Subgroups — C₂₃×#21462 #19169088

Order 5888.

1400 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#448	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2324	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1875	C₂	1	1	yes	maximal, characteristic
9	C₂₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1863	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1787	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1750	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	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
20	C₂₃×#519	—	2	4	no	—
21	C₂₃×#519	—	2	4	no	—
22	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
23	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
24	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#117	—	2	1	no	—
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	C₂₃×#448	C₄	1	8	yes	complemented
34	C₂₃×#440	—	2	4	no	—
35	C₄×SD₁₆×C₂₃	—	2	4	no	—
36	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#106	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×#103	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×#102	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	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
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×#386	—	2	1	no	—
55	C₂₃×#385	—	2	1	no	—
56	C₂₃×#380	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₂₃	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×#340	C₂²	1	1	yes	characteristic
62	C₂₃×#336	C₂²	1	1	yes	characteristic
63	C₂₃×#336	C₂²	1	1	yes	characteristic
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	—	2	1	no	—
69	C₂²×Q₈×C₂₃	—	2	2	no	—
70	C₂²×Q₈×C₂₃	C₂×C₄	1	4	yes	complemented
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	C₂×C₄	1	4	yes	—
83	C₂×SD₁₆×C₂₃	C₂×C₄	1	4	yes	—
84	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
88	C₂₃×#121	—	2	2	no	—
89	C₂₃×#121	C₂×C₄	1	4	yes	—
90	C₄×Q₈×C₂₃	—	2	8	no	—
91	C₄×Q₈×C₂₃	—	2	8	no	—
92	C₄×Q₈×C₂₃	—	2	2	no	—
93	C₄×Q₈×C₂₃	—	2	2	no	—
94	C₄×Q₈×C₂₃	—	2	2	no	—
95	C₄×Q₈×C₂₃	—	2	2	no	—
96	C₄×Q₈×C₂₃	—	2	2	no	—
97	C₄×Q₈×C₂₃	—	2	2	no	—
98	C₄×Q₈×C₂₃	D₄	1	4	yes	complemented
99	C₄×Q₈×C₂₃	D₄	1	4	yes	complemented
100	C₄×D₄×C₂₃	—	2	2	no	—
101	C₄×D₄×C₂₃	—	2	2	no	—
102	C₂₃×#117	—	2	8	no	—
103	C₂₃×#117	—	2	8	no	—
104	C₂₃×#117	—	2	2	no	—
105	C₂₃×#117	—	2	2	no	—
106	C₂₃×#117	—	2	2	no	—
107	C₂₃×#117	—	2	2	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	—	2	1	no	—
113	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₂₃	D₄	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×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
128	C₂×C₄²×C₂₃	—	2	1	no	—
129	C₂×C₄²×C₂₃	—	2	1	no	—
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	—	2	1	no	—
134	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
136	C₂₃×#107	—	2	2	no	—
137	C₂₃×#106	—	2	2	no	—
138	C₂₃×#103	—	2	2	no	—
139	C₂₃×#103	—	2	2	no	—
140	C₂₃×#103	—	2	2	no	—
141	C₂₃×#103	—	2	2	no	—
142	C₂₃×#103	C₂×C₄	1	4	yes	complemented
143	C₂₃×#103	C₂×C₄	1	4	yes	complemented
144	C₂₃×#102	—	2	2	no	—
145	C₂₃×#102	—	2	2	no	—
146	C₂₃×C₂²⋊C₈	—	2	2	no	—
147	C₂₃×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
