Subgroups — C₂₃×#34989 #19182615

Order 5888.

2834 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2849	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2847	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#2627	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2623	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2618	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2481	C₂	1	4	yes	maximal, complemented
10	C₂₃×#2473	C₂	1	4	yes	maximal, complemented
11	C₂₃×#2449	C₂	1	4	yes	maximal, complemented
12	C₂₃×#2443	C₂	1	4	yes	maximal, complemented
13	C₂₃×#2322	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2313	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂₃×#120	C₂	1	2	yes	maximal, complemented
16	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂₃×#539	—	2	8	no	—
20	C₂×C₂₃×#126	C₂²	1	2	yes	complemented
21	C₂×C₂₃×#125	C₂²	1	2	yes	complemented
22	C₂×C₂₃×#123	C₂²	1	2	yes	—
23	C₂×C₂₃×#123	C₂²	1	2	yes	—
24	C₂×C₂₃×#123	C₂²	1	2	yes	complemented
25	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#121	C₂²	1	2	yes	—
30	C₂×C₂₃×#120	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
33	C₂²×C₄⋊C₄×C₂₃	—	2	8	no	—
34	C₂²×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
35	C₂²×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
36	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
40	C₂₃×#400	C₂²	1	4	yes	complemented
41	C₂₃×#400	C₂²	1	2	yes	complemented
42	C₂₃×#399	C₂²	1	4	yes	complemented
43	C₂₃×#398	C₂²	1	4	yes	complemented
44	C₂₃×#398	C₂²	1	4	yes	complemented
45	C₂₃×#398	C₂²	1	2	yes	complemented
46	C₂₃×#397	C₂²	1	4	yes	complemented
47	C₂₃×#396	C₂²	1	4	yes	complemented
48	C₂₃×#395	C₂²	1	2	yes	complemented
49	C₂₃×#394	C₂²	1	2	yes	complemented
50	C₂₃×#389	C₂²	1	4	yes	complemented
51	C₂₃×#388	C₂²	1	4	yes	complemented
52	C₂₃×#387	C₂²	1	4	yes	complemented
53	C₂₃×#387	C₂²	1	4	yes	complemented
54	C₂₃×#387	C₂²	1	4	yes	complemented
55	C₂₃×#386	C₂²	1	4	yes	—
56	C₂₃×#386	C₂²	1	4	yes	—
57	C₂₃×#386	C₂²	1	4	yes	—
58	C₂₃×#386	C₂²	1	4	yes	—
59	C₂₃×#386	C₂²	1	2	yes	—
60	C₂₃×#386	C₂²	1	2	yes	—
61	C₂₃×#385	C₂²	1	4	yes	—
62	C₂₃×#385	C₂²	1	4	yes	—
63	C₂₃×#385	C₂²	1	4	yes	—
64	C₂₃×#385	C₂²	1	4	yes	—
65	C₂₃×#385	C₂²	1	2	yes	—
66	C₂₃×#385	C₂²	1	2	yes	—
67	C₂₃×#385	C₂²	1	4	yes	complemented
68	C₂₃×#381	C₂²	1	2	yes	—
69	C₂₃×#381	C₂²	1	2	yes	—
70	C₂₃×#380	C₂²	1	2	yes	—
71	C₂₃×#380	C₂²	1	2	yes	—
72	C₂₃×#380	C₂²	1	1	yes	characteristic
73	C₂₃×#380	C₂²	1	1	yes	characteristic
74	C₂₃×#379	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
76	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
77	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
80	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
81	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₂₃	—	2	4	no	—
