Subgroups — C₆₁×D₂₅₅ #44527445

Order 31110.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₇×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₆₁×D₈₅	—	3	1	no	maximal, Hall
3	C₆₁×D₅₁	—	5	1	no	maximal, Hall
4	C₅×C₁₇×C₆₁	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₇×C₆₁	D₅	1	1	yes	characteristic, complemented, Hall
6	D₁₇×C₆₁	—	15	1	no	Hall
7	D₁₅×C₆₁	—	17	1	no	maximal, Hall
8	C₁₇×C₆₁	D₁₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×C₆₁	D₁₇	1	1	yes	characteristic, complemented, Hall
10	D₅×C₆₁	—	51	1	no	Hall
11	D₂₅₅	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	D₃×C₆₁	—	85	1	no	Hall
13	C₅×C₆₁	D₅₁	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅×C₁₇	C₂×C₆₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₆₁	D₈₅	1	1	yes	characteristic, complemented, Hall
16	D₈₅	—	3	1	no	Hall
17	C₂×C₆₁	—	255	1	no	Hall
18	D₅₁	—	5	1	no	Hall
19	C₅×C₁₇	D₃×C₆₁	1	1	yes	characteristic, complemented, Hall
20	C₆₁	D₂₅₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₃×C₁₇	D₅×C₆₁	1	1	yes	characteristic, complemented, Hall
22	D₁₇	—	15	1	no	Hall
23	D₁₅	—	17	1	no	Hall
24	C₁₇	D₁₅×C₆₁	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₅	D₁₇×C₆₁	1	1	yes	characteristic, complemented, Hall
26	D₅	—	51	1	no	Hall
27	D₃	—	85	1	no	Hall
28	C₅	C₆₁×D₅₁	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₆₁×D₈₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	255	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₆₁	D₂₅₅
commutator, cosocle, hypocenter	C₃×C₅×C₁₇	C₂×C₆₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₆₁	C₂
LCS	G ▷ C₃×C₅×C₁₇
UCS	C₁ ◁ C₆₁

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.