Subgroups — C₂₅×C₂²⋊#4294 #30685396

Order 17100.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₁₉×C₂₅	C₃	1	1	yes	maximal, characteristic
2	C₂₅×#4294	—	4	1	no	maximal, Hall
3	C₅×C₂²⋊#4294	C₅	1	1	yes	maximal, characteristic
4	C₂×C₃×C₁₉×C₂₅	—	3	1	no	—
5	C₂²×C₁₉×C₂₅	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₉×C₂₅	A₄	1	1	yes	characteristic
7	C₂²×C₃×C₅×C₁₉	C₃×C₅	1	1	yes	characteristic
8	C₂×C₁₉×C₂₅	—	3	1	no	—
9	C₂₅×C₂²⋊C₉	—	19	1	no	maximal, Hall
10	C₅×#4294	—	4	1	no	—
11	C₂²⋊#4294	C₂₅	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃×C₅×C₁₉	—	3	1	no	—
13	C₁₉×C₂₅	C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
14	C₂²×C₅×C₁₉	C₅×C₉	1	1	yes	characteristic
15	C₂²×C₃×C₂₅	C₁₉⋊C₃	1	1	yes	characteristic
16	C₃×C₅×C₁₉	C₅×A₄	1	1	yes	characteristic
17	C₂²×C₃×C₁₉	C₃×C₂₅	1	1	yes	characteristic
18	C₉×C₂₅	—	76	1	no	Hall
19	C₂×C₅×C₁₉	—	3	1	no	—
20	C₅×C₂²⋊C₉	—	19	1	no	—
21	#4294	—	4	1	no	Hall
22	C₂×C₃×C₂₅	—	3	1	no	—
23	C₂×C₃×C₁₉	—	3	1	no	—
24	C₂²×C₂₅	#4294	1	1	yes	characteristic, complemented, Hall
25	C₅×C₁₉	C₅×C₂²⋊C₉	1	1	yes	characteristic
26	C₂²×C₁₉	C₉×C₂₅	1	1	yes	characteristic, complemented, Hall
27	C₃×C₂₅	C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
28	C₂²×C₃×C₅	C₅×C₁₉⋊C₃	1	1	yes	characteristic
29	C₃×C₁₉	A₄×C₂₅	1	1	yes	characteristic
30	C₂×C₂₅	—	3	1	no	—
31	C₅×C₉	—	76	1	no	—
32	C₂×C₁₉	—	3	1	no	—
33	C₂²⋊C₉	—	19	1	no	Hall
34	C₂×C₃×C₅	—	3	1	no	—
35	C₂₅	C₂²⋊#4294	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²×C₅	C₅×#4294	1	1	yes	characteristic
37	C₁₉	C₂₅×C₂²⋊C₉	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₅	C₅×C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
39	C₂²×C₃	C₂₅×C₁₉⋊C₃	1	1	yes	characteristic
40	C₂×C₅	—	3	1	no	—
41	C₉	—	76	1	no	Sylow
42	C₂×C₃	—	3	1	no	—
43	C₅	C₅×C₂²⋊#4294	1	1	yes	characteristic
44	C₂²	C₂₅×#4294	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₂₅×C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
46	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₂₅	C₂²⋊(C₁₉⋊C₃)
commutator, hypocenter	C₂²×C₁₉	C₉×C₂₅
Frattini	C₃×C₅	C₅×C₂²⋊(C₁₉⋊C₃)
Fitting	C₂²×C₃×C₁₉×C₂₅	C₃
socle, prime radical, cosocle	C₂²×C₃×C₅×C₁₉	C₃×C₅
LCS	G ▷ C₂²×C₁₉
UCS	C₁ ◁ C₃×C₂₅

Complements

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

N	H ≅ G/N	type
5. C₂²×C₁₉×C₂₅	C₉	semidirect
11. C₂²⋊#4294	C₂₅	direct (N × H)
13. C₁₉×C₂₅	C₂²⋊C₉	semidirect
24. C₂²×C₂₅	#4294	semidirect
26. C₂²×C₁₉	C₉×C₂₅	semidirect
35. C₂₅	C₂²⋊#4294	direct (N × H)
37. C₁₉	C₂₅×C₂²⋊C₉	semidirect
44. C₂²	C₂₅×#4294	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₁₉×C₂₅	3
C₂₅×#4294	4
C₅×C₂²⋊#4294	5
C₂₅×C₂²⋊C₉	19

Subgroups — C25×C22⋊#4294 #30685396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×C₂²⋊#4294 #30685396