Subgroups — C₂₃×#36586 #19184212

Order 5888.

1868 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#2850	C₂	1	2	yes	maximal
3	C₂₃×#2596	C₂	1	4	yes	maximal, complemented
4	C₂₃×#2571	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2547	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2514	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2510	C₂	1	4	yes	maximal, complemented
8	C₂₃×#2494	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2487	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2448	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2352	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2347	C₂	1	2	yes	maximal, complemented
15	C₄×C₂₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
16	C₄×C₂₃×#121	C₂	1	1	yes	maximal, characteristic
17	C₂×C₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#124	C₂²	1	2	yes	—
20	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#117	C₂²	1	2	yes	—
26	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
30	C₂₃×#401	C₂²	1	4	yes	—
31	C₂₃×#400	C₂²	1	4	yes	—
32	C₂₃×#400	C₂²	1	4	yes	—
33	C₂₃×#399	C₂²	1	4	yes	—
34	C₂₃×#397	C₂²	1	4	yes	—
35	C₂₃×#397	C₂²	1	4	yes	—
36	C₂₃×#391	C₂²	1	2	yes	—
37	C₂₃×#391	C₂²	1	2	yes	—
38	C₂₃×#391	C₂²	1	2	yes	—
39	C₂₃×#390	C₂²	1	1	yes	characteristic
40	C₂₃×#390	C₂²	1	2	yes	—
41	C₂₃×#389	C₂²	1	2	yes	—
42	C₂₃×#389	C₂²	1	2	yes	—
43	C₂₃×#389	C₂²	1	2	yes	—
44	C₂₃×#389	C₂²	1	2	yes	—
45	C₂₃×#389	C₂²	1	1	yes	characteristic
46	C₂₃×#389	C₂²	1	2	yes	—
47	C₂₃×#388	C₂²	1	4	yes	—
48	C₂₃×#388	C₂²	1	4	yes	—
49	C₂₃×#388	C₂²	1	4	yes	—
50	C₂₃×#388	C₂²	1	4	yes	—
51	C₂₃×#388	C₂²	1	2	yes	—
52	C₂₃×#388	C₂²	1	4	yes	—
53	C₂₃×#387	C₂²	1	4	yes	—
54	C₂₃×#387	C₂²	1	4	yes	—
55	C₂₃×#387	C₂²	1	4	yes	—
56	C₂₃×#386	C₂²	1	4	yes	—
57	C₂₃×#386	C₂²	1	2	yes	—
58	C₂₃×#386	C₂²	1	4	yes	—
59	C₂₃×#385	C₂²	1	4	yes	—
60	C₂₃×#384	C₂²	1	1	yes	characteristic
61	C₂₃×#383	C₂²	1	4	yes	—
62	C₂₃×#382	C₂²	1	2	yes	—
63	C₂₃×#382	C₂²	1	2	yes	—
64	C₂₃×#380	C₂²	1	2	yes	—
65	C₂₃×#380	C₂²	1	2	yes	—
66	C₂₃×#380	C₂²	1	2	yes	—
67	C₂₃×#380	C₂²	1	2	yes	—
68	C₂₃×#380	C₂²	1	2	yes	—
69	C₂₃×#380	C₂²	1	1	yes	characteristic
70	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
74	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
76	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
77	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
78	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
79	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
82	C₂×C₂₃×#95	C₂²	1	2	yes	—
83	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
84	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
85	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
87	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
89	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
92	C₂₃×C₄⋊Q₈	—	2	4	no	—
93	C₂₃×#124	—	4	4	no	—
