Subgroups — C₂₃×#60295 #19207921

Order 5888.

1760 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2991	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2990	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2989	C₂	1	4	yes	maximal, complemented
5	C₂₃×#2985	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2981	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2978	C₂	1	4	yes	maximal, complemented
8	C₂₃×#2969	C₂	1	4	yes	maximal, complemented
9	C₂₃×#2967	C₂	1	4	yes	maximal, complemented
10	C₂₃×#2925	C₂	1	4	yes	maximal, complemented
11	C₂₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#533	C₄	1	1	yes	characteristic
14	C₂₃×#533	C₄	1	1	yes	characteristic
15	C₂₃×#533	C₂²	1	1	yes	characteristic
16	C₂₃×#532	C₄	1	1	yes	characteristic
17	C₂₃×#532	C₄	1	1	yes	characteristic
18	C₂₃×#532	C₂²	1	1	yes	characteristic
19	C₂₃×#529	C₄	1	2	yes	—
20	C₂₃×#529	C₄	1	2	yes	—
21	C₂₃×#529	C₄	1	2	yes	—
22	C₂₃×#529	C₄	1	2	yes	—
23	C₂₃×#529	C₂²	1	2	yes	—
24	C₂₃×#529	C₂²	1	2	yes	—
25	C₂₃×#525	C₄	1	2	yes	—
26	C₂₃×#525	C₄	1	2	yes	—
27	C₂₃×#525	C₂²	1	2	yes	—
28	C₄×#41×C₂₃	C₂²	1	2	yes	—
29	C₄×#41×C₂₃	C₂²	1	2	yes	—
30	C₄×#41×C₂₃	C₂²	1	2	yes	—
31	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
32	C₂₃×#446	C₂²	1	8	yes	complemented
33	C₂₃×#446	C₂²	1	4	yes	complemented
34	C₈×Q₈×C₂₃	C₂²	1	4	yes	complemented
35	C₂₃×#436	C₂²	1	8	yes	—
36	C₂₃×#436	C₂²	1	8	yes	—
37	C₂₃×#436	C₂²	1	4	yes	complemented
38	C₂₃×#435	C₂²	1	8	yes	—
39	C₂₃×#435	C₂²	1	8	yes	—
40	C₂₃×#435	C₂²	1	8	yes	complemented
41	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
42	C₂₃×#433	C₂²	1	8	yes	—
43	C₂₃×#433	C₂²	1	8	yes	complemented
44	C₂₃×#432	C₂²	1	2	yes	—
45	C₂₃×#432	C₂²	1	2	yes	—
46	C₂₃×#432	C₂²	1	2	yes	—
47	C₂₃×#432	C₂²	1	2	yes	—
48	C₂₃×#432	C₂²	1	4	yes	complemented
49	C₂₃×#431	C₂²	1	2	yes	—
50	C₂₃×#431	C₂²	1	2	yes	—
51	C₂₃×#431	C₂²	1	2	yes	—
52	C₂₃×#431	C₂²	1	1	yes	characteristic
53	C₂₃×#431	C₂²	1	1	yes	characteristic
54	C₂₃×#431	C₂²	1	4	yes	complemented
55	C₂₃×#423	C₂²	1	2	yes	—
56	C₂₃×#423	C₂²	1	2	yes	—
57	C₂₃×#423	C₂²	1	4	yes	complemented
58	C₂×C₂₃×C₄⋊C₈	C₂²	1	4	yes	complemented
59	C₂₃×#408	C₂²	1	8	yes	—
60	C₂₃×#407	C₂²	1	2	yes	—
61	C₂₃×#407	C₂²	1	2	yes	—
62	C₂₃×#405	C₂²	1	8	yes	complemented
63	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
64	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
65	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
66	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
67	C₂×#41×C₂₃	C₂³	1	2	yes	—
68	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
71	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
72	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
73	C₂×M₁₆×C₂₃	C₂³	1	8	yes	—
74	C₂²×C₈×C₂₃	C₂³	1	8	yes	—
75	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
76	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
77	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
78	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
79	C₂₃×#126	C₂×C₄	1	4	yes	—
80	C₂₃×#126	C₂×C₄	1	4	yes	—
81	C₂₃×#125	C₂×C₄	1	2	yes	—
82	C₂₃×#125	C₂×C₄	1	2	yes	—
83	C₂₃×#125	C₂×C₄	1	2	yes	—
84	C₂₃×#124	C₂×C₄	1	2	yes	—
85	C₂₃×#124	C₂×C₄	1	2	yes	—
86	C₂₃×#124	C₂×C₄	1	2	yes	—
87	C₂₃×#123	C₂×C₄	1	4	yes	—
88	C₂₃×#123	C₂×C₄	1	4	yes	—
89	C₂₃×#123	C₂×C₄	1	4	yes	—
90	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
91	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
92	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
93	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
94	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
95	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
96	C₂₃×#121	C₂×C₄	1	2	yes	—
97	C₂₃×#121	C₂×C₄	1	2	yes	—
98	C₂₃×#121	C₂×C₄	1	2	yes	—
99	C₂₃×#121	C₂×C₄	1	2	yes	—
100	C₂₃×#121	C₂×C₄	1	2	yes	—
101	C₂₃×#121	C₂×C₄	1	2	yes	—
102	C₂₃×#120	C₂×C₄	1	4	yes	—
103	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
104	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
105	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
106	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
107	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
108	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
109	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
110	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
111	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
112	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
