Subgroups — C₂₃×#22882 #19170508

Order 5888.

1134 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	C₂×C₂₃×#452	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#417	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2339	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#1971	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1933	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1927	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1894	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1853	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1762	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂₃×#452	C₄	1	8	yes	complemented
26	C₄×SD₁₆×C₂₃	—	2	4	no	—
27	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
29	C₂₃×#417	—	2	4	no	—
30	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
41	C₂₃×#391	C₂²	1	1	yes	characteristic
42	C₂₃×#391	C₂²	1	1	yes	characteristic
43	C₂₃×#391	C₂²	1	1	yes	characteristic
44	C₂₃×#389	—	2	1	no	—
45	C₂₃×#389	C₂²	1	1	yes	characteristic
46	C₂₃×#387	—	2	1	no	—
47	C₂₃×#386	—	2	1	no	—
48	C₂₃×#386	—	2	1	no	—
49	C₂₃×#385	—	2	1	no	—
50	C₂₃×#381	—	2	1	no	—
51	C₂₃×#380	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
54	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
55	C₂×C₂₃×#95	—	2	1	no	—
56	C₂₃×#340	C₂²	1	1	yes	characteristic
57	C₂₃×#340	C₂²	1	1	yes	characteristic
58	C₂₃×#340	C₂²	1	1	yes	characteristic
59	C₂₃×#340	C₂²	1	1	yes	characteristic
60	C₂₃×#336	C₂²	1	1	yes	characteristic
61	C₂₃×#336	C₂²	1	1	yes	characteristic
62	C₂×#41×C₂₃	—	2	2	no	—
63	C₂×#41×C₂₃	—	2	2	no	—
64	C₂×#41×C₂₃	—	2	2	no	—
65	C₂×#41×C₂₃	—	4	1	no	—
66	C₂×#41×C₂₃	—	4	1	no	—
67	C₂×#41×C₂₃	C₂×C₄	1	4	yes	—
68	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₂₃	—	2	1	no	—
71	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₂₃	—	2	1	no	—
73	C₂³×C₄×C₂₃	—	2	1	no	—
74	C₂³×C₄×C₂₃	—	2	1	no	—
75	C₂³×C₄×C₂₃	—	2	1	no	—
76	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂×Q₁₆×C₂₃	—	4	1	no	—
78	C₂×Q₁₆×C₂₃	—	4	1	no	—
79	C₂×Q₁₆×C₂₃	C₂×C₄	1	4	yes	complemented
80	C₂×SD₁₆×C₂₃	—	2	2	no	—
81	C₂×SD₁₆×C₂₃	—	2	2	no	—
82	C₂×SD₁₆×C₂₃	C₂×C₄	1	4	yes	complemented
83	C₂×M₁₆×C₂₃	—	2	2	no	—
84	C₂×M₁₆×C₂₃	—	2	2	no	—
85	C₂×M₁₆×C₂₃	—	4	1	no	—
86	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
90	C₂₃×C₂²⋊Q₈	—	2	2	no	—
91	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	complemented
92	C₄×Q₈×C₂₃	—	2	2	no	—
93	C₄×Q₈×C₂₃	—	4	1	no	—
94	C₄×D₄×C₂₃	—	2	2	no	—
95	C₄×D₄×C₂₃	—	2	2	no	—
96	C₄×D₄×C₂₃	—	4	1	no	—
97	C₄×D₄×C₂₃	—	4	1	no	—
98	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
99	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
100	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
