Subgroups — C₂₃×#25099 #19172725

Order 5888.

1104 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#468	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#448	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₃×#419	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2434	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2363	C₂	1	1	yes	maximal, characteristic
7	C₂₃×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2013	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1928	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1873	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#121	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×#468	—	2	4	no	—
28	C₂₃×#461	—	2	4	no	—
29	C₂₃×#448	—	2	4	no	—
30	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×C₄⋊C₈	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×#103	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂₃×#395	—	2	1	no	—
46	C₂₃×#395	—	2	1	no	—
47	C₂₃×#391	C₂²	1	1	yes	characteristic
48	C₂₃×#391	C₂²	1	1	yes	characteristic
49	C₂₃×#390	—	2	1	no	—
50	C₂₃×#390	C₂²	1	1	yes	characteristic
51	C₂₃×#389	C₂²	1	1	yes	characteristic
52	C₂₃×#388	—	2	1	no	—
53	C₂₃×#386	—	2	1	no	—
54	C₂₃×#385	—	2	1	no	—
55	C₂₃×#385	—	2	1	no	—
56	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
58	C₄×C₂²⋊C₄×C₂₃	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	—	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	—	2	1	no	—
74	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₂₃	—	2	1	no	—
76	C₂³×C₄×C₂₃	—	2	1	no	—
77	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
78	C₂×SD₁₆×C₂₃	—	2	2	no	—
79	C₂×SD₁₆×C₂₃	—	2	2	no	—
80	C₂×SD₁₆×C₂₃	—	2	2	no	—
81	C₂×SD₁₆×C₂₃	—	2	2	no	—
82	C₂×SD₁₆×C₂₃	—	2	2	no	—
83	C₂×SD₁₆×C₂₃	—	2	2	no	—
84	C₂×SD₁₆×C₂₃	—	4	1	no	—
85	C₂×SD₁₆×C₂₃	—	4	1	no	—
86	C₂×SD₁₆×C₂₃	—	4	1	no	—
87	C₂×M₁₆×C₂₃	—	2	2	no	—
88	C₂×M₁₆×C₂₃	—	2	2	no	—
89	C₂×M₁₆×C₂₃	—	4	1	no	—
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	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
94	C₂₃×C₄⋊Q₈	—	2	2	no	—
95	C₂₃×C₄⋊Q₈	—	2	2	no	—
96	C₂₃×C₄⋊Q₈	—	4	1	no	—
97	C₂₃×C₄⋊Q₈	—	4	1	no	—
98	C₂₃×C₂²⋊Q₈	—	2	2	no	—
99	C₂₃×C₂²⋊Q₈	—	2	2	no	—
100	C₂₃×#121	—	2	2	no	—
101	C₂₃×#121	D₄	1	4	yes	—
102	C₄×D₄×C₂₃	—	2	2	no	—
103	C₄×D₄×C₂₃	—	4	1	no	—
104	C₂₃×#117	—	2	2	no	—
105	C₂₃×#117	—	4	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	—	2	1	no	—
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	D₄	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
124	C₂×C₄²×C₂₃	—	2	1	no	—
125	C₂×C₄²×C₂₃	—	2	1	no	—
126	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
128	C₂₃×#107	—	2	2	no	—
129	C₂₃×C₄⋊C₈	—	2	2	no	—
130	C₂₃×C₄⋊C₈	—	4	1	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	—	2	2	no	—
137	C₂₃×#103	—	2	2	no	—
138	C₂₃×#103	—	4	1	no	—
139	C₂₃×#103	D₄	1	4	yes	complemented
140	C₂₃×#102	—	2	2	no	—
141	C₂₃×C₂²⋊C₈	—	2	2	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	D₄	1	1	yes	characteristic
149	C₂₃×#95	D₄	1	1	yes	characteristic
150	C₂⁴×C₂₃	—	2	1	no	—
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	4	no	—
178	C₂×D₄×C₂₃	—	2	1	no	—
179	C₂×D₄×C₂₃	—	2	1	no	—
180	C₂×D₄×C₂₃	—	2	1	no	—
181	C₂×D₄×C₂₃	—	2	1	no	—
182	C₂×D₄×C₂₃	—	2	1	no	—
183	C₂×D₄×C₂₃	—	8	1	no	—
184	C₂×D₄×C₂₃	—	8	1	no	—
185	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
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	—	4	2	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	—	4	2	no	—
