Subgroups — C₂₃×#10050 #19157676

Order 5888.

702 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#459	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2547	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1982	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, complemented
7	C₂₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₈×C₂₃	—	2	1	no	—
9	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×#124	—	2	1	no	—
12	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
13	C₂₃×#486	—	2	2	no	—
14	C₂₃×#486	—	2	2	no	—
15	C₂₃×#459	—	2	2	no	—
16	C₂₃×#459	—	2	2	no	—
17	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#102	—	2	1	no	—
20	C₂×C₂₃×#102	—	2	2	no	—
21	C₂×C₂₃×#102	—	2	2	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×D₄×C₂₃	—	2	1	no	—
31	C₂²×D₄×C₂₃	—	2	1	no	—
32	C₂²×D₄×C₂₃	—	2	1	no	—
33	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₂₃	—	2	1	no	—
35	C₂×D₈×C₂₃	—	2	4	no	—
36	C₂×D₈×C₂₃	—	4	2	no	—
37	C₂×D₈×C₂₃	—	4	2	no	—
38	C₂²×C₈×C₂₃	—	2	1	no	—
39	C₂²×C₈×C₂₃	—	2	1	no	—
40	C₂²×C₈×C₂₃	—	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×#127	—	2	1	no	—
46	C₂₃×#127	—	2	1	no	—
47	C₂₃×#127	—	2	1	no	—
48	C₂₃×#127	D₄	1	2	yes	—
49	C₂₃×#124	—	4	2	no	—
50	C₂₃×#124	—	4	2	no	—
51	C₄×D₄×C₂₃	—	2	1	no	—
52	C₄×D₄×C₂₃	—	2	1	no	—
53	C₄×D₄×C₂₃	—	2	1	no	—
54	C₄×D₄×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×C₄⋊C₈	—	2	1	no	—
64	C₂₃×C₄⋊C₈	—	2	1	no	—
65	C₂₃×C₄⋊C₈	—	2	1	no	—
66	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
67	C₂₃×#102	—	2	4	no	—
68	C₂₃×#102	—	2	8	no	—
69	C₂₃×#102	—	4	4	no	—
70	C₄×C₈×C₂₃	—	2	1	no	—
71	C₄×C₈×C₂₃	D₄	1	2	yes	—
72	C₂₃×#95	—	2	4	no	—
73	C₂₃×#95	—	2	1	no	—
74	C₂⁴×C₂₃	—	2	1	no	—
75	C₂⁴×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×D₄×C₂₃	—	2	1	no	—
83	C₂×D₄×C₂₃	—	2	2	no	—
84	C₂×D₄×C₂₃	—	2	2	no	—
85	C₂×D₄×C₂₃	—	2	1	no	—
86	C₂×D₄×C₂₃	—	2	2	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	—	4	4	no	—
91	C₂×D₄×C₂₃	—	4	1	no	—
92	C₂×D₄×C₂₃	—	4	1	no	—
93	C₂×D₄×C₂₃	—	4	1	no	—
94	C₂×D₄×C₂₃	—	4	1	no	—
95	C₂×D₄×C₂₃	—	4	1	no	—
96	C₂×D₄×C₂₃	—	4	2	no	—
97	C₂×D₄×C₂₃	—	4	2	no	—
98	C₂×D₄×C₂₃	—	4	1	no	—
99	C₂×D₄×C₂₃	—	4	1	no	—
100	C₂×D₄×C₂₃	D₈	1	2	yes	—
101	C₂²×C₄×C₂₃	—	2	2	no	—
102	C₂²×C₄×C₂₃	—	2	2	no	—
103	C₂²×C₄×C₂₃	—	2	1	no	—
104	C₂²×C₄×C₂₃	—	4	1	no	—
105	C₂²×C₄×C₂₃	—	4	1	no	—
106	C₂²×C₄×C₂₃	—	4	2	no	—
107	C₂²×C₄×C₂₃	—	4	2	no	—
108	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
111	D₈×C₂₃	—	4	8	no	—
112	C₂×C₈×C₂₃	—	2	2	no	—
113	C₂×C₈×C₂₃	—	2	2	no	—
114	C₂×C₈×C₂₃	—	4	2	no	—
115	C₂×C₈×C₂₃	—	4	1	no	—
116	C₂×C₈×C₂₃	—	4	1	no	—
117	C₂×C₈×C₂₃	—	4	1	no	—
118	C₂×C₈×C₂₃	—	4	2	no	—
119	C₄⋊C₄×C₂₃	—	2	1	no	—
120	C₄⋊C₄×C₂₃	—	2	2	no	—
121	C₄⋊C₄×C₂₃	—	2	1	no	—
122	C₄⋊C₄×C₂₃	—	2	2	no	—
123	C₄⋊C₄×C₂₃	—	2	2	no	—
124	C₄⋊C₄×C₂₃	—	2	2	no	—
125	C₄⋊C₄×C₂₃	—	4	1	no	—
126	C₄⋊C₄×C₂₃	—	4	1	no	—
127	C₂²⋊C₄×C₂₃	—	4	8	no	—
