Subgroups — C₇²×D₃₃₅ #45659184

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	C₇²×D₆₇	—	5	1	no	maximal, Hall
3	C₇×D₃₃₅	C₇	1	8	yes	maximal, direct product factor
4	C₇²×C₆₇	D₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₇×C₆₇	C₂×C₇	1	8	yes	complemented
6	C₇×D₆₇	—	5	8	no	—
7	D₃₃₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
8	C₇²×D₅	—	67	1	no	maximal, Hall
9	C₇×C₆₇	C₇×D₅	1	8	yes	complemented
10	C₅×C₆₇	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
11	C₅×C₇²	D₆₇	1	1	yes	characteristic, complemented, Hall
12	D₆₇	—	5	1	no	Hall
13	C₂×C₇²	—	335	1	no	Hall
14	C₇×D₅	—	67	8	no	—
15	C₆₇	C₇²×D₅	1	1	yes	characteristic, complemented, Sylow
16	C₇²	D₃₃₅	1	1	yes	characteristic, direct product factor, Sylow
17	C₅×C₇	C₇×D₆₇	1	8	yes	complemented
18	C₂×C₇	—	335	8	no	—
19	D₅	—	67	1	no	Hall
20	C₇	C₇×D₃₃₅	1	8	yes	direct product factor
21	C₅	C₇²×D₆₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	335	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇²	D₃₃₅
commutator, cosocle, hypocenter	C₅×C₆₇	C₂×C₇²
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₆₇	C₂
LCS	G ▷ C₅×C₆₇
UCS	C₁ ◁ C₇²

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.