202	C₂²×C₄×C₂₃	—	8	1	no	—
203	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
207	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₂₃	#41	1	2	yes	—
210	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
211	SD₁₆×C₂₃	—	4	4	no	—
212	SD₁₆×C₂₃	—	4	4	no	—
213	SD₁₆×C₂₃	—	4	4	no	—
214	M₁₆×C₂₃	—	4	4	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	—	2	1	no	—
222	C₂×C₈×C₂₃	—	2	1	no	—
223	C₂×C₈×C₂₃	—	2	1	no	—
224	C₂×C₈×C₂₃	—	2	1	no	—
225	C₂×C₈×C₂₃	—	2	1	no	—
226	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
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	—	4	2	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	—	8	1	no	—
239	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
240	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
241	C₂²⋊C₄×C₂₃	—	2	4	no	—
242	C₂²⋊C₄×C₂₃	—	2	2	no	—
243	C₂²⋊C₄×C₂₃	—	2	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	—	8	1	no	—
249	C₄²×C₂₃	—	2	1	no	—
250	C₄²×C₂₃	—	2	1	no	—
251	C₄²×C₂₃	—	2	1	no	—
252	C₄²×C₂₃	—	2	1	no	—
253	C₄²×C₂₃	—	4	2	no	—
254	C₄²×C₂₃	—	8	1	no	—
255	#25099	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	2	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	#121	1	2	yes	—
270	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
271	Q₈×C₂₃	—	2	2	no	—
272	Q₈×C₂₃	—	2	2	no	—
273	Q₈×C₂₃	—	2	2	no	—
274	Q₈×C₂₃	—	2	2	no	—
275	Q₈×C₂₃	—	4	8	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	Q₈×C₂₃	—	4	1	no	—
282	Q₈×C₂₃	—	4	1	no	—
283	Q₈×C₂₃	—	4	1	no	—
284	D₄×C₂₃	—	2	2	no	—
285	D₄×C₂₃	—	2	2	no	—
286	D₄×C₂₃	—	4	1	no	—
287	D₄×C₂₃	—	4	1	no	—
288	D₄×C₂₃	—	8	4	no	—
289	C₂×C₄×C₂₃	—	2	1	no	—
290	C₂×C₄×C₂₃	—	2	1	no	—
291	C₂×C₄×C₂₃	—	2	1	no	—
292	C₂×C₄×C₂₃	—	2	1	no	—
293	C₂×C₄×C₂₃	—	2	1	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	2	no	—
298	C₂×C₄×C₂₃	—	2	2	no	—
299	C₂×C₄×C₂₃	—	2	2	no	—
300	C₂×C₄×C₂₃	—	2	1	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	2	no	—
303	C₂×C₄×C₂₃	—	2	1	no	—
304	C₂×C₄×C₂₃	—	2	2	no	—
305	C₂×C₄×C₂₃	—	2	1	no	—
306	C₂×C₄×C₂₃	—	2	1	no	—
307	C₂×C₄×C₂₃	—	2	1	no	—
308	C₂×C₄×C₂₃	—	2	1	no	—
309	C₂×C₄×C₂₃	—	4	8	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	—	4	1	no	—
326	C₂×C₄×C₂₃	—	4	1	no	—
327	C₂×C₄×C₂₃	—	8	4	no	—
328	C₂×C₄×C₂₃	#121	1	2	yes	—
329	C₂×C₄×C₂₃	#137	1	2	yes	—
330	C₂×C₄×C₂₃	#137	1	2	yes	—
331	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
334	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
335	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
336	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
337	C₈×C₂₃	—	2	2	no	—
338	C₈×C₂₃	—	4	1	no	—
339	C₈×C₂₃	—	4	1	no	—
340	C₈×C₂₃	—	4	1	no	—
341	C₂×#468	C₂×C₂₃	1	1	yes	characteristic
342	C₂×#461	C₂×C₂₃	1	1	yes	characteristic, complemented
343	C₂×#448	C₂×C₂₃	1	1	yes	characteristic
344	C₂×#419	C₂×C₂₃	1	1	yes	characteristic, complemented
345	#2434	C₂×C₂₃	1	1	yes	characteristic, complemented
346	#2363	C₂×C₂₃	1	1	yes	characteristic
347	#2068	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#2055	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#2043	C₂×C₂₃	1	1	yes	characteristic, complemented
350	#2013	C₂×C₂₃	1	1	yes	characteristic, complemented
351	#1981	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#1928	C₂×C₂₃	1	1	yes	characteristic, complemented
353	#1877	C₂×C₂₃	1	1	yes	characteristic, complemented
354	#1873	C₂×C₂₃	1	1	yes	characteristic, complemented