148	C₂₃×#97	—	2	2	no	—
149	C₄×C₈×C₂₃	—	2	2	no	—
150	C₂₃×#95	—	2	1	no	—
151	C₂₃×#95	—	2	1	no	—
152	C₂₃×#95	—	2	1	no	—
153	C₂⁴×C₂₃	—	2	1	no	—
154	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
155	C₂×Q₈×C₂₃	—	2	4	no	—
156	C₂×Q₈×C₂₃	—	2	8	no	—
157	C₂×Q₈×C₂₃	—	2	8	no	—
158	C₂×Q₈×C₂₃	—	2	4	no	—
159	C₂×Q₈×C₂₃	—	2	8	no	—
160	C₂×Q₈×C₂₃	—	2	8	no	—
161	C₂×Q₈×C₂₃	—	2	4	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	C₂²×C₄	1	2	yes	—
169	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
170	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
171	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
172	C₂×Q₈×C₂₃	#41	1	2	yes	—
173	C₂×Q₈×C₂₃	#41	1	2	yes	—
174	C₂×D₄×C₂₃	—	2	4	no	—
175	C₂×D₄×C₂₃	—	2	1	no	—
176	C₂×D₄×C₂₃	—	2	1	no	—
177	C₂×D₄×C₂₃	—	2	1	no	—
178	C₂×D₄×C₂₃	—	2	1	no	—
179	C₂×D₄×C₂₃	—	2	1	no	—
180	C₂×D₄×C₂₃	—	8	1	no	—
181	C₂×D₄×C₂₃	—	8	1	no	—
182	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
183	C₂²×C₄×C₂₃	—	2	4	no	—
184	C₂²×C₄×C₂₃	—	2	4	no	—
185	C₂²×C₄×C₂₃	—	2	4	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	—	4	2	no	—
198	C₂²×C₄×C₂₃	—	8	1	no	—
199	C₂²×C₄×C₂₃	—	8	1	no	—
200	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
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	SD₁₆×C₂₃	—	2	8	no	—
209	SD₁₆×C₂₃	—	2	8	no	—
210	C₂×C₈×C₂₃	—	2	1	no	—
211	C₂×C₈×C₂₃	—	2	1	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	C₂²×C₄	1	2	yes	—
221	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
222	C₄⋊C₄×C₂₃	—	2	4	no	—
223	C₄⋊C₄×C₂₃	—	2	4	no	—
224	C₄⋊C₄×C₂₃	—	2	4	no	—
225	C₄⋊C₄×C₂₃	—	2	4	no	—
226	C₄⋊C₄×C₂₃	—	2	2	no	—
227	C₄⋊C₄×C₂₃	—	2	2	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	—	2	1	no	—
235	C₄⋊C₄×C₂₃	—	8	1	no	—
236	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
237	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
238	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
239	C₂²⋊C₄×C₂₃	—	2	4	no	—
240	C₂²⋊C₄×C₂₃	—	2	4	no	—
241	C₂²⋊C₄×C₂₃	—	2	2	no	—
242	C₂²⋊C₄×C₂₃	—	2	2	no	—
243	C₂²⋊C₄×C₂₃	—	4	2	no	—
244	C₂²⋊C₄×C₂₃	—	8	1	no	—
245	C₂²⋊C₄×C₂₃	—	8	1	no	—
246	C₂²⋊C₄×C₂₃	—	8	1	no	—
247	C₄²×C₂₃	—	2	4	no	—
248	C₄²×C₂₃	—	2	4	no	—
249	C₄²×C₂₃	—	2	4	no	—
250	C₄²×C₂₃	—	2	4	no	—
251	C₄²×C₂₃	—	2	4	no	—
252	C₄²×C₂₃	—	2	1	no	—
253	C₄²×C₂₃	—	2	1	no	—
254	C₄²×C₂₃	—	8	1	no	—
255	C₄²×C₂₃	C₂×D₄	1	2	yes	—
256	C₄²×C₂₃	C₂×D₄	1	2	yes	—
257	#21462	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	2	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	—	4	1	no	—
271	C₂³×C₂₃	C₄×D₄	1	2	yes	—
272	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
273	Q₈×C₂₃	—	2	16	no	—
274	Q₈×C₂₃	—	2	2	no	—
275	Q₈×C₂₃	—	2	2	no	—
276	Q₈×C₂₃	—	2	2	no	—
277	Q₈×C₂₃	—	2	2	no	—
278	Q₈×C₂₃	—	2	2	no	—
279	Q₈×C₂₃	—	2	2	no	—
280	Q₈×C₂₃	C₄×D₄	1	4	yes	—
281	Q₈×C₂₃	C₄×D₄	1	4	yes	—
282	D₄×C₂₃	—	2	2	no	—
283	D₄×C₂₃	—	2	2	no	—
284	D₄×C₂₃	—	4	1	no	—
285	D₄×C₂₃	—	4	1	no	—
286	D₄×C₂₃	—	8	4	no	—
287	C₂×C₄×C₂₃	—	2	16	no	—
288	C₂×C₄×C₂₃	—	2	2	no	—
289	C₂×C₄×C₂₃	—	2	2	no	—
290	C₂×C₄×C₂₃	—	2	2	no	—
291	C₂×C₄×C₂₃	—	2	2	no	—
292	C₂×C₄×C₂₃	—	2	1	no	—
293	C₂×C₄×C₂₃	—	2	2	no	—
294	C₂×C₄×C₂₃	—	2	2	no	—
