Subgroups — C₂₃×#60291 #19207917

Order 5888.

1772 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2995	C₂	1	4	yes	maximal, complemented
3	C₂₃×#2992	C₂	1	4	yes	maximal, complemented
4	C₂₃×#2983	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2974	C₂	1	4	yes	maximal, complemented
6	C₂₃×#2973	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2968	C₂	1	4	yes	maximal, complemented
8	C₂₃×#2967	C₂	1	4	yes	maximal, complemented
9	C₂₃×#2924	C₂	1	4	yes	maximal, complemented
10	C₂₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#529	C₄	1	2	yes	—
13	C₂₃×#529	C₄	1	2	yes	—
14	C₂₃×#529	C₄	1	2	yes	—
15	C₂₃×#529	C₄	1	2	yes	—
16	C₂₃×#529	C₂²	1	2	yes	—
17	C₂₃×#529	C₂²	1	2	yes	—
18	C₂₃×#529	C₂²	1	2	yes	—
19	C₂₃×#529	C₂²	1	2	yes	—
20	C₂×C₂₃×#126	C₄	1	2	yes	—
21	C₂×C₂₃×#125	C₄	1	1	yes	characteristic
22	C₂×C₂₃×#124	C₄	1	1	yes	characteristic
23	C₂×C₂₃×#123	C₄	1	2	yes	—
24	C₂×C₂₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
25	C₂×C₂₃×#121	C₄	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
29	C₂×C₂₃×#117	C₂²	1	2	yes	—
30	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
31	C₂₃×#446	C₂²	1	8	yes	complemented
32	C₂₃×#446	C₂²	1	8	yes	complemented
33	C₂₃×#436	C₂²	1	8	yes	complemented
34	C₂₃×#435	C₂²	1	8	yes	complemented
35	C₂₃×#435	C₂²	1	8	yes	complemented
36	C₂₃×#435	C₂²	1	8	yes	complemented
37	C₂₃×#435	C₂²	1	8	yes	complemented
38	C₈×D₄×C₂₃	C₂²	1	8	yes	complemented
39	C₂₃×#433	C₂²	1	8	yes	complemented
40	C₂₃×#433	C₂²	1	8	yes	complemented
41	C₂₃×#432	C₂²	1	2	yes	—
42	C₂₃×#432	C₂²	1	2	yes	—
43	C₂₃×#432	C₂²	1	2	yes	—
44	C₂₃×#432	C₂²	1	4	yes	—
45	C₂₃×#432	C₂²	1	2	yes	complemented
46	C₂₃×#432	C₂²	1	2	yes	complemented
47	C₂₃×#432	C₂²	1	2	yes	complemented
48	C₂₃×#431	C₂²	1	2	yes	—
49	C₂₃×#431	C₂²	1	4	yes	—
50	C₂₃×#431	C₂²	1	2	yes	complemented
51	C₂₃×#424	C₂²	1	8	yes	complemented
52	C₂₃×#423	C₂²	1	2	yes	complemented
53	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	complemented
54	C₂₃×#407	C₂²	1	2	yes	—
55	C₂₃×#407	C₂²	1	4	yes	—
56	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
57	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	—
58	C₂₃×#405	C₂²	1	8	yes	complemented
59	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
60	C₂×C₂₃×#97	C₂²	1	2	yes	complemented
61	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
62	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
63	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
68	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
69	C₂×M₁₆×C₂₃	C₂³	1	8	yes	—
70	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
71	C₂²×C₈×C₂₃	C₂³	1	8	yes	—
72	C₂₃×#126	C₂×C₄	1	4	yes	—
73	C₂₃×#126	C₂×C₄	1	4	yes	—
74	C₂₃×#126	C₂×C₄	1	4	yes	—
75	C₂₃×#126	C₂×C₄	1	4	yes	—
76	C₂₃×#125	C₂×C₄	1	2	yes	—
77	C₂₃×#125	C₂×C₄	1	2	yes	—
78	C₂₃×#125	C₂×C₄	1	2	yes	—
79	C₂₃×#125	C₂×C₄	1	2	yes	—
80	C₂₃×#124	C₂×C₄	1	2	yes	—
81	C₂₃×#124	C₂×C₄	1	2	yes	—
82	C₂₃×#124	C₂×C₄	1	2	yes	—
83	C₂₃×#124	C₂×C₄	1	2	yes	—
84	C₂₃×#123	C₂×C₄	1	4	yes	—
85	C₂₃×#123	C₂×C₄	1	4	yes	—
86	C₂₃×#123	C₂×C₄	1	4	yes	—
87	C₂₃×#123	C₂×C₄	1	4	yes	—
88	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
89	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
90	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
91	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
92	C₂₃×#121	C₂×C₄	1	2	yes	—
93	C₂₃×#121	C₂×C₄	1	2	yes	—
94	C₂₃×#121	C₂×C₄	1	2	yes	—
95	C₂₃×#121	C₂×C₄	1	2	yes	—
96	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
97	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
98	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
99	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
100	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
101	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
102	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
103	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
104	C₄×D₄×C₂₃	C₂³	1	4	yes	—
105	C₄×D₄×C₂₃	C₂³	1	2	yes	—
106	C₄×D₄×C₂₃	C₂³	1	2	yes	—
107	C₄×D₄×C₂₃	C₂³	1	4	yes	—
108	C₂₃×#117	C₂×C₄	1	4	yes	—
109	C₂₃×#117	C₂×C₄	1	4	yes	—
110	C₂₃×#117	C₂³	1	4	yes	—
111	C₂₃×#117	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
113	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
114	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
116	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
118	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
119	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
120	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
121	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
