Subgroups — C₃×A₄×C₂₅×C₃₇ #45685924

Order 33300.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₄×C₂₅×C₃₇	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₂₅×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₂₅×C₃₇	—	4	1	no	maximal, Hall
4	C₃×C₅×A₄×C₃₇	C₅	1	1	yes	maximal, characteristic
5	C₂×C₃×C₂₅×C₃₇	—	3	1	no	—
6	C₂²×C₂₅×C₃₇	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₂₅×C₃₇	—	4	3	no	—
8	C₃×C₂₅×C₃₇	A₄	1	1	yes	characteristic, direct product factor
9	C₅×A₄×C₃₇	C₃×C₅	1	3	yes	—
10	C₂²×C₃×C₅×C₃₇	C₃×C₅	1	1	yes	characteristic
11	C₂×C₂₅×C₃₇	—	3	1	no	—
12	C₃²×C₅×C₃₇	—	4	1	no	—
13	C₃×A₄×C₃₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₅×C₃₇	—	3	1	no	—
15	C₂₅×C₃₇	C₃×A₄	1	1	yes	characteristic, direct product factor, Hall
16	C₃×A₄×C₂₅	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₅×C₃₇	C₃²×C₅	1	1	yes	characteristic
18	C₃×C₅×C₃₇	—	4	3	no	—
19	C₃×C₅×C₃₇	C₅×A₄	1	1	yes	characteristic
20	C₂²×C₃×C₃₇	C₃×C₂₅	1	1	yes	characteristic, complemented
21	A₄×C₃₇	C₃×C₂₅	1	3	yes	direct product factor
22	C₂×C₅×C₃₇	—	3	1	no	—
23	C₃²×C₃₇	—	4	1	no	Hall
24	C₂²×C₃×C₂₅	C₃×C₃₇	1	1	yes	characteristic, complemented
25	A₄×C₂₅	C₃×C₃₇	1	3	yes	direct product factor
26	C₃²×C₂₅	—	4	1	no	Hall
27	C₂×C₃×C₃₇	—	3	1	no	—
28	C₅×C₃₇	C₃×C₅×A₄	1	1	yes	characteristic
29	C₃×C₅×A₄	C₅×C₃₇	1	1	yes	characteristic
30	C₂×C₃×C₂₅	—	3	1	no	—
31	C₂²×C₃₇	C₃²×C₂₅	1	1	yes	characteristic, complemented, Hall
32	C₃×C₃₇	—	4	3	no	—
33	C₃×C₃₇	A₄×C₂₅	1	1	yes	characteristic, direct product factor
34	C₂²×C₂₅	C₃²×C₃₇	1	1	yes	characteristic, complemented, Hall
35	C₃×C₂₅	—	4	3	no	—
36	C₃×C₂₅	A₄×C₃₇	1	1	yes	characteristic, direct product factor
37	C₂×C₃₇	—	3	1	no	—
38	C₂²×C₃×C₅	C₃×C₅×C₃₇	1	1	yes	characteristic
39	C₅×A₄	C₃×C₅×C₃₇	1	3	yes	—
40	C₂×C₂₅	—	3	1	no	—
41	C₃²×C₅	—	4	1	no	—
42	C₃₇	C₃×A₄×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
43	C₃×A₄	C₂₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
44	C₂×C₃×C₅	—	3	1	no	—
45	C₂₅	C₃×A₄×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
46	C₂²×C₅	C₃²×C₅×C₃₇	1	1	yes	characteristic
47	C₃×C₅	—	4	3	no	—
48	C₃×C₅	C₅×A₄×C₃₇	1	1	yes	characteristic
49	C₂²×C₃	C₃×C₂₅×C₃₇	1	1	yes	characteristic, complemented
50	A₄	C₃×C₂₅×C₃₇	1	3	yes	direct product factor
51	C₂×C₅	—	3	1	no	—
52	C₃²	—	4	1	no	Sylow
53	C₂×C₃	—	3	1	no	—
54	C₅	C₃×C₅×A₄×C₃₇	1	1	yes	characteristic
55	C₂²	C₃²×C₂₅×C₃₇	1	1	yes	characteristic, complemented, Sylow
56	C₃	—	4	3	no	—
57	C₃	A₄×C₂₅×C₃₇	1	1	yes	characteristic, direct product factor
58	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₂₅×C₃₇	A₄
commutator, hypocenter	C₂²	C₃²×C₂₅×C₃₇
Frattini	C₅	C₃×C₅×A₄×C₃₇
Fitting	C₂²×C₃×C₂₅×C₃₇	C₃
socle	C₂²×C₃×C₅×C₃₇	C₃×C₅
prime radical	C₃×C₅×A₄×C₃₇	C₅
cosocle	C₂²×C₅	C₃²×C₅×C₃₇
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₂₅×C₃₇

Complements

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

N	H ≅ G/N	type
1. A₄×C₂₅×C₃₇	C₃	direct (N × H)
2. C₂²×C₃×C₂₅×C₃₇	C₃	semidirect
6. C₂²×C₂₅×C₃₇	C₃²	semidirect
8. C₃×C₂₅×C₃₇	A₄	direct (N × H)
13. C₃×A₄×C₃₇	C₂₅	direct (N × H)
15. C₂₅×C₃₇	C₃×A₄	direct (N × H)
16. C₃×A₄×C₂₅	C₃₇	direct (N × H)
20. C₂²×C₃×C₃₇	C₃×C₂₅	semidirect
21. A₄×C₃₇	C₃×C₂₅	direct (N × H)
24. C₂²×C₃×C₂₅	C₃×C₃₇	semidirect
25. A₄×C₂₅	C₃×C₃₇	direct (N × H)
31. C₂²×C₃₇	C₃²×C₂₅	semidirect
33. C₃×C₃₇	A₄×C₂₅	direct (N × H)
34. C₂²×C₂₅	C₃²×C₃₇	semidirect
36. C₃×C₂₅	A₄×C₃₇	direct (N × H)
42. C₃₇	C₃×A₄×C₂₅	direct (N × H)
43. C₃×A₄	C₂₅×C₃₇	direct (N × H)
45. C₂₅	C₃×A₄×C₃₇	direct (N × H)
49. C₂²×C₃	C₃×C₂₅×C₃₇	semidirect
50. A₄	C₃×C₂₅×C₃₇	direct (N × H)
55. C₂²	C₃²×C₂₅×C₃₇	semidirect
57. C₃	A₄×C₂₅×C₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
A₄×C₂₅×C₃₇	3
C₂²×C₃×C₂₅×C₃₇	3
C₃²×C₂₅×C₃₇	4
C₃×C₅×A₄×C₃₇	5
C₃×A₄×C₂₅	37

Subgroups — C3×A4×C25×C37 #45685924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×A₄×C₂₅×C₃₇ #45685924