Subgroups — C₂₃×#60318 #19207944

Order 5888.

1812 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3529	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2995	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2993	C₂	1	4	yes	maximal, complemented
4	C₂₃×#2980	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2979	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2977	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2976	C₂	1	4	yes	maximal, complemented
8	C₂₃×#2968	C₂	1	4	yes	maximal, complemented
9	C₂₃×#2966	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2933	C₂	1	4	yes	maximal, complemented
11	C₂₃×#2932	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2930	C₂	1	2	yes	maximal, complemented
14	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×#131	C₂²	1	2	yes	—
16	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
17	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	complemented
18	C₂₃×#563	C₄	1	2	yes	—
19	C₂₃×#563	C₄	1	1	yes	characteristic
20	C₂₃×#562	C₄	1	4	yes	—
21	C₂₃×#562	C₄	1	2	yes	—
22	C₂₃×H(3,𝔽₄)	C₄	1	1	yes	characteristic
23	C₂₃×#560	C₄	1	4	yes	—
24	C₂₃×#560	C₄	1	2	yes	—
25	C₂₃×#532	C₂²	1	1	yes	characteristic
26	C₂₃×#532	C₂²	1	2	yes	—
27	C₂₃×#529	C₂²	1	2	yes	—
28	C₂₃×#529	C₂²	1	4	yes	—
29	C₂₃×#525	C₂²	1	2	yes	—
30	C₂₃×#525	C₂²	1	4	yes	—
31	C₂₃×#446	C₂²	1	2	yes	complemented
32	C₂₃×#446	C₂²	1	4	yes	complemented
33	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
34	C₂₃×#436	C₂²	1	4	yes	—
35	C₂₃×#436	C₂²	1	2	yes	—
36	C₂₃×#436	C₂²	1	4	yes	complemented
37	C₂₃×#436	C₂²	1	4	yes	complemented
38	C₂₃×#436	C₂²	1	4	yes	complemented
39	C₂₃×#435	C₂²	1	4	yes	—
40	C₂₃×#435	C₂²	1	4	yes	—
41	C₂₃×#435	C₂²	1	4	yes	—
42	C₂₃×#435	C₂²	1	4	yes	complemented
43	C₂₃×#435	C₂²	1	4	yes	complemented
44	C₂₃×#435	C₂²	1	4	yes	complemented
45	C₂₃×#435	C₂²	1	4	yes	complemented
46	C₂₃×#435	C₂²	1	4	yes	complemented
47	C₂₃×#435	C₂²	1	4	yes	complemented
48	C₈×D₄×C₂₃	C₂²	1	4	yes	—
49	C₈×D₄×C₂₃	C₂²	1	2	yes	—
50	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
51	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
52	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
53	C₂₃×#433	C₂²	1	4	yes	complemented
54	C₂₃×#433	C₂²	1	4	yes	complemented
55	C₂₃×#433	C₂²	1	4	yes	complemented
56	C₂₃×#432	C₂²	1	2	yes	complemented
57	C₂₃×#431	C₂²	1	4	yes	complemented
58	C₂₃×#424	C₂²	1	2	yes	complemented
59	C₂₃×#424	C₂²	1	4	yes	complemented
60	C₂₃×#423	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#423	C₂²	1	2	yes	complemented
62	C₂₃×#408	C₂²	1	2	yes	—
63	C₂₃×#408	C₂²	1	1	yes	characteristic
64	C₂₃×#408	C₂²	1	2	yes	—
65	C₂₃×#408	C₂²	1	4	yes	—
66	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#408	C₂²	1	2	yes	complemented
68	C₂₃×#407	C₂²	1	2	yes	complemented
69	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
70	C₂₃×#405	C₂²	1	2	yes	complemented
71	C₂₃×#405	C₂²	1	4	yes	complemented
72	C₂×C₂₃×#97	C₂²	1	2	yes	complemented
73	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
74	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
75	C₂×#41×C₂₃	C₂³	1	2	yes	—
76	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
78	C₂₃×#131	—	4	2	no	—
79	C₂₃×#131	—	4	2	no	—
80	C₂₃×#131	—	4	4	no	—
81	C₂×M₁₆×C₂₃	—	4	4	no	—
82	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
83	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
84	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
85	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
86	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
87	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
88	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
89	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
90	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
91	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
93	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
94	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