122	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
123	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
124	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
125	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
126	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
127	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
128	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
129	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
135	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
136	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
137	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
138	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
139	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
140	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
141	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
142	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
143	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
144	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
145	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
146	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
147	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
148	C₂₃×#97	C₂³	1	4	yes	—
149	C₂₃×#97	C₂³	1	4	yes	—
150	C₂₃×#97	C₂³	1	4	yes	—
151	C₂₃×#97	C₂³	1	8	yes	—
152	C₄×C₈×C₂₃	C₂³	1	4	yes	—
153	C₄×C₈×C₂₃	C₂³	1	8	yes	—
154	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
155	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
156	C₂×Q₈×C₂₃	—	4	2	no	—
157	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
158	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
159	C₂×D₄×C₂₃	—	4	2	no	—
160	C₂×D₄×C₂₃	—	4	4	no	—
161	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
162	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
163	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
164	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
165	C₂²×C₄×C₂₃	—	4	2	no	—
166	C₂²×C₄×C₂₃	—	4	4	no	—
167	C₂²×C₄×C₂₃	—	4	2	no	—
168	C₂²×C₄×C₂₃	—	4	2	no	—
169	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
174	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
186	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
187	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
188	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
192	M₁₆×C₂₃	—	4	8	no	—
193	M₁₆×C₂₃	—	4	4	no	—
194	C₂×C₈×C₂₃	—	4	4	no	—
195	C₂×C₈×C₂₃	—	4	8	no	—
196	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
197	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
198	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
199	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
200	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
201	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
202	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
203	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
204	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
205	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
206	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
207	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
208	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
209	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
210	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
211	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
212	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
213	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
214	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
215	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
216	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
217	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
218	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
219	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
220	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
221	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
222	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
223	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
224	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
225	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
226	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
227	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
228	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
229	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
230	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
231	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
