Subgroups — C₃⋊(C₃⋊(C₅⋊D₂₄₅)) #36347713

Order 22050.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(C₅⋊D₂₄₅)	—	3	4	no	maximal
3	C₃⋊D₇₃₅	—	5	6	no	maximal
4	C₃×C₅²×C₄₉	D₃	1	4	yes	complemented
5	C₃⋊(C₃⋊(C₅⋊D₃₅))	—	7	1	no	maximal
6	C₅⋊D₂₄₅	—	9	1	no	Hall
7	C₃²×C₅×C₄₉	D₅	1	6	yes	complemented
8	C₃²×C₅²×C₇	D₇	1	1	yes	characteristic
9	D₇₃₅	—	15	24	no	—
10	C₅²×C₄₉	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
11	C₃⋊(C₅⋊D₃₅)	—	21	4	no	—
12	C₃⋊D₁₄₇	—	25	1	no	Hall
13	C₃×C₅×C₄₉	D₁₅	1	24	yes	complemented
14	C₃⋊D₁₀₅	—	35	6	no	—
15	C₃×C₅²×C₇	D₂₁	1	4	yes	—
16	D₂₄₅	—	45	6	no	—
17	C₃⋊(C₃⋊(C₅⋊D₅))	—	49	1	no	Hall
18	C₃²×C₄₉	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
19	C₅⋊D₃₅	—	63	1	no	—
20	C₃²×C₅×C₇	D₃₅	1	6	yes	—
21	D₁₄₇	—	75	4	no	—
22	C₅×C₄₉	C₃⋊D₁₅	1	6	yes	complemented
23	C₃²×C₅²	D₄₉	1	1	yes	characteristic, complemented, Hall
24	D₁₀₅	—	105	24	no	—
25	C₅²×C₇	C₃⋊D₂₁	1	1	yes	characteristic
26	C₃⋊(C₅⋊D₅)	—	147	4	no	—
27	C₃×C₄₉	C₃⋊(C₅⋊D₅)	1	4	yes	complemented
28	C₃⋊D₂₁	—	175	1	no	—
29	C₃×C₅×C₇	D₁₀₅	1	24	yes	—
30	D₄₉	—	225	1	no	Hall
31	C₃⋊D₁₅	—	245	6	no	—
32	C₃×C₅²	D₁₄₇	1	4	yes	complemented
33	D₃₅	—	315	6	no	—
34	C₃²×C₇	C₅⋊D₃₅	1	1	yes	characteristic
35	C₅⋊D₅	—	441	1	no	Hall
36	C₄₉	C₃⋊(C₃⋊(C₅⋊D₅))	1	1	yes	characteristic, complemented, Sylow
37	C₃²×C₅	D₂₄₅	1	6	yes	complemented
38	D₂₁	—	525	4	no	—
39	C₅×C₇	C₃⋊D₁₀₅	1	6	yes	—
40	D₁₅	—	735	24	no	—
41	C₅²	C₃⋊D₁₄₇	1	1	yes	characteristic, complemented, Sylow
42	C₃×C₇	C₃⋊(C₅⋊D₃₅)	1	4	yes	—
43	C₃⋊D₃	—	1225	1	no	Hall
44	C₃×C₅	D₇₃₅	1	24	yes	complemented
45	D₇	—	1575	1	no	—
46	D₅	—	2205	6	no	—
47	C₃²	C₅⋊D₂₄₅	1	1	yes	characteristic, complemented, Sylow
48	C₇	C₃⋊(C₃⋊(C₅⋊D₃₅))	1	1	yes	characteristic
49	D₃	—	3675	4	no	—
50	C₅	C₃⋊D₇₃₅	1	6	yes	complemented
51	C₃	C₃⋊(C₅⋊D₂₄₅)	1	4	yes	complemented
52	C₂	—	11025	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃²×C₅²×C₄₉	C₂
Frattini	C₇	C₃⋊(C₃⋊(C₅⋊D₃₅))
socle	C₃²×C₅²×C₇	D₇
LCS	G ▷ C₃²×C₅²×C₄₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×C₄₉	C₂	semidirect
4. C₃×C₅²×C₄₉	D₃	semidirect
7. C₃²×C₅×C₄₉	D₅	semidirect
10. C₅²×C₄₉	C₃⋊D₃	semidirect
13. C₃×C₅×C₄₉	D₁₅	semidirect
18. C₃²×C₄₉	C₅⋊D₅	semidirect
22. C₅×C₄₉	C₃⋊D₁₅	semidirect
23. C₃²×C₅²	D₄₉	semidirect
27. C₃×C₄₉	C₃⋊(C₅⋊D₅)	semidirect
32. C₃×C₅²	D₁₄₇	semidirect
36. C₄₉	C₃⋊(C₃⋊(C₅⋊D₅))	semidirect
37. C₃²×C₅	D₂₄₅	semidirect
41. C₅²	C₃⋊D₁₄₇	semidirect
44. C₃×C₅	D₇₃₅	semidirect
47. C₃²	C₅⋊D₂₄₅	semidirect
50. C₅	C₃⋊D₇₃₅	semidirect
51. C₃	C₃⋊(C₅⋊D₂₄₅)	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅²×C₄₉	2
C₃⋊(C₅⋊D₂₄₅)	3
C₃⋊D₇₃₅	5
C₃⋊(C₃⋊(C₅⋊D₃₅))	7

Subgroups — C3⋊(C3⋊(C5⋊D245)) #36347713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊(C₅⋊D₂₄₅)) #36347713