95	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
97	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
98	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
99	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
100	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
101	C₂₃×#127	C₂×C₄	1	2	yes	—
102	C₂₃×#126	C₂×C₄	1	4	yes	—
103	C₂₃×#126	C₂×C₄	1	4	yes	—
104	C₂₃×#126	C₂×C₄	1	4	yes	—
105	C₂₃×#125	C₂×C₄	1	2	yes	—
106	C₂₃×#125	C₂×C₄	1	4	yes	—
107	C₂₃×#124	C₂×C₄	1	2	yes	—
108	C₂₃×#124	C₂×C₄	1	4	yes	—
109	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
110	C₂₃×#124	C₂×C₄	1	2	yes	—
111	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
112	C₂₃×#124	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	2	yes	—
117	C₂₃×#123	C₂×C₄	1	4	yes	—
118	C₂₃×#123	C₂×C₄	1	2	yes	—
119	C₂₃×#123	C₂×C₄	1	4	yes	—
120	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
121	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
122	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
123	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
124	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
125	C₂₃×#121	C₂×C₄	1	2	yes	—
126	C₂₃×#121	C₂×C₄	1	4	yes	—
127	C₂₃×#121	C₂×C₄	1	4	yes	—
128	C₂₃×#121	C₂×C₄	1	4	yes	—
129	C₂₃×#121	C₂×C₄	1	4	yes	—
130	C₂₃×#121	C₂×C₄	1	4	yes	—
131	C₂₃×#121	C₂×C₄	1	4	yes	—
132	C₂₃×#121	C₂×C₄	1	4	yes	—
133	C₂₃×#120	C₂×C₄	1	2	yes	—
134	C₂₃×#120	C₂×C₄	1	4	yes	—
135	C₂₃×#120	C₂×C₄	1	2	yes	—
136	C₂₃×#120	C₂×C₄	1	4	yes	—
137	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
138	C₄×D₄×C₂₃	C₂³	1	4	yes	—
139	C₄×D₄×C₂₃	C₂³	1	2	yes	—
140	C₄×D₄×C₂₃	C₂³	1	4	yes	—
141	C₄×D₄×C₂₃	C₂³	1	4	yes	—
142	C₄×D₄×C₂₃	C₂³	1	4	yes	—
143	C₂₃×#117	C₂³	1	2	yes	—
144	C₂₃×#117	C₂³	1	4	yes	—
145	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
147	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
148	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
149	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
150	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
151	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
152	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
153	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
154	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
155	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
156	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
157	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
158	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
159	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
160	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
161	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
162	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
163	C₂₃×#97	C₂³	1	4	yes	—
164	C₂₃×#97	C₂³	1	4	yes	—
165	C₂₃×#97	C₂³	1	4	yes	—
166	C₄×C₈×C₂₃	C₂³	1	2	yes	—
167	C₄×C₈×C₂₃	C₂³	1	2	yes	—
168	C₄×C₈×C₂₃	C₂³	1	4	yes	—
169	C₄×C₈×C₂₃	C₂³	1	4	yes	—
170	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
171	#41×C₂₃	—	4	1	no	—
172	#41×C₂₃	—	4	1	no	—
173	#41×C₂₃	—	4	2	no	—
174	#41×C₂₃	—	4	2	no	—
175	#41×C₂₃	—	4	1	no	—
176	#41×C₂₃	—	4	1	no	—
177	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
178	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
179	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
180	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
181	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
182	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
183	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
184	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
185	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
186	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
187	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
188	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
189	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