355	#1851	C₂×C₂₃	1	1	yes	characteristic, complemented
356	C₂²×C₂₃	—	2	2	no	—
357	C₂²×C₂₃	—	2	2	no	—
358	C₂²×C₂₃	—	2	2	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	2	no	—
364	C₂²×C₂₃	—	4	2	no	—
365	C₂²×C₂₃	—	4	2	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	C₂×#121	1	1	yes	characteristic
371	C₂²×C₂₃	D₄²	1	1	yes	characteristic
372	C₂²×C₂₃	#546	1	1	yes	characteristic
373	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
374	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
375	C₂²×C₂₃	#577	1	1	yes	characteristic
376	C₂²×C₂₃	#577	1	1	yes	characteristic
377	C₄×C₂₃	—	2	2	no	—
378	C₄×C₂₃	—	2	2	no	—
379	C₄×C₂₃	—	2	2	no	—
380	C₄×C₂₃	—	4	1	no	—
381	C₄×C₂₃	—	4	2	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	—	8	1	no	—
387	C₄×C₂₃	—	8	1	no	—
388	C₄×C₂₃	—	8	1	no	—
389	C₄×C₂₃	#525	1	1	yes	characteristic
390	C₄×C₂₃	#538	1	1	yes	characteristic
391	C₄×C₂₃	D₄²	1	1	yes	characteristic
392	C₄×C₂₃	#546	1	1	yes	characteristic
393	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
394	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
395	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
396	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
397	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
398	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
399	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
400	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
401	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
402	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
403	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
404	#468	—	2	4	no	—
405	#461	—	2	4	no	—
406	#448	—	2	4	no	—
407	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
408	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
409	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
410	#419	—	2	4	no	—
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×#103	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×#103	C₂²×C₂₃	1	1	yes	characteristic
420	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
421	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
422	#395	—	2	1	no	—
423	#395	—	2	1	no	—
424	#391	C₂²×C₂₃	1	1	yes	characteristic
425	#391	C₂²×C₂₃	1	1	yes	characteristic
426	#390	—	2	1	no	—
427	#390	C₂²×C₂₃	1	1	yes	characteristic
428	#389	C₂²×C₂₃	1	1	yes	characteristic
429	#388	—	2	1	no	—
430	#386	—	2	1	no	—
431	#385	—	2	1	no	—
432	#385	—	2	1	no	—
433	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
434	C₄×C₂²⋊C₄	—	2	1	no	—
435	C₄×C₂²⋊C₄	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	2	no	—
442	C₂×C₂₃	#2424	1	1	yes	characteristic
443	C₂×C₂₃	#3039	1	1	yes	characteristic
444	C₂×C₂₃	#3042	1	1	yes	characteristic
445	C₂×C₂₃	#3266	1	1	yes	characteristic
446	C₂×C₂₃	#3278	1	1	yes	characteristic
447	C₂×C₂₃	#3320	1	1	yes	characteristic
448	C₂×C₂₃	#3329	1	1	yes	characteristic
449	C₂²×Q₈	—	2	1	no	—
450	C₂²×Q₈	—	2	2	no	—
451	C₂²×Q₈	—	2	2	no	—
452	C₂²×Q₈	—	2	2	no	—
453	C₂²×Q₈	—	2	2	no	—
454	C₂²×Q₈	—	4	1	no	—
455	C₂²×Q₈	—	4	1	no	—
456	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
457	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
458	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
459	C₂²×D₄	—	2	1	no	—
460	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
461	C₂³×C₄	—	2	1	no	—
462	C₂³×C₄	—	2	1	no	—
463	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
