Subgroups — C₂₃×#25103 #19172729

Order 5888.

1130 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#469	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#419	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2436	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2066	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2042	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1983	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1927	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1875	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
27	C₂₃×#469	—	2	4	no	—
28	C₂₃×#463	—	2	4	no	—
29	C₂₃×#448	—	2	4	no	—
30	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂₃×#419	—	2	4	no	—
34	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂₃×#393	—	2	1	no	—
46	C₂₃×#393	—	2	1	no	—
47	C₂₃×#391	C₂²	1	1	yes	characteristic
48	C₂₃×#391	C₂²	1	1	yes	characteristic
49	C₂₃×#390	—	2	1	no	—
50	C₂₃×#390	C₂²	1	1	yes	characteristic
51	C₂₃×#389	C₂²	1	1	yes	characteristic
52	C₂₃×#388	—	2	1	no	—
53	C₂₃×#386	—	2	1	no	—
54	C₂₃×#386	—	2	1	no	—
55	C₂₃×#386	—	2	1	no	—
56	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
58	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
59	C₂₃×#340	C₂²	1	1	yes	characteristic
60	C₂₃×#340	C₂²	1	1	yes	characteristic
61	C₂₃×#336	C₂²	1	1	yes	characteristic
62	C₂₃×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₂₃	—	2	1	no	—
64	C₂²×Q₈×C₂₃	—	2	2	no	—
65	C₂²×Q₈×C₂₃	—	2	2	no	—
66	C₂²×Q₈×C₂₃	—	2	2	no	—
67	C₂²×Q₈×C₂₃	—	2	2	no	—
68	C₂²×Q₈×C₂₃	—	4	1	no	—
69	C₂²×Q₈×C₂₃	—	4	1	no	—
70	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₂₃	—	2	1	no	—
73	C₂²×D₄×C₂₃	—	2	1	no	—
74	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₂₃	—	2	1	no	—
77	C₂³×C₄×C₂₃	—	2	1	no	—
78	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
79	C₂×SD₁₆×C₂₃	—	2	2	no	—
80	C₂×SD₁₆×C₂₃	—	2	2	no	—
81	C₂×SD₁₆×C₂₃	—	2	2	no	—
82	C₂×SD₁₆×C₂₃	—	2	2	no	—
83	C₂×SD₁₆×C₂₃	—	4	1	no	—
84	C₂×SD₁₆×C₂₃	—	4	1	no	—
85	C₂×D₈×C₂₃	—	2	2	no	—
86	C₂×D₈×C₂₃	—	2	2	no	—
87	C₂×D₈×C₂₃	—	4	1	no	—
88	C₂×M₁₆×C₂₃	—	2	2	no	—
89	C₂×M₁₆×C₂₃	—	2	2	no	—
90	C₂×M₁₆×C₂₃	—	4	1	no	—
91	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
95	C₂₃×#124	—	2	2	no	—
96	C₂₃×#124	—	2	2	no	—
97	C₂₃×#124	—	4	1	no	—
98	C₂₃×#124	—	4	1	no	—
99	C₂₃×#121	—	2	2	no	—
100	C₂₃×#121	—	2	2	no	—
101	C₂₃×#121	—	2	2	no	—
102	C₂₃×#121	D₄	1	4	yes	—
103	C₄×D₄×C₂₃	—	2	2	no	—
104	C₄×D₄×C₂₃	—	4	1	no	—
105	C₂₃×#117	—	2	2	no	—
106	C₂₃×#117	—	4	1	no	—