101	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
102	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
103	C₂×C₄⋊C₄×C₂₃	—	4	1	no	—
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	1	yes	characteristic
107	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₂₃	—	2	1	no	—
116	C₂×C₄²×C₂₃	—	2	1	no	—
117	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
119	C₂₃×#106	—	2	2	no	—
120	C₂₃×#106	—	4	1	no	—
121	C₂₃×#103	—	2	2	no	—
122	C₂₃×#103	—	2	2	no	—
123	C₂₃×#103	—	2	2	no	—
124	C₂₃×#103	—	4	1	no	—
125	C₂₃×#103	C₂×C₄	1	4	yes	complemented
126	C₂₃×#102	—	2	2	no	—
127	C₂₃×#102	C₂×C₄	1	4	yes	complemented
128	C₂₃×#102	D₄	1	4	yes	—
129	C₂₃×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
130	C₂₃×#97	—	4	1	no	—
131	C₄×C₈×C₂₃	—	2	2	no	—
132	C₂₃×#95	—	2	1	no	—
133	C₂₃×#95	—	2	1	no	—
134	C₂₃×#95	—	2	1	no	—
135	C₂₃×#95	—	2	1	no	—
136	C₂₃×#95	—	2	1	no	—
137	C₂₃×#95	—	2	1	no	—
138	C₂₃×#95	—	2	1	no	—
139	C₂₃×#95	—	2	1	no	—
140	C₂₃×#95	—	2	1	no	—
141	C₂₃×#95	D₄	1	1	yes	characteristic
142	C₂₃×#95	D₄	1	1	yes	characteristic
143	C₂⁴×C₂₃	—	2	1	no	—
144	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
145	#41×C₂₃	—	2	8	no	—
146	#41×C₂₃	—	4	4	no	—
147	#41×C₂₃	—	4	4	no	—
148	#41×C₂₃	—	4	4	no	—
149	C₂×Q₈×C₂₃	—	2	1	no	—
150	C₂×Q₈×C₂₃	—	2	1	no	—
151	C₂×Q₈×C₂₃	—	2	1	no	—
152	C₂×Q₈×C₂₃	—	2	1	no	—
153	C₂×Q₈×C₂₃	—	2	1	no	—
154	C₂×Q₈×C₂₃	—	2	1	no	—
155	C₂×Q₈×C₂₃	—	2	1	no	—
156	C₂×Q₈×C₂₃	—	2	1	no	—
157	C₂×Q₈×C₂₃	—	2	1	no	—
158	C₂×Q₈×C₂₃	—	2	1	no	—
159	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
160	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
161	C₂×D₄×C₂₃	—	2	4	no	—
162	C₂×D₄×C₂₃	—	2	1	no	—
163	C₂×D₄×C₂₃	—	2	1	no	—
164	C₂×D₄×C₂₃	—	2	1	no	—
165	C₂×D₄×C₂₃	—	4	2	no	—
166	C₂×D₄×C₂₃	—	4	2	no	—
167	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
168	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
169	C₂×D₄×C₂₃	#41	1	2	yes	—
170	C₂²×C₄×C₂₃	—	2	1	no	—
171	C₂²×C₄×C₂₃	—	2	1	no	—
172	C₂²×C₄×C₂₃	—	2	1	no	—
173	C₂²×C₄×C₂₃	—	2	1	no	—
174	C₂²×C₄×C₂₃	—	2	1	no	—
175	C₂²×C₄×C₂₃	—	2	1	no	—
176	C₂²×C₄×C₂₃	—	2	1	no	—
177	C₂²×C₄×C₂₃	—	2	1	no	—
178	C₂²×C₄×C₂₃	—	2	4	no	—
179	C₂²×C₄×C₂₃	—	2	1	no	—
180	C₂²×C₄×C₂₃	—	2	1	no	—
181	C₂²×C₄×C₂₃	—	2	1	no	—
182	C₂²×C₄×C₂₃	—	4	2	no	—
183	C₂²×C₄×C₂₃	—	4	2	no	—
184	C₂²×C₄×C₂₃	—	4	2	no	—
185	C₂²×C₄×C₂₃	—	4	2	no	—
186	C₂²×C₄×C₂₃	—	4	2	no	—
187	C₂²×C₄×C₂₃	—	4	2	no	—
188	C₂²×C₄×C₂₃	—	4	2	no	—
189	C₂²×C₄×C₂₃	—	4	2	no	—
190	C₂²×C₄×C₂₃	—	8	1	no	—
191	C₂²×C₄×C₂₃	—	8	1	no	—
192	C₂²×C₄×C₂₃	—	8	1	no	—
193	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
194	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₂₃	#41	1	2	yes	—
