Subgroups — C₂₃×#10074 #19157700

Order 5888.

618 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#474	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2547	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₂₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₂₃×#124	—	2	1	no	—
11	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
12	C₂₃×#498	—	2	2	no	—
13	C₂₃×#498	—	2	2	no	—
14	C₂₃×#474	—	2	2	no	—
15	C₂₃×#474	—	2	2	no	—
16	C₂×C₂₃×#107	—	2	1	no	—
17	C₂×C₂₃×#106	—	2	2	no	—
18	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#103	—	2	2	no	—
21	C₂×C₂₃×#102	—	2	1	no	—
22	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₂₃×#397	—	2	2	no	—
24	C₂₃×#391	—	2	1	no	—
25	C₂₃×#380	—	2	2	no	—
26	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#332	—	2	2	no	—
28	C₂₃×D₄⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₂₃	—	2	1	no	—
30	C₂²×Q₈×C₂₃	—	2	1	no	—
31	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₂₃	—	2	1	no	—
33	C₂²×C₈×C₂₃	—	2	1	no	—
34	C₂²×C₈×C₂₃	—	2	1	no	—
35	C₂²×C₈×C₂₃	—	2	1	no	—
36	C₂₃×C₄⋊Q₈	—	2	1	no	—
37	C₂₃×C₄⋊Q₈	—	2	1	no	—
38	C₂₃×C₄⋊Q₈	—	2	1	no	—
39	C₂₃×C₄⋊Q₈	—	2	1	no	—
40	C₂₃×C₄⋊Q₈	—	2	1	no	—
41	C₂₃×C₄⋊Q₈	—	2	1	no	—
42	C₂₃×C₄⋊Q₈	—	2	1	no	—
43	C₂₃×C₄⋊Q₈	D₄	1	2	yes	—
44	C₂₃×#124	—	4	2	no	—
45	C₂₃×#124	—	4	2	no	—
46	C₄×D₄×C₂₃	—	2	1	no	—
47	C₄×D₄×C₂₃	—	2	1	no	—
48	C₄×D₄×C₂₃	—	2	1	no	—
49	C₄×D₄×C₂₃	—	2	1	no	—
50	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
51	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
52	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
53	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
58	C₂×C₄²×C₂₃	—	2	1	no	—
59	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
60	C₂₃×#107	—	2	4	no	—
61	C₂₃×#106	—	2	8	no	—
62	C₂₃×C₄⋊C₈	—	2	1	no	—
63	C₂₃×C₄⋊C₈	—	2	1	no	—
64	C₂₃×C₄⋊C₈	—	2	1	no	—
65	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
66	C₂₃×#103	—	4	4	no	—
67	C₂₃×#102	—	2	4	no	—
68	C₄×C₈×C₂₃	—	2	1	no	—
69	C₄×C₈×C₂₃	D₄	1	2	yes	—
70	C₂₃×#95	—	2	4	no	—
71	C₂₃×#95	—	2	1	no	—
72	C₂⁴×C₂₃	—	2	1	no	—
73	C₂×Q₈×C₂₃	—	2	2	no	—
74	C₂×Q₈×C₂₃	—	4	1	no	—
75	C₂×Q₈×C₂₃	—	4	1	no	—
76	C₂×Q₈×C₂₃	—	4	1	no	—
77	C₂×Q₈×C₂₃	—	4	1	no	—
78	C₂×Q₈×C₂₃	—	4	1	no	—
79	C₂×Q₈×C₂₃	—	4	1	no	—
80	C₂×Q₈×C₂₃	—	4	1	no	—
81	C₂×Q₈×C₂₃	—	4	2	no	—
82	C₂×Q₈×C₂₃	—	4	2	no	—
83	C₂×D₄×C₂₃	—	2	1	no	—
84	C₂×D₄×C₂₃	—	2	1	no	—
85	C₂×D₄×C₂₃	—	2	1	no	—
86	C₂×D₄×C₂₃	—	2	1	no	—
87	C₂×D₄×C₂₃	—	2	1	no	—
88	C₂×D₄×C₂₃	SD₁₆	1	2	yes	—
89	C₂²×C₄×C₂₃	—	2	2	no	—
90	C₂²×C₄×C₂₃	—	2	2	no	—
91	C₂²×C₄×C₂₃	—	2	1	no	—
92	C₂²×C₄×C₂₃	—	4	1	no	—
93	C₂²×C₄×C₂₃	—	4	1	no	—
94	C₂²×C₄×C₂₃	—	4	1	no	—
95	C₂²×C₄×C₂₃	—	4	2	no	—
96	C₂²×C₄×C₂₃	—	4	2	no	—
97	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
100	C₂×C₈×C₂₃	—	2	4	no	—
101	C₂×C₈×C₂₃	—	2	2	no	—
102	C₂×C₈×C₂₃	—	2	2	no	—
