Subgroups — C₂₃×#25134 #19172760

Order 5888.

1068 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#436	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₃×#419	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2415	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#2409	C₂	1	1	yes	maximal, characteristic
7	C₂₃×#2066	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2056	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2001	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1933	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1894	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1894	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
27	C₂₃×#470	—	2	4	no	—
28	C₂₃×#451	—	2	4	no	—
29	C₂₃×#436	—	2	4	no	—
30	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂₃×#419	—	2	4	no	—
34	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
45	C₂₃×#397	—	2	1	no	—
46	C₂₃×#395	—	2	1	no	—
47	C₂₃×#394	—	2	1	no	—
48	C₂₃×#393	—	2	1	no	—
49	C₂₃×#391	C₂²	1	1	yes	characteristic
50	C₂₃×#391	C₂²	1	1	yes	characteristic
51	C₂₃×#391	C₂²	1	1	yes	characteristic
52	C₂₃×#389	—	2	1	no	—
53	C₂₃×#389	C₂²	1	1	yes	characteristic
54	C₂₃×#388	—	2	1	no	—
55	C₂₃×#386	—	2	1	no	—
56	C₂₃×#385	—	2	1	no	—
57	C₂₃×#380	C₂²	1	1	yes	characteristic
58	C₂₃×#380	C₂²	1	1	yes	characteristic
59	C₂₃×#340	C₂²	1	1	yes	characteristic
60	C₂₃×#340	C₂²	1	1	yes	characteristic
61	C₂₃×#340	C₂²	1	1	yes	characteristic
62	C₂₃×#340	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₂₃	—	2	1	no	—
64	C₂²×Q₈×C₂₃	—	2	2	no	—
65	C₂²×Q₈×C₂₃	—	2	2	no	—
66	C₂²×Q₈×C₂₃	—	2	2	no	—
67	C₂²×Q₈×C₂₃	—	2	2	no	—
68	C₂²×Q₈×C₂₃	—	4	1	no	—
69	C₂²×Q₈×C₂₃	—	4	1	no	—
70	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
74	C₂³×C₄×C₂₃	—	2	1	no	—
75	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂×Q₁₆×C₂₃	—	2	2	no	—
78	C₂×Q₁₆×C₂₃	—	2	2	no	—
79	C₂×Q₁₆×C₂₃	—	2	2	no	—
80	C₂×Q₁₆×C₂₃	—	2	2	no	—
81	C₂×Q₁₆×C₂₃	—	4	1	no	—
82	C₂×Q₁₆×C₂₃	—	4	1	no	—
83	C₂×M₁₆×C₂₃	—	2	2	no	—
84	C₂×M₁₆×C₂₃	—	2	2	no	—
85	C₂×M₁₆×C₂₃	—	2	2	no	—
86	C₂×M₁₆×C₂₃	—	2	2	no	—
87	C₂×M₁₆×C₂₃	—	4	1	no	—
88	C₂×M₁₆×C₂₃	—	4	1	no	—
89	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
93	C₂₃×C₂²⋊Q₈	—	2	2	no	—
94	C₂₃×C₂²⋊Q₈	—	2	2	no	—
95	C₂₃×C₂²⋊Q₈	—	2	2	no	—
96	C₂₃×C₂²⋊Q₈	—	2	2	no	—
97	C₂₃×C₂²⋊Q₈	—	2	2	no	—
98	C₂₃×C₂²⋊Q₈	—	4	1	no	—
99	C₂₃×C₂²⋊Q₈	—	4	1	no	—
100	C₂₃×C₂²⋊Q₈	—	4	1	no	—
101	C₄×D₄×C₂₃	—	2	2	no	—
102	C₄×D₄×C₂₃	—	2	2	no	—
103	C₂₃×#117	—	2	2	no	—
104	C₂₃×#117	—	4	1	no	—
105	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
106	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
107	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
108	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
109	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
110	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₂₃	—	2	1	no	—
