Subgroups — C₂₃×#10066 #19157692

Order 5888.

634 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#461	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2547	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1988	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	C₂²×SD₁₆×C₂₃	—	2	1	no	—
9	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×#124	—	2	1	no	—
12	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
13	C₂₃×#500	—	2	2	no	—
14	C₂₃×#500	—	2	2	no	—
15	C₂₃×#461	—	2	2	no	—
16	C₂₃×#461	—	2	2	no	—
17	C₂×C₂₃×#107	—	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	1	no	—
21	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
22	C₂₃×#397	—	2	2	no	—
23	C₂₃×#391	—	2	1	no	—
24	C₂₃×#380	—	2	2	no	—
25	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#340	—	2	2	no	—
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	C₂×SD₁₆×C₂₃	—	2	4	no	—
34	C₂×SD₁₆×C₂₃	—	4	2	no	—
35	C₂×SD₁₆×C₂₃	—	4	2	no	—
36	C₂²×C₈×C₂₃	—	2	1	no	—
37	C₂²×C₈×C₂₃	—	2	1	no	—
38	C₂²×C₈×C₂₃	—	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	—	2	1	no	—
44	C₂₃×C₄⋊Q₈	—	2	1	no	—
45	C₂₃×C₄⋊Q₈	—	2	1	no	—
46	C₂₃×C₄⋊Q₈	D₄	1	2	yes	—
47	C₂₃×#124	—	4	2	no	—
48	C₂₃×#124	—	4	2	no	—
49	C₄×D₄×C₂₃	—	2	1	no	—
50	C₄×D₄×C₂₃	—	2	1	no	—
51	C₄×D₄×C₂₃	—	2	1	no	—
52	C₄×D₄×C₂₃	—	2	1	no	—
53	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
54	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
55	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
56	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
61	C₂×C₄²×C₂₃	—	2	1	no	—
62	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
63	C₂₃×#107	—	2	8	no	—
64	C₂₃×C₄⋊C₈	—	2	1	no	—
65	C₂₃×C₄⋊C₈	—	2	1	no	—
66	C₂₃×C₄⋊C₈	—	2	1	no	—
67	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
68	C₂₃×#103	—	2	4	no	—
69	C₄×C₈×C₂₃	—	2	1	no	—
70	C₄×C₈×C₂₃	D₄	1	2	yes	—
71	C₂₃×#95	—	2	4	no	—
72	C₂₃×#95	—	2	1	no	—
73	C₂⁴×C₂₃	—	2	1	no	—
74	C₂×Q₈×C₂₃	—	2	2	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	1	no	—
82	C₂×Q₈×C₂₃	—	4	1	no	—
83	C₂×Q₈×C₂₃	—	4	1	no	—
84	C₂×Q₈×C₂₃	—	4	1	no	—
85	C₂×Q₈×C₂₃	—	4	1	no	—
86	C₂×D₄×C₂₃	—	2	1	no	—
87	C₂×D₄×C₂₃	—	2	1	no	—
88	C₂×D₄×C₂₃	—	2	1	no	—
89	C₂×D₄×C₂₃	—	2	1	no	—
90	C₂×D₄×C₂₃	—	2	1	no	—
91	C₂×D₄×C₂₃	D₈	1	2	yes	—
92	C₂²×C₄×C₂₃	—	2	2	no	—
93	C₂²×C₄×C₂₃	—	2	2	no	—
94	C₂²×C₄×C₂₃	—	2	1	no	—
95	C₂²×C₄×C₂₃	—	4	1	no	—
96	C₂²×C₄×C₂₃	—	4	1	no	—
97	C₂²×C₄×C₂₃	—	4	1	no	—
98	C₂²×C₄×C₂₃	—	4	2	no	—
99	C₂²×C₄×C₂₃	—	4	2	no	—
100	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
103	SD₁₆×C₂₃	—	4	8	no	—
104	C₂×C₈×C₂₃	—	2	4	no	—
105	C₂×C₈×C₂₃	—	2	2	no	—
106	C₂×C₈×C₂₃	—	2	2	no	—
107	C₂×C₈×C₂₃	—	4	1	no	—
108	C₂×C₈×C₂₃	—	4	1	no	—
109	C₂×C₈×C₂₃	—	4	1	no	—
110	C₂×C₈×C₂₃	—	4	2	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	—	2	1	no	—
116	C₄⋊C₄×C₂₃	—	2	2	no	—
117	C₄⋊C₄×C₂₃	—	2	2	no	—
118	C₄⋊C₄×C₂₃	—	2	2	no	—
119	C₄⋊C₄×C₂₃	—	4	1	no	—
120	C₄⋊C₄×C₂₃	—	4	1	no	—
121	C₄⋊C₄×C₂₃	—	4	1	no	—
122	C₄⋊C₄×C₂₃	—	4	1	no	—
123	C₂²⋊C₄×C₂₃	—	4	8	no	—
124	C₂²⋊C₄×C₂₃	—	4	1	no	—
125	C₂²⋊C₄×C₂₃	—	4	1	no	—
126	C₄²×C₂₃	—	4	1	no	—
127	C₄²×C₂₃	—	4	1	no	—
128	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₂₃	#41	1	1	yes	characteristic
132	#10066	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₂₃	—	2	2	no	—
134	C₂³×C₂₃	—	4	1	no	—
135	C₂³×C₂₃	—	4	1	no	—
136	C₂³×C₂₃	—	4	2	no	—
137	C₂³×C₂₃	—	4	2	no	—
138	C₂³×C₂₃	#120	1	1	yes	characteristic
139	Q₈×C₂₃	—	4	2	no	—
140	Q₈×C₂₃	—	4	2	no	—
141	Q₈×C₂₃	—	8	1	no	—
142	Q₈×C₂₃	—	8	1	no	—
143	Q₈×C₂₃	—	8	1	no	—
144	Q₈×C₂₃	—	8	1	no	—
145	Q₈×C₂₃	—	8	1	no	—
146	Q₈×C₂₃	—	8	1	no	—
147	D₄×C₂₃	—	2	2	no	—
148	D₄×C₂₃	—	2	2	no	—
149	D₄×C₂₃	—	4	1	no	—
150	D₄×C₂₃	—	4	1	no	—