232	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
233	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
234	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
235	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
236	C₄²×C₂₃	C₂⁴	1	4	yes	—
237	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
238	#60291	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂³×C₂₃	—	2	2	no	—
240	C₂³×C₂₃	—	2	2	no	—
241	C₂³×C₂₃	—	2	4	no	—
242	C₂³×C₂₃	—	4	1	no	—
243	C₂³×C₂₃	—	4	2	no	—
244	C₂³×C₂₃	—	4	2	no	—
245	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
246	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
247	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
248	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
249	Q₈×C₂₃	—	4	2	no	—
250	Q₈×C₂₃	—	4	2	no	—
251	D₄×C₂₃	—	2	8	no	—
252	D₄×C₂₃	—	4	2	no	—
253	D₄×C₂₃	—	4	2	no	—
254	D₄×C₂₃	—	4	4	no	—
255	C₂×C₄×C₂₃	—	2	2	no	—
256	C₂×C₄×C₂₃	—	2	2	no	—
257	C₂×C₄×C₂₃	—	2	2	no	—
258	C₂×C₄×C₂₃	—	2	2	no	—
259	C₂×C₄×C₂₃	—	2	4	no	—
260	C₂×C₄×C₂₃	—	2	2	no	—
261	C₂×C₄×C₂₃	—	2	8	no	—
262	C₂×C₄×C₂₃	—	2	2	no	—
263	C₂×C₄×C₂₃	—	2	2	no	—
264	C₂×C₄×C₂₃	—	4	1	no	—
265	C₂×C₄×C₂₃	—	4	1	no	—
266	C₂×C₄×C₂₃	—	4	4	no	—
267	C₂×C₄×C₂₃	—	4	1	no	—
268	C₂×C₄×C₂₃	—	4	2	no	—
269	C₂×C₄×C₂₃	—	4	1	no	—
270	C₂×C₄×C₂₃	—	4	1	no	—
271	C₂×C₄×C₂₃	—	4	1	no	—
272	C₂×C₄×C₂₃	—	4	1	no	—
273	C₂×C₄×C₂₃	—	4	1	no	—
274	C₂×C₄×C₂₃	—	4	1	no	—
275	C₂×C₄×C₂₃	—	4	1	no	—
276	C₂×C₄×C₂₃	—	4	1	no	—
277	C₂×C₄×C₂₃	—	4	2	no	—
278	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
279	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
280	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
281	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
282	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
283	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
284	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
285	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
286	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
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	4	yes	—
290	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
291	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
292	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
293	C₈×C₂₃	—	2	8	no	—
294	C₈×C₂₃	—	2	8	no	—
295	C₂×#529	C₂×C₂₃	1	1	yes	characteristic
296	#2995	C₂×C₂₃	1	4	yes	complemented
297	#2992	C₂×C₂₃	1	4	yes	complemented
298	#2983	C₂×C₂₃	1	2	yes	complemented
299	#2974	C₂×C₂₃	1	4	yes	complemented
300	#2973	C₂×C₂₃	1	2	yes	complemented
301	#2968	C₂×C₂₃	1	4	yes	complemented
302	#2967	C₂×C₂₃	1	4	yes	complemented
303	#2924	C₂×C₂₃	1	4	yes	complemented
304	#2920	C₂×C₂₃	1	1	yes	characteristic, complemented
305	C₂×#432	C₂×C₂₃	1	1	yes	characteristic, complemented
306	C₂²×C₂₃	—	2	1	no	—
307	C₂²×C₂₃	—	2	1	no	—
308	C₂²×C₂₃	—	2	1	no	—
309	C₂²×C₂₃	—	2	1	no	—
310	C₂²×C₂₃	—	2	1	no	—
311	C₂²×C₂₃	—	2	4	no	—
312	C₂²×C₂₃	—	2	1	no	—
313	C₂²×C₂₃	—	2	1	no	—
314	C₂²×C₂₃	—	2	4	no	—
315	C₂²×C₂₃	—	2	4	no	—
316	C₂²×C₂₃	—	4	4	no	—
317	C₂²×C₂₃	—	8	4	no	—
318	C₂²×C₂₃	#568	1	2	yes	—
319	C₂²×C₂₃	#568	1	2	yes	—
320	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
321	C₄×C₂₃	—	2	1	no	—
322	C₄×C₂₃	—	2	1	no	—
323	C₄×C₂₃	—	2	4	no	—
324	C₄×C₂₃	—	2	1	no	—
325	C₄×C₂₃	—	2	1	no	—
326	C₄×C₂₃	—	2	1	no	—
327	C₄×C₂₃	—	2	1	no	—
328	C₄×C₂₃	—	2	1	no	—
329	C₄×C₂₃	—	2	1	no	—
330	C₄×C₂₃	—	2	1	no	—
331	C₄×C₂₃	—	2	1	no	—
332	C₄×C₂₃	—	2	1	no	—
333	C₄×C₂₃	—	2	4	no	—
334	C₄×C₂₃	—	2	4	no	—
335	C₄×C₂₃	#585	1	2	yes	—
336	#529	C₄×C₂₃	1	2	yes	—
337	#529	C₄×C₂₃	1	2	yes	—
338	#529	C₄×C₂₃	1	2	yes	—
339	#529	C₄×C₂₃	1	2	yes	—
340	#529	C₂²×C₂₃	1	2	yes	—
341	#529	C₂²×C₂₃	1	2	yes	—
342	#529	C₂²×C₂₃	1	2	yes	—
343	#529	C₂²×C₂₃	1	2	yes	—
344	C₂×#126	C₄×C₂₃	1	2	yes	—
345	C₂×#125	C₄×C₂₃	1	1	yes	characteristic
346	C₂×#124	C₄×C₂₃	1	1	yes	characteristic
347	C₂×#123	C₄×C₂₃	1	2	yes	—
348	C₂×C₂²⋊Q₈	C₄×C₂₃	1	1	yes	characteristic
349	C₂×#121	C₄×C₂₃	1	1	yes	characteristic
350	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
351	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
352	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
353	C₂×#117	C₂²×C₂₃	1	2	yes	—
354	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
355	#446	C₂²×C₂₃	1	8	yes	complemented
356	#446	C₂²×C₂₃	1	8	yes	complemented
357	#436	C₂²×C₂₃	1	8	yes	complemented
358	#435	C₂²×C₂₃	1	8	yes	complemented
359	#435	C₂²×C₂₃	1	8	yes	complemented
360	#435	C₂²×C₂₃	1	8	yes	complemented
361	#435	C₂²×C₂₃	1	8	yes	complemented
362	C₈×D₄	C₂²×C₂₃	1	8	yes	complemented