200	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
201	Q₁₆×C₂₃	—	4	4	no	—
202	SD₁₆×C₂₃	—	2	8	no	—
203	M₁₆×C₂₃	—	4	4	no	—
204	C₂×C₈×C₂₃	—	2	1	no	—
205	C₂×C₈×C₂₃	—	2	1	no	—
206	C₂×C₈×C₂₃	—	2	1	no	—
207	C₂×C₈×C₂₃	—	2	1	no	—
208	C₂×C₈×C₂₃	—	2	1	no	—
209	C₂×C₈×C₂₃	—	2	1	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	C₂²×C₄	1	2	yes	—
214	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
215	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
216	C₄⋊C₄×C₂₃	—	2	4	no	—
217	C₄⋊C₄×C₂₃	—	2	1	no	—
218	C₄⋊C₄×C₂₃	—	2	1	no	—
219	C₄⋊C₄×C₂₃	—	2	1	no	—
220	C₄⋊C₄×C₂₃	—	2	1	no	—
221	C₄⋊C₄×C₂₃	—	2	1	no	—
222	C₄⋊C₄×C₂₃	—	2	1	no	—
223	C₄⋊C₄×C₂₃	—	2	1	no	—
224	C₄⋊C₄×C₂₃	—	2	1	no	—
225	C₄⋊C₄×C₂₃	—	4	2	no	—
226	C₄⋊C₄×C₂₃	—	4	2	no	—
227	C₄⋊C₄×C₂₃	—	8	1	no	—
228	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
229	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
230	C₂²⋊C₄×C₂₃	—	2	4	no	—
231	C₂²⋊C₄×C₂₃	—	2	2	no	—
232	C₂²⋊C₄×C₂₃	—	4	1	no	—
233	C₂²⋊C₄×C₂₃	—	4	2	no	—
234	C₂²⋊C₄×C₂₃	—	4	2	no	—
235	C₂²⋊C₄×C₂₃	—	8	1	no	—
236	C₄²×C₂₃	—	2	1	no	—
237	C₄²×C₂₃	—	2	1	no	—
238	C₄²×C₂₃	—	2	1	no	—
239	C₄²×C₂₃	—	2	1	no	—
240	C₄²×C₂₃	—	4	2	no	—
241	C₄²×C₂₃	—	8	1	no	—
242	#22882	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂³×C₂₃	—	2	2	no	—
244	C₂³×C₂₃	—	2	2	no	—
245	C₂³×C₂₃	—	2	1	no	—
246	C₂³×C₂₃	—	2	2	no	—
247	C₂³×C₂₃	—	2	1	no	—
248	C₂³×C₂₃	—	2	1	no	—
249	C₂³×C₂₃	—	2	1	no	—
250	C₂³×C₂₃	—	2	1	no	—
251	C₂³×C₂₃	—	2	1	no	—
252	C₂³×C₂₃	—	4	1	no	—
253	C₂³×C₂₃	—	4	1	no	—
254	C₂³×C₂₃	—	4	1	no	—
255	C₂³×C₂₃	—	4	1	no	—
256	C₂³×C₂₃	C₄×D₄	1	2	yes	—
257	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
258	Q₈×C₂₃	—	2	2	no	—
259	Q₈×C₂₃	—	2	2	no	—
260	Q₈×C₂₃	—	2	2	no	—
261	Q₈×C₂₃	—	2	2	no	—
262	Q₈×C₂₃	—	4	1	no	—
263	Q₈×C₂₃	—	4	1	no	—
264	Q₈×C₂₃	—	4	1	no	—
265	Q₈×C₂₃	—	4	1	no	—
266	D₄×C₂₃	—	2	2	no	—
267	D₄×C₂₃	—	2	2	no	—
268	D₄×C₂₃	—	2	2	no	—
269	D₄×C₂₃	—	4	8	no	—
270	D₄×C₂₃	C₄×D₄	1	4	yes	—
271	C₂×C₄×C₂₃	—	2	1	no	—
272	C₂×C₄×C₂₃	—	2	1	no	—
273	C₂×C₄×C₂₃	—	2	1	no	—
274	C₂×C₄×C₂₃	—	2	1	no	—
275	C₂×C₄×C₂₃	—	2	2	no	—
276	C₂×C₄×C₂₃	—	2	2	no	—
277	C₂×C₄×C₂₃	—	2	2	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	2	no	—
282	C₂×C₄×C₂₃	—	2	1	no	—
283	C₂×C₄×C₂₃	—	2	2	no	—
284	C₂×C₄×C₂₃	—	2	1	no	—
285	C₂×C₄×C₂₃	—	2	1	no	—
286	C₂×C₄×C₂₃	—	2	1	no	—
287	C₂×C₄×C₂₃	—	2	1	no	—
288	C₂×C₄×C₂₃	—	2	1	no	—
289	C₂×C₄×C₂₃	—	2	1	no	—
290	C₂×C₄×C₂₃	—	2	1	no	—
291	C₂×C₄×C₂₃	—	2	1	no	—
292	C₂×C₄×C₂₃	—	4	8	no	—
293	C₂×C₄×C₂₃	—	4	1	no	—
294	C₂×C₄×C₂₃	—	4	1	no	—
295	C₂×C₄×C₂₃	—	4	1	no	—
296	C₂×C₄×C₂₃	—	4	1	no	—
297	C₂×C₄×C₂₃	—	4	1	no	—
298	C₂×C₄×C₂₃	—	4	1	no	—
299	C₂×C₄×C₂₃	—	4	1	no	—
300	C₂×C₄×C₂₃	—	4	1	no	—
301	C₂×C₄×C₂₃	—	4	1	no	—
