Subgroups — C₃×C₇²×A₄×C₁₃ #37525650

Order 22932.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×A₄×C₁₃	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₇²×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₇²×C₁₃	—	4	1	no	maximal, Hall
4	C₂×C₃×C₇²×C₁₃	—	3	1	no	—
5	C₃×C₇×A₄×C₁₃	C₇	1	8	yes	maximal, direct product factor
6	C₂²×C₇²×C₁₃	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇²×C₁₃	—	4	3	no	—
8	C₃×C₇²×C₁₃	A₄	1	1	yes	characteristic, direct product factor
9	C₃×C₇²×A₄	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₇²×C₁₃	—	3	1	no	—
11	C₂²×C₃×C₇×C₁₃	C₃×C₇	1	8	yes	complemented
12	C₇×A₄×C₁₃	C₃×C₇	1	24	yes	direct product factor
13	C₃²×C₇×C₁₃	—	4	8	no	—
14	C₇²×C₁₃	C₃×A₄	1	1	yes	characteristic, direct product factor, Hall
15	C₂²×C₃×C₇²	C₃×C₁₃	1	1	yes	characteristic, complemented
16	C₇²×A₄	C₃×C₁₃	1	3	yes	direct product factor
17	C₂×C₃×C₇×C₁₃	—	3	8	no	—
18	C₃×A₄×C₁₃	C₇²	1	1	yes	characteristic, direct product factor, Hall
19	C₃²×C₇²	—	4	1	no	Hall
20	C₂²×C₇×C₁₃	C₃²×C₇	1	8	yes	complemented
21	C₂×C₃×C₇²	—	3	1	no	—
22	C₃×C₇×C₁₃	—	4	24	no	—
23	C₃×C₇×C₁₃	C₇×A₄	1	8	yes	direct product factor
24	C₃×C₇×A₄	C₇×C₁₃	1	8	yes	direct product factor
25	C₂²×C₇²	C₃²×C₁₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇×C₁₃	—	3	8	no	—
27	C₂²×C₃×C₁₃	C₃×C₇²	1	1	yes	characteristic, complemented
28	A₄×C₁₃	C₃×C₇²	1	3	yes	direct product factor
29	C₃×C₇²	—	4	3	no	—
30	C₃×C₇²	A₄×C₁₃	1	1	yes	characteristic, direct product factor
31	C₃²×C₁₃	—	4	1	no	Hall
32	C₂×C₇²	—	3	1	no	—
33	C₇×C₁₃	C₃×C₇×A₄	1	8	yes	direct product factor
34	C₂²×C₃×C₇	C₃×C₇×C₁₃	1	8	yes	complemented
35	C₇×A₄	C₃×C₇×C₁₃	1	24	yes	direct product factor
36	C₂×C₃×C₁₃	—	3	1	no	—
37	C₃²×C₇	—	4	8	no	—
38	C₂²×C₁₃	C₃²×C₇²	1	1	yes	characteristic, complemented, Hall
39	C₇²	C₃×A₄×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃×C₇	—	3	8	no	—
41	C₃×C₁₃	—	4	3	no	—
42	C₃×C₁₃	C₇²×A₄	1	1	yes	characteristic, direct product factor
43	C₃×A₄	C₇²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
44	C₂²×C₇	C₃²×C₇×C₁₃	1	8	yes	complemented
45	C₂×C₁₃	—	3	1	no	—
46	C₃×C₇	—	4	24	no	—
47	C₃×C₇	C₇×A₄×C₁₃	1	8	yes	direct product factor
48	C₂×C₇	—	3	8	no	—
49	C₁₃	C₃×C₇²×A₄	1	1	yes	characteristic, direct product factor, Sylow
50	C₂²×C₃	C₃×C₇²×C₁₃	1	1	yes	characteristic, complemented
51	A₄	C₃×C₇²×C₁₃	1	3	yes	direct product factor
52	C₃²	—	4	1	no	Sylow
53	C₇	C₃×C₇×A₄×C₁₃	1	8	yes	direct product factor
54	C₂×C₃	—	3	1	no	—
55	C₂²	C₃²×C₇²×C₁₃	1	1	yes	characteristic, complemented, Sylow
56	C₃	—	4	3	no	—
57	C₃	C₇²×A₄×C₁₃	1	1	yes	characteristic, direct product factor
58	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₇²×C₁₃	A₄
commutator, cosocle, hypocenter	C₂²	C₃²×C₇²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₇²×C₁₃	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₇²×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₇²×A₄×C₁₃	C₃	direct (N × H)
2. C₂²×C₃×C₇²×C₁₃	C₃	semidirect
5. C₃×C₇×A₄×C₁₃	C₇	direct (N × H)
6. C₂²×C₇²×C₁₃	C₃²	semidirect
8. C₃×C₇²×C₁₃	A₄	direct (N × H)
9. C₃×C₇²×A₄	C₁₃	direct (N × H)
11. C₂²×C₃×C₇×C₁₃	C₃×C₇	semidirect
12. C₇×A₄×C₁₃	C₃×C₇	direct (N × H)
14. C₇²×C₁₃	C₃×A₄	direct (N × H)
15. C₂²×C₃×C₇²	C₃×C₁₃	semidirect
16. C₇²×A₄	C₃×C₁₃	direct (N × H)
18. C₃×A₄×C₁₃	C₇²	direct (N × H)
20. C₂²×C₇×C₁₃	C₃²×C₇	semidirect
23. C₃×C₇×C₁₃	C₇×A₄	direct (N × H)
24. C₃×C₇×A₄	C₇×C₁₃	direct (N × H)
25. C₂²×C₇²	C₃²×C₁₃	semidirect
27. C₂²×C₃×C₁₃	C₃×C₇²	semidirect
28. A₄×C₁₃	C₃×C₇²	direct (N × H)
30. C₃×C₇²	A₄×C₁₃	direct (N × H)
33. C₇×C₁₃	C₃×C₇×A₄	direct (N × H)
34. C₂²×C₃×C₇	C₃×C₇×C₁₃	semidirect
35. C₇×A₄	C₃×C₇×C₁₃	direct (N × H)
38. C₂²×C₁₃	C₃²×C₇²	semidirect
39. C₇²	C₃×A₄×C₁₃	direct (N × H)
42. C₃×C₁₃	C₇²×A₄	direct (N × H)
43. C₃×A₄	C₇²×C₁₃	direct (N × H)
44. C₂²×C₇	C₃²×C₇×C₁₃	semidirect
47. C₃×C₇	C₇×A₄×C₁₃	direct (N × H)
49. C₁₃	C₃×C₇²×A₄	direct (N × H)
50. C₂²×C₃	C₃×C₇²×C₁₃	semidirect
51. A₄	C₃×C₇²×C₁₃	direct (N × H)
53. C₇	C₃×C₇×A₄×C₁₃	direct (N × H)
55. C₂²	C₃²×C₇²×C₁₃	semidirect
57. C₃	C₇²×A₄×C₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇²×A₄×C₁₃	3
C₂²×C₃×C₇²×C₁₃	3
C₃²×C₇²×C₁₃	4
C₃×C₇×A₄×C₁₃	7
C₃×C₇²×A₄	13

Subgroups — C3×C72×A4×C13 #37525650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇²×A₄×C₁₃ #37525650