363	#433	C₂²×C₂₃	1	8	yes	complemented
364	#433	C₂²×C₂₃	1	8	yes	complemented
365	#432	C₂²×C₂₃	1	2	yes	—
366	#432	C₂²×C₂₃	1	2	yes	—
367	#432	C₂²×C₂₃	1	2	yes	—
368	#432	C₂²×C₂₃	1	4	yes	—
369	#432	C₂²×C₂₃	1	2	yes	complemented
370	#432	C₂²×C₂₃	1	2	yes	complemented
371	#432	C₂²×C₂₃	1	2	yes	complemented
372	#431	C₂²×C₂₃	1	2	yes	—
373	#431	C₂²×C₂₃	1	4	yes	—
374	#431	C₂²×C₂₃	1	2	yes	complemented
375	#424	C₂²×C₂₃	1	8	yes	complemented
376	#423	C₂²×C₂₃	1	2	yes	complemented
377	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	complemented
378	#407	C₂²×C₂₃	1	2	yes	—
379	#407	C₂²×C₂₃	1	4	yes	—
380	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
381	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	—
382	#405	C₂²×C₂₃	1	8	yes	complemented
383	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
384	C₂×#97	C₂²×C₂₃	1	2	yes	complemented
385	C₂×C₂₃	—	2	2	no	—
386	C₂×C₂₃	—	2	2	no	—
387	C₂×C₂₃	—	4	1	no	—
388	C₂×C₂₃	—	4	4	no	—
389	C₂×C₂₃	#3428	1	1	yes	characteristic
390	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
391	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
392	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
393	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
394	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
395	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
396	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
397	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
398	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
399	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
400	C₂×M₁₆	C₂³×C₂₃	1	8	yes	—
401	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
402	C₂²×C₈	C₂³×C₂₃	1	8	yes	—
403	#126	C₂×C₄×C₂₃	1	4	yes	—
404	#126	C₂×C₄×C₂₃	1	4	yes	—
405	#126	C₂×C₄×C₂₃	1	4	yes	—
406	#126	C₂×C₄×C₂₃	1	4	yes	—
407	#125	C₂×C₄×C₂₃	1	2	yes	—
408	#125	C₂×C₄×C₂₃	1	2	yes	—
409	#125	C₂×C₄×C₂₃	1	2	yes	—
410	#125	C₂×C₄×C₂₃	1	2	yes	—
411	#124	C₂×C₄×C₂₃	1	2	yes	—
412	#124	C₂×C₄×C₂₃	1	2	yes	—
413	#124	C₂×C₄×C₂₃	1	2	yes	—
414	#124	C₂×C₄×C₂₃	1	2	yes	—
415	#123	C₂×C₄×C₂₃	1	4	yes	—
416	#123	C₂×C₄×C₂₃	1	4	yes	—
417	#123	C₂×C₄×C₂₃	1	4	yes	—
418	#123	C₂×C₄×C₂₃	1	4	yes	—
419	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
420	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
421	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
422	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
423	#121	C₂×C₄×C₂₃	1	2	yes	—
424	#121	C₂×C₄×C₂₃	1	2	yes	—
425	#121	C₂×C₄×C₂₃	1	2	yes	—
426	#121	C₂×C₄×C₂₃	1	2	yes	—
427	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
428	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
429	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
430	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
431	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
432	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
433	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
434	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
435	C₄×D₄	C₂³×C₂₃	1	4	yes	—
436	C₄×D₄	C₂³×C₂₃	1	2	yes	—
437	C₄×D₄	C₂³×C₂₃	1	2	yes	—
438	C₄×D₄	C₂³×C₂₃	1	4	yes	—
439	#117	C₂×C₄×C₂₃	1	4	yes	—
440	#117	C₂×C₄×C₂₃	1	4	yes	—
441	#117	C₂³×C₂₃	1	4	yes	—
442	#117	C₂³×C₂₃	1	4	yes	—
443	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
444	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
445	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
447	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
449	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
450	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
454	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
455	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
456	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
457	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
458	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
459	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
460	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
461	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
462	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
463	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
465	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
466	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
467	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
468	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
469	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
470	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
471	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
