Subgroups — C₃₁×#11744634 #42124511

Order 27900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×(C₅⋊D₅)⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃₁×C₃⋊#1044	—	3	1	no	maximal
3	C₃₁×C₅²⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₃₁×C₅⋊D₅	D₃	1	1	yes	characteristic
5	C₃₁×#1044	—	9	1	no	Hall
6	C₃×C₅²×C₃₁	Dic₃	1	1	yes	characteristic
7	C₃₁×ΓL(1,𝔽₁₆)	—	15	2	no	—
8	C₃₁×C₅⋊D₅	D₉	1	1	yes	characteristic
9	C₃₁×Dic₉	—	25	1	no	maximal, Hall
10	C₃×D₅×C₃₁	—	15	2	no	—
11	#11744634	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₅²×C₃₁	Dic₉	1	1	yes	characteristic, complemented, Hall
13	AGL(1,𝔽₅)×C₃₁	—	45	2	no	—
14	C₂×C₉×C₃₁	—	25	1	no	—
15	C₃×C₅×C₃₁	—	3	2	no	—
16	(C₅⋊D₅)⋊C₉	C₂×C₃₁	1	1	yes	characteristic
17	Dic₃×C₃₁	—	75	1	no	—
18	D₅×C₃₁	—	15	2	no	—
19	C₃⋊#1044	—	3	1	no	—
20	C₉×C₃₁	—	25	1	no	Hall
21	C₅²⋊C₉	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₃₁	—	25	1	no	—
23	C₅×C₃₁	—	3	2	no	—
24	C₃×C₅⋊D₅	D₃×C₃₁	1	1	yes	characteristic
25	C₄×C₃₁	—	225	1	no	Hall
26	#1044	—	9	1	no	Hall
27	C₃×C₃₁	#64480	1	1	yes	characteristic
28	C₃×C₅²	Dic₃×C₃₁	1	1	yes	characteristic
29	C₂×C₃₁	—	25	1	no	—
30	ΓL(1,𝔽₁₆)	—	15	2	no	—
31	C₅⋊D₅	D₉×C₃₁	1	1	yes	characteristic
32	Dic₉	—	25	1	no	Hall
33	C₃₁	#11744634	1	1	yes	characteristic, direct product factor, Sylow
34	C₃×D₅	—	15	2	no	—
35	C₅²	C₃₁×Dic₉	1	1	yes	characteristic, complemented, Sylow
36	AGL(1,𝔽₅)	—	45	2	no	—
37	C₂×C₉	—	25	1	no	—
38	C₃×C₅	—	3	2	no	—
39	Dic₃	—	75	1	no	—
40	D₅	—	15	2	no	—
41	C₉	—	25	1	no	Sylow
42	C₂×C₃	—	25	1	no	—
43	C₅	—	3	2	no	—
44	C₄	—	225	1	no	Sylow
45	C₃	C₃₁×#64480	1	1	yes	characteristic
46	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃₁	#11744634
commutator, hypocenter	C₅²⋊C₉	C₄×C₃₁
Frattini	C₃	C₃₁×#64480
Fitting, socle	C₃×C₅²×C₃₁	Dic₃
prime radical	C₃×C₃₁×C₅⋊D₅	D₃
cosocle	(C₅⋊D₅)⋊C₉	C₂×C₃₁
LCS	G ▷ C₅²⋊C₉
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
3. C₃₁×C₅²⋊C₉	C₄	semidirect
11. #11744634	C₃₁	direct (N × H)
12. C₅²×C₃₁	Dic₉	semidirect
21. C₅²⋊C₉	C₄×C₃₁	semidirect
33. C₃₁	#11744634	direct (N × H)
35. C₅²	C₃₁×Dic₉	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×(C₅⋊D₅)⋊C₉	2
C₃₁×C₃⋊#1044	3
C₃₁×Dic₉	25
#11744634	31

Subgroups — C31×#11744634 #42124511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#11744634 #42124511