126	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
127	C₂₃×#107	—	4	1	no	—
128	C₂₃×#106	—	2	2	no	—
129	C₂₃×C₄⋊C₈	—	2	2	no	—
130	C₂₃×#103	—	2	2	no	—
131	C₂₃×#103	—	2	2	no	—
132	C₂₃×#103	—	2	2	no	—
133	C₂₃×#103	—	2	2	no	—
134	C₂₃×#103	—	2	2	no	—
135	C₂₃×#103	—	2	2	no	—
136	C₂₃×#103	—	4	1	no	—
137	C₂₃×#103	D₄	1	4	yes	complemented
138	C₂₃×C₂²⋊C₈	—	2	2	no	—
139	C₂₃×C₂²⋊C₈	D₄	1	4	yes	—
140	C₄×C₈×C₂₃	—	2	2	no	—
141	C₂₃×#95	—	2	1	no	—
142	C₂₃×#95	—	2	1	no	—
143	C₂₃×#95	—	2	1	no	—
144	C₂₃×#95	—	2	1	no	—
145	C₂₃×#95	—	2	1	no	—
146	C₂₃×#95	—	2	1	no	—
147	C₂₃×#95	—	2	1	no	—
148	C₂₃×#95	—	2	1	no	—
149	C₂₃×#95	—	2	1	no	—
150	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
151	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
152	C₂×Q₈×C₂₃	—	2	1	no	—
153	C₂×Q₈×C₂₃	—	2	1	no	—
154	C₂×Q₈×C₂₃	—	2	8	no	—
155	C₂×Q₈×C₂₃	—	2	1	no	—
156	C₂×Q₈×C₂₃	—	2	1	no	—
157	C₂×Q₈×C₂₃	—	2	1	no	—
158	C₂×Q₈×C₂₃	—	2	1	no	—
159	C₂×Q₈×C₂₃	—	2	1	no	—
160	C₂×Q₈×C₂₃	—	2	1	no	—
161	C₂×Q₈×C₂₃	—	2	1	no	—
162	C₂×Q₈×C₂₃	—	2	1	no	—
163	C₂×Q₈×C₂₃	—	2	1	no	—
164	C₂×Q₈×C₂₃	—	2	1	no	—
165	C₂×Q₈×C₂₃	—	2	1	no	—
166	C₂×Q₈×C₂₃	—	2	1	no	—
167	C₂×Q₈×C₂₃	—	2	1	no	—
168	C₂×Q₈×C₂₃	—	2	1	no	—
169	C₂×Q₈×C₂₃	—	4	2	no	—
170	C₂×Q₈×C₂₃	—	4	2	no	—
171	C₂×Q₈×C₂₃	—	4	4	no	—
172	C₂×Q₈×C₂₃	—	4	4	no	—
173	C₂×Q₈×C₂₃	—	4	4	no	—
174	C₂×Q₈×C₂₃	—	4	2	no	—
175	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
176	C₂×Q₈×C₂₃	#41	1	2	yes	—
177	C₂×D₄×C₂₃	—	2	2	no	—
178	C₂×D₄×C₂₃	—	2	2	no	—
179	C₂×D₄×C₂₃	—	4	1	no	—
180	C₂²×C₄×C₂₃	—	2	1	no	—
181	C₂²×C₄×C₂₃	—	2	1	no	—
182	C₂²×C₄×C₂₃	—	2	1	no	—
183	C₂²×C₄×C₂₃	—	2	1	no	—
184	C₂²×C₄×C₂₃	—	2	1	no	—
185	C₂²×C₄×C₂₃	—	2	1	no	—
186	C₂²×C₄×C₂₃	—	2	1	no	—
187	C₂²×C₄×C₂₃	—	2	1	no	—
188	C₂²×C₄×C₂₃	—	2	1	no	—
189	C₂²×C₄×C₂₃	—	2	1	no	—
190	C₂²×C₄×C₂₃	—	2	1	no	—
191	C₂²×C₄×C₂₃	—	2	1	no	—
192	C₂²×C₄×C₂₃	—	2	1	no	—
193	C₂²×C₄×C₂₃	—	2	1	no	—
194	C₂²×C₄×C₂₃	—	2	1	no	—
195	C₂²×C₄×C₂₃	—	2	1	no	—
196	C₂²×C₄×C₂₃	—	2	1	no	—
197	C₂²×C₄×C₂₃	—	2	1	no	—
198	C₂²×C₄×C₂₃	—	4	2	no	—
199	C₂²×C₄×C₂₃	—	4	2	no	—
200	C₂²×C₄×C₂₃	—	4	2	no	—
201	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₂₃	#41	1	2	yes	—
207	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
208	Q₁₆×C₂₃	—	4	4	no	—
209	Q₁₆×C₂₃	—	4	4	no	—
210	M₁₆×C₂₃	—	4	4	no	—
211	M₁₆×C₂₃	—	4	4	no	—
212	C₂×C₈×C₂₃	—	2	1	no	—
213	C₂×C₈×C₂₃	—	2	1	no	—
214	C₂×C₈×C₂₃	—	2	1	no	—
215	C₂×C₈×C₂₃	—	2	1	no	—
216	C₂×C₈×C₂₃	—	2	1	no	—
217	C₂×C₈×C₂₃	—	2	1	no	—
218	C₂×C₈×C₂₃	—	2	1	no	—
219	C₂×C₈×C₂₃	—	2	1	no	—
220	C₂×C₈×C₂₃	—	2	1	no	—
221	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
222	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
223	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
224	C₄⋊C₄×C₂₃	—	2	2	no	—
225	C₄⋊C₄×C₂₃	—	2	1	no	—
226	C₄⋊C₄×C₂₃	—	2	1	no	—
