Subgroups — C₂₃×#25559 #19173185

Order 5888.

1174 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2414	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#2057	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2023	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1874	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1873	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1863	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#554	—	2	4	no	—
19	C₂₃×#554	—	2	4	no	—
20	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#125	—	2	1	no	—
22	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
23	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
24	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₂₃	—	2	1	no	—
30	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂₃×#480	—	2	4	no	—
35	C₂₃×#468	—	2	4	no	—
36	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#103	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×#102	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂₃×#394	—	2	1	no	—
49	C₂₃×#392	—	2	1	no	—
50	C₂₃×#390	—	2	1	no	—
51	C₂₃×#390	C₂²	1	1	yes	characteristic
52	C₂₃×#389	C₂²	1	1	yes	characteristic
53	C₂₃×#388	—	2	1	no	—
54	C₂₃×#380	C₂²	1	1	yes	characteristic
55	C₂₃×#340	C₂²	1	1	yes	characteristic
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×#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	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₂₃	—	2	1	no	—
66	C₂²×D₄×C₂₃	—	2	1	no	—
67	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
68	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₂₃	—	2	1	no	—
70	C₂³×C₄×C₂₃	—	2	1	no	—
71	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
73	C₂×SD₁₆×C₂₃	—	2	2	no	—
74	C₂×SD₁₆×C₂₃	—	2	2	no	—
75	C₂×SD₁₆×C₂₃	—	4	1	no	—
76	C₂×M₁₆×C₂₃	—	2	2	no	—
77	C₂×M₁₆×C₂₃	—	2	2	no	—
78	C₂×M₁₆×C₂₃	—	4	1	no	—
79	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
83	C₂₃×C₄⋊Q₈	—	2	2	no	—
84	C₂₃×C₄⋊Q₈	—	2	2	no	—
85	C₂₃×#125	—	2	8	no	—
86	C₂₃×C₂²⋊Q₈	—	2	8	no	—
87	C₂₃×C₂²⋊Q₈	—	2	8	no	—
88	C₂₃×C₂²⋊Q₈	—	2	2	no	—
89	C₂₃×C₂²⋊Q₈	—	2	2	no	—
90	C₂₃×C₂²⋊Q₈	—	2	2	no	—
91	C₂₃×C₂²⋊Q₈	D₄	1	4	yes	complemented
92	C₂₃×#121	—	2	2	no	—
93	C₂₃×#121	—	2	2	no	—
94	C₂₃×#121	—	2	2	no	—
95	C₂₃×#121	—	4	1	no	—
96	C₄×Q₈×C₂₃	—	2	2	no	—
97	C₄×Q₈×C₂₃	—	2	2	no	—
98	C₄×D₄×C₂₃	—	2	8	no	—
99	C₄×D₄×C₂₃	—	2	2	no	—
100	C₄×D₄×C₂₃	—	2	2	no	—
101	C₂₃×#117	—	2	2	no	—
102	C₂₃×#117	—	4	1	no	—
103	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
104	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
105	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
106	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
107	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
108	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
109	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
110	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
111	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
112	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
113	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₂₃	D₄	1	4	yes	complemented
115	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
130	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
