Subgroups — C₈₉×C₅⋊D₃₅ #44528279

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	D₃₅×C₈₉	—	5	6	no	maximal
3	C₅⋊D₅×C₈₉	—	7	1	no	maximal, Hall
4	C₅×C₇×C₈₉	D₅	1	6	yes	complemented
5	C₅²×C₈₉	D₇	1	1	yes	characteristic, complemented, Hall
6	D₇×C₈₉	—	25	1	no	Hall
7	D₅×C₈₉	—	35	6	no	—
8	C₇×C₈₉	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
9	C₅×C₈₉	D₃₅	1	6	yes	complemented
10	C₅⋊D₃₅	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₈₉	—	175	1	no	Hall
12	C₅²×C₇	C₂×C₈₉	1	1	yes	characteristic, complemented, Hall
13	C₈₉	C₅⋊D₃₅	1	1	yes	characteristic, direct product factor, Sylow
14	D₃₅	—	5	6	no	—
15	C₅⋊D₅	—	7	1	no	Hall
16	C₅×C₇	D₅×C₈₉	1	6	yes	complemented
17	C₅²	D₇×C₈₉	1	1	yes	characteristic, complemented, Sylow
18	D₇	—	25	1	no	Hall
19	D₅	—	35	6	no	—
20	C₇	C₅⋊D₅×C₈₉	1	1	yes	characteristic, complemented, Sylow
21	C₅	D₃₅×C₈₉	1	6	yes	complemented
22	C₂	—	175	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₈₉	C₅⋊D₃₅
commutator, cosocle, hypocenter	C₅²×C₇	C₂×C₈₉
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₈₉	C₂
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ 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.