Subgroups — C₂×D₉₁₇₅ #49144643

Order 36700.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₉₁₇₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₂₅×C₃₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₅×C₃₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₈₃₅	—	5	1	no	maximal
5	C₂×C₅×C₃₆₇	D₅	1	1	yes	characteristic
6	D₁₈₃₅	—	5	2	no	—
7	C₅×C₃₆₇	C₂×D₅	1	1	yes	characteristic
8	C₂×D₃₆₇	—	25	1	no	Hall
9	C₂×C₃₆₇	D₂₅	1	1	yes	characteristic, complemented
10	D₃₆₇	—	25	2	no	—
11	C₃₆₇	C₂×D₂₅	1	1	yes	characteristic, complemented, Sylow
12	C₂×D₂₅	—	367	1	no	maximal, Hall
13	C₂×C₂₅	D₃₆₇	1	1	yes	characteristic, complemented
14	D₂₅	—	367	2	no	—
15	C₂₅	C₂×D₃₆₇	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₅	—	1835	1	no	—
17	C₂×C₅	D₁₈₃₅	1	1	yes	characteristic
18	D₅	—	1835	2	no	—
19	C₅	C₂×D₁₈₃₅	1	1	yes	characteristic
20	C₂²	—	9175	1	no	Sylow
21	C₂	—	9175	2	no	—
22	C₂	D₉₁₇₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₉₁₇₅
commutator, cosocle, hypocenter	C₂₅×C₃₆₇	C₂²
Frattini	C₅	C₂×D₁₈₃₅
Fitting	C₂×C₂₅×C₃₆₇	C₂
socle	C₂×C₅×C₃₆₇	D₅
LCS	G ▷ C₂₅×C₃₆₇
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.