Subgroups — C₂×C₃×C₅×#460 #14276066

Order 1920.

1168 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×SD₁₆	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#460	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₅×#102	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#460	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₅×D₄	—	2	1	no	—
10	C₂²×C₃×C₅×D₄	—	2	1	no	—
11	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
12	C₂×C₃×C₅×SD₁₆	—	2	8	no	—
13	C₂×C₃×C₅×SD₁₆	C₂²	1	8	yes	complemented
14	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
15	C₃×C₅×#127	—	2	2	no	—
16	C₃×C₅×#127	C₂²	1	4	yes	—
17	C₃×C₄×C₅×Q₈	—	2	2	no	—
18	C₃×C₄×C₅×Q₈	C₂²	1	4	yes	complemented
19	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄²×C₅	—	2	1	no	—
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
24	C₃×C₅×#102	C₂²	1	8	yes	complemented
25	C₂×C₃×#460	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂²×C₅×SD₁₆	C₂×C₃	1	2	yes	complemented
27	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic
28	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
29	C₅×#460	C₂×C₃	1	8	yes	direct product factor
30	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×C₅×#102	C₂×C₃	1	2	yes	complemented
32	C₂⁴×C₃×C₅	—	2	2	no	—
33	C₂×C₃×C₅×Q₈	—	2	1	no	—
34	C₂×C₃×C₅×Q₈	—	2	2	no	—
35	C₂×C₃×C₅×Q₈	D₄	1	4	yes	complemented
36	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
37	C₂×C₃×C₅×D₄	—	2	4	no	—
38	C₂×C₃×C₅×D₄	—	2	4	no	—
39	C₂×C₃×C₅×D₄	—	2	4	no	—
40	C₂×C₃×C₅×D₄	—	2	2	no	—
41	C₂×C₃×C₅×D₄	—	2	4	no	—
42	C₂×C₃×C₅×D₄	—	4	4	no	—
43	C₂×C₃×C₅×D₄	—	4	4	no	—
44	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
45	C₂²×C₃×C₄×C₅	—	2	1	no	—
46	C₂²×C₃×C₄×C₅	—	2	1	no	—
47	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₃×C₅×SD₁₆	—	2	16	no	—
51	C₂×C₃×C₅×C₈	—	2	4	no	—
52	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
53	C₃×C₅×C₄⋊C₄	—	2	4	no	—
54	C₃×C₅×C₄⋊C₄	—	2	1	no	—
55	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
56	C₃×C₄²×C₅	—	2	4	no	—
57	C₃×C₄²×C₅	D₄	1	2	yes	—
58	C₃×C₄²×C₅	C₂³	1	2	yes	—
59	C₂²×C₃×SD₁₆	C₂×C₅	1	2	yes	complemented
60	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic
61	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
62	C₃×#460	C₂×C₅	1	8	yes	direct product factor
63	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
64	C₂×C₃×#102	C₂×C₅	1	2	yes	complemented
65	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
66	C₂²×C₅×D₄	—	2	1	no	—
67	C₂²×C₅×D₄	—	2	1	no	—
68	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
69	C₂×C₅×SD₁₆	—	2	8	no	—
70	C₂×C₅×SD₁₆	C₂²×C₃	1	8	yes	complemented
71	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
72	C₅×#127	—	2	2	no	—
73	C₅×#127	C₂²×C₃	1	4	yes	—
74	C₄×C₅×Q₈	—	2	2	no	—
75	C₄×C₅×Q₈	C₂²×C₃	1	4	yes	complemented
76	C₂×C₅×C₄⋊C₄	—	2	1	no	—
77	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₄²×C₅	—	2	1	no	—
79	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
80	C₅×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
81	C₅×#102	C₂²×C₃	1	8	yes	complemented
82	C₂×#460	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
83	C₂³×C₃×C₅	—	2	4	no	—
