Subgroups — C₂×C₅²×D₃₀₇ #44502002

Order 30700.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₃₀₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₃₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₃₀₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×D₃₀₇	C₅	1	6	yes	maximal, direct product factor
5	C₂×C₅×C₃₀₇	C₂×C₅	1	6	yes	complemented
6	C₅×D₃₀₇	C₂×C₅	1	12	yes	direct product factor
7	C₅×C₃₀₇	C₂²×C₅	1	6	yes	complemented
8	C₂×D₃₀₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃₀₇	C₂×C₅²	1	1	yes	characteristic, complemented
10	D₃₀₇	C₂×C₅²	1	2	yes	direct product factor
11	C₃₀₇	C₂²×C₅²	1	1	yes	characteristic, complemented, Sylow
12	C₂²×C₅²	—	307	1	no	maximal, Hall
13	C₂×C₅²	—	307	2	no	—
14	C₂×C₅²	D₃₀₇	1	1	yes	characteristic, direct product factor
15	C₅²	C₂×D₃₀₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂²×C₅	—	307	6	no	—
17	C₂×C₅	—	307	12	no	—
18	C₂×C₅	C₅×D₃₀₇	1	6	yes	direct product factor
19	C₅	C₂×C₅×D₃₀₇	1	6	yes	direct product factor
20	C₂²	—	307	1	no	Sylow
21	C₂	—	307	2	no	—
22	C₂	C₅²×D₃₀₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅²	D₃₀₇
commutator, cosocle, hypocenter	C₃₀₇	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₃₀₇	C₂
LCS	G ▷ C₃₀₇
UCS	C₁ ◁ C₂×C₅²

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.