107	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
108	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
124	C₂×C₄²×C₂₃	—	2	1	no	—
125	C₂×C₄²×C₂₃	—	2	1	no	—
126	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
128	C₂₃×#106	—	2	2	no	—
129	C₂₃×C₄⋊C₈	—	2	2	no	—
130	C₂₃×C₄⋊C₈	—	4	1	no	—
131	C₂₃×#103	—	2	2	no	—
132	C₂₃×#103	—	2	2	no	—
133	C₂₃×#103	—	2	2	no	—
134	C₂₃×#103	—	2	2	no	—
135	C₂₃×#103	—	2	2	no	—
136	C₂₃×#103	D₄	1	4	yes	complemented
137	C₂₃×#102	—	2	2	no	—
138	C₂₃×#102	—	2	2	no	—
139	C₂₃×#102	—	2	2	no	—
140	C₂₃×#102	—	4	1	no	—
141	C₂₃×C₂²⋊C₈	—	2	2	no	—
142	C₂₃×#95	—	2	1	no	—
143	C₂₃×#95	—	2	1	no	—
144	C₂₃×#95	—	2	1	no	—
145	C₂₃×#95	—	2	1	no	—
146	C₂₃×#95	—	2	1	no	—
147	C₂₃×#95	—	2	1	no	—
148	C₂₃×#95	D₄	1	1	yes	characteristic
149	C₂₃×#95	D₄	1	1	yes	characteristic
150	C₂⁴×C₂₃	—	2	1	no	—
151	C₂⁴×C₂₃	—	2	1	no	—
152	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
153	C₂×Q₈×C₂₃	—	2	1	no	—
154	C₂×Q₈×C₂₃	—	2	1	no	—
155	C₂×Q₈×C₂₃	—	2	8	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	—	2	1	no	—
160	C₂×Q₈×C₂₃	—	2	1	no	—
161	C₂×Q₈×C₂₃	—	2	1	no	—
162	C₂×Q₈×C₂₃	—	2	1	no	—
163	C₂×Q₈×C₂₃	—	2	1	no	—
164	C₂×Q₈×C₂₃	—	4	2	no	—
165	C₂×Q₈×C₂₃	—	4	2	no	—
166	C₂×Q₈×C₂₃	—	4	4	no	—
167	C₂×Q₈×C₂₃	—	4	4	no	—
168	C₂×Q₈×C₂₃	—	4	4	no	—
169	C₂×Q₈×C₂₃	—	4	2	no	—
170	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
171	C₂×Q₈×C₂₃	#41	1	2	yes	—
172	C₂×D₄×C₂₃	—	2	4	no	—
173	C₂×D₄×C₂₃	—	2	1	no	—
174	C₂×D₄×C₂₃	—	2	1	no	—
175	C₂×D₄×C₂₃	—	2	1	no	—
176	C₂×D₄×C₂₃	—	2	1	no	—
177	C₂×D₄×C₂₃	—	2	1	no	—
178	C₂×D₄×C₂₃	—	2	1	no	—
179	C₂×D₄×C₂₃	—	2	1	no	—
180	C₂×D₄×C₂₃	—	2	1	no	—
181	C₂×D₄×C₂₃	—	2	1	no	—
182	C₂×D₄×C₂₃	—	2	1	no	—
183	C₂×D₄×C₂₃	—	2	1	no	—
184	C₂×D₄×C₂₃	—	4	2	no	—
185	C₂×D₄×C₂₃	—	4	2	no	—
186	C₂×D₄×C₂₃	—	4	2	no	—
187	C₂×D₄×C₂₃	—	8	1	no	—
188	C₂×D₄×C₂₃	—	8	1	no	—
189	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
190	C₂²×C₄×C₂₃	—	2	1	no	—
191	C₂²×C₄×C₂₃	—	2	1	no	—
192	C₂²×C₄×C₂₃	—	2	1	no	—
193	C₂²×C₄×C₂₃	—	2	1	no	—
194	C₂²×C₄×C₂₃	—	2	1	no	—
195	C₂²×C₄×C₂₃	—	2	1	no	—
196	C₂²×C₄×C₂₃	—	2	1	no	—
197	C₂²×C₄×C₂₃	—	2	1	no	—
198	C₂²×C₄×C₂₃	—	2	1	no	—
199	C₂²×C₄×C₂₃	—	2	1	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	2	no	—
205	C₂²×C₄×C₂₃	—	8	1	no	—
206	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
212	C₂²×C₄×C₂₃	#41	1	2	yes	—
213	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
214	SD₁₆×C₂₃	—	4	4	no	—
215	SD₁₆×C₂₃	—	4	4	no	—
216	D₈×C₂₃	—	4	4	no	—
217	M₁₆×C₂₃	—	4	4	no	—
218	C₂×C₈×C₂₃	—	2	1	no	—
