Subgroups — C₂₃×#19227 #19166853

Order 5888.

628 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3247	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1696	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1695	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1688	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1687	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1678	C₂	1	2	yes	maximal, complemented
9	C₂₃×#1677	C₂	1	2	yes	maximal, complemented
10	C₂×C₂₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1551	C₂	1	2	yes	maximal, complemented
12	C₂₃×#532	C₂²	1	2	yes	—
13	C₂₃×#529	C₂²	1	1	yes	characteristic
14	C₂₃×#500	C₂²	1	1	yes	characteristic
15	C₂₃×#493	C₂²	1	1	yes	characteristic
16	C₂₃×#486	C₂²	1	2	yes	—
17	C₂₃×#478	—	2	2	no	—
18	C₂₃×#477	C₂²	1	2	yes	—
19	C₂₃×#476	C₂²	1	2	yes	—
20	C₂₃×#466	—	2	1	no	—
21	C₂₃×#466	—	2	1	no	—
22	C₂₃×#466	—	2	2	no	—
23	C₂₃×#465	—	2	2	no	—
24	C₂₃×#463	—	2	2	no	—
25	C₂₃×#460	C₂²	1	2	yes	—
26	C₂₃×#459	C₂²	1	2	yes	—
27	C₂₃×#446	C₂²	1	1	yes	characteristic
28	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₄×D₈×C₂₃	—	2	1	no	—
30	C₄×D₈×C₂₃	—	2	1	no	—
31	C₂₃×#436	C₂²	1	1	yes	characteristic
32	C₂₃×#435	—	2	1	no	—
33	C₈×D₄×C₂₃	—	2	1	no	—
34	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂₃×#433	—	2	1	no	—
36	C₂₃×#432	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
38	C₂₃×#405	—	2	1	no	—
39	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
40	C₂₃×#334	C₂²	1	2	yes	—
41	C₂₃×#334	C₂²	1	1	yes	characteristic
42	C₂₃×#334	C₂²	1	1	yes	characteristic
43	C₂₃×#333	C₂²	1	2	yes	—
44	C₂₃×#333	C₂²	1	2	yes	—
45	C₂₃×#331	C₂²	1	2	yes	—
46	C₂₃×#331	C₂²	1	2	yes	—
47	C₂×#41×C₂₃	—	2	2	no	—
48	C₂×SD₁₆×C₂₃	—	2	2	no	—
49	C₂×D₈×C₂₃	—	2	2	no	—
50	C₂×D₈×C₂₃	—	2	1	no	—
51	C₂×D₈×C₂₃	—	2	1	no	—
52	C₂×M₁₆×C₂₃	—	2	1	no	—
53	C₂²×C₈×C₂₃	—	2	2	no	—
54	C₂²×C₈×C₂₃	—	2	1	no	—
55	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
57	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₂₃×#127	C₂³	1	2	yes	—
59	C₂₃×#126	—	2	1	no	—
60	C₂₃×#125	D₄	1	1	yes	characteristic
61	C₂₃×#124	—	2	2	no	—
62	C₂₃×#124	D₄	1	1	yes	characteristic
63	C₂₃×#123	—	2	1	no	—
64	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
65	C₂₃×#121	—	2	2	no	—
66	C₂₃×#121	—	2	2	no	—
67	C₂₃×#121	D₄	1	1	yes	characteristic
68	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₂₃	—	2	1	no	—
70	C₄×D₄×C₂₃	—	2	2	no	—
71	C₄×D₄×C₂₃	—	2	2	no	—
72	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
73	C₂₃×#117	—	2	1	no	—
74	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
75	C₂₃×#107	—	2	1	no	—
76	C₂₃×#107	—	2	1	no	—
77	C₂₃×#107	—	2	2	no	—
78	C₂₃×#106	—	2	2	no	—
79	C₂₃×C₄⋊C₈	—	2	1	no	—
80	C₂₃×C₄⋊C₈	—	2	1	no	—
81	C₂₃×C₄⋊C₈	—	2	2	no	—
82	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
85	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
86	C₂₃×#103	—	2	2	no	—
87	C₂₃×#102	—	2	2	no	—
88	C₂₃×#102	—	2	2	no	—
89	C₂₃×#102	—	2	2	no	—
90	C₂₃×#102	—	2	2	no	—
91	C₂₃×#102	—	2	2	no	—
92	C₂₃×C₂²⋊C₈	—	2	1	no	—
93	C₂₃×C₂²⋊C₈	—	2	1	no	—
94	C₂₃×C₂²⋊C₈	—	2	1	no	—
95	C₂₃×#97	—	2	1	no	—
96	C₂₃×#97	—	2	1	no	—
97	C₄×C₈×C₂₃	—	2	1	no	—
98	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
99	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
102	#41×C₂₃	—	8	4	no	—
