Subgroups — C₂₃×#61683 #19209309

Order 5888.

2012 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3497	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3328	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3313	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3304	C₂	1	2	yes	maximal, complemented
6	D₄×Q₁₆×C₂₃	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3278	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3270	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3201	C₂	1	4	yes	maximal, complemented
12	C₂₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3011	C₂	1	4	yes	maximal, complemented
15	C₂₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	2	yes	—
17	C₂×C₂₃×#137	C₂²	1	4	yes	—
18	C₂²×Q₁₆×C₂₃	C₂²	1	4	yes	—
19	C₂₃×#563	—	2	2	no	—
20	C₂₃×#559	—	2	1	no	—
21	Q₈²×C₂₃	—	2	1	no	—
22	C₂₃×#556	C₂²	1	2	yes	—
23	C₂₃×#556	C₂²	1	2	yes	—
24	C₂₃×#550	—	2	1	no	—
25	C₂₃×#550	C₂²	1	2	yes	—
26	D₄×Q₈×C₂₃	—	2	1	no	—
27	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
28	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
29	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
30	C₂₃×#548	—	2	2	no	—
31	C₂₃×#548	C₂²	1	4	yes	—
32	C₂₃×#542	—	2	2	no	—
33	C₂₃×#542	—	2	2	no	—
34	C₂₃×#537	—	2	2	no	—
35	C₂₃×#537	C₂²	1	2	yes	—
36	C₂₃×#536	C₂²	1	4	yes	—
37	C₂₃×#533	C₂²	1	1	yes	characteristic
38	C₂₃×#533	C₂²	1	1	yes	characteristic
39	C₂₃×#532	—	2	2	no	—
40	C₂₃×#532	C₂²	1	1	yes	characteristic
41	C₂₃×#532	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
43	C₂₃×#497	C₂²	1	2	yes	—
44	C₂₃×#494	C₂²	1	1	yes	characteristic
45	C₂₃×#492	C₂²	1	1	yes	characteristic
46	C₂₃×#489	C₂²	1	2	yes	—
47	C₂₃×#487	C₂²	1	1	yes	characteristic
48	C₂₃×#486	C₂²	1	1	yes	characteristic
49	C₂₃×#485	C₂²	1	4	yes	—
50	C₂₃×#484	C₂²	1	2	yes	—
51	C₂₃×#483	C₂²	1	2	yes	—
52	C₂₃×#482	C₂²	1	4	yes	—
53	C₂₃×#477	C₂²	1	2	yes	—
54	C₂₃×#475	C₂²	1	2	yes	—
55	C₂₃×#470	C₂²	1	4	yes	—
56	C₂₃×#468	C₂²	1	4	yes	—
57	C₂₃×#467	C₂²	1	4	yes	—
58	C₂₃×#465	C₂²	1	4	yes	—
59	C₂₃×#464	C₂²	1	4	yes	—
60	C₂₃×#462	C₂²	1	2	yes	—
61	C₂₃×#462	C₂²	1	2	yes	—
62	C₂₃×#462	C₂²	1	2	yes	—
63	C₂₃×#460	C₂²	1	2	yes	—
64	C₂₃×#452	C₂²	1	4	yes	—
65	C₂₃×#452	C₂²	1	4	yes	—
66	C₂₃×#452	C₂²	1	4	yes	—
67	C₂₃×#452	C₂²	1	4	yes	—
68	C₂₃×#451	C₂²	1	4	yes	—
69	C₂₃×#451	C₂²	1	2	yes	—
70	C₂₃×#451	C₂²	1	2	yes	—
71	C₂₃×#451	C₂²	1	4	yes	—
72	C₂₃×#451	C₂²	1	4	yes	—
73	C₂₃×#448	C₂²	1	4	yes	—
74	C₂₃×#441	C₂²	1	4	yes	—
75	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
76	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
77	C₂₃×#436	C₂²	1	2	yes	—
78	C₂₃×#435	C₂²	1	4	yes	—
79	C₈×D₄×C₂₃	C₂²	1	2	yes	—
80	C₂₃×#432	C₂²	1	1	yes	characteristic
81	C₂₃×#431	C₂²	1	1	yes	characteristic
82	C₂₃×#419	C₂²	1	4	yes	—
83	C₂₃×#416	C₂²	1	4	yes	—
84	C₂₃×#408	C₂²	1	4	yes	—
85	C₂₃×2₋¹⁺⁴	—	4	8	no	—
86	C₂×#41×C₂₃	—	2	2	no	—
87	C₂×#41×C₂₃	—	2	4	no	—
88	C₂×#41×C₂₃	C₂³	1	4	yes	—
89	C₂×#41×C₂₃	C₂³	1	2	yes	—
90	C₂×#41×C₂₃	C₂³	1	2	yes	—
