Subgroups — #11993079

Order 1280.

390 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₈²	C₂	1	1	yes	maximal, characteristic
2	#10600555	C₂	1	6	yes	maximal
3	C₂×C₄×C₅×C₈	C₂²	1	3	yes	—
4	#65224	C₂²	1	4	yes	—
5	C₅×C₈²	C₄	1	4	yes	complemented
6	#64771	—	2	12	no	—
7	#8817	—	5	1	no	maximal, Sylow
8	C₂²×C₅×C₈	D₄	1	6	yes	—
9	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
10	C₂×C₄⋊Dic₅	—	2	12	no	—
11	C₄×C₅×C₈	C₂×C₄	1	6	yes	—
12	C₄×C₅×C₈	Q₈	1	6	yes	—
13	#1834	—	5	6	no	—
14	C₂×C₈²	D₅	1	1	yes	characteristic
15	C₂²×C₄×C₅	C₂×D₄	1	3	yes	—
16	C₂²×Dic₅	—	4	4	no	—
17	C₂×C₅×C₈	—	2	12	no	—
18	C₂×C₅×C₈	C₄⋊C₄	1	12	yes	—
19	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
20	C₄²×C₅	C₂×Q₈	1	3	yes	—
21	C₄⋊Dic₅	—	4	24	no	—
22	C₂×C₄×C₈	C₂×D₅	1	3	yes	—
23	#384	—	5	4	no	—
24	#340	—	10	12	no	—
25	C₈²	Dic₅	1	4	yes	complemented
26	C₂³×C₅	#127	1	1	yes	characteristic
27	C₂×C₄×C₅	C₂×C₄⋊C₄	1	3	yes	—
28	C₂×C₄×C₅	C₄⋊Q₈	1	3	yes	—
29	C₂×C₄×C₅	#135	1	12	yes	—
30	C₂×Dic₅	—	8	12	no	—
31	C₅×C₈	—	2	12	no	—
32	C₂²×C₈	D₂₀	1	6	yes	—
33	C₂×C₄⋊C₄	—	10	12	no	—
34	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
35	C₄×C₈	Dic₁₀	1	6	yes	—
36	C₄×C₈	C₂×Dic₅	1	6	yes	—
37	C₂²×C₅	#384	1	1	yes	characteristic
38	C₂²×C₅	#495	1	6	yes	—
39	C₄×C₅	#427	1	6	yes	—
40	C₄×C₅	#499	1	6	yes	—
41	Dic₅	—	16	4	no	—
42	C₂²×C₄	—	20	4	no	—
43	C₂²×C₄	C₂×D₂₀	1	3	yes	—
44	C₂×C₈	—	2	12	no	—
45	C₂×C₈	C₄⋊Dic₅	1	12	yes	—
46	C₄⋊C₄	—	20	24	no	—
47	C₄²	C₂×Dic₁₀	1	3	yes	—
48	C₄²	C₂²×Dic₅	1	1	yes	characteristic
49	C₂×C₅	#1711	1	4	yes	—
50	C₂×C₅	#1846	1	3	yes	—
51	C₂³	#4020	1	1	yes	characteristic
52	C₂×C₄	—	40	12	no	—
53	C₂×C₄	#4015	1	3	yes	—
54	C₂×C₄	#4050	1	12	yes	—
55	C₂×C₄	C₂×C₄⋊Dic₅	1	3	yes	—
56	C₈	—	2	12	no	—
57	C₅	#8817	1	1	yes	characteristic, complemented, Sylow
58	C₂²	#64985	1	6	yes	—
59	C₂²	#65224	1	1	yes	characteristic
60	C₄	—	80	4	no	—
61	C₄	#64972	1	6	yes	—
62	C₄	#65395	1	6	yes	—
63	C₂	#10598854	1	4	yes	—
64	C₂	#10600559	1	3	yes	—

	subgroup	G/H
center	C₂³	#4020
commutator	C₄²×C₅	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅
Fitting	C₂×C₅×C₈²	C₂
socle, prime radical	C₂³×C₅	#127
cosocle	C₂×C₄²×C₅	C₂³
hypercenter	C₂×C₈²	D₅
hypocenter	C₅	#8817
LCS	G ▷ C₄²×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
5. C₅×C₈²	C₄	semidirect
25. C₈²	Dic₅	semidirect
57. C₅	#8817	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₈²	2
#10600555	2
#8817	5