Subgroups — C₂₃×#60212 #19207838

Order 5888.

1874 conjugacy classes of subgroups.

The subgroup lattice has 672 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×#2969	C₂	1	4	yes	maximal, complemented
3	C₂₃×#2968	C₂	1	4	yes	maximal, complemented
4	C₂₃×#2967	C₂	1	4	yes	maximal, complemented
5	C₂₃×#2966	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×#2933	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2933	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2875	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2873	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#131	C₂²	1	2	yes	—
17	C₂×C₂₃×#131	C₂²	1	2	yes	—
18	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
19	C₂₃×#542	C₄	1	2	yes	—
20	C₂₃×#542	C₄	1	2	yes	—
21	C₂₃×#541	C₄	1	2	yes	—
22	C₂₃×#540	C₄	1	2	yes	—
23	C₂₃×#539	C₄	1	4	yes	—
24	C₂₃×#538	C₄	1	4	yes	—
25	C₂₃×#533	C₂²	1	1	yes	characteristic
26	C₂₃×#532	C₂²	1	1	yes	characteristic
27	C₂₃×#529	C₂²	1	4	yes	—
28	C₂₃×#529	C₂²	1	4	yes	—
29	C₂₃×#525	C₂²	1	1	yes	characteristic
30	C₂₃×#525	C₂²	1	1	yes	characteristic
31	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
32	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
34	C₂₃×#446	C₂²	1	4	yes	complemented
35	C₂₃×#446	C₂²	1	4	yes	complemented
36	C₂₃×#446	C₂²	1	4	yes	complemented
37	C₈×Q₈×C₂₃	C₂²	1	4	yes	complemented
38	C₂₃×#436	C₂²	1	4	yes	—
39	C₂₃×#436	C₂²	1	4	yes	—
40	C₂₃×#436	C₂²	1	4	yes	complemented
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	—
45	C₂₃×#435	C₂²	1	4	yes	complemented
46	C₂₃×#435	C₂²	1	4	yes	complemented
47	C₈×D₄×C₂₃	C₂²	1	4	yes	—
48	C₈×D₄×C₂₃	C₂²	1	4	yes	—
49	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
50	C₂₃×#433	C₂²	1	2	yes	—
51	C₂₃×#433	C₂²	1	2	yes	—
52	C₂₃×#433	C₂²	1	2	yes	—
53	C₂₃×#433	C₂²	1	2	yes	—
54	C₂₃×#433	C₂²	1	2	yes	complemented
55	C₂₃×#433	C₂²	1	2	yes	complemented
56	C₂₃×#433	C₂²	1	2	yes	complemented
57	C₂₃×#433	C₂²	1	2	yes	complemented
58	C₂₃×#432	C₂²	1	4	yes	complemented
59	C₂₃×#431	C₂²	1	4	yes	complemented
60	C₂₃×#424	C₂²	1	2	yes	—
61	C₂₃×#424	C₂²	1	2	yes	—
62	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
63	C₂₃×#408	C₂²	1	2	yes	—
64	C₂₃×#408	C₂²	1	2	yes	—
65	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
66	C₂₃×#405	C₂²	1	2	yes	—
67	C₂₃×#405	C₂²	1	2	yes	—
68	C₂₃×#405	C₂²	1	4	yes	—
69	C₂₃×#405	C₂²	1	4	yes	—
70	C₂₃×#405	C₂²	1	4	yes	complemented
71	C₂₃×#405	C₂²	1	4	yes	complemented
72	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
73	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
74	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
75	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
76	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
77	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
78	C₂×C₂₃×#97	C₂²	1	2	yes	complemented
79	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
80	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	complemented
81	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
82	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
84	C₂₃×#131	—	2	8	no	—
85	C₂₃×#131	—	2	8	no	—
86	C₂×M₁₆×C₂₃	—	2	8	no	—
87	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
88	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
89	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
90	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
91	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
92	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
93	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
94	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
95	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
96	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
97	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
98	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
99	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
100	C₂₃×#126	C₂×C₄	1	4	yes	—
101	C₂₃×#126	C₂×C₄	1	4	yes	—
102	C₂₃×#126	C₂×C₄	1	4	yes	—
103	C₂₃×#126	C₂×C₄	1	4	yes	—
104	C₂₃×#125	C₂×C₄	1	4	yes	—
105	C₂₃×#125	C₂×C₄	1	4	yes	—
106	C₂₃×#125	C₂×C₄	1	2	yes	—
107	C₂₃×#124	C₂×C₄	1	4	yes	—
108	C₂₃×#124	C₂×C₄	1	4	yes	—
