Subgroups — C₅×C₁₁×C₇⋊D₇ #19129136

Order 5390.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×C₇⋊D₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₁₁×D₇	—	7	8	no	maximal
4	C₇²×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₇⋊D₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₇×C₁₁	D₇	1	8	yes	complemented
7	C₅×C₇²	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
8	C₁₁×D₇	—	7	8	no	—
9	C₂×C₅×C₁₁	—	49	1	no	Hall
10	C₇⋊D₇	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
11	C₇×C₁₁	C₅×D₇	1	8	yes	complemented
12	C₅×D₇	—	7	8	no	—
13	C₅×C₁₁	C₇⋊D₇	1	1	yes	characteristic, direct product factor, Hall
14	C₇²	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
15	C₅×C₇	C₁₁×D₇	1	8	yes	complemented
16	C₂×C₁₁	—	49	1	no	Hall
17	D₇	—	7	8	no	—
18	C₁₁	C₅×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅	—	49	1	no	Hall
20	C₇	C₅×C₁₁×D₇	1	8	yes	complemented
21	C₅	C₁₁×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	49	1	no	Sylow

Splittings G = N ⋊ H with N normal; H ≅ G/N.