Subgroups — #127×C₁₀₁₃ #44569540

Order 32416.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₁₀₁₃	C₂	1	6	yes	maximal, complemented
2	C₄²×C₁₀₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₁₀₁₃	C₂²	1	4	yes	—
4	D₄×C₁₀₁₃	—	2	12	no	—
5	C₂×C₄×C₁₀₁₃	C₂²	1	3	yes	—
6	C₂²×C₁₀₁₃	—	2	12	no	—
7	C₂²×C₁₀₁₃	C₂³	1	1	yes	characteristic
8	C₄×C₁₀₁₃	D₄	1	6	yes	complemented
9	C₂×C₁₀₁₃	—	4	4	no	—
10	C₂×C₁₀₁₃	C₂×D₄	1	3	yes	—
11	C₁₀₁₃	#127	1	1	yes	characteristic, direct product factor, Sylow
12	#127	C₁₀₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×D₄	C₂×C₁₀₁₃	1	6	yes	complemented
14	C₄²	C₂×C₁₀₁₃	1	1	yes	characteristic, complemented
15	C₂³	C₂²×C₁₀₁₃	1	4	yes	—
16	D₄	—	2	12	no	—
17	C₂×C₄	C₂²×C₁₀₁₃	1	3	yes	—
18	C₂²	—	2	12	no	—
19	C₂²	C₂³×C₁₀₁₃	1	1	yes	characteristic
20	C₄	D₄×C₁₀₁₃	1	6	yes	complemented
21	C₂	—	4	4	no	—
22	C₂	C₂×D₄×C₁₀₁₃	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₀₁₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₁₀₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁₃ ◁ G

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.