Subgroups — #11760149

Order 1040.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₆₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₆₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×C₁₃	C₂²	1	1	yes	characteristic
5	C₂×D₆₅	—	2	1	no	—
6	C₂×D₆₅	—	2	1	no	—
7	C₂×D₆₅	C₄	1	2	yes	complemented
8	C₄×C₅×C₁₃	—	2	1	no	—
9	Dic₆₅	—	2	1	no	—
10	#6103	—	5	1	no	maximal, Hall
11	C₂×C₅×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₅×C₁₃	D₄	1	1	yes	characteristic
13	C₂×C₅×C₁₃	D₄	1	1	yes	characteristic
14	D₆₅	—	2	2	no	—
15	C₂²×D₁₃	—	5	1	no	—
16	C₂×C₄×C₁₃	D₅	1	1	yes	characteristic, complemented
17	C₂×Dic₁₃	—	5	1	no	—
18	#685	—	13	1	no	maximal, Hall
19	C₅×C₁₃	C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₁₃	C₂×D₅	1	1	yes	characteristic
21	C₂×D₁₃	—	5	2	no	—
22	C₂×D₁₃	—	10	1	no	—
23	C₂×D₁₃	—	10	1	no	—
24	C₄×C₁₃	—	2	1	no	—
25	Dic₁₃	—	10	1	no	—
26	C₂²×D₅	—	13	1	no	—
27	C₂×C₄×C₅	D₁₃	1	1	yes	characteristic, complemented
28	C₂×Dic₅	—	13	1	no	—
29	C₂×C₁₃	C₄×D₅	1	1	yes	characteristic
30	C₂×C₁₃	D₂₀	1	1	yes	characteristic
31	C₂×C₁₃	C₂²⋊D₅	1	1	yes	characteristic
32	D₁₃	—	10	2	no	—
33	C₂²×C₅	C₂×D₁₃	1	1	yes	characteristic
34	C₂×D₅	—	13	2	no	—
35	C₂×D₅	—	26	1	no	—
36	C₂×D₅	—	26	1	no	—
37	C₄×C₅	—	2	1	no	—
38	Dic₅	—	26	1	no	—
39	C₂²⋊C₄	—	65	1	no	Sylow
40	C₁₃	#685	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	C₄×D₁₃	1	1	yes	characteristic
42	C₂×C₅	D₅₂	1	1	yes	characteristic
43	C₂×C₅	C₂²⋊D₁₃	1	1	yes	characteristic
44	D₅	—	26	2	no	—
45	C₂³	—	65	1	no	—
46	C₂×C₄	—	65	1	no	—
47	C₂×C₄	D₆₅	1	1	yes	characteristic, complemented
48	C₅	#6103	1	1	yes	characteristic, complemented, Sylow
49	C₂²	—	65	2	no	—
50	C₂²	—	130	1	no	—
51	C₂²	—	130	1	no	—
52	C₂²	C₂×D₆₅	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	130	1	no	—
55	C₂	—	130	2	no	—
56	C₂	C₄×D₆₅	1	1	yes	characteristic
57	C₂	D₂₆₀	1	1	yes	characteristic
58	C₂	C₂²⋊D₆₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×D₆₅
commutator	C₂×C₅×C₁₃	C₂×C₄
Fitting	C₂×C₄×C₅×C₁₃	C₂
socle, cosocle	C₂²×C₅×C₁₃	C₂²
prime radical	C₂²×D₆₅	C₂
hypercenter	C₂×C₄	D₆₅
hypocenter	C₅×C₁₃	C₂²⋊C₄
LCS	G ▷ C₂×C₅×C₁₃ ▷ C₅×C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₅×C₁₃	C₂	semidirect
3. C₂×Dic₆₅	C₂	semidirect
7. C₂×D₆₅	C₄	semidirect
16. C₂×C₄×C₁₃	D₅	semidirect
19. C₅×C₁₃	C₂²⋊C₄	semidirect
27. C₂×C₄×C₅	D₁₃	semidirect
40. C₁₃	#685	semidirect
47. C₂×C₄	D₆₅	semidirect
48. C₅	#6103	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₆₅	2
C₂×C₄×C₅×C₁₃	2
C₂×Dic₆₅	2
#6103	5
#685	13