Subgroups — C₇×#713 #10587981

Order 560.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₂₀	C₂	1	3	yes	maximal, complemented
3	C₄×C₇×D₅	C₂	1	3	yes	maximal, complemented
4	C₂×C₇×D₅	C₂²	1	3	yes	—
5	C₄×C₅×C₇	C₂²	1	3	yes	—
6	C₇×Dic₅	C₂²	1	1	yes	characteristic
7	C₇×#41	—	5	1	no	maximal, Hall
8	#713	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₅×C₇	C₂³	1	1	yes	characteristic
10	C₇×D₅	—	2	3	no	—
11	C₇×Q₈	D₅	1	1	yes	characteristic, complemented
12	C₇×D₄	—	5	3	no	—
13	C₂×C₄×C₇	—	5	3	no	—
14	C₅×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
15	D₂₀	C₂×C₇	1	3	yes	complemented
16	C₄×D₅	C₂×C₇	1	3	yes	complemented
17	C₅×C₇	#41	1	1	yes	characteristic, complemented, Hall
18	C₂²×C₇	—	5	3	no	—
19	C₄×C₇	—	5	1	no	—
20	C₄×C₇	C₂×D₅	1	3	yes	—
21	C₂×D₅	C₂²×C₇	1	3	yes	—
22	C₄×C₅	C₂²×C₇	1	3	yes	—
23	Dic₅	C₂²×C₇	1	1	yes	characteristic
24	#41	—	5	1	no	Sylow
25	C₂×C₇	—	10	3	no	—
26	C₂×C₇	C₂²×D₅	1	1	yes	characteristic
27	C₂×C₅	C₂³×C₇	1	1	yes	characteristic
28	D₅	—	2	3	no	—
29	Q₈	C₇×D₅	1	1	yes	characteristic, complemented
30	D₄	—	5	3	no	—
31	C₂×C₄	—	5	3	no	—
32	C₇	#713	1	1	yes	characteristic, direct product factor, Sylow
33	C₅	C₇×#41	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	5	3	no	—
35	C₄	—	5	1	no	—
36	C₄	C₂×C₇×D₅	1	3	yes	—
37	C₂	—	10	3	no	—
38	C₂	C₂²×C₇×D₅	1	1	yes	characteristic

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.