Subgroups — C₅²×D₃₂ #13099652

Order 1600.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₁₆	C₂	1	2	yes	maximal, complemented
2	C₅²×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×D₈	—	2	2	no	—
4	C₅²×C₁₆	C₂²	1	1	yes	characteristic
5	C₅×D₃₂	C₅	1	6	yes	maximal, direct product factor
6	C₅²×D₄	—	4	2	no	—
7	C₅²×C₈	D₄	1	1	yes	characteristic
8	C₅×D₁₆	C₂×C₅	1	12	yes	complemented
9	C₅×C₃₂	C₂×C₅	1	6	yes	complemented
10	C₂²×C₅²	—	8	2	no	—
11	C₄×C₅²	D₈	1	1	yes	characteristic
12	C₅×D₈	—	2	12	no	—
13	C₅×C₁₆	C₂²×C₅	1	6	yes	—
14	D₃₂	C₅²	1	1	yes	characteristic, direct product factor, Sylow
15	C₂×C₅²	—	16	2	no	—
16	C₂×C₅²	D₁₆	1	1	yes	characteristic
17	C₅×D₄	—	4	12	no	—
18	C₅×C₈	C₅×D₄	1	6	yes	—
19	D₁₆	C₂×C₅²	1	2	yes	complemented
20	C₃₂	C₂×C₅²	1	1	yes	characteristic, complemented
21	C₅²	D₃₂	1	1	yes	characteristic, direct product factor, Sylow
22	C₂²×C₅	—	8	12	no	—
23	C₄×C₅	C₅×D₈	1	6	yes	—
24	D₈	—	2	2	no	—
25	C₁₆	C₂²×C₅²	1	1	yes	characteristic
26	C₂×C₅	—	16	12	no	—
27	C₂×C₅	C₅×D₁₆	1	6	yes	—
28	D₄	—	4	2	no	—
29	C₈	C₅²×D₄	1	1	yes	characteristic
30	C₅	C₅×D₃₂	1	6	yes	direct product factor
31	C₂²	—	8	2	no	—
32	C₄	C₅²×D₈	1	1	yes	characteristic
33	C₂	—	16	2	no	—
34	C₂	C₅²×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅²	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂²×C₅²
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅² ◁ C₄×C₅² ◁ C₅²×C₈ ◁ C₅²×C₁₆ ◁ 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.