Subgroups — C₂₃×#61007 #19208633

Order 5888.

1704 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3510	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3263	C₂	1	2	yes	maximal, complemented
3	C₂₃×#3262	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3233	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3211	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3202	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3200	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3199	C₂	1	1	yes	maximal, characteristic
9	C₂₃×#3183	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3168	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3121	C₂	1	4	yes	maximal, complemented
12	C₂₃×#3118	C₂	1	4	yes	maximal, complemented
13	C₂₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#559	—	2	4	no	—
15	C₂₃×#556	—	2	4	no	—
16	C₂₃×#551	—	2	4	no	—
17	C₂₃×#551	—	2	4	no	—
18	C₂₃×#542	C₂²	1	4	yes	—
19	C₂₃×#542	C₂²	1	4	yes	complemented
20	C₂₃×#536	C₂²	1	2	yes	—
21	C₂₃×#535	C₂²	1	2	yes	—
22	C₂₃×#533	C₂²	1	2	yes	complemented
23	C₂₃×#529	C₂²	1	4	yes	—
24	C₂₃×#529	C₂²	1	4	yes	complemented
25	C₂×C₂₃×#124	C₂²	1	2	yes	complemented
26	C₂₃×#519	C₂²	1	2	yes	complemented
27	C₂₃×#518	C₂²	1	2	yes	complemented
28	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#499	C₂²	1	2	yes	complemented
30	C₂₃×#499	C₂²	1	2	yes	complemented
31	C₂₃×#495	C₂²	1	2	yes	—
32	C₂₃×#495	C₂²	1	2	yes	—
33	C₂₃×#488	C₂²	1	4	yes	complemented
34	C₂₃×#488	C₂²	1	4	yes	complemented
35	C₂₃×#485	C₂²	1	4	yes	complemented
36	C₂₃×#485	C₂²	1	4	yes	complemented
37	C₂₃×#482	C₂²	1	4	yes	—
38	C₂₃×#482	C₂²	1	4	yes	—
39	C₂₃×#477	C₂²	1	4	yes	complemented
40	C₂₃×#476	C₂²	1	4	yes	complemented
41	C₂₃×#475	C₂²	1	4	yes	complemented
42	C₂₃×#474	C₂²	1	4	yes	complemented
43	C₂₃×#470	C₂²	1	2	yes	complemented
44	C₂₃×#469	C₂²	1	2	yes	—
45	C₂₃×#468	C₂²	1	4	yes	complemented
46	C₂₃×#467	C₂²	1	2	yes	complemented
47	C₂₃×#466	C₂²	1	2	yes	—
48	C₂₃×#465	C₂²	1	4	yes	complemented
49	C₂₃×#464	C₂²	1	4	yes	complemented
50	C₂₃×#464	C₂²	1	4	yes	complemented
51	C₂₃×#463	C₂²	1	4	yes	—
52	C₂₃×#463	C₂²	1	4	yes	—
53	C₂₃×#451	C₂²	1	4	yes	complemented
54	C₂₃×#450	C₂²	1	4	yes	complemented
55	C₂₃×#448	C₂²	1	4	yes	—
56	C₂₃×#447	C₂²	1	4	yes	—
57	C₂₃×#442	C₂²	1	2	yes	—
58	C₂₃×#441	C₂²	1	2	yes	complemented
59	C₂₃×#440	C₂²	1	4	yes	complemented
60	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
61	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
62	C₄×D₈×C₂₃	C₂²	1	2	yes	—
63	C₂₃×#433	C₂²	1	4	yes	complemented
64	C₂₃×#431	C₂²	1	4	yes	complemented
65	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#408	C₂²	1	1	yes	characteristic
68	C₂₃×#408	C₂²	1	1	yes	characteristic
69	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