94	C₂₃×C₂²⋊Q₈	—	2	8	no	—
95	C₂₃×#121	—	2	4	no	—
96	C₄×Q₈×C₂₃	—	4	4	no	—
97	C₄×D₄×C₂₃	—	2	8	no	—
98	C₄×D₄×C₂₃	—	2	4	no	—
99	C₂₃×#117	—	2	8	no	—
100	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
101	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
102	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
130	C₂×C₄²×C₂₃	—	2	4	no	—
131	C₂×C₄²×C₂₃	—	4	4	no	—
132	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
134	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
135	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
136	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
137	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
140	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
141	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
142	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
143	C₂₃×#95	C₂³	1	2	yes	—
144	C₂₃×#95	C₂³	1	2	yes	—
145	C₂₃×#95	C₂³	1	2	yes	—
146	C₂₃×#95	C₂³	1	2	yes	—
147	C₂₃×#95	C₂³	1	2	yes	—
148	C₂₃×#95	C₂³	1	4	yes	—
149	C₂₃×#95	C₂³	1	4	yes	—
150	C₂₃×#95	C₂³	1	2	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	4	yes	—
157	C₂₃×#95	C₂³	1	4	yes	—
158	C₂₃×#95	C₂³	1	4	yes	—
159	C₂₃×#95	C₂³	1	4	yes	—
160	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
161	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
162	C₂×Q₈×C₂₃	—	2	4	no	—
163	C₂×Q₈×C₂₃	—	2	4	no	—
164	C₂×Q₈×C₂₃	—	2	4	no	—
165	C₂×D₄×C₂₃	—	2	4	no	—
166	C₂×D₄×C₂₃	—	2	4	no	—
167	C₂×D₄×C₂₃	—	2	4	no	—
168	C₂×D₄×C₂₃	—	2	2	no	—
169	C₂×D₄×C₂₃	—	2	2	no	—
170	C₂×D₄×C₂₃	—	2	2	no	—
171	C₂²×C₄×C₂₃	—	2	2	no	—
172	C₂²×C₄×C₂₃	—	2	2	no	—
173	C₂²×C₄×C₂₃	—	2	2	no	—
174	C₂²×C₄×C₂₃	—	2	2	no	—
175	C₂²×C₄×C₂₃	—	2	4	no	—
176	C₂²×C₄×C₂₃	—	2	2	no	—
177	C₂²×C₄×C₂₃	—	2	4	no	—
178	C₂²×C₄×C₂₃	—	2	2	no	—
179	C₂²×C₄×C₂₃	—	2	4	no	—
180	C₂²×C₄×C₂₃	—	2	4	no	—
181	C₂²×C₄×C₂₃	—	2	4	no	—
182	C₂²×C₄×C₂₃	—	2	4	no	—
183	C₂²×C₄×C₂₃	—	4	2	no	—
184	C₂²×C₄×C₂₃	—	4	2	no	—
185	C₂²×C₄×C₂₃	—	4	1	no	—
186	C₂²×C₄×C₂₃	—	4	2	no	—
187	C₂²×C₄×C₂₃	#41	1	4	yes	—
188	C₂²×C₄×C₂₃	#41	1	4	yes	—
189	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
196	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
204	C₄⋊C₄×C₂₃	—	2	4	no	—
205	C₄⋊C₄×C₂₃	—	2	4	no	—
206	C₄⋊C₄×C₂₃	—	2	2	no	—
207	C₄⋊C₄×C₂₃	—	2	2	no	—
208	C₄⋊C₄×C₂₃	—	2	2	no	—
209	C₄⋊C₄×C₂₃	—	2	4	no	—
210	C₄⋊C₄×C₂₃	—	2	4	no	—
211	C₄⋊C₄×C₂₃	—	2	2	no	—
212	C₄⋊C₄×C₂₃	—	2	2	no	—
213	C₄⋊C₄×C₂₃	—	2	4	no	—
214	C₄⋊C₄×C₂₃	—	2	8	no	—
215	C₄⋊C₄×C₂₃	—	2	4	no	—
216	C₄⋊C₄×C₂₃	—	2	4	no	—
217	C₄⋊C₄×C₂₃	—	2	2	no	—
218	C₄⋊C₄×C₂₃	—	4	2	no	—
219	C₄⋊C₄×C₂₃	—	4	4	no	—
220	C₄⋊C₄×C₂₃	—	4	4	no	—
221	C₄⋊C₄×C₂₃	#41	1	4	yes	—
222	C₂²⋊C₄×C₂₃	—	2	4	no	—
223	C₂²⋊C₄×C₂₃	—	2	8	no	—
224	C₂²⋊C₄×C₂₃	—	2	8	no	—
225	C₂²⋊C₄×C₂₃	—	2	4	no	—
226	C₂²⋊C₄×C₂₃	—	2	4	no	—
227	C₂²⋊C₄×C₂₃	—	2	4	no	—
228	C₂²⋊C₄×C₂₃	—	4	2	no	—
229	C₂²⋊C₄×C₂₃	—	4	4	no	—
230	C₂²⋊C₄×C₂₃	—	4	4	no	—
