Subgroups — C₅×C₇×C₁₃×Dic₁₇ #44525852

Order 30940.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×C₁₃×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×C₁₃×Dic₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₃×Dic₁₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₁₃×C₁₇	C₂×C₅	1	1	yes	characteristic
6	C₅×C₇×Dic₁₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₁₃×C₁₇	C₂×C₇	1	1	yes	characteristic
8	C₄×C₅×C₇×C₁₃	—	17	1	no	maximal, Hall
9	C₇×C₁₃×C₁₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₇×C₁₇	C₂×C₁₃	1	1	yes	characteristic
11	C₅×C₁₃×C₁₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×C₇×C₁₃	D₁₇	1	1	yes	characteristic
13	C₁₃×Dic₁₇	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
14	C₅×C₇×C₁₇	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
15	C₇×Dic₁₇	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
16	C₅×C₇×C₁₃	Dic₁₇	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₁₃×C₁₇	C₂×C₅×C₇	1	1	yes	characteristic
18	C₄×C₇×C₁₃	—	17	1	no	Hall
19	C₅×Dic₁₇	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
20	C₄×C₅×C₁₃	—	17	1	no	Hall
21	C₂×C₇×C₁₇	C₂×C₅×C₁₃	1	1	yes	characteristic
22	C₁₃×C₁₇	C₄×C₅×C₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇×C₁₃	C₅×D₁₇	1	1	yes	characteristic
24	C₂×C₅×C₁₇	C₂×C₇×C₁₃	1	1	yes	characteristic
25	C₄×C₅×C₇	—	17	1	no	Hall
26	C₂×C₅×C₁₃	C₇×D₁₇	1	1	yes	characteristic
27	C₇×C₁₇	C₄×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
28	C₇×C₁₃	C₅×Dic₁₇	1	1	yes	characteristic, direct product factor, Hall
29	C₅×C₁₇	C₄×C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₅×C₇	C₁₃×D₁₇	1	1	yes	characteristic
31	Dic₁₇	C₅×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
32	C₅×C₁₃	C₇×Dic₁₇	1	1	yes	characteristic, direct product factor, Hall
33	C₄×C₁₃	—	17	1	no	Hall
34	C₅×C₇	C₁₃×Dic₁₇	1	1	yes	characteristic, direct product factor, Hall
35	C₂×C₁₇	C₂×C₅×C₇×C₁₃	1	1	yes	characteristic
36	C₄×C₇	—	17	1	no	Hall
37	C₂×C₁₃	C₅×C₇×D₁₇	1	1	yes	characteristic
38	C₄×C₅	—	17	1	no	Hall
39	C₁₇	C₄×C₅×C₇×C₁₃	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₇	C₅×C₁₃×D₁₇	1	1	yes	characteristic
41	C₁₃	C₅×C₇×Dic₁₇	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₅	C₇×C₁₃×D₁₇	1	1	yes	characteristic
43	C₇	C₅×C₁₃×Dic₁₇	1	1	yes	characteristic, direct product factor, Sylow
44	C₅	C₇×C₁₃×Dic₁₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₄	—	17	1	no	Sylow
46	C₂	C₅×C₇×C₁₃×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇×C₁₃	D₁₇
commutator, hypocenter	C₁₇	C₄×C₅×C₇×C₁₃
Frattini	C₂	C₅×C₇×C₁₃×D₁₇
Fitting, socle, prime radical	C₂×C₅×C₇×C₁₃×C₁₇	C₂
cosocle	C₂×C₁₇	C₂×C₅×C₇×C₁₃
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₅×C₇×C₁₃

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×C₁₃×Dic₁₇	C₅	direct (N × H)
4. C₅×C₁₃×Dic₁₇	C₇	direct (N × H)
6. C₅×C₇×Dic₁₇	C₁₃	direct (N × H)
9. C₇×C₁₃×C₁₇	C₄×C₅	semidirect
11. C₅×C₁₃×C₁₇	C₄×C₇	semidirect
13. C₁₃×Dic₁₇	C₅×C₇	direct (N × H)
14. C₅×C₇×C₁₇	C₄×C₁₃	semidirect
15. C₇×Dic₁₇	C₅×C₁₃	direct (N × H)
16. C₅×C₇×C₁₃	Dic₁₇	direct (N × H)
19. C₅×Dic₁₇	C₇×C₁₃	direct (N × H)
22. C₁₃×C₁₇	C₄×C₅×C₇	semidirect
27. C₇×C₁₇	C₄×C₅×C₁₃	semidirect
28. C₇×C₁₃	C₅×Dic₁₇	direct (N × H)
29. C₅×C₁₇	C₄×C₇×C₁₃	semidirect
31. Dic₁₇	C₅×C₇×C₁₃	direct (N × H)
32. C₅×C₁₃	C₇×Dic₁₇	direct (N × H)
34. C₅×C₇	C₁₃×Dic₁₇	direct (N × H)
39. C₁₇	C₄×C₅×C₇×C₁₃	semidirect
41. C₁₃	C₅×C₇×Dic₁₇	direct (N × H)
43. C₇	C₅×C₁₃×Dic₁₇	direct (N × H)
44. C₅	C₇×C₁₃×Dic₁₇	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×C₅×C₇×C₁₃×C₁₇	2
C₇×C₁₃×Dic₁₇	5
C₅×C₁₃×Dic₁₇	7
C₅×C₇×Dic₁₇	13
C₄×C₅×C₇×C₁₃	17

Subgroups — C5×C7×C13×Dic17 #44525852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×C₁₃×Dic₁₇ #44525852