71	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
73	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
74	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
75	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
76	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
77	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
78	C₂×D₈×C₂₃	C₂³	1	2	yes	—
79	C₂×D₈×C₂₃	C₂³	1	2	yes	—
80	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
81	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
84	C₂₃×C₄⋊Q₈	—	2	2	no	—
85	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
86	C₂₃×#127	—	2	2	no	—
87	C₂₃×#126	—	2	4	no	—
88	C₂₃×#126	—	2	4	no	—
89	C₂₃×#126	—	2	4	no	—
90	C₂₃×#126	—	2	4	no	—
91	C₂₃×#125	C₂³	1	4	yes	—
92	C₂₃×#124	—	2	2	no	—
93	C₂₃×#124	—	2	2	no	—
94	C₂₃×#124	—	2	4	no	—
95	C₂₃×#124	—	2	4	no	—
96	C₂₃×#124	—	2	4	no	—
97	C₂₃×#124	C₂³	1	4	yes	—
98	C₂₃×#124	C₂³	1	4	yes	—
99	C₂₃×#123	—	2	2	no	—
100	C₂₃×#123	—	2	2	no	—
101	C₂₃×#123	—	2	4	no	—
102	C₂₃×#123	—	2	4	no	—
103	C₂₃×#123	—	2	4	no	—
104	C₂₃×#123	—	2	4	no	—
105	C₂₃×C₂²⋊Q₈	—	2	4	no	—
106	C₂₃×C₂²⋊Q₈	—	2	4	no	—
107	C₂₃×C₂²⋊Q₈	—	2	4	no	—
108	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
109	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
110	C₂₃×#121	C₂³	1	4	yes	—
111	C₂₃×#121	C₂³	1	4	yes	—
112	C₂₃×#120	—	2	2	no	—
113	C₂₃×#120	—	2	2	no	—
114	C₄×Q₈×C₂₃	—	2	4	no	—
115	C₄×Q₈×C₂₃	—	2	4	no	—
116	C₄×Q₈×C₂₃	D₄	1	2	yes	—
117	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
118	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
119	C₄×D₄×C₂₃	—	2	4	no	—
120	C₄×D₄×C₂₃	—	2	4	no	—
121	C₄×D₄×C₂₃	—	2	4	no	—
122	C₄×D₄×C₂₃	D₄	1	2	yes	—
123	C₄×D₄×C₂₃	D₄	1	4	yes	—
124	C₄×D₄×C₂₃	C₂³	1	4	yes	—
125	C₄×D₄×C₂₃	C₂³	1	4	yes	—
126	C₂₃×#117	—	2	4	no	—
127	C₂₃×#117	—	2	4	no	—
128	C₂₃×#117	—	2	4	no	—
129	C₂₃×#117	C₂³	1	2	yes	—
130	C₂₃×#117	C₂³	1	2	yes	—
131	C₂₃×#117	C₂³	1	1	yes	characteristic
132	C₂₃×#117	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
134	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
135	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
137	C₂₃×#107	C₂³	1	2	yes	—
138	C₂₃×#107	C₂³	1	2	yes	—
139	C₂₃×#107	C₂³	1	4	yes	—
140	C₂₃×#106	C₂³	1	4	yes	—
141	C₂₃×#106	C₂³	1	2	yes	—
142	C₂₃×#106	C₂³	1	2	yes	—
143	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
144	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
145	C₂₃×#103	C₂³	1	4	yes	—
146	C₂₃×#103	C₂³	1	4	yes	—
147	C₂₃×#103	C₂³	1	4	yes	—
148	C₂₃×#103	C₂³	1	4	yes	—
149	C₂₃×#102	C₂³	1	4	yes	—
150	C₂₃×#102	C₂³	1	4	yes	—
151	C₂₃×#102	C₂³	1	4	yes	—
152	C₂₃×#102	C₂³	1	4	yes	—
153	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
154	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
155	C₂₃×#97	C₂³	1	2	yes	—
156	C₄×C₈×C₂₃	C₂³	1	2	yes	—