219	C₂×C₈×C₂₃	—	2	1	no	—
220	C₂×C₈×C₂₃	—	2	1	no	—
221	C₂×C₈×C₂₃	—	2	1	no	—
222	C₂×C₈×C₂₃	—	2	1	no	—
223	C₂×C₈×C₂₃	—	2	1	no	—
224	C₂×C₈×C₂₃	—	2	1	no	—
225	C₂×C₈×C₂₃	—	2	1	no	—
226	C₂×C₈×C₂₃	—	2	1	no	—
227	C₂×C₈×C₂₃	—	2	1	no	—
228	C₂×C₈×C₂₃	—	2	1	no	—
229	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
230	C₄⋊C₄×C₂₃	—	2	1	no	—
231	C₄⋊C₄×C₂₃	—	2	1	no	—
232	C₄⋊C₄×C₂₃	—	2	1	no	—
233	C₄⋊C₄×C₂₃	—	2	1	no	—
234	C₄⋊C₄×C₂₃	—	2	1	no	—
235	C₄⋊C₄×C₂₃	—	2	1	no	—
236	C₄⋊C₄×C₂₃	—	8	1	no	—
237	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
238	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
239	C₂²⋊C₄×C₂₃	—	2	4	no	—
240	C₂²⋊C₄×C₂₃	—	4	1	no	—
241	C₂²⋊C₄×C₂₃	—	4	1	no	—
242	C₂²⋊C₄×C₂₃	—	4	2	no	—
243	C₂²⋊C₄×C₂₃	—	4	2	no	—
244	C₂²⋊C₄×C₂₃	—	4	2	no	—
245	C₂²⋊C₄×C₂₃	—	4	2	no	—
246	C₂²⋊C₄×C₂₃	—	4	2	no	—
247	C₂²⋊C₄×C₂₃	—	4	2	no	—
248	C₂²⋊C₄×C₂₃	—	4	2	no	—
249	C₂²⋊C₄×C₂₃	—	4	2	no	—
250	C₂²⋊C₄×C₂₃	—	8	1	no	—
251	C₄²×C₂₃	—	2	1	no	—
252	C₄²×C₂₃	—	2	1	no	—
253	C₄²×C₂₃	—	2	1	no	—
254	C₄²×C₂₃	—	2	1	no	—
255	C₄²×C₂₃	—	4	2	no	—
256	C₄²×C₂₃	—	8	1	no	—
257	#25103	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
258	C₂³×C₂₃	—	2	1	no	—
259	C₂³×C₂₃	—	2	1	no	—
260	C₂³×C₂₃	—	2	1	no	—
261	C₂³×C₂₃	—	2	1	no	—
262	C₂³×C₂₃	—	2	1	no	—
263	C₂³×C₂₃	—	2	1	no	—
264	C₂³×C₂₃	—	2	2	no	—
265	C₂³×C₂₃	—	4	1	no	—
266	C₂³×C₂₃	—	4	1	no	—
267	C₂³×C₂₃	—	4	1	no	—
268	C₂³×C₂₃	—	4	1	no	—
269	C₂³×C₂₃	—	4	1	no	—
270	C₂³×C₂₃	—	4	1	no	—
271	C₂³×C₂₃	—	4	1	no	—
272	C₂³×C₂₃	—	4	1	no	—
273	C₂³×C₂₃	—	4	1	no	—
274	C₂³×C₂₃	—	4	1	no	—
275	C₂³×C₂₃	—	4	1	no	—
276	C₂³×C₂₃	—	4	1	no	—
277	C₂³×C₂₃	—	4	1	no	—
278	C₂³×C₂₃	#121	1	2	yes	—
279	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
280	Q₈×C₂₃	—	2	2	no	—
281	Q₈×C₂₃	—	2	2	no	—
282	Q₈×C₂₃	—	2	2	no	—
283	Q₈×C₂₃	—	2	2	no	—
284	Q₈×C₂₃	—	4	8	no	—
285	Q₈×C₂₃	—	4	1	no	—
286	Q₈×C₂₃	—	4	1	no	—
287	Q₈×C₂₃	—	4	1	no	—
288	Q₈×C₂₃	—	4	1	no	—
289	D₄×C₂₃	—	2	2	no	—
290	D₄×C₂₃	—	2	2	no	—
291	D₄×C₂₃	—	4	1	no	—
292	D₄×C₂₃	—	4	1	no	—
293	D₄×C₂₃	—	4	1	no	—
294	D₄×C₂₃	—	4	1	no	—
295	D₄×C₂₃	—	4	1	no	—
296	D₄×C₂₃	—	4	1	no	—
297	D₄×C₂₃	—	8	4	no	—
298	D₄×C₂₃	—	8	4	no	—
299	C₂×C₄×C₂₃	—	2	1	no	—
300	C₂×C₄×C₂₃	—	2	1	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	1	no	—
307	C₂×C₄×C₂₃	—	2	1	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	2	no	—
310	C₂×C₄×C₂₃	—	2	1	no	—
311	C₂×C₄×C₂₃	—	2	1	no	—
312	C₂×C₄×C₂₃	—	2	2	no	—
313	C₂×C₄×C₂₃	—	2	1	no	—
314	C₂×C₄×C₂₃	—	2	1	no	—
315	C₂×C₄×C₂₃	—	2	1	no	—
316	C₂×C₄×C₂₃	—	2	1	no	—