113	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
114	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
115	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
116	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
117	C₄×D₄×C₂₃	C₂³	1	2	yes	—
118	C₄×D₄×C₂₃	C₂³	1	4	yes	—
119	C₄×D₄×C₂₃	C₂³	1	4	yes	—
120	C₄×D₄×C₂₃	C₂³	1	2	yes	—
121	C₂₃×#117	C₂×C₄	1	2	yes	—
122	C₂₃×#117	C₂×C₄	1	2	yes	—
123	C₂₃×#117	C₂×C₄	1	4	yes	—
124	C₂₃×#117	C₂×C₄	1	4	yes	—
125	C₂₃×#117	C₂³	1	4	yes	—
126	C₂₃×#117	C₂³	1	2	yes	—
127	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
128	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
129	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
130	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
131	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
132	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
133	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
136	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
140	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
141	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
142	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
143	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
144	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
145	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
146	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
147	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
148	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
149	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
150	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
151	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
152	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
153	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
154	C₂₃×#97	C₂³	1	4	yes	—
155	C₂₃×#97	C₂³	1	4	yes	—
156	C₂₃×#97	C₂³	1	8	yes	—
157	C₄×C₈×C₂₃	C₂³	1	4	yes	—
158	C₄×C₈×C₂₃	C₂³	1	2	yes	—
159	C₄×C₈×C₂₃	C₂³	1	2	yes	—
160	C₄×C₈×C₂₃	C₂³	1	8	yes	—
161	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
162	#41×C₂₃	—	4	4	no	—
163	#41×C₂₃	—	4	4	no	—
164	#41×C₂₃	—	4	4	no	—
165	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
166	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
167	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
168	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
169	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
170	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
171	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
172	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
173	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
174	C₂²×C₄×C₂₃	—	4	2	no	—
175	C₂²×C₄×C₂₃	—	4	2	no	—
176	C₂²×C₄×C₂₃	—	4	2	no	—
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	4	yes	—
184	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
190	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₂₃	C₂²×C₄	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	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
198	M₁₆×C₂₃	—	4	4	no	—
199	M₁₆×C₂₃	—	4	4	no	—
200	M₁₆×C₂₃	—	4	8	no	—
201	C₂×C₈×C₂₃	—	4	8	no	—
202	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
203	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
204	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
205	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
206	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
207	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
208	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
209	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
210	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
211	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
212	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
213	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
214	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
215	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
216	C₄⋊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	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
221	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
222	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
223	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
224	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