157	C₄×C₈×C₂₃	C₂³	1	2	yes	—
158	C₄×C₈×C₂₃	C₂³	1	2	yes	—
159	C₂⁴×C₂₃	—	2	2	no	—
160	#41×C₂₃	—	4	1	no	—
161	#41×C₂₃	—	4	1	no	—
162	C₂×Q₈×C₂₃	—	2	2	no	—
163	C₂×Q₈×C₂₃	—	2	4	no	—
164	C₂×Q₈×C₂₃	—	4	2	no	—
165	C₂×Q₈×C₂₃	—	4	2	no	—
166	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
167	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
168	C₂×D₄×C₂₃	—	2	4	no	—
169	C₂×D₄×C₂₃	—	2	4	no	—
170	C₂×D₄×C₂₃	—	2	2	no	—
171	C₂×D₄×C₂₃	—	4	2	no	—
172	C₂×D₄×C₂₃	—	4	2	no	—
173	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
174	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
175	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₂₃	—	2	2	no	—
177	C₂²×C₄×C₂₃	—	2	4	no	—
178	C₂²×C₄×C₂₃	—	2	4	no	—
179	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
181	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
183	Q₁₆×C₂₃	—	4	2	no	—
184	Q₁₆×C₂₃	—	4	2	no	—
185	SD₁₆×C₂₃	—	4	4	no	—
186	SD₁₆×C₂₃	—	4	4	no	—
187	D₈×C₂₃	—	4	2	no	—
188	D₈×C₂₃	—	4	2	no	—
189	M₁₆×C₂₃	—	4	1	no	—
190	M₁₆×C₂₃	—	4	1	no	—
191	C₂×C₈×C₂₃	—	4	1	no	—
192	C₂×C₈×C₂₃	—	4	1	no	—
193	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
194	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
195	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
196	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
197	C₄⋊C₄×C₂₃	—	2	4	no	—
198	C₄⋊C₄×C₂₃	—	2	4	no	—
199	C₄⋊C₄×C₂₃	—	2	4	no	—
200	C₄⋊C₄×C₂₃	—	2	4	no	—
201	C₄⋊C₄×C₂₃	—	2	4	no	—
202	C₄⋊C₄×C₂₃	—	2	4	no	—
203	C₄⋊C₄×C₂₃	—	2	4	no	—
204	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
205	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
206	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
207	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
208	C₂²⋊C₄×C₂₃	—	2	2	no	—
209	C₂²⋊C₄×C₂₃	—	2	2	no	—
210	C₂²⋊C₄×C₂₃	—	2	4	no	—
211	C₂²⋊C₄×C₂₃	—	2	4	no	—
212	C₂²⋊C₄×C₂₃	—	2	4	no	—
213	C₂²⋊C₄×C₂₃	—	2	4	no	—
214	C₂²⋊C₄×C₂₃	—	2	4	no	—
215	C₂²⋊C₄×C₂₃	—	2	4	no	—
216	C₂²⋊C₄×C₂₃	—	2	4	no	—
217	C₂²⋊C₄×C₂₃	—	2	4	no	—
218	C₂²⋊C₄×C₂₃	—	2	4	no	—
219	C₂²⋊C₄×C₂₃	—	2	4	no	—
220	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
221	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
222	C₄²×C₂₃	—	2	4	no	—
223	C₄²×C₂₃	—	2	4	no	—
224	C₄²×C₂₃	—	2	2	no	—
225	C₄²×C₂₃	—	2	2	no	—
226	C₄²×C₂₃	C₂×D₄	1	2	yes	—
227	C₄²×C₂₃	C₂×D₄	1	4	yes	—
228	C₄²×C₂₃	C₂⁴	1	2	yes	—
229	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
230	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
231	#61007	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂³×C₂₃	—	2	4	no	—
233	C₂³×C₂₃	—	4	4	no	—
234	C₂³×C₂₃	—	8	4	no	—
235	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
236	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
237	Q₈×C₂₃	—	2	4	no	—
238	Q₈×C₂₃	—	2	4	no	—
