Subgroups — C₂₃×#29130 #19176756

Order 5888.

878 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₂₃×#127	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2100	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2041	C₂	1	2	yes	maximal
5	C₂₃×#1936	C₂	1	4	yes	maximal, complemented
6	C₂₃×#1802	C₂	1	2	yes	maximal, complemented
7	C₂₃×#1802	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
10	C₂×C₂₃×#125	—	2	1	no	—
11	C₂×C₄×D₄×C₂₃	—	2	1	no	—
12	C₂×C₄×D₄×C₂₃	—	2	1	no	—
13	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
14	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₂₃×#102	C₂²	1	4	yes	—
16	C₂×C₂₃×#102	C₂²	1	4	yes	—
17	C₂×C₂₃×#97	C₂²	1	2	yes	—
18	C₂₃×#390	—	2	1	no	—
19	C₂₃×#390	—	2	1	no	—
20	C₂₃×#390	C₂²	1	2	yes	—
21	C₂₃×#389	—	2	1	no	—
22	C₂₃×#389	—	2	1	no	—
23	C₂₃×#389	C₂²	1	2	yes	—
24	C₂₃×#389	C₂²	1	2	yes	—
25	C₂₃×#384	C₂²	1	1	yes	characteristic
26	C₂₃×#384	C₂²	1	1	yes	characteristic
27	C₂₃×#384	C₂²	1	1	yes	characteristic
28	C₂₃×#382	—	2	1	no	—
29	C₄³×C₂₃	C₂²	1	1	yes	characteristic
30	C₂₃×#340	C₂²	1	4	yes	—
31	C₂₃×#340	C₂²	1	4	yes	—
32	C₂₃×#336	C₂²	1	2	yes	—
33	C₂²×D₄×C₂₃	—	2	1	no	—
34	C₂²×D₄×C₂₃	—	2	1	no	—
35	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
36	C₂³×C₄×C₂₃	—	2	2	no	—
37	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
38	C₂₃×#127	—	2	4	no	—
39	C₂₃×#125	—	4	4	no	—
40	C₄×D₄×C₂₃	—	2	4	no	—
41	C₄×D₄×C₂₃	—	2	4	no	—
42	C₄×D₄×C₂₃	—	4	4	no	—
43	C₄×D₄×C₂₃	—	4	4	no	—
44	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
45	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
46	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
47	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
48	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
49	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
50	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
51	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
52	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
55	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
58	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
65	C₂₃×C₄⋊C₈	—	2	4	no	—
66	C₂₃×#102	—	2	8	no	—
67	C₂₃×#102	—	4	4	no	—
68	C₂₃×#97	—	4	2	no	—
69	C₂₃×#95	—	2	2	no	—
70	C₂₃×#95	—	2	2	no	—
71	C₂⁴×C₂₃	—	2	2	no	—
72	C₂×D₄×C₂₃	—	2	4	no	—
73	C₂×D₄×C₂₃	—	2	4	no	—
74	C₂×D₄×C₂₃	—	2	2	no	—
75	C₂×D₄×C₂₃	—	2	2	no	—
76	C₂×D₄×C₂₃	—	2	2	no	—
77	C₂×D₄×C₂₃	—	2	2	no	—
78	C₂×D₄×C₂₃	—	2	2	no	—
79	C₂×D₄×C₂₃	—	4	2	no	—
80	C₂×D₄×C₂₃	—	4	2	no	—
81	C₂×D₄×C₂₃	—	4	2	no	—
82	C₂×D₄×C₂₃	—	4	2	no	—
83	C₂×D₄×C₂₃	#41	1	4	yes	—
84	C₂²×C₄×C₂₃	—	2	2	no	—
85	C₂²×C₄×C₂₃	—	2	2	no	—
86	C₂²×C₄×C₂₃	—	2	2	no	—
87	C₂²×C₄×C₂₃	—	4	4	no	—
