Subgroups — C₂×C₃×D₁₂₁ #13089708

Order 1452.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₂₁	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₁₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₂₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₂₁	C₂×C₃	1	1	yes	characteristic, complemented
6	D₁₂₁	C₂×C₃	1	2	yes	direct product factor
7	C₂×C₃×D₁₁	—	11	1	no	maximal
8	C₁₂₁	C₂²×C₃	1	1	yes	characteristic, complemented, Sylow
9	C₂×C₃×C₁₁	D₁₁	1	1	yes	characteristic
10	C₃×D₁₁	—	11	2	no	—
11	C₂×D₁₁	—	11	1	no	—
12	C₃×C₁₁	C₂×D₁₁	1	1	yes	characteristic
13	C₂×C₁₁	C₃×D₁₁	1	1	yes	characteristic
14	D₁₁	—	11	2	no	—
15	C₂²×C₃	—	121	1	no	Hall
16	C₁₁	C₂×C₃×D₁₁	1	1	yes	characteristic
17	C₂×C₃	—	121	2	no	—
18	C₂×C₃	D₁₂₁	1	1	yes	characteristic, direct product factor
19	C₂²	—	121	1	no	Sylow
20	C₃	C₂×D₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₂	—	121	2	no	—
22	C₂	C₃×D₁₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₂₁
commutator, cosocle, hypocenter	C₁₂₁	C₂²×C₃
Frattini	C₁₁	C₂×C₃×D₁₁
Fitting	C₂×C₃×C₁₂₁	C₂
socle	C₂×C₃×C₁₁	D₁₁
LCS	G ▷ C₁₂₁
UCS	C₁ ◁ C₂×C₃

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.