Subgroups — C₁₃²×D₃₅ #26044813

Order 11830.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₃²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃²×D₇	—	5	1	no	maximal, Hall
3	D₅×C₁₃²	—	7	1	no	maximal, Hall
4	C₇×C₁₃²	D₅	1	1	yes	characteristic, complemented, Hall
5	C₁₃×D₃₅	C₁₃	1	14	yes	maximal, direct product factor
6	C₅×C₁₃²	D₇	1	1	yes	characteristic, complemented, Hall
7	C₅×C₇×C₁₃	C₂×C₁₃	1	14	yes	complemented
8	C₂×C₁₃²	—	35	1	no	Hall
9	C₁₃×D₇	—	5	14	no	—
10	C₁₃²	D₃₅	1	1	yes	characteristic, direct product factor, Sylow
11	D₅×C₁₃	—	7	14	no	—
12	C₇×C₁₃	D₅×C₁₃	1	14	yes	complemented
13	D₃₅	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
14	C₅×C₁₃	C₁₃×D₇	1	14	yes	complemented
15	C₅×C₇	C₂×C₁₃²	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃	—	35	14	no	—
17	D₇	—	5	1	no	Hall
18	C₁₃	C₁₃×D₃₅	1	14	yes	direct product factor
19	D₅	—	7	1	no	Hall
20	C₇	D₅×C₁₃²	1	1	yes	characteristic, complemented, Sylow
21	C₅	C₁₃²×D₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	35	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃²	D₃₅
commutator, cosocle, hypocenter	C₅×C₇	C₂×C₁₃²
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃²	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₁₃²

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.