Subgroups — C₂₃×#60206 #19207832

Order 5888.

1878 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3455	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2967	C₂	1	8	yes	maximal, complemented
3	C₂₃×#2966	C₂	1	8	yes	maximal, complemented
4	C₂₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2932	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2930	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2929	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2923	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2921	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₂₃×#131	C₂	1	2	yes	maximal, complemented
13	C₂×C₂₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#131	C₂²	1	2	yes	—
15	C₂×C₂₃×#131	C₂²	1	2	yes	—
16	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#542	C₄	1	4	yes	—
19	C₂₃×#541	C₄	1	2	yes	—
20	C₂₃×#540	C₄	1	2	yes	—
21	C₂₃×#539	C₄	1	4	yes	—
22	C₂₃×#538	C₄	1	4	yes	—
23	C₂₃×#533	C₂²	1	1	yes	characteristic
24	C₂₃×#532	C₂²	1	1	yes	characteristic
25	C₂₃×#529	C₂²	1	8	yes	—
26	C₂₃×#525	C₂²	1	2	yes	—
27	C₄×#41×C₂₃	C₂²	1	2	yes	—
28	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
29	C₂₃×#446	C₂²	1	4	yes	complemented
30	C₂₃×#446	C₂²	1	8	yes	complemented
31	C₈×Q₈×C₂₃	C₂²	1	4	yes	complemented
32	C₂₃×#436	C₂²	1	8	yes	—
33	C₂₃×#436	C₂²	1	4	yes	complemented
34	C₂₃×#435	C₂²	1	8	yes	—
35	C₂₃×#435	C₂²	1	8	yes	—
36	C₂₃×#435	C₂²	1	8	yes	complemented
37	C₈×D₄×C₂₃	C₂²	1	8	yes	—
38	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
39	C₂₃×#433	C₂²	1	8	yes	—
40	C₂₃×#433	C₂²	1	8	yes	complemented
41	C₂₃×#432	C₂²	1	8	yes	complemented
42	C₂₃×#424	C₂²	1	2	yes	—
43	C₂₃×#424	C₂²	1	2	yes	—
44	C₂₃×#423	C₂²	1	1	yes	characteristic
45	C₂₃×#423	C₂²	1	1	yes	characteristic
46	C₂₃×#408	C₂²	1	2	yes	—
47	C₂₃×#408	C₂²	1	2	yes	—
48	C₂₃×#407	C₂²	1	2	yes	—
49	C₂₃×#405	C₂²	1	2	yes	—
50	C₂₃×#405	C₂²	1	2	yes	—
51	C₂₃×#405	C₂²	1	4	yes	—
52	C₂₃×#405	C₂²	1	4	yes	—
53	C₂₃×#405	C₂²	1	4	yes	complemented
54	C₂₃×#405	C₂²	1	4	yes	complemented
55	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
56	C₄×M₁₆×C₂₃	C₂²	1	4	yes	complemented
57	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
59	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
60	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
61	C₂×C₄×C₈×C₂₃	C₂²	1	4	yes	complemented
62	C₂×#41×C₂₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
64	C₂₃×#131	—	2	8	no	—
65	C₂₃×#131	—	2	8	no	—
66	C₂×M₁₆×C₂₃	—	2	4	no	—
67	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
68	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
69	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
70	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
71	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
72	C₂²×C₈×C₂₃	—	2	4	no	—
73	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
75	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
77	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
78	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
79	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
81	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
82	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
83	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
84	C₂₃×#126	C₂×C₄	1	8	yes	—
85	C₂₃×#126	C₂×C₄	1	8	yes	—
86	C₂₃×#125	C₂×C₄	1	8	yes	—
87	C₂₃×#125	C₂×C₄	1	2	yes	—
88	C₂₃×#124	C₂×C₄	1	8	yes	—
89	C₂₃×#124	C₂×C₄	1	2	yes	—
90	C₂₃×#123	C₂×C₄	1	4	yes	—
91	C₂₃×#123	C₂×C₄	1	8	yes	—
92	C₂₃×#123	C₂×C₄	1	8	yes	—
93	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
94	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