91	C₂²×Q₈×C₂₃	—	2	2	no	—
92	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
93	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
94	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
95	C₂₃×#137	—	4	8	no	—
96	C₂×Q₁₆×C₂₃	—	4	8	no	—
97	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
98	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
99	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
100	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
101	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
104	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
105	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
106	C₂₃×C₄⋊Q₈	—	2	4	no	—
107	C₂₃×C₄⋊Q₈	—	2	2	no	—
108	C₂₃×C₄⋊Q₈	—	2	2	no	—
109	C₂₃×C₄⋊Q₈	—	2	2	no	—
110	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
111	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₂₃×#127	—	2	2	no	—
117	C₂₃×#127	D₄	1	1	yes	characteristic
118	C₂₃×#127	C₂³	1	1	yes	characteristic
119	C₂₃×#126	—	2	4	no	—
120	C₂₃×#126	—	2	4	no	—
121	C₂₃×#125	—	2	1	no	—
122	C₂₃×#125	—	2	1	no	—
123	C₂₃×#124	—	2	2	no	—
124	C₂₃×#124	—	2	2	no	—
125	C₂₃×#124	—	2	4	no	—
126	C₂₃×#124	—	2	4	no	—
127	C₂₃×#124	D₄	1	2	yes	—
128	C₂₃×#124	C₂³	1	2	yes	—
129	C₂₃×#123	—	2	4	no	—
130	C₂₃×#123	—	2	4	no	—
131	C₂₃×C₂²⋊Q₈	—	2	2	no	—
132	C₂₃×C₂²⋊Q₈	—	2	1	no	—
133	C₂₃×C₂²⋊Q₈	—	2	1	no	—
134	C₂₃×C₂²⋊Q₈	—	2	4	no	—
135	C₂₃×C₂²⋊Q₈	—	2	4	no	—
136	C₂₃×C₂²⋊Q₈	—	2	4	no	—
137	C₂₃×C₂²⋊Q₈	—	2	4	no	—
138	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
140	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
141	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
143	C₂₃×#121	—	2	2	no	—
144	C₂₃×#121	—	2	4	no	—
145	C₂₃×#121	—	2	4	no	—
146	C₂₃×#121	—	2	1	no	—
147	C₂₃×#121	—	2	1	no	—
148	C₂₃×#121	—	2	4	no	—
149	C₂₃×#121	D₄	1	2	yes	—
150	C₂₃×#121	D₄	1	2	yes	—
151	C₂₃×#121	C₂³	1	4	yes	—
152	C₄×Q₈×C₂₃	—	2	2	no	—
153	C₄×Q₈×C₂₃	—	2	2	no	—
154	C₄×Q₈×C₂₃	—	2	1	no	—
155	C₄×Q₈×C₂₃	—	2	1	no	—
156	C₄×Q₈×C₂₃	—	2	1	no	—
157	C₄×Q₈×C₂₃	—	2	1	no	—
158	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
160	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
161	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
162	C₄×D₄×C₂₃	—	2	2	no	—
163	C₄×D₄×C₂₃	—	2	2	no	—
164	C₄×D₄×C₂₃	—	2	2	no	—
165	C₄×D₄×C₂₃	—	2	2	no	—
166	C₄×D₄×C₂₃	—	2	4	no	—
167	C₄×D₄×C₂₃	—	2	1	no	—
168	C₄×D₄×C₂₃	—	2	1	no	—
169	C₄×D₄×C₂₃	C₂³	1	2	yes	—
170	C₄×D₄×C₂₃	C₂³	1	2	yes	—
171	C₂₃×#117	—	2	1	no	—
172	C₂₃×#117	—	2	1	no	—
173	C₂₃×#117	C₂³	1	4	yes	—
174	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
175	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₂₃	—	2	1	no	—
177	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
178	C₂₃×#107	C₂³	1	2	yes	—
179	C₂₃×#107	C₂³	1	2	yes	—
180	C₂₃×#106	C₂³	1	4	yes	—
181	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
182	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
183	C₂₃×#103	C₂³	1	2	yes	—
184	C₂₃×#103	C₂³	1	4	yes	—