151	C₂×C₄×C₂₃	—	2	2	no	—
152	C₂×C₄×C₂₃	—	4	1	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	—	4	2	no	—
161	C₂×C₄×C₂₃	—	8	1	no	—
162	C₂×C₄×C₂₃	—	8	1	no	—
163	C₂×C₄×C₂₃	—	8	2	no	—
164	C₂×C₄×C₂₃	—	8	1	no	—
165	C₂×C₄×C₂₃	—	8	1	no	—
166	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
167	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
168	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
169	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
170	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
171	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
172	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
173	C₂×C₄×C₂₃	#135	1	1	yes	characteristic
174	C₂×C₄×C₂₃	#135	1	2	yes	—
175	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
176	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₂×C₄×C₂₃	#137	1	2	yes	—
178	C₈×C₂₃	—	2	4	no	—
179	C₈×C₂₃	—	4	2	no	—
180	C₈×C₂₃	—	8	1	no	—
181	C₂×#500	C₂×C₂₃	1	1	yes	characteristic, complemented
182	C₂×#461	C₂×C₂₃	1	1	yes	characteristic
183	#2547	C₂×C₂₃	1	1	yes	characteristic
184	#1988	C₂×C₂₃	1	1	yes	characteristic, complemented
185	C₂×#332	C₂×C₂₃	1	1	yes	characteristic, complemented
186	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic
187	#1279	C₂×C₂₃	1	1	yes	characteristic, complemented
188	C₂²×C₂₃	—	4	4	no	—
189	C₂²×C₂₃	—	4	2	no	—
190	C₂²×C₂₃	—	8	2	no	—
191	C₂²×C₂₃	—	8	1	no	—
192	C₂²×C₂₃	—	8	1	no	—
193	C₂²×C₂₃	#392	1	1	yes	characteristic
194	C₂²×C₂₃	#447	1	1	yes	characteristic
195	C₂²×C₂₃	#449	1	1	yes	characteristic
196	C₂²×C₂₃	#452	1	2	yes	—
197	C₂²×C₂₃	#456	1	2	yes	—
198	C₄×C₂₃	—	2	1	no	—
199	C₄×C₂₃	—	2	1	no	—
200	C₄×C₂₃	—	8	2	no	—
201	C₄×C₂₃	—	8	2	no	—
202	C₄×C₂₃	—	8	2	no	—
203	C₄×C₂₃	—	8	1	no	—
204	C₄×C₂₃	#447	1	1	yes	characteristic
205	C₄×C₂₃	#449	1	1	yes	characteristic
206	C₄×C₂₃	#464	1	2	yes	—
207	C₄×C₂₃	#466	1	1	yes	characteristic
208	C₄×C₂₃	#469	1	1	yes	characteristic
209	C₄×C₂₃	#495	1	1	yes	characteristic
210	C₄×C₂₃	#497	1	1	yes	characteristic
211	C₂²×SD₁₆	—	2	1	no	—
212	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
213	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
214	C₂×#124	—	2	1	no	—
215	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
216	#500	—	2	2	no	—
217	#500	—	2	2	no	—
218	#461	—	2	2	no	—
219	#461	—	2	2	no	—
220	C₂×#107	—	2	2	no	—
221	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
222	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
223	C₂×#103	—	2	1	no	—
224	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
225	#397	—	2	2	no	—
226	#391	—	2	1	no	—
227	#380	—	2	2	no	—
228	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
229	#340	—	2	2	no	—
230	#332	—	2	2	no	—
231	D₄⋊C₈	—	2	2	no	—
232	C₂×C₂₃	—	8	2	no	—
233	C₂×C₂₃	#1647	1	2	yes	—
234	C₂×C₂₃	#1650	1	2	yes	—
235	C₂×C₂₃	#1999	1	1	yes	characteristic
236	C₂×C₂₃	#2005	1	1	yes	characteristic
237	C₂×C₂₃	#2015	1	1	yes	characteristic
238	C₂²×Q₈	—	2	1	no	—
239	C₂²×Q₈	—	2	1	no	—
240	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
241	C₂³×C₄	—	2	1	no	—
242	C₂×SD₁₆	—	2	4	no	—
243	C₂×SD₁₆	—	4	2	no	—
244	C₂×SD₁₆	—	4	2	no	—
245	C₂²×C₈	—	2	1	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	D₄×C₂₃	1	2	yes	—
256	#124	—	4	2	no	—
257	#124	—	4	2	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	1	no	—
261	C₄×D₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
266	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
267	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
268	C₂×C₂²⋊C₄	—	2	4	no	—
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
272	#107	—	2	8	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