83	C₂³×C₄×C₂₃	—	2	4	no	—
84	C₂³×C₄×C₂₃	—	2	4	no	—
85	C₂³×C₄×C₂₃	—	2	4	no	—
86	C₂³×C₄×C₂₃	—	2	4	no	—
87	C₂³×C₄×C₂₃	—	4	4	no	—
88	C₂³×C₄×C₂₃	—	4	4	no	—
89	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
90	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
91	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
98	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
100	C₂₃×#126	—	2	8	no	—
101	C₂₃×#125	—	2	8	no	—
102	C₂₃×#123	—	2	8	no	—
103	C₂₃×#123	—	2	8	no	—
104	C₂₃×#123	—	2	8	no	—
105	C₂₃×C₂²⋊Q₈	—	2	4	no	—
106	C₂₃×C₂²⋊Q₈	—	2	8	no	—
107	C₂₃×C₂²⋊Q₈	—	4	4	no	—
108	C₂₃×#121	—	2	4	no	—
109	C₂₃×#121	—	4	4	no	—
110	C₂₃×#120	—	2	8	no	—
111	C₄×D₄×C₂₃	—	2	8	no	—
112	C₄×D₄×C₂₃	—	4	8	no	—
113	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
114	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
115	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
116	C₂×C₄⋊C₄×C₂₃	—	2	16	no	—
117	C₂×C₄⋊C₄×C₂₃	—	2	16	no	—
118	C₂×C₄⋊C₄×C₂₃	D₄	1	8	yes	complemented
119	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
134	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
149	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
150	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
151	C₂₃×#95	C₂³	1	4	yes	—
152	C₂₃×#95	C₂³	1	4	yes	—
153	C₂₃×#95	C₂³	1	4	yes	—
154	C₂₃×#95	C₂³	1	2	yes	—
155	C₂₃×#95	C₂³	1	4	yes	—
156	C₂₃×#95	C₂³	1	2	yes	—
157	C₂₃×#95	C₂³	1	4	yes	—
158	C₂₃×#95	C₂³	1	4	yes	—
159	C₂₃×#95	C₂³	1	4	yes	—
160	C₂₃×#95	C₂³	1	4	yes	—
161	C₂₃×#95	C₂³	1	4	yes	—
162	C₂⁴×C₂₃	—	2	2	no	—
163	C₂⁴×C₂₃	—	2	2	no	—
164	C₂⁴×C₂₃	—	2	4	no	—
165	C₂⁴×C₂₃	—	2	4	no	—
166	C₂⁴×C₂₃	#41	1	4	yes	—
167	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
168	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
169	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
170	C₂×Q₈×C₂₃	—	2	2	no	—
171	C₂×Q₈×C₂₃	—	4	2	no	—
172	C₂×D₄×C₂₃	—	2	4	no	—
173	C₂×D₄×C₂₃	—	2	4	no	—
174	C₂×D₄×C₂₃	—	2	8	no	—
175	C₂×D₄×C₂₃	—	2	4	no	—
176	C₂×D₄×C₂₃	—	2	8	no	—
177	C₂×D₄×C₂₃	—	2	8	no	—
178	C₂×D₄×C₂₃	—	2	2	no	—
179	C₂×D₄×C₂₃	—	4	2	no	—
180	C₂²×C₄×C₂₃	—	2	32	no	—
181	C₂²×C₄×C₂₃	—	2	2	no	—
182	C₂²×C₄×C₂₃	—	2	8	no	—
183	C₂²×C₄×C₂₃	—	2	2	no	—
184	C₂²×C₄×C₂₃	—	2	2	no	—
185	C₂²×C₄×C₂₃	—	2	2	no	—
186	C₂²×C₄×C₂₃	—	2	8	no	—
187	C₂²×C₄×C₂₃	—	2	8	no	—
188	C₂²×C₄×C₂₃	—	2	2	no	—
189	C₂²×C₄×C₂₃	—	2	2	no	—
190	C₂²×C₄×C₂₃	—	2	8	no	—
191	C₂²×C₄×C₂₃	—	2	4	no	—
192	C₂²×C₄×C₂₃	—	2	4	no	—
193	C₂²×C₄×C₂₃	—	2	8	no	—
194	C₂²×C₄×C₂₃	—	2	4	no	—
195	C₂²×C₄×C₂₃	—	2	4	no	—
196	C₂²×C₄×C₂₃	—	2	4	no	—
197	C₂²×C₄×C₂₃	—	4	2	no	—
198	C₂²×C₄×C₂₃	—	4	4	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	—	4	2	no	—
203	C₂²×C₄×C₂₃	—	4	2	no	—
204	C₂²×C₄×C₂₃	—	4	4	no	—
205	C₂²×C₄×C₂₃	—	4	16	no	—
206	C₂²×C₄×C₂₃	—	4	16	no	—
207	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
