Subgroups — C₉⋊(Dic₃₁⋊C₂₅) #42124259

Order 27900.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₃₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(Dic₃₁⋊C₂₅)	—	3	1	no	maximal
3	C₉×C₃₁⋊C₂₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅×Dic₂₇₉	C₅	1	1	yes	maximal, characteristic
5	C₂×C₃×C₃₁⋊C₂₅	D₃	1	1	yes	characteristic
6	Dic₃₁⋊C₂₅	—	9	1	no	Hall
7	C₂×C₅×C₉×C₃₁	C₂×C₅	1	1	yes	characteristic
8	C₃×C₃₁⋊C₂₅	Dic₃	1	1	yes	characteristic
9	C₅×Dic₉₃	—	3	1	no	—
10	C₂×C₃₁⋊C₂₅	D₉	1	1	yes	characteristic
11	C₅×C₉×C₃₁	C₄×C₅	1	1	yes	characteristic
12	Dic₂₇₉	C₂₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₅×C₃₁	C₅×D₃	1	1	yes	characteristic
14	C₂₅×Dic₉	—	31	1	no	maximal, Hall
15	C₃₁⋊C₂₅	Dic₉	1	1	yes	characteristic, complemented, Hall
16	C₅×Dic₃₁	—	9	1	no	—
17	C₂×C₉×C₃₁	C₂×C₂₅	1	1	yes	characteristic
18	C₃×C₅×C₃₁	C₅×Dic₃	1	1	yes	characteristic
19	C₂×C₉×C₂₅	—	31	1	no	—
20	Dic₉₃	—	3	1	no	—
21	C₂×C₅×C₃₁	C₅×D₉	1	1	yes	characteristic
22	Dic₃×C₂₅	—	93	1	no	—
23	C₉×C₃₁	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
24	C₉×C₂₅	—	31	1	no	Hall
25	C₂×C₃×C₃₁	D₃×C₂₅	1	1	yes	characteristic
26	C₅×Dic₉	—	31	1	no	—
27	C₅×C₃₁	C₅×Dic₉	1	1	yes	characteristic
28	C₂×C₃×C₂₅	—	31	1	no	—
29	Dic₃₁	—	9	1	no	Hall
30	C₄×C₂₅	—	279	1	no	Hall
31	C₃×C₃₁	Dic₃×C₂₅	1	1	yes	characteristic
32	C₂×C₅×C₉	D₃₁⋊C₅	1	1	yes	characteristic
33	C₃×C₂₅	—	31	1	no	—
34	C₂×C₃₁	D₉×C₂₅	1	1	yes	characteristic
35	C₅×Dic₃	—	93	1	no	—
36	C₂×C₂₅	—	31	1	no	—
37	C₅×C₉	Dic₃₁⋊C₅	1	1	yes	characteristic
38	Dic₉	—	31	1	no	Hall
39	C₃₁	C₂₅×Dic₉	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃×C₅	C₃⋊(D₃₁⋊C₅)	1	1	yes	characteristic
41	C₂₅	—	31	1	no	Sylow
42	C₄×C₅	—	279	1	no	—
43	C₂×C₉	D₃₁⋊C₂₅	1	1	yes	characteristic
44	C₃×C₅	C₃⋊(Dic₃₁⋊C₅)	1	1	yes	characteristic
45	Dic₃	—	93	1	no	—
46	C₂×C₅	C₉⋊(D₃₁⋊C₅)	1	1	yes	characteristic
47	C₉	Dic₃₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	C₃⋊(D₃₁⋊C₂₅)	1	1	yes	characteristic
49	C₅	C₉⋊(Dic₃₁⋊C₅)	1	1	yes	characteristic
50	C₄	—	279	1	no	Sylow
51	C₃	C₃⋊(Dic₃₁⋊C₂₅)	1	1	yes	characteristic
52	C₂	C₉⋊(D₃₁⋊C₂₅)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	C₉⋊(D₃₁⋊C₅)
commutator, hypocenter	C₉×C₃₁	C₄×C₂₅
Frattini	C₂×C₃×C₅	C₃⋊(D₃₁⋊C₅)
Fitting, cosocle	C₂×C₅×C₉×C₃₁	C₂×C₅
socle, prime radical	C₂×C₃×C₅×C₃₁	C₅×D₃
LCS	G ▷ C₉×C₃₁
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
3. C₉×C₃₁⋊C₂₅	C₄	semidirect
12. Dic₂₇₉	C₂₅	semidirect
15. C₃₁⋊C₂₅	Dic₉	semidirect
23. C₉×C₃₁	C₄×C₂₅	semidirect
39. C₃₁	C₂₅×Dic₉	semidirect
47. C₉	Dic₃₁⋊C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×C₃₁⋊C₂₅	2
C₃⋊(Dic₃₁⋊C₂₅)	3
C₅×Dic₂₇₉	5
C₂₅×Dic₉	31

Subgroups — C9⋊(Dic31⋊C25) #42124259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉⋊(Dic₃₁⋊C₂₅) #42124259