128	C₂²⋊C₄×C₂₃	—	4	1	no	—
129	C₂²⋊C₄×C₂₃	—	4	1	no	—
130	C₄²×C₂₃	—	4	1	no	—
131	C₄²×C₂₃	—	4	1	no	—
132	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₂₃	#41	1	1	yes	characteristic
136	#10050	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₂₃	—	2	2	no	—
138	C₂³×C₂₃	—	4	1	no	—
139	C₂³×C₂₃	—	4	2	no	—
140	C₂³×C₂₃	—	4	1	no	—
141	C₂³×C₂₃	—	4	2	no	—
142	C₂³×C₂₃	—	4	2	no	—
143	C₂³×C₂₃	—	8	1	no	—
144	C₂³×C₂₃	—	8	1	no	—
145	C₂³×C₂₃	—	8	2	no	—
146	C₂³×C₂₃	—	8	2	no	—
147	C₂³×C₂₃	#120	1	1	yes	characteristic
148	Q₈×C₂₃	—	8	1	no	—
149	Q₈×C₂₃	—	8	1	no	—
150	Q₈×C₂₃	—	8	1	no	—
151	Q₈×C₂₃	—	8	1	no	—
152	D₄×C₂₃	—	2	2	no	—
153	D₄×C₂₃	—	2	2	no	—
154	D₄×C₂₃	—	4	4	no	—
155	D₄×C₂₃	—	4	2	no	—
156	D₄×C₂₃	—	4	1	no	—
157	D₄×C₂₃	—	4	2	no	—
158	D₄×C₂₃	—	4	4	no	—
159	D₄×C₂₃	—	4	1	no	—
160	D₄×C₂₃	—	8	2	no	—
161	D₄×C₂₃	—	8	1	no	—
162	D₄×C₂₃	—	8	1	no	—
163	D₄×C₂₃	—	8	1	no	—
164	D₄×C₂₃	—	8	1	no	—
165	C₂×C₄×C₂₃	—	2	2	no	—
166	C₂×C₄×C₂₃	—	4	1	no	—
167	C₂×C₄×C₂₃	—	4	2	no	—
168	C₂×C₄×C₂₃	—	4	2	no	—
169	C₂×C₄×C₂₃	—	4	2	no	—
170	C₂×C₄×C₂₃	—	4	2	no	—
171	C₂×C₄×C₂₃	—	4	2	no	—
172	C₂×C₄×C₂₃	—	4	2	no	—
173	C₂×C₄×C₂₃	—	4	2	no	—
174	C₂×C₄×C₂₃	—	8	2	no	—
175	C₂×C₄×C₂₃	—	8	1	no	—
176	C₂×C₄×C₂₃	—	8	1	no	—
177	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
178	C₂×C₄×C₂₃	#120	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	#121	1	1	yes	characteristic
182	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
183	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
184	C₂×C₄×C₂₃	#135	1	1	yes	characteristic
185	C₂×C₄×C₂₃	#135	1	2	yes	—
186	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
189	C₈×C₂₃	—	4	2	no	—
190	C₈×C₂₃	—	4	2	no	—
191	C₈×C₂₃	—	8	1	no	—
192	C₂×#486	C₂×C₂₃	1	1	yes	characteristic, complemented
193	C₂×#459	C₂×C₂₃	1	1	yes	characteristic
194	#2547	C₂×C₂₃	1	1	yes	characteristic, complemented
195	#1982	C₂×C₂₃	1	1	yes	characteristic, complemented
196	C₂×#332	C₂×C₂₃	1	1	yes	characteristic, complemented
197	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
198	#1279	C₂×C₂₃	1	1	yes	characteristic, complemented
199	C₂²×C₂₃	—	4	4	no	—
200	C₂²×C₂₃	—	4	2	no	—
201	C₂²×C₂₃	—	8	2	no	—
202	C₂²×C₂₃	—	8	1	no	—
203	C₂²×C₂₃	—	8	1	no	—
204	C₂²×C₂₃	—	8	2	no	—
205	C₂²×C₂₃	—	8	2	no	—
206	C₂²×C₂₃	—	8	2	no	—
207	C₂²×C₂₃	—	16	2	no	—
208	C₂²×C₂₃	—	16	2	no	—
209	C₂²×C₂₃	#392	1	1	yes	characteristic
210	C₂²×C₂₃	#447	1	1	yes	characteristic
211	C₂²×C₂₃	#449	1	2	yes	—
212	C₂²×C₂₃	#449	1	1	yes	characteristic
213	C₂²×C₂₃	#454	1	2	yes	—
214	C₄×C₂₃	—	2	1	no	—
215	C₄×C₂₃	—	2	1	no	—
216	C₄×C₂₃	—	8	2	no	—
217	C₄×C₂₃	—	8	2	no	—
218	C₄×C₂₃	—	8	1	no	—
219	C₄×C₂₃	#447	1	1	yes	characteristic
220	C₄×C₂₃	#449	1	1	yes	characteristic
221	C₄×C₂₃	#463	1	2	yes	—
222	C₄×C₂₃	#466	1	1	yes	characteristic
223	C₄×C₂₃	#469	1	1	yes	characteristic
224	C₄×C₂₃	#495	1	1	yes	characteristic
225	C₄×C₂₃	#496	1	1	yes	characteristic
226	C₂²×D₈	—	2	1	no	—
