Subgroups — C₂₃×#36834 #19184460

Order 5888.

1454 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2851	C₂	1	2	yes	maximal
2	C₂₃×#2788	C₂	1	2	yes	maximal
3	C₂₃×#2787	C₂	1	2	yes	maximal
4	C₂₃×#2774	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2770	C₂	1	2	yes	maximal
6	C₂₃×#2768	C₂	1	2	yes	maximal
7	C₂₃×#2766	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2726	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2719	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2655	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2611	C₂	1	1	yes	maximal, characteristic
12	C₂₃×#2606	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2599	C₂	1	1	yes	maximal, characteristic
14	C₂₃×#2590	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2584	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2475	C₂	1	2	yes	maximal
17	C₂₃×#2336	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2296	C₂	1	1	yes	maximal, characteristic
20	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#125	C₂²	1	2	yes	—
22	C₂×C₂₃×#125	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#401	C₂²	1	2	yes	—
28	C₂₃×#400	C₂²	1	2	yes	—
29	C₂₃×#400	C₂²	1	2	yes	—
30	C₂₃×#400	C₂²	1	2	yes	—
31	C₂₃×#400	C₂²	1	2	yes	—
32	C₂₃×#400	C₂²	1	2	yes	—
33	C₂₃×#400	C₂²	1	1	yes	characteristic
34	C₂₃×#400	C₂²	1	2	yes	—
35	C₂₃×#399	C₂²	1	1	yes	characteristic
36	C₂₃×#398	C₂²	1	2	yes	—
37	C₂₃×#398	C₂²	1	2	yes	—
38	C₂₃×#398	C₂²	1	2	yes	—
39	C₂₃×#398	C₂²	1	1	yes	characteristic
40	C₂₃×#398	C₂²	1	2	yes	—
41	C₂₃×#398	C₂²	1	2	yes	—
42	C₂₃×#398	C₂²	1	1	yes	characteristic
43	C₂₃×#398	C₂²	1	2	yes	—
44	C₂₃×#398	C₂²	1	2	yes	—
45	C₂₃×#398	C₂²	1	2	yes	—
46	C₂₃×#398	C₂²	1	2	yes	—
47	C₂₃×#398	C₂²	1	2	yes	—
48	C₂₃×#397	C₂²	1	2	yes	—
49	C₂₃×#397	C₂²	1	1	yes	characteristic
50	C₂₃×#397	C₂²	1	1	yes	characteristic
51	C₂₃×#396	C₂²	1	2	yes	—
52	C₂₃×#395	C₂²	1	1	yes	characteristic
53	C₂₃×#395	C₂²	1	2	yes	—
54	C₂₃×#393	C₂²	1	1	yes	characteristic
55	C₂₃×#391	C₂²	1	2	yes	—
56	C₂₃×#389	C₂²	1	2	yes	—
57	C₂₃×#389	C₂²	1	2	yes	—
58	C₂₃×#389	C₂²	1	2	yes	—
59	C₂₃×#389	C₂²	1	2	yes	—
60	C₂₃×#389	C₂²	1	2	yes	—
61	C₂₃×#389	C₂²	1	2	yes	—
62	C₂₃×#389	C₂²	1	2	yes	—
63	C₂₃×#389	C₂²	1	2	yes	—
64	C₂₃×#389	C₂²	1	2	yes	—
65	C₂₃×#389	C₂²	1	2	yes	—
66	C₂₃×#389	C₂²	1	2	yes	—
67	C₂₃×#389	C₂²	1	2	yes	—
68	C₂₃×#388	C₂²	1	2	yes	—
69	C₂₃×#388	C₂²	1	2	yes	—
70	C₂₃×#388	C₂²	1	2	yes	—
71	C₂₃×#388	C₂²	1	2	yes	—
72	C₂₃×#387	C₂²	1	2	yes	—
73	C₂₃×#387	C₂²	1	2	yes	—
74	C₂₃×#387	C₂²	1	2	yes	—
75	C₂₃×#387	C₂²	1	2	yes	—
76	C₂₃×#387	C₂²	1	2	yes	—
77	C₂₃×#387	C₂²	1	2	yes	—
78	C₂₃×#387	C₂²	1	2	yes	—
79	C₂₃×#387	C₂²	1	2	yes	—