131	C₂×C₄²×C₂₃	—	2	1	no	—
132	C₂×C₄²×C₂₃	—	2	1	no	—
133	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
134	C₂₃×#107	—	2	2	no	—
135	C₂₃×#107	—	2	2	no	—
136	C₂₃×#107	—	2	2	no	—
137	C₂₃×#103	—	2	2	no	—
138	C₂₃×#103	—	2	2	no	—
139	C₂₃×#103	—	4	1	no	—
140	C₂₃×#102	—	2	2	no	—
141	C₂₃×#102	—	2	2	no	—
142	C₂₃×#102	—	2	2	no	—
143	C₂₃×C₂²⋊C₈	—	2	2	no	—
144	C₂₃×C₂²⋊C₈	—	2	2	no	—
145	C₂₃×C₂²⋊C₈	—	4	1	no	—
146	C₂₃×#95	—	2	1	no	—
147	C₂₃×#95	—	2	1	no	—
148	C₂⁴×C₂₃	—	2	1	no	—
149	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
150	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
151	C₂×Q₈×C₂₃	—	2	4	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	—	8	1	no	—
158	C₂×Q₈×C₂₃	—	8	1	no	—
159	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₂₃	—	2	2	no	—
161	C₂×D₄×C₂₃	—	2	2	no	—
162	C₂×D₄×C₂₃	—	2	2	no	—
163	C₂×D₄×C₂₃	—	2	1	no	—
164	C₂×D₄×C₂₃	—	2	1	no	—
165	C₂×D₄×C₂₃	—	2	1	no	—
166	C₂×D₄×C₂₃	—	2	1	no	—
167	C₂×D₄×C₂₃	—	2	1	no	—
168	C₂×D₄×C₂₃	—	2	1	no	—
169	C₂×D₄×C₂₃	—	4	2	no	—
170	C₂×D₄×C₂₃	—	4	2	no	—
171	C₂×D₄×C₂₃	—	4	2	no	—
172	C₂×D₄×C₂₃	—	8	1	no	—
173	C₂×D₄×C₂₃	—	8	1	no	—
174	C₂×D₄×C₂₃	—	8	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	1	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	—	2	1	no	—
183	C₂²×C₄×C₂₃	—	2	1	no	—
184	C₂²×C₄×C₂₃	—	2	4	no	—
185	C₂²×C₄×C₂₃	—	2	4	no	—
186	C₂²×C₄×C₂₃	—	2	1	no	—
187	C₂²×C₄×C₂₃	—	2	1	no	—
188	C₂²×C₄×C₂₃	—	2	1	no	—
189	C₂²×C₄×C₂₃	—	2	1	no	—
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	—	8	1	no	—
195	C₂²×C₄×C₂₃	—	8	1	no	—
196	C₂²×C₄×C₂₃	—	8	1	no	—
197	C₂²×C₄×C₂₃	—	8	1	no	—
198	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
203	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
205	SD₁₆×C₂₃	—	4	4	no	—
206	M₁₆×C₂₃	—	4	4	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	—	2	1	no	—
214	C₂×C₈×C₂₃	—	2	1	no	—
215	C₂×C₈×C₂₃	—	2	1	no	—
216	C₂×C₈×C₂₃	—	2	1	no	—
217	C₂×C₈×C₂₃	—	2	1	no	—
218	C₂×C₈×C₂₃	#41	1	2	yes	—
219	C₄⋊C₄×C₂₃	—	2	4	no	—
220	C₄⋊C₄×C₂₃	—	2	4	no	—
221	C₄⋊C₄×C₂₃	—	2	4	no	—
222	C₄⋊C₄×C₂₃	—	2	4	no	—
223	C₄⋊C₄×C₂₃	—	2	4	no	—
224	C₄⋊C₄×C₂₃	—	2	4	no	—
225	C₄⋊C₄×C₂₃	—	2	2	no	—
226	C₄⋊C₄×C₂₃	—	2	1	no	—
227	C₄⋊C₄×C₂₃	—	2	1	no	—
228	C₄⋊C₄×C₂₃	—	2	1	no	—
229	C₄⋊C₄×C₂₃	—	2	1	no	—
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	—	8	1	no	—
235	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
236	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
237	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
238	C₄⋊C₄×C₂₃	#41	1	2	yes	—
239	C₂²⋊C₄×C₂₃	—	2	4	no	—
240	C₂²⋊C₄×C₂₃	—	2	4	no	—
241	C₂²⋊C₄×C₂₃	—	2	2	no	—
242	C₂²⋊C₄×C₂₃	—	2	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	—	8	1	no	—
248	C₂²⋊C₄×C₂₃	—	8	1	no	—
249	C₄²×C₂₃	—	2	4	no	—
250	C₄²×C₂₃	—	2	1	no	—
251	C₄²×C₂₃	—	2	1	no	—
252	C₄²×C₂₃	—	4	2	no	—
253	#25559	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂³×C₂₃	—	2	1	no	—
255	C₂³×C₂₃	—	2	1	no	—
256	C₂³×C₂₃	—	2	1	no	—
257	C₂³×C₂₃	—	2	1	no	—
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	1	no	—
265	C₂³×C₂₃	—	2	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	#120	1	2	yes	—
274	C₂³×C₂₃	#137	1	2	yes	—
275	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