295	C₂×C₄×C₂₃	—	2	1	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	—	2	1	no	—
300	C₂×C₄×C₂₃	—	2	2	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	2	no	—
303	C₂×C₄×C₂₃	—	2	2	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	2	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	1	no	—
310	C₂×C₄×C₂₃	—	2	1	no	—
311	C₂×C₄×C₂₃	—	2	1	no	—
312	C₂×C₄×C₂₃	—	2	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	—	8	4	no	—
326	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
327	C₂×C₄×C₂₃	#120	1	2	yes	—
328	C₂×C₄×C₂₃	#120	1	2	yes	—
329	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
330	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₂₃	C₂×#41	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	C₈×C₂₃	—	2	2	no	—
336	C₈×C₂₃	—	2	2	no	—
337	C₈×C₂₃	—	4	1	no	—
338	C₈×C₂₃	—	4	1	no	—
339	C₂×#519	C₂×C₂₃	1	1	yes	characteristic, complemented
340	C₂×#448	C₂×C₂₃	1	1	yes	characteristic
341	C₂×#440	C₂×C₂₃	1	1	yes	characteristic, complemented
342	C₂×C₄×SD₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
343	#2324	C₂×C₂₃	1	1	yes	characteristic
344	#1880	C₂×C₂₃	1	1	yes	characteristic, complemented
345	#1880	C₂×C₂₃	1	1	yes	characteristic, complemented
346	#1875	C₂×C₂₃	1	1	yes	characteristic
347	#1865	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#1863	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#1854	C₂×C₂₃	1	1	yes	characteristic, complemented
350	#1787	C₂×C₂₃	1	1	yes	characteristic, complemented
351	#1763	C₂×C₂₃	1	1	yes	characteristic, complemented
352	C₄×#103	C₂×C₂₃	1	1	yes	characteristic, complemented
353	#1750	C₂×C₂₃	1	1	yes	characteristic, complemented
354	C₂²×C₂₃	—	2	2	no	—
355	C₂²×C₂₃	—	2	2	no	—
356	C₂²×C₂₃	—	2	2	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	2	no	—
362	C₂²×C₂₃	—	4	2	no	—
363	C₂²×C₂₃	—	4	2	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	C₂×C₄×D₄	1	1	yes	characteristic
369	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
370	C₂²×C₂₃	#525	1	1	yes	characteristic
371	C₂²×C₂₃	#577	1	1	yes	characteristic
372	C₂²×C₂₃	#577	1	1	yes	characteristic
373	C₂²×C₂₃	#577	1	1	yes	characteristic
374	C₂²×C₂₃	#578	1	1	yes	characteristic
375	C₄×C₂₃	—	2	2	no	—
376	C₄×C₂₃	—	2	2	no	—
377	C₄×C₂₃	—	2	4	no	—
378	C₄×C₂₃	—	2	4	no	—
379	C₄×C₂₃	—	2	2	no	—
380	C₄×C₂₃	—	4	2	no	—
381	C₄×C₂₃	—	4	1	no	—
382	C₄×C₂₃	—	4	2	no	—
383	C₄×C₂₃	—	4	1	no	—
384	C₄×C₂₃	—	4	2	no	—
385	C₄×C₂₃	—	8	1	no	—
386	C₄×C₂₃	—	8	1	no	—
387	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
388	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
389	C₄×C₂₃	#525	1	1	yes	characteristic
390	C₄×C₂₃	#525	1	1	yes	characteristic
391	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
392	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
393	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
394	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
395	#519	—	2	4	no	—
396	#519	—	2	4	no	—
397	C₂×C₄×Q₈	—	2	1	no	—
398	C₂×C₄×Q₈	—	2	1	no	—
399	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
400	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
401	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