472	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
473	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
474	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
475	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
476	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
477	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
478	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
479	#97	C₂³×C₂₃	1	4	yes	—
480	#97	C₂³×C₂₃	1	4	yes	—
481	#97	C₂³×C₂₃	1	4	yes	—
482	#97	C₂³×C₂₃	1	8	yes	—
483	C₄×C₈	C₂³×C₂₃	1	4	yes	—
484	C₄×C₈	C₂³×C₂₃	1	8	yes	—
485	C₂₃	#60291	1	1	yes	characteristic, direct product factor, Sylow
486	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
487	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
488	C₂×Q₈	—	4	2	no	—
489	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
490	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
491	C₂×D₄	—	4	2	no	—
492	C₂×D₄	—	4	4	no	—
493	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
494	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
495	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
496	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
497	C₂²×C₄	—	4	2	no	—
498	C₂²×C₄	—	4	4	no	—
499	C₂²×C₄	—	4	2	no	—
500	C₂²×C₄	—	4	2	no	—
501	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
502	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
503	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
504	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
505	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
506	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
507	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
508	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
509	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
510	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
511	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
512	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
513	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
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	C₂⁴×C₂₃	1	1	yes	characteristic
521	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
522	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
523	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
524	M₁₆	—	4	8	no	—
525	M₁₆	—	4	4	no	—
526	C₂×C₈	—	4	4	no	—
527	C₂×C₈	—	4	8	no	—
528	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
529	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
530	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
531	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
532	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
533	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
534	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
535	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
536	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
537	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
538	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
539	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
540	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
541	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
542	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
543	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
544	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
545	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
546	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
547	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
548	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
549	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
550	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
551	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
552	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
553	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
554	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
555	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
556	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
557	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
558	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
559	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
560	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
561	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
562	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
563	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
564	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
