Subgroups — C₂²×C₇×D₅ #63333

Order 280.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×D₅	C₂	1	6	yes	maximal, direct product factor
3	C₂×C₅×C₇	C₂²	1	3	yes	complemented
4	C₇×D₅	C₂²	1	4	yes	direct product factor
5	C₂³×C₇	—	5	1	no	maximal, Hall
6	C₂²×D₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₇	C₂³	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₇	—	5	6	no	—
9	C₂²×C₇	D₅	1	1	yes	characteristic, direct product factor
10	C₂²×C₅	C₂×C₇	1	1	yes	characteristic, complemented
11	C₂×D₅	C₂×C₇	1	6	yes	direct product factor
12	C₂×C₇	—	5	4	no	—
13	C₂×C₇	C₂×D₅	1	3	yes	direct product factor
14	C₂×C₅	C₂²×C₇	1	3	yes	complemented
15	D₅	C₂²×C₇	1	4	yes	direct product factor
16	C₂³	—	5	1	no	Sylow
17	C₇	C₂²×D₅	1	1	yes	characteristic, direct product factor, Sylow
18	C₅	C₂³×C₇	1	1	yes	characteristic, complemented, Sylow
19	C₂²	—	5	6	no	—
20	C₂²	C₇×D₅	1	1	yes	characteristic, direct product factor
21	C₂	—	5	4	no	—
22	C₂	C₂×C₇×D₅	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₇	D₅
commutator, cosocle, hypocenter	C₅	C₂³×C₇
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₇	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂²×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.