Subgroups — C₂₃×#60267 #19207893

Order 5888.

1790 conjugacy classes of subgroups.

The subgroup lattice has 656 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×#2995	C₂	1	4	yes	maximal, complemented
3	C₂₃×#2994	C₂	1	4	yes	maximal, complemented
4	C₂₃×#2993	C₂	1	4	yes	maximal, complemented
5	C₂₃×#2992	C₂	1	4	yes	maximal, complemented
6	C₂₃×#2962	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2935	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2930	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2929	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2925	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2921	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2906	C₂	1	2	yes	maximal, complemented
13	C₂×C₂₃×#424	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	2	yes	—
19	C₂₃×#542	C₄	1	2	yes	—
20	C₂₃×#541	C₄	1	1	yes	characteristic
21	C₂₃×#541	C₄	1	1	yes	characteristic
22	C₂₃×#540	C₄	1	1	yes	characteristic
23	C₂₃×#540	C₄	1	1	yes	characteristic
24	C₂₃×#539	C₄	1	4	yes	—
25	C₂₃×#538	C₄	1	4	yes	—
26	C₂₃×#533	C₂²	1	1	yes	characteristic
27	C₂₃×#532	C₂²	1	1	yes	characteristic
28	C₂₃×#529	C₂²	1	4	yes	—
29	C₂₃×#529	C₂²	1	4	yes	—
30	C₂₃×#525	C₂²	1	2	yes	—
31	C₄×#41×C₂₃	C₂²	1	2	yes	—
32	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
33	C₂₃×#446	C₂²	1	4	yes	complemented
34	C₂₃×#446	C₂²	1	4	yes	complemented
35	C₂₃×#446	C₂²	1	4	yes	complemented
36	C₈×Q₈×C₂₃	C₂²	1	4	yes	complemented
37	C₂₃×#436	C₂²	1	4	yes	—
38	C₂₃×#436	C₂²	1	4	yes	—
39	C₂₃×#436	C₂²	1	4	yes	complemented
40	C₂₃×#435	C₂²	1	4	yes	—
41	C₂₃×#435	C₂²	1	4	yes	—
42	C₂₃×#435	C₂²	1	4	yes	—
43	C₂₃×#435	C₂²	1	4	yes	—
44	C₂₃×#435	C₂²	1	4	yes	complemented
45	C₂₃×#435	C₂²	1	4	yes	complemented
46	C₈×D₄×C₂₃	C₂²	1	4	yes	—
47	C₈×D₄×C₂₃	C₂²	1	4	yes	—
48	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
49	C₂₃×#433	C₂²	1	4	yes	—
50	C₂₃×#433	C₂²	1	4	yes	—
51	C₂₃×#433	C₂²	1	4	yes	complemented
52	C₂₃×#433	C₂²	1	4	yes	complemented
53	C₂₃×#432	C₂²	1	4	yes	complemented
54	C₂₃×#431	C₂²	1	4	yes	complemented
55	C₂₃×#424	C₂²	1	2	yes	—
56	C₂₃×#424	C₂²	1	2	yes	—
57	C₂₃×#424	C₂²	1	2	yes	—
58	C₂₃×#424	C₂²	1	2	yes	—
59	C₂₃×#424	C₂²	1	2	yes	—
60	C₂₃×#424	C₂²	1	2	yes	—
61	C₂₃×#424	C₂²	1	4	yes	complemented
62	C₂₃×#424	C₂²	1	4	yes	complemented
63	C₂₃×#423	C₂²	1	1	yes	characteristic
64	C₂₃×#423	C₂²	1	1	yes	characteristic
65	C₂₃×#423	C₂²	1	4	yes	complemented
66	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
67	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
68	C₂×C₂₃×C₄⋊C₈	C₂²	1	4	yes	complemented
69	C₂₃×#408	C₂²	1	2	yes	—
70	C₂₃×#408	C₂²	1	2	yes	—
71	C₂₃×#407	C₂²	1	2	yes	—
72	C₂₃×#405	C₂²	1	2	yes	—
73	C₂₃×#405	C₂²	1	2	yes	—
74	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
75	C₂×#41×C₂₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂₃×#131	—	4	4	no	—
78	C₂₃×#131	—	4	4	no	—
79	C₂×M₁₆×C₂₃	—	4	2	no	—
80	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
81	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
82	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
83	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
84	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
86	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
87	C₂²×C₈×C₂₃	—	4	2	no	—
88	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
89	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
90	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
92	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
94	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
95	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
96	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
97	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
98	C₂₃×#126	C₂×C₄	1	4	yes	—
99	C₂₃×#126	C₂×C₄	1	4	yes	—
100	C₂₃×#126	C₂×C₄	1	4	yes	—
101	C₂₃×#126	C₂×C₄	1	4	yes	—
102	C₂₃×#125	C₂×C₄	1	4	yes	—
103	C₂₃×#125	C₂×C₄	1	4	yes	—
104	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
105	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
106	C₂₃×#124	C₂×C₄	1	4	yes	—
107	C₂₃×#124	C₂×C₄	1	4	yes	—
108	C₂₃×#124	C₂×C₄	1	2	yes	—
109	C₂₃×#123	C₂×C₄	1	4	yes	—
110	C₂₃×#123	C₂×C₄	1	4	yes	—
111	C₂₃×#123	C₂×C₄	1	4	yes	—
112	C₂₃×#123	C₂×C₄	1	4	yes	—
113	C₂₃×#123	C₂×C₄	1	4	yes	—
114	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
115	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
116	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
117	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
118	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
119	C₂₃×#121	C₂×C₄	1	2	yes	—
120	C₂₃×#121	C₂×C₄	1	2	yes	—
121	C₂₃×#121	C₂×C₄	1	4	yes	—
122	C₂₃×#121	C₂×C₄	1	4	yes	—
123	C₂₃×#121	C₂×C₄	1	4	yes	—
124	C₂₃×#120	C₂×C₄	1	4	yes	—
125	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