402	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
403	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
404	C₂×#117	—	2	1	no	—
405	C₂×#117	—	2	1	no	—
406	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
407	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
408	#448	C₄×C₂₃	1	8	yes	complemented
409	#440	—	2	4	no	—
410	C₄×SD₁₆	—	2	4	no	—
411	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
412	C₂×#106	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×#102	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	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
424	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
425	#390	—	2	1	no	—
426	#390	C₂²×C₂₃	1	1	yes	characteristic
427	#389	C₂²×C₂₃	1	1	yes	characteristic
428	#388	—	2	1	no	—
429	#386	—	2	1	no	—
430	#385	—	2	1	no	—
431	#380	C₂²×C₂₃	1	1	yes	characteristic
432	C₄×C₄⋊C₄	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	#336	C₂²×C₂₃	1	1	yes	characteristic
438	#336	C₂²×C₂₃	1	1	yes	characteristic
439	C₂×C₂₃	—	4	2	no	—
440	C₂×C₂₃	—	8	2	no	—
441	C₂×C₂₃	C₄×#120	1	1	yes	characteristic
442	C₂×C₂₃	#2947	1	1	yes	characteristic
443	C₂×C₂₃	#2949	1	1	yes	characteristic
444	C₂×C₂₃	#3010	1	1	yes	characteristic
445	C₂×C₂₃	#3013	1	1	yes	characteristic
446	C₂×C₂₃	#3121	1	1	yes	characteristic
447	C₂×C₂₃	#3126	1	1	yes	characteristic
448	C₂²×Q₈	—	2	2	no	—
449	C₂²×Q₈	—	2	2	no	—
450	C₂²×Q₈	—	2	2	no	—
451	C₂²×Q₈	—	2	2	no	—
452	C₂²×Q₈	—	2	1	no	—
453	C₂²×Q₈	—	2	2	no	—
454	C₂²×Q₈	C₂×C₄×C₂₃	1	4	yes	complemented
455	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
456	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
457	C₂²×D₄	—	2	1	no	—
458	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
459	C₂³×C₄	—	2	1	no	—
460	C₂³×C₄	—	2	1	no	—
461	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
462	C₂×SD₁₆	—	2	2	no	—
463	C₂×SD₁₆	—	2	2	no	—
464	C₂×SD₁₆	—	2	2	no	—
465	C₂×SD₁₆	—	2	2	no	—
466	C₂×SD₁₆	C₂×C₄×C₂₃	1	4	yes	—
467	C₂×SD₁₆	C₂×C₄×C₂₃	1	4	yes	—
468	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
469	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
472	#121	—	2	2	no	—
473	#121	C₂×C₄×C₂₃	1	4	yes	—
474	C₄×Q₈	—	2	8	no	—
475	C₄×Q₈	—	2	8	no	—
476	C₄×Q₈	—	2	2	no	—
477	C₄×Q₈	—	2	2	no	—
478	C₄×Q₈	—	2	2	no	—
479	C₄×Q₈	—	2	2	no	—
480	C₄×Q₈	—	2	2	no	—
481	C₄×Q₈	—	2	2	no	—
482	C₄×Q₈	D₄×C₂₃	1	4	yes	complemented
483	C₄×Q₈	D₄×C₂₃	1	4	yes	complemented
484	C₄×D₄	—	2	2	no	—
485	C₄×D₄	—	2	2	no	—
486	#117	—	2	8	no	—
487	#117	—	2	8	no	—
488	#117	—	2	2	no	—
489	#117	—	2	2	no	—
490	#117	—	2	2	no	—
491	#117	—	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	D₄×C₂₃	1	1	yes	characteristic
498	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
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	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
511	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
512	C₂×C₄²	—	2	1	no	—
513	C₂×C₄²	—	2	1	no	—
514	C₂×C₄²	—	2	1	no	—
515	C₂×C₄²	—	2	1	no	—
516	C₂×C₄²	—	2	1	no	—
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
519	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
520	#107	—	2	2	no	—
521	#106	—	2	2	no	—
522	#103	—	2	2	no	—
