Subgroups — C₂×D₈₀₁₅ #44545446

Order 32060.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₀₁₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇×C₂₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×C₂₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₆₀₃	—	5	1	no	maximal, Hall
5	C₂×D₁₁₄₅	—	7	1	no	maximal, Hall
6	C₂×C₇×C₂₂₉	D₅	1	1	yes	characteristic, complemented
7	D₁₆₀₃	—	5	2	no	—
8	C₂×C₅×C₂₂₉	D₇	1	1	yes	characteristic, complemented
9	D₁₁₄₅	—	7	2	no	—
10	C₇×C₂₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₂₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
12	C₂×D₂₂₉	—	35	1	no	Hall
13	C₂×C₂₂₉	D₃₅	1	1	yes	characteristic, complemented
14	D₂₂₉	—	35	2	no	—
15	C₂₂₉	C₂×D₃₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₃₅	—	229	1	no	maximal, Hall
17	C₂×C₅×C₇	D₂₂₉	1	1	yes	characteristic, complemented
18	D₃₅	—	229	2	no	—
19	C₅×C₇	C₂×D₂₂₉	1	1	yes	characteristic, complemented, Hall
20	C₂×D₇	—	1145	1	no	Hall
21	C₂×D₅	—	1603	1	no	Hall
22	C₂×C₇	D₁₁₄₅	1	1	yes	characteristic, complemented
23	D₇	—	1145	2	no	—
24	C₂×C₅	D₁₆₀₃	1	1	yes	characteristic, complemented
25	D₅	—	1603	2	no	—
26	C₇	C₂×D₁₁₄₅	1	1	yes	characteristic, complemented, Sylow
27	C₅	C₂×D₁₆₀₃	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	8015	1	no	Sylow
29	C₂	—	8015	2	no	—
30	C₂	D₈₀₁₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₈₀₁₅
commutator, cosocle, hypocenter	C₅×C₇×C₂₂₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₂₂₉	C₂
LCS	G ▷ C₅×C₇×C₂₂₉
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.