239	Q₈×C₂₃	—	4	1	no	—
240	Q₈×C₂₃	—	4	4	no	—
241	Q₈×C₂₃	—	8	4	no	—
242	D₄×C₂₃	—	2	4	no	—
243	D₄×C₂₃	—	2	4	no	—
244	D₄×C₂₃	—	4	2	no	—
245	D₄×C₂₃	—	4	1	no	—
246	D₄×C₂₃	—	4	4	no	—
247	D₄×C₂₃	—	8	4	no	—
248	D₄×C₂₃	—	8	4	no	—
249	C₂×C₄×C₂₃	—	2	1	no	—
250	C₂×C₄×C₂₃	—	2	1	no	—
251	C₂×C₄×C₂₃	—	2	2	no	—
252	C₂×C₄×C₂₃	—	2	2	no	—
253	C₂×C₄×C₂₃	—	2	4	no	—
254	C₂×C₄×C₂₃	—	2	4	no	—
255	C₂×C₄×C₂₃	—	2	4	no	—
256	C₂×C₄×C₂₃	—	4	2	no	—
257	C₂×C₄×C₂₃	—	4	4	no	—
258	C₂×C₄×C₂₃	—	4	4	no	—
259	C₂×C₄×C₂₃	—	8	4	no	—
260	C₂×C₄×C₂₃	—	8	4	no	—
261	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
264	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
265	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
267	C₈×C₂₃	—	2	2	no	—
268	C₈×C₂₃	—	2	2	no	—
269	C₈×C₂₃	—	2	2	no	—
270	C₈×C₂₃	—	2	2	no	—
271	#3510	C₂×C₂₃	1	2	yes	complemented
272	#3263	C₂×C₂₃	1	2	yes	complemented
273	#3262	C₂×C₂₃	1	2	yes	complemented
274	#3233	C₂×C₂₃	1	4	yes	complemented
275	#3211	C₂×C₂₃	1	4	yes	complemented
276	#3202	C₂×C₂₃	1	1	yes	characteristic, complemented
277	#3200	C₂×C₂₃	1	2	yes	complemented
278	#3199	C₂×C₂₃	1	1	yes	characteristic
279	#3183	C₂×C₂₃	1	2	yes	complemented
280	#3168	C₂×C₂₃	1	2	yes	complemented
281	#3121	C₂×C₂₃	1	4	yes	complemented
282	#3118	C₂×C₂₃	1	4	yes	complemented
283	#2922	C₂×C₂₃	1	1	yes	characteristic, complemented
284	C₂²×C₂₃	—	2	2	no	—
285	C₂²×C₂₃	—	2	4	no	—
286	C₂²×C₂₃	—	2	2	no	—
287	C₂²×C₂₃	—	2	1	no	—
288	C₂²×C₂₃	—	4	4	no	—
289	C₂²×C₂₃	—	4	4	no	—
290	C₂²×C₂₃	—	4	4	no	—
291	C₂²×C₂₃	—	16	4	no	—
292	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
293	C₄×C₂₃	—	2	2	no	—
294	C₄×C₂₃	—	2	2	no	—
295	C₄×C₂₃	—	2	4	no	—
296	C₄×C₂₃	—	2	2	no	—
297	C₄×C₂₃	—	2	1	no	—
298	C₄×C₂₃	—	4	4	no	—
299	C₄×C₂₃	—	4	4	no	—
300	C₄×C₂₃	—	4	4	no	—
301	C₄×C₂₃	#585	1	1	yes	characteristic
302	C₄×C₂₃	#585	1	1	yes	characteristic
303	#559	—	2	4	no	—
304	#556	—	2	4	no	—
305	#551	—	2	4	no	—
306	#551	—	2	4	no	—
307	#542	C₂²×C₂₃	1	4	yes	—
308	#542	C₂²×C₂₃	1	4	yes	complemented
309	#536	C₂²×C₂₃	1	2	yes	—
310	#535	C₂²×C₂₃	1	2	yes	—
311	#533	C₂²×C₂₃	1	2	yes	complemented
312	#529	C₂²×C₂₃	1	4	yes	—
313	#529	C₂²×C₂₃	1	4	yes	complemented
314	C₂×#124	C₂²×C₂₃	1	2	yes	complemented
315	#519	C₂²×C₂₃	1	2	yes	complemented
316	#518	C₂²×C₂₃	1	2	yes	complemented
317	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
318	#499	C₂²×C₂₃	1	2	yes	complemented
319	#499	C₂²×C₂₃	1	2	yes	complemented
320	#495	C₂²×C₂₃	1	2	yes	—
321	#495	C₂²×C₂₃	1	2	yes	—
322	#488	C₂²×C₂₃	1	4	yes	complemented
323	#488	C₂²×C₂₃	1	4	yes	complemented
324	#485	C₂²×C₂₃	1	4	yes	complemented
325	#485	C₂²×C₂₃	1	4	yes	complemented
326	#482	C₂²×C₂₃	1	4	yes	—
327	#482	C₂²×C₂₃	1	4	yes	—
328	#477	C₂²×C₂₃	1	4	yes	complemented
329	#476	C₂²×C₂₃	1	4	yes	complemented