523	#103	—	2	2	no	—
524	#103	—	2	2	no	—
525	#103	—	2	2	no	—
526	#103	C₂×C₄×C₂₃	1	4	yes	complemented
527	#103	C₂×C₄×C₂₃	1	4	yes	complemented
528	#102	—	2	2	no	—
529	#102	—	2	2	no	—
530	C₂²⋊C₈	—	2	2	no	—
531	C₂²⋊C₈	C₂×C₄×C₂₃	1	4	yes	complemented
532	#97	—	2	2	no	—
533	C₄×C₈	—	2	2	no	—
534	#95	—	2	1	no	—
535	#95	—	2	1	no	—
536	#95	—	2	1	no	—
537	C₂₃	#21462	1	1	yes	characteristic, direct product factor, Sylow
538	C₂⁴	—	2	1	no	—
539	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
540	C₂×Q₈	—	2	4	no	—
541	C₂×Q₈	—	2	8	no	—
542	C₂×Q₈	—	2	8	no	—
543	C₂×Q₈	—	2	4	no	—
544	C₂×Q₈	—	2	8	no	—
545	C₂×Q₈	—	2	8	no	—
546	C₂×Q₈	—	2	4	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	C₂²×C₄×C₂₃	1	2	yes	—
554	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
555	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
556	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
557	C₂×Q₈	#41×C₂₃	1	2	yes	—
558	C₂×Q₈	#41×C₂₃	1	2	yes	—
559	C₂×D₄	—	2	4	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	8	1	no	—
566	C₂×D₄	—	8	1	no	—
567	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	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	—	2	1	no	—
582	C₂²×C₄	—	4	2	no	—
583	C₂²×C₄	—	8	1	no	—
584	C₂²×C₄	—	8	1	no	—
585	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
586	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
588	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
590	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
591	C₂²×C₄	#41×C₂₃	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
593	SD₁₆	—	2	8	no	—
594	SD₁₆	—	2	8	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	—	2	1	no	—
605	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
606	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	2	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	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	8	1	no	—
621	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
622	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
623	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	4	2	no	—
629	C₂²⋊C₄	—	8	1	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	4	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	2	4	no	—
637	C₄²	—	2	1	no	—
638	C₄²	—	2	1	no	—
639	C₄²	—	8	1	no	—
640	C₄²	C₂×D₄×C₂₃	1	2	yes	—
641	C₄²	C₂×D₄×C₂₃	1	2	yes	—
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	C₄×D₄×C₂₃	1	2	yes	—
656	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
657	Q₈	—	2	16	no	—
658	Q₈	—	2	2	no	—
659	Q₈	—	2	2	no	—
660	Q₈	—	2	2	no	—
661	Q₈	—	2	2	no	—
662	Q₈	—	2	2	no	—
663	Q₈	—	2	2	no	—
664	Q₈	C₄×D₄×C₂₃	1	4	yes	—
665	Q₈	C₄×D₄×C₂₃	1	4	yes	—
666	D₄	—	2	2	no	—
667	D₄	—	2	2	no	—
668	D₄	—	4	1	no	—
669	D₄	—	4	1	no	—
670	D₄	—	8	4	no	—
671	C₂×C₄	—	2	16	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	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	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	—	8	4	no	—
710	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
711	C₂×C₄	C₂₃×#120	1	2	yes	—
712	C₂×C₄	C₂₃×#120	1	2	yes	—
713	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
