Subgroups — C₁₇×Dic₆₅⋊C₃ #27210473

Order 13260.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₇×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₇×Dic₆₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₁₇×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₇×Dic₁₃⋊C₃	—	5	1	no	maximal, Hall
5	C₂×C₅×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic
6	C₂×C₁₇×C₁₃⋊C₃	D₅	1	1	yes	characteristic
7	C₅×C₁₃×C₁₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₇×Dic₅	—	13	1	no	maximal, Hall
9	C₁₇×Dic₁₃	—	5	1	no	Hall
10	Dic₆₅⋊C₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₁₇×C₁₃⋊C₃	Dic₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×C₁₇	—	13	1	no	—
13	C₂×C₁₃×C₁₇	C₃×D₅	1	1	yes	characteristic
14	C₂×C₅×C₁₃⋊C₃	C₂×C₁₇	1	1	yes	characteristic
15	C₁₇×Dic₅	—	13	1	no	Hall
16	Dic₆₅	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅×C₁₇	—	13	1	no	Hall
18	C₁₃×C₁₇	C₃×Dic₅	1	1	yes	characteristic, complemented, Hall
19	C₃×C₄×C₁₇	—	65	1	no	Hall
20	C₅×C₁₃⋊C₃	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×C₁₇	D₁₃⋊C₃	1	1	yes	characteristic
22	Dic₁₃⋊C₃	—	5	1	no	Hall
23	C₂×C₅×C₁₃	C₂×C₃×C₁₇	1	1	yes	characteristic
24	C₂×C₃×C₁₇	—	13	1	no	—
25	C₅×C₁₇	Dic₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₃⋊C₃	D₅×C₁₇	1	1	yes	characteristic
27	C₄×C₁₇	—	65	1	no	Hall
28	C₅×C₁₃	C₃×C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
29	C₃×Dic₅	—	13	1	no	Hall
30	Dic₁₃	—	5	1	no	Hall
31	C₃×C₁₇	—	13	1	no	Hall
32	C₁₃⋊C₃	C₁₇×Dic₅	1	1	yes	characteristic, complemented, Hall
33	C₂×C₁₇	C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic
34	C₂×C₃×C₅	—	13	1	no	—
35	C₂×C₁₃	C₃×D₅×C₁₇	1	1	yes	characteristic
36	Dic₅	—	13	1	no	Hall
37	C₁₇	Dic₆₅⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
38	C₃×C₅	—	13	1	no	Hall
39	C₁₃	C₃×C₁₇×Dic₅	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	65	1	no	Hall
41	C₂×C₅	C₁₇×D₁₃⋊C₃	1	1	yes	characteristic
42	C₂×C₃	—	13	1	no	—
43	C₅	C₁₇×Dic₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	65	1	no	Sylow
45	C₃	—	13	1	no	Sylow
46	C₂	C₁₇×C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₇	C₅⋊(D₁₃⋊C₃)
commutator, hypocenter	C₅×C₁₃	C₃×C₄×C₁₇
Frattini	C₂	C₁₇×C₅⋊(D₁₃⋊C₃)
Fitting, socle	C₂×C₅×C₁₃×C₁₇	C₂×C₃
prime radical	C₂×C₅×C₁₇×C₁₃⋊C₃	C₂
cosocle	C₂×C₅×C₁₃	C₂×C₃×C₁₇
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
2. C₁₇×Dic₆₅	C₃	semidirect
3. C₅×C₁₇×C₁₃⋊C₃	C₄	semidirect
7. C₅×C₁₃×C₁₇	C₃×C₄	semidirect
10. Dic₆₅⋊C₃	C₁₇	direct (N × H)
11. C₁₇×C₁₃⋊C₃	Dic₅	semidirect
16. Dic₆₅	C₃×C₁₇	semidirect
18. C₁₃×C₁₇	C₃×Dic₅	semidirect
20. C₅×C₁₃⋊C₃	C₄×C₁₇	semidirect
25. C₅×C₁₇	Dic₁₃⋊C₃	semidirect
28. C₅×C₁₃	C₃×C₄×C₁₇	semidirect
32. C₁₃⋊C₃	C₁₇×Dic₅	semidirect
37. C₁₇	Dic₆₅⋊C₃	direct (N × H)
39. C₁₃	C₃×C₁₇×Dic₅	semidirect
43. C₅	C₁₇×Dic₁₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₁₇×C₁₃⋊C₃	2
C₁₇×Dic₆₅	3
C₁₇×Dic₁₃⋊C₃	5
C₃×C₁₇×Dic₅	13
Dic₆₅⋊C₃	17

Subgroups — C17×Dic65⋊C3 #27210473

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×Dic₆₅⋊C₃ #27210473