Subgroups — C₃×D₄₉×C₁₀₁ #44445939

Order 29694.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₉×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₉×C₁₀₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₄₉×C₁₀₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₇×C₁₀₁	—	7	1	no	maximal
5	C₃×C₇×C₁₀₁	D₇	1	1	yes	characteristic
6	D₇×C₁₀₁	—	7	1	no	—
7	C₇×C₁₀₁	C₃×D₇	1	1	yes	characteristic
8	C₂×C₃×C₁₀₁	—	49	1	no	Hall
9	C₃×C₁₀₁	D₄₉	1	1	yes	characteristic, direct product factor, Hall
10	C₃×D₄₉	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₁₀₁	—	49	1	no	Hall
12	C₃×C₄₉	C₂×C₁₀₁	1	1	yes	characteristic, complemented, Hall
13	C₁₀₁	C₃×D₄₉	1	1	yes	characteristic, direct product factor, Sylow
14	D₄₉	C₃×C₁₀₁	1	1	yes	characteristic, direct product factor, Hall
15	C₄₉	C₂×C₃×C₁₀₁	1	1	yes	characteristic, complemented, Sylow
16	C₃×D₇	—	7	1	no	—
17	C₃×C₇	D₇×C₁₀₁	1	1	yes	characteristic
18	D₇	—	7	1	no	—
19	C₇	C₃×D₇×C₁₀₁	1	1	yes	characteristic
20	C₂×C₃	—	49	1	no	Hall
21	C₃	D₄₉×C₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₀₁	D₄₉
commutator, cosocle, hypocenter	C₄₉	C₂×C₃×C₁₀₁
Frattini	C₇	C₃×D₇×C₁₀₁
Fitting	C₃×C₄₉×C₁₀₁	C₂
socle	C₃×C₇×C₁₀₁	D₇
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₃×C₁₀₁

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.