185	C₂₃×#103	C₂³	1	2	yes	—
186	C₂₃×#103	C₂³	1	4	yes	—
187	C₂₃×#103	C₂³	1	4	yes	—
188	C₂₃×#103	C₂³	1	2	yes	—
189	C₂₃×#103	C₂³	1	2	yes	—
190	C₂₃×#103	C₂³	1	4	yes	—
191	C₂₃×#102	C₂³	1	4	yes	—
192	C₂₃×#102	C₂³	1	4	yes	—
193	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
196	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
197	C₂₃×#97	C₂³	1	2	yes	—
198	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
200	#41×C₂₃	—	2	8	no	—
201	#41×C₂₃	—	4	4	no	—
202	#41×C₂₃	—	4	4	no	—
203	#41×C₂₃	—	4	4	no	—
204	#41×C₂₃	—	4	16	no	—
205	#41×C₂₃	—	4	8	no	—
206	C₂×Q₈×C₂₃	—	2	4	no	—
207	C₂×Q₈×C₂₃	—	2	1	no	—
208	C₂×Q₈×C₂₃	—	2	1	no	—
209	C₂×Q₈×C₂₃	—	2	1	no	—
210	C₂×Q₈×C₂₃	—	2	4	no	—
211	C₂×Q₈×C₂₃	—	2	4	no	—
212	C₂×Q₈×C₂₃	—	2	8	no	—
213	C₂×Q₈×C₂₃	—	4	4	no	—
214	C₂×Q₈×C₂₃	—	4	4	no	—
215	C₂×Q₈×C₂₃	—	4	4	no	—
216	C₂×Q₈×C₂₃	—	4	8	no	—
217	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
218	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
219	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
220	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
221	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
222	C₂×D₄×C₂₃	—	2	2	no	—
223	C₂×D₄×C₂₃	—	2	4	no	—
224	C₂×D₄×C₂₃	—	2	4	no	—
225	C₂×D₄×C₂₃	—	2	1	no	—
226	C₂×D₄×C₂₃	—	2	1	no	—
227	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
228	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
229	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
230	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
231	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₂₃	—	2	1	no	—
233	C₂²×C₄×C₂₃	—	2	4	no	—
234	C₂²×C₄×C₂₃	—	2	1	no	—
235	C₂²×C₄×C₂₃	—	2	4	no	—
236	C₂²×C₄×C₂₃	—	2	4	no	—
237	C₂²×C₄×C₂₃	—	2	2	no	—
238	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
242	Q₁₆×C₂₃	—	2	4	no	—
243	Q₁₆×C₂₃	—	2	8	no	—
244	Q₁₆×C₂₃	—	2	4	no	—
245	Q₁₆×C₂₃	—	4	4	no	—
246	Q₁₆×C₂₃	—	4	4	no	—
247	SD₁₆×C₂₃	—	4	4	no	—
248	SD₁₆×C₂₃	—	4	4	no	—
249	M₁₆×C₂₃	—	4	4	no	—
250	C₂×C₈×C₂₃	—	4	4	no	—
251	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
252	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
253	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
254	C₄⋊C₄×C₂₃	—	2	2	no	—
255	C₄⋊C₄×C₂₃	—	2	2	no	—
256	C₄⋊C₄×C₂₃	—	2	1	no	—
257	C₄⋊C₄×C₂₃	—	2	1	no	—
258	C₄⋊C₄×C₂₃	—	2	1	no	—
259	C₄⋊C₄×C₂₃	—	2	1	no	—
260	C₄⋊C₄×C₂₃	—	2	1	no	—
261	C₄⋊C₄×C₂₃	—	2	1	no	—
262	C₄⋊C₄×C₂₃	—	2	1	no	—
263	C₄⋊C₄×C₂₃	—	2	1	no	—
264	C₄⋊C₄×C₂₃	—	2	1	no	—
265	C₄⋊C₄×C₂₃	—	2	4	no	—
266	C₄⋊C₄×C₂₃	—	2	4	no	—
267	C₄⋊C₄×C₂₃	—	2	4	no	—
268	C₄⋊C₄×C₂₃	—	2	2	no	—
269	C₄⋊C₄×C₂₃	—	2	2	no	—
270	C₄⋊C₄×C₂₃	—	2	2	no	—
271	C₄⋊C₄×C₂₃	—	2	2	no	—
272	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
273	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
274	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
275	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
276	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
277	C₂²⋊C₄×C₂₃	—	2	2	no	—
278	C₂²⋊C₄×C₂₃	—	2	2	no	—