208	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
209	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
210	C₂²×C₄×C₂₃	#41	1	4	yes	—
211	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
213	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
215	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
223	C₄⋊C₄×C₂₃	—	2	8	no	—
224	C₄⋊C₄×C₂₃	—	2	4	no	—
225	C₄⋊C₄×C₂₃	—	2	4	no	—
226	C₄⋊C₄×C₂₃	—	2	8	no	—
227	C₄⋊C₄×C₂₃	—	2	4	no	—
228	C₄⋊C₄×C₂₃	—	2	2	no	—
229	C₄⋊C₄×C₂₃	—	2	4	no	—
230	C₄⋊C₄×C₂₃	—	2	4	no	—
231	C₄⋊C₄×C₂₃	—	2	2	no	—
232	C₄⋊C₄×C₂₃	—	2	4	no	—
233	C₄⋊C₄×C₂₃	—	2	8	no	—
234	C₄⋊C₄×C₂₃	—	4	4	no	—
235	C₄⋊C₄×C₂₃	—	4	2	no	—
236	C₄⋊C₄×C₂₃	—	4	2	no	—
237	C₄⋊C₄×C₂₃	—	4	4	no	—
238	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
239	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
240	C₂²⋊C₄×C₂₃	—	2	4	no	—
241	C₂²⋊C₄×C₂₃	—	2	4	no	—
242	C₂²⋊C₄×C₂₃	—	2	8	no	—
243	C₂²⋊C₄×C₂₃	—	2	4	no	—
244	C₂²⋊C₄×C₂₃	—	2	8	no	—
245	C₂²⋊C₄×C₂₃	—	2	8	no	—
246	C₂²⋊C₄×C₂₃	—	2	4	no	—
247	C₂²⋊C₄×C₂₃	—	2	4	no	—
248	C₂²⋊C₄×C₂₃	—	2	4	no	—
249	C₂²⋊C₄×C₂₃	—	2	4	no	—
250	C₂²⋊C₄×C₂₃	—	2	8	no	—
251	C₂²⋊C₄×C₂₃	—	4	4	no	—
252	C₂²⋊C₄×C₂₃	—	4	4	no	—
253	C₄²×C₂₃	—	2	4	no	—
254	C₄²×C₂₃	—	4	4	no	—
255	#34989	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂³×C₂₃	—	2	8	no	—
257	C₂³×C₂₃	—	2	8	no	—
258	C₂³×C₂₃	—	2	16	no	—
259	C₂³×C₂₃	—	2	8	no	—
260	C₂³×C₂₃	—	2	16	no	—
261	C₂³×C₂₃	—	2	2	no	—
262	C₂³×C₂₃	—	2	2	no	—
263	C₂³×C₂₃	—	2	2	no	—
264	C₂³×C₂₃	—	2	2	no	—
265	C₂³×C₂₃	—	2	2	no	—
266	C₂³×C₂₃	—	2	2	no	—
267	C₂³×C₂₃	—	2	2	no	—
268	C₂³×C₂₃	—	2	2	no	—
269	C₂³×C₂₃	—	2	2	no	—
270	C₂³×C₂₃	—	2	4	no	—
271	C₂³×C₂₃	—	2	4	no	—
272	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
273	C₂³×C₂₃	C₂×#41	1	2	yes	—
274	C₂³×C₂₃	C₂×#41	1	2	yes	—
275	C₂³×C₂₃	C₂×#41	1	4	yes	—
276	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
277	C₂³×C₂₃	2₋¹⁺⁴	1	4	yes	—
278	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
279	Q₈×C₂₃	—	8	2	no	—
280	D₄×C₂₃	—	4	8	no	—
281	D₄×C₂₃	—	4	16	no	—
282	D₄×C₂₃	—	8	2	no	—
283	C₂×C₄×C₂₃	—	2	32	no	—
284	C₂×C₄×C₂₃	—	2	8	no	—
285	C₂×C₄×C₂₃	—	2	8	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	4	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	2	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	4	no	—
299	C₂×C₄×C₂₃	—	2	2	no	—
300	C₂×C₄×C₂₃	—	2	4	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	4	no	—
303	C₂×C₄×C₂₃	—	2	4	no	—
304	C₂×C₄×C₂₃	—	2	4	no	—
305	C₂×C₄×C₂₃	—	2	2	no	—
306	C₂×C₄×C₂₃	—	2	4	no	—
307	C₂×C₄×C₂₃	—	2	2	no	—
308	C₂×C₄×C₂₃	—	2	4	no	—
309	C₂×C₄×C₂₃	—	2	4	no	—
310	C₂×C₄×C₂₃	—	2	4	no	—
311	C₂×C₄×C₂₃	—	4	4	no	—
312	C₂×C₄×C₂₃	—	4	4	no	—
313	C₂×C₄×C₂₃	—	4	16	no	—
314	C₂×C₄×C₂₃	—	4	8	no	—
315	C₂×C₄×C₂₃	—	4	8	no	—
316	C₂×C₄×C₂₃	—	4	4	no	—