276	Q₈×C₂₃	—	2	2	no	—
277	Q₈×C₂₃	—	2	2	no	—
278	Q₈×C₂₃	—	4	1	no	—
279	Q₈×C₂₃	—	4	1	no	—
280	Q₈×C₂₃	—	8	4	no	—
281	D₄×C₂₃	—	2	8	no	—
282	D₄×C₂₃	—	4	1	no	—
283	D₄×C₂₃	—	4	1	no	—
284	D₄×C₂₃	—	4	1	no	—
285	D₄×C₂₃	—	4	1	no	—
286	D₄×C₂₃	—	8	4	no	—
287	D₄×C₂₃	—	8	4	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	—	2	2	no	—
293	C₂×C₄×C₂₃	—	2	2	no	—
294	C₂×C₄×C₂₃	—	2	2	no	—
295	C₂×C₄×C₂₃	—	2	2	no	—
296	C₂×C₄×C₂₃	—	2	2	no	—
297	C₂×C₄×C₂₃	—	2	1	no	—
298	C₂×C₄×C₂₃	—	2	2	no	—
299	C₂×C₄×C₂₃	—	2	1	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	1	no	—
304	C₂×C₄×C₂₃	—	2	1	no	—
305	C₂×C₄×C₂₃	—	2	1	no	—
306	C₂×C₄×C₂₃	—	2	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	—	4	1	no	—
311	C₂×C₄×C₂₃	—	4	1	no	—
312	C₂×C₄×C₂₃	—	4	1	no	—
313	C₂×C₄×C₂₃	—	4	1	no	—
314	C₂×C₄×C₂₃	—	4	1	no	—
315	C₂×C₄×C₂₃	—	4	1	no	—
316	C₂×C₄×C₂₃	—	4	1	no	—
317	C₂×C₄×C₂₃	—	4	1	no	—
318	C₂×C₄×C₂₃	—	4	1	no	—
319	C₂×C₄×C₂₃	—	4	1	no	—
320	C₂×C₄×C₂₃	—	4	1	no	—
321	C₂×C₄×C₂₃	—	4	1	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	—	8	4	no	—
328	C₂×C₄×C₂₃	—	8	4	no	—
329	C₂×C₄×C₂₃	#120	1	2	yes	—
330	C₂×C₄×C₂₃	#137	1	2	yes	—
331	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
334	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
335	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
336	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
337	C₈×C₂₃	—	2	2	no	—
338	C₈×C₂₃	—	4	1	no	—
339	C₈×C₂₃	—	4	1	no	—
340	C₈×C₂₃	—	4	1	no	—
341	C₂×#554	C₂×C₂₃	1	1	yes	characteristic, complemented
342	C₂×#480	C₂×C₂₃	1	1	yes	characteristic, complemented
343	C₂×#468	C₂×C₂₃	1	1	yes	characteristic, complemented
344	#2414	C₂×C₂₃	1	1	yes	characteristic
345	#2057	C₂×C₂₃	1	1	yes	characteristic, complemented
346	#2036	C₂×C₂₃	1	1	yes	characteristic, complemented
347	#2023	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#2000	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#1880	C₂×C₂₃	1	1	yes	characteristic, complemented
350	#1874	C₂×C₂₃	1	1	yes	characteristic, complemented
351	#1873	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#1870	C₂×C₂₃	1	1	yes	characteristic, complemented
353	#1863	C₂×C₂₃	1	1	yes	characteristic, complemented
354	#1852	C₂×C₂₃	1	1	yes	characteristic, complemented
355	#1736	C₂×C₂₃	1	1	yes	characteristic, complemented
356	C₂²×C₂₃	—	2	2	no	—
357	C₂²×C₂₃	—	2	2	no	—
358	C₂²×C₂₃	—	2	2	no	—
359	C₂²×C₂₃	—	2	2	no	—
360	C₂²×C₂₃	—	2	2	no	—
361	C₂²×C₂₃	—	2	2	no	—
362	C₂²×C₂₃	—	4	1	no	—
363	C₂²×C₂₃	—	4	1	no	—
364	C₂²×C₂₃	—	4	1	no	—
365	C₂²×C₂₃	—	4	1	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	—	8	1	no	—
371	C₂²×C₂₃	—	8	1	no	—
372	C₂²×C₂₃	—	8	1	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	C₂×#120	1	1	yes	characteristic
378	C₂²×C₂₃	#546	1	1	yes	characteristic
379	C₂²×C₂₃	#547	1	1	yes	characteristic
380	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
381	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
382	C₂²×C₂₃	#576	1	1	yes	characteristic
383	C₂²×C₂₃	#576	1	1	yes	characteristic
384	C₄×C₂₃	—	2	2	no	—
385	C₄×C₂₃	—	2	2	no	—
386	C₄×C₂₃	—	4	1	no	—
387	C₄×C₂₃	—	4	2	no	—
388	C₄×C₂₃	—	4	1	no	—
389	C₄×C₂₃	—	4	2	no	—
390	C₄×C₂₃	—	4	2	no	—
391	C₄×C₂₃	—	4	2	no	—
392	C₄×C₂₃	—	4	2	no	—