80	C₂₃×#387	C₂²	1	2	yes	—
81	C₂₃×#387	C₂²	1	2	yes	—
82	C₂₃×#387	C₂²	1	2	yes	—
83	C₂₃×#387	C₂²	1	2	yes	—
84	C₂₃×#387	C₂²	1	2	yes	—
85	C₂₃×#387	C₂²	1	2	yes	—
86	C₂₃×#387	C₂²	1	2	yes	—
87	C₂₃×#387	C₂²	1	2	yes	—
88	C₂₃×#387	C₂²	1	2	yes	—
89	C₂₃×#385	C₂²	1	2	yes	—
90	C₂₃×#385	C₂²	1	2	yes	—
91	C₂₃×#385	C₂²	1	2	yes	—
92	C₂₃×#385	C₂²	1	2	yes	—
93	C₂₃×#385	C₂²	1	2	yes	—
94	C₂₃×#385	C₂²	1	2	yes	—
95	C₂₃×#383	C₂²	1	2	yes	—
96	C₂₃×#383	C₂²	1	1	yes	characteristic
97	C₂₃×#382	C₂²	1	2	yes	—
98	C₂₃×#382	C₂²	1	2	yes	—
99	C₂₃×#380	C₂²	1	2	yes	—
100	C₂₃×#380	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
103	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
106	C₂₃×#376	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
110	C₂₃×#125	—	2	4	no	—
111	C₂₃×#125	—	4	4	no	—
112	C₂₃×#125	—	4	4	no	—
113	C₄×Q₈×C₂₃	—	2	4	no	—
114	C₂₃×#117	—	2	4	no	—
115	C₂₃×#117	—	4	2	no	—
116	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	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	1	yes	characteristic
125	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
130	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
154	C₂×C₄²×C₂₃	—	4	2	no	—
155	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
157	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
158	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
159	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
164	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
165	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
166	C₂₃×#95	C₂³	1	1	yes	characteristic
167	C₂₃×#95	C₂³	1	1	yes	characteristic
168	C₂₃×#95	C₂³	1	2	yes	—
169	C₂₃×#95	C₂³	1	2	yes	—
170	C₂₃×#95	C₂³	1	2	yes	—
171	C₂₃×#95	C₂³	1	2	yes	—
172	C₂₃×#95	C₂³	1	2	yes	—
173	C₂₃×#95	C₂³	1	2	yes	—
174	C₂₃×#95	C₂³	1	2	yes	—
175	C₂₃×#95	C₂³	1	2	yes	—
176	C₂₃×#95	C₂³	1	2	yes	—
177	C₂₃×#95	C₂³	1	2	yes	—
178	C₂₃×#95	C₂³	1	2	yes	—
179	C₂₃×#95	C₂³	1	2	yes	—
180	C₂₃×#95	C₂³	1	2	yes	—
181	C₂₃×#95	C₂³	1	2	yes	—
182	C₂₃×#95	C₂³	1	2	yes	—
183	C₂₃×#95	C₂³	1	2	yes	—
184	C₂₃×#95	C₂³	1	1	yes	characteristic
185	C₂₃×#95	C₂³	1	2	yes	—
186	C₂₃×#95	C₂³	1	2	yes	—
187	C₂₃×#95	C₂³	1	2	yes	—
188	C₂₃×#95	C₂³	1	1	yes	characteristic
189	C₂₃×#95	C₂³	1	2	yes	—
190	C₂₃×#95	C₂³	1	2	yes	—
191	C₂₃×#95	C₂³	1	2	yes	—
192	C₂₃×#95	C₂³	1	2	yes	—
193	C₂₃×#95	C₂³	1	2	yes	—
194	C₂₃×#95	C₂³	1	2	yes	—
195	C₂₃×#95	C₂³	1	2	yes	—
196	C₂₃×#95	C₂³	1	2	yes	—
197	C₂₃×#95	C₂³	1	2	yes	—
198	C₂₃×#95	C₂³	1	2	yes	—
199	C₂₃×#95	C₂³	1	2	yes	—
200	C₂₃×#95	C₂³	1	2	yes	—
201	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
202	C₂×Q₈×C₂₃	—	2	2	no	—
203	C₂×Q₈×C₂₃	—	4	2	no	—