317	C₂×C₄×C₂₃	—	4	4	no	—
318	C₂×C₄×C₂₃	—	8	4	no	—
319	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
320	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
321	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
324	C₂×#539	C₂×C₂₃	1	1	yes	characteristic, complemented
325	C₂³×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
326	#2849	C₂×C₂₃	1	2	yes	complemented
327	#2848	C₂×C₂₃	1	1	yes	characteristic, complemented
328	#2847	C₂×C₂₃	1	1	yes	characteristic
329	#2627	C₂×C₂₃	1	1	yes	characteristic, complemented
330	#2623	C₂×C₂₃	1	2	yes	complemented
331	#2618	C₂×C₂₃	1	1	yes	characteristic, complemented
332	#2481	C₂×C₂₃	1	4	yes	complemented
333	#2473	C₂×C₂₃	1	4	yes	complemented
334	#2449	C₂×C₂₃	1	4	yes	complemented
335	#2443	C₂×C₂₃	1	4	yes	complemented
336	#2322	C₂×C₂₃	1	2	yes	complemented
337	#2313	C₂×C₂₃	1	1	yes	characteristic, complemented
338	C₄×#120	C₂×C₂₃	1	2	yes	complemented
339	C₂²×C₂₃	—	2	32	no	—
340	C₂²×C₂₃	—	2	4	no	—
341	C₂²×C₂₃	—	2	4	no	—
342	C₂²×C₂₃	—	2	4	no	—
343	C₂²×C₂₃	—	2	2	no	—
344	C₂²×C₂₃	—	2	4	no	—
345	C₂²×C₂₃	—	2	2	no	—
346	C₂²×C₂₃	—	2	4	no	—
347	C₂²×C₂₃	—	2	4	no	—
348	C₂²×C₂₃	—	2	4	no	—
349	C₂²×C₂₃	—	2	4	no	—
350	C₂²×C₂₃	—	4	2	no	—
351	C₂²×C₂₃	—	4	4	no	—
352	C₂²×C₂₃	—	4	2	no	—
353	C₂²×C₂₃	—	4	2	no	—
354	C₂²×C₂₃	—	4	4	no	—
355	C₂²×C₂₃	#525	1	4	yes	—
356	C₂²×C₂₃	#539	1	8	yes	complemented
357	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
358	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
359	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
360	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
361	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
362	C₄×C₂₃	—	2	4	no	—
363	C₄×C₂₃	—	2	4	no	—
364	C₄×C₂₃	—	2	4	no	—
365	C₄×C₂₃	—	2	2	no	—
366	C₄×C₂₃	—	2	2	no	—
367	C₄×C₂₃	—	4	2	no	—
368	C₄×C₂₃	—	4	4	no	—
369	C₄×C₂₃	—	4	2	no	—
370	C₄×C₂₃	—	4	2	no	—
371	C₄×C₂₃	—	4	2	no	—
372	C₄×C₂₃	—	4	2	no	—
373	C₄×C₂₃	—	4	4	no	—
374	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
375	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
376	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
377	#539	—	2	8	no	—
378	C₂×#126	C₂²×C₂₃	1	2	yes	complemented
379	C₂×#125	C₂²×C₂₃	1	2	yes	complemented
380	C₂×#123	C₂²×C₂₃	1	2	yes	—
381	C₂×#123	C₂²×C₂₃	1	2	yes	—
382	C₂×#123	C₂²×C₂₃	1	2	yes	complemented
383	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
384	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
385	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
386	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
387	C₂×#121	C₂²×C₂₃	1	2	yes	—
388	C₂×#120	C₂²×C₂₃	1	2	yes	—
389	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
390	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
391	C₂²×C₄⋊C₄	—	2	8	no	—
392	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
