Subgroups — C₂₃×#25555 #19173181

Order 5888.

1136 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2414	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2025	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1875	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1873	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#552	—	2	4	no	—
19	C₂₃×#552	—	2	4	no	—
20	C₂×C₂₃×#126	—	2	1	no	—
21	C₂×C₂₃×#125	—	2	1	no	—
22	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#123	—	2	1	no	—
24	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#117	—	2	1	no	—
31	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂₃×#481	—	2	4	no	—
35	C₂₃×#468	—	2	4	no	—
36	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#106	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×#102	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂₃×#394	—	2	1	no	—
49	C₂₃×#392	—	2	1	no	—
50	C₂₃×#390	—	2	1	no	—
51	C₂₃×#390	C₂²	1	1	yes	characteristic
52	C₂₃×#389	C₂²	1	1	yes	characteristic
53	C₂₃×#388	—	2	1	no	—
54	C₂₃×#380	C₂²	1	1	yes	characteristic
55	C₂₃×#340	C₂²	1	1	yes	characteristic
56	C₂₃×#340	C₂²	1	1	yes	characteristic
57	C₂₃×#340	C₂²	1	1	yes	characteristic
58	C₂₃×#340	C₂²	1	1	yes	characteristic
59	C₂₃×#340	C₂²	1	1	yes	characteristic
60	C₂₃×#340	C₂²	1	1	yes	characteristic
61	C₂₃×#336	C₂²	1	1	yes	characteristic
62	C₂₃×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₂₃	—	2	1	no	—
65	C₂²×D₄×C₂₃	—	2	1	no	—
66	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
67	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₂₃	—	2	1	no	—
69	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
71	C₂×SD₁₆×C₂₃	—	2	2	no	—
72	C₂×SD₁₆×C₂₃	—	2	2	no	—
73	C₂×SD₁₆×C₂₃	—	4	1	no	—
74	C₂×M₁₆×C₂₃	—	2	2	no	—
75	C₂×M₁₆×C₂₃	—	2	2	no	—
76	C₂×M₁₆×C₂₃	—	4	1	no	—
77	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
81	C₂₃×#126	—	2	8	no	—
82	C₂₃×#125	—	2	8	no	—
83	C₂₃×#125	—	2	2	no	—
84	C₂₃×#125	—	2	2	no	—
85	C₂₃×#123	—	2	8	no	—
86	C₂₃×C₂²⋊Q₈	—	2	2	no	—
87	C₂₃×C₂²⋊Q₈	—	2	2	no	—
88	C₂₃×C₂²⋊Q₈	—	2	2	no	—
89	C₂₃×C₂²⋊Q₈	D₄	1	4	yes	complemented
90	C₂₃×#121	—	2	2	no	—
91	C₂₃×#121	—	2	2	no	—
92	C₂₃×#121	—	2	2	no	—
93	C₂₃×#121	—	4	1	no	—
94	C₄×Q₈×C₂₃	—	2	2	no	—
95	C₄×Q₈×C₂₃	—	2	2	no	—
96	C₄×D₄×C₂₃	—	2	2	no	—
97	C₄×D₄×C₂₃	—	2	2	no	—
98	C₂₃×#117	—	2	8	no	—
99	C₂₃×#117	—	2	2	no	—
100	C₂₃×#117	—	2	2	no	—
101	C₂₃×#117	—	2	2	no	—
102	C₂₃×#117	—	4	1	no	—
103	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
104	C₂×C₄⋊C₄×C₂₃	—	2	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	—	2	1	no	—
111	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₂₃	D₄	1	4	yes	complemented
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×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
130	C₂×C₄²×C₂₃	—	2	1	no	—
131	C₂×C₄²×C₂₃	—	2	1	no	—
132	C₂×C₄²×C₂₃	—	2	1	no	—
133	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
134	C₂₃×#107	—	2	2	no	—
135	C₂₃×#106	—	2	2	no	—
136	C₂₃×#106	—	2	2	no	—
137	C₂₃×#103	—	2	2	no	—
138	C₂₃×#103	—	2	2	no	—
139	C₂₃×#103	—	4	1	no	—
