no	—
251	#121	—	23	4	no	—
252	#121	—	23	2	no	—
253	#121	—	23	4	no	—
254	#121	—	23	4	no	—
255	#121	—	23	4	no	—
256	#121	C₂×D₂₃	1	4	yes	complemented
257	#121	C₂×D₂₃	1	2	yes	complemented
258	C₄×D₄	—	23	2	no	—
259	C₄×D₄	—	23	4	no	—
260	C₄×D₄	—	23	2	no	—
261	C₄×D₄	—	23	4	no	—
262	C₄×D₄	—	23	2	no	—
263	C₄×D₄	C₂×D₂₃	1	2	yes	complemented
264	#117	—	23	1	no	—
265	#117	—	23	2	no	—
266	#117	—	23	2	no	—
267	#117	—	23	1	no	—
268	#117	—	23	1	no	—
269	#117	C₂×D₂₃	1	1	yes	characteristic, complemented
270	C₂×C₄⋊C₄	—	23	2	no	—
271	C₂×C₄⋊C₄	—	23	2	no	—
272	C₂×C₄⋊C₄	—	23	4	no	—
273	C₂×C₂²⋊C₄	—	23	2	no	—
274	C₂×C₂²⋊C₄	—	23	4	no	—
275	C₂×C₂²⋊C₄	—	23	4	no	—
276	C₂×C₄²	—	23	1	no	—
277	C₂×C₄²	—	23	1	no	—
278	C₂₃	C₂×#540	1	1	yes	characteristic, complemented, Sylow
279	C₂⁴	—	23	1	no	—
280	C₂⁴	—	23	4	no	—
281	C₂×D₄	—	23	4	no	—
282	C₂×D₄	—	23	4	no	—
283	C₂×D₄	—	23	4	no	—
284	C₂×D₄	—	23	4	no	—
285	C₂×D₄	—	23	4	no	—
286	C₂×D₄	—	23	2	no	—
287	C₂×D₄	—	23	4	no	—
288	C₂×D₄	—	23	4	no	—
289	C₂×D₄	—	46	8	no	—
290	C₂×D₄	—	92	8	no	—
291	C₂×D₄	—	92	8	no	—
292	C₂×D₄	C₂²×D₂₃	1	2	yes	—
293	C₂×D₄	C₂²×D₂₃	1	4	yes	—
294	C₂×D₄	C₂²×D₂₃	1	4	yes	—
295	C₂²×C₄	—	23	1	no	—
296	C₂²×C₄	—	23	1	no	—
297	C₂²×C₄	—	23	4	no	—
298	C₂²×C₄	—	23	2	no	—
299	C₂²×C₄	—	23	2	no	—
300	C₂²×C₄	—	23	1	no	—
301	C₂²×C₄	—	23	4	no	—
302	C₂²×C₄	—	23	1	no	—
303	C₂²×C₄	—	23	1	no	—
304	C₂²×C₄	—	23	4	no	—
305	C₂²×C₄	—	23	4	no	—
306	C₂²×C₄	—	46	4	no	—
307	C₂²×C₄	—	92	8	no	—
308	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
309	C₂²×C₄	C₂²×D₂₃	1	4	yes	—
310	C₄⋊C₄	—	23	2	no	—
311	C₄⋊C₄	—	23	2	no	—
312	C₄⋊C₄	—	23	2	no	—
313	C₄⋊C₄	—	23	4	no	—
314	C₄⋊C₄	—	23	2	no	—
315	C₄⋊C₄	—	23	4	no	—
316	C₄⋊C₄	—	23	4	no	—
317	C₄⋊C₄	—	23	4	no	—
318	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
319	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
320	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
321	C₂²⋊C₄	—	23	2	no	—
322	C₂²⋊C₄	—	23	4	no	—
323	C₂²⋊C₄	—	23	4	no	—
324	C₂²⋊C₄	—	23	2	no	—
325	C₂²⋊C₄	—	23	2	no	—
326	C₂²⋊C₄	—	23	4	no	—
327	C₂²⋊C₄	—	23	4	no	—
328	C₂²⋊C₄	—	23	4	no	—
329	C₂²⋊C₄	—	23	4	no	—
330	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
331	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
332	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
333	C₄²	—	23	2	no	—
334	C₄²	—	23	1	no	—
335	C₄²	—	23	2	no	—
336	C₄²	—	23	1	no	—
337	C₄²	C₂²×D₂₃	1	1	yes	characteristic
338	C₄²	C₂²×D₂₃	1	1	yes	characteristic
339	C₂³	—	23	1	no	—
340	C₂³	—	23	1	no	—
341	C₂³	—	23	4	no	—
342	C₂³	—	46	2	no	—
343	C₂³	—	46	8	no	—
344	C₂³	—	46	8	no	—
345	C₂³	—	46	4	no	—
346	C₂³	—	46	8	no	—
347	C₂³	C₂³×D₂₃	1	1	yes	characteristic
348	C₂³	C₂³×D₂₃	1	4	yes	—
349	D₄	—	2	4	no	—
350	D₄	—	4	4	no	—
351	D₄	—	4	4	no	—
352	D₄	—	46	8	no	—
353	D₄	—	46	4	no	—
354	D₄	—	92	4	no	—
355	D₄	—	92	4	no	—
356	D₄	—	92	4	no	—
357	D₄	—	92	4	no	—
358	D₄	—	92	4	no	—
359	D₄	—	92	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	23	1	no	—
363	C₂×C₄	—	23	4	no	—
364	C₂×C₄	—	23	2	no	—
365	C₂×C₄	—	23	2	no	—
366	C₂×C₄	—	23	1	no	—
367	C₂×C₄	—	23	4	no	—
368	C₂×C₄	—	46	2	no	—
369	C₂×C₄	—	46	2	no	—
370	C₂×C₄	—	46	4	no	—
371	C₂×C₄	—	46	8	no	—
372	C₂×C₄	—	46	4	no	—
373	C₂×C₄	—	46	2	no	—
374	C₂×C₄	—	46	2	no	—
375	C₂×C₄	—	92	4	no	—
376	C₂×C₄	—	92	4	no	—
377	C₂×C₄	—	92	4	no	—
378	C₂×C₄	C₂³×D₂₃	1	2	yes	—