103	C₂×Q₈×C₂₃	—	2	2	no	—
104	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₂₃	—	2	1	no	—
106	C₂×D₄×C₂₃	—	2	2	no	—
107	C₂×D₄×C₂₃	—	2	2	no	—
108	C₂×D₄×C₂₃	—	2	2	no	—
109	C₂×D₄×C₂₃	—	4	2	no	—
110	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₂₃	—	2	1	no	—
112	C₂²×C₄×C₂₃	—	4	2	no	—
113	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
116	SD₁₆×C₂₃	—	8	2	no	—
117	D₈×C₂₃	—	4	2	no	—
118	D₈×C₂₃	—	4	2	no	—
119	D₈×C₂₃	—	8	2	no	—
120	M₁₆×C₂₃	—	4	2	no	—
121	C₂×C₈×C₂₃	—	2	2	no	—
122	C₂×C₈×C₂₃	—	2	2	no	—
123	C₂×C₈×C₂₃	—	2	2	no	—
124	C₂×C₈×C₂₃	—	2	1	no	—
125	C₂×C₈×C₂₃	—	2	1	no	—
126	C₂×C₈×C₂₃	—	4	1	no	—
127	C₂×C₈×C₂₃	—	4	2	no	—
128	C₂×C₈×C₂₃	—	8	2	no	—
129	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
133	C₄⋊C₄×C₂₃	—	2	1	no	—
134	C₄⋊C₄×C₂₃	—	2	1	no	—
135	C₄⋊C₄×C₂₃	—	2	1	no	—
136	C₄⋊C₄×C₂₃	—	2	1	no	—
137	C₄⋊C₄×C₂₃	—	2	2	no	—
138	C₄⋊C₄×C₂₃	—	2	2	no	—
139	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
140	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
141	C₂²⋊C₄×C₂₃	—	2	1	no	—
142	C₂²⋊C₄×C₂₃	—	2	1	no	—
143	C₂²⋊C₄×C₂₃	—	2	1	no	—
144	C₂²⋊C₄×C₂₃	—	2	1	no	—
145	C₂²⋊C₄×C₂₃	—	2	1	no	—
146	C₂²⋊C₄×C₂₃	—	4	2	no	—
147	C₂²⋊C₄×C₂₃	—	4	2	no	—
148	C₄²×C₂₃	—	2	1	no	—
149	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₂₃	#41	1	1	yes	characteristic
152	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
153	#19227	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₂₃	—	2	1	no	—
155	C₂³×C₂₃	—	4	2	no	—
156	C₂³×C₂₃	#121	1	1	yes	characteristic
157	Q₈×C₂₃	—	2	2	no	—
158	Q₈×C₂₃	—	8	2	no	—
159	D₄×C₂₃	—	2	2	no	—
160	D₄×C₂₃	—	4	2	no	—
161	D₄×C₂₃	—	4	2	no	—
162	D₄×C₂₃	—	4	2	no	—
163	D₄×C₂₃	—	4	2	no	—
164	D₄×C₂₃	—	4	2	no	—
165	D₄×C₂₃	—	8	2	no	—
166	D₄×C₂₃	—	8	4	no	—
167	C₂×C₄×C₂₃	—	2	2	no	—
168	C₂×C₄×C₂₃	—	2	1	no	—
169	C₂×C₄×C₂₃	—	2	1	no	—
170	C₂×C₄×C₂₃	—	2	2	no	—
171	C₂×C₄×C₂₃	—	2	1	no	—
172	C₂×C₄×C₂₃	—	2	1	no	—
173	C₂×C₄×C₂₃	—	2	1	no	—
174	C₂×C₄×C₂₃	—	4	1	no	—
175	C₂×C₄×C₂₃	—	4	1	no	—
176	C₂×C₄×C₂₃	—	4	2	no	—
177	C₂×C₄×C₂₃	—	8	4	no	—
178	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
179	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
180	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
181	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
184	C₈×C₂₃	—	2	1	no	—
185	C₈×C₂₃	—	2	1	no	—
186	C₈×C₂₃	—	2	1	no	—
187	C₈×C₂₃	—	4	1	no	—
188	C₈×C₂₃	—	4	1	no	—
189	C₈×C₂₃	—	4	2	no	—
190	C₈×C₂₃	—	4	2	no	—
191	C₈×C₂₃	#135	1	2	yes	—
192	#3247	C₂×C₂₃	1	2	yes	complemented
193	#3169	C₂×C₂₃	1	1	yes	characteristic, complemented
194	#2966	C₂×C₂₃	1	1	yes	characteristic, complemented
195	#1696	C₂×C₂₃	1	1	yes	characteristic, complemented
196	#1695	C₂×C₂₃	1	1	yes	characteristic, complemented
197	#1688	C₂×C₂₃	1	1	yes	characteristic, complemented
198	#1687	C₂×C₂₃	1	1	yes	characteristic, complemented
199	#1678	C₂×C₂₃	1	2	yes	complemented
200	#1677	C₂×C₂₃	1	2	yes	complemented
201	C₂×#334	C₂×C₂₃	1	1	yes	characteristic, complemented
202	#1551	C₂×C₂₃	1	2	yes	complemented
203	C₂²×C₂₃	—	2	1	no	—
204	C₂²×C₂₃	—	2	1	no	—
205	C₂²×C₂₃	—	4	1	no	—
206	C₂²×C₂₃	—	4	1	no	—
207	C₂²×C₂₃	—	4	1	no	—
208	C₂²×C₂₃	—	8	2	no	—
209	C₂²×C₂₃	—	8	2	no	—
210	C₂²×C₂₃	—	8	2	no	—
211	C₂²×C₂₃	#472	1	2	yes	—
212	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