140	C₂₃×#102	—	2	2	no	—
141	C₂₃×#102	—	2	2	no	—
142	C₂₃×#102	—	2	2	no	—
143	C₂₃×C₂²⋊C₈	—	2	2	no	—
144	C₂₃×C₂²⋊C₈	—	2	2	no	—
145	C₂₃×C₂²⋊C₈	—	4	1	no	—
146	C₂₃×#95	—	2	1	no	—
147	C₂₃×#95	—	2	1	no	—
148	C₂⁴×C₂₃	—	2	1	no	—
149	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
150	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
151	C₂×Q₈×C₂₃	—	2	1	no	—
152	C₂×Q₈×C₂₃	—	2	1	no	—
153	C₂×Q₈×C₂₃	—	2	1	no	—
154	C₂×Q₈×C₂₃	—	2	1	no	—
155	C₂×Q₈×C₂₃	—	2	1	no	—
156	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
157	C₂×D₄×C₂₃	—	2	2	no	—
158	C₂×D₄×C₂₃	—	2	1	no	—
159	C₂×D₄×C₂₃	—	2	1	no	—
160	C₂×D₄×C₂₃	—	2	1	no	—
161	C₂×D₄×C₂₃	—	2	1	no	—
162	C₂×D₄×C₂₃	—	2	1	no	—
163	C₂×D₄×C₂₃	—	2	1	no	—
164	C₂×D₄×C₂₃	—	4	1	no	—
165	C₂×D₄×C₂₃	—	4	1	no	—
166	C₂×D₄×C₂₃	—	4	2	no	—
167	C₂×D₄×C₂₃	—	4	2	no	—
168	C₂×D₄×C₂₃	—	4	2	no	—
169	C₂×D₄×C₂₃	—	8	1	no	—
170	C₂×D₄×C₂₃	—	8	1	no	—
171	C₂×D₄×C₂₃	—	8	1	no	—
172	C₂²×C₄×C₂₃	—	2	1	no	—
173	C₂²×C₄×C₂₃	—	2	1	no	—
174	C₂²×C₄×C₂₃	—	2	1	no	—
175	C₂²×C₄×C₂₃	—	2	1	no	—
176	C₂²×C₄×C₂₃	—	2	4	no	—
177	C₂²×C₄×C₂₃	—	2	1	no	—
178	C₂²×C₄×C₂₃	—	2	1	no	—
179	C₂²×C₄×C₂₃	—	2	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	—	4	2	no	—
191	C₂²×C₄×C₂₃	—	4	2	no	—
192	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
199	SD₁₆×C₂₃	—	4	4	no	—
200	M₁₆×C₂₃	—	4	4	no	—
201	C₂×C₈×C₂₃	—	2	1	no	—
202	C₂×C₈×C₂₃	—	2	1	no	—
203	C₂×C₈×C₂₃	—	2	1	no	—
204	C₂×C₈×C₂₃	—	2	1	no	—
205	C₂×C₈×C₂₃	—	2	1	no	—
206	C₂×C₈×C₂₃	—	2	1	no	—
207	C₂×C₈×C₂₃	—	2	1	no	—
208	C₂×C₈×C₂₃	—	2	1	no	—
209	C₂×C₈×C₂₃	—	2	1	no	—
210	C₂×C₈×C₂₃	—	2	1	no	—
211	C₂×C₈×C₂₃	—	2	1	no	—
212	C₂×C₈×C₂₃	#41	1	2	yes	—
213	C₄⋊C₄×C₂₃	—	2	4	no	—
214	C₄⋊C₄×C₂₃	—	2	4	no	—
215	C₄⋊C₄×C₂₃	—	2	4	no	—
216	C₄⋊C₄×C₂₃	—	2	4	no	—
217	C₄⋊C₄×C₂₃	—	2	4	no	—
218	C₄⋊C₄×C₂₃	—	2	4	no	—
219	C₄⋊C₄×C₂₃	—	2	2	no	—
220	C₄⋊C₄×C₂₃	—	2	1	no	—
221	C₄⋊C₄×C₂₃	—	2	1	no	—
222	C₄⋊C₄×C₂₃	—	2	1	no	—
223	C₄⋊C₄×C₂₃	—	2	1	no	—
224	C₄⋊C₄×C₂₃	—	2	1	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	—	8	1	no	—
229	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
230	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
231	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
232	C₄⋊C₄×C₂₃	#41	1	2	yes	—
233	C₂²⋊C₄×C₂₃	—	2	4	no	—
234	C₂²⋊C₄×C₂₃	—	2	4	no	—
235	C₂²⋊C₄×C₂₃	—	2	4	no	—
236	C₂²⋊C₄×C₂₃	—	2	2	no	—
237	C₂²⋊C₄×C₂₃	—	2	2	no	—
238	C₂²⋊C₄×C₂₃	—	4	2	no	—
239	C₂²⋊C₄×C₂₃	—	4	2	no	—
240	C₂²⋊C₄×C₂₃	—	4	2	no	—
241	C₂²⋊C₄×C₂₃	—	4	2	no	—
242	C₂²⋊C₄×C₂₃	—	8	1	no	—
243	C₂²⋊C₄×C₂₃	—	8	1	no	—
244	C₄²×C₂₃	—	2	4	no	—
245	C₄²×C₂₃	—	2	4	no	—
246	C₄²×C₂₃	—	2	1	no	—
247	C₄²×C₂₃	—	2	1	no	—
248	C₄²×C₂₃	—	4	2	no	—
249	#25555	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂³×C₂₃	—	2	1	no	—
251	C₂³×C₂₃	—	2	1	no	—
252	C₂³×C₂₃	—	2	1	no	—
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	—	4	1	no	—
264	C₂³×C₂₃	—	4	1	no	—
265	C₂³×C₂₃	—	4	1	no	—
266	C₂³×C₂₃	—	4	1	no	—
267	C₂³×C₂₃	—	4	1	no	—
268	C₂³×C₂₃	—	4	1	no	—
269	C₂³×C₂₃	—	4	1	no	—
270	C₂³×C₂₃	#120	1	2	yes	—
271	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