279	C₂²⋊C₄×C₂₃	—	2	4	no	—
280	C₂²⋊C₄×C₂₃	—	2	4	no	—
281	C₂²⋊C₄×C₂₃	—	2	4	no	—
282	C₂²⋊C₄×C₂₃	—	2	4	no	—
283	C₂²⋊C₄×C₂₃	—	2	2	no	—
284	C₂²⋊C₄×C₂₃	—	2	2	no	—
285	C₂²⋊C₄×C₂₃	—	2	4	no	—
286	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
287	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
288	C₄²×C₂₃	—	2	2	no	—
289	C₄²×C₂₃	—	2	2	no	—
290	C₄²×C₂₃	—	2	2	no	—
291	C₄²×C₂₃	—	2	2	no	—
292	C₄²×C₂₃	—	2	4	no	—
293	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
294	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
295	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
296	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
297	#61683	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
298	C₂³×C₂₃	—	2	2	no	—
299	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
300	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
301	Q₈×C₂₃	—	2	4	no	—
302	Q₈×C₂₃	—	2	2	no	—
303	Q₈×C₂₃	—	2	2	no	—
304	Q₈×C₂₃	—	2	4	no	—
305	Q₈×C₂₃	—	2	2	no	—
306	Q₈×C₂₃	—	2	4	no	—
307	Q₈×C₂₃	—	4	2	no	—
308	Q₈×C₂₃	—	4	8	no	—
309	Q₈×C₂₃	—	4	2	no	—
310	Q₈×C₂₃	—	4	2	no	—
311	Q₈×C₂₃	—	8	4	no	—
312	Q₈×C₂₃	H(5,𝔽₂)	1	4	yes	—
313	D₄×C₂₃	—	2	4	no	—
314	D₄×C₂₃	—	2	4	no	—
315	D₄×C₂₃	—	4	2	no	—
316	D₄×C₂₃	—	4	2	no	—
317	D₄×C₂₃	—	4	4	no	—
318	D₄×C₂₃	—	4	8	no	—
319	D₄×C₂₃	—	4	4	no	—
320	D₄×C₂₃	—	4	2	no	—
321	D₄×C₂₃	—	8	1	no	—
322	D₄×C₂₃	—	8	4	no	—
323	C₂×C₄×C₂₃	—	2	4	no	—
324	C₂×C₄×C₂₃	—	2	2	no	—
325	C₂×C₄×C₂₃	—	2	2	no	—
326	C₂×C₄×C₂₃	—	2	4	no	—
327	C₂×C₄×C₂₃	—	2	4	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	—	2	2	no	—
332	C₂×C₄×C₂₃	—	2	2	no	—
333	C₂×C₄×C₂₃	—	2	2	no	—
334	C₂×C₄×C₂₃	—	2	2	no	—
335	C₂×C₄×C₂₃	—	4	1	no	—
336	C₂×C₄×C₂₃	—	4	8	no	—
337	C₂×C₄×C₂₃	—	4	8	no	—
338	C₂×C₄×C₂₃	—	4	4	no	—
339	C₂×C₄×C₂₃	—	8	1	no	—
340	C₂×C₄×C₂₃	—	8	4	no	—
341	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
344	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
348	C₈×C₂₃	—	2	2	no	—
349	C₈×C₂₃	—	2	4	no	—
350	C₈×C₂₃	—	2	2	no	—
351	#3550	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#3497	C₂×C₂₃	1	1	yes	characteristic
353	#3328	C₂×C₂₃	1	2	yes	complemented
354	#3313	C₂×C₂₃	1	4	yes	complemented
355	#3304	C₂×C₂₃	1	2	yes	complemented
356	D₄×Q₁₆	C₂×C₂₃	1	2	yes	complemented
357	#3278	C₂×C₂₃	1	2	yes	complemented
358	#3270	C₂×C₂₃	1	4	yes	complemented
359	#3216	C₂×C₂₃	1	1	yes	characteristic, complemented
360	#3210	C₂×C₂₃	1	1	yes	characteristic, complemented
361	#3201	C₂×C₂₃	1	4	yes	complemented
362	#3113	C₂×C₂₃	1	1	yes	characteristic, complemented
363	#3104	C₂×C₂₃	1	1	yes	characteristic, complemented
364	#3011	C₂×C₂₃	1	4	yes	complemented
365	#2981	C₂×C₂₃	1	1	yes	characteristic, complemented
366	C₂²×C₂₃	—	2	1	no	—
367	C₂²×C₂₃	—	2	4	no	—
368	C₂²×C₂₃	—	2	1	no	—
369	C₂²×C₂₃	—	2	4	no	—
370	C₂²×C₂₃	—	2	1	no	—
371	C₂²×C₂₃	—	2	4	no	—
372	C₂²×C₂₃	—	4	2	no	—
373	C₂²×C₂₃	—	4	2	no	—
374	C₂²×C₂₃	—	4	2	no	—
375	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
376	C₄×C₂₃	—	2	1	no	—
377	C₄×C₂₃	—	2	1	no	—