213	C₄×C₂₃	—	2	1	no	—
214	C₄×C₂₃	—	2	1	no	—
215	C₄×C₂₃	—	2	1	no	—
216	C₄×C₂₃	—	2	1	no	—
217	C₄×C₂₃	—	4	1	no	—
218	C₄×C₂₃	—	4	1	no	—
219	C₄×C₂₃	—	4	1	no	—
220	C₄×C₂₃	—	8	2	no	—
221	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
222	C₄×C₂₃	#575	1	1	yes	characteristic
223	C₄×C₂₃	#577	1	2	yes	—
224	#532	C₂²×C₂₃	1	2	yes	—
225	#529	C₂²×C₂₃	1	1	yes	characteristic
226	#500	C₂²×C₂₃	1	1	yes	characteristic
227	#493	C₂²×C₂₃	1	1	yes	characteristic
228	#486	C₂²×C₂₃	1	2	yes	—
229	#478	—	2	2	no	—
230	#477	C₂²×C₂₃	1	2	yes	—
231	#476	C₂²×C₂₃	1	2	yes	—
232	#466	—	2	1	no	—
233	#466	—	2	1	no	—
234	#466	—	2	2	no	—
235	#465	—	2	2	no	—
236	#463	—	2	2	no	—
237	#460	C₂²×C₂₃	1	2	yes	—
238	#459	C₂²×C₂₃	1	2	yes	—
239	#446	C₂²×C₂₃	1	1	yes	characteristic
240	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
241	C₄×D₈	—	2	1	no	—
242	C₄×D₈	—	2	1	no	—
243	#436	C₂²×C₂₃	1	1	yes	characteristic
244	#435	—	2	1	no	—
245	C₈×D₄	—	2	1	no	—
246	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
247	#433	—	2	1	no	—
248	#432	C₂²×C₂₃	1	1	yes	characteristic
249	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
250	#405	—	2	1	no	—
251	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
252	#334	C₂²×C₂₃	1	2	yes	—
253	#334	C₂²×C₂₃	1	1	yes	characteristic
254	#334	C₂²×C₂₃	1	1	yes	characteristic
255	#333	C₂²×C₂₃	1	2	yes	—
256	#333	C₂²×C₂₃	1	2	yes	—
257	#331	C₂²×C₂₃	1	2	yes	—
258	#331	C₂²×C₂₃	1	2	yes	—
259	C₂×C₂₃	—	2	2	no	—
260	C₂×C₂₃	—	8	1	no	—
261	C₂×C₂₃	—	16	2	no	—
262	C₂×C₂₃	#3035	1	1	yes	characteristic
263	C₂×C₂₃	#3060	1	1	yes	characteristic
264	C₂×C₂₃	C₂×#472	1	1	yes	characteristic
265	C₂×#41	—	2	2	no	—
266	C₂×SD₁₆	—	2	2	no	—
267	C₂×D₈	—	2	2	no	—
268	C₂×D₈	—	2	1	no	—
269	C₂×D₈	—	2	1	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	—	2	1	no	—
273	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
274	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
275	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
276	#127	C₂³×C₂₃	1	2	yes	—
277	#126	—	2	1	no	—
278	#125	D₄×C₂₃	1	1	yes	characteristic
279	#124	—	2	2	no	—
280	#124	D₄×C₂₃	1	1	yes	characteristic
281	#123	—	2	1	no	—
282	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
283	#121	—	2	2	no	—
284	#121	—	2	2	no	—
285	#121	D₄×C₂₃	1	1	yes	characteristic
286	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
287	C₄×D₄	—	2	1	no	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
291	#117	—	2	1	no	—
292	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
293	#107	—	2	1	no	—
294	#107	—	2	1	no	—
295	#107	—	2	2	no	—
296	#106	—	2	2	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	—	2	2	no	—
300	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
301	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
302	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
303	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
304	#103	—	2	2	no	—
305	#102	—	2	2	no	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	#102	—	2	2	no	—
309	#102	—	2	2	no	—
310	C₂²⋊C₈	—	2	1	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	#97	—	2	1	no	—
314	#97	—	2	1	no	—
315	C₄×C₈	—	2	1	no	—
316	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
317	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
318	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