330	#475	C₂²×C₂₃	1	4	yes	complemented
331	#474	C₂²×C₂₃	1	4	yes	complemented
332	#470	C₂²×C₂₃	1	2	yes	complemented
333	#469	C₂²×C₂₃	1	2	yes	—
334	#468	C₂²×C₂₃	1	4	yes	complemented
335	#467	C₂²×C₂₃	1	2	yes	complemented
336	#466	C₂²×C₂₃	1	2	yes	—
337	#465	C₂²×C₂₃	1	4	yes	complemented
338	#464	C₂²×C₂₃	1	4	yes	complemented
339	#464	C₂²×C₂₃	1	4	yes	complemented
340	#463	C₂²×C₂₃	1	4	yes	—
341	#463	C₂²×C₂₃	1	4	yes	—
342	#451	C₂²×C₂₃	1	4	yes	complemented
343	#450	C₂²×C₂₃	1	4	yes	complemented
344	#448	C₂²×C₂₃	1	4	yes	—
345	#447	C₂²×C₂₃	1	4	yes	—
346	#442	C₂²×C₂₃	1	2	yes	—
347	#441	C₂²×C₂₃	1	2	yes	complemented
348	#440	C₂²×C₂₃	1	4	yes	complemented
349	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
350	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
351	C₄×D₈	C₂²×C₂₃	1	2	yes	—
352	#433	C₂²×C₂₃	1	4	yes	complemented
353	#431	C₂²×C₂₃	1	4	yes	complemented
354	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
355	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
356	#408	C₂²×C₂₃	1	1	yes	characteristic
357	#408	C₂²×C₂₃	1	1	yes	characteristic
358	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
359	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
360	C₂×C₂₃	—	4	1	no	—
361	C₂×C₂₃	—	4	2	no	—
362	C₂×C₂₃	—	8	4	no	—
363	C₂×C₂₃	#3449	1	1	yes	characteristic
364	C₂×C₂₃	#3584	1	2	yes	—
365	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
366	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
367	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
368	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
369	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
370	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
371	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
372	C₂×D₈	C₂³×C₂₃	1	2	yes	—
373	C₂×D₈	C₂³×C₂₃	1	2	yes	—
374	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
375	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
376	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
377	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
378	C₄⋊Q₈	—	2	2	no	—
379	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
380	#127	—	2	2	no	—
381	#126	—	2	4	no	—
382	#126	—	2	4	no	—
383	#126	—	2	4	no	—
384	#126	—	2	4	no	—
385	#125	C₂³×C₂₃	1	4	yes	—
386	#124	—	2	2	no	—
387	#124	—	2	2	no	—
388	#124	—	2	4	no	—
389	#124	—	2	4	no	—
390	#124	—	2	4	no	—
391	#124	C₂³×C₂₃	1	4	yes	—
392	#124	C₂³×C₂₃	1	4	yes	—
393	#123	—	2	2	no	—
394	#123	—	2	2	no	—
395	#123	—	2	4	no	—
396	#123	—	2	4	no	—
397	#123	—	2	4	no	—
398	#123	—	2	4	no	—
399	C₂²⋊Q₈	—	2	4	no	—
400	C₂²⋊Q₈	—	2	4	no	—
401	C₂²⋊Q₈	—	2	4	no	—
402	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
403	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
404	#121	C₂³×C₂₃	1	4	yes	—
405	#121	C₂³×C₂₃	1	4	yes	—