126	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
127	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
128	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
129	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
130	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
131	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
132	C₄×D₄×C₂₃	C₂³	1	4	yes	—
133	C₄×D₄×C₂₃	C₂³	1	4	yes	—
134	C₄×D₄×C₂₃	C₂³	1	4	yes	—
135	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
136	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
137	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
138	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
139	C₂₃×#117	C₂³	1	2	yes	—
140	C₂₃×#117	C₂³	1	2	yes	—
141	C₂₃×#117	C₂³	1	2	yes	—
142	C₂₃×#117	C₂³	1	4	yes	—
143	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
144	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
145	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
148	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
149	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
150	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
151	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
152	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
153	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
154	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
155	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
156	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
157	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
158	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
159	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
160	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
161	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
162	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
163	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
164	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
165	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
166	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
167	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
168	C₂₃×#97	C₂³	1	4	yes	—
169	C₂₃×#97	C₂³	1	4	yes	—
170	C₂₃×#97	C₂³	1	4	yes	—
171	C₄×C₈×C₂₃	C₂³	1	4	yes	—
172	C₄×C₈×C₂₃	C₂³	1	4	yes	—
173	C₄×C₈×C₂₃	C₂³	1	4	yes	—
174	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
175	#41×C₂₃	—	2	4	no	—
176	#41×C₂₃	—	2	4	no	—
177	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
178	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
179	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
180	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
181	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
182	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
183	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
184	C₂²×C₄×C₂₃	—	2	2	no	—
185	C₂²×C₄×C₂₃	—	2	2	no	—
186	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
190	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
191	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
192	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
193	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
197	M₁₆×C₂₃	—	2	4	no	—
198	M₁₆×C₂₃	—	2	4	no	—
199	M₁₆×C₂₃	—	4	1	no	—
200	M₁₆×C₂₃	—	4	2	no	—
201	M₁₆×C₂₃	—	4	1	no	—
202	M₁₆×C₂₃	—	4	4	no	—
203	M₁₆×C₂₃	—	4	4	no	—
204	C₂×C₈×C₂₃	—	2	4	no	—
205	C₂×C₈×C₂₃	—	2	4	no	—
206	C₂×C₈×C₂₃	—	4	1	no	—
207	C₂×C₈×C₂₃	—	4	2	no	—
208	C₂×C₈×C₂₃	—	4	1	no	—
209	C₂×C₈×C₂₃	—	4	4	no	—
210	C₂×C₈×C₂₃	—	4	4	no	—
211	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
212	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
213	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
214	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
215	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
216	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
217	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
218	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
219	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
220	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
221	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
222	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
223	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
224	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
225	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
226	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
227	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
228	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
229	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
230	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
231	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
