Subgroups — (Dic₃₁⋊C₉)⋊C₂₅ #42124255

Order 27900.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×(C₃₁⋊C₉)⋊C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₃₁⋊C₂₅	C₃	1	1	yes	maximal, characteristic
3	(C₃₁⋊C₉)⋊C₂₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅×Dic₃₁⋊C₉	C₅	1	1	yes	maximal, characteristic
5	C₂×C₃×C₃₁⋊C₂₅	C₂×C₃	1	1	yes	characteristic
6	Dic₃₁⋊C₂₅	C₉	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₃₁⋊C₉	C₂×C₅	1	1	yes	characteristic
8	C₃×C₃₁⋊C₂₅	C₃×C₄	1	1	yes	characteristic
9	C₃×C₅×Dic₃₁	C₃×C₅	1	1	yes	characteristic
10	C₂×C₃₁⋊C₂₅	C₂×C₉	1	1	yes	characteristic
11	C₅×C₃₁⋊C₉	C₄×C₅	1	1	yes	characteristic
12	Dic₃₁⋊C₉	C₂₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₅×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic
14	C₄×C₉×C₂₅	—	31	1	no	maximal, Hall
15	C₃₁⋊C₂₅	C₄×C₉	1	1	yes	characteristic, complemented, Hall
16	C₅×Dic₃₁	C₅×C₉	1	1	yes	characteristic
17	C₂×C₃₁⋊C₉	C₂×C₂₅	1	1	yes	characteristic
18	C₃×C₅×C₃₁	C₃×C₄×C₅	1	1	yes	characteristic
19	C₂×C₉×C₂₅	—	31	1	no	—
20	C₃×Dic₃₁	C₃×C₂₅	1	1	yes	characteristic
21	C₂×C₅×C₃₁	C₂×C₅×C₉	1	1	yes	characteristic
22	C₃×C₄×C₂₅	—	31	1	no	—
23	C₃₁⋊C₉	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
24	C₉×C₂₅	—	31	1	no	Hall
25	C₂×C₃×C₃₁	C₂×C₃×C₂₅	1	1	yes	characteristic
26	C₄×C₅×C₉	—	31	1	no	—
27	C₅×C₃₁	C₄×C₅×C₉	1	1	yes	characteristic
28	C₂×C₃×C₂₅	—	31	1	no	—
29	Dic₃₁	C₉×C₂₅	1	1	yes	characteristic, complemented, Hall
30	C₄×C₂₅	—	31	1	no	Hall
31	C₃×C₃₁	C₃×C₄×C₂₅	1	1	yes	characteristic
32	C₂×C₅×C₉	—	31	1	no	—
33	C₃×C₂₅	—	31	1	no	—
34	C₂×C₃₁	C₂×C₉×C₂₅	1	1	yes	characteristic
35	C₃×C₄×C₅	—	31	1	no	—
36	C₂×C₂₅	—	31	1	no	—
37	C₅×C₉	—	31	1	no	—
38	C₄×C₉	—	31	1	no	Hall
39	C₃₁	C₄×C₉×C₂₅	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃×C₅	AGL(1,𝔽₃₁)	1	1	yes	characteristic
41	C₂₅	—	31	1	no	Sylow
42	C₄×C₅	—	31	1	no	—
43	C₂×C₉	—	31	1	no	—
44	C₃×C₅	((C₃₁⋊C₃)⋊C₄)⋊C₅	1	1	yes	characteristic
45	C₃×C₄	—	31	1	no	—
46	C₂×C₅	(D₃₁⋊C₅)⋊C₉	1	1	yes	characteristic
47	C₉	—	31	1	no	Sylow
48	C₂×C₃	(D₃₁⋊C₃)⋊C₂₅	1	1	yes	characteristic
49	C₅	(Dic₃₁⋊C₅)⋊C₉	1	1	yes	characteristic
50	C₄	—	31	1	no	Sylow
51	C₃	((C₃₁⋊C₃)⋊C₄)⋊C₂₅	1	1	yes	characteristic
52	C₂	(D₃₁⋊C₉)⋊C₂₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃×C₅	AGL(1,𝔽₃₁)
commutator, hypocenter	C₃₁	C₄×C₉×C₂₅
Fitting, socle, prime radical, cosocle	C₂×C₃×C₅×C₃₁	C₂×C₃×C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₃×C₅

Complements

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

N	H ≅ G/N	type
3. (C₃₁⋊C₉)⋊C₂₅	C₄	semidirect
6. Dic₃₁⋊C₂₅	C₉	semidirect
12. Dic₃₁⋊C₉	C₂₅	semidirect
15. C₃₁⋊C₂₅	C₄×C₉	semidirect
23. C₃₁⋊C₉	C₄×C₂₅	semidirect
29. Dic₃₁	C₉×C₂₅	semidirect
39. C₃₁	C₄×C₉×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×(C₃₁⋊C₉)⋊C₂₅	2
C₃×Dic₃₁⋊C₂₅	3
C₅×Dic₃₁⋊C₉	5
C₄×C₉×C₂₅	31

Subgroups — (Dic31⋊C9)⋊C25 #42124255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (Dic₃₁⋊C₉)⋊C₂₅ #42124255