378	C₄×C₂₃	—	2	4	no	—
379	C₄×C₂₃	—	2	1	no	—
380	C₄×C₂₃	—	2	4	no	—
381	C₄×C₂₃	—	2	1	no	—
382	C₄×C₂₃	—	4	2	no	—
383	C₄×C₂₃	—	4	2	no	—
384	C₄×C₂₃	—	4	2	no	—
385	C₄×C₂₃	—	4	2	no	—
386	C₄×C₂₃	—	4	2	no	—
387	C₄×C₂₃	—	4	2	no	—
388	C₄×C₂₃	#578	1	2	yes	—
389	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
390	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	2	yes	—
391	C₂×#137	C₂²×C₂₃	1	4	yes	—
392	C₂²×Q₁₆	C₂²×C₂₃	1	4	yes	—
393	#563	—	2	2	no	—
394	#559	—	2	1	no	—
395	Q₈²	—	2	1	no	—
396	#556	C₂²×C₂₃	1	2	yes	—
397	#556	C₂²×C₂₃	1	2	yes	—
398	#550	—	2	1	no	—
399	#550	C₂²×C₂₃	1	2	yes	—
400	D₄×Q₈	—	2	1	no	—
401	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
402	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
403	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
404	#548	—	2	2	no	—
405	#548	C₂²×C₂₃	1	4	yes	—
406	#542	—	2	2	no	—
407	#542	—	2	2	no	—
408	#537	—	2	2	no	—
409	#537	C₂²×C₂₃	1	2	yes	—
410	#536	C₂²×C₂₃	1	4	yes	—
411	#533	C₂²×C₂₃	1	1	yes	characteristic
412	#533	C₂²×C₂₃	1	1	yes	characteristic
413	#532	—	2	2	no	—
414	#532	C₂²×C₂₃	1	1	yes	characteristic
415	#532	C₂²×C₂₃	1	1	yes	characteristic
416	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
417	#497	C₂²×C₂₃	1	2	yes	—
418	#494	C₂²×C₂₃	1	1	yes	characteristic
419	#492	C₂²×C₂₃	1	1	yes	characteristic
420	#489	C₂²×C₂₃	1	2	yes	—
421	#487	C₂²×C₂₃	1	1	yes	characteristic
422	#486	C₂²×C₂₃	1	1	yes	characteristic
423	#485	C₂²×C₂₃	1	4	yes	—
424	#484	C₂²×C₂₃	1	2	yes	—
425	#483	C₂²×C₂₃	1	2	yes	—
426	#482	C₂²×C₂₃	1	4	yes	—
427	#477	C₂²×C₂₃	1	2	yes	—
428	#475	C₂²×C₂₃	1	2	yes	—
429	#470	C₂²×C₂₃	1	4	yes	—
430	#468	C₂²×C₂₃	1	4	yes	—
431	#467	C₂²×C₂₃	1	4	yes	—
432	#465	C₂²×C₂₃	1	4	yes	—
433	#464	C₂²×C₂₃	1	4	yes	—
434	#462	C₂²×C₂₃	1	2	yes	—
435	#462	C₂²×C₂₃	1	2	yes	—
436	#462	C₂²×C₂₃	1	2	yes	—
437	#460	C₂²×C₂₃	1	2	yes	—
438	#452	C₂²×C₂₃	1	4	yes	—
439	#452	C₂²×C₂₃	1	4	yes	—
440	#452	C₂²×C₂₃	1	4	yes	—
441	#452	C₂²×C₂₃	1	4	yes	—
442	#451	C₂²×C₂₃	1	4	yes	—
443	#451	C₂²×C₂₃	1	2	yes	—
444	#451	C₂²×C₂₃	1	2	yes	—
445	#451	C₂²×C₂₃	1	4	yes	—
446	#451	C₂²×C₂₃	1	4	yes	—
447	#448	C₂²×C₂₃	1	4	yes	—
448	#441	C₂²×C₂₃	1	4	yes	—
449	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
450	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
451	#436	C₂²×C₂₃	1	2	yes	—
452	#435	C₂²×C₂₃	1	4	yes	—
453	C₈×D₄	C₂²×C₂₃	1	2	yes	—
454	#432	C₂²×C₂₃	1	1	yes	characteristic
455	#431	C₂²×C₂₃	1	1	yes	characteristic
456	#419	C₂²×C₂₃	1	4	yes	—
457	#416	C₂²×C₂₃	1	4	yes	—
458	#408	C₂²×C₂₃	1	4	yes	—
459	C₂×C₂₃	—	4	1	no	—
460	C₂×C₂₃	—	4	4	no	—
461	C₂×C₂₃	—	8	2	no	—
462	C₂×C₂₃	#3484	1	1	yes	characteristic
463	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
464	C₂×C₂₃	#3586	1	1	yes	characteristic
465	2₋¹⁺⁴	—	4	8	no	—
466	C₂×#41	—	2	4	no	—
467	C₂×#41	—	2	2	no	—
468	C₂×#41	C₂³×C₂₃	1	4	yes	—
469	C₂×#41	C₂³×C₂₃	1	2	yes	—
470	C₂×#41	C₂³×C₂₃	1	2	yes	—
471	C₂²×Q₈	—	2	2	no	—
472	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
