Subgroups — C₇²×D₅×C₆₇ #45659183

Order 32830.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₇²×C₆₇	—	5	1	no	maximal, Hall
3	C₇×D₅×C₆₇	C₇	1	8	yes	maximal, direct product factor
4	C₇²×C₆₇	D₅	1	1	yes	characteristic, direct product factor, Hall
5	C₅×C₇×C₆₇	C₂×C₇	1	8	yes	complemented
6	C₂×C₇×C₆₇	—	5	8	no	—
7	D₅×C₆₇	C₇²	1	1	yes	characteristic, direct product factor, Hall
8	C₇²×D₅	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₆₇	C₇×D₅	1	8	yes	direct product factor
10	C₅×C₆₇	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
11	C₅×C₇²	C₂×C₆₇	1	1	yes	characteristic, complemented, Hall
12	C₂×C₆₇	—	5	1	no	Hall
13	C₂×C₇²	—	5	1	no	Hall
14	C₇×D₅	C₇×C₆₇	1	8	yes	direct product factor
15	C₆₇	C₇²×D₅	1	1	yes	characteristic, direct product factor, Sylow
16	C₇²	D₅×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₅×C₇	C₂×C₇×C₆₇	1	8	yes	complemented
18	C₂×C₇	—	5	8	no	—
19	D₅	C₇²×C₆₇	1	1	yes	characteristic, direct product factor, Hall
20	C₇	C₇×D₅×C₆₇	1	8	yes	direct product factor
21	C₅	C₂×C₇²×C₆₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇²×C₆₇	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₇²×C₆₇
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₆₇	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₇²×C₆₇

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.