103	C₂×C₈×C₂₃	—	4	1	no	—
104	C₂×C₈×C₂₃	—	4	1	no	—
105	C₂×C₈×C₂₃	—	4	1	no	—
106	C₂×C₈×C₂₃	—	4	2	no	—
107	C₄⋊C₄×C₂₃	—	2	2	no	—
108	C₄⋊C₄×C₂₃	—	2	2	no	—
109	C₄⋊C₄×C₂₃	—	2	2	no	—
110	C₄⋊C₄×C₂₃	—	2	1	no	—
111	C₄⋊C₄×C₂₃	—	2	1	no	—
112	C₄⋊C₄×C₂₃	—	2	2	no	—
113	C₄⋊C₄×C₂₃	—	2	2	no	—
114	C₄⋊C₄×C₂₃	—	2	2	no	—
115	C₄⋊C₄×C₂₃	—	4	1	no	—
116	C₄⋊C₄×C₂₃	—	4	1	no	—
117	C₄⋊C₄×C₂₃	—	4	1	no	—
118	C₄⋊C₄×C₂₃	—	4	1	no	—
119	C₂²⋊C₄×C₂₃	—	4	8	no	—
120	C₂²⋊C₄×C₂₃	—	4	1	no	—
121	C₂²⋊C₄×C₂₃	—	4	1	no	—
122	C₄²×C₂₃	—	4	1	no	—
123	C₄²×C₂₃	—	4	1	no	—
124	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₂₃	#41	1	1	yes	characteristic
128	#10074	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₂₃	—	2	2	no	—
130	C₂³×C₂₃	—	4	1	no	—
131	C₂³×C₂₃	—	4	2	no	—
132	C₂³×C₂₃	—	4	1	no	—
133	C₂³×C₂₃	—	4	2	no	—
134	C₂³×C₂₃	#120	1	1	yes	characteristic
135	Q₈×C₂₃	—	4	4	no	—
136	Q₈×C₂₃	—	8	1	no	—
137	Q₈×C₂₃	—	8	1	no	—
138	Q₈×C₂₃	—	8	1	no	—
139	Q₈×C₂₃	—	8	1	no	—
140	Q₈×C₂₃	—	8	1	no	—
141	Q₈×C₂₃	—	8	1	no	—
142	D₄×C₂₃	—	2	2	no	—
143	D₄×C₂₃	—	2	2	no	—
144	D₄×C₂₃	—	4	1	no	—
145	D₄×C₂₃	—	4	1	no	—
146	C₂×C₄×C₂₃	—	2	2	no	—
147	C₂×C₄×C₂₃	—	4	1	no	—
148	C₂×C₄×C₂₃	—	4	2	no	—
149	C₂×C₄×C₂₃	—	4	2	no	—
150	C₂×C₄×C₂₃	—	4	2	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	—	8	2	no	—
157	C₂×C₄×C₂₃	—	8	2	no	—
158	C₂×C₄×C₂₃	—	8	1	no	—
159	C₂×C₄×C₂₃	—	8	1	no	—
160	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
161	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
162	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
163	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
164	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
165	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
166	C₂×C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
167	C₂×C₄×C₂₃	#135	1	1	yes	characteristic
168	C₂×C₄×C₂₃	#135	1	2	yes	—
169	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
171	C₂×C₄×C₂₃	#137	1	1	yes	characteristic
172	C₈×C₂₃	—	2	4	no	—
173	C₈×C₂₃	—	4	2	no	—
174	C₈×C₂₃	—	8	1	no	—
175	C₂×#498	C₂×C₂₃	1	1	yes	characteristic, complemented
176	C₂×#474	C₂×C₂₃	1	1	yes	characteristic
177	#2547	C₂×C₂₃	1	1	yes	characteristic
178	#1981	C₂×C₂₃	1	1	yes	characteristic, complemented
179	C₂×#332	C₂×C₂₃	1	1	yes	characteristic, complemented
180	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic
181	#1279	C₂×C₂₃	1	1	yes	characteristic, complemented
182	C₂²×C₂₃	—	4	4	no	—
183	C₂²×C₂₃	—	4	2	no	—
184	C₂²×C₂₃	—	8	2	no	—
185	C₂²×C₂₃	—	8	1	no	—
186	C₂²×C₂₃	—	8	1	no	—
187	C₂²×C₂₃	#392	1	1	yes	characteristic
188	C₂²×C₂₃	#449	1	2	yes	—
189	C₂²×C₂₃	#450	1	1	yes	characteristic
190	C₂²×C₂₃	#452	1	1	yes	characteristic
191	C₂²×C₂₃	#456	1	2	yes	—
192	C₄×C₂₃	—	2	1	no	—
193	C₄×C₂₃	—	2	1	no	—
194	C₄×C₂₃	—	8	2	no	—
195	C₄×C₂₃	—	8	2	no	—
196	C₄×C₂₃	—	8	1	no	—