88	C₂²×C₄×C₂₃	—	4	4	no	—
89	C₂²×C₄×C₂₃	—	4	4	no	—
90	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
97	C₂×C₈×C₂₃	—	2	4	no	—
98	C₂×C₈×C₂₃	—	2	4	no	—
99	C₂×C₈×C₂₃	—	2	4	no	—
100	C₄⋊C₄×C₂₃	—	2	4	no	—
101	C₄⋊C₄×C₂₃	—	2	2	no	—
102	C₄⋊C₄×C₂₃	—	2	2	no	—
103	C₄⋊C₄×C₂₃	—	2	2	no	—
104	C₄⋊C₄×C₂₃	—	2	2	no	—
105	C₄⋊C₄×C₂₃	—	4	2	no	—
106	C₄⋊C₄×C₂₃	—	4	2	no	—
107	C₄⋊C₄×C₂₃	—	4	2	no	—
108	C₄⋊C₄×C₂₃	—	4	2	no	—
109	C₄⋊C₄×C₂₃	—	4	4	no	—
110	C₄⋊C₄×C₂₃	—	4	2	no	—
111	C₄⋊C₄×C₂₃	—	4	2	no	—
112	C₄⋊C₄×C₂₃	—	4	4	no	—
113	C₂²⋊C₄×C₂₃	—	4	4	no	—
114	C₂²⋊C₄×C₂₃	—	4	4	no	—
115	C₂²⋊C₄×C₂₃	—	4	4	no	—
116	C₄²×C₂₃	—	2	2	no	—
117	C₄²×C₂₃	—	2	2	no	—
118	C₄²×C₂₃	—	2	2	no	—
119	C₄²×C₂₃	—	2	2	no	—
120	C₄²×C₂₃	—	2	2	no	—
121	C₄²×C₂₃	—	2	1	no	—
122	C₄²×C₂₃	—	2	1	no	—
123	C₄²×C₂₃	#41	1	4	yes	—
124	#29130	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂³×C₂₃	—	2	4	no	—
126	C₂³×C₂₃	—	4	2	no	—
127	C₂³×C₂₃	—	4	2	no	—
128	C₂³×C₂₃	—	4	2	no	—
129	C₂³×C₂₃	—	4	2	no	—
130	C₂³×C₂₃	—	4	2	no	—
131	C₂³×C₂₃	—	4	2	no	—
132	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
133	D₄×C₂₃	—	2	4	no	—
134	D₄×C₂₃	—	2	4	no	—
135	D₄×C₂₃	—	4	8	no	—
136	D₄×C₂₃	—	4	8	no	—
137	D₄×C₂₃	—	4	2	no	—
138	D₄×C₂₃	—	4	2	no	—
139	C₂×C₄×C₂₃	—	2	1	no	—
140	C₂×C₄×C₂₃	—	2	1	no	—
141	C₂×C₄×C₂₃	—	2	1	no	—
142	C₂×C₄×C₂₃	—	2	1	no	—
143	C₂×C₄×C₂₃	—	2	1	no	—
144	C₂×C₄×C₂₃	—	2	1	no	—
145	C₂×C₄×C₂₃	—	2	1	no	—
146	C₂×C₄×C₂₃	—	2	1	no	—
147	C₂×C₄×C₂₃	—	2	1	no	—
148	C₂×C₄×C₂₃	—	2	1	no	—
149	C₂×C₄×C₂₃	—	2	1	no	—
150	C₂×C₄×C₂₃	—	2	1	no	—
151	C₂×C₄×C₂₃	—	4	2	no	—
152	C₂×C₄×C₂₃	—	4	2	no	—
153	C₂×C₄×C₂₃	—	4	2	no	—
154	C₂×C₄×C₂₃	—	4	2	no	—
155	C₂×C₄×C₂₃	—	4	2	no	—
156	C₂×C₄×C₂₃	—	4	2	no	—
157	C₂×C₄×C₂₃	—	4	2	no	—
158	C₂×C₄×C₂₃	—	4	2	no	—
159	C₂×C₄×C₂₃	—	4	2	no	—
160	C₂×C₄×C₂₃	—	8	8	no	—
161	C₂×C₄×C₂₃	#124	1	2	yes	—
162	C₂×C₄×C₂₃	#124	1	2	yes	—
163	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
164	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
165	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×C₄×C₂₃	#137	1	2	yes	—
167	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
168	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
169	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
171	C₈×C₂₃	—	4	4	no	—
172	#2859	C₂×C₂₃	1	1	yes	characteristic, complemented
173	C₄×#127	C₂×C₂₃	1	1	yes	characteristic
174	#2100	C₂×C₂₃	1	2	yes	complemented
175	#2041	C₂×C₂₃	1	2	yes	—
176	#1936	C₂×C₂₃	1	4	yes	complemented
177	#1802	C₂×C₂₃	1	2	yes	complemented
178	#1802	C₂×C₂₃	1	2	yes	complemented
179	#1767	C₂×C₂₃	1	1	yes	characteristic, complemented
180	C₂²×C₂₃	—	4	4	no	—
181	C₂²×C₂₃	—	4	4	no	—
182	C₂²×C₂₃	—	4	4	no	—
183	C₂²×C₂₃	—	8	2	no	—
184	C₂²×C₂₃	—	8	2	no	—