190	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
191	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₂₃	—	4	2	no	—
193	C₂²×C₄×C₂₃	—	4	2	no	—
194	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
195	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
196	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
197	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
198	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
202	M₁₆×C₂₃	—	2	8	no	—
203	M₁₆×C₂₃	—	4	4	no	—
204	M₁₆×C₂₃	—	4	2	no	—
205	M₁₆×C₂₃	—	4	1	no	—
206	M₁₆×C₂₃	—	4	2	no	—
207	M₁₆×C₂₃	—	4	2	no	—
208	M₁₆×C₂₃	—	4	1	no	—
209	M₁₆×C₂₃	—	4	2	no	—
210	C₂×C₈×C₂₃	—	2	4	no	—
211	C₂×C₈×C₂₃	—	2	4	no	—
212	C₂×C₈×C₂₃	—	2	2	no	—
213	C₂×C₈×C₂₃	—	4	1	no	—
214	C₂×C₈×C₂₃	—	4	4	no	—
215	C₂×C₈×C₂₃	—	4	2	no	—
216	C₂×C₈×C₂₃	—	4	2	no	—
217	C₂×C₈×C₂₃	—	4	4	no	—
218	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
219	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
220	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
221	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
222	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
223	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
224	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
232	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
233	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
234	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
235	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
236	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
237	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	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	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	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	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
249	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
250	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
251	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
252	C₄²×C₂₃	C₂⁴	1	4	yes	—
253	C₄²×C₂₃	C₂⁴	1	2	yes	—
254	#60318	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂³×C₂₃	—	4	2	no	—
256	C₂³×C₂₃	—	4	4	no	—
257	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
258	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
259	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
260	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
261	Q₈×C₂₃	—	4	2	no	—
262	Q₈×C₂₃	—	4	1	no	—
263	Q₈×C₂₃	—	4	2	no	—
264	Q₈×C₂₃	—	4	1	no	—
265	D₄×C₂₃	—	4	4	no	—
266	D₄×C₂₃	—	4	4	no	—
267	D₄×C₂₃	—	4	4	no	—
268	D₄×C₂₃	—	4	4	no	—
269	D₄×C₂₃	—	4	2	no	—
270	D₄×C₂₃	—	4	2	no	—
271	D₄×C₂₃	—	4	4	no	—
272	D₄×C₂₃	—	4	1	no	—
273	D₄×C₂₃	—	4	2	no	—
274	D₄×C₂₃	—	4	2	no	—
275	D₄×C₂₃	—	4	1	no	—
276	C₂×C₄×C₂₃	—	2	2	no	—
277	C₂×C₄×C₂₃	—	2	2	no	—
278	C₂×C₄×C₂₃	—	2	1	no	—
279	C₂×C₄×C₂₃	—	2	4	no	—
280	C₂×C₄×C₂₃	—	2	4	no	—
281	C₂×C₄×C₂₃	—	2	1	no	—
282	C₂×C₄×C₂₃	—	2	2	no	—
283	C₂×C₄×C₂₃	—	2	2	no	—
284	C₂×C₄×C₂₃	—	4	4	no	—
285	C₂×C₄×C₂₃	—	4	2	no	—
286	C₂×C₄×C₂₃	—	4	2	no	—
287	C₂×C₄×C₂₃	—	4	4	no	—
288	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
289	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
290	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
291	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
292	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
293	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
294	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
295	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
296	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
297	C₈×C₂₃	—	2	2	no	—
298	C₈×C₂₃	—	2	2	no	—
299	C₈×C₂₃	—	2	1	no	—
300	C₈×C₂₃	—	2	4	no	—
301	C₈×C₂₃	—	2	2	no	—
302	C₈×C₂₃	—	2	4	no	—
303	C₈×C₂₃	H(5,𝔽₂)	1	2	yes	—
304	#3529	C₂×C₂₃	1	1	yes	characteristic
305	#2995	C₂×C₂₃	1	2	yes	complemented
306	#2993	C₂×C₂₃	1	4	yes	complemented
307	#2980	C₂×C₂₃	1	1	yes	characteristic, complemented
308	#2979	C₂×C₂₃	1	2	yes	complemented
