Subgroups — C₂₃×#17595 #19165221

Order 5888.

1274 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1519	C₂	1	4	yes	maximal, complemented
5	C₂₃×#1514	C₂	1	4	yes	maximal, complemented
6	C₂₃×#1505	C₂	1	4	yes	maximal, complemented
7	C₂²×#41×C₂₃	—	2	1	no	—
8	C₂₃×#532	—	2	1	no	—
9	C₂₃×#532	—	2	1	no	—
10	C₂₃×#532	—	2	1	no	—
11	C₂₃×#532	—	2	1	no	—
12	C₂₃×#532	C₄	1	2	yes	complemented
13	C₂₃×#532	C₄	1	2	yes	complemented
14	C₂₃×#532	C₂²	1	2	yes	—
15	C₂₃×#532	C₂²	1	2	yes	—
16	C₂×C₂₃×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
17	C₂×C₂₃×#127	C₄	1	1	yes	characteristic, complemented
18	C₂×C₂₃×#124	—	2	1	no	—
19	C₂×C₂₃×#121	—	2	1	no	—
20	C₂×C₂₃×#121	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₂₃	—	2	1	no	—
22	C₂×C₄×D₄×C₂₃	C₄	1	2	yes	complemented
23	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
24	C₂₃×#432	—	2	1	no	—
25	C₂₃×#432	—	2	1	no	—
26	C₂₃×#432	C₂²	1	2	yes	complemented
27	C₂₃×#432	C₂²	1	2	yes	complemented
28	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
29	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₂×C₂₃×#97	—	2	1	no	—
31	C₂₃×#383	C₂²	1	2	yes	complemented
32	C₂₃×#382	—	2	1	no	—
33	C₂₃×#381	—	2	1	no	—
34	C₂₃×#380	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
36	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
37	C₂₃×#376	C₂²	1	2	yes	complemented
38	C₂₃×#327	C₂²	1	16	yes	complemented
39	C₂×#41×C₂₃	—	2	2	no	—
40	C₂×#41×C₂₃	—	2	2	no	—
41	C₂×#41×C₂₃	—	2	2	no	—
42	C₂×#41×C₂₃	—	2	2	no	—
43	C₂×#41×C₂₃	—	4	8	no	—
44	C₂²×Q₈×C₂₃	—	2	1	no	—
45	C₂²×D₄×C₂₃	—	2	2	no	—
46	C₂²×D₄×C₂₃	—	2	1	no	—
47	C₂²×D₄×C₂₃	—	2	1	no	—
48	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₂₃	—	2	2	no	—
50	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₂₃	—	2	2	no	—
54	C₂₃×C₄⋊Q₈	—	2	1	no	—
55	C₂₃×C₄⋊Q₈	—	2	1	no	—
56	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
57	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
58	C₂₃×#127	—	2	1	no	—
59	C₂₃×#127	—	2	1	no	—
60	C₂₃×#127	C₂×C₄	1	2	yes	—
61	C₂₃×#127	C₂×C₄	1	2	yes	—
62	C₂₃×#124	—	2	2	no	—
63	C₂₃×#124	—	2	2	no	—
64	C₂₃×#124	—	2	2	no	—
65	C₂₃×#124	—	2	2	no	—
66	C₂₃×#121	—	2	2	no	—
67	C₂₃×#121	—	2	2	no	—
68	C₂₃×#121	—	2	2	no	—
69	C₂₃×#121	—	2	2	no	—
70	C₂₃×#121	—	2	2	no	—
71	C₂₃×#121	—	2	2	no	—
72	C₂₃×#121	C₂×C₄	1	4	yes	—
73	C₂₃×#121	C₂³	1	4	yes	—
74	C₄×D₄×C₂₃	—	2	2	no	—
75	C₄×D₄×C₂₃	—	2	2	no	—
76	C₄×D₄×C₂₃	—	2	2	no	—
77	C₄×D₄×C₂₃	—	2	2	no	—
78	C₄×D₄×C₂₃	—	2	2	no	—
79	C₄×D₄×C₂₃	—	2	2	no	—
80	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
81	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
82	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
84	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
88	C₂×C₄²×C₂₃	—	2	2	no	—
89	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
101	C₂₃×C₄⋊C₈	—	2	2	no	—
102	C₂₃×C₄⋊C₈	—	2	2	no	—
103	C₂₃×C₂²⋊C₈	—	2	2	no	—
104	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
105	C₂₃×#97	—	2	2	no	—
106	C₂₃×#97	—	2	2	no	—
107	C₂₃×#95	—	2	2	no	—
108	C₂₃×#95	—	2	2	no	—
109	C₂₃×#95	—	2	2	no	—
110	C₂₃×#95	C₂³	1	4	yes	—
111	C₂⁴×C₂₃	—	2	2	no	—
112	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
113	#41×C₂₃	—	4	8	no	—
114	#41×C₂₃	—	4	8	no	—
115	#41×C₂₃	—	4	8	no	—
116	#41×C₂₃	—	4	8	no	—
117	C₂×Q₈×C₂₃	—	2	2	no	—
118	C₂×Q₈×C₂₃	—	2	2	no	—
119	C₂×Q₈×C₂₃	—	4	4	no	—