95	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
96	C₂₃×#121	C₂×C₄	1	4	yes	—
97	C₂₃×#121	C₂×C₄	1	8	yes	—
98	C₂₃×#121	C₂×C₄	1	4	yes	—
99	C₂₃×#120	C₂×C₄	1	4	yes	—
100	C₄×Q₈×C₂₃	C₂×C₄	1	4	yes	—
101	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
102	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	—
103	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
104	C₄×D₄×C₂₃	C₂³	1	8	yes	—
105	C₄×D₄×C₂₃	C₂³	1	4	yes	—
106	C₂₃×#117	C₂×C₄	1	2	yes	—
107	C₂₃×#117	C₂×C₄	1	2	yes	—
108	C₂₃×#117	C₂³	1	2	yes	—
109	C₂₃×#117	C₂³	1	4	yes	—
110	C₂₃×#117	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
112	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
113	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
116	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
117	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
118	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
119	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
120	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
121	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
122	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
123	C₂₃×#97	C₂³	1	4	yes	—
124	C₂₃×#97	C₂³	1	4	yes	—
125	C₂₃×#97	C₂³	1	4	yes	—
126	C₂₃×#97	C₂³	1	4	yes	—
127	C₂₃×#97	C₂³	1	4	yes	—
128	C₄×C₈×C₂₃	C₂³	1	2	yes	—
129	C₄×C₈×C₂₃	C₂³	1	2	yes	—
130	C₄×C₈×C₂₃	C₂³	1	4	yes	—
131	C₄×C₈×C₂₃	C₂³	1	4	yes	—
132	C₄×C₈×C₂₃	C₂³	1	2	yes	—
133	C₄×C₈×C₂₃	C₂³	1	2	yes	—
134	C₄×C₈×C₂₃	C₂³	1	4	yes	—
135	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
136	#41×C₂₃	—	2	4	no	—
137	#41×C₂₃	—	2	4	no	—
138	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
139	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
140	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
141	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
142	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
143	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
144	C₂²×C₄×C₂₃	—	2	2	no	—
145	C₂²×C₄×C₂₃	—	2	2	no	—
146	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
150	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
151	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
154	M₁₆×C₂₃	—	2	4	no	—
155	M₁₆×C₂₃	—	2	4	no	—
156	M₁₆×C₂₃	—	2	8	no	—
157	M₁₆×C₂₃	—	2	8	no	—
158	M₁₆×C₂₃	—	2	8	no	—
159	C₂×C₈×C₂₃	—	2	2	no	—
160	C₂×C₈×C₂₃	—	2	2	no	—
161	C₂×C₈×C₂₃	—	2	4	no	—
162	C₂×C₈×C₂₃	—	2	4	no	—
163	C₂×C₈×C₂₃	—	2	8	no	—
164	C₂×C₈×C₂₃	—	2	8	no	—
165	C₂×C₈×C₂₃	#41	1	4	yes	—
166	C₂×C₈×C₂₃	#41	1	4	yes	—
167	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
168	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
169	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
170	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
171	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
173	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
174	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
175	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
176	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
177	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
178	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
179	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
180	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
181	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
182	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
183	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
184	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
185	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