309	#2977	C₂×C₂₃	1	2	yes	complemented
310	#2976	C₂×C₂₃	1	4	yes	complemented
311	#2968	C₂×C₂₃	1	4	yes	complemented
312	#2966	C₂×C₂₃	1	2	yes	complemented
313	#2933	C₂×C₂₃	1	4	yes	complemented
314	#2932	C₂×C₂₃	1	2	yes	complemented
315	#2931	C₂×C₂₃	1	1	yes	characteristic, complemented
316	#2930	C₂×C₂₃	1	2	yes	complemented
317	C₂²×C₂₃	—	2	2	no	—
318	C₂²×C₂₃	—	2	4	no	—
319	C₂²×C₂₃	—	2	2	no	—
320	C₂²×C₂₃	—	2	1	no	—
321	C₂²×C₂₃	—	2	2	no	—
322	C₂²×C₂₃	—	2	4	no	—
323	C₂²×C₂₃	—	2	4	no	—
324	C₂²×C₂₃	—	2	4	no	—
325	C₂²×C₂₃	—	2	4	no	—
326	C₂²×C₂₃	—	8	4	no	—
327	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
328	C₄×C₂₃	—	2	2	no	—
329	C₄×C₂₃	—	2	4	no	—
330	C₄×C₂₃	—	2	2	no	—
331	C₄×C₂₃	—	2	1	no	—
332	C₄×C₂₃	—	2	2	no	—
333	C₄×C₂₃	—	2	4	no	—
334	C₄×C₂₃	—	2	2	no	—
335	C₄×C₂₃	—	2	4	no	—
336	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
337	C₄×C₂₃	#585	1	1	yes	characteristic
338	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
339	C₂×#131	C₂²×C₂₃	1	2	yes	—
340	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
341	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	complemented
342	#563	C₄×C₂₃	1	2	yes	—
343	#563	C₄×C₂₃	1	1	yes	characteristic
344	#562	C₄×C₂₃	1	4	yes	—
345	#562	C₄×C₂₃	1	2	yes	—
346	H(3,𝔽₄)	C₄×C₂₃	1	1	yes	characteristic
347	#560	C₄×C₂₃	1	4	yes	—
348	#560	C₄×C₂₃	1	2	yes	—
349	#532	C₂²×C₂₃	1	1	yes	characteristic
350	#532	C₂²×C₂₃	1	2	yes	—
351	#529	C₂²×C₂₃	1	2	yes	—
352	#529	C₂²×C₂₃	1	4	yes	—
353	#525	C₂²×C₂₃	1	2	yes	—
354	#525	C₂²×C₂₃	1	4	yes	—
355	#446	C₂²×C₂₃	1	2	yes	complemented
356	#446	C₂²×C₂₃	1	4	yes	complemented
357	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
358	#436	C₂²×C₂₃	1	4	yes	—
359	#436	C₂²×C₂₃	1	2	yes	—
360	#436	C₂²×C₂₃	1	4	yes	complemented
361	#436	C₂²×C₂₃	1	4	yes	complemented
362	#436	C₂²×C₂₃	1	4	yes	complemented
363	#435	C₂²×C₂₃	1	4	yes	—
364	#435	C₂²×C₂₃	1	4	yes	—
365	#435	C₂²×C₂₃	1	4	yes	—
366	#435	C₂²×C₂₃	1	4	yes	complemented
367	#435	C₂²×C₂₃	1	4	yes	complemented
368	#435	C₂²×C₂₃	1	4	yes	complemented
369	#435	C₂²×C₂₃	1	4	yes	complemented
370	#435	C₂²×C₂₃	1	4	yes	complemented
371	#435	C₂²×C₂₃	1	4	yes	complemented
372	C₈×D₄	C₂²×C₂₃	1	4	yes	—
373	C₈×D₄	C₂²×C₂₃	1	2	yes	—
374	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
375	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
376	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
377	#433	C₂²×C₂₃	1	4	yes	complemented
378	#433	C₂²×C₂₃	1	4	yes	complemented
379	#433	C₂²×C₂₃	1	4	yes	complemented
380	#432	C₂²×C₂₃	1	2	yes	complemented
381	#431	C₂²×C₂₃	1	4	yes	complemented
382	#424	C₂²×C₂₃	1	2	yes	complemented
383	#424	C₂²×C₂₃	1	4	yes	complemented
384	#423	C₂²×C₂₃	1	1	yes	characteristic, complemented
385	#423	C₂²×C₂₃	1	2	yes	complemented
386	#408	C₂²×C₂₃	1	2	yes	—
387	#408	C₂²×C₂₃	1	1	yes	characteristic
388	#408	C₂²×C₂₃	1	2	yes	—
389	#408	C₂²×C₂₃	1	4	yes	—
390	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
391	#408	C₂²×C₂₃	1	2	yes	complemented
392	#407	C₂²×C₂₃	1	2	yes	complemented
393	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	complemented
394	#405	C₂²×C₂₃	1	2	yes	complemented
395	#405	C₂²×C₂₃	1	4	yes	complemented
396	C₂×#97	C₂²×C₂₃	1	2	yes	complemented
397	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
398	C₂×C₂₃	—	4	2	no	—
399	C₂×C₂₃	—	4	1	no	—
400	C₂×C₂₃	—	4	2	no	—
401	C₂×C₂₃	—	4	4	no	—
402	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
403	C₂×C₂₃	#3573	1	2	yes	—
404	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
405	C₂×#41	C₂³×C₂₃	1	2	yes	—
406	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
408	#131	—	4	2	no	—
409	#131	—	4	2	no	—
410	#131	—	4	4	no	—
411	C₂×M₁₆	—	4	4	no	—
412	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
413	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
414	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
415	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
416	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