277	#103	—	2	4	no	—
278	C₄×C₈	—	2	1	no	—
279	C₄×C₈	D₄×C₂₃	1	2	yes	—
280	#95	—	2	4	no	—
281	#95	—	2	1	no	—
282	C₂₃	#10066	1	1	yes	characteristic, direct product factor, Sylow
283	C₂⁴	—	2	1	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	4	1	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	4	1	no	—
290	C₂×Q₈	—	4	1	no	—
291	C₂×Q₈	—	4	1	no	—
292	C₂×Q₈	—	4	1	no	—
293	C₂×Q₈	—	4	1	no	—
294	C₂×Q₈	—	4	1	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	D₈×C₂₃	1	2	yes	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
313	SD₁₆	—	4	8	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	1	no	—
319	C₂×C₈	—	4	1	no	—
320	C₂×C₈	—	4	2	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₂²⋊C₄	—	4	8	no	—
334	C₂²⋊C₄	—	4	1	no	—
335	C₂²⋊C₄	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	—	4	1	no	—
338	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
339	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
340	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
341	C₄²	#41×C₂₃	1	1	yes	characteristic
342	C₂³	—	2	2	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	C₂₃×#120	1	1	yes	characteristic
348	Q₈	—	4	2	no	—
349	Q₈	—	4	2	no	—
350	Q₈	—	8	1	no	—
351	Q₈	—	8	1	no	—
352	Q₈	—	8	1	no	—
353	Q₈	—	8	1	no	—
354	Q₈	—	8	1	no	—
355	Q₈	—	8	1	no	—
356	D₄	—	2	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	4	1	no	—
359	D₄	—	4	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	1	no	—
371	C₂×C₄	—	8	1	no	—
372	C₂×C₄	—	8	2	no	—
373	C₂×C₄	—	8	1	no	—
374	C₂×C₄	—	8	1	no	—
375	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
376	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
377	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
378	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
379	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
380	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
381	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
382	C₂×C₄	C₂₃×#135	1	1	yes	characteristic
383	C₂×C₄	C₂₃×#135	1	2	yes	—
384	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
385	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
386	C₂×C₄	C₂₃×#137	1	2	yes	—
387	C₈	—	2	4	no	—
388	C₈	—	4	2	no	—
389	C₈	—	8	1	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	1	no	—
394	C₂²	—	8	1	no	—
395	C₂²	C₂₃×#392	1	1	yes	characteristic
396	C₂²	C₂₃×#447	1	1	yes	characteristic
397	C₂²	C₂₃×#449	1	1	yes	characteristic
398	C₂²	C₂₃×#452	1	2	yes	—
399	C₂²	C₂₃×#456	1	2	yes	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	8	2	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	2	no	—
405	C₄	—	8	1	no	—
406	C₄	C₂₃×#447	1	1	yes	characteristic
407	C₄	C₂₃×#449	1	1	yes	characteristic
408	C₄	C₂₃×#464	1	2	yes	—
409	C₄	C₂₃×#466	1	1	yes	characteristic
410	C₄	C₂₃×#469	1	1	yes	characteristic
411	C₄	C₂₃×#495	1	1	yes	characteristic
412	C₄	C₂₃×#497	1	1	yes	characteristic
413	C₂	—	8	2	no	—
414	C₂	C₂₃×#1647	1	2	yes	—
415	C₂	C₂₃×#1650	1	2	yes	—
416	C₂	C₂₃×#1999	1	1	yes	characteristic
417	C₂	C₂₃×#2005	1	1	yes	characteristic
418	C₂	C₂₃×#2015	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×#500	C₂	semidirect
4. C₂₃×#1988	C₂	semidirect
5. C₂×C₂₃×#332	C₂	semidirect
7. C₂₃×#1279	C₂	semidirect
132. #10066	C₂₃	direct (N × H)
181. C₂×#500	C₂×C₂₃	semidirect
184. #1988	C₂×C₂₃	semidirect
185. C₂×#332	C₂×C₂₃	semidirect
187. #1279	C₂×C₂₃	semidirect
282. C₂₃	#10066	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×#500	2
C₂×C₂₃×#461	2
C₂₃×#2547	2
C₂₃×#1988	2
C₂×C₂₃×#332	2
C₂×C₂₃×D₄⋊C₈	2
C₂₃×#1279	2
#10066	23

Subgroups — C23×#10066 #19157692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#10066 #19157692