204	C₂²×C₄×C₂₃	—	2	2	no	—
205	C₂²×C₄×C₂₃	—	2	2	no	—
206	C₂²×C₄×C₂₃	—	2	2	no	—
207	C₂²×C₄×C₂₃	—	2	4	no	—
208	C₂²×C₄×C₂₃	—	4	2	no	—
209	C₂²×C₄×C₂₃	—	4	2	no	—
210	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₂₃	C₂⁴	1	2	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	2	yes	—
220	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
228	C₄⋊C₄×C₂₃	—	2	2	no	—
229	C₄⋊C₄×C₂₃	—	2	2	no	—
230	C₄⋊C₄×C₂₃	—	2	2	no	—
231	C₄⋊C₄×C₂₃	—	2	4	no	—
232	C₄⋊C₄×C₂₃	—	2	2	no	—
233	C₄⋊C₄×C₂₃	—	2	2	no	—
234	C₄⋊C₄×C₂₃	—	2	4	no	—
235	C₄⋊C₄×C₂₃	—	2	4	no	—
236	C₄⋊C₄×C₂₃	—	2	4	no	—
237	C₄⋊C₄×C₂₃	—	2	4	no	—
238	C₄⋊C₄×C₂₃	—	2	4	no	—
239	C₄⋊C₄×C₂₃	—	2	4	no	—
240	C₄⋊C₄×C₂₃	—	2	4	no	—
241	C₄⋊C₄×C₂₃	—	2	4	no	—
242	C₄⋊C₄×C₂₃	—	2	4	no	—
243	C₄⋊C₄×C₂₃	—	4	2	no	—
244	C₄⋊C₄×C₂₃	—	4	2	no	—
245	C₄⋊C₄×C₂₃	—	4	2	no	—
246	C₄⋊C₄×C₂₃	—	4	2	no	—
247	C₄⋊C₄×C₂₃	—	4	2	no	—
248	C₄⋊C₄×C₂₃	—	4	2	no	—
249	C₄⋊C₄×C₂₃	—	4	2	no	—
250	C₄⋊C₄×C₂₃	—	4	2	no	—
251	C₄⋊C₄×C₂₃	—	4	2	no	—
252	C₄⋊C₄×C₂₃	—	4	2	no	—
253	C₄⋊C₄×C₂₃	—	4	2	no	—
254	C₄⋊C₄×C₂₃	—	4	2	no	—
255	C₄⋊C₄×C₂₃	—	4	2	no	—
256	C₄⋊C₄×C₂₃	—	4	2	no	—
257	C₄⋊C₄×C₂₃	—	4	2	no	—
258	C₄⋊C₄×C₂₃	—	4	2	no	—
259	C₂²⋊C₄×C₂₃	—	2	4	no	—
260	C₂²⋊C₄×C₂₃	—	2	4	no	—
261	C₂²⋊C₄×C₂₃	—	2	2	no	—
262	C₂²⋊C₄×C₂₃	—	2	2	no	—
263	C₂²⋊C₄×C₂₃	—	4	2	no	—
264	C₂²⋊C₄×C₂₃	—	4	2	no	—
265	C₂²⋊C₄×C₂₃	—	4	2	no	—
266	C₄²×C₂₃	—	2	2	no	—
267	C₄²×C₂₃	—	2	4	no	—
268	C₄²×C₂₃	—	2	4	no	—
269	C₄²×C₂₃	—	4	1	no	—
270	C₄²×C₂₃	—	4	1	no	—
271	C₄²×C₂₃	—	4	2	no	—
272	C₄²×C₂₃	—	4	2	no	—
273	C₄²×C₂₃	—	4	1	no	—
274	C₄²×C₂₃	—	4	1	no	—
275	C₄²×C₂₃	—	4	2	no	—
276	C₄²×C₂₃	#41	1	4	yes	—
277	#36834	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂³×C₂₃	—	2	1	no	—
279	C₂³×C₂₃	—	2	1	no	—
280	C₂³×C₂₃	—	2	2	no	—
281	C₂³×C₂₃	—	2	2	no	—
282	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
283	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
284	Q₈×C₂₃	—	4	4	no	—
285	C₂×C₄×C₂₃	—	2	8	no	—
286	C₂×C₄×C₂₃	—	2	1	no	—
287	C₂×C₄×C₂₃	—	2	2	no	—
288	C₂×C₄×C₂₃	—	2	1	no	—
289	C₂×C₄×C₂₃	—	2	2	no	—
290	C₂×C₄×C₂₃	—	2	1	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	1	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	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	2	no	—
306	C₂×C₄×C₂₃	—	2	2	no	—
307	C₂×C₄×C₂₃	—	2	2	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	2	no	—
310	C₂×C₄×C₂₃	—	2	2	no	—
311	C₂×C₄×C₂₃	—	2	2	no	—
312	C₂×C₄×C₂₃	—	2	2	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	2	no	—
315	C₂×C₄×C₂₃	—	2	2	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	2	no	—
318	C₂×C₄×C₂₃	—	2	2	no	—
319	C₂×C₄×C₂₃	—	2	2	no	—
320	C₂×C₄×C₂₃	—	2	2	no	—
321	C₂×C₄×C₂₃	—	2	2	no	—