227	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
228	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
229	C₂×#124	—	2	1	no	—
230	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
231	#486	—	2	2	no	—
232	#486	—	2	2	no	—
233	#459	—	2	2	no	—
234	#459	—	2	2	no	—
235	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
236	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
237	C₂×#102	—	2	2	no	—
238	C₂×#102	—	2	1	no	—
239	C₂×#102	—	2	2	no	—
240	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
241	#397	—	2	2	no	—
242	#391	—	2	1	no	—
243	#380	—	2	2	no	—
244	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
245	#332	—	2	2	no	—
246	D₄⋊C₈	—	2	2	no	—
247	C₂×C₂₃	—	8	2	no	—
248	C₂×C₂₃	—	16	2	no	—
249	C₂×C₂₃	#1625	1	2	yes	—
250	C₂×C₂₃	#1628	1	2	yes	—
251	C₂×C₂₃	#1999	1	1	yes	characteristic
252	C₂×C₂₃	#2003	1	1	yes	characteristic
253	C₂×C₂₃	#2012	1	1	yes	characteristic
254	C₂²×Q₈	—	2	1	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	—	2	1	no	—
258	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
259	C₂³×C₄	—	2	1	no	—
260	C₂×D₈	—	2	4	no	—
261	C₂×D₈	—	4	2	no	—
262	C₂×D₈	—	4	2	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	—	2	1	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	#127	—	2	1	no	—
271	#127	—	2	1	no	—
272	#127	—	2	1	no	—
273	#127	D₄×C₂₃	1	2	yes	—
274	#124	—	4	2	no	—
275	#124	—	4	2	no	—
276	C₄×D₄	—	2	1	no	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
282	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
283	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
284	C₂×C₂²⋊C₄	—	2	4	no	—
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
292	#102	—	2	4	no	—
293	#102	—	2	8	no	—
294	#102	—	4	4	no	—
295	C₄×C₈	—	2	1	no	—
296	C₄×C₈	D₄×C₂₃	1	2	yes	—
297	#95	—	2	4	no	—
298	#95	—	2	1	no	—
299	C₂₃	#10050	1	1	yes	characteristic, direct product factor, Sylow
300	C₂⁴	—	2	1	no	—
301	C₂⁴	—	4	1	no	—
302	C₂×Q₈	—	4	1	no	—
303	C₂×Q₈	—	4	1	no	—
304	C₂×Q₈	—	4	1	no	—
305	C₂×Q₈	—	4	1	no	—
306	C₂×Q₈	—	4	1	no	—
307	C₂×Q₈	—	4	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	4	4	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	2	no	—
323	C₂×D₄	—	4	2	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	D₈×C₂₃	1	2	yes	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
337	D₈	—	4	8	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	4	2	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	4	2	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₂²⋊C₄	—	4	8	no	—
354	C₂²⋊C₄	—	4	1	no	—
355	C₂²⋊C₄	—	4	1	no	—
356	C₄²	—	4	1	no	—
357	C₄²	—	4	1	no	—
358	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
359	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
360	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
361	C₄²	#41×C₂₃	1	1	yes	characteristic
362	C₂³	—	2	2	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	8	1	no	—
