Subgroups — C₃×D₅₅₅₁ #45686554

Order 33306.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₅₅₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₃×C₆₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₇₉₃	—	7	1	no	maximal, Hall
5	C₃×D₄₂₇	—	13	1	no	maximal, Hall
6	C₃×C₁₃×C₆₁	D₇	1	1	yes	characteristic, complemented, Hall
7	D₇₉₃	—	7	1	no	Hall
8	C₃×C₇×C₆₁	D₁₃	1	1	yes	characteristic, complemented, Hall
9	D₄₂₇	—	13	1	no	Hall
10	C₁₃×C₆₁	C₃×D₇	1	1	yes	characteristic, complemented, Hall
11	C₃×D₉₁	—	61	1	no	maximal, Hall
12	C₇×C₆₁	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
13	C₃×D₆₁	—	91	1	no	Hall
14	C₃×C₇×C₁₃	D₆₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₆₁	D₉₁	1	1	yes	characteristic, complemented, Hall
16	D₉₁	—	61	1	no	Hall
17	D₆₁	—	91	1	no	Hall
18	C₇×C₁₃	C₃×D₆₁	1	1	yes	characteristic, complemented, Hall
19	C₃×D₁₃	—	427	1	no	Hall
20	C₆₁	C₃×D₉₁	1	1	yes	characteristic, complemented, Sylow
21	C₃×D₇	—	793	1	no	Hall
22	C₃×C₁₃	D₄₂₇	1	1	yes	characteristic, complemented, Hall
23	D₁₃	—	427	1	no	Hall
24	C₃×C₇	D₇₉₃	1	1	yes	characteristic, complemented, Hall
25	D₇	—	793	1	no	Hall
26	C₁₃	C₃×D₄₂₇	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₃×D₇₉₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	5551	1	no	Hall
29	C₃	D₅₅₅₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	5551	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₅₅₅₁
commutator, cosocle, hypocenter	C₇×C₁₃×C₆₁	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₆₁	C₂
LCS	G ▷ C₇×C₁₃×C₆₁
UCS	C₁ ◁ C₃

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.