393	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
394	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
395	C₂²×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
396	C₂²×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
397	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
398	#400	C₂²×C₂₃	1	4	yes	complemented
399	#400	C₂²×C₂₃	1	2	yes	complemented
400	#399	C₂²×C₂₃	1	4	yes	complemented
401	#398	C₂²×C₂₃	1	2	yes	complemented
402	#398	C₂²×C₂₃	1	4	yes	complemented
403	#398	C₂²×C₂₃	1	4	yes	complemented
404	#397	C₂²×C₂₃	1	4	yes	complemented
405	#396	C₂²×C₂₃	1	4	yes	complemented
406	#395	C₂²×C₂₃	1	2	yes	complemented
407	#394	C₂²×C₂₃	1	2	yes	complemented
408	#389	C₂²×C₂₃	1	4	yes	complemented
409	#388	C₂²×C₂₃	1	4	yes	complemented
410	#387	C₂²×C₂₃	1	4	yes	complemented
411	#387	C₂²×C₂₃	1	4	yes	complemented
412	#387	C₂²×C₂₃	1	4	yes	complemented
413	#386	C₂²×C₂₃	1	2	yes	—
414	#386	C₂²×C₂₃	1	4	yes	—
415	#386	C₂²×C₂₃	1	4	yes	—
416	#386	C₂²×C₂₃	1	4	yes	—
417	#386	C₂²×C₂₃	1	2	yes	—
418	#386	C₂²×C₂₃	1	4	yes	—
419	#385	C₂²×C₂₃	1	2	yes	—
420	#385	C₂²×C₂₃	1	4	yes	—
421	#385	C₂²×C₂₃	1	4	yes	—
422	#385	C₂²×C₂₃	1	4	yes	—
423	#385	C₂²×C₂₃	1	2	yes	—
424	#385	C₂²×C₂₃	1	4	yes	—
425	#385	C₂²×C₂₃	1	4	yes	complemented
426	#381	C₂²×C₂₃	1	2	yes	—
427	#381	C₂²×C₂₃	1	2	yes	—
428	#380	C₂²×C₂₃	1	1	yes	characteristic
429	#380	C₂²×C₂₃	1	1	yes	characteristic
430	#380	C₂²×C₂₃	1	2	yes	—
431	#380	C₂²×C₂₃	1	2	yes	—
432	#379	C₂²×C₂₃	1	2	yes	—
433	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
434	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
435	C₂×C₂₃	—	2	4	no	—
436	C₂×C₂₃	—	2	8	no	—
437	C₂×C₂₃	—	8	2	no	—
438	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
439	C₂×C₂₃	C₂×#539	1	2	yes	—
440	C₂×C₂₃	#3484	1	1	yes	characteristic
441	C₂×C₂₃	#3486	1	1	yes	characteristic
442	C₂×C₂₃	#3492	1	2	yes	—
443	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
444	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
445	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
446	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
447	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
448	C₂³×C₄	—	2	4	no	—
449	C₂³×C₄	—	2	4	no	—
450	C₂³×C₄	—	2	4	no	—
451	C₂³×C₄	—	2	4	no	—
452	C₂³×C₄	—	2	4	no	—
453	C₂³×C₄	—	4	4	no	—
454	C₂³×C₄	—	4	4	no	—
455	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
456	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
457	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
458	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
459	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
461	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
462	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
464	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