84	C₂³×C₃×C₅	—	4	4	no	—
85	C₂³×C₃×C₅	—	4	4	no	—
86	C₂³×C₃×C₅	—	4	4	no	—
87	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
88	C₃×C₅×Q₈	—	2	4	no	—
89	C₃×C₅×Q₈	—	2	2	no	—
90	C₃×C₅×Q₈	C₂×D₄	1	4	yes	complemented
91	C₃×C₅×D₄	—	2	4	no	—
92	C₃×C₅×D₄	—	2	4	no	—
93	C₃×C₅×D₄	—	4	8	no	—
94	C₃×C₅×D₄	—	4	4	no	—
95	C₃×C₅×D₄	—	4	8	no	—
96	C₂×C₃×C₄×C₅	—	2	4	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	4	2	no	—
101	C₂×C₃×C₄×C₅	SD₁₆	1	4	yes	complemented
102	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
106	C₂×C₃×C₄×C₅	#41	1	2	yes	—
107	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
108	C₃×C₅×C₈	—	2	4	no	—
109	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
110	C₂²×C₃×D₄	—	2	1	no	—
111	C₂²×C₃×D₄	—	2	1	no	—
112	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
113	C₂×C₃×SD₁₆	—	2	8	no	—
114	C₂×C₃×SD₁₆	C₂²×C₅	1	8	yes	complemented
115	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
116	C₃×#127	—	2	2	no	—
117	C₃×#127	C₂²×C₅	1	4	yes	—
118	C₃×C₄×Q₈	—	2	2	no	—
119	C₃×C₄×Q₈	C₂²×C₅	1	4	yes	complemented
120	C₂×C₃×C₄⋊C₄	—	2	1	no	—
121	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
122	C₂×C₃×C₄²	—	2	1	no	—
123	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
124	C₃×C₄⋊C₈	C₂²×C₅	1	4	yes	complemented
125	C₃×#102	C₂²×C₅	1	8	yes	complemented
126	C₂⁴×C₅	—	2	2	no	—
127	C₂×C₅×Q₈	—	2	1	no	—
128	C₂×C₅×Q₈	—	2	2	no	—
129	C₂×C₅×Q₈	C₃×D₄	1	4	yes	complemented
130	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
131	C₂×C₅×D₄	—	2	4	no	—
132	C₂×C₅×D₄	—	2	2	no	—
133	C₂×C₅×D₄	—	2	4	no	—
134	C₂×C₅×D₄	—	2	4	no	—
135	C₂×C₅×D₄	—	2	4	no	—
136	C₂×C₅×D₄	—	4	4	no	—
137	C₂×C₅×D₄	—	4	4	no	—
138	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
144	C₅×SD₁₆	—	2	16	no	—
145	C₂×C₅×C₈	—	2	4	no	—
146	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
147	C₅×C₄⋊C₄	—	2	4	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
150	C₄²×C₅	—	2	4	no	—
151	C₄²×C₅	C₃×D₄	1	2	yes	—
152	C₄²×C₅	C₂³×C₃	1	2	yes	—
153	C₂²×SD₁₆	C₂×C₃×C₅	1	2	yes	complemented
154	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic
155	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
156	#460	C₂×C₃×C₅	1	8	yes	direct product factor
157	C₂×C₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
158	C₂×#102	C₂×C₃×C₅	1	2	yes	complemented
159	C₂²×C₃×C₅	—	4	4	no	—
160	C₂²×C₃×C₅	—	4	4	no	—
161	C₂²×C₃×C₅	—	4	4	no	—
162	C₂²×C₃×C₅	—	8	8	no	—
163	C₂²×C₃×C₅	#121	1	2	yes	—
164	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
165	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
166	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
167	C₃×C₄×C₅	—	2	4	no	—
168	C₃×C₄×C₅	—	2	2	no	—
169	C₃×C₄×C₅	—	4	2	no	—
170	C₃×C₄×C₅	#121	1	2	yes	—
171	C₃×C₄×C₅	C₂×SD₁₆	1	4	yes	complemented
172	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
173	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
174	C₂⁴×C₃	—	2	2	no	—
175	C₂×C₃×Q₈	—	2	1	no	—
176	C₂×C₃×Q₈	—	2	2	no	—
177	C₂×C₃×Q₈	C₅×D₄	1	4	yes	complemented
178	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
179	C₂×C₃×D₄	—	2	4	no	—
180	C₂×C₃×D₄	—	2	2	no	—
181	C₂×C₃×D₄	—	2	4	no	—