322	C₂×C₄×C₂₃	—	2	2	no	—
323	C₂×C₄×C₂₃	—	2	2	no	—
324	C₂×C₄×C₂₃	—	2	2	no	—
325	C₂×C₄×C₂₃	—	2	2	no	—
326	C₂×C₄×C₂₃	—	2	2	no	—
327	C₂×C₄×C₂₃	—	2	2	no	—
328	C₂×C₄×C₂₃	—	2	2	no	—
329	C₂×C₄×C₂₃	—	2	2	no	—
330	C₂×C₄×C₂₃	—	2	2	no	—
331	C₂×C₄×C₂₃	—	4	8	no	—
332	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
333	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
334	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
335	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
336	C₂×C₄×C₂₃	2₋¹⁺⁴	1	4	yes	—
337	#2851	C₂×C₂₃	1	2	yes	—
338	#2788	C₂×C₂₃	1	2	yes	—
339	#2787	C₂×C₂₃	1	2	yes	—
340	#2774	C₂×C₂₃	1	2	yes	complemented
341	#2770	C₂×C₂₃	1	2	yes	—
342	#2768	C₂×C₂₃	1	2	yes	—
343	#2766	C₂×C₂₃	1	2	yes	complemented
344	#2726	C₂×C₂₃	1	2	yes	complemented
345	#2719	C₂×C₂₃	1	2	yes	complemented
346	#2655	C₂×C₂₃	1	2	yes	complemented
347	#2611	C₂×C₂₃	1	1	yes	characteristic
348	#2606	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#2599	C₂×C₂₃	1	1	yes	characteristic
350	#2590	C₂×C₂₃	1	2	yes	complemented
351	#2584	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#2475	C₂×C₂₃	1	2	yes	—
353	#2336	C₂×C₂₃	1	1	yes	characteristic, complemented
354	#2320	C₂×C₂₃	1	1	yes	characteristic, complemented
355	#2296	C₂×C₂₃	1	1	yes	characteristic
356	C₂²×C₂₃	—	2	2	no	—
357	C₂²×C₂₃	—	2	4	no	—
358	C₂²×C₂₃	—	4	1	no	—
359	C₂²×C₂₃	—	4	1	no	—
360	C₂²×C₂₃	—	4	2	no	—
361	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
362	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
364	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
365	C₂²×C₂₃	#585	1	2	yes	—
366	C₄×C₂₃	—	2	2	no	—
367	C₄×C₂₃	—	2	2	no	—
368	C₄×C₂₃	—	2	2	no	—
369	C₄×C₂₃	—	2	2	no	—
370	C₄×C₂₃	—	2	4	no	—
371	C₄×C₂₃	—	4	1	no	—
372	C₄×C₂₃	—	4	2	no	—
373	C₄×C₂₃	—	4	2	no	—
374	C₄×C₂₃	—	4	2	no	—
375	C₄×C₂₃	—	4	2	no	—
376	C₄×C₂₃	—	4	1	no	—
377	C₄×C₂₃	—	4	2	no	—
378	C₄×C₂₃	—	4	2	no	—
379	C₄×C₂₃	—	4	2	no	—
380	C₄×C₂₃	—	4	2	no	—
381	C₄×C₂₃	—	4	2	no	—
382	C₄×C₂₃	—	4	2	no	—
383	C₄×C₂₃	—	4	2	no	—
384	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
385	C₂×#125	C₂²×C₂₃	1	2	yes	—
386	C₂×#125	C₂²×C₂₃	1	2	yes	—
387	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
388	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
389	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
390	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
391	#401	C₂²×C₂₃	1	2	yes	—
392	#400	C₂²×C₂₃	1	2	yes	—
393	#400	C₂²×C₂₃	1	1	yes	characteristic
394	#400	C₂²×C₂₃	1	2	yes	—
395	#400	C₂²×C₂₃	1	2	yes	—
396	#400	C₂²×C₂₃	1	2	yes	—
397	#400	C₂²×C₂₃	1	2	yes	—
398	#400	C₂²×C₂₃	1	2	yes	—
399	#399	C₂²×C₂₃	1	1	yes	characteristic