379	C₂×C₄	C₂³×D₂₃	1	2	yes	—
380	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
381	C₂×C₄	C₂³×D₂₃	1	4	yes	—
382	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
383	C₂²	—	2	1	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	23	2	no	—
389	C₂²	—	23	4	no	—
390	C₂²	—	46	1	no	—
391	C₂²	—	46	4	no	—
392	C₂²	—	46	4	no	—
393	C₂²	—	46	2	no	—
394	C₂²	—	46	4	no	—
395	C₂²	—	92	4	no	—
396	C₂²	—	92	16	no	—
397	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	4	no	—
401	C₄	—	2	2	no	—
402	C₄	—	23	2	no	—
403	C₄	—	46	1	no	—
404	C₄	—	46	2	no	—
405	C₄	—	46	4	no	—
406	C₄	—	46	2	no	—
407	C₄	#41×D₂₃	1	2	yes	—
408	C₂	—	4	1	no	—
409	C₂	—	4	4	no	—
410	C₂	—	23	4	no	—
411	C₂	—	92	1	no	—
412	C₂	—	92	4	no	—
413	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
414	C₂	H(5,𝔽₂)×D₂₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Fitting	C₂₃×#540	C₂
hypercenter	#540	D₂₃
hypocenter	C₂₃	C₂×#540
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. #13093023	C₂	semidirect
2. #13093022	C₂	semidirect
3. #13093021	C₂	semidirect
4. #13093020	C₂	semidirect
5. #13093019	C₂	semidirect
6. #13093018	C₂	semidirect
7. #13093017	C₂	semidirect
8. #127×D₂₃	C₂	semidirect
9. #125×D₂₃	C₂	semidirect
10. #123×D₂₃	C₂	semidirect
11. #121×D₂₃	C₂	semidirect
12. #121×D₂₃	C₂	semidirect
13. C₄×D₄×D₂₃	C₂	semidirect
14. #117×D₂₃	C₂	semidirect
15. C₂₃×#540	C₂	semidirect
21. C₂₃×#127	C₂²	semidirect
22. C₂₃×#125	C₂²	semidirect
23. C₂₃×#123	C₂²	semidirect
24. C₂₃×#121	C₂²	semidirect
25. C₂₃×#121	C₂²	semidirect
26. C₄×D₄×C₂₃	C₂²	semidirect
27. C₂₃×#117	C₂²	semidirect
28. #10625111	C₂²	semidirect
29. #10625111	C₂²	semidirect
30. #10625110	C₂²	semidirect
31. #10625110	C₂²	semidirect
32. #10625110	C₂²	semidirect
33. #10625109	C₂²	semidirect
34. #10625109	C₂²	semidirect
35. #10625106	C₂²	semidirect
36. D₄×Dic₂₃	C₂²	semidirect
37. #10625101	C₂²	semidirect
38. #10625101	C₂²	semidirect
39. #10625100	C₂²	semidirect
40. C₄×C₂²⋊D₂₃	C₂²	semidirect
41. #10625097	C₂²	semidirect
42. #10625066	C₂²	semidirect
43. #10625066	C₂²	semidirect
44. #10625065	C₂²	semidirect
45. #10625065	C₂²	semidirect
46. #10625064	C₂²	semidirect
47. #10625063	C₂²	semidirect
51. #10625061	C₂²	semidirect
52. #10625060	C₂²	semidirect
53. #10625057	C₂²	semidirect
54. #10625055	C₂²	semidirect
55. #10625055	C₂²	semidirect
56. #10625055	C₂²	semidirect
57. #10625054	C₂²	semidirect
58. #10625054	C₂²	semidirect
59. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
63. #10625048	C₂²	semidirect
64. #10625045	C₂²	semidirect
65. C₄×D₉₂	C₂²	semidirect
66. #10625043	C₂²	semidirect
67. #10625043	C₂²	semidirect
70. #10625041	C₂²	semidirect
208. #540	D₂₃	direct (N × H)
222. D₂₃	#540	direct (N × H)
231. #127	C₂×D₂₃	semidirect
235. #125	C₂×D₂₃	semidirect
243. #123	C₂×D₂₃	semidirect
256. #121	C₂×D₂₃	semidirect
257. #121	C₂×D₂₃	semidirect
263. C₄×D₄	C₂×D₂₃	semidirect
269. #117	C₂×D₂₃	semidirect
278. C₂₃	C₂×#540	semidirect

Maximal subgroups

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

subgroup	index
#13093023	2
#13093022	2
#13093021	2
#13093020	2
#13093019	2
#13093018	2
#13093017	2
#127×D₂₃	2
#125×D₂₃	2
#123×D₂₃	2
#121×D₂₃	2
C₄×D₄×D₂₃	2
#117×D₂₃	2
C₂₃×#540	2
C₂×#540	23

Subgroups — D23×#540 #15686751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×#540 #15686751