Subgroups — D₇×Dic₅ #63302

Order 280.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₇	C₂	1	1	yes	maximal, characteristic
2	Dic₃₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₇	C₂²	1	1	yes	characteristic
5	C₅×D₇	C₄	1	2	yes	complemented
6	C₄×D₇	—	5	1	no	maximal, Hall
7	C₂×Dic₅	—	7	1	no	maximal, Hall
8	C₅×C₇	C₂×C₄	1	1	yes	characteristic, complemented, Hall
9	C₂×D₇	D₅	1	1	yes	characteristic
10	C₄×C₇	—	5	1	no	—
11	Dic₇	—	5	1	no	—
12	C₂²×C₅	—	7	1	no	—
13	Dic₅	—	7	1	no	—
14	Dic₅	D₇	1	1	yes	characteristic, direct product factor
15	C₂×C₇	C₂×D₅	1	1	yes	characteristic
16	D₇	Dic₅	1	2	yes	direct product factor
17	C₂×C₅	—	7	2	no	—
18	C₂×C₅	C₂×D₇	1	1	yes	characteristic
19	C₂×C₄	—	35	1	no	Sylow
20	C₇	C₂×Dic₅	1	1	yes	characteristic, complemented, Sylow
21	C₅	C₄×D₇	1	1	yes	characteristic, complemented, Sylow
22	C₂²	—	7	1	no	—
23	C₄	—	5	1	no	—
24	C₄	—	35	1	no	—
25	C₂	—	7	2	no	—
26	C₂	D₅×D₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×D₇
commutator, hypocenter	C₅×C₇	C₂×C₄
Fitting, socle, cosocle	C₂×C₅×C₇	C₂²
prime radical	C₂×C₅×D₇	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂

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.