Subgroups — C₂×C₁₃⋊D₃₂₅ #30683405

Order 16900.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊D₃₂₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₃²×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃²×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅⋊(C₁₃⋊D₁₃)	—	5	1	no	maximal
5	C₂×C₅×C₁₃²	D₅	1	1	yes	characteristic
6	C₅⋊(C₁₃⋊D₁₃)	—	5	2	no	—
7	C₂×D₃₂₅	—	13	14	no	maximal
8	C₅×C₁₃²	C₂×D₅	1	1	yes	characteristic
9	C₂×C₁₃⋊D₁₃	—	25	1	no	Hall
10	C₂×C₁₃×C₂₅	D₁₃	1	14	yes	complemented
11	D₃₂₅	—	13	28	no	—
12	C₂×C₁₃²	D₂₅	1	1	yes	characteristic, complemented
13	C₁₃⋊D₁₃	—	25	2	no	—
14	C₁₃×C₂₅	C₂×D₁₃	1	14	yes	complemented
15	C₂×D₆₅	—	65	14	no	—
16	C₁₃²	C₂×D₂₅	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₅×C₁₃	D₆₅	1	14	yes	—
18	D₆₅	—	65	28	no	—
19	C₂×D₂₅	—	169	1	no	Hall
20	C₅×C₁₃	C₂×D₆₅	1	14	yes	—
21	C₂×D₁₃	—	325	14	no	—
22	C₂×C₂₅	C₁₃⋊D₁₃	1	1	yes	characteristic, complemented
23	D₂₅	—	169	2	no	—
24	C₂×C₁₃	D₃₂₅	1	14	yes	complemented
25	D₁₃	—	325	28	no	—
26	C₂₅	C₂×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×D₅	—	845	1	no	—
28	C₁₃	C₂×D₃₂₅	1	14	yes	complemented
29	C₂×C₅	C₅⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic
30	D₅	—	845	2	no	—
31	C₅	C₂×C₅⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic
32	C₂²	—	4225	1	no	Sylow
33	C₂	—	4225	2	no	—
34	C₂	C₁₃⋊D₃₂₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₁₃⋊D₃₂₅
commutator, cosocle, hypocenter	C₁₃²×C₂₅	C₂²
Frattini	C₅	C₂×C₅⋊(C₁₃⋊D₁₃)
Fitting	C₂×C₁₃²×C₂₅	C₂
socle	C₂×C₅×C₁₃²	D₅
LCS	G ▷ C₁₃²×C₂₅
UCS	C₁ ◁ C₂

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.