Subgroups — C₅×D₃₁₇₇ #44540925

Order 31770.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₃₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₀₅₉	—	3	1	no	maximal
3	D₃₁₇₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₃₅₃	D₃	1	1	yes	characteristic
5	C₅×D₃₅₃	—	9	1	no	Hall
6	C₉×C₃₅₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	D₁₀₅₉	—	3	1	no	—
8	C₅×C₃₅₃	D₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₃₅₃	C₅×D₃	1	1	yes	characteristic
10	D₃₅₃	—	9	1	no	Hall
11	C₃₅₃	C₅×D₉	1	1	yes	characteristic, complemented, Sylow
12	C₅×D₉	—	353	1	no	maximal, Hall
13	C₅×C₉	D₃₅₃	1	1	yes	characteristic, complemented, Hall
14	C₅×D₃	—	1059	1	no	—
15	D₉	—	353	1	no	Hall
16	C₃×C₅	D₁₀₅₉	1	1	yes	characteristic
17	C₂×C₅	—	3177	1	no	Hall
18	C₉	C₅×D₃₅₃	1	1	yes	characteristic, complemented, Sylow
19	D₃	—	1059	1	no	—
20	C₅	D₃₁₇₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₅×D₁₀₅₉	1	1	yes	characteristic
22	C₂	—	3177	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₃₁₇₇
commutator, cosocle, hypocenter	C₉×C₃₅₃	C₂×C₅
Frattini	C₃	C₅×D₁₀₅₉
Fitting	C₅×C₉×C₃₅₃	C₂
socle	C₃×C₅×C₃₅₃	D₃
LCS	G ▷ C₉×C₃₅₃
UCS	C₁ ◁ C₅

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.