Subgroups — C₃₇⋊C₃×#3874 #30659270

Order 16650.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²⋊C₃×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₇×#3874	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅×D₅×C₃₇⋊C₃	—	3	1	no	maximal
4	C₅²⋊(C₃₇⋊C₃)	—	2	1	no	—
5	C₃₇×C₅²⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₅²×C₃₇⋊C₃	D₃	1	1	yes	characteristic, complemented
7	C₅×D₅×C₃₇	—	3	1	no	Hall
8	C₂×C₅×C₃₇⋊C₃	—	15	1	no	—
9	D₅×C₃₇⋊C₃	—	3	1	no	—
10	C₅²×C₃₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃×C₃₇⋊C₃	—	25	1	no	maximal, Hall
12	C₅×C₃₇⋊C₃	—	6	1	no	—
13	C₅×C₃₇⋊C₃	—	6	1	no	—
14	C₃×#3874	—	37	1	no	maximal, Hall
15	C₂×C₅×C₃₇	—	15	1	no	—
16	D₅×C₃₇	—	3	1	no	—
17	C₃×C₃₇⋊C₃	—	25	1	no	Hall
18	C₃×C₅²⋊C₃	—	37	1	no	Hall
19	D₃×C₃₇	—	25	1	no	—
20	C₂×C₃₇⋊C₃	—	15	1	no	—
21	C₅×C₃₇	—	3	1	no	—
22	C₅×C₃₇	—	6	1	no	—
23	C₃×C₅×D₅	—	111	1	no	—
24	#3874	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
25	C₃×C₃₇	—	50	1	no	—
26	C₃₇⋊C₃	—	50	1	no	—
27	C₃₇⋊C₃	#3874	1	1	yes	characteristic, direct product factor
28	C₃×C₅²	—	37	1	no	—
29	C₅²⋊C₃	—	74	1	no	—
30	C₅²⋊C₃	C₂×C₃₇⋊C₃	1	1	yes	characteristic, complemented
31	C₂×C₃₇	—	15	1	no	Hall
32	C₅×D₅	—	3	1	no	Hall
33	C₃₇	C₃×#3874	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃×C₅	—	555	1	no	—
35	C₃×D₅	—	111	1	no	—
36	C₅²	D₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
37	C₃×D₃	—	925	1	no	Hall
38	C₃×C₅	—	222	1	no	—
39	C₃×C₅	—	222	1	no	—
40	C₂×C₅	—	15	1	no	—
41	D₅	—	3	1	no	—
42	C₃²	—	1850	1	no	Sylow
43	C₂×C₃	—	555	1	no	—
44	D₃	—	25	1	no	—
45	C₅	—	6	1	no	—
46	C₅	—	6	1	no	—
47	C₃	—	37	1	no	—
48	C₃	—	50	1	no	—
49	C₃	—	1850	1	no	—
50	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃₇×C₅²⋊C₃	C₂×C₃
Fitting, socle	C₅²×C₃₇	C₃×D₃
LCS	G ▷ C₃₇×C₅²⋊C₃
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅²⋊C₃×C₃₇⋊C₃	C₂	semidirect
2. C₃₇×#3874	C₃	semidirect
5. C₃₇×C₅²⋊C₃	C₂×C₃	semidirect
6. C₅²×C₃₇⋊C₃	D₃	semidirect
10. C₅²×C₃₇	C₃×D₃	semidirect
24. #3874	C₃₇⋊C₃	direct (N × H)
27. C₃₇⋊C₃	#3874	direct (N × H)
30. C₅²⋊C₃	C₂×C₃₇⋊C₃	semidirect
33. C₃₇	C₃×#3874	semidirect
36. C₅²	D₃×C₃₇⋊C₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅²⋊C₃×C₃₇⋊C₃	2
C₃₇×#3874	3
C₅×D₅×C₃₇⋊C₃	3
D₃×C₃₇⋊C₃	25
C₃×#3874	37

Subgroups — C37⋊C3×#3874 #30659270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇⋊C₃×#3874 #30659270