231	C₂²⋊C₄×C₂₃	—	4	4	no	—
232	C₄²×C₂₃	—	2	2	no	—
233	C₄²×C₂₃	—	2	2	no	—
234	C₄²×C₂₃	—	2	2	no	—
235	C₄²×C₂₃	—	2	8	no	—
236	C₄²×C₂₃	—	2	4	no	—
237	C₄²×C₂₃	—	2	4	no	—
238	C₄²×C₂₃	—	2	4	no	—
239	C₄²×C₂₃	—	4	2	no	—
240	C₄²×C₂₃	—	4	2	no	—
241	C₄²×C₂₃	—	4	4	no	—
242	C₄²×C₂₃	#41	1	4	yes	—
243	#36586	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂³×C₂₃	—	2	1	no	—
245	C₂³×C₂₃	—	2	1	no	—
246	C₂³×C₂₃	—	2	1	no	—
247	C₂³×C₂₃	—	2	1	no	—
248	C₂³×C₂₃	—	2	2	no	—
249	C₂³×C₂₃	—	2	2	no	—
250	C₂³×C₂₃	—	2	2	no	—
251	C₂³×C₂₃	—	2	2	no	—
252	C₂³×C₂₃	—	2	2	no	—
253	C₂³×C₂₃	—	2	2	no	—
254	C₂³×C₂₃	—	2	2	no	—
255	C₂³×C₂₃	C₂×#41	1	2	yes	—
256	C₂³×C₂₃	C₂×#41	1	2	yes	—
257	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
258	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
259	Q₈×C₂₃	—	4	8	no	—
260	D₄×C₂₃	—	4	8	no	—
261	D₄×C₂₃	—	4	4	no	—
262	C₂×C₄×C₂₃	—	2	1	no	—
263	C₂×C₄×C₂₃	—	2	1	no	—
264	C₂×C₄×C₂₃	—	2	1	no	—
265	C₂×C₄×C₂₃	—	2	2	no	—
266	C₂×C₄×C₂₃	—	2	1	no	—
267	C₂×C₄×C₂₃	—	2	1	no	—
268	C₂×C₄×C₂₃	—	2	2	no	—
269	C₂×C₄×C₂₃	—	2	1	no	—
270	C₂×C₄×C₂₃	—	2	8	no	—
271	C₂×C₄×C₂₃	—	2	8	no	—
272	C₂×C₄×C₂₃	—	2	2	no	—
273	C₂×C₄×C₂₃	—	2	1	no	—
274	C₂×C₄×C₂₃	—	2	2	no	—
275	C₂×C₄×C₂₃	—	2	4	no	—
276	C₂×C₄×C₂₃	—	2	2	no	—
277	C₂×C₄×C₂₃	—	2	4	no	—
278	C₂×C₄×C₂₃	—	2	2	no	—
279	C₂×C₄×C₂₃	—	2	2	no	—
280	C₂×C₄×C₂₃	—	2	2	no	—
281	C₂×C₄×C₂₃	—	2	4	no	—
282	C₂×C₄×C₂₃	—	2	2	no	—
283	C₂×C₄×C₂₃	—	2	2	no	—
284	C₂×C₄×C₂₃	—	2	2	no	—
285	C₂×C₄×C₂₃	—	2	4	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	1	no	—
292	C₂×C₄×C₂₃	—	2	2	no	—
293	C₂×C₄×C₂₃	—	2	2	no	—
294	C₂×C₄×C₂₃	—	2	1	no	—
295	C₂×C₄×C₂₃	—	2	2	no	—
296	C₂×C₄×C₂₃	—	2	4	no	—
297	C₂×C₄×C₂₃	—	2	2	no	—
298	C₂×C₄×C₂₃	—	2	2	no	—
299	C₂×C₄×C₂₃	—	4	4	no	—
300	C₂×C₄×C₂₃	—	4	8	no	—
301	C₂×C₄×C₂₃	—	4	8	no	—
302	C₂×C₄×C₂₃	—	4	8	no	—
303	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
304	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
305	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
306	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
307	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
308	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
309	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
310	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
311	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
312	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
313	#2857	C₂×C₂₃	1	1	yes	characteristic, complemented
314	#2850	C₂×C₂₃	1	2	yes	—
315	#2596	C₂×C₂₃	1	4	yes	complemented
316	#2571	C₂×C₂₃	1	1	yes	characteristic, complemented
317	#2547	C₂×C₂₃	1	1	yes	characteristic, complemented
318	#2514	C₂×C₂₃	1	2	yes	complemented
319	#2510	C₂×C₂₃	1	4	yes	complemented
320	#2494	C₂×C₂₃	1	2	yes	complemented
321	#2487	C₂×C₂₃	1	2	yes	complemented
322	#2448	C₂×C₂₃	1	2	yes	complemented
323	#2365	C₂×C₂₃	1	1	yes	characteristic, complemented