400	#398	C₂²×C₂₃	1	2	yes	—
401	#398	C₂²×C₂₃	1	2	yes	—
402	#398	C₂²×C₂₃	1	2	yes	—
403	#398	C₂²×C₂₃	1	2	yes	—
404	#398	C₂²×C₂₃	1	1	yes	characteristic
405	#398	C₂²×C₂₃	1	2	yes	—
406	#398	C₂²×C₂₃	1	2	yes	—
407	#398	C₂²×C₂₃	1	1	yes	characteristic
408	#398	C₂²×C₂₃	1	2	yes	—
409	#398	C₂²×C₂₃	1	2	yes	—
410	#398	C₂²×C₂₃	1	2	yes	—
411	#398	C₂²×C₂₃	1	2	yes	—
412	#397	C₂²×C₂₃	1	1	yes	characteristic
413	#397	C₂²×C₂₃	1	1	yes	characteristic
414	#397	C₂²×C₂₃	1	2	yes	—
415	#396	C₂²×C₂₃	1	2	yes	—
416	#395	C₂²×C₂₃	1	2	yes	—
417	#395	C₂²×C₂₃	1	1	yes	characteristic
418	#393	C₂²×C₂₃	1	1	yes	characteristic
419	#391	C₂²×C₂₃	1	2	yes	—
420	#389	C₂²×C₂₃	1	2	yes	—
421	#389	C₂²×C₂₃	1	2	yes	—
422	#389	C₂²×C₂₃	1	2	yes	—
423	#389	C₂²×C₂₃	1	2	yes	—
424	#389	C₂²×C₂₃	1	2	yes	—
425	#389	C₂²×C₂₃	1	2	yes	—
426	#389	C₂²×C₂₃	1	2	yes	—
427	#389	C₂²×C₂₃	1	2	yes	—
428	#389	C₂²×C₂₃	1	2	yes	—
429	#389	C₂²×C₂₃	1	2	yes	—
430	#389	C₂²×C₂₃	1	2	yes	—
431	#389	C₂²×C₂₃	1	2	yes	—
432	#388	C₂²×C₂₃	1	2	yes	—
433	#388	C₂²×C₂₃	1	2	yes	—
434	#388	C₂²×C₂₃	1	2	yes	—
435	#388	C₂²×C₂₃	1	2	yes	—
436	#387	C₂²×C₂₃	1	2	yes	—
437	#387	C₂²×C₂₃	1	2	yes	—
438	#387	C₂²×C₂₃	1	2	yes	—
439	#387	C₂²×C₂₃	1	2	yes	—
440	#387	C₂²×C₂₃	1	2	yes	—
441	#387	C₂²×C₂₃	1	2	yes	—
442	#387	C₂²×C₂₃	1	2	yes	—
443	#387	C₂²×C₂₃	1	2	yes	—
444	#387	C₂²×C₂₃	1	2	yes	—
445	#387	C₂²×C₂₃	1	2	yes	—
446	#387	C₂²×C₂₃	1	2	yes	—
447	#387	C₂²×C₂₃	1	2	yes	—
448	#387	C₂²×C₂₃	1	2	yes	—
449	#387	C₂²×C₂₃	1	2	yes	—
450	#387	C₂²×C₂₃	1	2	yes	—
451	#387	C₂²×C₂₃	1	2	yes	—
452	#387	C₂²×C₂₃	1	2	yes	—
453	#385	C₂²×C₂₃	1	2	yes	—
454	#385	C₂²×C₂₃	1	2	yes	—
455	#385	C₂²×C₂₃	1	2	yes	—
456	#385	C₂²×C₂₃	1	2	yes	—
457	#385	C₂²×C₂₃	1	2	yes	—
458	#385	C₂²×C₂₃	1	2	yes	—
459	#383	C₂²×C₂₃	1	2	yes	—
460	#383	C₂²×C₂₃	1	1	yes	characteristic
461	#382	C₂²×C₂₃	1	2	yes	—
462	#382	C₂²×C₂₃	1	2	yes	—
463	#380	C₂²×C₂₃	1	2	yes	—
464	#380	C₂²×C₂₃	1	2	yes	—
465	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
466	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
467	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
468	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
469	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
470	#376	C₂²×C₂₃	1	1	yes	characteristic
471	C₂×C₂₃	—	4	2	no	—
472	C₂×C₂₃	#3455	1	1	yes	characteristic
473	C₂×C₂₃	#3492	1	1	yes	characteristic
474	C₂×C₂₃	#3509	1	1	yes	characteristic
475	C₂×C₂₃	#3541	1	2	yes	—
476	C₂×C₂₃	#3563	1	2	yes	—
477	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
480	#125	—	2	4	no	—
481	#125	—	4	4	no	—
482	#125	—	4	4	no	—
483	C₄×Q₈	—	2	4	no	—
484	#117	—	2	4	no	—
485	#117	—	4	2	no	—
