Subgroups — C₅×C₇×C₁₇×#261 #44525869

Order 30940.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₇×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×C₁₃×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×C₁₇×#261	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₇×#261	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₇×D₁₃	C₂×C₅	1	1	yes	characteristic
6	C₄×C₅×C₇×C₁₇	—	13	1	no	maximal, Hall
7	C₅×C₁₇×D₁₃	C₂×C₇	1	1	yes	characteristic
8	C₅×C₇×#261	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₁₃×C₁₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₇×C₁₇	—	13	1	no	—
11	C₅×C₁₃×C₁₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₅×C₇×D₁₃	C₂×C₁₇	1	1	yes	characteristic
13	C₁₇×#261	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
14	C₅×C₇×C₁₇	#261	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₇×C₁₇	—	13	1	no	Hall
16	C₅×C₇×C₁₃	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
17	C₁₇×D₁₃	C₂×C₅×C₇	1	1	yes	characteristic
18	C₇×#261	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
19	C₄×C₅×C₁₇	—	13	1	no	Hall
20	C₅×#261	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₇×C₁₇	—	13	1	no	—
22	C₁₃×C₁₇	C₄×C₅×C₇	1	1	yes	characteristic, complemented, Hall
23	C₇×D₁₃	C₂×C₅×C₁₇	1	1	yes	characteristic
24	C₂×C₅×C₁₇	—	13	1	no	—
25	C₄×C₅×C₇	—	13	1	no	Hall
26	C₅×D₁₃	C₂×C₇×C₁₇	1	1	yes	characteristic
27	C₇×C₁₇	C₅×#261	1	1	yes	characteristic, direct product factor, Hall
28	C₇×C₁₃	C₄×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
29	C₅×C₁₇	C₇×#261	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₅×C₇	—	13	1	no	—
31	C₄×C₁₇	—	13	1	no	Hall
32	C₅×C₁₃	C₄×C₇×C₁₇	1	1	yes	characteristic, complemented, Hall
33	#261	C₅×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
34	C₅×C₇	C₁₇×#261	1	1	yes	characteristic, direct product factor, Hall
35	C₂×C₁₇	—	13	1	no	—
36	C₄×C₇	—	13	1	no	Hall
37	D₁₃	C₂×C₅×C₇×C₁₇	1	1	yes	characteristic
38	C₄×C₅	—	13	1	no	Hall
39	C₁₇	C₅×C₇×#261	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₇	—	13	1	no	—
41	C₁₃	C₄×C₅×C₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₅	—	13	1	no	—
43	C₇	C₅×C₁₇×#261	1	1	yes	characteristic, direct product factor, Sylow
44	C₅	C₇×C₁₇×#261	1	1	yes	characteristic, direct product factor, Sylow
45	C₄	—	13	1	no	Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₇×C₁₇	#261
commutator, hypocenter	C₁₃	C₄×C₅×C₇×C₁₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃×C₁₇	C₄
prime radical	C₅×C₇×C₁₇×D₁₃	C₂
cosocle	D₁₃	C₂×C₅×C₇×C₁₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₅×C₇×C₁₇

Complements

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

N	H ≅ G/N	type
2. C₅×C₇×C₁₃×C₁₇	C₄	semidirect
3. C₇×C₁₇×#261	C₅	direct (N × H)
4. C₅×C₁₇×#261	C₇	direct (N × H)
8. C₅×C₇×#261	C₁₇	direct (N × H)
9. C₇×C₁₃×C₁₇	C₄×C₅	semidirect
11. C₅×C₁₃×C₁₇	C₄×C₇	semidirect
13. C₁₇×#261	C₅×C₇	direct (N × H)
14. C₅×C₇×C₁₇	#261	direct (N × H)
16. C₅×C₇×C₁₃	C₄×C₁₇	semidirect
18. C₇×#261	C₅×C₁₇	direct (N × H)
20. C₅×#261	C₇×C₁₇	direct (N × H)
22. C₁₃×C₁₇	C₄×C₅×C₇	semidirect
27. C₇×C₁₇	C₅×#261	direct (N × H)
28. C₇×C₁₃	C₄×C₅×C₁₇	semidirect
29. C₅×C₁₇	C₇×#261	direct (N × H)
32. C₅×C₁₃	C₄×C₇×C₁₇	semidirect
33. #261	C₅×C₇×C₁₇	direct (N × H)
34. C₅×C₇	C₁₇×#261	direct (N × H)
39. C₁₇	C₅×C₇×#261	direct (N × H)
41. C₁₃	C₄×C₅×C₇×C₁₇	semidirect
43. C₇	C₅×C₁₇×#261	direct (N × H)
44. C₅	C₇×C₁₇×#261	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₇×C₁₇×D₁₃	2
C₇×C₁₇×#261	5
C₅×C₁₇×#261	7
C₄×C₅×C₇×C₁₇	13
C₅×C₇×#261	17

Subgroups — C5×C7×C17×#261 #44525869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×C₁₇×#261 #44525869