120	C₂×D₄×C₂₃	—	2	4	no	—
121	C₂×D₄×C₂₃	—	2	4	no	—
122	C₂×D₄×C₂₃	—	2	2	no	—
123	C₂×D₄×C₂₃	—	2	2	no	—
124	C₂×D₄×C₂₃	—	2	2	no	—
125	C₂×D₄×C₂₃	—	2	2	no	—
126	C₂×D₄×C₂₃	—	2	2	no	—
127	C₂×D₄×C₂₃	—	4	4	no	—
128	C₂×D₄×C₂₃	—	4	4	no	—
129	C₂×D₄×C₂₃	—	4	4	no	—
130	C₂×D₄×C₂₃	—	4	8	no	—
131	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
132	C₂²×C₄×C₂₃	—	2	4	no	—
133	C₂²×C₄×C₂₃	—	2	2	no	—
134	C₂²×C₄×C₂₃	—	2	4	no	—
135	C₂²×C₄×C₂₃	—	2	4	no	—
136	C₂²×C₄×C₂₃	—	2	4	no	—
137	C₂²×C₄×C₂₃	—	4	2	no	—
138	C₂²×C₄×C₂₃	—	4	2	no	—
139	C₂²×C₄×C₂₃	—	4	8	no	—
140	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
141	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
142	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
143	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
144	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
145	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
146	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
147	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
158	C₂×C₈×C₂₃	—	2	4	no	—
159	C₂×C₈×C₂₃	—	4	4	no	—
160	C₄⋊C₄×C₂₃	—	2	2	no	—
161	C₄⋊C₄×C₂₃	—	2	2	no	—
162	C₄⋊C₄×C₂₃	—	2	2	no	—
163	C₄⋊C₄×C₂₃	—	4	4	no	—
164	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
165	C₂²⋊C₄×C₂₃	—	2	4	no	—
166	C₂²⋊C₄×C₂₃	—	2	4	no	—
167	C₂²⋊C₄×C₂₃	—	2	4	no	—
168	C₂²⋊C₄×C₂₃	—	2	4	no	—
169	C₂²⋊C₄×C₂₃	—	4	4	no	—
170	C₄²×C₂₃	—	4	4	no	—
171	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
172	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
173	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
174	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
175	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
176	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
177	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
178	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
179	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
180	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
182	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
183	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
187	#17595	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂³×C₂₃	—	2	4	no	—
189	C₂³×C₂₃	—	4	1	no	—
190	C₂³×C₂₃	—	4	1	no	—
191	C₂³×C₂₃	—	4	4	no	—
192	C₂³×C₂₃	—	4	4	no	—
193	C₂³×C₂₃	—	4	4	no	—
194	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂³×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
197	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
198	Q₈×C₂₃	—	4	4	no	—
199	Q₈×C₂₃	—	4	4	no	—
200	D₄×C₂₃	—	4	4	no	—
201	D₄×C₂₃	—	4	4	no	—
202	D₄×C₂₃	—	4	4	no	—
203	D₄×C₂₃	—	4	4	no	—
204	D₄×C₂₃	—	4	8	no	—
205	D₄×C₂₃	—	4	8	no	—
206	D₄×C₂₃	—	4	4	no	—
207	D₄×C₂₃	—	4	4	no	—
208	C₂×C₄×C₂₃	—	2	2	no	—
209	C₂×C₄×C₂₃	—	2	2	no	—
210	C₂×C₄×C₂₃	—	2	2	no	—
211	C₂×C₄×C₂₃	—	2	2	no	—
212	C₂×C₄×C₂₃	—	2	2	no	—
213	C₂×C₄×C₂₃	—	2	2	no	—
214	C₂×C₄×C₂₃	—	2	2	no	—
215	C₂×C₄×C₂₃	—	2	2	no	—
216	C₂×C₄×C₂₃	—	2	2	no	—
217	C₂×C₄×C₂₃	—	2	2	no	—
218	C₂×C₄×C₂₃	—	2	2	no	—
219	C₂×C₄×C₂₃	—	2	2	no	—
220	C₂×C₄×C₂₃	—	2	4	no	—
221	C₂×C₄×C₂₃	—	4	1	no	—
222	C₂×C₄×C₂₃	—	4	1	no	—
223	C₂×C₄×C₂₃	—	4	1	no	—
224	C₂×C₄×C₂₃	—	4	1	no	—
225	C₂×C₄×C₂₃	—	4	1	no	—
226	C₂×C₄×C₂₃	—	4	1	no	—
227	C₂×C₄×C₂₃	—	4	8	no	—
228	C₂×C₄×C₂₃	—	4	8	no	—
229	C₂×C₄×C₂₃	—	4	4	no	—
230	C₂×C₄×C₂₃	—	4	4	no	—
231	C₂×C₄×C₂₃	—	4	4	no	—