109	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
110	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
111	C₂₃×#123	C₂×C₄	1	2	yes	—
112	C₂₃×#123	C₂×C₄	1	2	yes	—
113	C₂₃×#123	C₂×C₄	1	4	yes	—
114	C₂₃×#123	C₂×C₄	1	4	yes	—
115	C₂₃×#123	C₂×C₄	1	4	yes	—
116	C₂₃×#123	C₂×C₄	1	4	yes	—
117	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
118	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
119	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
120	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
121	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
122	C₂₃×#121	C₂×C₄	1	2	yes	—
123	C₂₃×#121	C₂×C₄	1	2	yes	—
124	C₂₃×#121	C₂×C₄	1	4	yes	—
125	C₂₃×#121	C₂×C₄	1	4	yes	—
126	C₂₃×#121	C₂×C₄	1	4	yes	—
127	C₂₃×#120	C₂×C₄	1	2	yes	—
128	C₂₃×#120	C₂×C₄	1	2	yes	—
129	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
130	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
131	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
132	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
133	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
134	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
135	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
136	C₄×D₄×C₂₃	C₂³	1	4	yes	—
137	C₄×D₄×C₂₃	C₂³	1	4	yes	—
138	C₄×D₄×C₂₃	C₂³	1	4	yes	—
139	C₂₃×#117	C₂×C₄	1	2	yes	—
140	C₂₃×#117	C₂×C₄	1	2	yes	—
141	C₂₃×#117	C₂³	1	1	yes	characteristic
142	C₂₃×#117	C₂³	1	1	yes	characteristic
143	C₂₃×#117	C₂³	1	2	yes	—
144	C₂₃×#117	C₂³	1	2	yes	—
145	C₂₃×#117	C₂³	1	2	yes	—
146	C₂₃×#117	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
148	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
149	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
151	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
152	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
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	2	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×C₂²⋊C₈	C₂³	1	2	yes	—
162	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
163	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
164	C₂₃×C₂²⋊C₈	C₂³	1	2	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×C₂²⋊C₈	C₂³	1	4	yes	—
169	C₂₃×#97	C₂³	1	1	yes	characteristic
170	C₂₃×#97	C₂³	1	1	yes	characteristic
171	C₂₃×#97	C₂³	1	2	yes	—
172	C₂₃×#97	C₂³	1	2	yes	—
173	C₂₃×#97	C₂³	1	4	yes	—
174	C₂₃×#97	C₂³	1	2	yes	—
175	C₂₃×#97	C₂³	1	4	yes	—
176	C₂₃×#97	C₂³	1	4	yes	—
177	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
178	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
179	C₄×C₈×C₂₃	C₂³	1	2	yes	—
180	C₄×C₈×C₂₃	C₂³	1	2	yes	—
181	C₄×C₈×C₂₃	C₂³	1	4	yes	—
182	C₄×C₈×C₂₃	C₂³	1	2	yes	—
183	C₄×C₈×C₂₃	C₂³	1	4	yes	—
184	C₄×C₈×C₂₃	C₂³	1	4	yes	—
185	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
186	#41×C₂₃	—	2	4	no	—
187	#41×C₂₃	—	2	4	no	—
188	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
189	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
190	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
191	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
192	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
193	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
194	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
195	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
196	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
197	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
198	C₂²×C₄×C₂₃	—	2	4	no	—
199	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
201	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
202	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
203	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
204	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
205	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
209	M₁₆×C₂₃	—	2	4	no	—
210	M₁₆×C₂₃	—	2	8	no	—
211	M₁₆×C₂₃	—	2	8	no	—
212	M₁₆×C₂₃	—	2	8	no	—
213	M₁₆×C₂₃	#41	1	8	yes	—
214	C₂×C₈×C₂₃	—	2	4	no	—
215	C₂×C₈×C₂₃	—	2	4	no	—
216	C₂×C₈×C₂₃	—	2	8	no	—
217	C₂×C₈×C₂₃	—	2	8	no	—
218	C₂×C₈×C₂₃	—	2	8	no	—
219	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
220	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