227	C₄⋊C₄×C₂₃	—	2	1	no	—
228	C₄⋊C₄×C₂₃	—	2	1	no	—
229	C₄⋊C₄×C₂₃	—	2	1	no	—
230	C₄⋊C₄×C₂₃	—	2	1	no	—
231	C₄⋊C₄×C₂₃	—	2	1	no	—
232	C₄⋊C₄×C₂₃	—	2	1	no	—
233	C₄⋊C₄×C₂₃	—	2	1	no	—
234	C₄⋊C₄×C₂₃	—	4	2	no	—
235	C₄⋊C₄×C₂₃	—	4	2	no	—
236	C₄⋊C₄×C₂₃	—	4	2	no	—
237	C₄⋊C₄×C₂₃	—	4	2	no	—
238	C₄⋊C₄×C₂₃	—	4	2	no	—
239	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
240	C₂²⋊C₄×C₂₃	—	2	2	no	—
241	C₂²⋊C₄×C₂₃	—	2	2	no	—
242	C₂²⋊C₄×C₂₃	—	4	2	no	—
243	C₂²⋊C₄×C₂₃	—	4	2	no	—
244	C₂²⋊C₄×C₂₃	—	4	2	no	—
245	C₂²⋊C₄×C₂₃	—	4	2	no	—
246	C₂²⋊C₄×C₂₃	—	4	2	no	—
247	C₂²⋊C₄×C₂₃	—	4	2	no	—
248	C₂²⋊C₄×C₂₃	—	4	2	no	—
249	C₄²×C₂₃	—	2	1	no	—
250	C₄²×C₂₃	—	2	1	no	—
251	C₄²×C₂₃	—	4	2	no	—
252	#25134	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₂³×C₂₃	—	2	1	no	—
254	C₂³×C₂₃	—	2	1	no	—
255	C₂³×C₂₃	—	2	1	no	—
256	C₂³×C₂₃	—	2	1	no	—
257	C₂³×C₂₃	—	2	1	no	—
258	C₂³×C₂₃	—	2	1	no	—
259	C₂³×C₂₃	—	2	1	no	—
260	C₂³×C₂₃	—	2	1	no	—
261	C₂³×C₂₃	—	2	1	no	—
262	C₂³×C₂₃	—	2	1	no	—
263	C₂³×C₂₃	—	2	1	no	—
264	C₂³×C₂₃	—	2	1	no	—
265	C₂³×C₂₃	—	2	1	no	—
266	C₂³×C₂₃	#121	1	2	yes	—
267	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
268	Q₈×C₂₃	—	2	2	no	—
269	Q₈×C₂₃	—	2	2	no	—
270	Q₈×C₂₃	—	2	2	no	—
271	Q₈×C₂₃	—	2	2	no	—
272	Q₈×C₂₃	—	4	8	no	—
273	Q₈×C₂₃	—	4	1	no	—
274	Q₈×C₂₃	—	4	1	no	—
275	Q₈×C₂₃	—	4	1	no	—
276	Q₈×C₂₃	—	4	1	no	—
277	Q₈×C₂₃	—	4	1	no	—
278	Q₈×C₂₃	—	4	1	no	—
279	Q₈×C₂₃	—	4	1	no	—
280	Q₈×C₂₃	—	4	1	no	—
281	D₄×C₂₃	—	4	4	no	—
282	C₂×C₄×C₂₃	—	2	1	no	—
283	C₂×C₄×C₂₃	—	2	1	no	—
284	C₂×C₄×C₂₃	—	2	1	no	—
285	C₂×C₄×C₂₃	—	2	1	no	—
286	C₂×C₄×C₂₃	—	2	2	no	—
287	C₂×C₄×C₂₃	—	2	2	no	—
288	C₂×C₄×C₂₃	—	2	2	no	—
289	C₂×C₄×C₂₃	—	2	2	no	—
290	C₂×C₄×C₂₃	—	2	1	no	—
291	C₂×C₄×C₂₃	—	2	1	no	—
292	C₂×C₄×C₂₃	—	2	2	no	—
293	C₂×C₄×C₂₃	—	2	2	no	—
294	C₂×C₄×C₂₃	—	2	1	no	—
295	C₂×C₄×C₂₃	—	2	2	no	—
296	C₂×C₄×C₂₃	—	2	1	no	—
297	C₂×C₄×C₂₃	—	2	1	no	—
298	C₂×C₄×C₂₃	—	2	1	no	—
299	C₂×C₄×C₂₃	—	4	8	no	—
300	C₂×C₄×C₂₃	—	4	1	no	—
301	C₂×C₄×C₂₃	—	4	1	no	—
302	C₂×C₄×C₂₃	—	4	1	no	—
303	C₂×C₄×C₂₃	—	4	1	no	—
304	C₂×C₄×C₂₃	—	4	1	no	—
305	C₂×C₄×C₂₃	—	4	1	no	—
306	C₂×C₄×C₂₃	—	4	1	no	—
307	C₂×C₄×C₂₃	—	4	1	no	—
308	C₂×C₄×C₂₃	—	4	1	no	—
309	C₂×C₄×C₂₃	—	4	1	no	—
310	C₂×C₄×C₂₃	—	4	1	no	—
311	C₂×C₄×C₂₃	—	4	1	no	—
312	C₂×C₄×C₂₃	—	4	1	no	—
313	C₂×C₄×C₂₃	—	4	1	no	—
314	C₂×C₄×C₂₃	—	4	1	no	—
315	C₂×C₄×C₂₃	—	4	1	no	—
316	C₂×C₄×C₂₃	—	4	1	no	—
317	C₂×C₄×C₂₃	—	4	1	no	—
318	C₂×C₄×C₂₃	—	4	1	no	—
319	C₂×C₄×C₂₃	—	4	1	no	—
320	C₂×C₄×C₂₃	—	4	1	no	—
321	C₂×C₄×C₂₃	—	4	1	no	—
322	C₂×C₄×C₂₃	—	4	1	no	—
323	C₂×C₄×C₂₃	—	4	1	no	—
324	C₂×C₄×C₂₃	—	4	1	no	—
325	C₂×C₄×C₂₃	#121	1	2	yes	—
326	C₂×C₄×C₂₃	#137	1	2	yes	—
327	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
330	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
331	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
332	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
