Subgroups — #11987107

Order 1280.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#1397	C₂	1	1	yes	maximal, characteristic
2	#10598078	C₂	1	2	yes	maximal
3	C₂×C₅×C₃₂	C₄	1	1	yes	characteristic
4	C₂×C₅×C₃₂	C₂²	1	1	yes	characteristic
5	C₄×C₅×C₁₆	C₄	1	1	yes	characteristic
6	#64663	C₄	1	4	yes	complemented
7	#7511	—	5	1	no	maximal, Sylow
8	C₂×C₅×C₁₆	C₈	1	1	yes	characteristic
9	C₂×C₅×C₁₆	C₂×C₄	1	1	yes	characteristic
10	C₄×C₅×C₈	C₈	1	1	yes	characteristic
11	C₅×C₃₂	C₈	1	2	yes	—
12	C₅×C₃₂	C₂×C₄	1	2	yes	—
13	M₁₂₈	—	5	2	no	—
14	#1397	D₅	1	1	yes	characteristic
15	C₂×C₅×C₈	C₁₆	1	1	yes	characteristic
16	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
17	C₄²×C₅	C₁₆	1	1	yes	characteristic
18	C₅×C₁₆	C₁₆	1	2	yes	—
19	C₅×C₁₆	C₄²	1	1	yes	characteristic
20	C₅×C₁₆	C₂×C₈	1	1	yes	characteristic
21	C₂×C₃₂	Dic₅	1	1	yes	characteristic
22	C₂×C₃₂	C₂×D₅	1	1	yes	characteristic
23	C₄×C₁₆	Dic₅	1	1	yes	characteristic
24	C₆₄	—	5	4	no	—
25	C₂×C₄×C₅	—	2	1	no	—
26	C₂×C₄×C₅	C₂×C₁₆	1	1	yes	characteristic
27	C₅×C₈	—	2	1	no	—
28	C₅×C₈	C₄×C₈	1	1	yes	characteristic
29	C₅×C₈	C₂×C₁₆	1	1	yes	characteristic
30	C₂×C₁₆	#168	1	1	yes	characteristic
31	C₂×C₁₆	C₂×Dic₅	1	1	yes	characteristic
32	C₄×C₈	#168	1	1	yes	characteristic
33	C₃₂	#168	1	2	yes	—
34	C₃₂	C₄×D₅	1	2	yes	—
35	C₂²×C₅	M₆₄	1	1	yes	characteristic
36	C₄×C₅	—	4	1	no	—
37	C₄×C₅	C₄×C₁₆	1	1	yes	characteristic
38	C₄×C₅	M₆₄	1	1	yes	characteristic
39	C₂×C₈	#672	1	1	yes	characteristic
40	C₂×C₈	C₂×#168	1	1	yes	characteristic
41	C₄²	#672	1	1	yes	characteristic
42	C₁₆	#672	1	2	yes	—
43	C₁₆	C₂×#168	1	1	yes	characteristic
44	C₁₆	C₄×Dic₅	1	1	yes	characteristic
45	C₂×C₅	—	2	1	no	—
46	C₂×C₅	#1397	1	1	yes	characteristic
47	C₂×C₄	—	2	1	no	—
48	C₂×C₄	C₂×#672	1	1	yes	characteristic
49	C₈	—	2	1	no	—
50	C₈	C₄×#168	1	1	yes	characteristic
51	C₈	C₂×#672	1	1	yes	characteristic
52	C₅	#7511	1	1	yes	characteristic, complemented, Sylow
53	C₂²	#64719	1	1	yes	characteristic
54	C₄	—	4	1	no	—
55	C₄	C₄×#672	1	1	yes	characteristic
56	C₄	#64719	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	#10597999	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₄×Dic₅
commutator	C₄×C₅	C₄×C₁₆
Frattini	C₂×C₃₂	C₂×D₅
Fitting	C₅×#1397	C₂
socle	C₂×C₅	#1397
prime radical	C₂²×C₅	M₆₄
cosocle	C₂×C₅×C₃₂	C₂²
hypercenter	#1397	D₅
hypocenter	C₅	#7511
LCS	G ▷ C₄×C₅ ▷ C₅
UCS	C₁ ◁ C₁₆ ◁ #1397

Complements

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

N	H ≅ G/N	type
6. #64663	C₄	semidirect
52. C₅	#7511	semidirect

Maximal subgroups

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

subgroup	index
C₅×#1397	2
#10598078	2
#7511	5