232	C₂×C₄×C₂₃	—	4	4	no	—
233	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
245	C₈×C₂₃	—	4	4	no	—
246	C₂×#532	C₂×C₂₃	1	1	yes	characteristic
247	C₂×#432	C₂×C₂₃	1	1	yes	characteristic, complemented
248	#2283	C₂×C₂₃	1	1	yes	characteristic, complemented
249	#1519	C₂×C₂₃	1	4	yes	complemented
250	#1514	C₂×C₂₃	1	4	yes	complemented
251	#1505	C₂×C₂₃	1	4	yes	complemented
252	C₂²×C₂₃	—	2	1	no	—
253	C₂²×C₂₃	—	2	1	no	—
254	C₂²×C₂₃	—	2	1	no	—
255	C₂²×C₂₃	—	2	1	no	—
256	C₂²×C₂₃	—	2	1	no	—
257	C₂²×C₂₃	—	2	1	no	—
258	C₂²×C₂₃	—	4	4	no	—
259	C₂²×C₂₃	—	4	4	no	—
260	C₂²×C₂₃	—	4	4	no	—
261	C₂²×C₂₃	—	4	4	no	—
262	C₂²×C₂₃	—	8	8	no	—
263	C₂²×C₂₃	#418	1	2	yes	—
264	C₂²×C₂₃	#418	1	2	yes	—
265	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
266	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
267	C₄×C₂₃	—	2	1	no	—
268	C₄×C₂₃	—	2	1	no	—
269	C₄×C₂₃	—	2	1	no	—
270	C₄×C₂₃	—	2	1	no	—
271	C₄×C₂₃	—	2	1	no	—
272	C₄×C₂₃	—	2	1	no	—
273	C₄×C₂₃	—	2	1	no	—
274	C₄×C₂₃	—	2	1	no	—
275	C₄×C₂₃	—	2	1	no	—
276	C₄×C₂₃	—	2	1	no	—
277	C₄×C₂₃	—	4	4	no	—
278	C₄×C₂₃	—	8	4	no	—
279	C₄×C₂₃	#410	1	2	yes	—
280	C₄×C₂₃	#421	1	2	yes	—
281	C₂²×#41	—	2	1	no	—
282	#532	—	2	1	no	—
283	#532	—	2	1	no	—
284	#532	—	2	1	no	—
285	#532	—	2	1	no	—
286	#532	C₄×C₂₃	1	2	yes	complemented
287	#532	C₄×C₂₃	1	2	yes	complemented
288	#532	C₂²×C₂₃	1	2	yes	—
289	#532	C₂²×C₂₃	1	2	yes	—
290	C₂×C₄⋊Q₈	C₄×C₂₃	1	1	yes	characteristic, complemented
291	C₂×#127	C₄×C₂₃	1	1	yes	characteristic, complemented
292	C₂×#124	—	2	1	no	—
293	C₂×#121	—	2	1	no	—
294	C₂×#121	C₂²×C₂₃	1	2	yes	—
295	C₂×C₄×D₄	—	2	1	no	—
296	C₂×C₄×D₄	C₄×C₂₃	1	2	yes	complemented
297	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
298	#432	—	2	1	no	—
299	#432	—	2	1	no	—
300	#432	C₂²×C₂₃	1	2	yes	complemented
301	#432	C₂²×C₂₃	1	2	yes	complemented
302	C₂×C₄⋊C₈	—	2	1	no	—
303	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
304	C₂×#97	—	2	1	no	—
305	#383	C₂²×C₂₃	1	2	yes	complemented
306	#382	—	2	1	no	—
307	#381	—	2	1	no	—
308	#380	C₂²×C₂₃	1	2	yes	—
309	C₄×C₄⋊C₄	—	2	1	no	—
310	C₄×C₂²⋊C₄	—	2	1	no	—
311	#376	C₂²×C₂₃	1	2	yes	complemented
312	#327	C₂²×C₂₃	1	16	yes	complemented
313	C₂×C₂₃	—	2	2	no	—
314	C₂×C₂₃	—	2	2	no	—
315	C₂×C₂₃	—	2	2	no	—
316	C₂×C₂₃	—	8	4	no	—
317	C₂×C₂₃	C₂×#410	1	1	yes	characteristic
318	C₂×C₂₃	C₂×#418	1	1	yes	characteristic
319	C₂×C₂₃	C₂×#421	1	1	yes	characteristic
320	C₂×#41	—	2	2	no	—
321	C₂×#41	—	2	2	no	—
322	C₂×#41	—	2	2	no	—
323	C₂×#41	—	2	2	no	—
324	C₂×#41	—	4	8	no	—
325	C₂²×Q₈	—	2	1	no	—
326	C₂²×D₄	—	2	2	no	—
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
330	C₂³×C₄	—	2	2	no	—
331	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
332	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
333	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
334	C₂²×C₈	—	2	2	no	—
335	C₄⋊Q₈	—	2	1	no	—
336	C₄⋊Q₈	—	2	1	no	—
337	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
338	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
339	#127	—	2	1	no	—
340	#127	—	2	1	no	—
341	#127	C₂×C₄×C₂₃	1	2	yes	—
342	#127	C₂×C₄×C₂₃	1	2	yes	—
343	#124	—	2	2	no	—
344	#124	—	2	2	no	—
345	#124	—	2	2	no	—
346	#124	—	2	2	no	—
347	#121	—	2	2	no	—
348	#121	—	2	2	no	—
349	#121	—	2	2	no	—
350	#121	—	2	2	no	—
351	#121	—	2	2	no	—
352	#121	—	2	2	no	—
353	#121	C₂×C₄×C₂₃	1	4	yes	—
