Subgroups — C₃²×C₄₉×C₅⋊D₅ #36347700

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×C₄₉×C₅⋊D₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₅×C₄₉	—	5	6	no	maximal
4	C₃×C₅²×C₄₉	C₂×C₃	1	4	yes	complemented
5	C₃²×C₇×C₅⋊D₅	C₇	1	1	yes	maximal, characteristic
6	C₄₉×C₅⋊D₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₅×C₄₉	D₅	1	6	yes	complemented
8	C₃²×C₅²×C₇	C₂×C₇	1	1	yes	characteristic
9	C₃×D₅×C₄₉	—	5	24	no	—
10	C₅²×C₄₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×C₅⋊D₅	C₃×C₇	1	4	yes	—
12	C₂×C₃²×C₄₉	—	25	1	no	Hall
13	C₃×C₅×C₄₉	C₃×D₅	1	24	yes	complemented
14	C₃²×C₇×D₅	—	5	6	no	—
15	C₃×C₅²×C₇	C₂×C₃×C₇	1	4	yes	—
16	D₅×C₄₉	—	5	6	no	—
17	C₃²×C₅⋊D₅	C₄₉	1	1	yes	characteristic, direct product factor, Hall
18	C₃²×C₄₉	C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
19	C₇×C₅⋊D₅	C₃²×C₇	1	1	yes	characteristic
20	C₃²×C₅×C₇	C₇×D₅	1	6	yes	—
21	C₂×C₃×C₄₉	—	25	4	no	—
22	C₅×C₄₉	C₃²×D₅	1	6	yes	complemented
23	C₃²×C₅²	C₂×C₄₉	1	1	yes	characteristic, complemented, Hall
24	C₃×C₇×D₅	—	5	24	no	—
25	C₅²×C₇	C₂×C₃²×C₇	1	1	yes	characteristic
26	C₃×C₅⋊D₅	C₃×C₄₉	1	4	yes	direct product factor
27	C₃×C₄₉	C₃×C₅⋊D₅	1	4	yes	direct product factor
28	C₂×C₃²×C₇	—	25	1	no	—
29	C₃×C₅×C₇	C₃×C₇×D₅	1	24	yes	—
30	C₂×C₄₉	—	25	1	no	Hall
31	C₃²×D₅	—	5	6	no	—
32	C₃×C₅²	C₂×C₃×C₄₉	1	4	yes	complemented
33	C₇×D₅	—	5	6	no	—
34	C₃²×C₇	C₇×C₅⋊D₅	1	1	yes	characteristic
35	C₅⋊D₅	C₃²×C₄₉	1	1	yes	characteristic, direct product factor, Hall
36	C₄₉	C₃²×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
37	C₃²×C₅	D₅×C₄₉	1	6	yes	complemented
38	C₂×C₃×C₇	—	25	4	no	—
39	C₅×C₇	C₃²×C₇×D₅	1	6	yes	—
40	C₃×D₅	—	5	24	no	—
41	C₅²	C₂×C₃²×C₄₉	1	1	yes	characteristic, complemented, Sylow
42	C₃×C₇	C₃×C₇×C₅⋊D₅	1	4	yes	—
43	C₂×C₃²	—	25	1	no	Hall
44	C₃×C₅	C₃×D₅×C₄₉	1	24	yes	complemented
45	C₂×C₇	—	25	1	no	—
46	D₅	—	5	6	no	—
47	C₃²	C₄₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
48	C₇	C₃²×C₇×C₅⋊D₅	1	1	yes	characteristic
49	C₂×C₃	—	25	4	no	—
50	C₅	C₃²×D₅×C₄₉	1	6	yes	complemented
51	C₃	C₃×C₄₉×C₅⋊D₅	1	4	yes	direct product factor
52	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₄₉	C₅⋊D₅
commutator, hypocenter	C₅²	C₂×C₃²×C₄₉
Frattini	C₇	C₃²×C₇×C₅⋊D₅
Fitting	C₃²×C₅²×C₄₉	C₂
socle	C₃²×C₅²×C₇	C₂×C₇
prime radical	C₃²×C₇×C₅⋊D₅	C₇
cosocle	C₅²×C₇	C₂×C₃²×C₇
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃²×C₄₉

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×C₄₉	C₂	semidirect
2. C₃×C₄₉×C₅⋊D₅	C₃	direct (N × H)
4. C₃×C₅²×C₄₉	C₂×C₃	semidirect
6. C₄₉×C₅⋊D₅	C₃²	direct (N × H)
7. C₃²×C₅×C₄₉	D₅	semidirect
10. C₅²×C₄₉	C₂×C₃²	semidirect
13. C₃×C₅×C₄₉	C₃×D₅	semidirect
17. C₃²×C₅⋊D₅	C₄₉	direct (N × H)
18. C₃²×C₄₉	C₅⋊D₅	direct (N × H)
22. C₅×C₄₉	C₃²×D₅	semidirect
23. C₃²×C₅²	C₂×C₄₉	semidirect
26. C₃×C₅⋊D₅	C₃×C₄₉	direct (N × H)
27. C₃×C₄₉	C₃×C₅⋊D₅	direct (N × H)
32. C₃×C₅²	C₂×C₃×C₄₉	semidirect
35. C₅⋊D₅	C₃²×C₄₉	direct (N × H)
36. C₄₉	C₃²×C₅⋊D₅	direct (N × H)
37. C₃²×C₅	D₅×C₄₉	semidirect
41. C₅²	C₂×C₃²×C₄₉	semidirect
44. C₃×C₅	C₃×D₅×C₄₉	semidirect
47. C₃²	C₄₉×C₅⋊D₅	direct (N × H)
50. C₅	C₃²×D₅×C₄₉	semidirect
51. C₃	C₃×C₄₉×C₅⋊D₅	direct (N × H)

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×C₄₉×C₅⋊D₅	3
C₃²×D₅×C₄₉	5
C₃²×C₇×C₅⋊D₅	7

Subgroups — C32×C49×C5⋊D5 #36347700

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₄₉×C₅⋊D₅ #36347700