Subgroups — C₂₅×C₃₁×#157 #42124449

Order 27900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₂₅×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₂₅×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₅×C₃₁×#157	C₅	1	1	yes	maximal, characteristic
4	D₃×C₂₅×C₃₁	—	6	2	no	—
5	C₄×C₂₅×C₃₁	—	9	1	no	maximal, Hall
6	C₅×C₃⋊D₃×C₃₁	C₂×C₅	1	1	yes	characteristic
7	C₃×C₂₅×C₃₁	—	2	2	no	—
8	C₂×C₂₅×C₃₁	—	9	1	no	—
9	C₃²×C₅×C₃₁	C₄×C₅	1	1	yes	characteristic
10	C₃₁×#157	C₂₅	1	1	yes	characteristic, direct product factor, Hall
11	C₅×D₃×C₃₁	—	6	2	no	—
12	C₂₅×#157	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂₅×C₃₁	#157	1	1	yes	characteristic, direct product factor, Hall
14	C₄×C₅×C₃₁	—	9	1	no	—
15	C₃⋊D₃×C₃₁	C₂×C₂₅	1	1	yes	characteristic
16	C₃×C₅×C₃₁	—	2	2	no	—
17	C₃⋊D₃×C₂₅	C₂×C₃₁	1	1	yes	characteristic
18	C₂×C₅×C₃₁	—	9	1	no	—
19	C₃²×C₃₁	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₂₅	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
21	D₃×C₃₁	—	6	2	no	—
22	C₅×#157	C₅×C₃₁	1	1	yes	characteristic
23	C₅×C₃₁	C₅×#157	1	1	yes	characteristic
24	D₃×C₂₅	—	6	2	no	—
25	C₄×C₃₁	—	9	1	no	Hall
26	C₄×C₂₅	—	9	1	no	Hall
27	C₃×C₃₁	—	2	2	no	—
28	C₅×C₃⋊D₃	C₂×C₅×C₃₁	1	1	yes	characteristic
29	C₃×C₂₅	—	2	2	no	—
30	C₂×C₃₁	—	9	1	no	—
31	C₂×C₂₅	—	9	1	no	—
32	C₃²×C₅	C₄×C₅×C₃₁	1	1	yes	characteristic
33	#157	C₂₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
34	C₃₁	C₂₅×#157	1	1	yes	characteristic, direct product factor, Sylow
35	C₅×D₃	—	6	2	no	—
36	C₂₅	C₃₁×#157	1	1	yes	characteristic, direct product factor, Sylow
37	C₄×C₅	—	9	1	no	—
38	C₃⋊D₃	C₂×C₂₅×C₃₁	1	1	yes	characteristic
39	C₃×C₅	—	2	2	no	—
40	C₂×C₅	—	9	1	no	—
41	C₃²	C₄×C₂₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	6	2	no	—
43	C₅	C₅×C₃₁×#157	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×C₃₁	#157
commutator, hypocenter	C₃²	C₄×C₂₅×C₃₁
Frattini	C₅	C₅×C₃₁×#157
Fitting	C₃²×C₂₅×C₃₁	C₄
socle	C₃²×C₅×C₃₁	C₄×C₅
prime radical	C₅×C₃⋊D₃×C₃₁	C₂×C₅
cosocle	C₅×C₃⋊D₃	C₂×C₅×C₃₁
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂₅×C₃₁

Complements

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

N	H ≅ G/N	type
2. C₃²×C₂₅×C₃₁	C₄	semidirect
10. C₃₁×#157	C₂₅	direct (N × H)
12. C₂₅×#157	C₃₁	direct (N × H)
13. C₂₅×C₃₁	#157	direct (N × H)
19. C₃²×C₃₁	C₄×C₂₅	semidirect
20. C₃²×C₂₅	C₄×C₃₁	semidirect
33. #157	C₂₅×C₃₁	direct (N × H)
34. C₃₁	C₂₅×#157	direct (N × H)
36. C₂₅	C₃₁×#157	direct (N × H)
41. C₃²	C₄×C₂₅×C₃₁	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×C₃₁	2
C₅×C₃₁×#157	5
C₄×C₂₅×C₃₁	9
C₂₅×#157	31

Subgroups — C25×C31×#157 #42124449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×C₃₁×#157 #42124449