464	C₂×SD₁₆	—	2	2	no	—
465	C₂×SD₁₆	—	2	2	no	—
466	C₂×SD₁₆	—	2	2	no	—
467	C₂×SD₁₆	—	2	2	no	—
468	C₂×SD₁₆	—	2	2	no	—
469	C₂×SD₁₆	—	2	2	no	—
470	C₂×SD₁₆	—	4	1	no	—
471	C₂×SD₁₆	—	4	1	no	—
472	C₂×SD₁₆	—	4	1	no	—
473	C₂×M₁₆	—	2	2	no	—
474	C₂×M₁₆	—	2	2	no	—
475	C₂×M₁₆	—	4	1	no	—
476	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
479	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
480	C₄⋊Q₈	—	2	2	no	—
481	C₄⋊Q₈	—	2	2	no	—
482	C₄⋊Q₈	—	4	1	no	—
483	C₄⋊Q₈	—	4	1	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	#121	—	2	2	no	—
487	#121	D₄×C₂₃	1	4	yes	—
488	C₄×D₄	—	2	2	no	—
489	C₄×D₄	—	4	1	no	—
490	#117	—	2	2	no	—
491	#117	—	4	1	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	C₂³×C₂₃	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
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	—	2	1	no	—
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
510	C₂×C₄²	—	2	1	no	—
511	C₂×C₄²	—	2	1	no	—
512	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
513	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
514	#107	—	2	2	no	—
515	C₄⋊C₈	—	2	2	no	—
516	C₄⋊C₈	—	4	1	no	—
517	#103	—	2	2	no	—
518	#103	—	2	2	no	—
519	#103	—	2	2	no	—
520	#103	—	2	2	no	—
521	#103	—	2	2	no	—
522	#103	—	2	2	no	—
523	#103	—	2	2	no	—
524	#103	—	4	1	no	—
525	#103	D₄×C₂₃	1	4	yes	complemented
526	#102	—	2	2	no	—
527	C₂²⋊C₈	—	2	2	no	—
528	#95	—	2	1	no	—
529	#95	—	2	1	no	—
530	#95	—	2	1	no	—
531	#95	—	2	1	no	—
532	#95	—	2	1	no	—
533	#95	—	2	1	no	—
534	#95	D₄×C₂₃	1	1	yes	characteristic
535	#95	D₄×C₂₃	1	1	yes	characteristic
536	C₂₃	#25099	1	1	yes	characteristic, direct product factor, Sylow
537	C₂⁴	—	2	1	no	—
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	8	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	—	2	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	4	2	no	—
557	C₂×Q₈	—	4	2	no	—
558	C₂×Q₈	—	4	4	no	—
559	C₂×Q₈	—	4	4	no	—
560	C₂×Q₈	—	4	4	no	—
561	C₂×Q₈	—	4	2	no	—
562	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
563	C₂×Q₈	#41×C₂₃	1	2	yes	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	8	1	no	—
571	C₂×D₄	—	8	1	no	—
572	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
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	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	2	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	4	2	no	—
588	C₂²×C₄	—	4	2	no	—
589	C₂²×C₄	—	8	1	no	—
590	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
591	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
594	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
596	C₂²×C₄	#41×C₂₃	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
598	SD₁₆	—	4	4	no	—
599	SD₁₆	—	4	4	no	—
600	SD₁₆	—	4	4	no	—
601	M₁₆	—	4	4	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	4	2	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	2	no	—
624	C₄⋊C₄	—	4	2	no	—
625	C₄⋊C₄	—	8	1	no	—
626	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
627	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	4	2	no	—
632	C₂²⋊C₄	—	4	2	no	—
633	C₂²⋊C₄	—	4	2	no	—
634	C₂²⋊C₄	—	4	2	no	—
635	C₂²⋊C₄	—	8	1	no	—
636	C₄²	—	2	1	no	—
637	C₄²	—	2	1	no	—
638	C₄²	—	2	1	no	—
639	C₄²	—	2	1	no	—
640	C₄²	—	4	2	no	—
641	C₄²	—	8	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	2	no	—
649	C₂³	—	4	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	C₂₃×#121	1	2	yes	—
656	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
