Subgroups — C₂×C₁₃×C₃⋊D₃×C₄₉ #37524315

Order 22932.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₃×C₄₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₃×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₁₃×C₄₉	—	3	4	no	maximal
4	C₃²×C₁₃×C₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃×C₁₃×C₄₉	—	3	8	no	—
6	C₂×C₃×C₁₃×C₄₉	D₃	1	4	yes	complemented
7	C₂×C₇×C₁₃×C₃⋊D₃	C₇	1	1	yes	maximal, characteristic
8	C₂²×C₁₃×C₄₉	—	9	1	no	Hall
9	C₃×C₁₃×C₄₉	C₂×D₃	1	4	yes	complemented
10	C₂×C₃⋊D₃×C₄₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃²×C₇×C₁₃	C₂×C₇	1	1	yes	characteristic
12	C₇×C₁₃×C₃⋊D₃	C₂×C₇	1	2	yes	—
13	C₂×C₁₃×C₄₉	—	9	2	no	—
14	C₂×C₁₃×C₄₉	C₃⋊D₃	1	1	yes	characteristic, direct product factor
15	C₂×D₃×C₇×C₁₃	—	3	4	no	—
16	C₂×C₃²×C₄₉	C₂×C₁₃	1	1	yes	characteristic, complemented
17	C₃⋊D₃×C₄₉	C₂×C₁₃	1	2	yes	direct product factor
18	C₃²×C₇×C₁₃	C₂²×C₇	1	1	yes	characteristic
19	C₁₃×C₄₉	C₂×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
20	C₂×D₃×C₄₉	—	3	4	no	—
21	C₂×C₃×C₇×C₁₃	D₃×C₇	1	4	yes	—
22	D₃×C₇×C₁₃	—	3	8	no	—
23	C₂×C₁₃×C₃⋊D₃	C₄₉	1	1	yes	characteristic, direct product factor, Hall
24	C₃²×C₄₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂²×C₇×C₁₃	—	9	1	no	—
26	C₂×C₃×C₄₉	D₃×C₁₃	1	4	yes	complemented
27	D₃×C₄₉	—	3	8	no	—
28	C₃×C₇×C₁₃	C₂×D₃×C₇	1	4	yes	—
29	C₂×C₇×C₃⋊D₃	C₇×C₁₃	1	1	yes	characteristic
30	C₂×C₃²×C₁₃	C₂×C₄₉	1	1	yes	characteristic, complemented
31	C₁₃×C₃⋊D₃	C₂×C₄₉	1	2	yes	direct product factor
32	C₂²×C₄₉	—	9	1	no	Hall
33	C₂×C₇×C₁₃	—	9	2	no	—
34	C₂×C₇×C₁₃	C₇×C₃⋊D₃	1	1	yes	characteristic
35	C₂×D₃×C₁₃	—	3	4	no	—
36	C₃×C₄₉	C₂×D₃×C₁₃	1	4	yes	complemented
37	C₂×C₃²×C₇	C₂×C₇×C₁₃	1	1	yes	characteristic
38	C₇×C₃⋊D₃	C₂×C₇×C₁₃	1	2	yes	—
39	C₃²×C₁₃	C₂²×C₄₉	1	1	yes	characteristic, complemented, Hall
40	C₂×C₄₉	—	9	2	no	—
41	C₂×C₄₉	C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
42	C₇×C₁₃	C₂×C₇×C₃⋊D₃	1	1	yes	characteristic
43	C₂×D₃×C₇	—	3	4	no	—
44	C₂×C₃×C₁₃	D₃×C₄₉	1	4	yes	complemented
45	D₃×C₁₃	—	3	8	no	—
46	C₃²×C₇	C₂²×C₇×C₁₃	1	1	yes	characteristic
47	C₂²×C₁₃	—	9	1	no	Hall
48	C₄₉	C₂×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
49	C₂×C₃×C₇	D₃×C₇×C₁₃	1	4	yes	—
50	D₃×C₇	—	3	8	no	—
51	C₃×C₁₃	C₂×D₃×C₄₉	1	4	yes	complemented
52	C₂×C₃⋊D₃	C₁₃×C₄₉	1	1	yes	characteristic, direct product factor, Hall
53	C₂²×C₇	—	9	1	no	—
54	C₂×C₁₃	—	9	2	no	—
55	C₂×C₁₃	C₃⋊D₃×C₄₉	1	1	yes	characteristic, direct product factor
56	C₃×C₇	C₂×D₃×C₇×C₁₃	1	4	yes	—
57	C₂×C₃²	C₂×C₁₃×C₄₉	1	1	yes	characteristic, complemented
58	C₃⋊D₃	C₂×C₁₃×C₄₉	1	2	yes	direct product factor
59	C₂×C₇	—	9	2	no	—
60	C₂×C₇	C₇×C₁₃×C₃⋊D₃	1	1	yes	characteristic
61	C₁₃	C₂×C₃⋊D₃×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
62	C₂×D₃	—	3	4	no	—
63	C₃²	C₂²×C₁₃×C₄₉	1	1	yes	characteristic, complemented, Sylow
64	C₇	C₂×C₇×C₁₃×C₃⋊D₃	1	1	yes	characteristic
65	C₂×C₃	D₃×C₁₃×C₄₉	1	4	yes	complemented
66	D₃	—	3	8	no	—
67	C₂²	—	9	1	no	Sylow
68	C₃	C₂×D₃×C₁₃×C₄₉	1	4	yes	complemented
69	C₂	—	9	2	no	—
70	C₂	C₁₃×C₃⋊D₃×C₄₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₄₉	C₃⋊D₃
commutator, hypocenter	C₃²	C₂²×C₁₃×C₄₉
Frattini	C₇	C₂×C₇×C₁₃×C₃⋊D₃
Fitting	C₂×C₃²×C₁₃×C₄₉	C₂
socle	C₂×C₃²×C₇×C₁₃	C₂×C₇
prime radical	C₂×C₇×C₁₃×C₃⋊D₃	C₇
cosocle	C₃²×C₇	C₂²×C₇×C₁₃
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₁₃×C₄₉