466	#126	—	2	8	no	—
467	#125	—	2	8	no	—
468	#123	—	2	8	no	—
469	#123	—	2	8	no	—
470	#123	—	2	8	no	—
471	C₂²⋊Q₈	—	2	4	no	—
472	C₂²⋊Q₈	—	2	8	no	—
473	C₂²⋊Q₈	—	4	4	no	—
474	#121	—	2	4	no	—
475	#121	—	4	4	no	—
476	#120	—	2	8	no	—
477	C₄×D₄	—	2	8	no	—
478	C₄×D₄	—	4	8	no	—
479	C₂×C₄⋊C₄	—	2	4	no	—
480	C₂×C₄⋊C₄	—	2	4	no	—
481	C₂×C₄⋊C₄	—	2	4	no	—
482	C₂×C₄⋊C₄	—	2	16	no	—
483	C₂×C₄⋊C₄	—	2	16	no	—
484	C₂×C₄⋊C₄	D₄×C₂₃	1	8	yes	complemented
485	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
486	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
496	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
497	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
500	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
515	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
516	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
517	#95	C₂³×C₂₃	1	4	yes	—
518	#95	C₂³×C₂₃	1	4	yes	—
519	#95	C₂³×C₂₃	1	4	yes	—
520	#95	C₂³×C₂₃	1	2	yes	—
521	#95	C₂³×C₂₃	1	4	yes	—
522	#95	C₂³×C₂₃	1	2	yes	—
523	#95	C₂³×C₂₃	1	4	yes	—
524	#95	C₂³×C₂₃	1	4	yes	—
525	#95	C₂³×C₂₃	1	4	yes	—
526	#95	C₂³×C₂₃	1	4	yes	—
527	#95	C₂³×C₂₃	1	4	yes	—
528	C₂₃	#34989	1	1	yes	characteristic, direct product factor, Sylow
529	C₂⁴	—	2	2	no	—
530	C₂⁴	—	2	2	no	—
531	C₂⁴	—	2	4	no	—
532	C₂⁴	—	2	4	no	—
533	C₂⁴	#41×C₂₃	1	4	yes	—
534	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
535	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
536	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
537	C₂×Q₈	—	2	2	no	—
538	C₂×Q₈	—	4	2	no	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	8	no	—
542	C₂×D₄	—	2	4	no	—
543	C₂×D₄	—	2	8	no	—
544	C₂×D₄	—	2	8	no	—
545	C₂×D₄	—	2	2	no	—
546	C₂×D₄	—	4	2	no	—
547	C₂²×C₄	—	2	32	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	8	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	8	no	—
554	C₂²×C₄	—	2	8	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	8	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	8	no	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	4	2	no	—
565	C₂²×C₄	—	4	4	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	4	2	no	—
569	C₂²×C₄	—	4	2	no	—
570	C₂²×C₄	—	4	2	no	—
571	C₂²×C₄	—	4	4	no	—
572	C₂²×C₄	—	4	16	no	—
573	C₂²×C₄	—	4	16	no	—
574	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
575	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
576	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
577	C₂²×C₄	#41×C₂₃	1	4	yes	—
578	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
579	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
581	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
590	C₄⋊C₄	—	2	8	no	—
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	8	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	8	no	—