182	C₂×C₃×D₄	—	2	4	no	—
183	C₂×C₃×D₄	—	2	4	no	—
184	C₂×C₃×D₄	—	4	4	no	—
185	C₂×C₃×D₄	—	4	4	no	—
186	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
187	C₂²×C₃×C₄	—	2	1	no	—
188	C₂²×C₃×C₄	—	2	1	no	—
189	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
190	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
191	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
192	C₃×SD₁₆	—	2	16	no	—
193	C₂×C₃×C₈	—	2	4	no	—
194	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
195	C₃×C₄⋊C₄	—	2	4	no	—
196	C₃×C₄⋊C₄	—	2	1	no	—
197	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
198	C₃×C₄²	—	2	4	no	—
199	C₃×C₄²	C₅×D₄	1	2	yes	—
200	C₃×C₄²	C₂³×C₅	1	2	yes	—
201	C₂³×C₅	—	2	4	no	—
202	C₂³×C₅	—	4	4	no	—
203	C₂³×C₅	—	4	4	no	—
204	C₂³×C₅	—	4	4	no	—
205	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
206	C₅×Q₈	—	2	4	no	—
207	C₅×Q₈	—	2	2	no	—
208	C₅×Q₈	C₂×C₃×D₄	1	4	yes	complemented
209	C₅×D₄	—	2	4	no	—
210	C₅×D₄	—	2	4	no	—
211	C₅×D₄	—	4	8	no	—
212	C₅×D₄	—	4	4	no	—
213	C₅×D₄	—	4	8	no	—
214	C₂×C₄×C₅	—	2	4	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	4	2	no	—
219	C₂×C₄×C₅	C₃×SD₁₆	1	4	yes	complemented
220	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
221	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
223	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
224	C₂×C₄×C₅	C₃×#41	1	2	yes	—
225	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
226	C₅×C₈	—	2	4	no	—
227	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
228	C₂²×D₄	—	2	1	no	—
229	C₂²×D₄	—	2	1	no	—
230	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
231	C₂×SD₁₆	—	2	8	no	—
232	C₂×SD₁₆	C₂²×C₃×C₅	1	8	yes	complemented
233	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
234	#127	—	2	2	no	—
235	#127	C₂²×C₃×C₅	1	4	yes	—
236	C₄×Q₈	—	2	2	no	—
237	C₄×Q₈	C₂²×C₃×C₅	1	4	yes	complemented
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
240	C₂×C₄²	—	2	1	no	—
241	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
242	C₄⋊C₈	C₂²×C₃×C₅	1	4	yes	complemented
243	#102	C₂²×C₃×C₅	1	8	yes	complemented
244	C₂×C₃×C₅	—	8	4	no	—
245	C₂×C₃×C₅	#460	1	4	yes	direct product factor
246	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
247	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
248	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
249	C₂³×C₃	—	2	4	no	—
250	C₂³×C₃	—	4	4	no	—
251	C₂³×C₃	—	4	4	no	—
252	C₂³×C₃	—	4	4	no	—
253	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
254	C₃×Q₈	—	2	4	no	—
255	C₃×Q₈	—	2	2	no	—
256	C₃×Q₈	C₂×C₅×D₄	1	4	yes	complemented
257	C₃×D₄	—	2	4	no	—
258	C₃×D₄	—	2	4	no	—
259	C₃×D₄	—	4	8	no	—
260	C₃×D₄	—	4	4	no	—
261	C₃×D₄	—	4	8	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	4	2	no	—
267	C₂×C₃×C₄	C₅×SD₁₆	1	4	yes	complemented
268	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
269	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
271	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
272	C₂×C₃×C₄	C₅×#41	1	2	yes	—
273	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
274	C₃×C₈	—	2	4	no	—
275	C₂²×C₅	—	4	4	no	—
276	C₂²×C₅	—	4	4	no	—
277	C₂²×C₅	—	4	4	no	—
278	C₂²×C₅	—	8	8	no	—