317	C₂×C₄×C₂₃	—	2	1	no	—
318	C₂×C₄×C₂₃	—	2	1	no	—
319	C₂×C₄×C₂₃	—	2	1	no	—
320	C₂×C₄×C₂₃	—	2	1	no	—
321	C₂×C₄×C₂₃	—	4	8	no	—
322	C₂×C₄×C₂₃	—	4	1	no	—
323	C₂×C₄×C₂₃	—	4	1	no	—
324	C₂×C₄×C₂₃	—	4	1	no	—
325	C₂×C₄×C₂₃	—	4	1	no	—
326	C₂×C₄×C₂₃	—	4	1	no	—
327	C₂×C₄×C₂₃	—	4	1	no	—
328	C₂×C₄×C₂₃	—	4	1	no	—
329	C₂×C₄×C₂₃	—	4	1	no	—
330	C₂×C₄×C₂₃	—	4	1	no	—
331	C₂×C₄×C₂₃	—	4	1	no	—
332	C₂×C₄×C₂₃	—	4	1	no	—
333	C₂×C₄×C₂₃	—	4	1	no	—
334	C₂×C₄×C₂₃	—	4	1	no	—
335	C₂×C₄×C₂₃	—	4	1	no	—
336	C₂×C₄×C₂₃	—	8	4	no	—
337	C₂×C₄×C₂₃	#121	1	2	yes	—
338	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
341	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
342	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
343	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
344	C₈×C₂₃	—	2	2	no	—
345	C₈×C₂₃	—	4	1	no	—
346	C₈×C₂₃	—	4	1	no	—
347	C₈×C₂₃	—	4	1	no	—
348	C₂×#469	C₂×C₂₃	1	1	yes	characteristic
349	C₂×#463	C₂×C₂₃	1	1	yes	characteristic, complemented
350	C₂×#448	C₂×C₂₃	1	1	yes	characteristic, complemented
351	C₂×#419	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#2436	C₂×C₂₃	1	1	yes	characteristic, complemented
353	#2363	C₂×C₂₃	1	1	yes	characteristic, complemented
354	#2066	C₂×C₂₃	1	1	yes	characteristic, complemented
355	#2055	C₂×C₂₃	1	1	yes	characteristic, complemented
356	#2042	C₂×C₂₃	1	1	yes	characteristic, complemented
357	#2012	C₂×C₂₃	1	1	yes	characteristic, complemented
358	#1983	C₂×C₂₃	1	1	yes	characteristic, complemented
359	#1927	C₂×C₂₃	1	1	yes	characteristic, complemented
360	#1877	C₂×C₂₃	1	1	yes	characteristic, complemented
361	#1875	C₂×C₂₃	1	1	yes	characteristic, complemented
362	#1851	C₂×C₂₃	1	1	yes	characteristic, complemented
363	C₂²×C₂₃	—	2	2	no	—
364	C₂²×C₂₃	—	2	2	no	—
365	C₂²×C₂₃	—	2	2	no	—
366	C₂²×C₂₃	—	4	1	no	—
367	C₂²×C₂₃	—	4	1	no	—
368	C₂²×C₂₃	—	4	1	no	—
369	C₂²×C₂₃	—	4	1	no	—
370	C₂²×C₂₃	—	4	2	no	—
371	C₂²×C₂₃	—	4	2	no	—
372	C₂²×C₂₃	—	4	2	no	—
373	C₂²×C₂₃	—	8	1	no	—
374	C₂²×C₂₃	—	8	1	no	—
375	C₂²×C₂₃	—	8	1	no	—
376	C₂²×C₂₃	—	8	1	no	—
377	C₂²×C₂₃	—	8	1	no	—
378	C₂²×C₂₃	—	8	1	no	—
379	C₂²×C₂₃	—	8	1	no	—
380	C₂²×C₂₃	—	8	1	no	—
381	C₂²×C₂₃	—	8	1	no	—
382	C₂²×C₂₃	—	8	1	no	—
383	C₂²×C₂₃	—	8	1	no	—
384	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
385	C₂²×C₂₃	D₄²	1	1	yes	characteristic
386	C₂²×C₂₃	#546	1	1	yes	characteristic
387	C₂²×C₂₃	#575	1	1	yes	characteristic
388	C₂²×C₂₃	#575	1	1	yes	characteristic
389	C₂²×C₂₃	#577	1	1	yes	characteristic
390	C₂²×C₂₃	#577	1	1	yes	characteristic