393	C₄×C₂₃	—	8	1	no	—
394	C₄×C₂₃	—	8	1	no	—
395	C₄×C₂₃	#532	1	1	yes	characteristic
396	C₄×C₂₃	#537	1	1	yes	characteristic
397	C₄×C₂₃	#546	1	1	yes	characteristic
398	C₄×C₂₃	#547	1	1	yes	characteristic
399	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
400	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
401	#554	—	2	4	no	—
402	#554	—	2	4	no	—
403	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
404	C₂×#125	—	2	1	no	—
405	C₂×C₂²⋊Q₈	—	2	1	no	—
406	C₂×C₂²⋊Q₈	—	2	1	no	—
407	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
408	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
409	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
410	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
411	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
412	C₂×C₄×D₄	—	2	1	no	—
413	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
414	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
415	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
416	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
417	#480	—	2	4	no	—
418	#468	—	2	4	no	—
419	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
420	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
421	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
424	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
425	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
426	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
428	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
429	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
430	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
431	#394	—	2	1	no	—
432	#392	—	2	1	no	—
433	#390	—	2	1	no	—
434	#390	C₂²×C₂₃	1	1	yes	characteristic
435	#389	C₂²×C₂₃	1	1	yes	characteristic
436	#388	—	2	1	no	—
437	#380	C₂²×C₂₃	1	1	yes	characteristic
438	#340	C₂²×C₂₃	1	1	yes	characteristic
439	#340	C₂²×C₂₃	1	1	yes	characteristic
440	#340	C₂²×C₂₃	1	1	yes	characteristic
441	#340	C₂²×C₂₃	1	1	yes	characteristic
442	#340	C₂²×C₂₃	1	1	yes	characteristic
443	#340	C₂²×C₂₃	1	1	yes	characteristic
444	#336	C₂²×C₂₃	1	1	yes	characteristic
445	#336	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×C₂₃	—	4	2	no	—
447	C₂×C₂₃	—	4	2	no	—
448	C₂×C₂₃	—	16	1	no	—
449	C₂×C₂₃	#2430	1	1	yes	characteristic
450	C₂×C₂₃	#3004	1	1	yes	characteristic
451	C₂×C₂₃	#3008	1	1	yes	characteristic
452	C₂×C₂₃	#3314	1	1	yes	characteristic
453	C₂×C₂₃	#3333	1	1	yes	characteristic
454	C₂×C₂₃	#3346	1	1	yes	characteristic
455	C₂×C₂₃	#3357	1	1	yes	characteristic
456	C₂²×Q₈	—	2	1	no	—
457	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	—	2	1	no	—
460	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
461	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
462	C₂³×C₄	—	2	1	no	—
463	C₂³×C₄	—	2	1	no	—
464	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
466	C₂×SD₁₆	—	2	2	no	—
467	C₂×SD₁₆	—	2	2	no	—
468	C₂×SD₁₆	—	4	1	no	—
469	C₂×M₁₆	—	2	2	no	—
470	C₂×M₁₆	—	2	2	no	—
471	C₂×M₁₆	—	4	1	no	—
472	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
475	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
476	C₄⋊Q₈	—	2	2	no	—
477	C₄⋊Q₈	—	2	2	no	—
478	#125	—	2	8	no	—
479	C₂²⋊Q₈	—	2	8	no	—
480	C₂²⋊Q₈	—	2	8	no	—