279	C₂²×C₅	C₃×#121	1	2	yes	—
280	C₂²×C₅	C₂×C₃×SD₁₆	1	2	yes	—
281	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
282	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
283	C₄×C₅	—	2	2	no	—
284	C₄×C₅	—	2	4	no	—
285	C₄×C₅	—	4	2	no	—
286	C₄×C₅	C₃×#121	1	2	yes	—
287	C₄×C₅	C₂×C₃×SD₁₆	1	4	yes	complemented
288	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
289	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
290	C₂⁴	—	2	2	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	C₃×C₅×D₄	1	4	yes	complemented
294	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	4	4	no	—
301	C₂×D₄	—	4	4	no	—
302	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
306	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
307	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
308	SD₁₆	—	2	16	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
314	C₄²	—	2	4	no	—
315	C₄²	C₃×C₅×D₄	1	2	yes	—
316	C₄²	C₂³×C₃×C₅	1	2	yes	—
317	C₃×C₅	C₂×#460	1	1	yes	characteristic, direct product factor, Hall
318	C₂²×C₃	—	4	4	no	—
319	C₂²×C₃	—	4	4	no	—
320	C₂²×C₃	—	4	4	no	—
321	C₂²×C₃	—	8	8	no	—
322	C₂²×C₃	C₅×#121	1	2	yes	—
323	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
324	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
325	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
326	C₃×C₄	—	2	4	no	—
327	C₃×C₄	—	2	2	no	—
328	C₃×C₄	—	4	2	no	—
329	C₃×C₄	C₅×#121	1	2	yes	—
330	C₃×C₄	C₂×C₅×SD₁₆	1	4	yes	complemented
331	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
332	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
333	C₂×C₅	—	8	4	no	—
334	C₂×C₅	C₃×#460	1	4	yes	direct product factor
335	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
336	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
337	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
338	C₂³	—	2	4	no	—
339	C₂³	—	4	4	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	4	no	—
342	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
343	Q₈	—	2	4	no	—
344	Q₈	—	2	2	no	—
345	Q₈	C₂×C₃×C₅×D₄	1	4	yes	complemented
346	D₄	—	2	4	no	—
347	D₄	—	2	4	no	—
348	D₄	—	4	8	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	8	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	C₃×C₅×SD₁₆	1	4	yes	complemented
357	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
358	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
359	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
360	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
361	C₂×C₄	C₃×C₅×#41	1	2	yes	—
362	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
363	C₈	—	2	4	no	—
364	C₂×C₃	—	8	4	no	—
365	C₂×C₃	C₅×#460	1	4	yes	direct product factor
366	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
367	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
368	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
369	C₅	C₂×C₃×#460	1	1	yes	characteristic, direct product factor, Sylow
370	C₂²	—	4	4	no	—
371	C₂²	—	4	4	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	8	8	no	—
374	C₂²	C₃×C₅×#121	1	2	yes	—
375	C₂²	C₂×C₃×C₅×SD₁₆	1	2	yes	—
376	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
