Subgroups — C₇×C₅⋊D₅×C₈₉ #44528277

Order 31150.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₅×C₈₉	—	5	6	no	maximal
3	C₅⋊D₅×C₈₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₈₉	D₅	1	6	yes	complemented
5	C₅²×C₈₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₂×C₇×C₈₉	—	25	1	no	Hall
7	D₅×C₈₉	—	5	6	no	—
8	C₇×C₈₉	C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
9	C₅×C₈₉	C₇×D₅	1	6	yes	complemented
10	C₇×C₅⋊D₅	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₈₉	—	25	1	no	Hall
12	C₅²×C₇	C₂×C₈₉	1	1	yes	characteristic, complemented, Hall
13	C₈₉	C₇×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
14	C₇×D₅	—	5	6	no	—
15	C₅⋊D₅	C₇×C₈₉	1	1	yes	characteristic, direct product factor, Hall
16	C₅×C₇	D₅×C₈₉	1	6	yes	complemented
17	C₅²	C₂×C₇×C₈₉	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₇	—	25	1	no	Hall
19	D₅	—	5	6	no	—
20	C₇	C₅⋊D₅×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₇×D₅×C₈₉	1	6	yes	complemented
22	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₈₉	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₇×C₈₉
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₈₉	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₇×C₈₉

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

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