391	C₄×C₂₃	—	2	2	no	—
392	C₄×C₂₃	—	4	2	no	—
393	C₄×C₂₃	—	4	2	no	—
394	C₄×C₂₃	—	4	1	no	—
395	C₄×C₂₃	—	4	1	no	—
396	C₄×C₂₃	—	4	2	no	—
397	C₄×C₂₃	—	4	2	no	—
398	C₄×C₂₃	—	4	1	no	—
399	C₄×C₂₃	—	4	1	no	—
400	C₄×C₂₃	—	8	1	no	—
401	C₄×C₂₃	—	8	1	no	—
402	C₄×C₂₃	#525	1	1	yes	characteristic
403	C₄×C₂₃	#538	1	1	yes	characteristic
404	C₄×C₂₃	D₄²	1	1	yes	characteristic
405	C₄×C₂₃	#546	1	1	yes	characteristic
406	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
407	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
408	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
409	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
410	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
411	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
412	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
413	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
414	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
415	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
416	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
417	#469	—	2	4	no	—
418	#463	—	2	4	no	—
419	#448	—	2	4	no	—
420	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
421	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
423	#419	—	2	4	no	—
424	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
425	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
426	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
428	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
429	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
430	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
433	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
434	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
435	#393	—	2	1	no	—
436	#393	—	2	1	no	—
437	#391	C₂²×C₂₃	1	1	yes	characteristic
438	#391	C₂²×C₂₃	1	1	yes	characteristic
439	#390	—	2	1	no	—
440	#390	C₂²×C₂₃	1	1	yes	characteristic
441	#389	C₂²×C₂₃	1	1	yes	characteristic
442	#388	—	2	1	no	—
443	#386	—	2	1	no	—
444	#386	—	2	1	no	—
445	#386	—	2	1	no	—
446	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
447	C₄×C₂²⋊C₄	—	2	1	no	—
448	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
449	#340	C₂²×C₂₃	1	1	yes	characteristic
450	#340	C₂²×C₂₃	1	1	yes	characteristic
451	#336	C₂²×C₂₃	1	1	yes	characteristic
452	#336	C₂²×C₂₃	1	1	yes	characteristic
453	C₂×C₂₃	—	4	2	no	—
454	C₂×C₂₃	—	8	2	no	—
455	C₂×C₂₃	—	16	1	no	—
456	C₂×C₂₃	#2424	1	1	yes	characteristic
457	C₂×C₂₃	#3040	1	1	yes	characteristic