225	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
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	1	yes	characteristic
233	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
234	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
235	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
236	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
237	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
238	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
239	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
240	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
241	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
242	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
243	C₄²×C₂₃	C₂⁴	1	4	yes	—
244	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
245	#60295	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
246	C₂³×C₂₃	—	4	1	no	—
247	C₂³×C₂₃	—	4	1	no	—
248	C₂³×C₂₃	—	4	1	no	—
249	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
250	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
251	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
252	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
253	Q₈×C₂₃	—	2	4	no	—
254	Q₈×C₂₃	—	4	2	no	—
255	Q₈×C₂₃	—	4	2	no	—
256	D₄×C₂₃	—	2	4	no	—
257	D₄×C₂₃	—	4	2	no	—
258	D₄×C₂₃	—	4	4	no	—
259	D₄×C₂₃	—	4	2	no	—
260	D₄×C₂₃	—	4	4	no	—
261	D₄×C₂₃	—	4	4	no	—
262	C₂×C₄×C₂₃	—	2	2	no	—
263	C₂×C₄×C₂₃	—	2	2	no	—
264	C₂×C₄×C₂₃	—	2	2	no	—
265	C₂×C₄×C₂₃	—	2	2	no	—
266	C₂×C₄×C₂₃	—	2	2	no	—
267	C₂×C₄×C₂₃	—	2	2	no	—
268	C₂×C₄×C₂₃	—	2	8	no	—
269	C₂×C₄×C₂₃	—	2	4	no	—
270	C₂×C₄×C₂₃	—	2	2	no	—
271	C₂×C₄×C₂₃	—	2	2	no	—
272	C₂×C₄×C₂₃	—	2	4	no	—
273	C₂×C₄×C₂₃	—	2	2	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	1	no	—
278	C₂×C₄×C₂₃	—	4	1	no	—
279	C₂×C₄×C₂₃	—	4	1	no	—
280	C₂×C₄×C₂₃	—	4	1	no	—
281	C₂×C₄×C₂₃	—	4	1	no	—
282	C₂×C₄×C₂₃	—	4	1	no	—
283	C₂×C₄×C₂₃	—	4	4	no	—
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	1	yes	characteristic
290	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
291	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
292	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
293	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
294	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
295	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
296	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
297	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
298	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
299	C₈×C₂₃	—	2	4	no	—
300	C₈×C₂₃	—	2	8	no	—
301	C₈×C₂₃	—	2	4	no	—
302	#3444	C₂×C₂₃	1	1	yes	characteristic
303	#2991	C₂×C₂₃	1	2	yes	complemented
304	#2990	C₂×C₂₃	1	2	yes	complemented
305	#2989	C₂×C₂₃	1	4	yes	complemented
306	#2985	C₂×C₂₃	1	2	yes	complemented
307	#2981	C₂×C₂₃	1	2	yes	complemented
308	#2978	C₂×C₂₃	1	4	yes	complemented
309	#2969	C₂×C₂₃	1	4	yes	complemented
310	#2967	C₂×C₂₃	1	4	yes	complemented
311	#2925	C₂×C₂₃	1	4	yes	complemented
312	#2920	C₂×C₂₃	1	1	yes	characteristic, complemented
313	#2920	C₂×C₂₃	1	1	yes	characteristic, complemented
314	C₂²×C₂₃	—	2	1	no	—
315	C₂²×C₂₃	—	2	1	no	—
316	C₂²×C₂₃	—	2	1	no	—
317	C₂²×C₂₃	—	2	4	no	—
318	C₂²×C₂₃	—	2	1	no	—
319	C₂²×C₂₃	—	2	1	no	—
320	C₂²×C₂₃	—	2	1	no	—
321	C₂²×C₂₃	—	2	1	no	—
322	C₂²×C₂₃	—	2	1	no	—
323	C₂²×C₂₃	—	2	1	no	—
324	C₂²×C₂₃	—	2	4	no	—
325	C₂²×C₂₃	—	2	4	no	—
326	C₂²×C₂₃	—	4	4	no	—
327	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
328	C₄×C₂₃	—	2	1	no	—
329	C₄×C₂₃	—	2	1	no	—
330	C₄×C₂₃	—	2	1	no	—
331	C₄×C₂₃	—	2	4	no	—
332	C₄×C₂₃	—	2	1	no	—
333	C₄×C₂₃	—	2	1	no	—
334	C₄×C₂₃	—	2	1	no	—
335	C₄×C₂₃	—	2	1	no	—
336	C₄×C₂₃	—	2	1	no	—
337	C₄×C₂₃	—	2	1	no	—
338	C₄×C₂₃	—	2	4	no	—
339	C₄×C₂₃	—	2	4	no	—
340	C₄×C₂₃	#568	1	2	yes	—
341	C₄×C₂₃	#568	1	2	yes	—
342	C₄×C₂₃	#585	1	2	yes	—
343	#533	C₄×C₂₃	1	1	yes	characteristic
344	#533	C₄×C₂₃	1	1	yes	characteristic
345	#533	C₂²×C₂₃	1	1	yes	characteristic
346	#532	C₄×C₂₃	1	1	yes	characteristic
347	#532	C₄×C₂₃	1	1	yes	characteristic
348	#532	C₂²×C₂₃	1	1	yes	characteristic
349	#529	C₄×C₂₃	1	2	yes	—
350	#529	C₄×C₂₃	1	2	yes	—
351	#529	C₄×C₂₃	1	2	yes	—
352	#529	C₄×C₂₃	1	2	yes	—
353	#529	C₂²×C₂₃	1	2	yes	—
354	#529	C₂²×C₂₃	1	2	yes	—
355	#525	C₄×C₂₃	1	2	yes	—
356	#525	C₄×C₂₃	1	2	yes	—
357	#525	C₂²×C₂₃	1	2	yes	—
358	C₄×#41	C₂²×C₂₃	1	2	yes	—
359	C₄×#41	C₂²×C₂₃	1	2	yes	—
360	C₄×#41	C₂²×C₂₃	1	2	yes	—
361	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