481	C₂²⋊Q₈	—	2	2	no	—
482	C₂²⋊Q₈	—	2	2	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	D₄×C₂₃	1	4	yes	complemented
485	#121	—	2	2	no	—
486	#121	—	2	2	no	—
487	#121	—	2	2	no	—
488	#121	—	4	1	no	—
489	C₄×Q₈	—	2	2	no	—
490	C₄×Q₈	—	2	2	no	—
491	C₄×D₄	—	2	8	no	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	—	2	2	no	—
494	#117	—	2	2	no	—
495	#117	—	4	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	2	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	2	no	—
504	C₂×C₄⋊C₄	—	2	2	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	D₄×C₂₃	1	4	yes	complemented
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×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
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	#107	—	2	2	no	—
528	#107	—	2	2	no	—
529	#107	—	2	2	no	—
530	#103	—	2	2	no	—
531	#103	—	2	2	no	—
532	#103	—	4	1	no	—
533	#102	—	2	2	no	—
534	#102	—	2	2	no	—
535	#102	—	2	2	no	—
536	C₂²⋊C₈	—	2	2	no	—
537	C₂²⋊C₈	—	2	2	no	—
538	C₂²⋊C₈	—	4	1	no	—
539	#95	—	2	1	no	—
540	#95	—	2	1	no	—
541	C₂₃	#25559	1	1	yes	characteristic, direct product factor, Sylow
542	C₂⁴	—	2	1	no	—
543	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
544	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
545	C₂×Q₈	—	2	4	no	—
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	—	2	1	no	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	8	1	no	—
552	C₂×Q₈	—	8	1	no	—
553	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	4	2	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	8	1	no	—
567	C₂×D₄	—	8	1	no	—
568	C₂×D₄	—	8	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	8	1	no	—
589	C₂²×C₄	—	8	1	no	—
590	C₂²×C₄	—	8	1	no	—
591	C₂²×C₄	—	8	1	no	—
592	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
596	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
597	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
599	SD₁₆	—	4	4	no	—
600	M₁₆	—	4	4	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	#41×C₂₃	1	2	yes	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	8	1	no	—
629	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
630	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
631	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
632	C₄⋊C₄	#41×C₂₃	1	2	yes	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	4	2	no	—
639	C₂²⋊C₄	—	4	2	no	—
640	C₂²⋊C₄	—	4	2	no	—
641	C₂²⋊C₄	—	8	1	no	—
642	C₂²⋊C₄	—	8	1	no	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	1	no	—
645	C₄²	—	2	1	no	—
646	C₄²	—	4	2	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	1	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	4	1	no	—
663	C₂³	—	4	1	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	C₂₃×#120	1	2	yes	—
667	C₂³	C₂₃×#137	1	2	yes	—
668	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
669	Q₈	—	2	2	no	—
670	Q₈	—	2	2	no	—
671	Q₈	—	4	1	no	—
672	Q₈	—	4	1	no	—
673	Q₈	—	8	4	no	—
674	D₄	—	2	8	no	—
675	D₄	—	4	1	no	—
676	D₄	—	4	1	no	—
677	D₄	—	4	1	no	—
678	D₄	—	4	1	no	—
679	D₄	—	8	4	no	—
680	D₄	—	8	4	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	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	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	8	4	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	C₂₃×#120	1	2	yes	—