302	C₂×C₄×C₂₃	—	4	1	no	—
303	C₂×C₄×C₂₃	—	4	1	no	—
304	C₂×C₄×C₂₃	—	4	1	no	—
305	C₂×C₄×C₂₃	—	4	1	no	—
306	C₂×C₄×C₂₃	—	4	1	no	—
307	C₂×C₄×C₂₃	—	4	1	no	—
308	C₂×C₄×C₂₃	—	4	1	no	—
309	C₂×C₄×C₂₃	—	4	1	no	—
310	C₂×C₄×C₂₃	—	8	4	no	—
311	C₂×C₄×C₂₃	—	8	4	no	—
312	C₂×C₄×C₂₃	—	8	4	no	—
313	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
314	C₂×C₄×C₂₃	#137	1	2	yes	—
315	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
316	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
318	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
319	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
320	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
321	C₈×C₂₃	—	2	2	no	—
322	C₈×C₂₃	—	2	2	no	—
323	C₈×C₂₃	—	2	2	no	—
324	C₈×C₂₃	—	4	1	no	—
325	C₂×#452	C₂×C₂₃	1	1	yes	characteristic
326	C₂×C₄×SD₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
327	C₂×#417	C₂×C₂₃	1	1	yes	characteristic
328	#2360	C₂×C₂₃	1	1	yes	characteristic, complemented
329	#2339	C₂×C₂₃	1	1	yes	characteristic
330	#1971	C₂×C₂₃	1	1	yes	characteristic, complemented
331	#1933	C₂×C₂₃	1	1	yes	characteristic, complemented
332	#1927	C₂×C₂₃	1	1	yes	characteristic, complemented
333	#1894	C₂×C₂₃	1	1	yes	characteristic, complemented
334	#1878	C₂×C₂₃	1	1	yes	characteristic, complemented
335	#1877	C₂×C₂₃	1	1	yes	characteristic, complemented
336	#1864	C₂×C₂₃	1	1	yes	characteristic, complemented
337	#1853	C₂×C₂₃	1	1	yes	characteristic, complemented
338	#1762	C₂×C₂₃	1	1	yes	characteristic, complemented
339	#1753	C₂×C₂₃	1	1	yes	characteristic, complemented
340	C₂²×C₂₃	—	2	2	no	—
341	C₂²×C₂₃	—	2	4	no	—
342	C₂²×C₂₃	—	2	2	no	—
343	C₂²×C₂₃	—	2	2	no	—
344	C₂²×C₂₃	—	4	1	no	—
345	C₂²×C₂₃	—	4	2	no	—
346	C₂²×C₂₃	—	4	2	no	—
347	C₂²×C₂₃	—	4	2	no	—
348	C₂²×C₂₃	—	4	2	no	—
349	C₂²×C₂₃	—	4	1	no	—
350	C₂²×C₂₃	—	4	1	no	—
351	C₂²×C₂₃	—	4	2	no	—
352	C₂²×C₂₃	—	4	2	no	—
353	C₂²×C₂₃	—	4	1	no	—
354	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
355	C₂²×C₂₃	D₄²	1	1	yes	characteristic
356	C₂²×C₂₃	#546	1	1	yes	characteristic
357	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
358	C₂²×C₂₃	#575	1	1	yes	characteristic
359	C₂²×C₂₃	#577	1	1	yes	characteristic
360	C₂²×C₂₃	#577	1	1	yes	characteristic
361	C₄×C₂₃	—	2	2	no	—
362	C₄×C₂₃	—	2	2	no	—
363	C₄×C₂₃	—	4	1	no	—
364	C₄×C₂₃	—	4	2	no	—
365	C₄×C₂₃	—	4	2	no	—
366	C₄×C₂₃	—	4	2	no	—
367	C₄×C₂₃	—	4	1	no	—
368	C₄×C₂₃	—	4	2	no	—
369	C₄×C₂₃	—	4	1	no	—
370	C₄×C₂₃	—	8	1	no	—
371	C₄×C₂₃	—	8	1	no	—
372	C₄×C₂₃	—	8	1	no	—
373	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
374	C₄×C₂₃	#518	1	1	yes	characteristic
375	C₄×C₂₃	#546	1	1	yes	characteristic
376	C₄×C₂₃	#551	1	1	yes	characteristic
377	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