272	Q₈×C₂₃	—	2	2	no	—
273	Q₈×C₂₃	—	2	2	no	—
274	Q₈×C₂₃	—	4	1	no	—
275	Q₈×C₂₃	—	4	1	no	—
276	D₄×C₂₃	—	4	4	no	—
277	D₄×C₂₃	—	4	1	no	—
278	D₄×C₂₃	—	4	1	no	—
279	D₄×C₂₃	—	4	1	no	—
280	D₄×C₂₃	—	4	1	no	—
281	D₄×C₂₃	—	8	4	no	—
282	D₄×C₂₃	—	8	4	no	—
283	C₂×C₄×C₂₃	—	2	1	no	—
284	C₂×C₄×C₂₃	—	2	1	no	—
285	C₂×C₄×C₂₃	—	2	2	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	1	no	—
290	C₂×C₄×C₂₃	—	2	1	no	—
291	C₂×C₄×C₂₃	—	2	2	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	2	no	—
297	C₂×C₄×C₂₃	—	2	1	no	—
298	C₂×C₄×C₂₃	—	2	1	no	—
299	C₂×C₄×C₂₃	—	2	1	no	—
300	C₂×C₄×C₂₃	—	2	1	no	—
301	C₂×C₄×C₂₃	—	2	1	no	—
302	C₂×C₄×C₂₃	—	2	1	no	—
303	C₂×C₄×C₂₃	—	4	8	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	#120	1	2	yes	—
325	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
328	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
329	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
331	C₈×C₂₃	—	2	2	no	—
332	C₈×C₂₃	—	4	1	no	—
333	C₈×C₂₃	—	4	1	no	—
334	C₈×C₂₃	—	4	1	no	—
335	C₂×#552	C₂×C₂₃	1	1	yes	characteristic, complemented
336	C₂×#481	C₂×C₂₃	1	1	yes	characteristic, complemented
337	C₂×#468	C₂×C₂₃	1	1	yes	characteristic, complemented
338	#2414	C₂×C₂₃	1	1	yes	characteristic
339	#2059	C₂×C₂₃	1	1	yes	characteristic, complemented
340	#2035	C₂×C₂₃	1	1	yes	characteristic, complemented
341	#2025	C₂×C₂₃	1	1	yes	characteristic, complemented
342	#2000	C₂×C₂₃	1	1	yes	characteristic, complemented
343	#1880	C₂×C₂₃	1	1	yes	characteristic, complemented
344	#1875	C₂×C₂₃	1	1	yes	characteristic, complemented
345	#1873	C₂×C₂₃	1	1	yes	characteristic, complemented
346	#1870	C₂×C₂₃	1	1	yes	characteristic, complemented
347	#1865	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#1854	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#1736	C₂×C₂₃	1	1	yes	characteristic, complemented
350	C₂²×C₂₃	—	2	2	no	—
351	C₂²×C₂₃	—	2	2	no	—
352	C₂²×C₂₃	—	2	2	no	—
353	C₂²×C₂₃	—	4	1	no	—
354	C₂²×C₂₃	—	4	1	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	—	8	1	no	—
365	C₂²×C₂₃	—	8	1	no	—
366	C₂²×C₂₃	—	8	1	no	—
367	C₂²×C₂₃	—	8	1	no	—
368	C₂²×C₂₃	—	8	1	no	—
369	C₂²×C₂₃	—	8	1	no	—
370	C₂²×C₂₃	—	8	1	no	—
371	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
372	C₂²×C₂₃	#546	1	1	yes	characteristic
373	C₂²×C₂₃	#547	1	1	yes	characteristic
374	C₂²×C₂₃	#575	1	1	yes	characteristic
375	C₂²×C₂₃	#575	1	1	yes	characteristic
376	C₂²×C₂₃	#577	1	1	yes	characteristic
377	C₂²×C₂₃	#577	1	1	yes	characteristic
378	C₄×C₂₃	—	2	2	no	—
379	C₄×C₂₃	—	4	1	no	—
380	C₄×C₂₃	—	4	2	no	—
381	C₄×C₂₃	—	4	1	no	—
382	C₄×C₂₃	—	4	2	no	—
383	C₄×C₂₃	—	4	2	no	—
384	C₄×C₂₃	—	4	1	no	—
385	C₄×C₂₃	—	4	2	no	—
386	C₄×C₂₃	—	4	2	no	—
387	C₄×C₂₃	—	8	1	no	—
388	C₄×C₂₃	—	8	1	no	—
389	C₄×C₂₃	#532	1	1	yes	characteristic
390	C₄×C₂₃	#537	1	1	yes	characteristic
391	C₄×C₂₃	#546	1	1	yes	characteristic
392	C₄×C₂₃	#547	1	1	yes	characteristic
393	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
394	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
395	#552	—	2	4	no	—
396	#552	—	2	4	no	—
397	C₂×#126	—	2	1	no	—
