Subgroups — C₂×C₅²×D₇ #10622012

Order 700.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₇	C₂	1	2	yes	maximal, direct product factor
3	C₅²×C₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×D₇	C₅	1	6	yes	maximal, direct product factor
5	C₂²×C₅²	—	7	1	no	maximal, Hall
6	C₂×C₅×C₇	C₂×C₅	1	6	yes	complemented
7	C₅×D₇	C₂×C₅	1	12	yes	direct product factor
8	C₂×C₅²	—	7	2	no	—
9	C₂×C₅²	D₇	1	1	yes	characteristic, direct product factor
10	C₅×C₇	C₂²×C₅	1	6	yes	complemented
11	C₂×D₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
12	C₅²	C₂×D₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₂²×C₅	—	7	6	no	—
14	C₂×C₇	C₂×C₅²	1	1	yes	characteristic, complemented
15	D₇	C₂×C₅²	1	2	yes	direct product factor
16	C₂×C₅	—	7	12	no	—
17	C₂×C₅	C₅×D₇	1	6	yes	direct product factor
18	C₇	C₂²×C₅²	1	1	yes	characteristic, complemented, Sylow
19	C₅	C₂×C₅×D₇	1	6	yes	direct product factor
20	C₂²	—	7	1	no	Sylow
21	C₂	—	7	2	no	—
22	C₂	C₅²×D₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅²	D₇
commutator, cosocle, hypocenter	C₇	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₅²

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.