324	#2354	C₂×C₂₃	1	1	yes	characteristic, complemented
325	#2352	C₂×C₂₃	1	2	yes	complemented
326	#2347	C₂×C₂₃	1	2	yes	complemented
327	C₄×C₂²⋊Q₈	C₂×C₂₃	1	2	yes	complemented
328	C₄×#121	C₂×C₂₃	1	1	yes	characteristic
329	C₂×C₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
330	C₂²×C₂₃	—	2	2	no	—
331	C₂²×C₂₃	—	2	2	no	—
332	C₂²×C₂₃	—	2	2	no	—
333	C₂²×C₂₃	—	2	2	no	—
334	C₂²×C₂₃	—	2	2	no	—
335	C₂²×C₂₃	—	2	2	no	—
336	C₂²×C₂₃	—	4	2	no	—
337	C₂²×C₂₃	—	4	2	no	—
338	C₂²×C₂₃	—	4	2	no	—
339	C₂²×C₂₃	—	4	2	no	—
340	C₂²×C₂₃	—	4	2	no	—
341	C₂²×C₂₃	—	4	2	no	—
342	C₂²×C₂₃	—	4	2	no	—
343	C₂²×C₂₃	#556	1	4	yes	—
344	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
345	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
346	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
347	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
348	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
349	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
350	C₂²×C₂₃	#585	1	1	yes	characteristic
351	C₄×C₂₃	—	2	2	no	—
352	C₄×C₂₃	—	2	2	no	—
353	C₄×C₂₃	—	2	2	no	—
354	C₄×C₂₃	—	2	4	no	—
355	C₄×C₂₃	—	4	2	no	—
356	C₄×C₂₃	—	4	4	no	—
357	C₄×C₂₃	—	4	2	no	—
358	C₄×C₂₃	—	4	4	no	—
359	C₄×C₂₃	—	4	1	no	—
360	C₄×C₂₃	—	4	2	no	—
361	C₄×C₂₃	—	4	2	no	—
362	C₄×C₂₃	—	4	2	no	—
363	C₄×C₂₃	—	4	2	no	—
364	C₄×C₂₃	#529	1	4	yes	—
365	C₄×C₂₃	#553	1	4	yes	—
366	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
367	C₂×#124	C₂²×C₂₃	1	2	yes	—
368	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
369	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
370	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
371	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
372	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
373	C₂×#117	C₂²×C₂₃	1	2	yes	—
374	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
375	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
376	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
377	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
378	#401	C₂²×C₂₃	1	4	yes	—
379	#400	C₂²×C₂₃	1	4	yes	—
380	#400	C₂²×C₂₃	1	4	yes	—
381	#399	C₂²×C₂₃	1	4	yes	—
382	#397	C₂²×C₂₃	1	4	yes	—
383	#397	C₂²×C₂₃	1	4	yes	—
384	#391	C₂²×C₂₃	1	2	yes	—
385	#391	C₂²×C₂₃	1	2	yes	—
386	#391	C₂²×C₂₃	1	2	yes	—
387	#390	C₂²×C₂₃	1	2	yes	—
388	#390	C₂²×C₂₃	1	1	yes	characteristic
389	#389	C₂²×C₂₃	1	2	yes	—
390	#389	C₂²×C₂₃	1	2	yes	—
391	#389	C₂²×C₂₃	1	2	yes	—
392	#389	C₂²×C₂₃	1	2	yes	—
393	#389	C₂²×C₂₃	1	2	yes	—
394	#389	C₂²×C₂₃	1	1	yes	characteristic
395	#388	C₂²×C₂₃	1	4	yes	—
396	#388	C₂²×C₂₃	1	4	yes	—
397	#388	C₂²×C₂₃	1	2	yes	—
398	#388	C₂²×C₂₃	1	4	yes	—
399	#388	C₂²×C₂₃	1	4	yes	—
400	#388	C₂²×C₂₃	1	4	yes	—
401	#387	C₂²×C₂₃	1	4	yes	—
402	#387	C₂²×C₂₃	1	4	yes	—
403	#387	C₂²×C₂₃	1	4	yes	—
404	#386	C₂²×C₂₃	1	4	yes	—
405	#386	C₂²×C₂₃	1	4	yes	—
406	#386	C₂²×C₂₃	1	2	yes	—