406	#120	—	2	2	no	—
407	#120	—	2	2	no	—
408	C₄×Q₈	—	2	4	no	—
409	C₄×Q₈	—	2	4	no	—
410	C₄×Q₈	D₄×C₂₃	1	2	yes	—
411	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
412	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
413	C₄×D₄	—	2	4	no	—
414	C₄×D₄	—	2	4	no	—
415	C₄×D₄	—	2	4	no	—
416	C₄×D₄	D₄×C₂₃	1	2	yes	—
417	C₄×D₄	D₄×C₂₃	1	4	yes	—
418	C₄×D₄	C₂³×C₂₃	1	4	yes	—
419	C₄×D₄	C₂³×C₂₃	1	4	yes	—
420	#117	—	2	4	no	—
421	#117	—	2	4	no	—
422	#117	—	2	4	no	—
423	#117	C₂³×C₂₃	1	2	yes	—
424	#117	C₂³×C₂₃	1	2	yes	—
425	#117	C₂³×C₂₃	1	2	yes	—
426	#117	C₂³×C₂₃	1	1	yes	characteristic
427	C₂×C₂²⋊C₄	—	2	4	no	—
428	C₂×C₂²⋊C₄	—	2	4	no	—
429	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
430	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
431	#107	C₂³×C₂₃	1	2	yes	—
432	#107	C₂³×C₂₃	1	2	yes	—
433	#107	C₂³×C₂₃	1	4	yes	—
434	#106	C₂³×C₂₃	1	4	yes	—
435	#106	C₂³×C₂₃	1	2	yes	—
436	#106	C₂³×C₂₃	1	2	yes	—
437	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
438	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
439	#103	C₂³×C₂₃	1	4	yes	—
440	#103	C₂³×C₂₃	1	4	yes	—
441	#103	C₂³×C₂₃	1	4	yes	—
442	#103	C₂³×C₂₃	1	4	yes	—
443	#102	C₂³×C₂₃	1	4	yes	—
444	#102	C₂³×C₂₃	1	4	yes	—
445	#102	C₂³×C₂₃	1	4	yes	—
446	#102	C₂³×C₂₃	1	4	yes	—
447	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
448	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
449	#97	C₂³×C₂₃	1	2	yes	—
450	C₄×C₈	C₂³×C₂₃	1	2	yes	—
451	C₄×C₈	C₂³×C₂₃	1	2	yes	—
452	C₄×C₈	C₂³×C₂₃	1	2	yes	—
453	C₂₃	#61007	1	1	yes	characteristic, direct product factor, Sylow
454	C₂⁴	—	2	2	no	—
455	#41	—	4	1	no	—
456	#41	—	4	1	no	—
457	C₂×Q₈	—	2	2	no	—
458	C₂×Q₈	—	2	4	no	—
459	C₂×Q₈	—	4	2	no	—
460	C₂×Q₈	—	4	2	no	—
461	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
462	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
463	C₂×D₄	—	2	4	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	4	2	no	—
467	C₂×D₄	—	4	2	no	—
468	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
469	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
470	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
475	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
476	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
477	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
478	Q₁₆	—	4	2	no	—
479	Q₁₆	—	4	2	no	—
480	SD₁₆	—	4	4	no	—
481	SD₁₆	—	4	4	no	—
482	D₈	—	4	2	no	—
483	D₈	—	4	2	no	—
484	M₁₆	—	4	1	no	—
485	M₁₆	—	4	1	no	—
486	C₂×C₈	—	4	1	no	—
487	C₂×C₈	—	4	1	no	—
488	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
489	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
490	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
491	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
492	C₄⋊C₄	—	2	4	no	—
