Subgroups — C₅×C₁₇×C₃⋊#261 #27210555

Order 13260.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₇×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇×#261	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₃×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₇×C₃⋊#261	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₇×D₁₃	D₃	1	1	yes	characteristic
6	C₃×C₁₇×D₁₃	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₃×C₁₇	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₅×Dic₃×C₁₇	—	13	1	no	maximal, Hall
9	C₁₇×#261	—	3	1	no	Hall
10	C₅×C₃⋊#261	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₁₃×C₁₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×C₁₇	—	13	1	no	—
13	C₁₇×D₁₃	C₅×D₃	1	1	yes	characteristic
14	C₃×C₅×D₁₃	C₂×C₁₇	1	1	yes	characteristic
15	C₄×C₅×C₁₇	—	39	1	no	Hall
16	C₅×#261	—	3	1	no	Hall
17	C₃×C₅×C₁₇	#261	1	1	yes	characteristic, complemented, Hall
18	C₁₃×C₁₇	C₅×Dic₃	1	1	yes	characteristic, complemented, Hall
19	Dic₃×C₁₇	—	13	1	no	Hall
20	C₃×C₅×C₁₃	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×C₁₇	—	13	1	no	—
22	C₃⋊#261	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
23	C₅×D₁₃	D₃×C₁₇	1	1	yes	characteristic
24	C₂×C₃×C₁₇	—	13	1	no	—
25	C₅×C₁₇	C₃⋊#261	1	1	yes	characteristic, direct product factor, Hall
26	C₃×D₁₃	C₂×C₅×C₁₇	1	1	yes	characteristic
27	C₄×C₁₇	—	39	1	no	Hall
28	C₅×C₁₃	Dic₃×C₁₇	1	1	yes	characteristic, complemented, Hall
29	C₅×Dic₃	—	13	1	no	Hall
30	#261	—	3	1	no	Hall
31	C₃×C₁₇	C₅×#261	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₃	C₄×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
33	C₂×C₁₇	—	13	1	no	—
34	C₂×C₃×C₅	—	13	1	no	—
35	D₁₃	C₅×D₃×C₁₇	1	1	yes	characteristic
36	C₄×C₅	—	39	1	no	Hall
37	C₁₇	C₅×C₃⋊#261	1	1	yes	characteristic, direct product factor, Sylow
38	C₃×C₅	C₁₇×#261	1	1	yes	characteristic, complemented, Hall
39	C₁₃	C₅×Dic₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
40	Dic₃	—	13	1	no	Hall
41	C₂×C₅	—	13	1	no	—
42	C₂×C₃	—	13	1	no	—
43	C₅	C₁₇×C₃⋊#261	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	39	1	no	Sylow
45	C₃	C₅×C₁₇×#261	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₁₇	C₃⋊#261
commutator, hypocenter	C₃×C₁₃	C₄×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₁₇	C₄
prime radical	C₃×C₅×C₁₇×D₁₃	C₂
cosocle	C₃×D₁₃	C₂×C₅×C₁₇
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₅×C₁₇

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₃×C₁₇	C₄	semidirect
4. C₁₇×C₃⋊#261	C₅	direct (N × H)
7. C₅×C₁₃×C₁₇	Dic₃	semidirect
10. C₅×C₃⋊#261	C₁₇	direct (N × H)
11. C₃×C₁₃×C₁₇	C₄×C₅	semidirect
17. C₃×C₅×C₁₇	#261	semidirect
18. C₁₃×C₁₇	C₅×Dic₃	semidirect
20. C₃×C₅×C₁₃	C₄×C₁₇	semidirect
22. C₃⋊#261	C₅×C₁₇	direct (N × H)
25. C₅×C₁₇	C₃⋊#261	direct (N × H)
28. C₅×C₁₃	Dic₃×C₁₇	semidirect
31. C₃×C₁₇	C₅×#261	semidirect
32. C₃×C₁₃	C₄×C₅×C₁₇	semidirect
37. C₁₇	C₅×C₃⋊#261	direct (N × H)
38. C₃×C₅	C₁₇×#261	semidirect
39. C₁₃	C₅×Dic₃×C₁₇	semidirect
43. C₅	C₁₇×C₃⋊#261	direct (N × H)
45. C₃	C₅×C₁₇×#261	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₇×D₁₃	2
C₅×C₁₇×#261	3
C₁₇×C₃⋊#261	5
C₅×Dic₃×C₁₇	13
C₅×C₃⋊#261	17

Subgroups — C5×C17×C3⋊#261 #27210555

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₇×C₃⋊#261 #27210555