221	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
222	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
223	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
224	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
225	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
226	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
227	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
228	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
229	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
230	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
231	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
232	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
233	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
234	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
235	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
236	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
237	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
238	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
239	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
240	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
241	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
242	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
243	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
244	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
245	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
246	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
247	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
248	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
249	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
250	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
251	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
252	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
253	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
254	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
255	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
256	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
257	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
258	C₄²×C₂₃	C₂⁴	1	2	yes	—
259	C₄²×C₂₃	C₂⁴	1	2	yes	—
260	C₄²×C₂₃	C₂⁴	1	2	yes	—
261	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
262	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
263	#60212	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
264	C₂³×C₂₃	—	2	2	no	—
265	C₂³×C₂₃	—	4	2	no	—
266	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
267	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
268	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
269	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
270	Q₈×C₂₃	—	2	2	no	—
271	Q₈×C₂₃	—	2	2	no	—
272	Q₈×C₂₃	—	4	4	no	—
273	D₄×C₂₃	—	2	4	no	—
274	D₄×C₂₃	—	2	4	no	—
275	D₄×C₂₃	—	2	2	no	—
276	D₄×C₂₃	—	2	2	no	—
277	D₄×C₂₃	—	4	4	no	—
278	D₄×C₂₃	—	4	4	no	—
279	D₄×C₂₃	—	4	4	no	—
280	C₂×C₄×C₂₃	—	2	2	no	—
281	C₂×C₄×C₂₃	—	2	4	no	—
282	C₂×C₄×C₂₃	—	2	2	no	—
283	C₂×C₄×C₂₃	—	2	4	no	—
284	C₂×C₄×C₂₃	—	2	4	no	—
285	C₂×C₄×C₂₃	—	2	2	no	—
286	C₂×C₄×C₂₃	—	4	2	no	—
287	C₂×C₄×C₂₃	—	4	4	no	—
288	C₂×C₄×C₂₃	—	4	4	no	—
289	C₂×C₄×C₂₃	—	4	2	no	—
290	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
291	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
292	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
293	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
294	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
295	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
296	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
297	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
298	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
299	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
300	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
301	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
302	C₈×C₂₃	—	2	2	no	—
303	C₈×C₂₃	—	2	2	no	—
304	C₈×C₂₃	—	2	2	no	—
305	C₈×C₂₃	—	2	2	no	—
306	C₈×C₂₃	—	2	4	no	—
307	C₈×C₂₃	C₂×#41	1	8	yes	—
308	#3455	C₂×C₂₃	1	1	yes	characteristic
309	#2969	C₂×C₂₃	1	4	yes	complemented