354	#121	C₂³×C₂₃	1	4	yes	—
355	C₄×D₄	—	2	2	no	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
362	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	2	no	—
365	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₄²	—	2	2	no	—
370	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
371	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
372	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
373	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
374	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
375	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
376	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
377	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
378	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
379	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
382	C₄⋊C₈	—	2	2	no	—
383	C₄⋊C₈	—	2	2	no	—
384	C₂²⋊C₈	—	2	2	no	—
385	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
386	#97	—	2	2	no	—
387	#97	—	2	2	no	—
388	#95	—	2	2	no	—
389	#95	—	2	2	no	—
390	#95	—	2	2	no	—
391	#95	C₂³×C₂₃	1	4	yes	—
392	C₂₃	#17595	1	1	yes	characteristic, direct product factor, Sylow
393	C₂⁴	—	2	2	no	—
394	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
395	#41	—	4	8	no	—
396	#41	—	4	8	no	—
397	#41	—	4	8	no	—
398	#41	—	4	8	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	4	4	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	—	4	4	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂×D₄	—	4	8	no	—
413	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	4	2	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	—	4	8	no	—
422	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
423	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
424	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
425	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
426	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
427	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
428	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
429	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
430	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
431	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
439	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
440	C₂×C₈	—	2	4	no	—
441	C₂×C₈	—	4	4	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	4	4	no	—
446	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	4	4	no	—
452	C₄²	—	4	4	no	—
453	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
454	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
455	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
456	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
457	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
458	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
459	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
460	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
461	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
462	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
463	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
464	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
465	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
466	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
467	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