407	#385	C₂²×C₂₃	1	4	yes	—
408	#384	C₂²×C₂₃	1	1	yes	characteristic
409	#383	C₂²×C₂₃	1	4	yes	—
410	#382	C₂²×C₂₃	1	2	yes	—
411	#382	C₂²×C₂₃	1	2	yes	—
412	#380	C₂²×C₂₃	1	2	yes	—
413	#380	C₂²×C₂₃	1	2	yes	—
414	#380	C₂²×C₂₃	1	2	yes	—
415	#380	C₂²×C₂₃	1	2	yes	—
416	#380	C₂²×C₂₃	1	2	yes	—
417	#380	C₂²×C₂₃	1	1	yes	characteristic
418	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
419	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
420	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
421	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
422	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
423	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
424	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
425	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
426	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
427	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
428	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
429	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
430	C₂×#95	C₂²×C₂₃	1	2	yes	—
431	C₂×C₂₃	—	2	4	no	—
432	C₂×C₂₃	—	8	2	no	—
433	C₂×C₂₃	C₂×#529	1	1	yes	characteristic
434	C₂×C₂₃	C₂×#553	1	1	yes	characteristic
435	C₂×C₂₃	C₂×#556	1	1	yes	characteristic
436	C₂×C₂₃	#3480	1	1	yes	characteristic
437	C₂×C₂₃	#3495	1	1	yes	characteristic
438	C₂×C₂₃	#3506	1	1	yes	characteristic
439	C₂×C₂₃	#3520	1	1	yes	characteristic
440	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
441	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
442	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
443	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
444	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
445	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
446	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
448	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
449	C₄⋊Q₈	—	2	4	no	—
450	#124	—	4	4	no	—
451	C₂²⋊Q₈	—	2	8	no	—
452	#121	—	2	4	no	—
453	C₄×Q₈	—	4	4	no	—
454	C₄×D₄	—	2	8	no	—
455	C₄×D₄	—	2	4	no	—
456	#117	—	2	8	no	—
457	C₂×C₄⋊C₄	—	2	4	no	—
458	C₂×C₄⋊C₄	—	2	4	no	—
459	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
471	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
474	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
475	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
477	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
487	C₂×C₄²	—	2	4	no	—
488	C₂×C₄²	—	4	4	no	—
489	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
490	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
491	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
492	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
493	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
497	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
498	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