417	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
418	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
419	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
420	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
421	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
422	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
423	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
424	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
425	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
426	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
427	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
428	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
429	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
430	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
431	#127	C₂×C₄×C₂₃	1	2	yes	—
432	#126	C₂×C₄×C₂₃	1	4	yes	—
433	#126	C₂×C₄×C₂₃	1	4	yes	—
434	#126	C₂×C₄×C₂₃	1	4	yes	—
435	#125	C₂×C₄×C₂₃	1	2	yes	—
436	#125	C₂×C₄×C₂₃	1	4	yes	—
437	#124	C₂×C₄×C₂₃	1	2	yes	—
438	#124	C₂×C₄×C₂₃	1	4	yes	—
439	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
440	#124	C₂×C₄×C₂₃	1	2	yes	—
441	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
442	#124	C₂×C₄×C₂₃	1	2	yes	—
443	#123	C₂×C₄×C₂₃	1	2	yes	—
444	#123	C₂×C₄×C₂₃	1	4	yes	—
445	#123	C₂×C₄×C₂₃	1	2	yes	—
446	#123	C₂×C₄×C₂₃	1	4	yes	—
447	#123	C₂×C₄×C₂₃	1	4	yes	—
448	#123	C₂×C₄×C₂₃	1	4	yes	—
449	#123	C₂×C₄×C₂₃	1	4	yes	—
450	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
451	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
452	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
453	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
454	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
455	#121	C₂×C₄×C₂₃	1	4	yes	—
456	#121	C₂×C₄×C₂₃	1	4	yes	—
457	#121	C₂×C₄×C₂₃	1	4	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	#121	C₂×C₄×C₂₃	1	4	yes	—
463	#120	C₂×C₄×C₂₃	1	2	yes	—
464	#120	C₂×C₄×C₂₃	1	4	yes	—
465	#120	C₂×C₄×C₂₃	1	2	yes	—
466	#120	C₂×C₄×C₂₃	1	4	yes	—
467	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
468	C₄×D₄	C₂³×C₂₃	1	4	yes	—
469	C₄×D₄	C₂³×C₂₃	1	2	yes	—
470	C₄×D₄	C₂³×C₂₃	1	4	yes	—
471	C₄×D₄	C₂³×C₂₃	1	4	yes	—
472	C₄×D₄	C₂³×C₂₃	1	4	yes	—
473	#117	C₂³×C₂₃	1	2	yes	—
474	#117	C₂³×C₂₃	1	4	yes	—
475	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
477	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
478	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
479	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
480	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
481	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
482	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
483	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
484	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
485	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
486	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
487	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
488	C₂²⋊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	#97	C₂³×C₂₃	1	4	yes	—
494	#97	C₂³×C₂₃	1	4	yes	—
495	#97	C₂³×C₂₃	1	4	yes	—
496	C₄×C₈	C₂³×C₂₃	1	2	yes	—
497	C₄×C₈	C₂³×C₂₃	1	2	yes	—
498	C₄×C₈	C₂³×C₂₃	1	4	yes	—
499	C₄×C₈	C₂³×C₂₃	1	4	yes	—
500	C₂₃	#60318	1	1	yes	characteristic, direct product factor, Sylow
501	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
502	#41	—	4	1	no	—
503	#41	—	4	1	no	—
504	#41	—	4	2	no	—
505	#41	—	4	2	no	—
506	#41	—	4	1	no	—
507	#41	—	4	1	no	—
508	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
509	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
510	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
511	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
512	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
513	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
514	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
515	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
