Subgroups — C₄×C₅²⋊(C₃₁⋊C₉) #42124367

Order 27900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²⋊(C₃₁⋊C₉)	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅²×C₃₁	C₃	1	1	yes	maximal, characteristic
3	C₅²⋊(C₃₁⋊C₉)	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₅²×C₃₁	C₂×C₃	1	1	yes	characteristic
5	C₄×C₅²×C₃₁	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅²×C₃₁	C₃×C₄	1	1	yes	characteristic
7	C₃×C₄×C₅×C₃₁	—	3	2	no	—
8	C₂×C₅²×C₃₁	C₂×C₉	1	1	yes	characteristic
9	C₄×C₃₁⋊C₉	—	25	1	no	maximal, Hall
10	C₂×C₃×C₅×C₃₁	—	3	2	no	—
11	C₄×C₅²⋊C₉	—	31	1	no	maximal, Hall
12	C₅²×C₃₁	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	C₄×C₅×C₃₁	—	3	2	no	—
14	C₂×C₃₁⋊C₉	—	25	1	no	—
15	C₃×C₅×C₃₁	—	3	2	no	—
16	C₂×C₅²⋊C₉	—	31	1	no	—
17	C₃×C₄×C₃₁	C₅²⋊C₃	1	1	yes	characteristic
18	C₂×C₅×C₃₁	—	3	2	no	—
19	C₃×C₄×C₅²	C₃₁⋊C₃	1	1	yes	characteristic
20	C₃₁⋊C₉	—	25	1	no	Hall
21	C₅²⋊C₉	—	31	1	no	Hall
22	C₂×C₃×C₃₁	C₂×C₅²⋊C₃	1	1	yes	characteristic
23	C₅×C₃₁	—	3	2	no	—
24	C₂×C₃×C₅²	C₂×C₃₁⋊C₃	1	1	yes	characteristic
25	C₄×C₃₁	C₅²⋊C₉	1	1	yes	characteristic, complemented, Hall
26	C₄×C₅²	C₃₁⋊C₉	1	1	yes	characteristic, complemented, Hall
27	C₃×C₃₁	C₄×C₅²⋊C₃	1	1	yes	characteristic
28	C₃×C₅²	C₄×C₃₁⋊C₃	1	1	yes	characteristic
29	C₂×C₃₁	C₂×C₅²⋊C₉	1	1	yes	characteristic
30	C₃×C₄×C₅	—	3	2	no	—
31	C₂×C₅²	C₂×C₃₁⋊C₉	1	1	yes	characteristic
32	C₄×C₉	—	775	1	no	Hall
33	C₃₁	C₄×C₅²⋊C₉	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃×C₅	—	3	2	no	—
35	C₅²	C₄×C₃₁⋊C₉	1	1	yes	characteristic, complemented, Sylow
36	C₄×C₅	—	3	2	no	—
37	C₂×C₉	—	775	1	no	—
38	C₃×C₅	—	3	2	no	—
39	C₃×C₄	C₅²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
40	C₂×C₅	—	3	2	no	—
41	C₉	—	775	1	no	Sylow
42	C₂×C₃	C₂×C₅²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
43	C₅	—	3	2	no	—
44	C₄	C₅²⋊(C₃₁⋊C₉)	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₄×C₅²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
46	C₂	C₂×C₅²⋊(C₃₁⋊C₉)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₅²⋊(C₃₁⋊C₉)	C₄	direct (N × H)
5. C₄×C₅²×C₃₁	C₉	semidirect
12. C₅²×C₃₁	C₄×C₉	semidirect
25. C₄×C₃₁	C₅²⋊C₉	semidirect
26. C₄×C₅²	C₃₁⋊C₉	semidirect
33. C₃₁	C₄×C₅²⋊C₉	semidirect
35. C₅²	C₄×C₃₁⋊C₉	semidirect
44. C₄	C₅²⋊(C₃₁⋊C₉)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅²⋊(C₃₁⋊C₉)	2
C₃×C₄×C₅²×C₃₁	3
C₄×C₃₁⋊C₉	25
C₄×C₅²⋊C₉	31

Subgroups — C4×C52⋊(C31⋊C9) #42124367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅²⋊(C₃₁⋊C₉) #42124367