Subgroups — D₁₅₅⋊D₅₃ #45659592

Order 32860.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×D₁₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×D₂₆₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₁₆₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₃₁×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃₁×D₅₃	—	5	1	no	maximal, Hall
6	D₁₆₄₃	D₅	1	1	yes	characteristic, complemented
7	C₃₁×D₅₃	—	5	1	no	—
8	C₅₃×D₃₁	—	5	1	no	—
9	C₃₁×C₅₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
10	D₅×D₅₃	—	31	1	no	maximal, Hall
11	D₅×D₃₁	—	53	1	no	maximal, Hall
12	D₂₆₅	D₃₁	1	1	yes	characteristic, complemented
13	C₅×D₅₃	—	31	1	no	—
14	D₅×C₅₃	—	31	1	no	—
15	D₁₅₅	D₅₃	1	1	yes	characteristic, complemented
16	C₅×D₃₁	—	53	1	no	—
17	D₅×C₃₁	—	53	1	no	—
18	C₅×C₅₃	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
19	C₂×D₅₃	—	155	1	no	Hall
20	C₅×C₃₁	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
21	C₂×D₃₁	—	265	1	no	Hall
22	C₂×C₅₃	—	155	1	no	—
23	D₅₃	—	5	1	no	—
24	D₅₃	—	31	1	no	—
25	C₂×C₃₁	—	265	1	no	—
26	D₃₁	—	5	1	no	—
27	D₃₁	—	53	1	no	—
28	C₅₃	D₅×D₃₁	1	1	yes	characteristic, complemented, Sylow
29	C₃₁	D₅×D₅₃	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₅	—	1643	1	no	Hall
31	C₂×C₅	—	1643	1	no	—
32	D₅	—	31	1	no	—
33	D₅	—	53	1	no	—
34	C₅	D₃₁×D₅₃	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	8215	1	no	Sylow
36	C₂	—	265	1	no	—
37	C₂	—	1643	1	no	—
38	C₂	—	155	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₃₁×C₅₃	C₂²
LCS	G ▷ C₅×C₃₁×C₅₃
UCS	C₁

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.