486	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
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	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	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	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
524	C₂×C₄²	—	4	2	no	—
525	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
527	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
528	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
531	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
532	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
535	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
536	#95	C₂³×C₂₃	1	1	yes	characteristic
537	#95	C₂³×C₂₃	1	1	yes	characteristic
538	#95	C₂³×C₂₃	1	2	yes	—
539	#95	C₂³×C₂₃	1	2	yes	—
540	#95	C₂³×C₂₃	1	2	yes	—
541	#95	C₂³×C₂₃	1	2	yes	—
542	#95	C₂³×C₂₃	1	2	yes	—
543	#95	C₂³×C₂₃	1	2	yes	—
544	#95	C₂³×C₂₃	1	2	yes	—
545	#95	C₂³×C₂₃	1	2	yes	—
546	#95	C₂³×C₂₃	1	2	yes	—
547	#95	C₂³×C₂₃	1	2	yes	—
548	#95	C₂³×C₂₃	1	2	yes	—
549	#95	C₂³×C₂₃	1	2	yes	—
550	#95	C₂³×C₂₃	1	2	yes	—
551	#95	C₂³×C₂₃	1	2	yes	—
552	#95	C₂³×C₂₃	1	2	yes	—
553	#95	C₂³×C₂₃	1	2	yes	—
554	#95	C₂³×C₂₃	1	1	yes	characteristic
555	#95	C₂³×C₂₃	1	2	yes	—
556	#95	C₂³×C₂₃	1	2	yes	—
557	#95	C₂³×C₂₃	1	2	yes	—
558	#95	C₂³×C₂₃	1	1	yes	characteristic
559	#95	C₂³×C₂₃	1	2	yes	—
560	#95	C₂³×C₂₃	1	2	yes	—
561	#95	C₂³×C₂₃	1	2	yes	—
562	#95	C₂³×C₂₃	1	2	yes	—
563	#95	C₂³×C₂₃	1	2	yes	—
564	#95	C₂³×C₂₃	1	2	yes	—
565	#95	C₂³×C₂₃	1	2	yes	—
566	#95	C₂³×C₂₃	1	2	yes	—
567	#95	C₂³×C₂₃	1	2	yes	—
568	#95	C₂³×C₂₃	1	2	yes	—
569	#95	C₂³×C₂₃	1	2	yes	—
570	#95	C₂³×C₂₃	1	2	yes	—
571	C₂₃	#36834	1	1	yes	characteristic, direct product factor, Sylow
572	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	4	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	4	2	no	—
580	C₂²×C₄	—	4	2	no	—
581	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
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	2	yes	—
589	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
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	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₄⋊C₄	—	4	2	no	—
616	C₄⋊C₄	—	4	2	no	—
617	C₄⋊C₄	—	4	2	no	—
618	C₄⋊C₄	—	4	2	no	—
619	C₄⋊C₄	—	4	2	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	—	4	2	no	—
626	C₄⋊C₄	—	4	2	no	—
627	C₄⋊C₄	—	4	2	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	4	2	no	—
635	C₂²⋊C₄	—	4	2	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₄²	—	2	2	no	—
638	C₄²	—	2	4	no	—
639	C₄²	—	2	4	no	—
640	C₄²	—	4	1	no	—
641	C₄²	—	4	1	no	—
642	C₄²	—	4	1	no	—
643	C₄²	—	4	1	no	—
644	C₄²	—	4	2	no	—
