Subgroups — C₅×#63252 #13062821

Order 1360.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₂²⋊D₁₇	C₂	1	2	yes	maximal, complemented
3	C₅×D₆₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×D₁₇	C₂	1	2	yes	maximal, complemented
5	C₅×Dic₃₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₅×C₁₇	C₂²	1	1	yes	characteristic
7	C₂×C₅×D₁₇	C₂²	1	2	yes	—
8	C₄×C₅×C₁₇	C₂²	1	1	yes	characteristic
9	C₄×C₅×C₁₇	C₂²	1	1	yes	characteristic
10	C₅×Dic₁₇	C₂²	1	2	yes	—
11	#63252	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₅×C₁₇	—	2	1	no	—
13	C₂×C₅×C₁₇	C₂³	1	1	yes	characteristic
14	C₅×D₁₇	—	2	2	no	—
15	C₂×C₄×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented
16	C₂²⋊D₁₇	C₂×C₅	1	2	yes	complemented
17	D₆₈	C₂×C₅	1	1	yes	characteristic, complemented
18	C₄×D₁₇	C₂×C₅	1	2	yes	complemented
19	Dic₃₄	C₂×C₅	1	1	yes	characteristic, complemented
20	C₅×C₁₇	#41	1	1	yes	characteristic, complemented, Hall
21	C₅×#41	—	17	1	no	maximal, Hall
22	C₂²×C₁₇	C₂²×C₅	1	1	yes	characteristic
23	C₂×D₁₇	C₂²×C₅	1	2	yes	—
24	C₄×C₁₇	C₂²×C₅	1	1	yes	characteristic
25	C₄×C₁₇	C₂²×C₅	1	1	yes	characteristic
26	Dic₁₇	C₂²×C₅	1	2	yes	—
27	C₅×Q₈	—	17	1	no	—
28	C₅×D₄	—	17	2	no	—
29	C₅×D₄	—	17	1	no	—
30	C₂×C₄×C₅	—	17	2	no	—
31	C₂×C₄×C₅	D₁₇	1	1	yes	characteristic, complemented
32	C₂×C₁₇	—	2	1	no	—
33	C₂×C₁₇	C₂³×C₅	1	1	yes	characteristic
34	D₁₇	—	2	2	no	—
35	C₂²×C₅	—	17	2	no	—
36	C₂²×C₅	C₂×D₁₇	1	1	yes	characteristic
37	C₄×C₅	—	17	2	no	—
38	C₄×C₅	C₂×D₁₇	1	1	yes	characteristic
39	C₄×C₅	C₂×D₁₇	1	1	yes	characteristic
40	C₁₇	C₅×#41	1	1	yes	characteristic, complemented, Sylow
41	#41	—	17	1	no	Sylow
42	C₂×C₅	—	2	1	no	—
43	C₂×C₅	—	34	2	no	—
44	C₂×C₅	C₂²×D₁₇	1	1	yes	characteristic
45	Q₈	—	17	1	no	—
46	D₄	—	17	2	no	—
47	D₄	—	17	1	no	—
48	C₂×C₄	—	17	2	no	—
49	C₂×C₄	C₅×D₁₇	1	1	yes	characteristic, complemented
50	C₅	#63252	1	1	yes	characteristic, direct product factor, Sylow
51	C₂²	—	17	2	no	—
52	C₂²	C₂×C₅×D₁₇	1	1	yes	characteristic
53	C₄	—	17	2	no	—
54	C₄	C₂×C₅×D₁₇	1	1	yes	characteristic
55	C₄	C₂×C₅×D₁₇	1	1	yes	characteristic
56	C₂	—	2	1	no	—
57	C₂	—	34	2	no	—
58	C₂	C₂²×C₅×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	C₂×D₁₇
commutator, cosocle	C₂×C₁₇	C₂³×C₅
Frattini	C₂	C₂²×C₅×D₁₇
Fitting	C₂×C₄×C₅×C₁₇	C₂
socle	C₂×C₅×C₁₇	C₂³
hypercenter	C₂×C₄×C₅	D₁₇
hypocenter	C₁₇	C₅×#41
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄×C₅ ◁ C₂×C₄×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₅×C₁₇	C₂	semidirect
2. C₅×C₂²⋊D₁₇	C₂	semidirect
3. C₅×D₆₈	C₂	semidirect
4. C₄×C₅×D₁₇	C₂	semidirect
5. C₅×Dic₃₄	C₂	semidirect
11. #63252	C₅	direct (N × H)
15. C₂×C₄×C₁₇	C₂×C₅	semidirect
16. C₂²⋊D₁₇	C₂×C₅	semidirect
17. D₆₈	C₂×C₅	semidirect
18. C₄×D₁₇	C₂×C₅	semidirect
19. Dic₃₄	C₂×C₅	semidirect
20. C₅×C₁₇	#41	semidirect
31. C₂×C₄×C₅	D₁₇	semidirect
40. C₁₇	C₅×#41	semidirect
49. C₂×C₄	C₅×D₁₇	semidirect
50. C₅	#63252	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×C₁₇	2
C₅×C₂²⋊D₁₇	2
C₅×D₆₈	2
C₄×C₅×D₁₇	2
C₅×Dic₃₄	2
#63252	5
C₅×#41	17

Subgroups — C5×#63252 #13062821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#63252 #13062821