468	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
469	C₂³	—	2	4	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	4	no	—
473	C₂³	—	4	4	no	—
474	C₂³	—	4	4	no	—
475	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
476	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
477	C₂³	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
478	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
479	Q₈	—	4	4	no	—
480	Q₈	—	4	4	no	—
481	D₄	—	4	4	no	—
482	D₄	—	4	4	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	4	no	—
485	D₄	—	4	8	no	—
486	D₄	—	4	8	no	—
487	D₄	—	4	4	no	—
488	D₄	—	4	4	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	8	no	—
509	C₂×C₄	—	4	8	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	—	4	4	no	—
513	C₂×C₄	—	4	4	no	—
514	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
515	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
516	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
517	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
518	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
519	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
520	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
521	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
522	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
523	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
524	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
525	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
526	C₈	—	4	4	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	4	4	no	—
534	C₂²	—	4	4	no	—
535	C₂²	—	4	4	no	—
536	C₂²	—	4	4	no	—
537	C₂²	—	8	8	no	—
538	C₂²	C₂₃×#418	1	2	yes	—
539	C₂²	C₂₃×#418	1	2	yes	—
540	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
541	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	4	4	no	—
553	C₄	—	8	4	no	—
554	C₄	C₂₃×#410	1	2	yes	—
555	C₄	C₂₃×#421	1	2	yes	—
556	C₂	—	2	2	no	—
557	C₂	—	2	2	no	—
558	C₂	—	2	2	no	—
559	C₂	—	8	4	no	—
560	C₂	C₂×C₂₃×#410	1	1	yes	characteristic
561	C₂	C₂×C₂₃×#418	1	1	yes	characteristic
562	C₂	C₂×C₂₃×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#432	C₂	semidirect
3. C₂₃×#2283	C₂	semidirect
4. C₂₃×#1519	C₂	semidirect
5. C₂₃×#1514	C₂	semidirect
6. C₂₃×#1505	C₂	semidirect
12. C₂₃×#532	C₄	semidirect
13. C₂₃×#532	C₄	semidirect
16. C₂×C₂₃×C₄⋊Q₈	C₄	semidirect
17. C₂×C₂₃×#127	C₄	semidirect
22. C₂×C₄×D₄×C₂₃	C₄	semidirect
26. C₂₃×#432	C₂²	semidirect
27. C₂₃×#432	C₂²	semidirect
31. C₂₃×#383	C₂²	semidirect
37. C₂₃×#376	C₂²	semidirect
38. C₂₃×#327	C₂²	semidirect
187. #17595	C₂₃	direct (N × H)
247. C₂×#432	C₂×C₂₃	semidirect
248. #2283	C₂×C₂₃	semidirect
249. #1519	C₂×C₂₃	semidirect
250. #1514	C₂×C₂₃	semidirect
251. #1505	C₂×C₂₃	semidirect
286. #532	C₄×C₂₃	semidirect
287. #532	C₄×C₂₃	semidirect
290. C₂×C₄⋊Q₈	C₄×C₂₃	semidirect
291. C₂×#127	C₄×C₂₃	semidirect
296. C₂×C₄×D₄	C₄×C₂₃	semidirect
300. #432	C₂²×C₂₃	semidirect
301. #432	C₂²×C₂₃	semidirect
305. #383	C₂²×C₂₃	semidirect
311. #376	C₂²×C₂₃	semidirect
312. #327	C₂²×C₂₃	semidirect
392. C₂₃	#17595	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×#532	2
C₂×C₂₃×#432	2
C₂₃×#2283	2
C₂₃×#1519	2
C₂₃×#1514	2
C₂₃×#1505	2
#17595	23

Subgroups — C23×#17595 #19165221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#17595 #19165221