232	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
233	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
234	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
235	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
236	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
237	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
238	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
239	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
240	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
241	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
242	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
243	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
244	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
245	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
246	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
247	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
248	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
249	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
250	C₄²×C₂₃	C₂⁴	1	2	yes	—
251	C₄²×C₂₃	C₂⁴	1	2	yes	—
252	C₄²×C₂₃	C₂⁴	1	4	yes	—
253	#60267	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂³×C₂₃	—	2	2	no	—
255	C₂³×C₂₃	—	4	2	no	—
256	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
257	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
258	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
259	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
260	Q₈×C₂₃	—	2	4	no	—
261	Q₈×C₂₃	—	4	4	no	—
262	D₄×C₂₃	—	2	8	no	—
263	D₄×C₂₃	—	2	4	no	—
264	D₄×C₂₃	—	4	4	no	—
265	D₄×C₂₃	—	4	4	no	—
266	D₄×C₂₃	—	4	4	no	—
267	C₂×C₄×C₂₃	—	2	2	no	—
268	C₂×C₄×C₂₃	—	2	2	no	—
269	C₂×C₄×C₂₃	—	2	2	no	—
270	C₂×C₄×C₂₃	—	2	1	no	—
271	C₂×C₄×C₂₃	—	2	1	no	—
272	C₂×C₄×C₂₃	—	2	4	no	—
273	C₂×C₄×C₂₃	—	2	1	no	—
274	C₂×C₄×C₂₃	—	2	1	no	—
275	C₂×C₄×C₂₃	—	2	4	no	—
276	C₂×C₄×C₂₃	—	4	2	no	—
277	C₂×C₄×C₂₃	—	4	4	no	—
278	C₂×C₄×C₂₃	—	4	4	no	—
279	C₂×C₄×C₂₃	—	4	2	no	—
280	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
281	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
282	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
283	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
284	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
285	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
286	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
287	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
288	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
289	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
290	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
291	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
292	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
293	C₈×C₂₃	—	2	2	no	—
294	C₈×C₂₃	—	2	2	no	—
295	C₈×C₂₃	—	2	2	no	—
296	C₈×C₂₃	—	2	2	no	—
297	C₈×C₂₃	—	2	4	no	—
298	C₈×C₂₃	—	2	4	no	—
299	#3455	C₂×C₂₃	1	1	yes	characteristic
300	#2995	C₂×C₂₃	1	4	yes	complemented
301	#2994	C₂×C₂₃	1	4	yes	complemented
302	#2993	C₂×C₂₃	1	4	yes	complemented
303	#2992	C₂×C₂₃	1	4	yes	complemented
304	#2962	C₂×C₂₃	1	2	yes	complemented
305	#2935	C₂×C₂₃	1	2	yes	complemented
306	#2930	C₂×C₂₃	1	2	yes	complemented
307	#2929	C₂×C₂₃	1	2	yes	complemented
308	#2925	C₂×C₂₃	1	2	yes	complemented
309	#2921	C₂×C₂₃	1	1	yes	characteristic, complemented
310	#2906	C₂×C₂₃	1	2	yes	complemented
311	C₂×#424	C₂×C₂₃	1	1	yes	characteristic, complemented
312	C₂²×C₂₃	—	2	2	no	—
313	C₂²×C₂₃	—	2	1	no	—
314	C₂²×C₂₃	—	2	1	no	—
315	C₂²×C₂₃	—	2	4	no	—
316	C₂²×C₂₃	—	2	4	no	—
317	C₂²×C₂₃	—	2	4	no	—
318	C₂²×C₂₃	—	2	2	no	—
319	C₂²×C₂₃	—	2	2	no	—
320	C₂²×C₂₃	—	4	4	no	—
321	C₂²×C₂₃	#520	1	2	yes	—
322	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
323	C₄×C₂₃	—	2	1	no	—
324	C₄×C₂₃	—	2	1	no	—
325	C₄×C₂₃	—	2	4	no	—
326	C₄×C₂₃	—	2	2	no	—
327	C₄×C₂₃	—	2	2	no	—
328	C₄×C₂₃	—	2	2	no	—
329	C₄×C₂₃	—	2	4	no	—
330	C₄×C₂₃	—	2	4	no	—
331	C₄×C₂₃	—	2	2	no	—
332	C₄×C₂₃	#520	1	2	yes	—
333	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
334	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
335	C₂×#131	C₂²×C₂₃	1	2	yes	—
336	C₂×#131	C₂²×C₂₃	1	2	yes	—
337	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
338	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
339	#542	C₄×C₂₃	1	2	yes	—
340	#542	C₄×C₂₃	1	2	yes	—
341	#541	C₄×C₂₃	1	1	yes	characteristic
342	#541	C₄×C₂₃	1	1	yes	characteristic
343	#540	C₄×C₂₃	1	1	yes	characteristic
344	#540	C₄×C₂₃	1	1	yes	characteristic
345	#539	C₄×C₂₃	1	4	yes	—
346	#538	C₄×C₂₃	1	4	yes	—
347	#533	C₂²×C₂₃	1	1	yes	characteristic
348	#532	C₂²×C₂₃	1	1	yes	characteristic
349	#529	C₂²×C₂₃	1	4	yes	—
350	#529	C₂²×C₂₃	1	4	yes	—
351	#525	C₂²×C₂₃	1	2	yes	—
352	C₄×#41	C₂²×C₂₃	1	2	yes	—
353	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
