Subgroups — C₁₃×C₃⋊Dic₃×C₄₉ #37524176

Order 22932.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₃×C₄₉	C₂	1	1	yes	maximal, characteristic
2	Dic₃×C₁₃×C₄₉	—	3	4	no	maximal
3	C₃²×C₁₃×C₄₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃×C₄₉	D₃	1	4	yes	—
5	C₇×C₁₃×C₃⋊Dic₃	C₇	1	1	yes	maximal, characteristic
6	C₄×C₁₃×C₄₉	—	9	1	no	Hall
7	C₃×C₁₃×C₄₉	Dic₃	1	4	yes	complemented
8	C₃⋊Dic₃×C₄₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃²×C₇×C₁₃	C₂×C₇	1	1	yes	characteristic
10	C₂×C₁₃×C₄₉	C₃⋊D₃	1	1	yes	characteristic
11	C₇×Dic₃×C₁₃	—	3	4	no	—
12	C₂×C₃²×C₄₉	C₂×C₁₃	1	1	yes	characteristic
13	C₃²×C₇×C₁₃	C₄×C₇	1	1	yes	characteristic
14	C₁₃×C₄₉	C₃⋊Dic₃	1	1	yes	characteristic, direct product factor, Hall
15	Dic₃×C₄₉	—	3	4	no	—
16	C₂×C₃×C₇×C₁₃	D₃×C₇	1	4	yes	—
17	C₁₃×C₃⋊Dic₃	C₄₉	1	1	yes	characteristic, direct product factor, Hall
18	C₃²×C₄₉	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
19	C₄×C₇×C₁₃	—	9	1	no	—
20	C₂×C₃×C₄₉	D₃×C₁₃	1	4	yes	—
21	C₃×C₇×C₁₃	C₇×Dic₃	1	4	yes	—
22	C₇×C₃⋊Dic₃	C₇×C₁₃	1	1	yes	characteristic
23	C₂×C₃²×C₁₃	C₂×C₄₉	1	1	yes	characteristic
24	C₄×C₄₉	—	9	1	no	Hall
25	C₂×C₇×C₁₃	C₇×C₃⋊D₃	1	1	yes	characteristic
26	Dic₃×C₁₃	—	3	4	no	—
27	C₃×C₄₉	Dic₃×C₁₃	1	4	yes	complemented
28	C₂×C₃²×C₇	C₂×C₇×C₁₃	1	1	yes	characteristic
29	C₃²×C₁₃	C₄×C₄₉	1	1	yes	characteristic, complemented, Hall
30	C₂×C₄₉	C₁₃×C₃⋊D₃	1	1	yes	characteristic
31	C₇×C₁₃	C₇×C₃⋊Dic₃	1	1	yes	characteristic
32	C₇×Dic₃	—	3	4	no	—
33	C₂×C₃×C₁₃	D₃×C₄₉	1	4	yes	—
34	C₃²×C₇	C₄×C₇×C₁₃	1	1	yes	characteristic
35	C₄×C₁₃	—	9	1	no	Hall
36	C₄₉	C₁₃×C₃⋊Dic₃	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₃×C₇	D₃×C₇×C₁₃	1	4	yes	—
38	C₃×C₁₃	Dic₃×C₄₉	1	4	yes	complemented
39	C₃⋊Dic₃	C₁₃×C₄₉	1	1	yes	characteristic, direct product factor, Hall
40	C₄×C₇	—	9	1	no	—
41	C₂×C₁₃	C₃⋊D₃×C₄₉	1	1	yes	characteristic
42	C₃×C₇	C₇×Dic₃×C₁₃	1	4	yes	—
43	C₂×C₃²	C₂×C₁₃×C₄₉	1	1	yes	characteristic
44	C₂×C₇	C₇×C₁₃×C₃⋊D₃	1	1	yes	characteristic
45	C₁₃	C₃⋊Dic₃×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
46	Dic₃	—	3	4	no	—
47	C₃²	C₄×C₁₃×C₄₉	1	1	yes	characteristic, complemented, Sylow
48	C₇	C₇×C₁₃×C₃⋊Dic₃	1	1	yes	characteristic
49	C₂×C₃	D₃×C₁₃×C₄₉	1	4	yes	—
50	C₄	—	9	1	no	Sylow
51	C₃	Dic₃×C₁₃×C₄₉	1	4	yes	complemented
52	C₂	C₁₃×C₃⋊D₃×C₄₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₄₉	C₃⋊D₃
commutator, hypocenter	C₃²	C₄×C₁₃×C₄₉
Frattini	C₂×C₇	C₇×C₁₃×C₃⋊D₃
Fitting	C₂×C₃²×C₁₃×C₄₉	C₂
socle, prime radical	C₂×C₃²×C₇×C₁₃	C₂×C₇
cosocle	C₂×C₃²×C₇	C₂×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
3. C₃²×C₁₃×C₄₉	C₄	semidirect
7. C₃×C₁₃×C₄₉	Dic₃	semidirect
8. C₃⋊Dic₃×C₄₉	C₁₃	direct (N × H)
14. C₁₃×C₄₉	C₃⋊Dic₃	direct (N × H)
17. C₁₃×C₃⋊Dic₃	C₄₉	direct (N × H)
18. C₃²×C₄₉	C₄×C₁₃	semidirect
27. C₃×C₄₉	Dic₃×C₁₃	semidirect
29. C₃²×C₁₃	C₄×C₄₉	semidirect
36. C₄₉	C₁₃×C₃⋊Dic₃	direct (N × H)
38. C₃×C₁₃	Dic₃×C₄₉	semidirect
39. C₃⋊Dic₃	C₁₃×C₄₉	direct (N × H)
45. C₁₃	C₃⋊Dic₃×C₄₉	direct (N × H)
47. C₃²	C₄×C₁₃×C₄₉	semidirect
51. C₃	Dic₃×C₁₃×C₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₁₃×C₄₉	2
Dic₃×C₁₃×C₄₉	3
C₇×C₁₃×C₃⋊Dic₃	7
C₃⋊Dic₃×C₄₉	13

Subgroups — C13×C3⋊Dic3×C49 #37524176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₃⋊Dic₃×C₄₉ #37524176