Subgroups — C₁₇×C₇⋊#1044 #26045430

Order 11900.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₇×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₇×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₇×C₇⋊AGL(1,𝔽₅)	—	5	2	no	maximal
4	C₁₇×#1044	—	7	1	no	maximal, Hall
5	C₇×D₅×C₁₇	—	5	2	no	—
6	C₇×D₅×C₁₇	—	10	2	no	—
7	C₁₇×C₅⋊D₅	D₇	1	1	yes	characteristic
8	C₇⋊#1044	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₇×C₁₇	—	2	2	no	—
10	C₅×C₇×C₁₇	AGL(1,𝔽₅)	1	2	yes	complemented
11	C₁₇×Dic₇	—	25	1	no	Hall
12	C₅²×C₁₇	Dic₇	1	1	yes	characteristic, complemented, Hall
13	C₇×C₅⋊D₅	C₂×C₁₇	1	1	yes	characteristic
14	C₁₇×AGL(1,𝔽₅)	—	35	2	no	—
15	C₂×C₇×C₁₇	—	25	1	no	—
16	C₅²×C₇	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
17	D₅×C₁₇	—	5	2	no	—
18	D₅×C₁₇	—	10	2	no	—
19	C₇⋊AGL(1,𝔽₅)	—	5	2	no	—
20	C₇×C₁₇	#1044	1	1	yes	characteristic, complemented, Hall
21	#1044	—	7	1	no	Hall
22	C₅×C₁₇	—	2	2	no	—
23	C₅×C₁₇	C₇⋊AGL(1,𝔽₅)	1	2	yes	complemented
24	C₇×D₅	—	5	2	no	—
25	C₇×D₅	—	10	2	no	—
26	C₄×C₁₇	—	175	1	no	Hall
27	C₅⋊D₅	D₇×C₁₇	1	1	yes	characteristic
28	C₅×C₇	—	2	2	no	—
29	C₅×C₇	C₁₇×AGL(1,𝔽₅)	1	2	yes	complemented
30	C₂×C₁₇	—	25	1	no	—
31	Dic₇	—	25	1	no	Hall
32	C₅²	C₁₇×Dic₇	1	1	yes	characteristic, complemented, Sylow
33	AGL(1,𝔽₅)	—	35	2	no	—
34	C₁₇	C₇⋊#1044	1	1	yes	characteristic, direct product factor, Sylow
35	C₂×C₇	—	25	1	no	—
36	D₅	—	5	2	no	—
37	D₅	—	10	2	no	—
38	C₇	C₁₇×#1044	1	1	yes	characteristic, complemented, Sylow
39	C₅	—	2	2	no	—
40	C₅	C₁₇×C₇⋊AGL(1,𝔽₅)	1	2	yes	complemented
41	C₄	—	175	1	no	Sylow
42	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇	C₇⋊#1044
commutator, hypocenter	C₅²×C₇	C₄×C₁₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₁₇	C₄
prime radical	C₇×C₁₇×C₅⋊D₅	C₂
cosocle	C₇×C₅⋊D₅	C₂×C₁₇
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
2. C₅²×C₇×C₁₇	C₄	semidirect
8. C₇⋊#1044	C₁₇	direct (N × H)
10. C₅×C₇×C₁₇	AGL(1,𝔽₅)	semidirect
12. C₅²×C₁₇	Dic₇	semidirect
16. C₅²×C₇	C₄×C₁₇	semidirect
20. C₇×C₁₇	#1044	semidirect
23. C₅×C₁₇	C₇⋊AGL(1,𝔽₅)	semidirect
29. C₅×C₇	C₁₇×AGL(1,𝔽₅)	semidirect
32. C₅²	C₁₇×Dic₇	semidirect
34. C₁₇	C₇⋊#1044	direct (N × H)
38. C₇	C₁₇×#1044	semidirect
40. C₅	C₁₇×C₇⋊AGL(1,𝔽₅)	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₇×C₅⋊D₅	2
C₁₇×C₇⋊AGL(1,𝔽₅)	5
C₁₇×#1044	7
C₇⋊#1044	17

Subgroups — C17×C7⋊#1044 #26045430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×C₇⋊#1044 #26045430