362	#446	C₂²×C₂₃	1	8	yes	complemented
363	#446	C₂²×C₂₃	1	4	yes	complemented
364	C₈×Q₈	C₂²×C₂₃	1	4	yes	complemented
365	#436	C₂²×C₂₃	1	8	yes	—
366	#436	C₂²×C₂₃	1	8	yes	—
367	#436	C₂²×C₂₃	1	4	yes	complemented
368	#435	C₂²×C₂₃	1	8	yes	—
369	#435	C₂²×C₂₃	1	8	yes	—
370	#435	C₂²×C₂₃	1	8	yes	complemented
371	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
372	#433	C₂²×C₂₃	1	8	yes	—
373	#433	C₂²×C₂₃	1	8	yes	complemented
374	#432	C₂²×C₂₃	1	2	yes	—
375	#432	C₂²×C₂₃	1	2	yes	—
376	#432	C₂²×C₂₃	1	2	yes	—
377	#432	C₂²×C₂₃	1	2	yes	—
378	#432	C₂²×C₂₃	1	4	yes	complemented
379	#431	C₂²×C₂₃	1	2	yes	—
380	#431	C₂²×C₂₃	1	2	yes	—
381	#431	C₂²×C₂₃	1	2	yes	—
382	#431	C₂²×C₂₃	1	1	yes	characteristic
383	#431	C₂²×C₂₃	1	1	yes	characteristic
384	#431	C₂²×C₂₃	1	4	yes	complemented
385	#423	C₂²×C₂₃	1	2	yes	—
386	#423	C₂²×C₂₃	1	2	yes	—
387	#423	C₂²×C₂₃	1	4	yes	complemented
388	C₂×C₄⋊C₈	C₂²×C₂₃	1	4	yes	complemented
389	#408	C₂²×C₂₃	1	8	yes	—
390	#407	C₂²×C₂₃	1	2	yes	—
391	#407	C₂²×C₂₃	1	2	yes	—
392	#405	C₂²×C₂₃	1	8	yes	complemented
393	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
394	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
395	C₂×C₂₃	—	4	4	no	—
396	C₂×C₂₃	—	4	1	no	—
397	C₂×C₂₃	—	4	1	no	—
398	C₂×C₂₃	—	4	1	no	—
399	C₂×C₂₃	#3428	1	1	yes	characteristic
400	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
401	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
402	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
403	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
404	C₂×#41	C₂³×C₂₃	1	2	yes	—
405	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
406	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
408	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
409	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
410	C₂×M₁₆	C₂³×C₂₃	1	8	yes	—
411	C₂²×C₈	C₂³×C₂₃	1	8	yes	—
412	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
413	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
414	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
415	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
416	#126	C₂×C₄×C₂₃	1	4	yes	—
417	#126	C₂×C₄×C₂₃	1	4	yes	—
418	#125	C₂×C₄×C₂₃	1	2	yes	—
419	#125	C₂×C₄×C₂₃	1	2	yes	—
420	#125	C₂×C₄×C₂₃	1	2	yes	—
421	#124	C₂×C₄×C₂₃	1	2	yes	—
422	#124	C₂×C₄×C₂₃	1	2	yes	—
423	#124	C₂×C₄×C₂₃	1	2	yes	—
424	#123	C₂×C₄×C₂₃	1	4	yes	—
425	#123	C₂×C₄×C₂₃	1	4	yes	—
426	#123	C₂×C₄×C₂₃	1	4	yes	—
427	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
428	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
429	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
430	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
431	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
432	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
433	#121	C₂×C₄×C₂₃	1	2	yes	—
434	#121	C₂×C₄×C₂₃	1	2	yes	—
435	#121	C₂×C₄×C₂₃	1	2	yes	—
436	#121	C₂×C₄×C₂₃	1	2	yes	—
437	#121	C₂×C₄×C₂₃	1	2	yes	—
438	#121	C₂×C₄×C₂₃	1	2	yes	—
439	#120	C₂×C₄×C₂₃	1	4	yes	—
440	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
441	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
442	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
443	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
444	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
445	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
446	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
447	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
448	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
449	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
450	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
451	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
452	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
453	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
454	C₄×D₄	C₂³×C₂₃	1	4	yes	—
455	C₄×D₄	C₂³×C₂₃	1	4	yes	—
456	C₄×D₄	C₂³×C₂₃	1	2	yes	—
457	C₄×D₄	C₂³×C₂₃	1	2	yes	—
458	#117	C₂×C₄×C₂₃	1	2	yes	—
459	#117	C₂×C₄×C₂₃	1	2	yes	—
460	#117	C₂×C₄×C₂₃	1	4	yes	—
461	#117	C₂×C₄×C₂₃	1	4	yes	—
462	#117	C₂³×C₂₃	1	2	yes	—
463	#117	C₂³×C₂₃	1	4	yes	—
464	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
465	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
466	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
467	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
468	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
