Subgroups — C₅²×C₃⋊D₃×C₄₉ #36347708

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	C₅²×D₃×C₄₉	—	3	4	no	maximal
3	C₅×C₃⋊D₃×C₄₉	C₅	1	6	yes	maximal, direct product factor
4	C₃×C₅²×C₄₉	D₃	1	4	yes	complemented
5	C₅²×C₇×C₃⋊D₃	C₇	1	1	yes	maximal, characteristic
6	C₂×C₅²×C₄₉	—	9	1	no	Hall
7	C₃²×C₅×C₄₉	C₂×C₅	1	6	yes	complemented
8	C₃²×C₅²×C₇	C₂×C₇	1	1	yes	characteristic
9	C₅×D₃×C₄₉	—	3	24	no	—
10	C₅²×C₄₉	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
11	C₅²×D₃×C₇	—	3	4	no	—
12	C₃⋊D₃×C₄₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×C₄₉	C₅×D₃	1	24	yes	complemented
14	C₅×C₇×C₃⋊D₃	C₅×C₇	1	6	yes	—
15	C₃×C₅²×C₇	D₃×C₇	1	4	yes	—
16	C₂×C₅×C₄₉	—	9	6	no	—
17	C₅²×C₃⋊D₃	C₄₉	1	1	yes	characteristic, direct product factor, Hall
18	C₃²×C₄₉	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅²×C₇	—	9	1	no	—
20	C₃²×C₅×C₇	C₂×C₅×C₇	1	6	yes	—
21	D₃×C₄₉	—	3	4	no	—
22	C₅×C₄₉	C₅×C₃⋊D₃	1	6	yes	direct product factor
23	C₃²×C₅²	C₂×C₄₉	1	1	yes	characteristic, complemented, Hall
24	C₅×D₃×C₇	—	3	24	no	—
25	C₅²×C₇	C₇×C₃⋊D₃	1	1	yes	characteristic
26	C₅²×D₃	—	3	4	no	—
27	C₃×C₄₉	C₅²×D₃	1	4	yes	complemented
28	C₇×C₃⋊D₃	C₅²×C₇	1	1	yes	characteristic
29	C₃×C₅×C₇	C₅×D₃×C₇	1	24	yes	—
30	C₂×C₄₉	—	9	1	no	Hall
31	C₅×C₃⋊D₃	C₅×C₄₉	1	6	yes	direct product factor
32	C₃×C₅²	D₃×C₄₉	1	4	yes	complemented
33	C₂×C₅×C₇	—	9	6	no	—
34	C₃²×C₇	C₂×C₅²×C₇	1	1	yes	characteristic
35	C₂×C₅²	—	9	1	no	Hall
36	C₄₉	C₅²×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
37	C₃²×C₅	C₂×C₅×C₄₉	1	6	yes	complemented
38	D₃×C₇	—	3	4	no	—
39	C₅×C₇	C₅×C₇×C₃⋊D₃	1	6	yes	—
40	C₅×D₃	—	3	24	no	—
41	C₅²	C₃⋊D₃×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
42	C₃×C₇	C₅²×D₃×C₇	1	4	yes	—
43	C₃⋊D₃	C₅²×C₄₉	1	1	yes	characteristic, direct product factor, Hall
44	C₃×C₅	C₅×D₃×C₄₉	1	24	yes	complemented
45	C₂×C₇	—	9	1	no	—
46	C₂×C₅	—	9	6	no	—
47	C₃²	C₂×C₅²×C₄₉	1	1	yes	characteristic, complemented, Sylow
48	C₇	C₅²×C₇×C₃⋊D₃	1	1	yes	characteristic
49	D₃	—	3	4	no	—
50	C₅	C₅×C₃⋊D₃×C₄₉	1	6	yes	direct product factor
51	C₃	C₅²×D₃×C₄₉	1	4	yes	complemented
52	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²×C₄₉	C₃⋊D₃
commutator, hypocenter	C₃²	C₂×C₅²×C₄₉
Frattini	C₇	C₅²×C₇×C₃⋊D₃
Fitting	C₃²×C₅²×C₄₉	C₂
socle	C₃²×C₅²×C₇	C₂×C₇
prime radical	C₅²×C₇×C₃⋊D₃	C₇
cosocle	C₃²×C₇	C₂×C₅²×C₇
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅²×C₄₉

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×C₄₉	C₂	semidirect
3. C₅×C₃⋊D₃×C₄₉	C₅	direct (N × H)
4. C₃×C₅²×C₄₉	D₃	semidirect
7. C₃²×C₅×C₄₉	C₂×C₅	semidirect
10. C₅²×C₄₉	C₃⋊D₃	direct (N × H)
12. C₃⋊D₃×C₄₉	C₅²	direct (N × H)
13. C₃×C₅×C₄₉	C₅×D₃	semidirect
17. C₅²×C₃⋊D₃	C₄₉	direct (N × H)
18. C₃²×C₄₉	C₂×C₅²	semidirect
22. C₅×C₄₉	C₅×C₃⋊D₃	direct (N × H)
23. C₃²×C₅²	C₂×C₄₉	semidirect
27. C₃×C₄₉	C₅²×D₃	semidirect
31. C₅×C₃⋊D₃	C₅×C₄₉	direct (N × H)
32. C₃×C₅²	D₃×C₄₉	semidirect
36. C₄₉	C₅²×C₃⋊D₃	direct (N × H)
37. C₃²×C₅	C₂×C₅×C₄₉	semidirect
41. C₅²	C₃⋊D₃×C₄₉	direct (N × H)
43. C₃⋊D₃	C₅²×C₄₉	direct (N × H)
44. C₃×C₅	C₅×D₃×C₄₉	semidirect
47. C₃²	C₂×C₅²×C₄₉	semidirect
50. C₅	C₅×C₃⋊D₃×C₄₉	direct (N × H)
51. C₃	C₅²×D₃×C₄₉	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
C₅²×D₃×C₄₉	3
C₅×C₃⋊D₃×C₄₉	5
C₅²×C₇×C₃⋊D₃	7

Subgroups — C52×C3⋊D3×C49 #36347708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×C₃⋊D₃×C₄₉ #36347708