473	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
474	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
475	#137	—	4	8	no	—
476	C₂×Q₁₆	—	4	8	no	—
477	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
478	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
479	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
480	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
481	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
482	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
483	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
484	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
485	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
486	C₄⋊Q₈	—	2	4	no	—
487	C₄⋊Q₈	—	2	2	no	—
488	C₄⋊Q₈	—	2	2	no	—
489	C₄⋊Q₈	—	2	2	no	—
490	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
491	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
492	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
493	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
494	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
495	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
496	#127	—	2	2	no	—
497	#127	D₄×C₂₃	1	1	yes	characteristic
498	#127	C₂³×C₂₃	1	1	yes	characteristic
499	#126	—	2	4	no	—
500	#126	—	2	4	no	—
501	#125	—	2	1	no	—
502	#125	—	2	1	no	—
503	#124	—	2	4	no	—
504	#124	—	2	2	no	—
505	#124	—	2	2	no	—
506	#124	—	2	4	no	—
507	#124	D₄×C₂₃	1	2	yes	—
508	#124	C₂³×C₂₃	1	2	yes	—
509	#123	—	2	4	no	—
510	#123	—	2	4	no	—
511	C₂²⋊Q₈	—	2	2	no	—
512	C₂²⋊Q₈	—	2	1	no	—
513	C₂²⋊Q₈	—	2	1	no	—
514	C₂²⋊Q₈	—	2	4	no	—
515	C₂²⋊Q₈	—	2	4	no	—
516	C₂²⋊Q₈	—	2	4	no	—
517	C₂²⋊Q₈	—	2	4	no	—
518	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
519	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
520	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
521	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
522	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
523	#121	—	2	4	no	—
524	#121	—	2	4	no	—
525	#121	—	2	2	no	—
526	#121	—	2	1	no	—
527	#121	—	2	1	no	—
528	#121	—	2	4	no	—
529	#121	D₄×C₂₃	1	2	yes	—
530	#121	D₄×C₂₃	1	2	yes	—
531	#121	C₂³×C₂₃	1	4	yes	—
532	C₄×Q₈	—	2	2	no	—
533	C₄×Q₈	—	2	2	no	—
534	C₄×Q₈	—	2	1	no	—
535	C₄×Q₈	—	2	1	no	—
536	C₄×Q₈	—	2	1	no	—
537	C₄×Q₈	—	2	1	no	—
538	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
539	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
540	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
541	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	—	2	2	no	—
544	C₄×D₄	—	2	2	no	—
545	C₄×D₄	—	2	2	no	—
546	C₄×D₄	—	2	4	no	—
547	C₄×D₄	—	2	1	no	—
548	C₄×D₄	—	2	1	no	—
549	C₄×D₄	C₂³×C₂₃	1	2	yes	—
550	C₄×D₄	C₂³×C₂₃	1	2	yes	—
551	#117	—	2	1	no	—
552	#117	—	2	1	no	—
553	#117	C₂³×C₂₃	1	4	yes	—
554	C₂×C₄⋊C₄	—	2	1	no	—
555	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
556	C₂×C₄²	—	2	1	no	—
557	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
558	#107	C₂³×C₂₃	1	2	yes	—