319	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
320	C₂₃	#19227	1	1	yes	characteristic, direct product factor, Sylow
321	#41	—	8	4	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
334	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
335	SD₁₆	—	8	2	no	—
336	D₈	—	4	2	no	—
337	D₈	—	4	2	no	—
338	D₈	—	8	2	no	—
339	M₁₆	—	4	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	4	1	no	—
346	C₂×C₈	—	4	2	no	—
347	C₂×C₈	—	8	2	no	—
348	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
349	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
350	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
351	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
359	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
360	C₂²⋊C₄	—	2	1	no	—
361	C₂²⋊C₄	—	2	1	no	—
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	4	2	no	—
366	C₂²⋊C₄	—	4	2	no	—
367	C₄²	—	2	1	no	—
368	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
369	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
370	C₄²	#41×C₂₃	1	1	yes	characteristic
371	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
372	C₂³	—	2	1	no	—
373	C₂³	—	4	2	no	—
374	C₂³	C₂₃×#121	1	1	yes	characteristic
375	Q₈	—	2	2	no	—
376	Q₈	—	8	2	no	—
377	D₄	—	2	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	8	2	no	—
384	D₄	—	8	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	8	4	no	—
396	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
397	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
398	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
400	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
401	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	4	1	no	—
406	C₈	—	4	1	no	—
407	C₈	—	4	2	no	—
408	C₈	—	4	2	no	—
409	C₈	C₂₃×#135	1	2	yes	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	2	no	—
418	C₂²	C₂₃×#472	1	2	yes	—
419	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₄	—	8	2	no	—
428	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
429	C₄	C₂₃×#575	1	1	yes	characteristic
430	C₄	C₂₃×#577	1	2	yes	—
431	C₂	—	2	2	no	—
432	C₂	—	8	1	no	—
433	C₂	—	16	2	no	—
434	C₂	C₂₃×#3035	1	1	yes	characteristic
435	C₂	C₂₃×#3060	1	1	yes	characteristic
436	C₂	C₂×C₂₃×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3247	C₂	semidirect
2. C₂₃×#3169	C₂	semidirect
3. C₂₃×#2966	C₂	semidirect
4. C₂₃×#1696	C₂	semidirect
5. C₂₃×#1695	C₂	semidirect
6. C₂₃×#1688	C₂	semidirect
7. C₂₃×#1687	C₂	semidirect
8. C₂₃×#1678	C₂	semidirect
9. C₂₃×#1677	C₂	semidirect
10. C₂×C₂₃×#334	C₂	semidirect
11. C₂₃×#1551	C₂	semidirect
153. #19227	C₂₃	direct (N × H)
192. #3247	C₂×C₂₃	semidirect
193. #3169	C₂×C₂₃	semidirect
194. #2966	C₂×C₂₃	semidirect
195. #1696	C₂×C₂₃	semidirect
196. #1695	C₂×C₂₃	semidirect
197. #1688	C₂×C₂₃	semidirect
198. #1687	C₂×C₂₃	semidirect
199. #1678	C₂×C₂₃	semidirect
200. #1677	C₂×C₂₃	semidirect
201. C₂×#334	C₂×C₂₃	semidirect
202. #1551	C₂×C₂₃	semidirect
320. C₂₃	#19227	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×#3247	2
C₂₃×#3169	2
C₂₃×#2966	2
C₂₃×#1696	2
C₂₃×#1695	2
C₂₃×#1688	2
C₂₃×#1687	2
C₂₃×#1678	2
C₂₃×#1677	2
C₂×C₂₃×#334	2
C₂₃×#1551	2
#19227	23

Subgroups — C23×#19227 #19166853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#19227 #19166853