657	Q₈	—	2	2	no	—
658	Q₈	—	2	2	no	—
659	Q₈	—	2	2	no	—
660	Q₈	—	2	2	no	—
661	Q₈	—	4	8	no	—
662	Q₈	—	4	1	no	—
663	Q₈	—	4	1	no	—
664	Q₈	—	4	1	no	—
665	Q₈	—	4	1	no	—
666	Q₈	—	4	1	no	—
667	Q₈	—	4	1	no	—
668	Q₈	—	4	1	no	—
669	Q₈	—	4	1	no	—
670	D₄	—	2	2	no	—
671	D₄	—	2	2	no	—
672	D₄	—	4	1	no	—
673	D₄	—	4	1	no	—
674	D₄	—	8	4	no	—
675	C₂×C₄	—	2	1	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	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	4	8	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	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	8	4	no	—
714	C₂×C₄	C₂₃×#121	1	2	yes	—
715	C₂×C₄	C₂₃×#137	1	2	yes	—
716	C₂×C₄	C₂₃×#137	1	2	yes	—
717	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
718	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
719	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
720	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
721	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
722	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
723	C₈	—	2	2	no	—
724	C₈	—	4	1	no	—
725	C₈	—	4	1	no	—
726	C₈	—	4	1	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	8	1	no	—
738	C₂²	—	8	1	no	—
739	C₂²	—	8	1	no	—
740	C₂²	—	8	1	no	—
741	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
742	C₂²	D₄²×C₂₃	1	1	yes	characteristic
743	C₂²	C₂₃×#546	1	1	yes	characteristic
744	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
745	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
746	C₂²	C₂₃×#577	1	1	yes	characteristic
747	C₂²	C₂₃×#577	1	1	yes	characteristic
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	1	no	—
757	C₄	—	8	1	no	—
758	C₄	—	8	1	no	—
759	C₄	—	8	1	no	—
760	C₄	C₂₃×#525	1	1	yes	characteristic
761	C₄	C₂₃×#538	1	1	yes	characteristic
762	C₄	D₄²×C₂₃	1	1	yes	characteristic
763	C₄	C₂₃×#546	1	1	yes	characteristic
764	C₂	—	4	2	no	—
765	C₂	—	8	2	no	—
766	C₂	C₂₃×#2424	1	1	yes	characteristic
767	C₂	C₂₃×#3039	1	1	yes	characteristic
768	C₂	C₂₃×#3042	1	1	yes	characteristic
769	C₂	C₂₃×#3266	1	1	yes	characteristic
770	C₂	C₂₃×#3278	1	1	yes	characteristic
771	C₂	C₂₃×#3320	1	1	yes	characteristic
772	C₂	C₂₃×#3329	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₄×C₂²⋊C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#461	C₂	semidirect
4. C₂×C₂₃×#419	C₂	semidirect
5. C₂₃×#2434	C₂	semidirect
7. C₂₃×#2068	C₂	semidirect
8. C₂₃×#2055	C₂	semidirect
9. C₂₃×#2043	C₂	semidirect
10. C₂₃×#2013	C₂	semidirect
11. C₂₃×#1981	C₂	semidirect
12. C₂₃×#1928	C₂	semidirect
13. C₂₃×#1877	C₂	semidirect
14. C₂₃×#1873	C₂	semidirect
15. C₂₃×#1851	C₂	semidirect
139. C₂₃×#103	D₄	semidirect
255. #25099	C₂₃	direct (N × H)
342. C₂×#461	C₂×C₂₃	semidirect
344. C₂×#419	C₂×C₂₃	semidirect
345. #2434	C₂×C₂₃	semidirect
347. #2068	C₂×C₂₃	semidirect
348. #2055	C₂×C₂₃	semidirect
349. #2043	C₂×C₂₃	semidirect
350. #2013	C₂×C₂₃	semidirect
351. #1981	C₂×C₂₃	semidirect
352. #1928	C₂×C₂₃	semidirect
353. #1877	C₂×C₂₃	semidirect
354. #1873	C₂×C₂₃	semidirect
355. #1851	C₂×C₂₃	semidirect
525. #103	D₄×C₂₃	semidirect
536. C₂₃	#25099	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×#468	2
C₂×C₂₃×#461	2
C₂×C₂₃×#448	2
C₂×C₂₃×#419	2
C₂₃×#2434	2
C₂₃×#2363	2
C₂₃×#2068	2
C₂₃×#2055	2
C₂₃×#2043	2
C₂₃×#2013	2
C₂₃×#1981	2
C₂₃×#1928	2
C₂₃×#1877	2
C₂₃×#1873	2
C₂₃×#1851	2
#25099	23

Subgroups — C23×#25099 #19172725

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25099 #19172725