458	C₂×C₂₃	#3042	1	1	yes	characteristic
459	C₂×C₂₃	#3271	1	1	yes	characteristic
460	C₂×C₂₃	#3275	1	1	yes	characteristic
461	C₂×C₂₃	#3321	1	1	yes	characteristic
462	C₂×C₂₃	#3326	1	1	yes	characteristic
463	C₂²×Q₈	—	2	1	no	—
464	C₂²×Q₈	—	2	2	no	—
465	C₂²×Q₈	—	2	2	no	—
466	C₂²×Q₈	—	2	2	no	—
467	C₂²×Q₈	—	2	2	no	—
468	C₂²×Q₈	—	4	1	no	—
469	C₂²×Q₈	—	4	1	no	—
470	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
471	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
472	C₂²×D₄	—	2	1	no	—
473	C₂²×D₄	—	2	1	no	—
474	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
475	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
476	C₂³×C₄	—	2	1	no	—
477	C₂³×C₄	—	2	1	no	—
478	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
479	C₂×SD₁₆	—	2	2	no	—
480	C₂×SD₁₆	—	2	2	no	—
481	C₂×SD₁₆	—	2	2	no	—
482	C₂×SD₁₆	—	2	2	no	—
483	C₂×SD₁₆	—	4	1	no	—
484	C₂×SD₁₆	—	4	1	no	—
485	C₂×D₈	—	2	2	no	—
486	C₂×D₈	—	2	2	no	—
487	C₂×D₈	—	4	1	no	—
488	C₂×M₁₆	—	2	2	no	—
489	C₂×M₁₆	—	2	2	no	—
490	C₂×M₁₆	—	4	1	no	—
491	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
495	#124	—	2	2	no	—
496	#124	—	2	2	no	—
497	#124	—	4	1	no	—
498	#124	—	4	1	no	—
499	#121	—	2	2	no	—
500	#121	—	2	2	no	—
501	#121	—	2	2	no	—
502	#121	D₄×C₂₃	1	4	yes	—
503	C₄×D₄	—	2	2	no	—
504	C₄×D₄	—	4	1	no	—
505	#117	—	2	2	no	—
506	#117	—	4	1	no	—
507	C₂×C₄⋊C₄	—	2	1	no	—
508	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
524	C₂×C₄²	—	2	1	no	—
525	C₂×C₄²	—	2	1	no	—
526	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
528	#106	—	2	2	no	—
529	C₄⋊C₈	—	2	2	no	—
530	C₄⋊C₈	—	4	1	no	—
531	#103	—	2	2	no	—
532	#103	—	2	2	no	—
533	#103	—	2	2	no	—
534	#103	—	2	2	no	—
535	#103	—	2	2	no	—
536	#103	D₄×C₂₃	1	4	yes	complemented
537	#102	—	2	2	no	—
538	#102	—	2	2	no	—
539	#102	—	2	2	no	—
540	#102	—	4	1	no	—
541	C₂²⋊C₈	—	2	2	no	—
542	#95	—	2	1	no	—
543	#95	—	2	1	no	—
544	#95	—	2	1	no	—
545	#95	—	2	1	no	—
546	#95	—	2	1	no	—
547	#95	—	2	1	no	—
548	#95	D₄×C₂₃	1	1	yes	characteristic
549	#95	D₄×C₂₃	1	1	yes	characteristic
550	C₂₃	#25103	1	1	yes	characteristic, direct product factor, Sylow
551	C₂⁴	—	2	1	no	—
552	C₂⁴	—	2	1	no	—
553	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	8	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	4	2	no	—
566	C₂×Q₈	—	4	2	no	—
567	C₂×Q₈	—	4	4	no	—
568	C₂×Q₈	—	4	4	no	—
569	C₂×Q₈	—	4	4	no	—
570	C₂×Q₈	—	4	2	no	—
571	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
572	C₂×Q₈	#41×C₂₃	1	2	yes	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	4	2	no	—
