Subgroups — D₅₇×C₁₁⋊C₂₅ #44535451

Order 31350.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×C₁₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₉×C₁₁⋊C₂₅	—	3	1	no	maximal, Hall
3	C₅×C₁₁×D₅₇	C₅	1	1	yes	maximal, characteristic
4	C₁₉×C₁₁⋊C₂₅	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₁×C₁₉	C₂×C₅	1	1	yes	characteristic
6	C₂₅×D₅₇	—	11	1	no	maximal, Hall
7	C₅×C₁₁×D₁₉	—	3	1	no	—
8	D₃×C₁₁⋊C₂₅	—	19	1	no	maximal, Hall
9	C₃×C₁₉×C₂₅	—	11	1	no	Hall
10	C₁₁×D₅₇	C₂₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₁₁×C₁₉	C₅×D₃	1	1	yes	characteristic
12	C₂₅×D₁₉	—	33	1	no	Hall
13	C₃×C₁₁⋊C₂₅	D₁₉	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₁×C₁₉	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
15	C₅×D₅₇	C₁₁⋊C₅	1	1	yes	characteristic
16	C₂×C₁₁⋊C₂₅	—	57	1	no	Hall
17	C₁₉×C₂₅	—	11	1	no	Hall
18	C₁₁×D₁₉	—	3	1	no	Hall
19	C₅×D₃×C₁₁	—	19	1	no	—
20	C₃×C₅×C₁₉	C₂×C₁₁⋊C₅	1	1	yes	characteristic
21	C₁₁⋊C₂₅	D₅₇	1	1	yes	characteristic, direct product factor, Hall
22	C₁₁×C₁₉	D₃×C₂₅	1	1	yes	characteristic, complemented, Hall
23	C₅×D₁₉	—	3	1	no	—
24	C₃×C₅×C₁₁	C₅×D₁₉	1	1	yes	characteristic
25	D₃×C₂₅	—	209	1	no	Hall
26	D₅₇	C₁₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₅×C₁₁	—	57	1	no	—
28	C₅×C₁₉	D₃×C₁₁⋊C₅	1	1	yes	characteristic
29	C₃×C₂₅	—	11	1	no	Hall
30	D₃×C₁₁	—	19	1	no	Hall
31	C₃×C₁₉	C₂×C₁₁⋊C₂₅	1	1	yes	characteristic, complemented, Hall
32	C₅×C₁₁	C₅×D₅₇	1	1	yes	characteristic
33	C₂×C₂₅	—	627	1	no	Hall
34	D₁₉	—	3	1	no	Hall
35	C₃×C₁₁	C₂₅×D₁₉	1	1	yes	characteristic, complemented, Hall
36	C₅×D₃	—	19	1	no	—
37	C₂₅	—	11	1	no	Sylow
38	C₂×C₁₁	—	57	1	no	Hall
39	C₁₉	D₃×C₁₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₅	D₁₉×C₁₁⋊C₅	1	1	yes	characteristic
41	C₁₁	C₂₅×D₅₇	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₅	—	57	1	no	—
43	D₃	—	19	1	no	Hall
44	C₅	C₁₁⋊C₅×D₅₇	1	1	yes	characteristic
45	C₃	D₁₉×C₁₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	57	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₅	C₁₁⋊C₅×D₅₇
commutator, hypocenter	C₃×C₁₁×C₁₉	C₂×C₂₅
Fitting, socle, cosocle	C₃×C₅×C₁₁×C₁₉	C₂×C₅
prime radical	C₅×C₁₁×D₅₇	C₅
LCS	G ▷ C₃×C₁₁×C₁₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×C₁₁⋊C₂₅	C₂	semidirect
4. C₁₉×C₁₁⋊C₂₅	D₃	semidirect
10. C₁₁×D₅₇	C₂₅	semidirect
13. C₃×C₁₁⋊C₂₅	D₁₉	semidirect
14. C₃×C₁₁×C₁₉	C₂×C₂₅	semidirect
21. C₁₁⋊C₂₅	D₅₇	direct (N × H)
22. C₁₁×C₁₉	D₃×C₂₅	semidirect
26. D₅₇	C₁₁⋊C₂₅	direct (N × H)
31. C₃×C₁₉	C₂×C₁₁⋊C₂₅	semidirect
35. C₃×C₁₁	C₂₅×D₁₉	semidirect
39. C₁₉	D₃×C₁₁⋊C₂₅	semidirect
41. C₁₁	C₂₅×D₅₇	semidirect
45. C₃	D₁₉×C₁₁⋊C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₉×C₁₁⋊C₂₅	2
D₁₉×C₁₁⋊C₂₅	3
C₅×C₁₁×D₅₇	5
C₂₅×D₅₇	11
D₃×C₁₁⋊C₂₅	19

Subgroups — D57×C11⋊C25 #44535451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₇×C₁₁⋊C₂₅ #44535451