Subgroups — C₇×C₁₇×#63118 #44525921

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	—	5	1	no	maximal, Hall
4	C₁₇×#63118	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₇×D₁₃	D₅	1	1	yes	characteristic
6	C₇×C₁₇×Dic₅	—	13	1	no	maximal, Hall
7	C₅×C₁₇×D₁₃	C₂×C₇	1	1	yes	characteristic
8	C₇×#63118	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₁₃×C₁₇	Dic₅	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	—	5	1	no	Hall
14	C₅×C₇×C₁₇	#261	1	1	yes	characteristic, complemented, Hall
15	C₄×C₇×C₁₇	—	65	1	no	Hall
16	C₅×C₇×C₁₃	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
17	C₁₇×D₁₃	C₇×D₅	1	1	yes	characteristic
18	C₇×#261	—	5	1	no	Hall
19	C₁₇×Dic₅	—	13	1	no	Hall
20	#63118	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₇×C₁₇	—	13	1	no	—
22	C₁₃×C₁₇	C₇×Dic₅	1	1	yes	characteristic, complemented, Hall
23	C₇×D₁₃	D₅×C₁₇	1	1	yes	characteristic
24	C₂×C₅×C₁₇	—	13	1	no	—
25	C₇×Dic₅	—	13	1	no	Hall
26	C₅×D₁₃	C₂×C₇×C₁₇	1	1	yes	characteristic
27	C₇×C₁₇	#63118	1	1	yes	characteristic, direct product factor, Hall
28	C₇×C₁₃	C₁₇×Dic₅	1	1	yes	characteristic, complemented, Hall
29	C₅×C₁₇	C₇×#261	1	1	yes	characteristic, complemented, Hall
30	C₂×C₅×C₇	—	13	1	no	—
31	C₄×C₁₇	—	65	1	no	Hall
32	C₅×C₁₃	C₄×C₇×C₁₇	1	1	yes	characteristic, complemented, Hall
33	#261	—	5	1	no	Hall
34	C₅×C₇	C₁₇×#261	1	1	yes	characteristic, complemented, Hall
35	C₂×C₁₇	—	13	1	no	—
36	C₄×C₇	—	65	1	no	Hall
37	D₁₃	C₇×D₅×C₁₇	1	1	yes	characteristic
38	Dic₅	—	13	1	no	Hall
39	C₁₇	C₇×#63118	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₇	—	13	1	no	—
41	C₁₃	C₇×C₁₇×Dic₅	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₅	—	13	1	no	—
43	C₇	C₁₇×#63118	1	1	yes	characteristic, direct product factor, Sylow
44	C₅	C₇×C₁₇×#261	1	1	yes	characteristic, complemented, Sylow
45	C₄	—	65	1	no	Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₇×C₁₇	#63118
commutator, hypocenter	C₅×C₁₃	C₄×C₇×C₁₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃×C₁₇	C₄
prime radical	C₅×C₇×C₁₇×D₁₃	C₂
cosocle	C₅×D₁₃	C₂×C₇×C₁₇
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ 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
4. C₁₇×#63118	C₇	direct (N × H)
8. C₇×#63118	C₁₇	direct (N × H)
9. C₇×C₁₃×C₁₇	Dic₅	semidirect
11. C₅×C₁₃×C₁₇	C₄×C₇	semidirect
14. C₅×C₇×C₁₇	#261	semidirect
16. C₅×C₇×C₁₃	C₄×C₁₇	semidirect
20. #63118	C₇×C₁₇	direct (N × H)
22. C₁₃×C₁₇	C₇×Dic₅	semidirect
27. C₇×C₁₇	#63118	direct (N × H)
28. C₇×C₁₃	C₁₇×Dic₅	semidirect
29. C₅×C₁₇	C₇×#261	semidirect
32. C₅×C₁₃	C₄×C₇×C₁₇	semidirect
34. C₅×C₇	C₁₇×#261	semidirect
39. C₁₇	C₇×#63118	direct (N × H)
41. C₁₃	C₇×C₁₇×Dic₅	semidirect
43. C₇	C₁₇×#63118	direct (N × H)
44. C₅	C₇×C₁₇×#261	semidirect

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
C₁₇×#63118	7
C₇×C₁₇×Dic₅	13
C₇×#63118	17

Subgroups — C7×C17×#63118 #44525921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₇×#63118 #44525921