Subgroups — #11987104

Order 1280.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₆₄	C₂	1	1	yes	maximal, characteristic
2	Dic₅×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂×#64663	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×C₃₂	C₂²	1	1	yes	characteristic
5	C₁₆×Dic₅	C₄	1	1	yes	characteristic
6	C₂×#3926	C₄	1	1	yes	characteristic
7	C₅×C₆₄	C₄	1	2	yes	complemented
8	#64663	C₄	1	2	yes	complemented
9	#7510	—	5	1	no	maximal, Sylow
10	C₂×C₅×C₁₆	C₂×C₄	1	1	yes	characteristic
11	C₈×Dic₅	C₈	1	1	yes	characteristic
12	C₂×#672	C₈	1	1	yes	characteristic
13	C₅×C₃₂	C₂×C₄	1	1	yes	characteristic
14	C₅×C₃₂	C₂×C₄	1	1	yes	characteristic
15	#3926	C₈	1	2	yes	—
16	C₂×C₆₄	—	5	1	no	—
17	C₂×C₆₄	D₅	1	1	yes	characteristic
18	C₄×C₃₂	—	5	1	no	—
19	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
20	C₄×Dic₅	C₁₆	1	1	yes	characteristic
21	C₂×#168	C₁₆	1	1	yes	characteristic
22	C₅×C₁₆	C₄²	1	1	yes	characteristic
23	C₅×C₁₆	C₂×C₈	1	1	yes	characteristic
24	#672	C₁₆	1	2	yes	—
25	C₂×C₃₂	—	5	1	no	—
26	C₂×C₃₂	C₂×D₅	1	1	yes	characteristic
27	C₄×C₁₆	—	5	1	no	—
28	C₆₄	—	5	2	no	—
29	C₆₄	Dic₅	1	2	yes	complemented
30	C₂×C₄×C₅	C₂×C₁₆	1	1	yes	characteristic
31	C₂×Dic₅	C₃₂	1	2	yes	—
32	C₅×C₈	C₄×C₈	1	1	yes	characteristic
33	C₅×C₈	C₂×C₁₆	1	1	yes	characteristic
34	#168	C₃₂	1	2	yes	—
35	C₂×C₁₆	—	5	1	no	—
36	C₂×C₁₆	C₄×D₅	1	1	yes	characteristic
37	C₄×C₈	—	5	1	no	—
38	C₃₂	—	5	2	no	—
39	C₃₂	C₄×D₅	1	1	yes	characteristic
40	C₃₂	C₂×Dic₅	1	1	yes	characteristic
41	C₂²×C₅	C₂×C₃₂	1	1	yes	characteristic
42	C₄×C₅	C₄×C₁₆	1	1	yes	characteristic
43	C₄×C₅	C₂×C₃₂	1	1	yes	characteristic
44	Dic₅	—	2	2	no	—
45	C₂×C₈	—	5	1	no	—
46	C₂×C₈	C₈×D₅	1	1	yes	characteristic
47	C₄²	—	5	1	no	—
48	C₁₆	—	5	2	no	—
49	C₁₆	C₈×D₅	1	1	yes	characteristic
50	C₁₆	C₄×Dic₅	1	1	yes	characteristic
51	C₂×C₅	C₄×C₃₂	1	1	yes	characteristic
52	C₂×C₅	M₁₂₈	1	2	yes	—
53	C₂×C₄	—	5	2	no	—
54	C₂×C₄	D₅×C₁₆	1	1	yes	characteristic
55	C₈	—	5	2	no	—
56	C₈	D₅×C₁₆	1	1	yes	characteristic
57	C₈	C₈×Dic₅	1	1	yes	characteristic
58	C₅	#7510	1	1	yes	characteristic, complemented, Sylow
59	C₂²	D₅×C₃₂	1	1	yes	characteristic
60	C₄	—	10	2	no	—
61	C₄	D₅×C₃₂	1	1	yes	characteristic
62	C₄	C₁₆×Dic₅	1	1	yes	characteristic
63	C₂	#10597923	1	2	yes	—
64	C₂	Dic₅×C₃₂	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₃₂	C₂×D₅
commutator	C₂×C₅	C₄×C₃₂
Fitting	C₂×C₅×C₆₄	C₂
socle, prime radical	C₂²×C₅	C₂×C₃₂
cosocle	C₂×C₅×C₃₂	C₂²
hypercenter	C₂×C₆₄	D₅
hypocenter	C₅	#7510
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
7. C₅×C₆₄	C₄	semidirect
8. #64663	C₄	semidirect
29. C₆₄	Dic₅	semidirect
58. C₅	#7510	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₆₄	2
Dic₅×C₃₂	2
C₂×#64663	2
#7510	5