310	#2968	C₂×C₂₃	1	4	yes	complemented
311	#2967	C₂×C₂₃	1	4	yes	complemented
312	#2966	C₂×C₂₃	1	4	yes	complemented
313	#2962	C₂×C₂₃	1	2	yes	complemented
314	#2935	C₂×C₂₃	1	2	yes	complemented
315	#2933	C₂×C₂₃	1	2	yes	complemented
316	#2933	C₂×C₂₃	1	2	yes	complemented
317	#2923	C₂×C₂₃	1	1	yes	characteristic, complemented
318	#2922	C₂×C₂₃	1	1	yes	characteristic, complemented
319	C₂×#433	C₂×C₂₃	1	1	yes	characteristic, complemented
320	#2875	C₂×C₂₃	1	1	yes	characteristic, complemented
321	C₄×#131	C₂×C₂₃	1	1	yes	characteristic, complemented
322	#2873	C₂×C₂₃	1	1	yes	characteristic, complemented
323	C₂²×C₂₃	—	2	2	no	—
324	C₂²×C₂₃	—	2	2	no	—
325	C₂²×C₂₃	—	2	2	no	—
326	C₂²×C₂₃	—	2	2	no	—
327	C₂²×C₂₃	—	2	4	no	—
328	C₂²×C₂₃	—	2	4	no	—
329	C₂²×C₂₃	—	2	2	no	—
330	C₂²×C₂₃	—	2	2	no	—
331	C₂²×C₂₃	—	8	2	no	—
332	C₂²×C₂₃	C₄×#41	1	2	yes	—
333	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
334	C₄×C₂₃	—	2	2	no	—
335	C₄×C₂₃	—	2	2	no	—
336	C₄×C₂₃	—	2	2	no	—
337	C₄×C₂₃	—	2	2	no	—
338	C₄×C₂₃	—	2	2	no	—
339	C₄×C₂₃	—	2	2	no	—
340	C₄×C₂₃	—	2	4	no	—
341	C₄×C₂₃	—	2	4	no	—
342	C₄×C₂₃	—	2	2	no	—
343	C₄×C₂₃	C₄×#41	1	2	yes	—
344	C₄×C₂₃	C₂²×#41	1	2	yes	—
345	C₂×#131	C₂²×C₂₃	1	2	yes	—
346	C₂×#131	C₂²×C₂₃	1	2	yes	—
347	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
348	#542	C₄×C₂₃	1	2	yes	—
349	#542	C₄×C₂₃	1	2	yes	—
350	#541	C₄×C₂₃	1	2	yes	—
351	#540	C₄×C₂₃	1	2	yes	—
352	#539	C₄×C₂₃	1	4	yes	—
353	#538	C₄×C₂₃	1	4	yes	—
354	#533	C₂²×C₂₃	1	1	yes	characteristic
355	#532	C₂²×C₂₃	1	1	yes	characteristic
356	#529	C₂²×C₂₃	1	4	yes	—
357	#529	C₂²×C₂₃	1	4	yes	—
358	#525	C₂²×C₂₃	1	1	yes	characteristic
359	#525	C₂²×C₂₃	1	1	yes	characteristic
360	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
361	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
362	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
363	#446	C₂²×C₂₃	1	4	yes	complemented
364	#446	C₂²×C₂₃	1	4	yes	complemented
365	#446	C₂²×C₂₃	1	4	yes	complemented
366	C₈×Q₈	C₂²×C₂₃	1	4	yes	complemented
367	#436	C₂²×C₂₃	1	4	yes	—
368	#436	C₂²×C₂₃	1	4	yes	—
369	#436	C₂²×C₂₃	1	4	yes	complemented
370	#435	C₂²×C₂₃	1	4	yes	—
371	#435	C₂²×C₂₃	1	4	yes	—
372	#435	C₂²×C₂₃	1	4	yes	—
373	#435	C₂²×C₂₃	1	4	yes	—
374	#435	C₂²×C₂₃	1	4	yes	complemented
375	#435	C₂²×C₂₃	1	4	yes	complemented
376	C₈×D₄	C₂²×C₂₃	1	4	yes	—
377	C₈×D₄	C₂²×C₂₃	1	4	yes	—
378	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
379	#433	C₂²×C₂₃	1	2	yes	—
380	#433	C₂²×C₂₃	1	2	yes	—
381	#433	C₂²×C₂₃	1	2	yes	—
382	#433	C₂²×C₂₃	1	2	yes	—
383	#433	C₂²×C₂₃	1	2	yes	complemented
384	#433	C₂²×C₂₃	1	2	yes	complemented
385	#433	C₂²×C₂₃	1	2	yes	complemented
386	#433	C₂²×C₂₃	1	2	yes	complemented
387	#432	C₂²×C₂₃	1	4	yes	complemented
388	#431	C₂²×C₂₃	1	4	yes	complemented
389	#424	C₂²×C₂₃	1	2	yes	—
390	#424	C₂²×C₂₃	1	2	yes	—
391	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
392	#408	C₂²×C₂₃	1	2	yes	—
393	#408	C₂²×C₂₃	1	2	yes	—
394	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
395	#405	C₂²×C₂₃	1	4	yes	—
396	#405	C₂²×C₂₃	1	4	yes	—
397	#405	C₂²×C₂₃	1	2	yes	—
398	#405	C₂²×C₂₃	1	2	yes	—
399	#405	C₂²×C₂₃	1	4	yes	complemented
400	#405	C₂²×C₂₃	1	4	yes	complemented
401	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
402	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
403	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
404	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
405	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
406	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
407	C₂×#97	C₂²×C₂₃	1	2	yes	complemented
408	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
409	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
410	C₂×C₂₃	—	2	2	no	—
411	C₂×C₂₃	—	4	2	no	—
412	C₂×C₂₃	—	4	2	no	—
413	C₂×C₂₃	—	4	2	no	—
414	C₂×C₂₃	C₂×C₄×#41	1	1	yes	characteristic
415	C₂×C₂₃	#3573	1	2	yes	—
416	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
417	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
418	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
419	#131	—	2	8	no	—
420	#131	—	2	8	no	—
421	C₂×M₁₆	—	2	8	no	—
422	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