333	C₈×C₂₃	—	2	2	no	—
334	C₈×C₂₃	—	2	2	no	—
335	C₈×C₂₃	—	2	2	no	—
336	C₈×C₂₃	—	4	1	no	—
337	C₂×#470	C₂×C₂₃	1	1	yes	characteristic, complemented
338	C₂×#451	C₂×C₂₃	1	1	yes	characteristic, complemented
339	C₂×#436	C₂×C₂₃	1	1	yes	characteristic
340	C₂×#419	C₂×C₂₃	1	1	yes	characteristic, complemented
341	#2415	C₂×C₂₃	1	1	yes	characteristic
342	#2409	C₂×C₂₃	1	1	yes	characteristic
343	#2066	C₂×C₂₃	1	1	yes	characteristic, complemented
344	#2056	C₂×C₂₃	1	1	yes	characteristic, complemented
345	#2036	C₂×C₂₃	1	1	yes	characteristic, complemented
346	#2001	C₂×C₂₃	1	1	yes	characteristic, complemented
347	#1969	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#1933	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#1894	C₂×C₂₃	1	1	yes	characteristic, complemented
350	#1894	C₂×C₂₃	1	1	yes	characteristic, complemented
351	#1854	C₂×C₂₃	1	1	yes	characteristic, complemented
352	C₂²×C₂₃	—	2	2	no	—
353	C₂²×C₂₃	—	2	2	no	—
354	C₂²×C₂₃	—	2	2	no	—
355	C₂²×C₂₃	—	4	1	no	—
356	C₂²×C₂₃	—	4	1	no	—
357	C₂²×C₂₃	—	4	1	no	—
358	C₂²×C₂₃	—	4	1	no	—
359	C₂²×C₂₃	—	4	1	no	—
360	C₂²×C₂₃	—	4	1	no	—
361	C₂²×C₂₃	—	4	1	no	—
362	C₂²×C₂₃	—	4	1	no	—
363	C₂²×C₂₃	—	4	1	no	—
364	C₂²×C₂₃	—	4	1	no	—
365	C₂²×C₂₃	—	4	1	no	—
366	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
367	C₂²×C₂₃	D₄²	1	1	yes	characteristic
368	C₂²×C₂₃	#546	1	1	yes	characteristic
369	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
370	C₂²×C₂₃	#575	1	1	yes	characteristic
371	C₂²×C₂₃	#578	1	1	yes	characteristic
372	C₂²×C₂₃	#578	1	1	yes	characteristic
373	C₄×C₂₃	—	2	2	no	—
374	C₄×C₂₃	—	2	2	no	—
375	C₄×C₂₃	—	4	1	no	—
376	C₄×C₂₃	—	4	2	no	—
377	C₄×C₂₃	—	4	2	no	—
378	C₄×C₂₃	—	4	2	no	—
379	C₄×C₂₃	—	4	1	no	—
380	C₄×C₂₃	—	8	1	no	—
381	C₄×C₂₃	—	8	1	no	—
382	C₄×C₂₃	—	8	1	no	—
383	C₄×C₂₃	—	8	1	no	—
384	C₄×C₂₃	—	8	1	no	—
385	C₄×C₂₃	#525	1	1	yes	characteristic
386	C₄×C₂₃	#538	1	1	yes	characteristic
387	C₄×C₂₃	D₄²	1	1	yes	characteristic
388	C₄×C₂₃	#546	1	1	yes	characteristic
389	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
390	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
391	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
392	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
393	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
394	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
395	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
396	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
397	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
398	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
399	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
400	#470	—	2	4	no	—
401	#451	—	2	4	no	—
402	#436	—	2	4	no	—
403	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
404	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