185	C₂²×C₂₃	—	8	2	no	—
186	C₂²×C₂₃	—	8	2	no	—
187	C₂²×C₂₃	#525	1	1	yes	characteristic
188	C₂²×C₂₃	C₂×#124	1	1	yes	characteristic
189	C₂²×C₂₃	#537	1	1	yes	characteristic
190	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
192	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
194	C₄×C₂₃	—	2	2	no	—
195	C₄×C₂₃	—	2	2	no	—
196	C₄×C₂₃	—	2	2	no	—
197	C₄×C₂₃	—	4	1	no	—
198	C₄×C₂₃	—	4	1	no	—
199	C₄×C₂₃	—	8	2	no	—
200	C₄×C₂₃	—	8	2	no	—
201	C₄×C₂₃	—	8	2	no	—
202	C₄×C₂₃	#490	1	4	yes	—
203	C₄×C₂₃	#552	1	2	yes	—
204	C₄×C₂₃	#553	1	2	yes	—
205	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
206	C₂×#125	—	2	1	no	—
207	C₂×C₄×D₄	—	2	1	no	—
208	C₂×C₄×D₄	—	2	1	no	—
209	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
210	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
211	C₂×#102	C₂²×C₂₃	1	4	yes	—
212	C₂×#102	C₂²×C₂₃	1	4	yes	—
213	C₂×#97	C₂²×C₂₃	1	2	yes	—
214	#390	—	2	1	no	—
215	#390	—	2	1	no	—
216	#390	C₂²×C₂₃	1	2	yes	—
217	#389	—	2	1	no	—
218	#389	—	2	1	no	—
219	#389	C₂²×C₂₃	1	2	yes	—
220	#389	C₂²×C₂₃	1	2	yes	—
221	#384	C₂²×C₂₃	1	1	yes	characteristic
222	#384	C₂²×C₂₃	1	1	yes	characteristic
223	#384	C₂²×C₂₃	1	1	yes	characteristic
224	#382	—	2	1	no	—
225	C₄³	C₂²×C₂₃	1	1	yes	characteristic
226	#340	C₂²×C₂₃	1	4	yes	—
227	#340	C₂²×C₂₃	1	4	yes	—
228	#336	C₂²×C₂₃	1	2	yes	—
229	C₂×C₂₃	—	8	4	no	—
230	C₂×C₂₃	#2562	1	1	yes	characteristic
231	C₂×C₂₃	#3109	1	1	yes	characteristic
232	C₂×C₂₃	#3110	1	1	yes	characteristic
233	C₂×C₂₃	C₂×#490	1	1	yes	characteristic
234	C₂×C₂₃	#3141	1	1	yes	characteristic
235	C₂×C₂₃	#3253	1	1	yes	characteristic
236	C₂×C₂₃	#3254	1	1	yes	characteristic
237	C₂²×D₄	—	2	1	no	—
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
240	C₂³×C₄	—	2	2	no	—
241	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
242	#127	—	2	4	no	—
243	#125	—	4	4	no	—
244	C₄×D₄	—	2	4	no	—
245	C₄×D₄	—	2	4	no	—
246	C₄×D₄	—	4	4	no	—
247	C₄×D₄	—	4	4	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
263	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
264	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
265	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
269	C₄⋊C₈	—	2	4	no	—
270	#102	—	2	8	no	—
271	#102	—	4	4	no	—
272	#97	—	4	2	no	—
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	C₂₃	#29130	1	1	yes	characteristic, direct product factor, Sylow
276	C₂⁴	—	2	2	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	#41×C₂₃	1	4	yes	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	4	4	no	—
293	C₂²×C₄	—	4	4	no	—
294	C₂²×C₄	—	4	4	no	—
295	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
