Subgroups — C₂×D₇₈₁₅ #44530482

Order 31260.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₈₁₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₅₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₆₀₅	—	3	1	no	maximal, Hall
4	C₃×C₅×C₅₂₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₅₆₃	—	5	1	no	maximal, Hall
6	C₂×C₅×C₅₂₁	D₃	1	1	yes	characteristic, complemented
7	D₂₆₀₅	—	3	2	no	—
8	C₂×C₃×C₅₂₁	D₅	1	1	yes	characteristic, complemented
9	D₁₅₆₃	—	5	2	no	—
10	C₅×C₅₂₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₅₂₁	—	15	1	no	Hall
12	C₃×C₅₂₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅₂₁	D₁₅	1	1	yes	characteristic, complemented
14	D₅₂₁	—	15	2	no	—
15	C₅₂₁	C₂×D₁₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₁₅	—	521	1	no	maximal, Hall
17	C₂×C₃×C₅	D₅₂₁	1	1	yes	characteristic, complemented
18	D₁₅	—	521	2	no	—
19	C₂×D₅	—	1563	1	no	Hall
20	C₃×C₅	C₂×D₅₂₁	1	1	yes	characteristic, complemented, Hall
21	C₂×D₃	—	2605	1	no	Hall
22	C₂×C₅	D₁₅₆₃	1	1	yes	characteristic, complemented
23	D₅	—	1563	2	no	—
24	C₂×C₃	D₂₆₀₅	1	1	yes	characteristic, complemented
25	D₃	—	2605	2	no	—
26	C₅	C₂×D₁₅₆₃	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	7815	1	no	Sylow
28	C₃	C₂×D₂₆₀₅	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	7815	2	no	—
30	C₂	D₇₈₁₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₇₈₁₅
commutator, cosocle, hypocenter	C₃×C₅×C₅₂₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₅₂₁	C₂
LCS	G ▷ C₃×C₅×C₅₂₁
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.