Subgroups — C₇×C₁₇×#63120 #44525899

Order 30940.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₅×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×C₁₃×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×C₁₇×Dic₁₃	—	5	1	no	maximal, Hall
4	C₁₇×#63120	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₁₃×C₁₇	—	5	1	no	—
6	C₇×C₁₇×AGL(1,𝔽₅)	—	13	1	no	maximal, Hall
7	D₅×C₁₃×C₁₇	C₂×C₇	1	1	yes	characteristic
8	C₇×#63120	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₁₃×C₁₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
10	C₇×D₅×C₁₇	D₁₃	1	1	yes	characteristic
11	C₅×C₁₃×C₁₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×D₅×C₁₃	C₂×C₁₇	1	1	yes	characteristic
13	C₁₇×Dic₁₃	—	5	1	no	Hall
14	C₅×C₇×C₁₇	Dic₁₃	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	C₂×C₁₃×C₁₇	—	5	1	no	—
18	C₇×Dic₁₃	—	5	1	no	Hall
19	C₁₇×AGL(1,𝔽₅)	—	13	1	no	Hall
20	#63120	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₇×C₁₇	—	5	1	no	—
22	C₁₃×C₁₇	C₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇×C₁₃	—	5	1	no	—
24	D₅×C₁₇	C₇×D₁₃	1	1	yes	characteristic
25	C₇×AGL(1,𝔽₅)	—	13	1	no	Hall
26	D₅×C₁₃	C₂×C₇×C₁₇	1	1	yes	characteristic
27	C₇×C₁₇	#63120	1	1	yes	characteristic, direct product factor, Hall
28	C₇×C₁₃	C₁₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
29	C₅×C₁₇	C₇×Dic₁₃	1	1	yes	characteristic, complemented, Hall
30	C₇×D₅	C₁₇×D₁₃	1	1	yes	characteristic
31	C₄×C₁₇	—	65	1	no	Hall
32	C₅×C₁₃	C₄×C₇×C₁₇	1	1	yes	characteristic, complemented, Hall
33	Dic₁₃	—	5	1	no	Hall
34	C₅×C₇	C₁₇×Dic₁₃	1	1	yes	characteristic, complemented, Hall
35	C₂×C₁₇	—	5	1	no	—
36	C₄×C₇	—	65	1	no	Hall
37	C₂×C₁₃	—	5	1	no	—
38	AGL(1,𝔽₅)	—	13	1	no	Hall
39	C₁₇	C₇×#63120	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₇	—	5	1	no	—
41	C₁₃	C₇×C₁₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
42	D₅	C₇×C₁₇×D₁₃	1	1	yes	characteristic
43	C₇	C₁₇×#63120	1	1	yes	characteristic, direct product factor, Sylow
44	C₅	C₇×C₁₇×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
45	C₄	—	65	1	no	Sylow
46	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₇×C₁₇	#63120
commutator, hypocenter	C₅×C₁₃	C₄×C₇×C₁₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃×C₁₇	C₄
prime radical	C₇×D₅×C₁₃×C₁₇	C₂
cosocle	D₅×C₁₃	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×#63120	C₇	direct (N × H)
8. C₇×#63120	C₁₇	direct (N × H)
9. C₇×C₁₃×C₁₇	AGL(1,𝔽₅)	semidirect
11. C₅×C₁₃×C₁₇	C₄×C₇	semidirect
14. C₅×C₇×C₁₇	Dic₁₃	semidirect
16. C₅×C₇×C₁₃	C₄×C₁₇	semidirect
20. #63120	C₇×C₁₇	direct (N × H)
22. C₁₃×C₁₇	C₇×AGL(1,𝔽₅)	semidirect
27. C₇×C₁₇	#63120	direct (N × H)
28. C₇×C₁₃	C₁₇×AGL(1,𝔽₅)	semidirect
29. C₅×C₁₇	C₇×Dic₁₃	semidirect
32. C₅×C₁₃	C₄×C₇×C₁₇	semidirect
34. C₅×C₇	C₁₇×Dic₁₃	semidirect
39. C₁₇	C₇×#63120	direct (N × H)
41. C₁₃	C₇×C₁₇×AGL(1,𝔽₅)	semidirect
43. C₇	C₁₇×#63120	direct (N × H)
44. C₅	C₇×C₁₇×Dic₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₇×D₅×C₁₃×C₁₇	2
C₇×C₁₇×Dic₁₃	5
C₁₇×#63120	7
C₇×C₁₇×AGL(1,𝔽₅)	13
C₇×#63120	17

Subgroups — C7×C17×#63120 #44525899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₇×#63120 #44525899