Subgroups — C₃₁⋊#11744634 #42124512

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	C₃⋊(C₃₁⋊#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	C₃⋊(C₃₁⋊AGL(1,𝔽₅))	—	15	2	no	—
8	C₃₁×C₅⋊D₅	D₉	1	1	yes	characteristic
9	Dic₂₇₉	—	25	1	no	maximal, Hall
10	C₃×D₅×C₃₁	—	15	2	no	—
11	#11744634	—	31	1	no	maximal, Hall
12	C₅²×C₃₁	Dic₉	1	1	yes	characteristic, complemented, Hall
13	C₃₁⋊AGL(1,𝔽₅)	—	45	2	no	—
14	C₂×C₉×C₃₁	—	25	1	no	—
15	C₃×C₅×C₃₁	—	3	2	no	—
16	(C₅⋊D₅)⋊C₉	D₃₁	1	1	yes	characteristic
17	Dic₉₃	—	75	1	no	—
18	D₅×C₃₁	—	15	2	no	—
19	C₃⋊#1044	—	93	1	no	—
20	C₉×C₃₁	—	25	1	no	Hall
21	C₅²⋊C₉	Dic₃₁	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₃₁	—	25	1	no	—
23	C₅×C₃₁	—	3	2	no	—
24	C₃×C₅⋊D₅	D₉₃	1	1	yes	characteristic
25	Dic₃₁	—	225	1	no	Hall
26	#1044	—	279	1	no	Hall
27	C₃×C₃₁	#64480	1	1	yes	characteristic
28	C₃×C₅²	Dic₉₃	1	1	yes	characteristic
29	C₂×C₃₁	—	25	1	no	—
30	ΓL(1,𝔽₁₆)	—	465	2	no	—
31	C₅⋊D₅	D₂₇₉	1	1	yes	characteristic
32	Dic₉	—	775	1	no	Hall
33	C₃₁	#11744634	1	1	yes	characteristic, complemented, Sylow
34	C₃×D₅	—	15	2	no	—
35	C₅²	Dic₂₇₉	1	1	yes	characteristic, complemented, Sylow
36	AGL(1,𝔽₅)	—	1395	2	no	—
37	C₂×C₉	—	25	1	no	—
38	C₃×C₅	—	3	2	no	—
39	Dic₃	—	2325	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	—	6975	1	no	Sylow
45	C₃	C₃₁⋊#64480	1	1	yes	characteristic
46	C₂	—	25	1	no	—

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

Complements

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

N	H ≅ G/N	type
3. C₃₁×C₅²⋊C₉	C₄	semidirect
12. C₅²×C₃₁	Dic₉	semidirect
21. C₅²⋊C₉	Dic₃₁	semidirect
33. C₃₁	#11744634	semidirect
35. C₅²	Dic₂₇₉	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
C₃⋊(C₃₁⋊#1044)	3
Dic₂₇₉	25
#11744634	31

Subgroups — C31⋊#11744634 #42124512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁⋊#11744634 #42124512