405	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
406	#419	—	2	4	no	—
407	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
408	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
409	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
410	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
411	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
412	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
413	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
414	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
415	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
416	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
418	#397	—	2	1	no	—
419	#395	—	2	1	no	—
420	#394	—	2	1	no	—
421	#393	—	2	1	no	—
422	#391	C₂²×C₂₃	1	1	yes	characteristic
423	#391	C₂²×C₂₃	1	1	yes	characteristic
424	#391	C₂²×C₂₃	1	1	yes	characteristic
425	#389	—	2	1	no	—
426	#389	C₂²×C₂₃	1	1	yes	characteristic
427	#388	—	2	1	no	—
428	#386	—	2	1	no	—
429	#385	—	2	1	no	—
430	#380	C₂²×C₂₃	1	1	yes	characteristic
431	#380	C₂²×C₂₃	1	1	yes	characteristic
432	#340	C₂²×C₂₃	1	1	yes	characteristic
433	#340	C₂²×C₂₃	1	1	yes	characteristic
434	#340	C₂²×C₂₃	1	1	yes	characteristic
435	#340	C₂²×C₂₃	1	1	yes	characteristic
436	C₂×C₂₃	—	4	2	no	—
437	C₂×C₂₃	—	8	1	no	—
438	C₂×C₂₃	#2424	1	1	yes	characteristic
439	C₂×C₂₃	#3056	1	1	yes	characteristic
440	C₂×C₂₃	#3059	1	1	yes	characteristic
441	C₂×C₂₃	#3276	1	1	yes	characteristic
442	C₂×C₂₃	#3277	1	1	yes	characteristic
443	C₂×C₂₃	#3327	1	1	yes	characteristic
444	C₂×C₂₃	#3328	1	1	yes	characteristic
445	C₂²×Q₈	—	2	1	no	—
446	C₂²×Q₈	—	2	2	no	—
447	C₂²×Q₈	—	2	2	no	—
448	C₂²×Q₈	—	2	2	no	—
449	C₂²×Q₈	—	2	2	no	—
450	C₂²×Q₈	—	4	1	no	—
451	C₂²×Q₈	—	4	1	no	—
452	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
453	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
454	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
455	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
456	C₂³×C₄	—	2	1	no	—
457	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
458	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
459	C₂×Q₁₆	—	2	2	no	—
460	C₂×Q₁₆	—	2	2	no	—
461	C₂×Q₁₆	—	2	2	no	—
462	C₂×Q₁₆	—	2	2	no	—
463	C₂×Q₁₆	—	4	1	no	—
464	C₂×Q₁₆	—	4	1	no	—
465	C₂×M₁₆	—	2	2	no	—
466	C₂×M₁₆	—	2	2	no	—
467	C₂×M₁₆	—	2	2	no	—
468	C₂×M₁₆	—	2	2	no	—
469	C₂×M₁₆	—	4	1	no	—
470	C₂×M₁₆	—	4	1	no	—
471	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
475	C₂²⋊Q₈	—	2	2	no	—
476	C₂²⋊Q₈	—	2	2	no	—
477	C₂²⋊Q₈	—	2	2	no	—
478	C₂²⋊Q₈	—	2	2	no	—
479	C₂²⋊Q₈	—	2	2	no	—
480	C₂²⋊Q₈	—	4	1	no	—
481	C₂²⋊Q₈	—	4	1	no	—
482	C₂²⋊Q₈	—	4	1	no	—
483	C₄×D₄	—	2	2	no	—
484	C₄×D₄	—	2	2	no	—
485	#117	—	2	2	no	—
486	#117	—	4	1	no	—
487	C₂×C₄⋊C₄	—	2	1	no	—
488	C₂×C₄⋊C₄	—	2	1	no	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	—	2	1	no	—