586	C₂×D₄	—	4	2	no	—
587	C₂×D₄	—	4	2	no	—
588	C₂×D₄	—	8	1	no	—
589	C₂×D₄	—	8	1	no	—
590	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	4	2	no	—
602	C₂²×C₄	—	4	2	no	—
603	C₂²×C₄	—	4	2	no	—
604	C₂²×C₄	—	4	2	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	—	8	1	no	—
607	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
609	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
610	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
611	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
613	C₂²×C₄	#41×C₂₃	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
615	SD₁₆	—	4	4	no	—
616	SD₁₆	—	4	4	no	—
617	D₈	—	4	4	no	—
618	M₁₆	—	4	4	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	—	2	1	no	—
629	C₂×C₈	—	2	1	no	—
630	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	8	1	no	—
638	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
639	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	4	1	no	—
642	C₂²⋊C₄	—	4	1	no	—
643	C₂²⋊C₄	—	4	2	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	—	4	2	no	—
651	C₂²⋊C₄	—	8	1	no	—
652	C₄²	—	2	1	no	—
653	C₄²	—	2	1	no	—
654	C₄²	—	2	1	no	—
655	C₄²	—	2	1	no	—
656	C₄²	—	4	2	no	—
657	C₄²	—	8	1	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	1	no	—
678	C₂³	C₂₃×#121	1	2	yes	—
679	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
680	Q₈	—	2	2	no	—
681	Q₈	—	2	2	no	—
682	Q₈	—	2	2	no	—
683	Q₈	—	2	2	no	—
684	Q₈	—	4	8	no	—
685	Q₈	—	4	1	no	—
686	Q₈	—	4	1	no	—
687	Q₈	—	4	1	no	—
688	Q₈	—	4	1	no	—
689	D₄	—	2	2	no	—
690	D₄	—	2	2	no	—
691	D₄	—	4	1	no	—
692	D₄	—	4	1	no	—
693	D₄	—	4	1	no	—
694	D₄	—	4	1	no	—
695	D₄	—	4	1	no	—
696	D₄	—	4	1	no	—
697	D₄	—	8	4	no	—
698	D₄	—	8	4	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	4	8	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	8	4	no	—
737	C₂×C₄	C₂₃×#121	1	2	yes	—
738	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
739	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
740	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
741	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
742	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
743	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
744	C₈	—	2	2	no	—
745	C₈	—	4	1	no	—
746	C₈	—	4	1	no	—
747	C₈	—	4	1	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	1	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	8	1	no	—
759	C₂²	—	8	1	no	—
760	C₂²	—	8	1	no	—
761	C₂²	—	8	1	no	—
762	C₂²	—	8	1	no	—