723	C₂×C₄	C₂₃×#137	1	2	yes	—
724	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
726	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
727	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
728	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
729	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
730	C₈	—	2	2	no	—
731	C₈	—	4	1	no	—
732	C₈	—	4	1	no	—
733	C₈	—	4	1	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	4	1	no	—
741	C₂²	—	4	1	no	—
742	C₂²	—	4	1	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	8	1	no	—
749	C₂²	—	8	1	no	—
750	C₂²	—	8	1	no	—
751	C₂²	—	8	1	no	—
752	C₂²	—	8	1	no	—
753	C₂²	—	8	1	no	—
754	C₂²	—	8	1	no	—
755	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
756	C₂²	C₂₃×#546	1	1	yes	characteristic
757	C₂²	C₂₃×#547	1	1	yes	characteristic
758	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
759	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
760	C₂²	C₂₃×#576	1	1	yes	characteristic
761	C₂²	C₂₃×#576	1	1	yes	characteristic
762	C₄	—	2	2	no	—
763	C₄	—	2	2	no	—
764	C₄	—	4	1	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	1	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	8	1	no	—
772	C₄	—	8	1	no	—
773	C₄	C₂₃×#532	1	1	yes	characteristic
774	C₄	C₂₃×#537	1	1	yes	characteristic
775	C₄	C₂₃×#546	1	1	yes	characteristic
776	C₄	C₂₃×#547	1	1	yes	characteristic
777	C₂	—	4	2	no	—
778	C₂	—	4	2	no	—
779	C₂	—	16	1	no	—
780	C₂	C₂₃×#2430	1	1	yes	characteristic
781	C₂	C₂₃×#3004	1	1	yes	characteristic
782	C₂	C₂₃×#3008	1	1	yes	characteristic
783	C₂	C₂₃×#3314	1	1	yes	characteristic
784	C₂	C₂₃×#3333	1	1	yes	characteristic
785	C₂	C₂₃×#3346	1	1	yes	characteristic
786	C₂	C₂₃×#3357	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂₃×#2414	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#554	C₂	semidirect
2. C₂×C₂₃×#480	C₂	semidirect
3. C₂×C₂₃×#468	C₂	semidirect
5. C₂₃×#2057	C₂	semidirect
6. C₂₃×#2036	C₂	semidirect
7. C₂₃×#2023	C₂	semidirect
8. C₂₃×#2000	C₂	semidirect
9. C₂₃×#1880	C₂	semidirect
10. C₂₃×#1874	C₂	semidirect
11. C₂₃×#1873	C₂	semidirect
12. C₂₃×#1870	C₂	semidirect
13. C₂₃×#1863	C₂	semidirect
14. C₂₃×#1852	C₂	semidirect
15. C₂₃×#1736	C₂	semidirect
91. C₂₃×C₂²⋊Q₈	D₄	semidirect
114. C₂×C₄⋊C₄×C₂₃	D₄	semidirect
253. #25559	C₂₃	direct (N × H)
341. C₂×#554	C₂×C₂₃	semidirect
342. C₂×#480	C₂×C₂₃	semidirect
343. C₂×#468	C₂×C₂₃	semidirect
345. #2057	C₂×C₂₃	semidirect
346. #2036	C₂×C₂₃	semidirect
347. #2023	C₂×C₂₃	semidirect
348. #2000	C₂×C₂₃	semidirect
349. #1880	C₂×C₂₃	semidirect
350. #1874	C₂×C₂₃	semidirect
351. #1873	C₂×C₂₃	semidirect
352. #1870	C₂×C₂₃	semidirect
353. #1863	C₂×C₂₃	semidirect
354. #1852	C₂×C₂₃	semidirect
355. #1736	C₂×C₂₃	semidirect
484. C₂²⋊Q₈	D₄×C₂₃	semidirect
507. C₂×C₄⋊C₄	D₄×C₂₃	semidirect
541. C₂₃	#25559	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×#554	2
C₂×C₂₃×#480	2
C₂×C₂₃×#468	2
C₂₃×#2414	2
C₂₃×#2057	2
C₂₃×#2036	2
C₂₃×#2023	2
C₂₃×#2000	2
C₂₃×#1880	2
C₂₃×#1874	2
C₂₃×#1873	2
C₂₃×#1870	2
C₂₃×#1863	2
C₂₃×#1852	2
C₂₃×#1736	2
#25559	23

Subgroups — C23×#25559 #19173185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25559 #19173185