398	C₂×#125	—	2	1	no	—
399	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
400	C₂×#123	—	2	1	no	—
401	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
402	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
403	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
404	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
405	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
406	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
407	C₂×#117	—	2	1	no	—
408	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
409	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
410	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
411	#481	—	2	4	no	—
412	#468	—	2	4	no	—
413	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
414	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
415	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
416	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
418	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
419	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
420	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
421	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
424	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
425	#394	—	2	1	no	—
426	#392	—	2	1	no	—
427	#390	—	2	1	no	—
428	#390	C₂²×C₂₃	1	1	yes	characteristic
429	#389	C₂²×C₂₃	1	1	yes	characteristic
430	#388	—	2	1	no	—
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	#340	C₂²×C₂₃	1	1	yes	characteristic
437	#340	C₂²×C₂₃	1	1	yes	characteristic
438	#336	C₂²×C₂₃	1	1	yes	characteristic
439	#336	C₂²×C₂₃	1	1	yes	characteristic
440	C₂×C₂₃	—	4	2	no	—
441	C₂×C₂₃	—	8	1	no	—
442	C₂×C₂₃	—	16	1	no	—
443	C₂×C₂₃	#2430	1	1	yes	characteristic
444	C₂×C₂₃	#3005	1	1	yes	characteristic
445	C₂×C₂₃	#3010	1	1	yes	characteristic
446	C₂×C₂₃	#3317	1	1	yes	characteristic
447	C₂×C₂₃	#3323	1	1	yes	characteristic
448	C₂×C₂₃	#3348	1	1	yes	characteristic
449	C₂×C₂₃	#3351	1	1	yes	characteristic
450	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
451	C₂²×D₄	—	2	1	no	—
452	C₂²×D₄	—	2	1	no	—
453	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
454	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
455	C₂³×C₄	—	2	1	no	—
456	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
458	C₂×SD₁₆	—	2	2	no	—
459	C₂×SD₁₆	—	2	2	no	—
460	C₂×SD₁₆	—	4	1	no	—
461	C₂×M₁₆	—	2	2	no	—
462	C₂×M₁₆	—	2	2	no	—
463	C₂×M₁₆	—	4	1	no	—
464	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
465	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
466	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
467	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
468	#126	—	2	8	no	—
469	#125	—	2	8	no	—
470	#125	—	2	2	no	—
471	#125	—	2	2	no	—
472	#123	—	2	8	no	—
473	C₂²⋊Q₈	—	2	2	no	—
474	C₂²⋊Q₈	—	2	2	no	—
475	C₂²⋊Q₈	—	2	2	no	—
476	C₂²⋊Q₈	D₄×C₂₃	1	4	yes	complemented
477	#121	—	2	2	no	—
478	#121	—	2	2	no	—
479	#121	—	2	2	no	—
480	#121	—	4	1	no	—
481	C₄×Q₈	—	2	2	no	—
482	C₄×Q₈	—	2	2	no	—
483	C₄×D₄	—	2	2	no	—
484	C₄×D₄	—	2	2	no	—