423	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
424	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
425	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
426	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
427	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
428	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
429	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
430	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
431	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
432	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
433	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
434	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
435	#126	C₂×C₄×C₂₃	1	4	yes	—
436	#126	C₂×C₄×C₂₃	1	4	yes	—
437	#126	C₂×C₄×C₂₃	1	4	yes	—
438	#126	C₂×C₄×C₂₃	1	4	yes	—
439	#125	C₂×C₄×C₂₃	1	4	yes	—
440	#125	C₂×C₄×C₂₃	1	4	yes	—
441	#125	C₂×C₄×C₂₃	1	2	yes	—
442	#124	C₂×C₄×C₂₃	1	4	yes	—
443	#124	C₂×C₄×C₂₃	1	4	yes	—
444	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
445	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
446	#123	C₂×C₄×C₂₃	1	2	yes	—
447	#123	C₂×C₄×C₂₃	1	2	yes	—
448	#123	C₂×C₄×C₂₃	1	4	yes	—
449	#123	C₂×C₄×C₂₃	1	4	yes	—
450	#123	C₂×C₄×C₂₃	1	4	yes	—
451	#123	C₂×C₄×C₂₃	1	4	yes	—
452	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
453	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
454	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
455	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
456	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
457	#121	C₂×C₄×C₂₃	1	2	yes	—
458	#121	C₂×C₄×C₂₃	1	2	yes	—
459	#121	C₂×C₄×C₂₃	1	4	yes	—
460	#121	C₂×C₄×C₂₃	1	4	yes	—
461	#121	C₂×C₄×C₂₃	1	4	yes	—
462	#120	C₂×C₄×C₂₃	1	2	yes	—
463	#120	C₂×C₄×C₂₃	1	2	yes	—
464	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
465	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
466	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
467	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
468	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
469	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
470	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
471	C₄×D₄	C₂³×C₂₃	1	4	yes	—
472	C₄×D₄	C₂³×C₂₃	1	4	yes	—
473	C₄×D₄	C₂³×C₂₃	1	4	yes	—
474	#117	C₂×C₄×C₂₃	1	2	yes	—
475	#117	C₂×C₄×C₂₃	1	2	yes	—
476	#117	C₂³×C₂₃	1	2	yes	—
477	#117	C₂³×C₂₃	1	2	yes	—
478	#117	C₂³×C₂₃	1	1	yes	characteristic
479	#117	C₂³×C₂₃	1	1	yes	characteristic
480	#117	C₂³×C₂₃	1	2	yes	—
481	#117	C₂³×C₂₃	1	2	yes	—
482	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
483	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
484	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
485	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
486	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
487	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
488	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
489	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
490	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
491	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
492	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
493	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
494	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
495	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
496	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
497	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
498	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
499	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
500	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
501	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
502	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
503	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
504	#97	C₂³×C₂₃	1	1	yes	characteristic
505	#97	C₂³×C₂₃	1	1	yes	characteristic
506	#97	C₂³×C₂₃	1	2	yes	—
507	#97	C₂³×C₂₃	1	2	yes	—
508	#97	C₂³×C₂₃	1	4	yes	—
509	#97	C₂³×C₂₃	1	2	yes	—
510	#97	C₂³×C₂₃	1	4	yes	—
511	#97	C₂³×C₂₃	1	4	yes	—
512	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
513	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