559	#107	C₂³×C₂₃	1	2	yes	—
560	#106	C₂³×C₂₃	1	4	yes	—
561	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
562	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
563	#103	C₂³×C₂₃	1	2	yes	—
564	#103	C₂³×C₂₃	1	4	yes	—
565	#103	C₂³×C₂₃	1	2	yes	—
566	#103	C₂³×C₂₃	1	4	yes	—
567	#103	C₂³×C₂₃	1	4	yes	—
568	#103	C₂³×C₂₃	1	2	yes	—
569	#103	C₂³×C₂₃	1	2	yes	—
570	#103	C₂³×C₂₃	1	4	yes	—
571	#102	C₂³×C₂₃	1	4	yes	—
572	#102	C₂³×C₂₃	1	4	yes	—
573	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
574	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
575	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
576	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
577	#97	C₂³×C₂₃	1	2	yes	—
578	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
579	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
580	C₂₃	#61683	1	1	yes	characteristic, direct product factor, Sylow
581	#41	—	2	8	no	—
582	#41	—	4	4	no	—
583	#41	—	4	4	no	—
584	#41	—	4	4	no	—
585	#41	—	4	16	no	—
586	#41	—	4	8	no	—
587	C₂×Q₈	—	2	4	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	—	2	4	no	—
592	C₂×Q₈	—	2	4	no	—
593	C₂×Q₈	—	2	8	no	—
594	C₂×Q₈	—	4	4	no	—
595	C₂×Q₈	—	4	4	no	—
596	C₂×Q₈	—	4	4	no	—
597	C₂×Q₈	—	4	8	no	—
598	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
599	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
600	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
601	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
602	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
609	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
610	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
611	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
612	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
621	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
623	Q₁₆	—	2	4	no	—
624	Q₁₆	—	2	8	no	—
625	Q₁₆	—	2	4	no	—
626	Q₁₆	—	4	4	no	—
627	Q₁₆	—	4	4	no	—
628	SD₁₆	—	4	4	no	—
629	SD₁₆	—	4	4	no	—
630	M₁₆	—	4	4	no	—
631	C₂×C₈	—	4	4	no	—
632	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
633	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
634	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
654	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
655	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
656	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
657	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	2	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
668	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
669	C₄²	—	2	2	no	—
670	C₄²	—	2	2	no	—
671	C₄²	—	2	2	no	—
672	C₄²	—	2	2	no	—
673	C₄²	—	2	4	no	—
674	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
675	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
676	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
677	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
678	C₂³	—	2	2	no	—
679	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