601	C₄⋊C₄	—	4	4	no	—
602	C₄⋊C₄	—	4	2	no	—
603	C₄⋊C₄	—	4	2	no	—
604	C₄⋊C₄	—	4	4	no	—
605	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
606	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	8	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	8	no	—
612	C₂²⋊C₄	—	2	8	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	8	no	—
618	C₂²⋊C₄	—	4	4	no	—
619	C₂²⋊C₄	—	4	4	no	—
620	C₄²	—	2	4	no	—
621	C₄²	—	4	4	no	—
622	C₂³	—	2	8	no	—
623	C₂³	—	2	8	no	—
624	C₂³	—	2	16	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	8	no	—
632	C₂³	—	2	16	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	4	no	—
637	C₂³	—	2	4	no	—
638	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
639	C₂³	C₂×#41×C₂₃	1	2	yes	—
640	C₂³	C₂×#41×C₂₃	1	2	yes	—
641	C₂³	C₂×#41×C₂₃	1	4	yes	—
642	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
643	C₂³	C₂₃×2₋¹⁺⁴	1	4	yes	—
644	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
645	Q₈	—	8	2	no	—
646	D₄	—	4	8	no	—
647	D₄	—	4	16	no	—
648	D₄	—	8	2	no	—
649	C₂×C₄	—	2	32	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	8	no	—
658	C₂×C₄	—	2	8	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	4	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	4	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	4	4	no	—
678	C₂×C₄	—	4	4	no	—
679	C₂×C₄	—	4	16	no	—
680	C₂×C₄	—	4	8	no	—
681	C₂×C₄	—	4	8	no	—
682	C₂×C₄	—	4	4	no	—
683	C₂×C₄	—	4	4	no	—
684	C₂×C₄	—	8	4	no	—
685	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
686	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
687	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
688	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
689	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
690	C₂²	—	2	32	no	—
691	C₂²	—	2	4	no	—
692	C₂²	—	2	4	no	—
693	C₂²	—	2	4	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	4	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	4	no	—
698	C₂²	—	2	4	no	—
699	C₂²	—	2	4	no	—
700	C₂²	—	2	4	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	4	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	4	no	—
706	C₂²	C₂₃×#525	1	4	yes	—
707	C₂²	C₂₃×#539	1	8	yes	complemented
708	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
709	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
710	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
711	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
712	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
713	C₄	—	2	4	no	—
714	C₄	—	2	4	no	—
715	C₄	—	2	4	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	4	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	4	no	—
725	C₂	—	2	4	no	—
726	C₂	—	2	8	no	—
727	C₂	—	8	2	no	—
728	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
729	C₂	C₂×C₂₃×#539	1	2	yes	—