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	2	4	no	—
499	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
500	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
501	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
502	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	4	no	—
506	C₂²⋊C₄	—	2	4	no	—
507	C₂²⋊C₄	—	2	4	no	—
508	C₂²⋊C₄	—	2	4	no	—
509	C₂²⋊C₄	—	2	4	no	—
510	C₂²⋊C₄	—	2	4	no	—
511	C₂²⋊C₄	—	2	4	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	2	4	no	—
514	C₂²⋊C₄	—	2	4	no	—
515	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
516	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
517	C₄²	—	2	4	no	—
518	C₄²	—	2	4	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	2	no	—
521	C₄²	C₂×D₄×C₂₃	1	2	yes	—
522	C₄²	C₂×D₄×C₂₃	1	4	yes	—
523	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
524	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
525	C₄²	C₂⁴×C₂₃	1	2	yes	—
526	C₂³	—	2	4	no	—
527	C₂³	—	4	4	no	—
528	C₂³	—	8	4	no	—
529	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
530	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
531	Q₈	—	2	4	no	—
532	Q₈	—	2	4	no	—
533	Q₈	—	4	1	no	—
534	Q₈	—	4	4	no	—
535	Q₈	—	8	4	no	—
536	D₄	—	2	4	no	—
537	D₄	—	2	4	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	4	no	—
541	D₄	—	8	4	no	—
542	D₄	—	8	4	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	4	no	—
553	C₂×C₄	—	8	4	no	—
554	C₂×C₄	—	8	4	no	—
555	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
556	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
557	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
558	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
559	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
560	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
561	C₈	—	2	2	no	—
562	C₈	—	2	2	no	—
563	C₈	—	2	2	no	—
564	C₈	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	4	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	16	4	no	—
573	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
574	C₄	—	2	2	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	4	no	—
579	C₄	—	4	4	no	—
580	C₄	—	4	4	no	—
581	C₄	—	4	4	no	—
582	C₄	C₂₃×#585	1	1	yes	characteristic
583	C₄	C₂₃×#585	1	1	yes	characteristic
584	C₂	—	4	2	no	—
585	C₂	—	4	1	no	—
586	C₂	—	8	4	no	—
587	C₂	C₂₃×#3449	1	1	yes	characteristic
588	C₂	C₂₃×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3199	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3510	C₂	semidirect
2. C₂₃×#3263	C₂	semidirect
3. C₂₃×#3262	C₂	semidirect
4. C₂₃×#3233	C₂	semidirect
5. C₂₃×#3211	C₂	semidirect
6. C₂₃×#3202	C₂	semidirect
7. C₂₃×#3200	C₂	semidirect
9. C₂₃×#3183	C₂	semidirect
10. C₂₃×#3168	C₂	semidirect
11. C₂₃×#3121	C₂	semidirect
12. C₂₃×#3118	C₂	semidirect
