Subgroups — C₂₅×#157×C₃₇ #45685913

Order 33300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₂₅×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₂₅×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₅×#157×C₃₇	C₅	1	1	yes	maximal, characteristic
4	D₃×C₂₅×C₃₇	—	6	2	no	—
5	C₄×C₂₅×C₃₇	—	9	1	no	maximal, Hall
6	C₅×C₃⋊D₃×C₃₇	C₂×C₅	1	1	yes	characteristic
7	C₃×C₂₅×C₃₇	—	2	2	no	—
8	C₂×C₂₅×C₃₇	—	9	1	no	—
9	C₃²×C₅×C₃₇	C₄×C₅	1	1	yes	characteristic
10	#157×C₃₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
11	C₅×D₃×C₃₇	—	6	2	no	—
12	C₂₅×C₃₇	#157	1	1	yes	characteristic, direct product factor, Hall
13	C₂₅×#157	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₄×C₅×C₃₇	—	9	1	no	—
15	C₃⋊D₃×C₃₇	C₂×C₂₅	1	1	yes	characteristic
16	C₃×C₅×C₃₇	—	2	2	no	—
17	C₃⋊D₃×C₂₅	C₂×C₃₇	1	1	yes	characteristic
18	C₂×C₅×C₃₇	—	9	1	no	—
19	C₃²×C₃₇	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₂₅	C₄×C₃₇	1	1	yes	characteristic, complemented, Hall
21	D₃×C₃₇	—	6	2	no	—
22	C₅×C₃₇	C₅×#157	1	1	yes	characteristic
23	C₅×#157	C₅×C₃₇	1	1	yes	characteristic
24	D₃×C₂₅	—	6	2	no	—
25	C₄×C₃₇	—	9	1	no	Hall
26	C₃×C₃₇	—	2	2	no	—
27	C₄×C₂₅	—	9	1	no	Hall
28	C₅×C₃⋊D₃	C₂×C₅×C₃₇	1	1	yes	characteristic
29	C₃×C₂₅	—	2	2	no	—
30	C₂×C₃₇	—	9	1	no	—
31	C₂×C₂₅	—	9	1	no	—
32	C₃²×C₅	C₄×C₅×C₃₇	1	1	yes	characteristic
33	C₃₇	C₂₅×#157	1	1	yes	characteristic, direct product factor, Sylow
34	#157	C₂₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
35	C₅×D₃	—	6	2	no	—
36	C₂₅	#157×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
37	C₄×C₅	—	9	1	no	—
38	C₃⋊D₃	C₂×C₂₅×C₃₇	1	1	yes	characteristic
39	C₃×C₅	—	2	2	no	—
40	C₂×C₅	—	9	1	no	—
41	C₃²	C₄×C₂₅×C₃₇	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	6	2	no	—
43	C₅	C₅×#157×C₃₇	1	1	yes	characteristic
44	C₄	—	9	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₂₅×C₃₇	#157
commutator, hypocenter	C₃²	C₄×C₂₅×C₃₇
Frattini	C₅	C₅×#157×C₃₇
Fitting	C₃²×C₂₅×C₃₇	C₄
socle	C₃²×C₅×C₃₇	C₄×C₅
prime radical	C₅×C₃⋊D₃×C₃₇	C₂×C₅
cosocle	C₅×C₃⋊D₃	C₂×C₅×C₃₇
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂₅×C₃₇

Complements

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

N	H ≅ G/N	type
2. C₃²×C₂₅×C₃₇	C₄	semidirect
10. #157×C₃₇	C₂₅	direct (N × H)
12. C₂₅×C₃₇	#157	direct (N × H)
13. C₂₅×#157	C₃₇	direct (N × H)
19. C₃²×C₃₇	C₄×C₂₅	semidirect
20. C₃²×C₂₅	C₄×C₃₇	semidirect
33. C₃₇	C₂₅×#157	direct (N × H)
34. #157	C₂₅×C₃₇	direct (N × H)
36. C₂₅	#157×C₃₇	direct (N × H)
41. C₃²	C₄×C₂₅×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₃×C₂₅×C₃₇	2
C₅×#157×C₃₇	5
C₄×C₂₅×C₃₇	9
C₂₅×#157	37

Subgroups — C25×#157×C37 #45685913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#157×C₃₇ #45685913