730	C₂	C₂₃×#3484	1	1	yes	characteristic
731	C₂	C₂₃×#3486	1	1	yes	characteristic
732	C₂	C₂₃×#3492	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂₃×#2847	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#539	C₂	semidirect
2. C₂³×C₄⋊C₄×C₂₃	C₂	semidirect
3. C₂₃×#2849	C₂	semidirect
4. C₂₃×#2848	C₂	semidirect
6. C₂₃×#2627	C₂	semidirect
7. C₂₃×#2623	C₂	semidirect
8. C₂₃×#2618	C₂	semidirect
9. C₂₃×#2481	C₂	semidirect
10. C₂₃×#2473	C₂	semidirect
11. C₂₃×#2449	C₂	semidirect
12. C₂₃×#2443	C₂	semidirect
13. C₂₃×#2322	C₂	semidirect
14. C₂₃×#2313	C₂	semidirect
15. C₄×C₂₃×#120	C₂	semidirect
20. C₂×C₂₃×#126	C₂²	semidirect
21. C₂×C₂₃×#125	C₂²	semidirect
24. C₂×C₂₃×#123	C₂²	semidirect
27. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
40. C₂₃×#400	C₂²	semidirect
41. C₂₃×#400	C₂²	semidirect
42. C₂₃×#399	C₂²	semidirect
43. C₂₃×#398	C₂²	semidirect
44. C₂₃×#398	C₂²	semidirect
45. C₂₃×#398	C₂²	semidirect
46. C₂₃×#397	C₂²	semidirect
47. C₂₃×#396	C₂²	semidirect
48. C₂₃×#395	C₂²	semidirect
49. C₂₃×#394	C₂²	semidirect
50. C₂₃×#389	C₂²	semidirect
51. C₂₃×#388	C₂²	semidirect
52. C₂₃×#387	C₂²	semidirect
53. C₂₃×#387	C₂²	semidirect
54. C₂₃×#387	C₂²	semidirect
67. C₂₃×#385	C₂²	semidirect
118. C₂×C₄⋊C₄×C₂₃	D₄	semidirect
255. #34989	C₂₃	direct (N × H)
324. C₂×#539	C₂×C₂₃	semidirect
325. C₂³×C₄⋊C₄	C₂×C₂₃	semidirect
326. #2849	C₂×C₂₃	semidirect
327. #2848	C₂×C₂₃	semidirect
329. #2627	C₂×C₂₃	semidirect
330. #2623	C₂×C₂₃	semidirect
331. #2618	C₂×C₂₃	semidirect
332. #2481	C₂×C₂₃	semidirect
333. #2473	C₂×C₂₃	semidirect
334. #2449	C₂×C₂₃	semidirect
335. #2443	C₂×C₂₃	semidirect
336. #2322	C₂×C₂₃	semidirect
337. #2313	C₂×C₂₃	semidirect
338. C₄×#120	C₂×C₂₃	semidirect
356. C₂²×C₂₃	#539	semidirect
378. C₂×#126	C₂²×C₂₃	semidirect
379. C₂×#125	C₂²×C₂₃	semidirect
382. C₂×#123	C₂²×C₂₃	semidirect
385. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
398. #400	C₂²×C₂₃	semidirect
399. #400	C₂²×C₂₃	semidirect
400. #399	C₂²×C₂₃	semidirect
401. #398	C₂²×C₂₃	semidirect
402. #398	C₂²×C₂₃	semidirect
403. #398	C₂²×C₂₃	semidirect
404. #397	C₂²×C₂₃	semidirect
405. #396	C₂²×C₂₃	semidirect
406. #395	C₂²×C₂₃	semidirect
407. #394	C₂²×C₂₃	semidirect
408. #389	C₂²×C₂₃	semidirect
409. #388	C₂²×C₂₃	semidirect
410. #387	C₂²×C₂₃	semidirect
411. #387	C₂²×C₂₃	semidirect
412. #387	C₂²×C₂₃	semidirect
425. #385	C₂²×C₂₃	semidirect
484. C₂×C₄⋊C₄	D₄×C₂₃	semidirect
528. C₂₃	#34989	direct (N × H)
707. C₂²	C₂₃×#539	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₂₃×#539	2
C₂³×C₄⋊C₄×C₂₃	2
C₂₃×#2849	2
C₂₃×#2848	2
C₂₃×#2847	2
C₂₃×#2627	2
C₂₃×#2623	2
C₂₃×#2618	2
C₂₃×#2481	2
C₂₃×#2473	2
C₂₃×#2449	2
C₂₃×#2443	2
C₂₃×#2322	2
C₂₃×#2313	2
C₄×C₂₃×#120	2
#34989	23

Subgroups — C23×#34989 #19182615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34989 #19182615