565	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
566	C₄²	C₂⁴×C₂₃	1	4	yes	—
567	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
568	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
569	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
570	C₂³	—	2	2	no	—
571	C₂³	—	2	2	no	—
572	C₂³	—	2	4	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	2	no	—
575	C₂³	—	4	2	no	—
576	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
577	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
578	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
579	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
580	Q₈	—	4	2	no	—
581	Q₈	—	4	2	no	—
582	D₄	—	2	8	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	4	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	8	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	4	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
610	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
611	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
612	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
613	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
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×C₄×C₂₃	1	1	yes	characteristic
618	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
619	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
620	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
621	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
622	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
623	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
624	C₈	—	2	8	no	—
625	C₈	—	2	8	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	4	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	4	no	—
635	C₂²	—	2	4	no	—
636	C₂²	—	4	4	no	—
637	C₂²	—	8	4	no	—
638	C₂²	C₂₃×#568	1	2	yes	—
639	C₂²	C₂₃×#568	1	2	yes	—
640	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
641	C₄	—	2	1	no	—
642	C₄	—	2	1	no	—
643	C₄	—	2	4	no	—
644	C₄	—	2	1	no	—
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	4	no	—
654	C₄	—	2	4	no	—
655	C₄	C₂₃×#585	1	2	yes	—
656	C₂	—	2	2	no	—
657	C₂	—	2	2	no	—
658	C₂	—	4	1	no	—
659	C₂	—	4	4	no	—
660	C₂	C₂₃×#3428	1	1	yes	characteristic
661	C₂	C₂×C₂₃×#568	1	1	yes	characteristic
662	C₂	C₂×C₂₃×#568	1	1	yes	characteristic

	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	C₂×C₂₃×#121	C₄
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×#2992	C₂	semidirect
4. C₂₃×#2983	C₂	semidirect
5. C₂₃×#2974	C₂	semidirect
6. C₂₃×#2973	C₂	semidirect
7. C₂₃×#2968	C₂	semidirect
8. C₂₃×#2967	C₂	semidirect
9. C₂₃×#2924	C₂	semidirect
10. C₂₃×#2920	C₂	semidirect
11. C₂×C₂₃×#432	C₂	semidirect
31. C₂₃×#446	C₂²	semidirect
32. C₂₃×#446	C₂²	semidirect
33. C₂₃×#436	C₂²	semidirect
34. C₂₃×#435	C₂²	semidirect
35. C₂₃×#435	C₂²	semidirect
36. C₂₃×#435	C₂²	semidirect
37. C₂₃×#435	C₂²	semidirect
38. C₈×D₄×C₂₃	C₂²	semidirect
39. C₂₃×#433	C₂²	semidirect
40. C₂₃×#433	C₂²	semidirect
45. C₂₃×#432	C₂²	semidirect
46. C₂₃×#432	C₂²	semidirect
47. C₂₃×#432	C₂²	semidirect
50. C₂₃×#431	C₂²	semidirect
51. C₂₃×#424	C₂²	semidirect
52. C₂₃×#423	C₂²	semidirect
53. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
58. C₂₃×#405	C₂²	semidirect
59. C₄×M₁₆×C₂₃	C₂²	semidirect
60. C₂×C₂₃×#97	C₂²	semidirect
238. #60291	C₂₃	direct (N × H)
296. #2995	C₂×C₂₃	semidirect
297. #2992	C₂×C₂₃	semidirect
298. #2983	C₂×C₂₃	semidirect
299. #2974	C₂×C₂₃	semidirect
300. #2973	C₂×C₂₃	semidirect
301. #2968	C₂×C₂₃	semidirect
302. #2967	C₂×C₂₃	semidirect
303. #2924	C₂×C₂₃	semidirect
304. #2920	C₂×C₂₃	semidirect
305. C₂×#432	C₂×C₂₃	semidirect
355. #446	C₂²×C₂₃	semidirect
356. #446	C₂²×C₂₃	semidirect
357. #436	C₂²×C₂₃	semidirect
358. #435	C₂²×C₂₃	semidirect
359. #435	C₂²×C₂₃	semidirect
360. #435	C₂²×C₂₃	semidirect
361. #435	C₂²×C₂₃	semidirect
362. C₈×D₄	C₂²×C₂₃	semidirect
363. #433	C₂²×C₂₃	semidirect
364. #433	C₂²×C₂₃	semidirect
369. #432	C₂²×C₂₃	semidirect
370. #432	C₂²×C₂₃	semidirect
371. #432	C₂²×C₂₃	semidirect
374. #431	C₂²×C₂₃	semidirect
375. #424	C₂²×C₂₃	semidirect
376. #423	C₂²×C₂₃	semidirect
377. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
382. #405	C₂²×C₂₃	semidirect
383. C₄×M₁₆	C₂²×C₂₃	semidirect
384. C₂×#97	C₂²×C₂₃	semidirect
485. C₂₃	#60291	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×#529	2
C₂₃×#2995	2
C₂₃×#2992	2
C₂₃×#2983	2
C₂₃×#2974	2
C₂₃×#2973	2
C₂₃×#2968	2
C₂₃×#2967	2
C₂₃×#2924	2
C₂₃×#2920	2
C₂×C₂₃×#432	2
#60291	23

Subgroups — C23×#60291 #19207917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60291 #19207917