Subgroups — C₃×C₅⋊D₅×D₄₉ #28412972

Order 14700.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊D₂₄₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅²×D₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅⋊D₅×D₄₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅²×C₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₅×D₄₉	—	5	6	no	maximal
7	C₅⋊D₂₄₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₄₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅²×D₄₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₇×C₅⋊D₅	—	7	1	no	maximal
11	C₃×D₂₄₅	—	5	6	no	—
12	C₃×D₅×C₄₉	—	5	6	no	—
13	C₃×C₅×D₄₉	D₅	1	6	yes	complemented
14	C₅²×C₄₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅⋊D₃₅	—	7	1	no	—
16	C₃×C₇×C₅⋊D₅	D₇	1	1	yes	characteristic
17	C₃×C₅²×D₇	—	7	1	no	—
18	D₅×D₄₉	—	5	6	no	—
19	C₃×C₅×C₄₉	C₂×D₅	1	6	yes	complemented
20	D₇×C₅⋊D₅	—	7	1	no	—
21	C₂×C₃×D₄₉	—	25	1	no	Hall
22	C₃×C₅²×C₇	C₂×D₇	1	1	yes	characteristic
23	D₂₄₅	—	5	6	no	—
24	C₅×D₄₉	C₃×D₅	1	6	yes	complemented
25	D₅×C₄₉	—	5	6	no	—
26	C₃×D₅×D₇	—	35	6	no	—
27	C₅⋊D₃₅	—	7	1	no	—
28	C₇×C₅⋊D₅	C₃×D₇	1	1	yes	characteristic
29	C₅²×D₇	—	7	1	no	—
30	C₂×C₃×C₅⋊D₅	—	49	1	no	Hall
31	C₂×C₃×C₄₉	—	25	1	no	—
32	C₃×D₄₉	—	25	1	no	—
33	C₃×D₄₉	C₅⋊D₅	1	1	yes	characteristic, direct product factor
34	C₅×C₄₉	C₂×C₃×D₅	1	6	yes	complemented
35	C₃×D₃₅	—	35	6	no	—
36	C₃×C₇×D₅	—	5	6	no	—
37	C₃×C₅×D₇	—	7	6	no	—
38	C₂×D₄₉	—	25	1	no	Hall
39	C₅²×C₇	C₂×C₃×D₇	1	1	yes	characteristic
40	C₂×C₃×C₅²	—	49	1	no	—
41	C₃×C₅⋊D₅	—	49	1	no	—
42	C₃×C₅⋊D₅	D₄₉	1	1	yes	characteristic, direct product factor
43	C₃×C₄₉	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
44	D₅×D₇	—	35	6	no	—
45	C₃×C₅×C₇	D₅×D₇	1	6	yes	—
46	C₂×C₅⋊D₅	—	49	1	no	Hall
47	C₂×C₄₉	—	25	1	no	—
48	D₄₉	—	25	1	no	—
49	D₄₉	C₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor
50	C₂×C₃×D₇	—	175	1	no	—
51	C₃×C₅²	C₂×D₄₉	1	1	yes	characteristic, complemented, Hall
52	D₃₅	—	35	6	no	—
53	C₅×D₇	—	7	6	no	—
54	C₇×D₅	—	5	6	no	—
55	C₂×C₃×D₅	—	245	6	no	—
56	C₂×C₅²	—	49	1	no	—
57	C₅⋊D₅	—	49	1	no	—
58	C₅⋊D₅	C₃×D₄₉	1	1	yes	characteristic, direct product factor
59	C₄₉	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₃×C₇	—	25	1	no	—
61	C₃×D₇	—	7	1	no	—
62	C₃×D₇	—	175	1	no	—
63	C₅×C₇	C₃×D₅×D₇	1	6	yes	—
64	C₂×C₃×C₅	—	49	6	no	—
65	C₃×D₅	—	5	6	no	—
66	C₃×D₅	—	245	6	no	—
67	C₂×D₇	—	175	1	no	—
68	C₅²	C₂×C₃×D₄₉	1	1	yes	characteristic, complemented, Sylow
69	C₃×C₇	D₇×C₅⋊D₅	1	1	yes	characteristic
70	C₂×D₅	—	245	6	no	—
71	C₃×C₅	D₅×D₄₉	1	6	yes	complemented
72	C₂×C₇	—	25	1	no	—
73	D₇	—	7	1	no	—
74	D₇	—	175	1	no	—
75	C₂²×C₃	—	1225	1	no	Hall
76	C₂×C₅	—	49	6	no	—
77	D₅	—	5	6	no	—
78	D₅	—	245	6	no	—
79	C₇	C₃×D₇×C₅⋊D₅	1	1	yes	characteristic
80	C₂×C₃	—	25	1	no	—
81	C₂×C₃	—	49	1	no	—
82	C₂×C₃	—	1225	1	no	—
83	C₅	C₃×D₅×D₄₉	1	6	yes	complemented
84	C₂²	—	1225	1	no	Sylow
85	C₃	C₅⋊D₅×D₄₉	1	1	yes	characteristic, direct product factor, Sylow
86	C₂	—	25	1	no	—
87	C₂	—	49	1	no	—
88	C₂	—	1225	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₅⋊D₅×D₄₉
commutator, cosocle, hypocenter	C₅²×C₄₉	C₂²×C₃
Frattini	C₇	C₃×D₇×C₅⋊D₅
Fitting	C₃×C₅²×C₄₉	C₂²
socle	C₃×C₅²×C₇	C₂×D₇
LCS	G ▷ C₅²×C₄₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅⋊D₂₄₅	C₂	semidirect
2. C₃×C₄₉×C₅⋊D₅	C₂	semidirect
3. C₃×C₅²×D₄₉	C₂	semidirect
4. C₅⋊D₅×D₄₉	C₃	direct (N × H)
5. C₃×C₅²×C₄₉	C₂²	semidirect
7. C₅⋊D₂₄₅	C₂×C₃	semidirect
8. C₄₉×C₅⋊D₅	C₂×C₃	semidirect
9. C₅²×D₄₉	C₂×C₃	semidirect
13. C₃×C₅×D₄₉	D₅	semidirect
14. C₅²×C₄₉	C₂²×C₃	semidirect
19. C₃×C₅×C₄₉	C₂×D₅	semidirect
24. C₅×D₄₉	C₃×D₅	semidirect
33. C₃×D₄₉	C₅⋊D₅	direct (N × H)
34. C₅×C₄₉	C₂×C₃×D₅	semidirect
42. C₃×C₅⋊D₅	D₄₉	direct (N × H)
43. C₃×C₄₉	C₂×C₅⋊D₅	semidirect
49. D₄₉	C₃×C₅⋊D₅	direct (N × H)
51. C₃×C₅²	C₂×D₄₉	semidirect
58. C₅⋊D₅	C₃×D₄₉	direct (N × H)
59. C₄₉	C₂×C₃×C₅⋊D₅	semidirect
68. C₅²	C₂×C₃×D₄₉	semidirect
71. C₃×C₅	D₅×D₄₉	semidirect
83. C₅	C₃×D₅×D₄₉	semidirect
85. C₃	C₅⋊D₅×D₄₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅⋊D₂₄₅	2
C₃×C₄₉×C₅⋊D₅	2
C₃×C₅²×D₄₉	2
C₅⋊D₅×D₄₉	3
C₃×D₅×D₄₉	5
C₃×D₇×C₅⋊D₅	7

Subgroups — C3×C5⋊D5×D49 #28412972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅⋊D₅×D₄₉ #28412972