378	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
379	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
380	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
381	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
382	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
383	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
384	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
385	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
386	#452	C₄×C₂₃	1	8	yes	complemented
387	C₄×SD₁₆	—	2	4	no	—
388	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
389	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
390	#417	—	2	4	no	—
391	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
392	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
393	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
394	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
395	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
396	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
397	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
398	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
399	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
400	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
401	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
402	#391	C₂²×C₂₃	1	1	yes	characteristic
403	#391	C₂²×C₂₃	1	1	yes	characteristic
404	#391	C₂²×C₂₃	1	1	yes	characteristic
405	#389	—	2	1	no	—
406	#389	C₂²×C₂₃	1	1	yes	characteristic
407	#387	—	2	1	no	—
408	#386	—	2	1	no	—
409	#386	—	2	1	no	—
410	#385	—	2	1	no	—
411	#381	—	2	1	no	—
412	#380	C₂²×C₂₃	1	1	yes	characteristic
413	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
414	C₄×C₂²⋊C₄	—	2	1	no	—
415	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
416	C₂×#95	—	2	1	no	—
417	#340	C₂²×C₂₃	1	1	yes	characteristic
418	#340	C₂²×C₂₃	1	1	yes	characteristic
419	#340	C₂²×C₂₃	1	1	yes	characteristic
420	#340	C₂²×C₂₃	1	1	yes	characteristic
421	#336	C₂²×C₂₃	1	1	yes	characteristic
422	#336	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×C₂₃	—	4	2	no	—
424	C₂×C₂₃	—	4	4	no	—
425	C₂×C₂₃	#2358	1	1	yes	characteristic
426	C₂×C₂₃	C₄×#137	1	1	yes	characteristic
427	C₂×C₂₃	#2952	1	1	yes	characteristic
428	C₂×C₂₃	#3266	1	1	yes	characteristic
429	C₂×C₂₃	#3267	1	1	yes	characteristic
430	C₂×C₂₃	#3323	1	1	yes	characteristic
431	C₂×C₂₃	#3331	1	1	yes	characteristic
432	C₂×#41	—	2	2	no	—
433	C₂×#41	—	2	2	no	—
434	C₂×#41	—	2	2	no	—
435	C₂×#41	—	4	1	no	—
436	C₂×#41	—	4	1	no	—
437	C₂×#41	C₂×C₄×C₂₃	1	4	yes	—
438	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
439	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