514	C₄×C₈	C₂³×C₂₃	1	2	yes	—
515	C₄×C₈	C₂³×C₂₃	1	2	yes	—
516	C₄×C₈	C₂³×C₂₃	1	4	yes	—
517	C₄×C₈	C₂³×C₂₃	1	2	yes	—
518	C₄×C₈	C₂³×C₂₃	1	4	yes	—
519	C₄×C₈	C₂³×C₂₃	1	4	yes	—
520	C₂₃	#60212	1	1	yes	characteristic, direct product factor, Sylow
521	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
522	#41	—	2	4	no	—
523	#41	—	2	4	no	—
524	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
525	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
526	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
527	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
528	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
529	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
530	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
531	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
532	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
533	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
536	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
537	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
538	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
539	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
540	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
541	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
545	M₁₆	—	2	4	no	—
546	M₁₆	—	2	8	no	—
547	M₁₆	—	2	8	no	—
548	M₁₆	—	2	8	no	—
549	M₁₆	#41×C₂₃	1	8	yes	—
550	C₂×C₈	—	2	4	no	—
551	C₂×C₈	—	2	4	no	—
552	C₂×C₈	—	2	8	no	—
553	C₂×C₈	—	2	8	no	—
554	C₂×C₈	—	2	8	no	—
555	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
556	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
557	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
558	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
559	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
560	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
561	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
562	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
563	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
564	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
565	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
566	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
567	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
568	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
569	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
570	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
571	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
572	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
573	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
574	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
575	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
576	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
577	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
578	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
579	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
580	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
581	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
582	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
583	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
584	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
585	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
586	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
587	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
588	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
589	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
590	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
591	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
592	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
593	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
594	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
595	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
596	C₄²	C₂⁴×C₂₃	1	2	yes	—
597	C₄²	C₂⁴×C₂₃	1	2	yes	—
598	C₄²	C₂⁴×C₂₃	1	2	yes	—
599	C₂³	—	2	2	no	—
600	C₂³	—	4	2	no	—
601	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
602	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
