Subgroups — C₅×C₇⋊(D₄₃⋊C₇) #35231069

Order 21070.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₄₃⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇⋊(D₄₃⋊C₇)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×D₄₃⋊C₇	—	7	1	no	maximal
4	C₅×D₃₀₁	C₇	1	1	yes	maximal, characteristic, complemented
5	C₇×C₄₃⋊C₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×C₇×C₄₃	C₂×C₇	1	1	yes	characteristic, complemented
7	C₅×C₄₃⋊C₇	—	2	3	no	—
8	C₅×C₄₃⋊C₇	D₇	1	1	yes	characteristic, complemented
9	D₃₀₁	C₅×C₇	1	1	yes	characteristic, complemented
10	D₄₃⋊C₇	—	7	1	no	—
11	C₅×C₇×D₇	—	43	1	no	maximal, Hall
12	C₅×D₄₃	—	7	1	no	Hall
13	C₇×C₄₃	C₂×C₅×C₇	1	1	yes	characteristic, complemented
14	C₄₃⋊C₇	—	2	3	no	—
15	C₄₃⋊C₇	C₅×D₇	1	1	yes	characteristic, complemented
16	C₅×C₇²	—	43	1	no	Hall
17	C₅×C₄₃	C₇×D₇	1	1	yes	characteristic, complemented, Hall
18	C₇×D₇	—	43	1	no	Hall
19	D₄₃	—	7	1	no	Hall
20	C₂×C₅×C₇	—	301	1	no	—
21	C₅×D₇	—	43	1	no	—
22	C₇²	—	43	1	no	Sylow
23	C₄₃	C₅×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
24	C₅×C₇	—	43	1	no	—
25	C₅×C₇	—	86	3	no	—
26	C₅×C₇	D₄₃⋊C₇	1	1	yes	characteristic, complemented
27	C₂×C₇	—	301	1	no	—
28	D₇	—	43	1	no	—
29	C₂×C₅	—	301	1	no	Hall
30	C₇	—	43	1	no	—
31	C₇	—	86	3	no	—
32	C₇	C₅×D₄₃⋊C₇	1	1	yes	characteristic, complemented
33	C₅	C₇⋊(D₄₃⋊C₇)	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	301	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₇⋊(D₄₃⋊C₇)
commutator, cosocle, hypocenter	C₇×C₄₃	C₂×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₄₃	C₂×C₇
LCS	G ▷ C₇×C₄₃
UCS	C₁ ◁ C₅

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.