440	C₂²×D₄	—	2	1	no	—
441	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
442	C₂³×C₄	—	2	1	no	—
443	C₂³×C₄	—	2	1	no	—
444	C₂³×C₄	—	2	1	no	—
445	C₂³×C₄	—	2	1	no	—
446	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
447	C₂×Q₁₆	—	4	1	no	—
448	C₂×Q₁₆	—	4	1	no	—
449	C₂×Q₁₆	C₂×C₄×C₂₃	1	4	yes	complemented
450	C₂×SD₁₆	—	2	2	no	—
451	C₂×SD₁₆	—	2	2	no	—
452	C₂×SD₁₆	C₂×C₄×C₂₃	1	4	yes	complemented
453	C₂×M₁₆	—	2	2	no	—
454	C₂×M₁₆	—	2	2	no	—
455	C₂×M₁₆	—	4	1	no	—
456	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
457	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
458	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
459	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
460	C₂²⋊Q₈	—	2	2	no	—
461	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	complemented
462	C₄×Q₈	—	2	2	no	—
463	C₄×Q₈	—	4	1	no	—
464	C₄×D₄	—	2	2	no	—
465	C₄×D₄	—	2	2	no	—
466	C₄×D₄	—	4	1	no	—
467	C₄×D₄	—	4	1	no	—
468	C₂×C₄⋊C₄	—	2	1	no	—
469	C₂×C₄⋊C₄	—	2	2	no	—
470	C₂×C₄⋊C₄	—	2	1	no	—
471	C₂×C₄⋊C₄	—	2	1	no	—
472	C₂×C₄⋊C₄	—	2	1	no	—
473	C₂×C₄⋊C₄	—	4	1	no	—
474	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	—	2	1	no	—
480	C₂×C₂²⋊C₄	—	2	1	no	—
481	C₂×C₂²⋊C₄	—	2	1	no	—
482	C₂×C₂²⋊C₄	—	2	1	no	—
483	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
485	C₂×C₄²	—	2	1	no	—
486	C₂×C₄²	—	2	1	no	—
487	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
488	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
489	#106	—	2	2	no	—
490	#106	—	4	1	no	—
491	#103	—	2	2	no	—
492	#103	—	2	2	no	—
493	#103	—	2	2	no	—
494	#103	—	4	1	no	—
495	#103	C₂×C₄×C₂₃	1	4	yes	complemented
496	#102	—	2	2	no	—
497	#102	C₂×C₄×C₂₃	1	4	yes	complemented
498	#102	D₄×C₂₃	1	4	yes	—
499	C₂²⋊C₈	C₂×C₄×C₂₃	1	4	yes	complemented
500	#97	—	4	1	no	—
501	C₄×C₈	—	2	2	no	—
502	#95	—	2	1	no	—
503	#95	—	2	1	no	—
504	#95	—	2	1	no	—
505	#95	—	2	1	no	—
506	#95	—	2	1	no	—
507	#95	—	2	1	no	—
508	#95	—	2	1	no	—
509	#95	—	2	1	no	—
510	#95	—	2	1	no	—
511	#95	D₄×C₂₃	1	1	yes	characteristic
512	#95	D₄×C₂₃	1	1	yes	characteristic
513	C₂₃	#22882	1	1	yes	characteristic, direct product factor, Sylow
514	C₂⁴	—	2	1	no	—
515	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
516	#41	—	2	8	no	—
517	#41	—	4	4	no	—
518	#41	—	4	4	no	—
519	#41	—	4	4	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
531	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
532	C₂×D₄	—	2	4	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	4	2	no	—
537	C₂×D₄	—	4	2	no	—
538	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
539	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
540	C₂×D₄	#41×C₂₃	1	2	yes	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	4	2	no	—