603	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
604	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
605	Q₈	—	2	2	no	—
606	Q₈	—	2	2	no	—
607	Q₈	—	4	4	no	—
608	D₄	—	2	4	no	—
609	D₄	—	2	4	no	—
610	D₄	—	2	2	no	—
611	D₄	—	2	2	no	—
612	D₄	—	4	4	no	—
613	D₄	—	4	4	no	—
614	D₄	—	4	4	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	4	2	no	—
622	C₂×C₄	—	4	4	no	—
623	C₂×C₄	—	4	4	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
626	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
627	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
628	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
629	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
630	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
631	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
632	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
633	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
634	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
635	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
636	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
637	C₈	—	2	2	no	—
638	C₈	—	2	2	no	—
639	C₈	—	2	2	no	—
640	C₈	—	2	2	no	—
641	C₈	—	2	4	no	—
642	C₈	C₂×#41×C₂₃	1	8	yes	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	4	no	—
648	C₂²	—	2	4	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	8	2	no	—
652	C₂²	C₄×#41×C₂₃	1	2	yes	—
653	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	2	no	—
660	C₄	—	2	4	no	—
661	C₄	—	2	4	no	—
662	C₄	—	2	2	no	—
663	C₄	C₄×#41×C₂₃	1	2	yes	—
664	C₄	C₂²×#41×C₂₃	1	2	yes	—
665	C₂	—	2	2	no	—
666	C₂	—	4	2	no	—
667	C₂	—	4	2	no	—
668	C₂	—	4	2	no	—
669	C₂	C₂×C₄×#41×C₂₃	1	1	yes	characteristic
670	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×#2969	C₂	semidirect
3. C₂₃×#2968	C₂	semidirect
4. C₂₃×#2967	C₂	semidirect
5. C₂₃×#2966	C₂	semidirect
6. C₂₃×#2962	C₂	semidirect
7. C₂₃×#2935	C₂	semidirect
8. C₂₃×#2933	C₂	semidirect
9. C₂₃×#2933	C₂	semidirect
10. C₂₃×#2923	C₂	semidirect
11. C₂₃×#2922	C₂	semidirect
12. C₂×C₂₃×#433	C₂	semidirect
13. C₂₃×#2875	C₂	semidirect
14. C₄×C₂₃×#131	C₂	semidirect
15. C₂₃×#2873	C₂	semidirect
34. C₂₃×#446	C₂²	semidirect
35. C₂₃×#446	C₂²	semidirect
36. C₂₃×#446	C₂²	semidirect
37. C₈×Q₈×C₂₃	C₂²	semidirect
40. C₂₃×#436	C₂²	semidirect
45. C₂₃×#435	C₂²	semidirect
46. C₂₃×#435	C₂²	semidirect
49. C₈×D₄×C₂₃	C₂²	semidirect
54. C₂₃×#433	C₂²	semidirect
55. C₂₃×#433	C₂²	semidirect
56. C₂₃×#433	C₂²	semidirect
57. C₂₃×#433	C₂²	semidirect
58. C₂₃×#432	C₂²	semidirect
59. C₂₃×#431	C₂²	semidirect
70. C₂₃×#405	C₂²	semidirect
71. C₂₃×#405	C₂²	semidirect
75. C₄×M₁₆×C₂₃	C₂²	semidirect
76. C₄×M₁₆×C₂₃	C₂²	semidirect
78. C₂×C₂₃×#97	C₂²	semidirect
80. C₂×C₄×C₈×C₂₃	C₂²	semidirect
263. #60212	C₂₃	direct (N × H)
309. #2969	C₂×C₂₃	semidirect
310. #2968	C₂×C₂₃	semidirect
311. #2967	C₂×C₂₃	semidirect
312. #2966	C₂×C₂₃	semidirect
313. #2962	C₂×C₂₃	semidirect
314. #2935	C₂×C₂₃	semidirect
315. #2933	C₂×C₂₃	semidirect
316. #2933	C₂×C₂₃	semidirect
317. #2923	C₂×C₂₃	semidirect
318. #2922	C₂×C₂₃	semidirect
319. C₂×#433	C₂×C₂₃	semidirect
320. #2875	C₂×C₂₃	semidirect
321. C₄×#131	C₂×C₂₃	semidirect
322. #2873	C₂×C₂₃	semidirect
363. #446	C₂²×C₂₃	semidirect
364. #446	C₂²×C₂₃	semidirect
365. #446	C₂²×C₂₃	semidirect
366. C₈×Q₈	C₂²×C₂₃	semidirect
369. #436	C₂²×C₂₃	semidirect
374. #435	C₂²×C₂₃	semidirect
375. #435	C₂²×C₂₃	semidirect
378. C₈×D₄	C₂²×C₂₃	semidirect
383. #433	C₂²×C₂₃	semidirect
384. #433	C₂²×C₂₃	semidirect
385. #433	C₂²×C₂₃	semidirect
386. #433	C₂²×C₂₃	semidirect
387. #432	C₂²×C₂₃	semidirect
388. #431	C₂²×C₂₃	semidirect
399. #405	C₂²×C₂₃	semidirect
400. #405	C₂²×C₂₃	semidirect
404. C₄×M₁₆	C₂²×C₂₃	semidirect
405. C₄×M₁₆	C₂²×C₂₃	semidirect
407. C₂×#97	C₂²×C₂₃	semidirect
409. C₂×C₄×C₈	C₂²×C₂₃	semidirect
520. C₂₃	#60212	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×#2969	2
C₂₃×#2968	2
C₂₃×#2967	2
C₂₃×#2966	2
C₂₃×#2962	2
C₂₃×#2935	2
C₂₃×#2933	2
C₂₃×#2923	2
C₂₃×#2922	2
C₂×C₂₃×#433	2
C₂₃×#2875	2
C₄×C₂₃×#131	2
C₂₃×#2873	2
#60212	23

Subgroups — C23×#60212 #19207838

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60212 #19207838