197	C₄×C₂₃	—	8	2	no	—
198	C₄×C₂₃	#448	1	1	yes	characteristic
199	C₄×C₂₃	#449	1	1	yes	characteristic
200	C₄×C₂₃	#463	1	2	yes	—
201	C₄×C₂₃	#465	1	1	yes	characteristic
202	C₄×C₂₃	#468	1	1	yes	characteristic
203	C₄×C₂₃	#495	1	1	yes	characteristic
204	C₄×C₂₃	#496	1	1	yes	characteristic
205	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
206	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
207	C₂×#124	—	2	1	no	—
208	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
209	#498	—	2	2	no	—
210	#498	—	2	2	no	—
211	#474	—	2	2	no	—
212	#474	—	2	2	no	—
213	C₂×#107	—	2	1	no	—
214	C₂×#106	—	2	2	no	—
215	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
217	C₂×#103	—	2	2	no	—
218	C₂×#102	—	2	1	no	—
219	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
220	#397	—	2	2	no	—
221	#391	—	2	1	no	—
222	#380	—	2	2	no	—
223	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
224	#332	—	2	2	no	—
225	D₄⋊C₈	—	2	2	no	—
226	C₂×C₂₃	—	8	2	no	—
227	C₂×C₂₃	#1652	1	2	yes	—
228	C₂×C₂₃	#1654	1	2	yes	—
229	C₂×C₂₃	#2000	1	1	yes	characteristic
230	C₂×C₂₃	#2005	1	1	yes	characteristic
231	C₂×C₂₃	#2012	1	1	yes	characteristic
232	C₂²×Q₈	—	2	1	no	—
233	C₂²×Q₈	—	2	1	no	—
234	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
235	C₂³×C₄	—	2	1	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	—	2	1	no	—
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	D₄×C₂₃	1	2	yes	—
247	#124	—	4	2	no	—
248	#124	—	4	2	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
257	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
258	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
259	C₂×C₂²⋊C₄	—	2	4	no	—
260	C₂×C₂²⋊C₄	—	2	1	no	—
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
263	#107	—	2	4	no	—
264	#106	—	2	8	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
269	#103	—	4	4	no	—
270	#102	—	2	4	no	—
271	C₄×C₈	—	2	1	no	—
272	C₄×C₈	D₄×C₂₃	1	2	yes	—
273	#95	—	2	4	no	—
274	#95	—	2	1	no	—
275	C₂₃	#10074	1	1	yes	characteristic, direct product factor, Sylow
276	C₂⁴	—	2	1	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	4	1	no	—
279	C₂×Q₈	—	4	1	no	—
280	C₂×Q₈	—	4	1	no	—
281	C₂×Q₈	—	4	1	no	—
282	C₂×Q₈	—	4	1	no	—
283	C₂×Q₈	—	4	1	no	—
284	C₂×Q₈	—	4	1	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×Q₈	—	4	2	no	—
287	C₂×D₄	—	2	1	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	SD₁₆×C₂₃	1	2	yes	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
304	C₂×C₈	—	2	4	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	—	4	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₂²⋊C₄	—	4	8	no	—
324	C₂²⋊C₄	—	4	1	no	—
325	C₂²⋊C₄	—	4	1	no	—
326	C₄²	—	4	1	no	—
327	C₄²	—	4	1	no	—
328	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
329	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
