Subgroups — D₅₇×C₆₁⋊C₃ #35210010

Order 20862.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×C₆₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₉×C₆₁⋊C₃	—	3	1	no	maximal
3	C₆₁×D₅₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₉×C₆₁	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₉×C₆₁⋊C₃	—	2	1	no	—
6	C₁₉×C₆₁⋊C₃	D₃	1	1	yes	characteristic, complemented
7	D₁₉×C₆₁	—	3	1	no	Hall
8	C₁₉×C₆₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	D₃×C₆₁⋊C₃	—	19	1	no	maximal, Hall
10	C₃×C₆₁⋊C₃	D₁₉	1	1	yes	characteristic, complemented, Hall
11	D₃×C₆₁	—	19	1	no	—
12	C₂×C₆₁⋊C₃	—	57	1	no	—
13	C₃×D₅₇	—	61	1	no	maximal, Hall
14	C₃×C₆₁	C₃×D₁₉	1	1	yes	characteristic, complemented
15	C₆₁⋊C₃	—	2	1	no	—
16	C₆₁⋊C₃	D₅₇	1	1	yes	characteristic, direct product factor
17	C₃²×C₁₉	—	61	1	no	Hall
18	C₂×C₆₁	—	57	1	no	Hall
19	D₅₇	C₆₁⋊C₃	1	1	yes	characteristic, direct product factor
20	C₃×D₁₉	—	183	1	no	—
21	C₆₁	C₃×D₅₇	1	1	yes	characteristic, complemented, Sylow
22	C₃×C₁₉	—	61	1	no	—
23	C₃×C₁₉	—	122	1	no	—
24	C₃×C₁₉	C₂×C₆₁⋊C₃	1	1	yes	characteristic, complemented
25	D₁₉	—	3	1	no	Hall
26	C₁₉	D₃×C₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₃	—	1159	1	no	Hall
28	C₃²	—	61	1	no	Sylow
29	C₂×C₃	—	3477	1	no	—
30	D₃	—	19	1	no	—
31	C₃	—	61	1	no	—
32	C₃	—	122	1	no	—
33	C₃	D₁₉×C₆₁⋊C₃	1	1	yes	characteristic, complemented
34	C₂	—	57	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₉×C₆₁	C₂×C₃
LCS	G ▷ C₃×C₁₉×C₆₁
UCS	C₁

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.