469	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
471	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
472	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
473	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
474	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
475	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
477	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
478	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
479	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
480	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
481	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
482	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
483	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
484	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
485	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
486	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
487	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
488	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
489	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
490	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
491	#97	C₂³×C₂₃	1	4	yes	—
492	#97	C₂³×C₂₃	1	4	yes	—
493	#97	C₂³×C₂₃	1	8	yes	—
494	C₄×C₈	C₂³×C₂₃	1	4	yes	—
495	C₄×C₈	C₂³×C₂₃	1	2	yes	—
496	C₄×C₈	C₂³×C₂₃	1	2	yes	—
497	C₄×C₈	C₂³×C₂₃	1	8	yes	—
498	C₂₃	#60295	1	1	yes	characteristic, direct product factor, Sylow
499	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
500	#41	—	4	4	no	—
501	#41	—	4	4	no	—
502	#41	—	4	4	no	—
503	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
504	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
505	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
506	C₂×D₄	C₂²×C₄×C₂₃	1	2	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	2	yes	—
512	C₂²×C₄	—	4	2	no	—
513	C₂²×C₄	—	4	2	no	—
514	C₂²×C₄	—	4	2	no	—
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	1	yes	characteristic
518	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
519	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
520	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
521	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
522	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
523	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
524	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
525	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
526	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
527	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
528	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
529	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
530	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
531	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
532	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
536	M₁₆	—	4	4	no	—
537	M₁₆	—	4	4	no	—
538	M₁₆	—	4	8	no	—
539	C₂×C₈	—	4	8	no	—
540	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
541	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
542	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
543	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
544	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
545	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
546	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	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	4	yes	—
550	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
551	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
552	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
553	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
554	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
555	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
556	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
557	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
558	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
559	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
560	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
561	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
562	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
563	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
564	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
565	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
566	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