369	C₂³	—	8	1	no	—
370	C₂³	—	8	2	no	—
371	C₂³	—	8	2	no	—
372	C₂³	C₂₃×#120	1	1	yes	characteristic
373	Q₈	—	8	1	no	—
374	Q₈	—	8	1	no	—
375	Q₈	—	8	1	no	—
376	Q₈	—	8	1	no	—
377	D₄	—	2	2	no	—
378	D₄	—	2	2	no	—
379	D₄	—	4	4	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	1	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	4	no	—
384	D₄	—	4	1	no	—
385	D₄	—	8	2	no	—
386	D₄	—	8	1	no	—
387	D₄	—	8	1	no	—
388	D₄	—	8	1	no	—
389	D₄	—	8	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	—	8	1	no	—
401	C₂×C₄	—	8	1	no	—
402	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
403	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
404	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
405	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
406	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
407	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
408	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
409	C₂×C₄	C₂₃×#135	1	1	yes	characteristic
410	C₂×C₄	C₂₃×#135	1	2	yes	—
411	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
412	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
413	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
414	C₈	—	4	2	no	—
415	C₈	—	4	2	no	—
416	C₈	—	8	1	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	16	2	no	—
426	C₂²	—	16	2	no	—
427	C₂²	C₂₃×#392	1	1	yes	characteristic
428	C₂²	C₂₃×#447	1	1	yes	characteristic
429	C₂²	C₂₃×#449	1	1	yes	characteristic
430	C₂²	C₂₃×#449	1	2	yes	—
431	C₂²	C₂₃×#454	1	2	yes	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	8	2	no	—
435	C₄	—	8	1	no	—
436	C₄	—	8	2	no	—
437	C₄	C₂₃×#447	1	1	yes	characteristic
438	C₄	C₂₃×#449	1	1	yes	characteristic
439	C₄	C₂₃×#463	1	2	yes	—
440	C₄	C₂₃×#466	1	1	yes	characteristic
441	C₄	C₂₃×#469	1	1	yes	characteristic
442	C₄	C₂₃×#495	1	1	yes	characteristic
443	C₄	C₂₃×#496	1	1	yes	characteristic
444	C₂	—	8	2	no	—
445	C₂	—	16	2	no	—
446	C₂	C₂₃×#1625	1	2	yes	—
447	C₂	C₂₃×#1628	1	2	yes	—
448	C₂	C₂₃×#1999	1	1	yes	characteristic
449	C₂	C₂₃×#2003	1	1	yes	characteristic
450	C₂	C₂₃×#2012	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
prime radical	C₂×C₂₃×#459	C₂
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×#486	C₂	semidirect
3. C₂₃×#2547	C₂	semidirect
4. C₂₃×#1982	C₂	semidirect
5. C₂×C₂₃×#332	C₂	semidirect
6. C₂×C₂₃×D₄⋊C₈	C₂	semidirect
7. C₂₃×#1279	C₂	semidirect
136. #10050	C₂₃	direct (N × H)
192. C₂×#486	C₂×C₂₃	semidirect
194. #2547	C₂×C₂₃	semidirect
195. #1982	C₂×C₂₃	semidirect
196. C₂×#332	C₂×C₂₃	semidirect
197. C₂×D₄⋊C₈	C₂×C₂₃	semidirect
198. #1279	C₂×C₂₃	semidirect
299. C₂₃	#10050	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×#486	2
C₂×C₂₃×#459	2
C₂₃×#2547	2
C₂₃×#1982	2
C₂×C₂₃×#332	2
C₂×C₂₃×D₄⋊C₈	2
C₂₃×#1279	2
#10050	23

Subgroups — C23×#10050 #19157676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#10050 #19157676