377	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
378	C₄	—	2	4	no	—
379	C₄	—	2	2	no	—
380	C₄	—	4	2	no	—
381	C₄	C₃×C₅×#121	1	2	yes	—
382	C₄	C₂×C₃×C₅×SD₁₆	1	4	yes	complemented
383	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
384	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
385	C₃	C₂×C₅×#460	1	1	yes	characteristic, direct product factor, Sylow
386	C₂	—	8	4	no	—
387	C₂	C₃×C₅×#460	1	4	yes	direct product factor
388	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
389	C₂	C₂²×C₃×C₅×SD₁₆	1	1	yes	characteristic
390	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×SD₁₆	C₂	semidirect
3. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
4. C₃×C₅×#460	C₂	direct (N × H)
5. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
6. C₂×C₃×C₅×#102	C₂	semidirect
7. C₂×C₅×#460	C₃	direct (N × H)
13. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
18. C₃×C₄×C₅×Q₈	C₂²	semidirect
23. C₃×C₅×C₄⋊C₈	C₂²	semidirect
24. C₃×C₅×#102	C₂²	semidirect
25. C₂×C₃×#460	C₅	direct (N × H)
26. C₂²×C₅×SD₁₆	C₂×C₃	semidirect
28. C₂×C₄×C₅×Q₈	C₂×C₃	semidirect
29. C₅×#460	C₂×C₃	direct (N × H)
30. C₂×C₅×C₄⋊C₈	C₂×C₃	semidirect
31. C₂×C₅×#102	C₂×C₃	semidirect
35. C₂×C₃×C₅×Q₈	D₄	semidirect
59. C₂²×C₃×SD₁₆	C₂×C₅	semidirect
61. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
62. C₃×#460	C₂×C₅	direct (N × H)
63. C₂×C₃×C₄⋊C₈	C₂×C₅	semidirect
64. C₂×C₃×#102	C₂×C₅	semidirect
70. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
75. C₄×C₅×Q₈	C₂²×C₃	semidirect
80. C₅×C₄⋊C₈	C₂²×C₃	semidirect
81. C₅×#102	C₂²×C₃	semidirect
82. C₂×#460	C₃×C₅	direct (N × H)
90. C₃×C₅×Q₈	C₂×D₄	semidirect
101. C₂×C₃×C₄×C₅	SD₁₆	semidirect
114. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
119. C₃×C₄×Q₈	C₂²×C₅	semidirect
124. C₃×C₄⋊C₈	C₂²×C₅	semidirect
125. C₃×#102	C₂²×C₅	semidirect
129. C₂×C₅×Q₈	C₃×D₄	semidirect
153. C₂²×SD₁₆	C₂×C₃×C₅	semidirect
155. C₂×C₄×Q₈	C₂×C₃×C₅	semidirect
156. #460	C₂×C₃×C₅	direct (N × H)
157. C₂×C₄⋊C₈	C₂×C₃×C₅	semidirect
158. C₂×#102	C₂×C₃×C₅	semidirect
171. C₃×C₄×C₅	C₂×SD₁₆	semidirect
177. C₂×C₃×Q₈	C₅×D₄	semidirect
208. C₅×Q₈	C₂×C₃×D₄	semidirect
219. C₂×C₄×C₅	C₃×SD₁₆	semidirect
232. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
237. C₄×Q₈	C₂²×C₃×C₅	semidirect
242. C₄⋊C₈	C₂²×C₃×C₅	semidirect
243. #102	C₂²×C₃×C₅	semidirect
245. C₂×C₃×C₅	#460	direct (N × H)
256. C₃×Q₈	C₂×C₅×D₄	semidirect
267. C₂×C₃×C₄	C₅×SD₁₆	semidirect
287. C₄×C₅	C₂×C₃×SD₁₆	semidirect
293. C₂×Q₈	C₃×C₅×D₄	semidirect
317. C₃×C₅	C₂×#460	direct (N × H)
330. C₃×C₄	C₂×C₅×SD₁₆	semidirect
334. C₂×C₅	C₃×#460	direct (N × H)
345. Q₈	C₂×C₃×C₅×D₄	semidirect
356. C₂×C₄	C₃×C₅×SD₁₆	semidirect
365. C₂×C₃	C₅×#460	direct (N × H)
369. C₅	C₂×C₃×#460	direct (N × H)
382. C₄	C₂×C₃×C₅×SD₁₆	semidirect
385. C₃	C₂×C₅×#460	direct (N × H)
387. C₂	C₃×C₅×#460	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₅×SD₁₆	2
C₂×C₃×C₅×#127	2
C₂×C₃×C₄×C₅×Q₈	2
C₃×C₅×#460	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₃×C₅×#102	2
C₂×C₅×#460	3
C₂×C₃×#460	5

Subgroups — C2×C3×C5×#460 #14276066

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#460 #14276066