516	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
517	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
518	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
519	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
520	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
521	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
522	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	4	2	no	—
525	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
526	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
527	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
528	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
533	M₁₆	—	2	8	no	—
534	M₁₆	—	4	4	no	—
535	M₁₆	—	4	1	no	—
536	M₁₆	—	4	2	no	—
537	M₁₆	—	4	2	no	—
538	M₁₆	—	4	1	no	—
539	M₁₆	—	4	2	no	—
540	M₁₆	—	4	2	no	—
541	C₂×C₈	—	2	4	no	—
542	C₂×C₈	—	2	4	no	—
543	C₂×C₈	—	2	2	no	—
544	C₂×C₈	—	4	2	no	—
545	C₂×C₈	—	4	4	no	—
546	C₂×C₈	—	4	1	no	—
547	C₂×C₈	—	4	4	no	—
548	C₂×C₈	—	4	2	no	—
549	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
550	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
551	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
552	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
553	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
554	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
555	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
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	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
560	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
561	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
562	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	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	4	yes	—
566	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
567	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
568	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	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	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
573	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
574	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
575	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
576	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
577	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
578	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
579	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
580	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
581	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
582	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
583	C₄²	C₂⁴×C₂₃	1	2	yes	—
584	C₄²	C₂⁴×C₂₃	1	4	yes	—
585	C₂³	—	4	2	no	—
586	C₂³	—	4	4	no	—
587	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
588	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
589	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
590	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
591	Q₈	—	4	1	no	—
592	Q₈	—	4	2	no	—
593	Q₈	—	4	1	no	—
594	Q₈	—	4	2	no	—
595	D₄	—	4	2	no	—
596	D₄	—	4	4	no	—
597	D₄	—	4	1	no	—
598	D₄	—	4	2	no	—
599	D₄	—	4	2	no	—
600	D₄	—	4	1	no	—
601	D₄	—	4	4	no	—
602	D₄	—	4	4	no	—
603	D₄	—	4	4	no	—
604	D₄	—	4	4	no	—
605	D₄	—	4	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	4	4	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	4	no	—
618	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
619	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
620	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
621	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
622	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
623	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
624	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
625	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
626	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
627	C₈	—	2	2	no	—
628	C₈	—	2	2	no	—
629	C₈	—	2	1	no	—