554	C₂²×C₄	—	4	2	no	—
555	C₂²×C₄	—	4	2	no	—
556	C₂²×C₄	—	4	2	no	—
557	C₂²×C₄	—	4	2	no	—
558	C₂²×C₄	—	4	2	no	—
559	C₂²×C₄	—	4	2	no	—
560	C₂²×C₄	—	4	2	no	—
561	C₂²×C₄	—	8	1	no	—
562	C₂²×C₄	—	8	1	no	—
563	C₂²×C₄	—	8	1	no	—
564	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
565	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
566	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
567	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
568	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
569	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
570	C₂²×C₄	#41×C₂₃	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
572	Q₁₆	—	4	4	no	—
573	SD₁₆	—	2	8	no	—
574	M₁₆	—	4	4	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
585	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
586	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	4	2	no	—
597	C₄⋊C₄	—	4	2	no	—
598	C₄⋊C₄	—	8	1	no	—
599	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
600	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	4	1	no	—
604	C₂²⋊C₄	—	4	2	no	—
605	C₂²⋊C₄	—	4	2	no	—
606	C₂²⋊C₄	—	8	1	no	—
607	C₄²	—	2	1	no	—
608	C₄²	—	2	1	no	—
609	C₄²	—	2	1	no	—
610	C₄²	—	2	1	no	—
611	C₄²	—	4	2	no	—
612	C₄²	—	8	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	4	1	no	—
623	C₂³	—	4	1	no	—
624	C₂³	—	4	1	no	—
625	C₂³	—	4	1	no	—
626	C₂³	C₄×D₄×C₂₃	1	2	yes	—
627	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
628	Q₈	—	2	2	no	—
629	Q₈	—	2	2	no	—
630	Q₈	—	2	2	no	—
631	Q₈	—	2	2	no	—
632	Q₈	—	4	1	no	—
633	Q₈	—	4	1	no	—
634	Q₈	—	4	1	no	—
635	Q₈	—	4	1	no	—
636	D₄	—	2	2	no	—
637	D₄	—	2	2	no	—
638	D₄	—	2	2	no	—
639	D₄	—	4	8	no	—
640	D₄	C₄×D₄×C₂₃	1	4	yes	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	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	—	4	8	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	8	4	no	—
681	C₂×C₄	—	8	4	no	—
682	C₂×C₄	—	8	4	no	—
683	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
684	C₂×C₄	C₂₃×#137	1	2	yes	—
685	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
686	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
687	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
688	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
689	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
690	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
691	C₈	—	2	2	no	—
692	C₈	—	2	2	no	—
693	C₈	—	2	2	no	—
694	C₈	—	4	1	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	4	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	1	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	2	no	—
709	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