186	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
187	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
188	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
189	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
190	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
191	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
192	C₄²×C₂₃	C₂²×C₄	1	8	yes	—
193	C₄²×C₂₃	C₂⁴	1	2	yes	—
194	C₄²×C₂₃	C₂⁴	1	4	yes	—
195	C₄²×C₂₃	C₂⁴	1	2	yes	—
196	#60206	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂³×C₂₃	—	2	2	no	—
198	C₂³×C₂₃	—	4	2	no	—
199	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
200	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
201	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
202	Q₈×C₂₃	—	2	4	no	—
203	Q₈×C₂₃	—	4	4	no	—
204	D₄×C₂₃	—	2	8	no	—
205	D₄×C₂₃	—	2	4	no	—
206	D₄×C₂₃	—	4	4	no	—
207	D₄×C₂₃	—	4	8	no	—
208	C₂×C₄×C₂₃	—	2	2	no	—
209	C₂×C₄×C₂₃	—	2	4	no	—
210	C₂×C₄×C₂₃	—	2	2	no	—
211	C₂×C₄×C₂₃	—	2	4	no	—
212	C₂×C₄×C₂₃	—	2	4	no	—
213	C₂×C₄×C₂₃	—	2	2	no	—
214	C₂×C₄×C₂₃	—	4	2	no	—
215	C₂×C₄×C₂₃	—	4	8	no	—
216	C₂×C₄×C₂₃	—	4	2	no	—
217	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
218	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
219	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
220	C₂×C₄×C₂₃	C₂³×C₄	1	8	yes	—
221	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
222	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
223	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
224	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
225	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
226	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
227	C₈×C₂₃	—	2	2	no	—
228	C₈×C₂₃	—	2	2	no	—
229	C₈×C₂₃	—	2	4	no	—
230	C₈×C₂₃	—	2	4	no	—
231	C₈×C₂₃	C₂×#41	1	2	yes	—
232	C₈×C₂₃	C₂×#41	1	2	yes	—
233	C₈×C₂₃	C₂×#41	1	4	yes	—
234	#3455	C₂×C₂₃	1	1	yes	characteristic
235	#2967	C₂×C₂₃	1	8	yes	complemented
236	#2966	C₂×C₂₃	1	8	yes	complemented
237	#2961	C₂×C₂₃	1	1	yes	characteristic, complemented
238	#2960	C₂×C₂₃	1	1	yes	characteristic, complemented
239	#2932	C₂×C₂₃	1	1	yes	characteristic, complemented
240	#2931	C₂×C₂₃	1	1	yes	characteristic, complemented
241	#2930	C₂×C₂₃	1	2	yes	complemented
242	#2929	C₂×C₂₃	1	2	yes	complemented
243	#2923	C₂×C₂₃	1	2	yes	complemented
244	#2921	C₂×C₂₃	1	1	yes	characteristic, complemented
245	C₄×#131	C₂×C₂₃	1	2	yes	complemented
246	C₂×#405	C₂×C₂₃	1	1	yes	characteristic, complemented
247	C₂²×C₂₃	—	2	2	no	—
248	C₂²×C₂₃	—	2	2	no	—
249	C₂²×C₂₃	—	2	4	no	—
250	C₂²×C₂₃	—	2	8	no	—
251	C₂²×C₂₃	—	2	4	no	—
252	C₂²×C₂₃	—	4	4	no	—
253	C₂²×C₂₃	C₄×#41	1	2	yes	—
254	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
255	C₄×C₂₃	—	2	2	no	—
256	C₄×C₂₃	—	2	4	no	—
257	C₄×C₂₃	—	2	4	no	—
258	C₄×C₂₃	—	2	2	no	—
259	C₄×C₂₃	—	2	8	no	—
260	C₄×C₂₃	—	2	2	no	—
261	C₄×C₂₃	C₄×#41	1	2	yes	—
262	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
263	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
264	C₂×#131	C₂²×C₂₃	1	2	yes	—
265	C₂×#131	C₂²×C₂₃	1	2	yes	—
266	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
267	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
268	#542	C₄×C₂₃	1	4	yes	—
269	#541	C₄×C₂₃	1	2	yes	—
270	#540	C₄×C₂₃	1	2	yes	—
271	#539	C₄×C₂₃	1	4	yes	—
272	#538	C₄×C₂₃	1	4	yes	—
273	#533	C₂²×C₂₃	1	1	yes	characteristic
274	#532	C₂²×C₂₃	1	1	yes	characteristic
275	#529	C₂²×C₂₃	1	8	yes	—
276	#525	C₂²×C₂₃	1	2	yes	—
277	C₄×#41	C₂²×C₂₃	1	2	yes	—
278	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
279	#446	C₂²×C₂₃	1	4	yes	complemented
280	#446	C₂²×C₂₃	1	8	yes	complemented
