Subgroups — D₇×A₅ #11719835

Order 840.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×A₅	C₂	1	1	yes	maximal, characteristic, complemented
2	A₄×D₇	—	5	1	no	maximal, Hall
3	D₅×D₇	—	6	1	no	maximal
4	C₂×A₅	—	7	1	no	maximal, Hall
5	C₇×A₄	—	5	1	no	—
6	D₃×D₇	—	10	1	no	maximal
7	D₃₅	—	6	1	no	—
8	C₅×D₇	—	6	1	no	—
9	C₇×D₅	—	6	1	no	—
10	A₅	D₇	1	1	yes	characteristic, direct product factor
11	C₂²×D₇	—	5	1	no	Hall
12	D₂₁	—	10	1	no	—
13	C₃×D₇	—	10	1	no	—
14	D₃×C₇	—	10	1	no	—
15	C₅×C₇	—	6	1	no	Hall
16	C₂²×C₇	—	5	1	no	—
17	C₂×D₇	—	15	1	no	—
18	C₂×D₇	—	15	1	no	—
19	C₂×A₄	—	35	1	no	Hall
20	C₃×C₇	—	10	1	no	Hall
21	C₂×D₅	—	42	1	no	—
22	C₂×C₇	—	15	1	no	—
23	D₇	—	15	1	no	—
24	D₇	A₅	1	1	yes	maximal normal, characteristic, direct product factor
25	C₂×D₃	—	70	1	no	—
26	A₄	—	5	1	no	—
27	C₂×C₅	—	42	1	no	—
28	D₅	—	6	1	no	—
29	D₅	—	42	1	no	—
30	C₂³	—	35	1	no	Sylow
31	C₇	C₂×A₅	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃	—	70	1	no	—
33	D₃	—	10	1	no	—
34	D₃	—	70	1	no	—
35	C₅	—	6	1	no	Sylow
36	C₂²	—	5	1	no	—
37	C₂²	—	105	1	no	—
38	C₂²	—	105	1	no	—
39	C₃	—	10	1	no	Sylow
40	C₂	—	7	1	no	—
41	C₂	—	15	1	no	—
42	C₂	—	105	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, hypocenter	C₇×A₅	C₂
Fitting, cosocle	C₇	C₂×A₅
LCS	G ▷ C₇×A₅
UCS	C₁

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.