645	C₄²	—	4	2	no	—
646	C₄²	—	4	2	no	—
647	C₄²	#41×C₂₃	1	4	yes	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	2	no	—
652	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
653	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
654	Q₈	—	4	4	no	—
655	C₂×C₄	—	2	8	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	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	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	4	8	no	—
702	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
703	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
704	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
705	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
706	C₂×C₄	C₂₃×2₋¹⁺⁴	1	4	yes	—
707	C₂²	—	2	2	no	—
708	C₂²	—	2	4	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	2	no	—
712	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
713	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
714	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
715	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
716	C₂²	C₂₃×#585	1	2	yes	—
717	C₄	—	2	2	no	—
718	C₄	—	2	2	no	—
719	C₄	—	2	2	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	4	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	2	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₂	—	4	2	no	—
736	C₂	C₂₃×#3455	1	1	yes	characteristic
737	C₂	C₂₃×#3492	1	1	yes	characteristic
738	C₂	C₂₃×#3509	1	1	yes	characteristic
739	C₂	C₂₃×#3541	1	2	yes	—
740	C₂	C₂₃×#3563	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂⁴×C₂₃	C₂⁴
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
4. C₂₃×#2774	C₂	semidirect
7. C₂₃×#2766	C₂	semidirect
8. C₂₃×#2726	C₂	semidirect
9. C₂₃×#2719	C₂	semidirect
10. C₂₃×#2655	C₂	semidirect
12. C₂₃×#2606	C₂	semidirect
14. C₂₃×#2590	C₂	semidirect
15. C₂₃×#2584	C₂	semidirect
17. C₂₃×#2336	C₂	semidirect
18. C₂₃×#2320	C₂	semidirect
277. #36834	C₂₃	direct (N × H)
340. #2774	C₂×C₂₃	semidirect
343. #2766	C₂×C₂₃	semidirect
344. #2726	C₂×C₂₃	semidirect
345. #2719	C₂×C₂₃	semidirect
346. #2655	C₂×C₂₃	semidirect
348. #2606	C₂×C₂₃	semidirect
350. #2590	C₂×C₂₃	semidirect
351. #2584	C₂×C₂₃	semidirect
353. #2336	C₂×C₂₃	semidirect
354. #2320	C₂×C₂₃	semidirect
571. C₂₃	#36834	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×#2851	2
C₂₃×#2788	2
C₂₃×#2787	2
C₂₃×#2774	2
C₂₃×#2770	2
C₂₃×#2768	2
C₂₃×#2766	2
C₂₃×#2726	2
C₂₃×#2719	2
C₂₃×#2655	2
C₂₃×#2611	2
C₂₃×#2606	2
C₂₃×#2599	2
C₂₃×#2590	2
C₂₃×#2584	2
C₂₃×#2475	2
C₂₃×#2336	2
C₂₃×#2320	2
C₂₃×#2296	2
#36834	23

Subgroups — C23×#36834 #19184460

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36834 #19184460