281	C₈×Q₈	C₂²×C₂₃	1	4	yes	complemented
282	#436	C₂²×C₂₃	1	8	yes	—
283	#436	C₂²×C₂₃	1	4	yes	complemented
284	#435	C₂²×C₂₃	1	8	yes	—
285	#435	C₂²×C₂₃	1	8	yes	—
286	#435	C₂²×C₂₃	1	8	yes	complemented
287	C₈×D₄	C₂²×C₂₃	1	8	yes	—
288	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
289	#433	C₂²×C₂₃	1	8	yes	—
290	#433	C₂²×C₂₃	1	8	yes	complemented
291	#432	C₂²×C₂₃	1	8	yes	complemented
292	#424	C₂²×C₂₃	1	2	yes	—
293	#424	C₂²×C₂₃	1	2	yes	—
294	#423	C₂²×C₂₃	1	1	yes	characteristic
295	#423	C₂²×C₂₃	1	1	yes	characteristic
296	#408	C₂²×C₂₃	1	2	yes	—
297	#408	C₂²×C₂₃	1	2	yes	—
298	#407	C₂²×C₂₃	1	2	yes	—
299	#405	C₂²×C₂₃	1	4	yes	—
300	#405	C₂²×C₂₃	1	4	yes	—
301	#405	C₂²×C₂₃	1	2	yes	—
302	#405	C₂²×C₂₃	1	2	yes	—
303	#405	C₂²×C₂₃	1	4	yes	complemented
304	#405	C₂²×C₂₃	1	4	yes	complemented
305	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
306	C₄×M₁₆	C₂²×C₂₃	1	4	yes	complemented
307	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
308	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
309	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
310	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
311	C₂×C₄×C₈	C₂²×C₂₃	1	4	yes	complemented
312	C₂×C₂₃	—	2	2	no	—
313	C₂×C₂₃	—	4	4	no	—
314	C₂×C₂₃	—	4	2	no	—
315	C₂×C₂₃	C₂×C₄×#41	1	1	yes	characteristic
316	C₂×C₂₃	#3573	1	2	yes	—
317	C₂×#41	C₂³×C₂₃	1	2	yes	—
318	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
319	#131	—	2	8	no	—
320	#131	—	2	8	no	—
321	C₂×M₁₆	—	2	4	no	—
322	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
323	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
324	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
325	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
326	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
327	C₂²×C₈	—	2	4	no	—
328	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
329	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
330	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
331	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
333	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
334	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
336	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
337	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
338	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
339	#126	C₂×C₄×C₂₃	1	8	yes	—
340	#126	C₂×C₄×C₂₃	1	8	yes	—
341	#125	C₂×C₄×C₂₃	1	8	yes	—
342	#125	C₂×C₄×C₂₃	1	2	yes	—
343	#124	C₂×C₄×C₂₃	1	8	yes	—
344	#124	C₂×C₄×C₂₃	1	2	yes	—
345	#123	C₂×C₄×C₂₃	1	4	yes	—
346	#123	C₂×C₄×C₂₃	1	8	yes	—
347	#123	C₂×C₄×C₂₃	1	8	yes	—
348	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
349	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	—
350	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
351	#121	C₂×C₄×C₂₃	1	4	yes	—
352	#121	C₂×C₄×C₂₃	1	8	yes	—
353	#121	C₂×C₄×C₂₃	1	4	yes	—
354	#120	C₂×C₄×C₂₃	1	4	yes	—
355	C₄×Q₈	C₂×C₄×C₂₃	1	4	yes	—
356	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
357	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	—
358	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
359	C₄×D₄	C₂³×C₂₃	1	8	yes	—
360	C₄×D₄	C₂³×C₂₃	1	4	yes	—
361	#117	C₂×C₄×C₂₃	1	2	yes	—
362	#117	C₂×C₄×C₂₃	1	2	yes	—
363	#117	C₂³×C₂₃	1	4	yes	—
364	#117	C₂³×C₂₃	1	2	yes	—
365	#117	C₂³×C₂₃	1	4	yes	—
366	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
367	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
368	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
369	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
370	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