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
506	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
507	C₂×C₄²	—	2	1	no	—
508	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
509	#107	—	4	1	no	—
510	#106	—	2	2	no	—
511	C₄⋊C₈	—	2	2	no	—
512	#103	—	2	2	no	—
513	#103	—	2	2	no	—
514	#103	—	2	2	no	—
515	#103	—	2	2	no	—
516	#103	—	2	2	no	—
517	#103	—	2	2	no	—
518	#103	—	4	1	no	—
519	#103	D₄×C₂₃	1	4	yes	complemented
520	C₂²⋊C₈	—	2	2	no	—
521	C₂²⋊C₈	D₄×C₂₃	1	4	yes	—
522	C₄×C₈	—	2	2	no	—
523	#95	—	2	1	no	—
524	#95	—	2	1	no	—
525	#95	—	2	1	no	—
526	#95	—	2	1	no	—
527	#95	—	2	1	no	—
528	#95	—	2	1	no	—
529	#95	—	2	1	no	—
530	#95	—	2	1	no	—
531	#95	—	2	1	no	—
532	C₂₃	#25134	1	1	yes	characteristic, direct product factor, Sylow
533	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
534	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	8	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	1	no	—
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	—	2	1	no	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	4	2	no	—
553	C₂×Q₈	—	4	2	no	—
554	C₂×Q₈	—	4	4	no	—
555	C₂×Q₈	—	4	4	no	—
556	C₂×Q₈	—	4	4	no	—
557	C₂×Q₈	—	4	2	no	—
558	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
559	C₂×Q₈	#41×C₂₃	1	2	yes	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	4	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	4	2	no	—
582	C₂²×C₄	—	4	2	no	—
583	C₂²×C₄	—	4	2	no	—
584	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
586	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
588	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
589	C₂²×C₄	#41×C₂₃	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
591	Q₁₆	—	4	4	no	—
592	Q₁₆	—	4	4	no	—
593	M₁₆	—	4	4	no	—
594	M₁₆	—	4	4	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	2	1	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
605	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
606	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	4	2	no	—
618	C₄⋊C₄	—	4	2	no	—
619	C₄⋊C₄	—	4	2	no	—
620	C₄⋊C₄	—	4	2	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
623	C₂²⋊C₄	—	2	2	no	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	4	2	no	—
626	C₂²⋊C₄	—	4	2	no	—
627	C₂²⋊C₄	—	4	2	no	—
628	C₂²⋊C₄	—	4	2	no	—
629	C₂²⋊C₄	—	4	2	no	—
630	C₂²⋊C₄	—	4	2	no	—
631	C₂²⋊C₄	—	4	2	no	—
632	C₄²	—	2	1	no	—
633	C₄²	—	2	1	no	—
634	C₄²	—	4	2	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	C₂₃×#121	1	2	yes	—
649	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
650	Q₈	—	2	2	no	—
651	Q₈	—	2	2	no	—
652	Q₈	—	2	2	no	—
653	Q₈	—	2	2	no	—
654	Q₈	—	4	8	no	—
655	Q₈	—	4	1	no	—
656	Q₈	—	4	1	no	—
657	Q₈	—	4	1	no	—
658	Q₈	—	4	1	no	—
659	Q₈	—	4	1	no	—
660	Q₈	—	4	1	no	—
661	Q₈	—	4	1	no	—
662	Q₈	—	4	1	no	—
663	D₄	—	4	4	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	4	8	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	C₂₃×#121	1	2	yes	—