630	C₈	—	2	4	no	—
631	C₈	—	2	2	no	—
632	C₈	—	2	4	no	—
633	C₈	C₂₃×H(5,𝔽₂)	1	2	yes	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	4	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	4	no	—
640	C₂²	—	2	4	no	—
641	C₂²	—	2	4	no	—
642	C₂²	—	2	4	no	—
643	C₂²	—	8	4	no	—
644	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
645	C₄	—	2	2	no	—
646	C₄	—	2	4	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	4	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	4	no	—
653	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
654	C₄	C₂₃×#585	1	1	yes	characteristic
655	C₂	—	4	2	no	—
656	C₂	—	4	4	no	—
657	C₂	—	4	2	no	—
658	C₂	—	4	1	no	—
659	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
660	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×#3529	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×#2993	C₂	semidirect
4. C₂₃×#2980	C₂	semidirect
5. C₂₃×#2979	C₂	semidirect
6. C₂₃×#2977	C₂	semidirect
7. C₂₃×#2976	C₂	semidirect
8. C₂₃×#2968	C₂	semidirect
9. C₂₃×#2966	C₂	semidirect
10. C₂₃×#2933	C₂	semidirect
11. C₂₃×#2932	C₂	semidirect
12. C₂₃×#2931	C₂	semidirect
13. C₂₃×#2930	C₂	semidirect
16. C₂×C₂₃×#131	C₂²	semidirect
17. C₂²×M₁₆×C₂₃	C₂²	semidirect
31. C₂₃×#446	C₂²	semidirect
32. C₂₃×#446	C₂²	semidirect
33. C₈×Q₈×C₂₃	C₂²	semidirect
36. C₂₃×#436	C₂²	semidirect
37. C₂₃×#436	C₂²	semidirect
38. C₂₃×#436	C₂²	semidirect
42. C₂₃×#435	C₂²	semidirect
43. C₂₃×#435	C₂²	semidirect
44. C₂₃×#435	C₂²	semidirect
45. C₂₃×#435	C₂²	semidirect
46. C₂₃×#435	C₂²	semidirect
47. C₂₃×#435	C₂²	semidirect
50. C₈×D₄×C₂₃	C₂²	semidirect
51. C₈×D₄×C₂₃	C₂²	semidirect
52. C₈×D₄×C₂₃	C₂²	semidirect
53. C₂₃×#433	C₂²	semidirect
54. C₂₃×#433	C₂²	semidirect
55. C₂₃×#433	C₂²	semidirect
56. C₂₃×#432	C₂²	semidirect
57. C₂₃×#431	C₂²	semidirect
58. C₂₃×#424	C₂²	semidirect
59. C₂₃×#424	C₂²	semidirect
60. C₂₃×#423	C₂²	semidirect
61. C₂₃×#423	C₂²	semidirect
66. C₂₃×#408	C₂²	semidirect
67. C₂₃×#408	C₂²	semidirect
68. C₂₃×#407	C₂²	semidirect
69. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
70. C₂₃×#405	C₂²	semidirect
71. C₂₃×#405	C₂²	semidirect
72. C₂×C₂₃×#97	C₂²	semidirect
73. C₂×C₄×C₈×C₂₃	C₂²	semidirect
254. #60318	C₂₃	direct (N × H)
305. #2995	C₂×C₂₃	semidirect
306. #2993	C₂×C₂₃	semidirect
307. #2980	C₂×C₂₃	semidirect
308. #2979	C₂×C₂₃	semidirect
309. #2977	C₂×C₂₃	semidirect
310. #2976	C₂×C₂₃	semidirect
311. #2968	C₂×C₂₃	semidirect
312. #2966	C₂×C₂₃	semidirect
313. #2933	C₂×C₂₃	semidirect
314. #2932	C₂×C₂₃	semidirect
315. #2931	C₂×C₂₃	semidirect
316. #2930	C₂×C₂₃	semidirect
340. C₂×#131	C₂²×C₂₃	semidirect
341. C₂²×M₁₆	C₂²×C₂₃	semidirect
355. #446	C₂²×C₂₃	semidirect
356. #446	C₂²×C₂₃	semidirect
357. C₈×Q₈	C₂²×C₂₃	semidirect
360. #436	C₂²×C₂₃	semidirect
361. #436	C₂²×C₂₃	semidirect
362. #436	C₂²×C₂₃	semidirect
366. #435	C₂²×C₂₃	semidirect
367. #435	C₂²×C₂₃	semidirect
368. #435	C₂²×C₂₃	semidirect
369. #435	C₂²×C₂₃	semidirect
370. #435	C₂²×C₂₃	semidirect
371. #435	C₂²×C₂₃	semidirect
374. C₈×D₄	C₂²×C₂₃	semidirect
375. C₈×D₄	C₂²×C₂₃	semidirect
376. C₈×D₄	C₂²×C₂₃	semidirect
377. #433	C₂²×C₂₃	semidirect
378. #433	C₂²×C₂₃	semidirect
379. #433	C₂²×C₂₃	semidirect
380. #432	C₂²×C₂₃	semidirect
381. #431	C₂²×C₂₃	semidirect
382. #424	C₂²×C₂₃	semidirect
383. #424	C₂²×C₂₃	semidirect
384. #423	C₂²×C₂₃	semidirect
385. #423	C₂²×C₂₃	semidirect
390. #408	C₂²×C₂₃	semidirect
391. #408	C₂²×C₂₃	semidirect
392. #407	C₂²×C₂₃	semidirect
393. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
394. #405	C₂²×C₂₃	semidirect
395. #405	C₂²×C₂₃	semidirect
396. C₂×#97	C₂²×C₂₃	semidirect
397. C₂×C₄×C₈	C₂²×C₂₃	semidirect
500. C₂₃	#60318	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×#3529	2
C₂₃×#2995	2
C₂₃×#2993	2
C₂₃×#2980	2
C₂₃×#2979	2
C₂₃×#2977	2
C₂₃×#2976	2
C₂₃×#2968	2
C₂₃×#2966	2
C₂₃×#2933	2
C₂₃×#2932	2
C₂₃×#2931	2
C₂₃×#2930	2
#60318	23

Subgroups — C23×#60318 #19207944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60318 #19207944