371	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
372	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
373	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
374	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
375	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
376	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
377	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
378	#97	C₂³×C₂₃	1	4	yes	—
379	#97	C₂³×C₂₃	1	4	yes	—
380	#97	C₂³×C₂₃	1	4	yes	—
381	#97	C₂³×C₂₃	1	4	yes	—
382	#97	C₂³×C₂₃	1	4	yes	—
383	C₄×C₈	C₂³×C₂₃	1	2	yes	—
384	C₄×C₈	C₂³×C₂₃	1	2	yes	—
385	C₄×C₈	C₂³×C₂₃	1	2	yes	—
386	C₄×C₈	C₂³×C₂₃	1	2	yes	—
387	C₄×C₈	C₂³×C₂₃	1	4	yes	—
388	C₄×C₈	C₂³×C₂₃	1	4	yes	—
389	C₄×C₈	C₂³×C₂₃	1	4	yes	—
390	C₂₃	#60206	1	1	yes	characteristic, direct product factor, Sylow
391	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
392	#41	—	2	4	no	—
393	#41	—	2	4	no	—
394	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
395	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
396	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
397	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
398	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
399	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
403	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
404	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
405	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
406	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
407	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
408	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
409	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
410	M₁₆	—	2	4	no	—
411	M₁₆	—	2	4	no	—
412	M₁₆	—	2	8	no	—
413	M₁₆	—	2	8	no	—
414	M₁₆	—	2	8	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	4	no	—
418	C₂×C₈	—	2	4	no	—
419	C₂×C₈	—	2	8	no	—
420	C₂×C₈	—	2	8	no	—
421	C₂×C₈	#41×C₂₃	1	4	yes	—
422	C₂×C₈	#41×C₂₃	1	4	yes	—
423	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
424	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
425	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
426	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
427	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
428	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
429	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
430	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
431	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
432	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
433	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
434	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
435	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
436	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
437	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
438	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
439	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
440	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
441	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
442	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
443	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
444	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
445	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
446	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
447	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
448	C₄²	C₂²×C₄×C₂₃	1	8	yes	—
449	C₄²	C₂⁴×C₂₃	1	2	yes	—
450	C₄²	C₂⁴×C₂₃	1	2	yes	—
451	C₄²	C₂⁴×C₂₃	1	4	yes	—
452	C₂³	—	2	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