708	C₂×C₄	C₂₃×#137	1	2	yes	—
709	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
711	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
712	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
713	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
714	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
715	C₈	—	2	2	no	—
716	C₈	—	2	2	no	—
717	C₈	—	2	2	no	—
718	C₈	—	4	1	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	4	1	no	—
723	C₂²	—	4	1	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	1	no	—
733	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
734	C₂²	D₄²×C₂₃	1	1	yes	characteristic
735	C₂²	C₂₃×#546	1	1	yes	characteristic
736	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
737	C₂²	C₂₃×#575	1	1	yes	characteristic
738	C₂²	C₂₃×#578	1	1	yes	characteristic
739	C₂²	C₂₃×#578	1	1	yes	characteristic
740	C₄	—	2	2	no	—
741	C₄	—	2	2	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	1	no	—
747	C₄	—	8	1	no	—
748	C₄	—	8	1	no	—
749	C₄	—	8	1	no	—
750	C₄	—	8	1	no	—
751	C₄	—	8	1	no	—
752	C₄	C₂₃×#525	1	1	yes	characteristic
753	C₄	C₂₃×#538	1	1	yes	characteristic
754	C₄	D₄²×C₂₃	1	1	yes	characteristic
755	C₄	C₂₃×#546	1	1	yes	characteristic
756	C₂	—	4	2	no	—
757	C₂	—	8	1	no	—
758	C₂	C₂₃×#2424	1	1	yes	characteristic
759	C₂	C₂₃×#3056	1	1	yes	characteristic
760	C₂	C₂₃×#3059	1	1	yes	characteristic
761	C₂	C₂₃×#3276	1	1	yes	characteristic
762	C₂	C₂₃×#3277	1	1	yes	characteristic
763	C₂	C₂₃×#3327	1	1	yes	characteristic
764	C₂	C₂₃×#3328	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂²×D₄×C₂₃	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#470	C₂	semidirect
2. C₂×C₂₃×#451	C₂	semidirect
4. C₂×C₂₃×#419	C₂	semidirect
7. C₂₃×#2066	C₂	semidirect
8. C₂₃×#2056	C₂	semidirect
9. C₂₃×#2036	C₂	semidirect
10. C₂₃×#2001	C₂	semidirect
11. C₂₃×#1969	C₂	semidirect
12. C₂₃×#1933	C₂	semidirect
13. C₂₃×#1894	C₂	semidirect
14. C₂₃×#1894	C₂	semidirect
15. C₂₃×#1854	C₂	semidirect
137. C₂₃×#103	D₄	semidirect
252. #25134	C₂₃	direct (N × H)
337. C₂×#470	C₂×C₂₃	semidirect
338. C₂×#451	C₂×C₂₃	semidirect
340. C₂×#419	C₂×C₂₃	semidirect
343. #2066	C₂×C₂₃	semidirect
344. #2056	C₂×C₂₃	semidirect
345. #2036	C₂×C₂₃	semidirect
346. #2001	C₂×C₂₃	semidirect
347. #1969	C₂×C₂₃	semidirect
348. #1933	C₂×C₂₃	semidirect
349. #1894	C₂×C₂₃	semidirect
350. #1894	C₂×C₂₃	semidirect
351. #1854	C₂×C₂₃	semidirect
519. #103	D₄×C₂₃	semidirect
532. C₂₃	#25134	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×#470	2
C₂×C₂₃×#451	2
C₂×C₂₃×#436	2
C₂×C₂₃×#419	2
C₂₃×#2415	2
C₂₃×#2409	2
C₂₃×#2066	2
C₂₃×#2056	2
C₂₃×#2036	2
C₂₃×#2001	2
C₂₃×#1969	2
C₂₃×#1933	2
C₂₃×#1894	2
C₂₃×#1854	2
#25134	23

Subgroups — C23×#25134 #19172760

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25134 #19172760