763	C₂²	—	8	1	no	—
764	C₂²	—	8	1	no	—
765	C₂²	—	8	1	no	—
766	C₂²	—	8	1	no	—
767	C₂²	—	8	1	no	—
768	C₂²	—	8	1	no	—
769	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
770	C₂²	D₄²×C₂₃	1	1	yes	characteristic
771	C₂²	C₂₃×#546	1	1	yes	characteristic
772	C₂²	C₂₃×#575	1	1	yes	characteristic
773	C₂²	C₂₃×#575	1	1	yes	characteristic
774	C₂²	C₂₃×#577	1	1	yes	characteristic
775	C₂²	C₂₃×#577	1	1	yes	characteristic
776	C₄	—	2	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	1	no	—
780	C₄	—	4	1	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	1	no	—
785	C₄	—	8	1	no	—
786	C₄	—	8	1	no	—
787	C₄	C₂₃×#525	1	1	yes	characteristic
788	C₄	C₂₃×#538	1	1	yes	characteristic
789	C₄	D₄²×C₂₃	1	1	yes	characteristic
790	C₄	C₂₃×#546	1	1	yes	characteristic
791	C₂	—	4	2	no	—
792	C₂	—	8	2	no	—
793	C₂	—	16	1	no	—
794	C₂	C₂₃×#2424	1	1	yes	characteristic
795	C₂	C₂₃×#3040	1	1	yes	characteristic
796	C₂	C₂₃×#3042	1	1	yes	characteristic
797	C₂	C₂₃×#3271	1	1	yes	characteristic
798	C₂	C₂₃×#3275	1	1	yes	characteristic
799	C₂	C₂₃×#3321	1	1	yes	characteristic
800	C₂	C₂₃×#3326	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#469	C₂
LCS	G ▷ C₂²×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×C₂₃×#463	C₂	semidirect
3. C₂×C₂₃×#448	C₂	semidirect
4. C₂×C₂₃×#419	C₂	semidirect
5. C₂₃×#2436	C₂	semidirect
6. C₂₃×#2363	C₂	semidirect
7. C₂₃×#2066	C₂	semidirect
8. C₂₃×#2055	C₂	semidirect
9. C₂₃×#2042	C₂	semidirect
10. C₂₃×#2012	C₂	semidirect
11. C₂₃×#1983	C₂	semidirect
12. C₂₃×#1927	C₂	semidirect
13. C₂₃×#1877	C₂	semidirect
14. C₂₃×#1875	C₂	semidirect
15. C₂₃×#1851	C₂	semidirect
136. C₂₃×#103	D₄	semidirect
257. #25103	C₂₃	direct (N × H)
349. C₂×#463	C₂×C₂₃	semidirect
350. C₂×#448	C₂×C₂₃	semidirect
351. C₂×#419	C₂×C₂₃	semidirect
352. #2436	C₂×C₂₃	semidirect
353. #2363	C₂×C₂₃	semidirect
354. #2066	C₂×C₂₃	semidirect
355. #2055	C₂×C₂₃	semidirect
356. #2042	C₂×C₂₃	semidirect
357. #2012	C₂×C₂₃	semidirect
358. #1983	C₂×C₂₃	semidirect
359. #1927	C₂×C₂₃	semidirect
360. #1877	C₂×C₂₃	semidirect
361. #1875	C₂×C₂₃	semidirect
362. #1851	C₂×C₂₃	semidirect
536. #103	D₄×C₂₃	semidirect
550. C₂₃	#25103	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×#469	2
C₂×C₂₃×#463	2
C₂×C₂₃×#448	2
C₂×C₂₃×#419	2
C₂₃×#2436	2
C₂₃×#2363	2
C₂₃×#2066	2
C₂₃×#2055	2
C₂₃×#2042	2
C₂₃×#2012	2
C₂₃×#1983	2
C₂₃×#1927	2
C₂₃×#1877	2
C₂₃×#1875	2
C₂₃×#1851	2
#25103	23

Subgroups — C23×#25103 #19172729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25103 #19172729