Subgroups — C₃₁×#11744621 #42124451

Order 27900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×C₃⋊D₇₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₂₅×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃₁×#4380	—	5	1	no	maximal
4	C₃₁×D₇₅	—	6	2	no	—
5	C₃₁×#1035	—	9	1	no	maximal, Hall
6	C₃₁×C₃⋊D₁₅	—	5	1	no	—
7	C₃×C₂₅×C₃₁	—	2	2	no	—
8	C₃₁×D₂₅	—	9	1	no	—
9	C₃²×C₅×C₃₁	AGL(1,𝔽₅)	1	1	yes	characteristic
10	C₃₁×#157	—	25	1	no	Hall
11	D₁₅×C₃₁	—	30	2	no	—
12	#11744621	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂₅×C₃₁	#157	1	1	yes	characteristic, complemented, Hall
14	AGL(1,𝔽₅)×C₃₁	—	45	1	no	—
15	C₃⋊D₃×C₃₁	—	25	1	no	—
16	C₃×C₅×C₃₁	—	2	2	no	—
17	C₃⋊D₇₅	C₂×C₃₁	1	1	yes	characteristic
18	D₅×C₃₁	—	45	1	no	—
19	C₃²×C₃₁	#1035	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₂₅	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
21	D₃×C₃₁	—	150	2	no	—
22	#4380	—	5	1	no	—
23	C₅×C₃₁	#4380	1	1	yes	characteristic
24	D₇₅	—	6	2	no	—
25	C₄×C₃₁	—	225	1	no	Hall
26	#1035	—	9	1	no	Hall
27	C₃×C₃₁	—	2	2	no	—
28	C₃⋊D₁₅	—	5	1	no	—
29	C₃×C₂₅	—	2	2	no	—
30	C₂×C₃₁	—	225	1	no	—
31	D₂₅	—	9	1	no	—
32	C₃²×C₅	AGL(1,𝔽₅)×C₃₁	1	1	yes	characteristic
33	#157	—	25	1	no	Hall
34	C₃₁	#11744621	1	1	yes	characteristic, direct product factor, Sylow
35	D₁₅	—	30	2	no	—
36	C₂₅	C₃₁×#157	1	1	yes	characteristic, complemented, Sylow
37	AGL(1,𝔽₅)	—	45	1	no	—
38	C₃⋊D₃	—	25	1	no	—
39	C₃×C₅	—	2	2	no	—
40	D₅	—	45	1	no	—
41	C₃²	C₃₁×#1035	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	150	2	no	—
43	C₅	C₃₁×#4380	1	1	yes	characteristic
44	C₄	—	225	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	225	1	no	—

	subgroup	G/H
center, hypercenter	C₃₁	#11744621
commutator, hypocenter	C₃²×C₂₅	C₄×C₃₁
Frattini	C₅	C₃₁×#4380
Fitting	C₃²×C₂₅×C₃₁	C₄
socle	C₃²×C₅×C₃₁	AGL(1,𝔽₅)
prime radical	C₃₁×C₃⋊D₇₅	C₂
cosocle	C₃⋊D₇₅	C₂×C₃₁
LCS	G ▷ C₃²×C₂₅
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
2. C₃²×C₂₅×C₃₁	C₄	semidirect
12. #11744621	C₃₁	direct (N × H)
13. C₂₅×C₃₁	#157	semidirect
19. C₃²×C₃₁	#1035	semidirect
20. C₃²×C₂₅	C₄×C₃₁	semidirect
34. C₃₁	#11744621	direct (N × H)
36. C₂₅	C₃₁×#157	semidirect
41. C₃²	C₃₁×#1035	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×C₃⋊D₇₅	2
C₃₁×#4380	5
C₃₁×#1035	9
#11744621	31

Subgroups — C31×#11744621 #42124451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#11744621 #42124451