Subgroups — #14519974

Order 1960.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊Dic₃₅	C₂	1	1	yes	maximal, characteristic
2	C₇²×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₅×C₇⋊Dic₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×C₇²	C₂²	1	1	yes	characteristic
5	#87648	—	5	1	no	maximal, Hall
6	#63308	—	7	8	no	maximal
7	C₅×C₇²	Q₈	1	1	yes	characteristic, complemented, Hall
8	C₄×C₇²	—	5	1	no	—
9	C₇⋊Dic₇	—	5	1	no	—
10	C₇⋊Dic₇	D₅	1	1	yes	characteristic
11	Dic₃₅	—	7	8	no	—
12	C₅×Dic₇	—	7	8	no	—
13	C₇×Dic₅	D₇	1	8	yes	—
14	C₂×C₇²	C₂×D₅	1	1	yes	characteristic
15	C₂×C₅×C₇	C₂×D₇	1	8	yes	—
16	Dic₁₄	—	35	8	no	—
17	C₇²	Dic₁₀	1	1	yes	characteristic, complemented, Sylow
18	Dic₁₀	—	49	1	no	Hall
19	C₅×C₇	Dic₁₄	1	8	yes	complemented
20	C₄×C₇	—	5	8	no	—
21	Dic₇	—	7	8	no	—
22	Dic₇	—	35	8	no	—
23	C₄×C₅	—	49	1	no	—
24	Dic₅	—	49	1	no	—
25	Dic₅	C₇⋊D₇	1	1	yes	characteristic
26	C₂×C₇	D₅×D₇	1	8	yes	—
27	C₂×C₅	C₂×C₇⋊D₇	1	1	yes	characteristic
28	Q₈	—	245	1	no	Sylow
29	C₇	#63308	1	8	yes	complemented
30	C₅	#87648	1	1	yes	characteristic, complemented, Sylow
31	C₄	—	5	1	no	—
32	C₄	—	49	1	no	—
33	C₄	—	245	1	no	—
34	C₂	D₅×C₇⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×C₇⋊D₇
commutator, Fitting, socle, prime radical, cosocle	C₂×C₅×C₇²	C₂²
hypocenter	C₅×C₇²	Q₈
LCS	G ▷ C₂×C₅×C₇² ▷ C₅×C₇²
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.