567	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
568	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
569	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
570	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
571	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
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	1	yes	characteristic
579	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
580	C₄²	C₂⁴×C₂₃	1	4	yes	—
581	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
582	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
583	C₂³	—	4	1	no	—
584	C₂³	—	4	1	no	—
585	C₂³	—	4	1	no	—
586	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
587	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
588	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
589	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
590	Q₈	—	2	4	no	—
591	Q₈	—	4	2	no	—
592	Q₈	—	4	2	no	—
593	D₄	—	2	4	no	—
594	D₄	—	4	2	no	—
595	D₄	—	4	4	no	—
596	D₄	—	4	2	no	—
597	D₄	—	4	4	no	—
598	D₄	—	4	4	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	8	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	4	no	—
621	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
622	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
623	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
624	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
625	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
626	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
627	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
628	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
629	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
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	4	yes	—
633	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
634	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
635	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
636	C₈	—	2	4	no	—
637	C₈	—	2	8	no	—
638	C₈	—	2	4	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	4	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	4	no	—
650	C₂²	—	2	4	no	—
651	C₂²	—	4	4	no	—
652	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	4	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	4	no	—
664	C₄	—	2	4	no	—
665	C₄	C₂₃×#568	1	2	yes	—
666	C₄	C₂₃×#568	1	2	yes	—
667	C₄	C₂₃×#585	1	2	yes	—
668	C₂	—	4	1	no	—
669	C₂	—	4	1	no	—
670	C₂	—	4	1	no	—
671	C₂	—	4	4	no	—
672	C₂	C₂₃×#3428	1	1	yes	characteristic
673	C₂	C₂×C₂₃×#568	1	1	yes	characteristic
674	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	C₂₃×#3444	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×#2991	C₂	semidirect
3. C₂₃×#2990	C₂	semidirect
4. C₂₃×#2989	C₂	semidirect
5. C₂₃×#2985	C₂	semidirect
6. C₂₃×#2981	C₂	semidirect
7. C₂₃×#2978	C₂	semidirect
8. C₂₃×#2969	C₂	semidirect
9. C₂₃×#2967	C₂	semidirect
10. C₂₃×#2925	C₂	semidirect
11. C₂₃×#2920	C₂	semidirect
12. C₂₃×#2920	C₂	semidirect
32. C₂₃×#446	C₂²	semidirect
33. C₂₃×#446	C₂²	semidirect
34. C₈×Q₈×C₂₃	C₂²	semidirect
37. C₂₃×#436	C₂²	semidirect
40. C₂₃×#435	C₂²	semidirect
41. C₈×D₄×C₂₃	C₂²	semidirect
43. C₂₃×#433	C₂²	semidirect
48. C₂₃×#432	C₂²	semidirect
54. C₂₃×#431	C₂²	semidirect
57. C₂₃×#423	C₂²	semidirect
58. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
62. C₂₃×#405	C₂²	semidirect
245. #60295	C₂₃	direct (N × H)
303. #2991	C₂×C₂₃	semidirect
304. #2990	C₂×C₂₃	semidirect
305. #2989	C₂×C₂₃	semidirect
306. #2985	C₂×C₂₃	semidirect
307. #2981	C₂×C₂₃	semidirect
308. #2978	C₂×C₂₃	semidirect
309. #2969	C₂×C₂₃	semidirect
310. #2967	C₂×C₂₃	semidirect
311. #2925	C₂×C₂₃	semidirect
312. #2920	C₂×C₂₃	semidirect
313. #2920	C₂×C₂₃	semidirect
362. #446	C₂²×C₂₃	semidirect
363. #446	C₂²×C₂₃	semidirect
364. C₈×Q₈	C₂²×C₂₃	semidirect
367. #436	C₂²×C₂₃	semidirect
370. #435	C₂²×C₂₃	semidirect
371. C₈×D₄	C₂²×C₂₃	semidirect
373. #433	C₂²×C₂₃	semidirect
378. #432	C₂²×C₂₃	semidirect
384. #431	C₂²×C₂₃	semidirect
387. #423	C₂²×C₂₃	semidirect
388. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
392. #405	C₂²×C₂₃	semidirect
498. C₂₃	#60295	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×#3444	2
C₂₃×#2991	2
C₂₃×#2990	2
C₂₃×#2989	2
C₂₃×#2985	2
C₂₃×#2981	2
C₂₃×#2978	2
C₂₃×#2969	2
C₂₃×#2967	2
C₂₃×#2925	2
C₂₃×#2920	2
#60295	23

Subgroups — C23×#60295 #19207921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60295 #19207921