499	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
500	#95	C₂³×C₂₃	1	2	yes	—
501	#95	C₂³×C₂₃	1	2	yes	—
502	#95	C₂³×C₂₃	1	2	yes	—
503	#95	C₂³×C₂₃	1	2	yes	—
504	#95	C₂³×C₂₃	1	2	yes	—
505	#95	C₂³×C₂₃	1	4	yes	—
506	#95	C₂³×C₂₃	1	4	yes	—
507	#95	C₂³×C₂₃	1	2	yes	—
508	#95	C₂³×C₂₃	1	4	yes	—
509	#95	C₂³×C₂₃	1	4	yes	—
510	#95	C₂³×C₂₃	1	4	yes	—
511	#95	C₂³×C₂₃	1	2	yes	—
512	#95	C₂³×C₂₃	1	4	yes	—
513	#95	C₂³×C₂₃	1	4	yes	—
514	#95	C₂³×C₂₃	1	4	yes	—
515	#95	C₂³×C₂₃	1	4	yes	—
516	#95	C₂³×C₂₃	1	4	yes	—
517	C₂₃	#36586	1	1	yes	characteristic, direct product factor, Sylow
518	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
519	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
520	C₂×Q₈	—	2	4	no	—
521	C₂×Q₈	—	2	4	no	—
522	C₂×Q₈	—	2	4	no	—
523	C₂×D₄	—	2	4	no	—
524	C₂×D₄	—	2	4	no	—
525	C₂×D₄	—	2	4	no	—
526	C₂×D₄	—	2	2	no	—
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	4	1	no	—
544	C₂²×C₄	—	4	2	no	—
545	C₂²×C₄	#41×C₂₃	1	4	yes	—
546	C₂²×C₄	#41×C₂₃	1	4	yes	—
547	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
554	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
555	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
557	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
560	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
561	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	8	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	4	4	no	—
577	C₄⋊C₄	—	4	2	no	—
578	C₄⋊C₄	—	4	4	no	—
579	C₄⋊C₄	#41×C₂₃	1	4	yes	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	—	2	8	no	—
582	C₂²⋊C₄	—	2	8	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	4	4	no	—
587	C₂²⋊C₄	—	4	4	no	—
588	C₂²⋊C₄	—	4	2	no	—
589	C₂²⋊C₄	—	4	4	no	—
590	C₄²	—	2	2	no	—
591	C₄²	—	2	2	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	2	8	no	—
594	C₄²	—	2	4	no	—
595	C₄²	—	2	4	no	—
596	C₄²	—	2	4	no	—
597	C₄²	—	4	2	no	—
598	C₄²	—	4	2	no	—
599	C₄²	—	4	4	no	—
600	C₄²	#41×C₂₃	1	4	yes	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	2	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	2	no	—
612	C₂³	C₂×#41×C₂₃	1	2	yes	—
613	C₂³	C₂×#41×C₂₃	1	2	yes	—
614	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
615	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
616	Q₈	—	4	8	no	—
617	D₄	—	4	8	no	—
618	D₄	—	4	4	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	8	no	—
628	C₂×C₄	—	2	8	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	4	4	no	—
657	C₂×C₄	—	4	8	no	—
658	C₂×C₄	—	4	8	no	—
659	C₂×C₄	—	4	8	no	—
660	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
661	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
662	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
663	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
664	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
665	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