354	#446	C₂²×C₂₃	1	4	yes	complemented
355	#446	C₂²×C₂₃	1	4	yes	complemented
356	#446	C₂²×C₂₃	1	4	yes	complemented
357	C₈×Q₈	C₂²×C₂₃	1	4	yes	complemented
358	#436	C₂²×C₂₃	1	4	yes	—
359	#436	C₂²×C₂₃	1	4	yes	—
360	#436	C₂²×C₂₃	1	4	yes	complemented
361	#435	C₂²×C₂₃	1	4	yes	—
362	#435	C₂²×C₂₃	1	4	yes	—
363	#435	C₂²×C₂₃	1	4	yes	—
364	#435	C₂²×C₂₃	1	4	yes	—
365	#435	C₂²×C₂₃	1	4	yes	complemented
366	#435	C₂²×C₂₃	1	4	yes	complemented
367	C₈×D₄	C₂²×C₂₃	1	4	yes	—
368	C₈×D₄	C₂²×C₂₃	1	4	yes	—
369	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
370	#433	C₂²×C₂₃	1	4	yes	—
371	#433	C₂²×C₂₃	1	4	yes	—
372	#433	C₂²×C₂₃	1	4	yes	complemented
373	#433	C₂²×C₂₃	1	4	yes	complemented
374	#432	C₂²×C₂₃	1	4	yes	complemented
375	#431	C₂²×C₂₃	1	4	yes	complemented
376	#424	C₂²×C₂₃	1	2	yes	—
377	#424	C₂²×C₂₃	1	2	yes	—
378	#424	C₂²×C₂₃	1	2	yes	—
379	#424	C₂²×C₂₃	1	2	yes	—
380	#424	C₂²×C₂₃	1	2	yes	—
381	#424	C₂²×C₂₃	1	2	yes	—
382	#424	C₂²×C₂₃	1	4	yes	complemented
383	#424	C₂²×C₂₃	1	4	yes	complemented
384	#423	C₂²×C₂₃	1	1	yes	characteristic
385	#423	C₂²×C₂₃	1	1	yes	characteristic
386	#423	C₂²×C₂₃	1	4	yes	complemented
387	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
388	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
389	C₂×C₄⋊C₈	C₂²×C₂₃	1	4	yes	complemented
390	#408	C₂²×C₂₃	1	2	yes	—
391	#408	C₂²×C₂₃	1	2	yes	—
392	#407	C₂²×C₂₃	1	2	yes	—
393	#405	C₂²×C₂₃	1	2	yes	—
394	#405	C₂²×C₂₃	1	2	yes	—
395	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
396	C₂×C₂₃	—	2	2	no	—
397	C₂×C₂₃	—	4	4	no	—
398	C₂×C₂₃	—	4	1	no	—
399	C₂×C₂₃	—	4	1	no	—
400	C₂×C₂₃	C₂×#520	1	1	yes	characteristic
401	C₂×C₂₃	#3573	1	2	yes	—
402	C₂×#41	C₂³×C₂₃	1	2	yes	—
403	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
404	#131	—	4	4	no	—
405	#131	—	4	4	no	—
406	C₂×M₁₆	—	4	2	no	—
407	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
408	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
409	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
410	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
411	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
412	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
413	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
414	C₂²×C₈	—	4	2	no	—
415	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
416	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
417	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
418	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
419	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
420	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
421	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
422	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
423	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
424	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
425	#126	C₂×C₄×C₂₃	1	4	yes	—
426	#126	C₂×C₄×C₂₃	1	4	yes	—
427	#126	C₂×C₄×C₂₃	1	4	yes	—
428	#126	C₂×C₄×C₂₃	1	4	yes	—
429	#125	C₂×C₄×C₂₃	1	4	yes	—
430	#125	C₂×C₄×C₂₃	1	4	yes	—
431	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
432	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
433	#124	C₂×C₄×C₂₃	1	4	yes	—
434	#124	C₂×C₄×C₂₃	1	4	yes	—
435	#124	C₂×C₄×C₂₃	1	2	yes	—
436	#123	C₂×C₄×C₂₃	1	4	yes	—
437	#123	C₂×C₄×C₂₃	1	4	yes	—
438	#123	C₂×C₄×C₂₃	1	4	yes	—
439	#123	C₂×C₄×C₂₃	1	4	yes	—
440	#123	C₂×C₄×C₂₃	1	4	yes	—
441	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
442	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
443	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
444	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
445	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
446	#121	C₂×C₄×C₂₃	1	2	yes	—
447	#121	C₂×C₄×C₂₃	1	2	yes	—
448	#121	C₂×C₄×C₂₃	1	4	yes	—
449	#121	C₂×C₄×C₂₃	1	4	yes	—
450	#121	C₂×C₄×C₂₃	1	4	yes	—
451	#120	C₂×C₄×C₂₃	1	4	yes	—
452	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
453	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
454	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
455	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
456	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
457	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
458	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
459	C₄×D₄	C₂³×C₂₃	1	4	yes	—
460	C₄×D₄	C₂³×C₂₃	1	4	yes	—
461	C₄×D₄	C₂³×C₂₃	1	4	yes	—
462	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
463	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
464	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
465	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
466	#117	C₂³×C₂₃	1	2	yes	—
467	#117	C₂³×C₂₃	1	2	yes	—
468	#117	C₂³×C₂₃	1	2	yes	—
469	#117	C₂³×C₂₃	1	4	yes	—
470	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