710	C₂²	D₄²×C₂₃	1	1	yes	characteristic
711	C₂²	C₂₃×#546	1	1	yes	characteristic
712	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
713	C₂²	C₂₃×#575	1	1	yes	characteristic
714	C₂²	C₂₃×#577	1	1	yes	characteristic
715	C₂²	C₂₃×#577	1	1	yes	characteristic
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	1	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	2	no	—
725	C₄	—	8	1	no	—
726	C₄	—	8	1	no	—
727	C₄	—	8	1	no	—
728	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
729	C₄	C₂₃×#518	1	1	yes	characteristic
730	C₄	C₂₃×#546	1	1	yes	characteristic
731	C₄	C₂₃×#551	1	1	yes	characteristic
732	C₂	—	4	2	no	—
733	C₂	—	4	4	no	—
734	C₂	C₂₃×#2358	1	1	yes	characteristic
735	C₂	C₄×C₂₃×#137	1	1	yes	characteristic
736	C₂	C₂₃×#2952	1	1	yes	characteristic
737	C₂	C₂₃×#3266	1	1	yes	characteristic
738	C₂	C₂₃×#3267	1	1	yes	characteristic
739	C₂	C₂₃×#3323	1	1	yes	characteristic
740	C₂	C₂₃×#3331	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	C₂²×#41×C₂₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₄×C₂²⋊C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×SD₁₆×C₂₃	C₂	semidirect
4. C₂₃×#2360	C₂	semidirect
6. C₂₃×#1971	C₂	semidirect
7. C₂₃×#1933	C₂	semidirect
8. C₂₃×#1927	C₂	semidirect
9. C₂₃×#1894	C₂	semidirect
10. C₂₃×#1878	C₂	semidirect
11. C₂₃×#1877	C₂	semidirect
12. C₂₃×#1864	C₂	semidirect
13. C₂₃×#1853	C₂	semidirect
14. C₂₃×#1762	C₂	semidirect
15. C₂₃×#1753	C₂	semidirect
25. C₂₃×#452	C₄	semidirect
79. C₂×Q₁₆×C₂₃	C₂×C₄	semidirect
82. C₂×SD₁₆×C₂₃	C₂×C₄	semidirect
91. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
125. C₂₃×#103	C₂×C₄	semidirect
127. C₂₃×#102	C₂×C₄	semidirect
129. C₂₃×C₂²⋊C₈	C₂×C₄	semidirect
242. #22882	C₂₃	direct (N × H)
326. C₂×C₄×SD₁₆	C₂×C₂₃	semidirect
328. #2360	C₂×C₂₃	semidirect
330. #1971	C₂×C₂₃	semidirect
331. #1933	C₂×C₂₃	semidirect
332. #1927	C₂×C₂₃	semidirect
333. #1894	C₂×C₂₃	semidirect
334. #1878	C₂×C₂₃	semidirect
335. #1877	C₂×C₂₃	semidirect
336. #1864	C₂×C₂₃	semidirect
337. #1853	C₂×C₂₃	semidirect
338. #1762	C₂×C₂₃	semidirect
339. #1753	C₂×C₂₃	semidirect
386. #452	C₄×C₂₃	semidirect
449. C₂×Q₁₆	C₂×C₄×C₂₃	semidirect
452. C₂×SD₁₆	C₂×C₄×C₂₃	semidirect
461. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
495. #103	C₂×C₄×C₂₃	semidirect
497. #102	C₂×C₄×C₂₃	semidirect
499. C₂²⋊C₈	C₂×C₄×C₂₃	semidirect
513. C₂₃	#22882	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×#452	2
C₂×C₄×SD₁₆×C₂₃	2
C₂×C₂₃×#417	2
C₂₃×#2360	2
C₂₃×#2339	2
C₂₃×#1971	2
C₂₃×#1933	2
C₂₃×#1927	2
C₂₃×#1894	2
C₂₃×#1878	2
C₂₃×#1877	2
C₂₃×#1864	2
C₂₃×#1853	2
C₂₃×#1762	2
C₂₃×#1753	2
#22882	23

Subgroups — C23×#22882 #19170508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#22882 #19170508