Subgroups — D₃₂×C₅₀₃ #44565784

Order 32192.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆×C₅₀₃	C₂	1	2	yes	maximal, complemented
2	C₃₂×C₅₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×C₅₀₃	—	2	2	no	—
4	C₁₆×C₅₀₃	C₂²	1	1	yes	characteristic
5	D₄×C₅₀₃	—	4	2	no	—
6	C₈×C₅₀₃	D₄	1	1	yes	characteristic
7	C₂²×C₅₀₃	—	8	2	no	—
8	C₄×C₅₀₃	D₈	1	1	yes	characteristic
9	C₂×C₅₀₃	—	16	2	no	—
10	C₂×C₅₀₃	D₁₆	1	1	yes	characteristic
11	C₅₀₃	D₃₂	1	1	yes	characteristic, direct product factor, Sylow
12	D₃₂	C₅₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	D₁₆	C₂×C₅₀₃	1	2	yes	complemented
14	C₃₂	C₂×C₅₀₃	1	1	yes	characteristic, complemented
15	D₈	—	2	2	no	—
16	C₁₆	C₂²×C₅₀₃	1	1	yes	characteristic
17	D₄	—	4	2	no	—
18	C₈	D₄×C₅₀₃	1	1	yes	characteristic
19	C₂²	—	8	2	no	—
20	C₄	D₈×C₅₀₃	1	1	yes	characteristic
21	C₂	—	16	2	no	—
22	C₂	D₁₆×C₅₀₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅₀₃	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂²×C₅₀₃
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₀₃ ◁ C₄×C₅₀₃ ◁ C₈×C₅₀₃ ◁ C₁₆×C₅₀₃ ◁ 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.