472	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
473	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
474	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
475	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
476	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
477	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
478	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
479	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
480	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
481	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
482	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
483	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
484	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
485	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
486	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
487	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
488	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
489	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
490	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
491	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
492	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
493	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
494	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
495	#97	C₂³×C₂₃	1	4	yes	—
496	#97	C₂³×C₂₃	1	4	yes	—
497	#97	C₂³×C₂₃	1	4	yes	—
498	C₄×C₈	C₂³×C₂₃	1	4	yes	—
499	C₄×C₈	C₂³×C₂₃	1	4	yes	—
500	C₄×C₈	C₂³×C₂₃	1	4	yes	—
501	C₂₃	#60267	1	1	yes	characteristic, direct product factor, Sylow
502	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
503	#41	—	2	4	no	—
504	#41	—	2	4	no	—
505	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
506	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
507	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
508	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
509	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
510	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
511	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
515	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
516	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
517	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
518	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
519	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
520	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
521	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
522	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
523	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
524	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
525	M₁₆	—	2	4	no	—
526	M₁₆	—	2	4	no	—
527	M₁₆	—	4	1	no	—
528	M₁₆	—	4	2	no	—
529	M₁₆	—	4	1	no	—
530	M₁₆	—	4	4	no	—
531	M₁₆	—	4	4	no	—
532	C₂×C₈	—	2	4	no	—
533	C₂×C₈	—	2	4	no	—
534	C₂×C₈	—	4	1	no	—
535	C₂×C₈	—	4	2	no	—
536	C₂×C₈	—	4	1	no	—
537	C₂×C₈	—	4	4	no	—
538	C₂×C₈	—	4	4	no	—
539	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
540	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
541	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
542	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
543	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
544	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
545	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
546	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
547	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
548	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
549	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
550	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
551	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
552	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
553	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
554	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
555	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
556	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
557	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
558	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
559	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
560	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
561	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
562	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
563	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
564	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
565	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
566	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
567	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
568	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
569	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
