Subgroups — C₅×C₇⋊Dic₂₅₉ #49136397

Order 36260.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇²×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇²×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇⋊Dic₂₅₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×Dic₂₅₉	—	7	8	no	maximal
5	C₂×C₇²×C₃₇	C₂×C₅	1	1	yes	characteristic
6	C₂×C₅×C₇×C₃₇	D₇	1	8	yes	—
7	C₇²×C₃₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₇×C₃₇	Dic₇	1	8	yes	complemented
9	Dic₂₅₉	—	7	8	no	—
10	C₅×C₇⋊Dic₇	—	37	1	no	maximal, Hall
11	C₅×Dic₃₇	—	49	1	no	Hall
12	C₂×C₇×C₃₇	C₅×D₇	1	8	yes	—
13	C₂×C₅×C₇²	D₃₇	1	1	yes	characteristic
14	C₂×C₅×C₃₇	C₇⋊D₇	1	1	yes	characteristic
15	C₇×C₃₇	C₅×Dic₇	1	8	yes	complemented
16	C₅×C₇²	Dic₃₇	1	1	yes	characteristic, complemented, Hall
17	C₇⋊Dic₇	—	37	1	no	Hall
18	C₅×C₃₇	C₇⋊Dic₇	1	1	yes	characteristic, complemented, Hall
19	Dic₃₇	—	49	1	no	Hall
20	C₅×Dic₇	—	259	8	no	—
21	C₂×C₇²	C₅×D₃₇	1	1	yes	characteristic
22	C₂×C₃₇	C₅×C₇⋊D₇	1	1	yes	characteristic
23	C₂×C₅×C₇	D₂₅₉	1	8	yes	—
24	C₇²	C₅×Dic₃₇	1	1	yes	characteristic, complemented, Sylow
25	C₃₇	C₅×C₇⋊Dic₇	1	1	yes	characteristic, complemented, Sylow
26	C₅×C₇	Dic₂₅₉	1	8	yes	complemented
27	Dic₇	—	259	8	no	—
28	C₄×C₅	—	1813	1	no	Hall
29	C₂×C₇	C₅×D₂₅₉	1	8	yes	—
30	C₂×C₅	C₇⋊D₂₅₉	1	1	yes	characteristic
31	C₇	C₅×Dic₂₅₉	1	8	yes	complemented
32	C₅	C₇⋊Dic₂₅₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₄	—	1813	1	no	Sylow
34	C₂	C₅×C₇⋊D₂₅₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	C₇⋊D₂₅₉
commutator, hypocenter	C₇²×C₃₇	C₄×C₅
Frattini	C₂	C₅×C₇⋊D₂₅₉
Fitting, socle, prime radical	C₂×C₅×C₇²×C₃₇	C₂
cosocle	C₂×C₇²×C₃₇	C₂×C₅
LCS	G ▷ C₇²×C₃₇
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×C₇²×C₃₇	C₄	semidirect
3. C₇⋊Dic₂₅₉	C₅	direct (N × H)
7. C₇²×C₃₇	C₄×C₅	semidirect
8. C₅×C₇×C₃₇	Dic₇	semidirect
15. C₇×C₃₇	C₅×Dic₇	semidirect
16. C₅×C₇²	Dic₃₇	semidirect
18. C₅×C₃₇	C₇⋊Dic₇	semidirect
24. C₇²	C₅×Dic₃₇	semidirect
25. C₃₇	C₅×C₇⋊Dic₇	semidirect
26. C₅×C₇	Dic₂₅₉	semidirect
31. C₇	C₅×Dic₂₅₉	semidirect
32. C₅	C₇⋊Dic₂₅₉	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×C₇²×C₃₇	2
C₇⋊Dic₂₅₉	5
C₅×Dic₂₅₉	7
C₅×C₇⋊Dic₇	37

Subgroups — C5×C7⋊Dic259 #49136397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇⋊Dic₂₅₉ #49136397