Subgroups — #14519983

Order 1960.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₃₅	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×C₇²	C₂²	1	1	yes	characteristic
4	C₅×C₇⋊D₇	C₄	1	2	yes	complemented
5	#87639	—	5	1	no	maximal, Hall
6	D₇×Dic₅	—	7	2	no	maximal
7	C₅×C₇²	C₂×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂×C₇⋊D₇	D₅	1	1	yes	characteristic
9	C₇×Dic₇	—	5	2	no	—
10	C₂×C₅×D₇	—	7	2	no	—
11	C₂×C₅×D₇	—	14	3	no	—
12	Dic₃₅	D₇	1	2	yes	complemented
13	C₇×Dic₅	—	7	2	no	—
14	C₂×C₇²	C₂×D₅	1	1	yes	characteristic
15	C₇⋊D₇	Dic₅	1	2	yes	complemented
16	C₂×C₅×C₇	—	2	3	no	—
17	C₂×C₅×C₇	C₂×D₇	1	2	yes	—
18	C₅×D₇	—	7	4	no	—
19	C₅×D₇	—	14	6	no	—
20	C₄×D₇	—	35	2	no	—
21	C₇²	C₂×Dic₅	1	1	yes	characteristic, complemented, Sylow
22	C₂×Dic₅	—	49	1	no	Hall
23	C₅×C₇	—	2	3	no	—
24	C₅×C₇	C₄×D₇	1	2	yes	complemented
25	C₂×D₇	—	7	2	no	—
26	C₂×D₇	—	14	3	no	—
27	C₄×C₇	—	35	2	no	—
28	Dic₇	—	5	2	no	—
29	C₂²×C₅	—	49	1	no	—
30	Dic₅	—	7	2	no	—
31	C₂×C₇	—	2	3	no	—
32	C₂×C₇	D₅×D₇	1	2	yes	—
33	D₇	—	7	4	no	—
34	D₇	—	14	6	no	—
35	C₂×C₅	—	49	2	no	—
36	C₂×C₅	D₇²	1	1	yes	characteristic
37	C₂×C₄	—	245	1	no	Sylow
38	C₇	—	2	3	no	—
39	C₇	D₇×Dic₅	1	2	yes	complemented
40	C₅	#87639	1	1	yes	characteristic, complemented, Sylow
41	C₂²	—	49	1	no	—
42	C₄	—	35	2	no	—
43	C₂	—	49	2	no	—
44	C₂	D₃₅⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃₅⋊D₇
commutator, hypocenter	C₅×C₇²	C₂×C₄
Fitting, socle, cosocle	C₂×C₅×C₇²	C₂²
prime radical	C₂×C₅×C₇⋊D₇	C₂
LCS	G ▷ 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.