570	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
571	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
572	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
573	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
574	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
575	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
576	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
577	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
578	C₄²	C₂⁴×C₂₃	1	2	yes	—
579	C₄²	C₂⁴×C₂₃	1	4	yes	—
580	C₄²	C₂⁴×C₂₃	1	2	yes	—
581	C₂³	—	2	2	no	—
582	C₂³	—	4	2	no	—
583	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
584	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
585	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
586	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
587	Q₈	—	2	4	no	—
588	Q₈	—	4	4	no	—
589	D₄	—	2	8	no	—
590	D₄	—	2	4	no	—
591	D₄	—	4	4	no	—
592	D₄	—	4	4	no	—
593	D₄	—	4	4	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	4	no	—
605	C₂×C₄	—	4	4	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
608	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
609	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
610	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
611	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
612	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
613	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
614	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
615	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
616	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
617	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
618	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
619	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
620	C₈	—	2	2	no	—
621	C₈	—	2	2	no	—
622	C₈	—	2	2	no	—
623	C₈	—	2	2	no	—
624	C₈	—	2	4	no	—
625	C₈	—	2	4	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	4	no	—
630	C₂²	—	2	4	no	—
631	C₂²	—	2	4	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	4	4	no	—
635	C₂²	C₂₃×#520	1	2	yes	—
636	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	4	no	—
640	C₄	—	2	2	no	—
641	C₄	—	2	2	no	—
642	C₄	—	2	2	no	—
643	C₄	—	2	4	no	—
644	C₄	—	2	4	no	—
645	C₄	—	2	2	no	—
646	C₄	C₂₃×#520	1	2	yes	—
647	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
648	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
649	C₂	—	2	2	no	—
650	C₂	—	4	1	no	—
651	C₂	—	4	1	no	—
652	C₂	—	4	4	no	—
653	C₂	C₂×C₂₃×#520	1	1	yes	characteristic
654	C₂	C₂₃×#3573	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁵
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×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2995	C₂	semidirect
3. C₂₃×#2994	C₂	semidirect
4. C₂₃×#2993	C₂	semidirect
5. C₂₃×#2992	C₂	semidirect
6. C₂₃×#2962	C₂	semidirect
7. C₂₃×#2935	C₂	semidirect
8. C₂₃×#2930	C₂	semidirect
9. C₂₃×#2929	C₂	semidirect
10. C₂₃×#2925	C₂	semidirect
11. C₂₃×#2921	C₂	semidirect
12. C₂₃×#2906	C₂	semidirect
13. C₂×C₂₃×#424	C₂	semidirect
33. C₂₃×#446	C₂²	semidirect
34. C₂₃×#446	C₂²	semidirect
35. C₂₃×#446	C₂²	semidirect
36. C₈×Q₈×C₂₃	C₂²	semidirect
39. C₂₃×#436	C₂²	semidirect
44. C₂₃×#435	C₂²	semidirect
45. C₂₃×#435	C₂²	semidirect
48. C₈×D₄×C₂₃	C₂²	semidirect
51. C₂₃×#433	C₂²	semidirect
52. C₂₃×#433	C₂²	semidirect
53. C₂₃×#432	C₂²	semidirect
54. C₂₃×#431	C₂²	semidirect
61. C₂₃×#424	C₂²	semidirect
62. C₂₃×#424	C₂²	semidirect
65. C₂₃×#423	C₂²	semidirect
68. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
253. #60267	C₂₃	direct (N × H)
300. #2995	C₂×C₂₃	semidirect
301. #2994	C₂×C₂₃	semidirect
302. #2993	C₂×C₂₃	semidirect
303. #2992	C₂×C₂₃	semidirect
304. #2962	C₂×C₂₃	semidirect
305. #2935	C₂×C₂₃	semidirect
306. #2930	C₂×C₂₃	semidirect
307. #2929	C₂×C₂₃	semidirect
308. #2925	C₂×C₂₃	semidirect
309. #2921	C₂×C₂₃	semidirect
310. #2906	C₂×C₂₃	semidirect
311. C₂×#424	C₂×C₂₃	semidirect
354. #446	C₂²×C₂₃	semidirect
355. #446	C₂²×C₂₃	semidirect
356. #446	C₂²×C₂₃	semidirect
357. C₈×Q₈	C₂²×C₂₃	semidirect
360. #436	C₂²×C₂₃	semidirect
365. #435	C₂²×C₂₃	semidirect
366. #435	C₂²×C₂₃	semidirect
369. C₈×D₄	C₂²×C₂₃	semidirect
372. #433	C₂²×C₂₃	semidirect
373. #433	C₂²×C₂₃	semidirect
374. #432	C₂²×C₂₃	semidirect
375. #431	C₂²×C₂₃	semidirect
382. #424	C₂²×C₂₃	semidirect
383. #424	C₂²×C₂₃	semidirect
386. #423	C₂²×C₂₃	semidirect
389. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
501. C₂₃	#60267	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×#2995	2
C₂₃×#2994	2
C₂₃×#2993	2
C₂₃×#2992	2
C₂₃×#2962	2
C₂₃×#2935	2
C₂₃×#2930	2
C₂₃×#2929	2
C₂₃×#2925	2
C₂₃×#2921	2
C₂₃×#2906	2
C₂×C₂₃×#424	2
#60267	23

Subgroups — C23×#60267 #19207893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60267 #19207893