Subgroups — C₅²×C₇×D₈₉ #44528270

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	C₅×C₇×D₈₉	C₅	1	6	yes	maximal, direct product factor
3	C₅²×D₈₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₈₉	C₂×C₅	1	6	yes	complemented
5	C₅²×C₈₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₇×D₈₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
7	C₅×D₈₉	C₅×C₇	1	6	yes	direct product factor
8	C₇×C₈₉	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
9	C₅×C₈₉	C₂×C₅×C₇	1	6	yes	complemented
10	C₂×C₅²×C₇	—	89	1	no	maximal, Hall
11	D₈₉	C₅²×C₇	1	1	yes	characteristic, direct product factor, Hall
12	C₅²×C₇	D₈₉	1	1	yes	characteristic, direct product factor, Hall
13	C₈₉	C₂×C₅²×C₇	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₅×C₇	—	89	6	no	—
15	C₂×C₅²	—	89	1	no	Hall
16	C₅×C₇	C₅×D₈₉	1	6	yes	direct product factor
17	C₅²	C₇×D₈₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₇	—	89	1	no	Hall
19	C₂×C₅	—	89	6	no	—
20	C₇	C₅²×D₈₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₅×C₇×D₈₉	1	6	yes	direct product factor
22	C₂	—	89	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²×C₇	D₈₉
commutator, cosocle, hypocenter	C₈₉	C₂×C₅²×C₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₈₉	C₂
LCS	G ▷ C₈₉
UCS	C₁ ◁ C₅²×C₇

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.