301	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	2	4	no	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	4	no	—
315	C₄⋊C₄	—	4	4	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₂²⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	4	4	no	—
320	C₂²⋊C₄	—	4	4	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	1	no	—
328	C₄²	#41×C₂₃	1	4	yes	—
329	C₂³	—	2	4	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
337	D₄	—	2	4	no	—
338	D₄	—	2	4	no	—
339	D₄	—	4	8	no	—
340	D₄	—	4	8	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	8	8	no	—
365	C₂×C₄	C₂₃×#124	1	2	yes	—
366	C₂×C₄	C₂₃×#124	1	2	yes	—
367	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
368	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
369	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
370	C₂×C₄	C₂₃×#137	1	2	yes	—
371	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
372	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
373	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
374	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
375	C₈	—	4	4	no	—
376	C₂²	—	4	4	no	—
377	C₂²	—	4	4	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	8	2	no	—
383	C₂²	C₂₃×#525	1	1	yes	characteristic
384	C₂²	C₂×C₂₃×#124	1	1	yes	characteristic
385	C₂²	C₂₃×#537	1	1	yes	characteristic
386	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
387	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
388	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
389	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	8	2	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	2	no	—
398	C₄	C₂₃×#490	1	4	yes	—
399	C₄	C₂₃×#552	1	2	yes	—
400	C₄	C₂₃×#553	1	2	yes	—
401	C₂	—	8	4	no	—
402	C₂	C₂₃×#2562	1	1	yes	characteristic
403	C₂	C₂₃×#3109	1	1	yes	characteristic
404	C₂	C₂₃×#3110	1	1	yes	characteristic
405	C₂	C₂×C₂₃×#490	1	1	yes	characteristic
406	C₂	C₂₃×#3141	1	1	yes	characteristic
407	C₂	C₂₃×#3253	1	1	yes	characteristic
408	C₂	C₂₃×#3254	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₄³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#2859	C₂	semidirect
3. C₂₃×#2100	C₂	semidirect
5. C₂₃×#1936	C₂	semidirect
6. C₂₃×#1802	C₂	semidirect
7. C₂₃×#1802	C₂	semidirect
8. C₂₃×#1767	C₂	semidirect
124. #29130	C₂₃	direct (N × H)
172. #2859	C₂×C₂₃	semidirect
174. #2100	C₂×C₂₃	semidirect
176. #1936	C₂×C₂₃	semidirect
177. #1802	C₂×C₂₃	semidirect
178. #1802	C₂×C₂₃	semidirect
179. #1767	C₂×C₂₃	semidirect
275. C₂₃	#29130	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×#2859	2
C₄×C₂₃×#127	2
C₂₃×#2100	2
C₂₃×#2041	2
C₂₃×#1936	2
C₂₃×#1802	2
C₂₃×#1767	2
#29130	23

Subgroups — C23×#29130 #19176756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#29130 #19176756