455	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
456	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
457	Q₈	—	2	4	no	—
458	Q₈	—	4	4	no	—
459	D₄	—	2	8	no	—
460	D₄	—	2	4	no	—
461	D₄	—	4	4	no	—
462	D₄	—	4	8	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	8	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
473	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
474	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
475	C₂×C₄	C₂³×C₄×C₂₃	1	8	yes	—
476	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
477	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
478	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
479	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
480	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
481	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
482	C₈	—	2	2	no	—
483	C₈	—	2	2	no	—
484	C₈	—	2	4	no	—
485	C₈	—	2	4	no	—
486	C₈	C₂×#41×C₂₃	1	2	yes	—
487	C₈	C₂×#41×C₂₃	1	2	yes	—
488	C₈	C₂×#41×C₂₃	1	4	yes	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	2	8	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	4	4	no	—
495	C₂²	C₄×#41×C₂₃	1	2	yes	—
496	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
497	C₄	—	2	2	no	—
498	C₄	—	2	4	no	—
499	C₄	—	2	4	no	—
500	C₄	—	2	2	no	—
501	C₄	—	2	8	no	—
502	C₄	—	2	2	no	—
503	C₄	C₄×#41×C₂₃	1	2	yes	—
504	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
505	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
506	C₂	—	2	2	no	—
507	C₂	—	4	2	no	—
508	C₂	—	4	4	no	—
509	C₂	C₂×C₄×#41×C₂₃	1	1	yes	characteristic
510	C₂	C₂₃×#3573	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₂₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂⁴×C₄
prime radical	C₂₃×#3455	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2967	C₂	semidirect
3. C₂₃×#2966	C₂	semidirect
4. C₂₃×#2961	C₂	semidirect
5. C₂₃×#2960	C₂	semidirect
6. C₂₃×#2932	C₂	semidirect
7. C₂₃×#2931	C₂	semidirect
8. C₂₃×#2930	C₂	semidirect
9. C₂₃×#2929	C₂	semidirect
10. C₂₃×#2923	C₂	semidirect
11. C₂₃×#2921	C₂	semidirect
12. C₄×C₂₃×#131	C₂	semidirect
13. C₂×C₂₃×#405	C₂	semidirect
29. C₂₃×#446	C₂²	semidirect
30. C₂₃×#446	C₂²	semidirect
31. C₈×Q₈×C₂₃	C₂²	semidirect
33. C₂₃×#436	C₂²	semidirect
36. C₂₃×#435	C₂²	semidirect
38. C₈×D₄×C₂₃	C₂²	semidirect
40. C₂₃×#433	C₂²	semidirect
41. C₂₃×#432	C₂²	semidirect
53. C₂₃×#405	C₂²	semidirect
54. C₂₃×#405	C₂²	semidirect
56. C₄×M₁₆×C₂₃	C₂²	semidirect
61. C₂×C₄×C₈×C₂₃	C₂²	semidirect
196. #60206	C₂₃	direct (N × H)
235. #2967	C₂×C₂₃	semidirect
236. #2966	C₂×C₂₃	semidirect
237. #2961	C₂×C₂₃	semidirect
238. #2960	C₂×C₂₃	semidirect
239. #2932	C₂×C₂₃	semidirect
240. #2931	C₂×C₂₃	semidirect
241. #2930	C₂×C₂₃	semidirect
242. #2929	C₂×C₂₃	semidirect
243. #2923	C₂×C₂₃	semidirect
244. #2921	C₂×C₂₃	semidirect
245. C₄×#131	C₂×C₂₃	semidirect
246. C₂×#405	C₂×C₂₃	semidirect
279. #446	C₂²×C₂₃	semidirect
280. #446	C₂²×C₂₃	semidirect
281. C₈×Q₈	C₂²×C₂₃	semidirect
283. #436	C₂²×C₂₃	semidirect
286. #435	C₂²×C₂₃	semidirect
288. C₈×D₄	C₂²×C₂₃	semidirect
290. #433	C₂²×C₂₃	semidirect
291. #432	C₂²×C₂₃	semidirect
303. #405	C₂²×C₂₃	semidirect
304. #405	C₂²×C₂₃	semidirect
306. C₄×M₁₆	C₂²×C₂₃	semidirect
311. C₂×C₄×C₈	C₂²×C₂₃	semidirect
390. C₂₃	#60206	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×#3455	2
C₂₃×#2967	2
C₂₃×#2966	2
C₂₃×#2961	2
C₂₃×#2960	2
C₂₃×#2932	2
C₂₃×#2931	2
C₂₃×#2930	2
C₂₃×#2929	2
C₂₃×#2923	2
C₂₃×#2921	2
C₄×C₂₃×#131	2
C₂×C₂₃×#405	2
#60206	23

Subgroups — C23×#60206 #19207832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60206 #19207832