666	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
667	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
668	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
669	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	4	2	no	—
677	C₂²	—	4	2	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	2	no	—
682	C₂²	—	4	2	no	—
683	C₂²	C₂₃×#556	1	4	yes	—
684	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
685	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
686	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
687	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
688	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
689	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
690	C₂²	C₂₃×#585	1	1	yes	characteristic
691	C₄	—	2	2	no	—
692	C₄	—	2	2	no	—
693	C₄	—	2	2	no	—
694	C₄	—	2	4	no	—
695	C₄	—	4	2	no	—
696	C₄	—	4	4	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	4	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	2	no	—
701	C₄	—	4	2	no	—
702	C₄	—	4	2	no	—
703	C₄	—	4	2	no	—
704	C₄	C₂₃×#529	1	4	yes	—
705	C₄	C₂₃×#553	1	4	yes	—
706	C₂	—	2	4	no	—
707	C₂	—	8	2	no	—
708	C₂	C₂×C₂₃×#529	1	1	yes	characteristic
709	C₂	C₂×C₂₃×#553	1	1	yes	characteristic
710	C₂	C₂×C₂₃×#556	1	1	yes	characteristic
711	C₂	C₂₃×#3480	1	1	yes	characteristic
712	C₂	C₂₃×#3495	1	1	yes	characteristic
713	C₂	C₂₃×#3506	1	1	yes	characteristic
714	C₂	C₂₃×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#121	C₂²
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. C₂₃×#2857	C₂	semidirect
3. C₂₃×#2596	C₂	semidirect
4. C₂₃×#2571	C₂	semidirect
5. C₂₃×#2547	C₂	semidirect
6. C₂₃×#2514	C₂	semidirect
7. C₂₃×#2510	C₂	semidirect
8. C₂₃×#2494	C₂	semidirect
9. C₂₃×#2487	C₂	semidirect
10. C₂₃×#2448	C₂	semidirect
11. C₂₃×#2365	C₂	semidirect
12. C₂₃×#2354	C₂	semidirect
13. C₂₃×#2352	C₂	semidirect
14. C₂₃×#2347	C₂	semidirect
15. C₄×C₂₃×C₂²⋊Q₈	C₂	semidirect
17. C₂×C₄×C₄⋊C₄×C₂₃	C₂	semidirect
243. #36586	C₂₃	direct (N × H)
313. #2857	C₂×C₂₃	semidirect
315. #2596	C₂×C₂₃	semidirect
316. #2571	C₂×C₂₃	semidirect
317. #2547	C₂×C₂₃	semidirect
318. #2514	C₂×C₂₃	semidirect
319. #2510	C₂×C₂₃	semidirect
320. #2494	C₂×C₂₃	semidirect
321. #2487	C₂×C₂₃	semidirect
322. #2448	C₂×C₂₃	semidirect
323. #2365	C₂×C₂₃	semidirect
324. #2354	C₂×C₂₃	semidirect
325. #2352	C₂×C₂₃	semidirect
326. #2347	C₂×C₂₃	semidirect
327. C₄×C₂²⋊Q₈	C₂×C₂₃	semidirect
329. C₂×C₄×C₄⋊C₄	C₂×C₂₃	semidirect
517. C₂₃	#36586	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#2857	2
C₂₃×#2850	2
C₂₃×#2596	2
C₂₃×#2571	2
C₂₃×#2547	2
C₂₃×#2514	2
C₂₃×#2510	2
C₂₃×#2494	2
C₂₃×#2487	2
C₂₃×#2448	2
C₂₃×#2365	2
C₂₃×#2354	2
C₂₃×#2352	2
C₂₃×#2347	2
C₄×C₂₃×C₂²⋊Q₈	2
C₄×C₂₃×#121	2
C₂×C₄×C₄⋊C₄×C₂₃	2
#36586	23

Subgroups — C23×#36586 #19184212

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36586 #19184212