13. C₂₃×#2922	C₂	semidirect
19. C₂₃×#542	C₂²	semidirect
22. C₂₃×#533	C₂²	semidirect
24. C₂₃×#529	C₂²	semidirect
25. C₂×C₂₃×#124	C₂²	semidirect
26. C₂₃×#519	C₂²	semidirect
27. C₂₃×#518	C₂²	semidirect
29. C₂₃×#499	C₂²	semidirect
30. C₂₃×#499	C₂²	semidirect
33. C₂₃×#488	C₂²	semidirect
34. C₂₃×#488	C₂²	semidirect
35. C₂₃×#485	C₂²	semidirect
36. C₂₃×#485	C₂²	semidirect
39. C₂₃×#477	C₂²	semidirect
40. C₂₃×#476	C₂²	semidirect
41. C₂₃×#475	C₂²	semidirect
42. C₂₃×#474	C₂²	semidirect
43. C₂₃×#470	C₂²	semidirect
45. C₂₃×#468	C₂²	semidirect
46. C₂₃×#467	C₂²	semidirect
48. C₂₃×#465	C₂²	semidirect
49. C₂₃×#464	C₂²	semidirect
50. C₂₃×#464	C₂²	semidirect
53. C₂₃×#451	C₂²	semidirect
54. C₂₃×#450	C₂²	semidirect
58. C₂₃×#441	C₂²	semidirect
59. C₂₃×#440	C₂²	semidirect
60. C₄×Q₁₆×C₂₃	C₂²	semidirect
61. C₄×SD₁₆×C₂₃	C₂²	semidirect
63. C₂₃×#433	C₂²	semidirect
64. C₂₃×#431	C₂²	semidirect
65. C₂₃×#424	C₂²	semidirect
66. C₂₃×#424	C₂²	semidirect
69. C₄×M₁₆×C₂₃	C₂²	semidirect
70. C₂×C₄×C₈×C₂₃	C₂²	semidirect
231. #61007	C₂₃	direct (N × H)
271. #3510	C₂×C₂₃	semidirect
272. #3263	C₂×C₂₃	semidirect
273. #3262	C₂×C₂₃	semidirect
274. #3233	C₂×C₂₃	semidirect
275. #3211	C₂×C₂₃	semidirect
276. #3202	C₂×C₂₃	semidirect
277. #3200	C₂×C₂₃	semidirect
279. #3183	C₂×C₂₃	semidirect
280. #3168	C₂×C₂₃	semidirect
281. #3121	C₂×C₂₃	semidirect
282. #3118	C₂×C₂₃	semidirect
283. #2922	C₂×C₂₃	semidirect
308. #542	C₂²×C₂₃	semidirect
311. #533	C₂²×C₂₃	semidirect
313. #529	C₂²×C₂₃	semidirect
314. C₂×#124	C₂²×C₂₃	semidirect
315. #519	C₂²×C₂₃	semidirect
316. #518	C₂²×C₂₃	semidirect
318. #499	C₂²×C₂₃	semidirect
319. #499	C₂²×C₂₃	semidirect
322. #488	C₂²×C₂₃	semidirect
323. #488	C₂²×C₂₃	semidirect
324. #485	C₂²×C₂₃	semidirect
325. #485	C₂²×C₂₃	semidirect
328. #477	C₂²×C₂₃	semidirect
329. #476	C₂²×C₂₃	semidirect
330. #475	C₂²×C₂₃	semidirect
331. #474	C₂²×C₂₃	semidirect
332. #470	C₂²×C₂₃	semidirect
334. #468	C₂²×C₂₃	semidirect
335. #467	C₂²×C₂₃	semidirect
337. #465	C₂²×C₂₃	semidirect
338. #464	C₂²×C₂₃	semidirect
339. #464	C₂²×C₂₃	semidirect
342. #451	C₂²×C₂₃	semidirect
343. #450	C₂²×C₂₃	semidirect
347. #441	C₂²×C₂₃	semidirect
348. #440	C₂²×C₂₃	semidirect
349. C₄×Q₁₆	C₂²×C₂₃	semidirect
350. C₄×SD₁₆	C₂²×C₂₃	semidirect
352. #433	C₂²×C₂₃	semidirect
353. #431	C₂²×C₂₃	semidirect
354. #424	C₂²×C₂₃	semidirect
355. #424	C₂²×C₂₃	semidirect
358. C₄×M₁₆	C₂²×C₂₃	semidirect
359. C₂×C₄×C₈	C₂²×C₂₃	semidirect
453. C₂₃	#61007	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×#3510	2
C₂₃×#3263	2
C₂₃×#3262	2
C₂₃×#3233	2
C₂₃×#3211	2
C₂₃×#3202	2
C₂₃×#3200	2
C₂₃×#3199	2
C₂₃×#3183	2
C₂₃×#3168	2
C₂₃×#3121	2
C₂₃×#3118	2
C₂₃×#2922	2
#61007	23

Subgroups — C23×#61007 #19208633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61007 #19208633