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃⋊D₃×C₄₉	C₂	direct (N × H)
2. C₂×C₃²×C₁₃×C₄₉	C₂	semidirect
4. C₃²×C₁₃×C₄₉	C₂²	semidirect
6. C₂×C₃×C₁₃×C₄₉	D₃	semidirect
9. C₃×C₁₃×C₄₉	C₂×D₃	semidirect
10. C₂×C₃⋊D₃×C₄₉	C₁₃	direct (N × H)
14. C₂×C₁₃×C₄₉	C₃⋊D₃	direct (N × H)
16. C₂×C₃²×C₄₉	C₂×C₁₃	semidirect
17. C₃⋊D₃×C₄₉	C₂×C₁₃	direct (N × H)
19. C₁₃×C₄₉	C₂×C₃⋊D₃	direct (N × H)
23. C₂×C₁₃×C₃⋊D₃	C₄₉	direct (N × H)
24. C₃²×C₄₉	C₂²×C₁₃	semidirect
26. C₂×C₃×C₄₉	D₃×C₁₃	semidirect
30. C₂×C₃²×C₁₃	C₂×C₄₉	semidirect
31. C₁₃×C₃⋊D₃	C₂×C₄₉	direct (N × H)
36. C₃×C₄₉	C₂×D₃×C₁₃	semidirect
39. C₃²×C₁₃	C₂²×C₄₉	semidirect
41. C₂×C₄₉	C₁₃×C₃⋊D₃	direct (N × H)
44. C₂×C₃×C₁₃	D₃×C₄₉	semidirect
48. C₄₉	C₂×C₁₃×C₃⋊D₃	direct (N × H)
51. C₃×C₁₃	C₂×D₃×C₄₉	semidirect
52. C₂×C₃⋊D₃	C₁₃×C₄₉	direct (N × H)
55. C₂×C₁₃	C₃⋊D₃×C₄₉	direct (N × H)
57. C₂×C₃²	C₂×C₁₃×C₄₉	semidirect
58. C₃⋊D₃	C₂×C₁₃×C₄₉	direct (N × H)
61. C₁₃	C₂×C₃⋊D₃×C₄₉	direct (N × H)
63. C₃²	C₂²×C₁₃×C₄₉	semidirect
65. C₂×C₃	D₃×C₁₃×C₄₉	semidirect
68. C₃	C₂×D₃×C₁₃×C₄₉	semidirect
70. C₂	C₁₃×C₃⋊D₃×C₄₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×C₃⋊D₃×C₄₉	2
C₂×C₃²×C₁₃×C₄₉	2
C₂×D₃×C₁₃×C₄₉	3
C₂×C₇×C₁₃×C₃⋊D₃	7
C₂×C₃⋊D₃×C₄₉	13

Subgroups — C2×C13×C3⋊D3×C49 #37524315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×C₃⋊D₃×C₄₉ #37524315