485	#117	—	2	8	no	—
486	#117	—	2	2	no	—
487	#117	—	2	2	no	—
488	#117	—	2	2	no	—
489	#117	—	4	1	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	—	2	2	no	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
499	C₂×C₄⋊C₄	D₄×C₂₃	1	4	yes	complemented
500	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	—	2	1	no	—
519	C₂×C₄²	—	2	1	no	—
520	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
521	#107	—	2	2	no	—
522	#106	—	2	2	no	—
523	#106	—	2	2	no	—
524	#103	—	2	2	no	—
525	#103	—	2	2	no	—
526	#103	—	4	1	no	—
527	#102	—	2	2	no	—
528	#102	—	2	2	no	—
529	#102	—	2	2	no	—
530	C₂²⋊C₈	—	2	2	no	—
531	C₂²⋊C₈	—	2	2	no	—
532	C₂²⋊C₈	—	4	1	no	—
533	#95	—	2	1	no	—
534	#95	—	2	1	no	—
535	C₂₃	#25555	1	1	yes	characteristic, direct product factor, Sylow
536	C₂⁴	—	2	1	no	—
537	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
538	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
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	C₂×D₄×C₂₃	1	2	yes	—
545	C₂×D₄	—	2	2	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	4	1	no	—
553	C₂×D₄	—	4	1	no	—
554	C₂×D₄	—	4	2	no	—
555	C₂×D₄	—	4	2	no	—
556	C₂×D₄	—	4	2	no	—
557	C₂×D₄	—	8	1	no	—
558	C₂×D₄	—	8	1	no	—
559	C₂×D₄	—	8	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	4	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	—	4	2	no	—
579	C₂²×C₄	—	4	2	no	—
580	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
583	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
585	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
587	SD₁₆	—	4	4	no	—
588	M₁₆	—	4	4	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	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	#41×C₂₃	1	2	yes	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
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	—	8	1	no	—
617	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
618	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
619	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
620	C₄⋊C₄	#41×C₂₃	1	2	yes	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	2	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	—	8	1	no	—
631	C₂²⋊C₄	—	8	1	no	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	1	no	—
635	C₄²	—	2	1	no	—
636	C₄²	—	4	2	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	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	4	1	no	—
651	C₂³	—	4	1	no	—
652	C₂³	—	4	1	no	—
653	C₂³	—	4	1	no	—
654	C₂³	—	4	1	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	C₂₃×#120	1	2	yes	—
658	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
659	Q₈	—	2	2	no	—
660	Q₈	—	2	2	no	—
661	Q₈	—	4	1	no	—
662	Q₈	—	4	1	no	—
663	D₄	—	4	4	no	—
664	D₄	—	4	1	no	—
665	D₄	—	4	1	no	—
666	D₄	—	4	1	no	—
667	D₄	—	4	1	no	—
668	D₄	—	8	4	no	—
669	D₄	—	8	4	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	4	8	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	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	C₂₃×#120	1	2	yes	—
712	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
