Subgroups — C₅²×D₇×C₈₉ #44528271

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

	subgroup	G/H
center, hypercenter	C₅²×C₈₉	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₅²×C₈₉
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₈₉	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₅²×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.