330	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
331	C₄²	#41×C₂₃	1	1	yes	characteristic
332	C₂³	—	2	2	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	1	no	—
336	C₂³	—	4	2	no	—
337	C₂³	C₂₃×#120	1	1	yes	characteristic
338	Q₈	—	4	4	no	—
339	Q₈	—	8	1	no	—
340	Q₈	—	8	1	no	—
341	Q₈	—	8	1	no	—
342	Q₈	—	8	1	no	—
343	Q₈	—	8	1	no	—
344	Q₈	—	8	1	no	—
345	D₄	—	2	2	no	—
346	D₄	—	2	2	no	—
347	D₄	—	4	1	no	—
348	D₄	—	4	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	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	—	8	2	no	—
360	C₂×C₄	—	8	2	no	—
361	C₂×C₄	—	8	1	no	—
362	C₂×C₄	—	8	1	no	—
363	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
364	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
365	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
366	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
367	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
368	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
369	C₂×C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
370	C₂×C₄	C₂₃×#135	1	1	yes	characteristic
371	C₂×C₄	C₂₃×#135	1	2	yes	—
372	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
373	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
374	C₂×C₄	C₂₃×#137	1	1	yes	characteristic
375	C₈	—	2	4	no	—
376	C₈	—	4	2	no	—
377	C₈	—	8	1	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	1	no	—
382	C₂²	—	8	1	no	—
383	C₂²	C₂₃×#392	1	1	yes	characteristic
384	C₂²	C₂₃×#449	1	2	yes	—
385	C₂²	C₂₃×#450	1	1	yes	characteristic
386	C₂²	C₂₃×#452	1	1	yes	characteristic
387	C₂²	C₂₃×#456	1	2	yes	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	8	2	no	—
391	C₄	—	8	2	no	—
392	C₄	—	8	1	no	—
393	C₄	—	8	2	no	—
394	C₄	C₂₃×#448	1	1	yes	characteristic
395	C₄	C₂₃×#449	1	1	yes	characteristic
396	C₄	C₂₃×#463	1	2	yes	—
397	C₄	C₂₃×#465	1	1	yes	characteristic
398	C₄	C₂₃×#468	1	1	yes	characteristic
399	C₄	C₂₃×#495	1	1	yes	characteristic
400	C₄	C₂₃×#496	1	1	yes	characteristic
401	C₂	—	8	2	no	—
402	C₂	C₂₃×#1652	1	2	yes	—
403	C₂	C₂₃×#1654	1	2	yes	—
404	C₂	C₂₃×#2000	1	1	yes	characteristic
405	C₂	C₂₃×#2005	1	1	yes	characteristic
406	C₂	C₂₃×#2012	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
prime radical	C₂²×D₄×C₂₃	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#498	C₂	semidirect
4. C₂₃×#1981	C₂	semidirect
5. C₂×C₂₃×#332	C₂	semidirect
7. C₂₃×#1279	C₂	semidirect
128. #10074	C₂₃	direct (N × H)
175. C₂×#498	C₂×C₂₃	semidirect
178. #1981	C₂×C₂₃	semidirect
179. C₂×#332	C₂×C₂₃	semidirect
181. #1279	C₂×C₂₃	semidirect
275. C₂₃	#10074	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#498	2
C₂×C₂₃×#474	2
C₂₃×#2547	2
C₂₃×#1981	2
C₂×C₂₃×#332	2
C₂×C₂₃×D₄⋊C₈	2
C₂₃×#1279	2
#10074	23

Subgroups — C23×#10074 #19157700

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#10074 #19157700