680	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
681	Q₈	—	2	4	no	—
682	Q₈	—	2	2	no	—
683	Q₈	—	2	2	no	—
684	Q₈	—	2	4	no	—
685	Q₈	—	2	2	no	—
686	Q₈	—	2	4	no	—
687	Q₈	—	4	2	no	—
688	Q₈	—	4	8	no	—
689	Q₈	—	4	2	no	—
690	Q₈	—	4	2	no	—
691	Q₈	—	8	4	no	—
692	Q₈	C₂₃×H(5,𝔽₂)	1	4	yes	—
693	D₄	—	2	4	no	—
694	D₄	—	2	4	no	—
695	D₄	—	4	2	no	—
696	D₄	—	4	4	no	—
697	D₄	—	4	2	no	—
698	D₄	—	4	8	no	—
699	D₄	—	4	4	no	—
700	D₄	—	4	2	no	—
701	D₄	—	8	1	no	—
702	D₄	—	8	4	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	8	no	—
717	C₂×C₄	—	4	8	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	8	4	no	—
720	C₂×C₄	—	8	1	no	—
721	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
722	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
723	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
724	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
726	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
727	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
728	C₈	—	2	2	no	—
729	C₈	—	2	4	no	—
730	C₈	—	2	2	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	4	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	4	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
741	C₄	—	2	4	no	—
742	C₄	—	2	1	no	—
743	C₄	—	2	4	no	—
744	C₄	—	2	1	no	—
745	C₄	—	2	1	no	—
746	C₄	—	2	1	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	2	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	2	no	—
753	C₄	C₂₃×#578	1	2	yes	—
754	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
755	C₂	—	4	1	no	—
756	C₂	—	4	4	no	—
757	C₂	—	8	2	no	—
758	C₂	C₂₃×#3484	1	1	yes	characteristic
759	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
760	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3497	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3550	C₂	semidirect
3. C₂₃×#3328	C₂	semidirect
4. C₂₃×#3313	C₂	semidirect
5. C₂₃×#3304	C₂	semidirect
6. D₄×Q₁₆×C₂₃	C₂	semidirect
7. C₂₃×#3278	C₂	semidirect
8. C₂₃×#3270	C₂	semidirect
9. C₂₃×#3216	C₂	semidirect
10. C₂₃×#3210	C₂	semidirect
11. C₂₃×#3201	C₂	semidirect
12. C₂₃×#3113	C₂	semidirect
13. C₂₃×#3104	C₂	semidirect
14. C₂₃×#3011	C₂	semidirect
15. C₂₃×#2981	C₂	semidirect
297. #61683	C₂₃	direct (N × H)
351. #3550	C₂×C₂₃	semidirect
353. #3328	C₂×C₂₃	semidirect
354. #3313	C₂×C₂₃	semidirect
355. #3304	C₂×C₂₃	semidirect
356. D₄×Q₁₆	C₂×C₂₃	semidirect
357. #3278	C₂×C₂₃	semidirect
358. #3270	C₂×C₂₃	semidirect
359. #3216	C₂×C₂₃	semidirect
360. #3210	C₂×C₂₃	semidirect
361. #3201	C₂×C₂₃	semidirect
362. #3113	C₂×C₂₃	semidirect
363. #3104	C₂×C₂₃	semidirect
364. #3011	C₂×C₂₃	semidirect
365. #2981	C₂×C₂₃	semidirect
580. C₂₃	#61683	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×#3550	2
C₂₃×#3497	2
C₂₃×#3328	2
C₂₃×#3313	2
C₂₃×#3304	2
D₄×Q₁₆×C₂₃	2
C₂₃×#3278	2
C₂₃×#3270	2
C₂₃×#3216	2
C₂₃×#3210	2
C₂₃×#3201	2
C₂₃×#3113	2
C₂₃×#3104	2
C₂₃×#3011	2
C₂₃×#2981	2
#61683	23

Subgroups — C23×#61683 #19209309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61683 #19209309