714	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
715	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
716	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
717	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
718	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
719	C₈	—	2	2	no	—
720	C₈	—	2	2	no	—
721	C₈	—	4	1	no	—
722	C₈	—	4	1	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	8	1	no	—
734	C₂²	—	8	1	no	—
735	C₂²	—	8	1	no	—
736	C₂²	—	8	1	no	—
737	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
738	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
739	C₂²	C₂₃×#525	1	1	yes	characteristic
740	C₂²	C₂₃×#577	1	1	yes	characteristic
741	C₂²	C₂₃×#577	1	1	yes	characteristic
742	C₂²	C₂₃×#577	1	1	yes	characteristic
743	C₂²	C₂₃×#578	1	1	yes	characteristic
744	C₄	—	2	2	no	—
745	C₄	—	2	2	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	4	no	—
748	C₄	—	2	2	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	1	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	2	no	—
754	C₄	—	8	1	no	—
755	C₄	—	8	1	no	—
756	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
757	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
758	C₄	C₂₃×#525	1	1	yes	characteristic
759	C₄	C₂₃×#525	1	1	yes	characteristic
760	C₂	—	4	2	no	—
761	C₂	—	8	2	no	—
762	C₂	C₄×C₂₃×#120	1	1	yes	characteristic
763	C₂	C₂₃×#2947	1	1	yes	characteristic
764	C₂	C₂₃×#2949	1	1	yes	characteristic
765	C₂	C₂₃×#3010	1	1	yes	characteristic
766	C₂	C₂₃×#3013	1	1	yes	characteristic
767	C₂	C₂₃×#3121	1	1	yes	characteristic
768	C₂	C₂₃×#3126	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#519	C₂	semidirect
3. C₂×C₂₃×#440	C₂	semidirect
4. C₂×C₄×SD₁₆×C₂₃	C₂	semidirect
6. C₂₃×#1880	C₂	semidirect
7. C₂₃×#1880	C₂	semidirect
9. C₂₃×#1865	C₂	semidirect
10. C₂₃×#1863	C₂	semidirect
11. C₂₃×#1854	C₂	semidirect
12. C₂₃×#1787	C₂	semidirect
13. C₂₃×#1763	C₂	semidirect
14. C₄×C₂₃×#103	C₂	semidirect
15. C₂₃×#1750	C₂	semidirect
33. C₂₃×#448	C₄	semidirect
70. C₂²×Q₈×C₂₃	C₂×C₄	semidirect
98. C₄×Q₈×C₂₃	D₄	semidirect
99. C₄×Q₈×C₂₃	D₄	semidirect
142. C₂₃×#103	C₂×C₄	semidirect
143. C₂₃×#103	C₂×C₄	semidirect
147. C₂₃×C₂²⋊C₈	C₂×C₄	semidirect
257. #21462	C₂₃	direct (N × H)
339. C₂×#519	C₂×C₂₃	semidirect
341. C₂×#440	C₂×C₂₃	semidirect
342. C₂×C₄×SD₁₆	C₂×C₂₃	semidirect
344. #1880	C₂×C₂₃	semidirect
345. #1880	C₂×C₂₃	semidirect
347. #1865	C₂×C₂₃	semidirect
348. #1863	C₂×C₂₃	semidirect
349. #1854	C₂×C₂₃	semidirect
350. #1787	C₂×C₂₃	semidirect
351. #1763	C₂×C₂₃	semidirect
352. C₄×#103	C₂×C₂₃	semidirect
353. #1750	C₂×C₂₃	semidirect
408. #448	C₄×C₂₃	semidirect
454. C₂²×Q₈	C₂×C₄×C₂₃	semidirect
482. C₄×Q₈	D₄×C₂₃	semidirect
483. C₄×Q₈	D₄×C₂₃	semidirect
526. #103	C₂×C₄×C₂₃	semidirect
527. #103	C₂×C₄×C₂₃	semidirect
531. C₂²⋊C₈	C₂×C₄×C₂₃	semidirect
537. C₂₃	#21462	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×#519	2
C₂×C₂₃×#448	2
C₂×C₂₃×#440	2
C₂×C₄×SD₁₆×C₂₃	2
C₂₃×#2324	2
C₂₃×#1880	2
C₂₃×#1875	2
C₂₃×#1865	2
C₂₃×#1863	2
C₂₃×#1854	2
C₂₃×#1787	2
C₂₃×#1763	2
C₄×C₂₃×#103	2
C₂₃×#1750	2
#21462	23

Subgroups — C23×#21462 #19169088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21462 #19169088