713	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
714	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
715	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
716	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
717	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
718	C₈	—	2	2	no	—
719	C₈	—	4	1	no	—
720	C₈	—	4	1	no	—
721	C₈	—	4	1	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	2	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	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	8	1	no	—
737	C₂²	—	8	1	no	—
738	C₂²	—	8	1	no	—
739	C₂²	—	8	1	no	—
740	C₂²	—	8	1	no	—
741	C₂²	—	8	1	no	—
742	C₂²	—	8	1	no	—
743	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
744	C₂²	C₂₃×#546	1	1	yes	characteristic
745	C₂²	C₂₃×#547	1	1	yes	characteristic
746	C₂²	C₂₃×#575	1	1	yes	characteristic
747	C₂²	C₂₃×#575	1	1	yes	characteristic
748	C₂²	C₂₃×#577	1	1	yes	characteristic
749	C₂²	C₂₃×#577	1	1	yes	characteristic
750	C₄	—	2	2	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	1	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	—	8	1	no	—
760	C₄	—	8	1	no	—
761	C₄	C₂₃×#532	1	1	yes	characteristic
762	C₄	C₂₃×#537	1	1	yes	characteristic
763	C₄	C₂₃×#546	1	1	yes	characteristic
764	C₄	C₂₃×#547	1	1	yes	characteristic
765	C₂	—	4	2	no	—
766	C₂	—	8	1	no	—
767	C₂	—	16	1	no	—
768	C₂	C₂₃×#2430	1	1	yes	characteristic
769	C₂	C₂₃×#3005	1	1	yes	characteristic
770	C₂	C₂₃×#3010	1	1	yes	characteristic
771	C₂	C₂₃×#3317	1	1	yes	characteristic
772	C₂	C₂₃×#3323	1	1	yes	characteristic
773	C₂	C₂₃×#3348	1	1	yes	characteristic
774	C₂	C₂₃×#3351	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂₃×#2414	C₂
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×#552	C₂	semidirect
2. C₂×C₂₃×#481	C₂	semidirect
3. C₂×C₂₃×#468	C₂	semidirect
5. C₂₃×#2059	C₂	semidirect
6. C₂₃×#2035	C₂	semidirect
7. C₂₃×#2025	C₂	semidirect
8. C₂₃×#2000	C₂	semidirect
9. C₂₃×#1880	C₂	semidirect
10. C₂₃×#1875	C₂	semidirect
11. C₂₃×#1873	C₂	semidirect
12. C₂₃×#1870	C₂	semidirect
13. C₂₃×#1865	C₂	semidirect
14. C₂₃×#1854	C₂	semidirect
15. C₂₃×#1736	C₂	semidirect
89. C₂₃×C₂²⋊Q₈	D₄	semidirect
112. C₂×C₄⋊C₄×C₂₃	D₄	semidirect
249. #25555	C₂₃	direct (N × H)
335. C₂×#552	C₂×C₂₃	semidirect
336. C₂×#481	C₂×C₂₃	semidirect
337. C₂×#468	C₂×C₂₃	semidirect
339. #2059	C₂×C₂₃	semidirect
340. #2035	C₂×C₂₃	semidirect
341. #2025	C₂×C₂₃	semidirect
342. #2000	C₂×C₂₃	semidirect
343. #1880	C₂×C₂₃	semidirect
344. #1875	C₂×C₂₃	semidirect
345. #1873	C₂×C₂₃	semidirect
346. #1870	C₂×C₂₃	semidirect
347. #1865	C₂×C₂₃	semidirect
348. #1854	C₂×C₂₃	semidirect
349. #1736	C₂×C₂₃	semidirect
476. C₂²⋊Q₈	D₄×C₂₃	semidirect
499. C₂×C₄⋊C₄	D₄×C₂₃	semidirect
535. C₂₃	#25555	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×#552	2
C₂×C₂₃×#481	2
C₂×C₂₃×#468	2
C₂₃×#2414	2
C₂₃×#2059	2
C₂₃×#2035	2
C₂₃×#2025	2
C₂₃×#2000	2
C₂₃×#1880	2
C₂₃×#1875	2
C₂₃×#1873	2
C₂₃×#1870	2
C₂₃×#1865	2
C₂₃×#1854	2
C₂₃×#1736	2
#25555	23

Subgroups — C23×#25555 #19173181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25555 #19173181