Subgroups — C₇×C₁₃×C₁₇×Dic₅ #44525859

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	C₄×C₇×C₁₃×C₁₇	—	5	1	no	maximal, Hall
4	C₁₃×C₁₇×Dic₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₁₃×C₁₇	D₅	1	1	yes	characteristic
6	C₇×C₁₇×Dic₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₁₃×C₁₇	C₂×C₇	1	1	yes	characteristic
8	C₇×C₁₃×Dic₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₁₃×C₁₇	Dic₅	1	1	yes	characteristic, direct product factor, 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	C₂×C₁₇	1	1	yes	characteristic
13	C₄×C₁₃×C₁₇	—	5	1	no	Hall
14	C₅×C₇×C₁₇	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
15	C₄×C₇×C₁₇	—	5	1	no	Hall
16	C₅×C₇×C₁₃	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₃×C₁₇	C₇×D₅	1	1	yes	characteristic
18	C₄×C₇×C₁₃	—	5	1	no	Hall
19	C₁₇×Dic₅	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
20	C₁₃×Dic₅	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₇×C₁₇	D₅×C₁₃	1	1	yes	characteristic
22	C₁₃×C₁₇	C₇×Dic₅	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₇×C₁₃	D₅×C₁₇	1	1	yes	characteristic
24	C₂×C₅×C₁₇	C₂×C₇×C₁₃	1	1	yes	characteristic
25	C₇×Dic₅	C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₅×C₁₃	C₂×C₇×C₁₇	1	1	yes	characteristic
27	C₇×C₁₇	C₁₃×Dic₅	1	1	yes	characteristic, direct product factor, Hall
28	C₇×C₁₃	C₁₇×Dic₅	1	1	yes	characteristic, direct product factor, Hall
29	C₅×C₁₇	C₄×C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₅×C₇	C₂×C₁₃×C₁₇	1	1	yes	characteristic
31	C₄×C₁₇	—	5	1	no	Hall
32	C₅×C₁₃	C₄×C₇×C₁₇	1	1	yes	characteristic, complemented, Hall
33	C₄×C₁₃	—	5	1	no	Hall
34	C₅×C₇	C₄×C₁₃×C₁₇	1	1	yes	characteristic, complemented, Hall
35	C₂×C₁₇	C₇×D₅×C₁₃	1	1	yes	characteristic
36	C₄×C₇	—	5	1	no	Hall
37	C₂×C₁₃	C₇×D₅×C₁₇	1	1	yes	characteristic
38	Dic₅	C₇×C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
39	C₁₇	C₇×C₁₃×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₇	D₅×C₁₃×C₁₇	1	1	yes	characteristic
41	C₁₃	C₇×C₁₇×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₅	C₂×C₇×C₁₃×C₁₇	1	1	yes	characteristic
43	C₇	C₁₃×C₁₇×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
44	C₅	C₄×C₇×C₁₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
45	C₄	—	5	1	no	Sylow
46	C₂	C₇×D₅×C₁₃×C₁₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₃×C₁₇	D₅
commutator, hypocenter	C₅	C₄×C₇×C₁₃×C₁₇
Frattini	C₂	C₇×D₅×C₁₃×C₁₇
Fitting, socle, prime radical	C₂×C₅×C₇×C₁₃×C₁₇	C₂
cosocle	C₂×C₅	C₂×C₇×C₁₃×C₁₇
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₇×C₁₃×C₁₇

Complements

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

N	H ≅ G/N	type
2. C₅×C₇×C₁₃×C₁₇	C₄	semidirect
4. C₁₃×C₁₇×Dic₅	C₇	direct (N × H)
6. C₇×C₁₇×Dic₅	C₁₃	direct (N × H)
8. C₇×C₁₃×Dic₅	C₁₇	direct (N × H)
9. C₇×C₁₃×C₁₇	Dic₅	direct (N × H)
11. C₅×C₁₃×C₁₇	C₄×C₇	semidirect
14. C₅×C₇×C₁₇	C₄×C₁₃	semidirect
16. C₅×C₇×C₁₃	C₄×C₁₇	semidirect
19. C₁₇×Dic₅	C₇×C₁₃	direct (N × H)
20. C₁₃×Dic₅	C₇×C₁₇	direct (N × H)
22. C₁₃×C₁₇	C₇×Dic₅	direct (N × H)
25. C₇×Dic₅	C₁₃×C₁₇	direct (N × H)
27. C₇×C₁₇	C₁₃×Dic₅	direct (N × H)
28. C₇×C₁₃	C₁₇×Dic₅	direct (N × H)
29. C₅×C₁₇	C₄×C₇×C₁₃	semidirect
32. C₅×C₁₃	C₄×C₇×C₁₇	semidirect
34. C₅×C₇	C₄×C₁₃×C₁₇	semidirect
38. Dic₅	C₇×C₁₃×C₁₇	direct (N × H)
39. C₁₇	C₇×C₁₃×Dic₅	direct (N × H)
41. C₁₃	C₇×C₁₇×Dic₅	direct (N × H)
43. C₇	C₁₃×C₁₇×Dic₅	direct (N × H)
44. C₅	C₄×C₇×C₁₃×C₁₇	semidirect

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
C₄×C₇×C₁₃×C₁₇	5
C₁₃×C₁₇×Dic₅	7
C₇×C₁₇×Dic₅	13
C₇×C₁₃×Dic₅	17

Subgroups — C7×C13×C17×Dic5 #44525859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₃×C₁₇×Dic₅ #44525859