Subgroups — C₂×C₄×C₁₃×D₇ #13089893

Order 1456.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×D₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₇×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₃×D₇	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₇×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₁₃×D₇	C₄	1	4	yes	direct product factor
7	C₂×C₁₃×D₇	C₂²	1	2	yes	—
8	C₄×C₇×C₁₃	C₂²	1	2	yes	complemented
9	C₁₃×Dic₇	C₂²	1	2	yes	complemented
10	C₂²×C₄×C₁₃	—	7	1	no	maximal, Hall
11	C₂×C₇×C₁₃	C₂×C₄	1	2	yes	complemented
12	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
13	C₁₃×D₇	C₂×C₄	1	4	yes	direct product factor
14	C₂×C₄×D₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂³×C₁₃	—	7	1	no	—
16	C₂×C₄×C₁₃	—	7	1	no	—
17	C₂×C₄×C₁₃	—	7	4	no	—
18	C₂×C₄×C₁₃	D₇	1	1	yes	characteristic, direct product factor
19	C₇×C₁₃	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
20	C₂²×D₇	C₂×C₁₃	1	1	yes	characteristic
21	C₂×C₄×C₇	C₂×C₁₃	1	1	yes	characteristic, complemented
22	C₂×Dic₇	C₂×C₁₃	1	1	yes	characteristic, complemented
23	C₄×D₇	C₂×C₁₃	1	4	yes	direct product factor
24	C₂²×C₁₃	—	7	4	no	—
25	C₂²×C₁₃	—	7	2	no	—
26	C₂²×C₁₃	C₂×D₇	1	1	yes	characteristic
27	C₄×C₁₃	—	7	2	no	—
28	C₄×C₁₃	C₂×D₇	1	2	yes	direct product factor
29	C₂²×C₇	C₂²×C₁₃	1	1	yes	characteristic
30	C₂×D₇	C₄×C₁₃	1	4	yes	direct product factor
31	C₂×D₇	C₂²×C₁₃	1	2	yes	—
32	C₄×C₇	C₂²×C₁₃	1	2	yes	complemented
33	Dic₇	C₂²×C₁₃	1	2	yes	complemented
34	C₂×C₁₃	—	7	4	no	—
35	C₂×C₁₃	C₄×D₇	1	2	yes	direct product factor
36	C₂×C₁₃	C₂²×D₇	1	1	yes	characteristic
37	C₂²×C₄	—	7	1	no	Sylow
38	C₂×C₇	C₂×C₄×C₁₃	1	2	yes	complemented
39	C₂×C₇	C₂³×C₁₃	1	1	yes	characteristic
40	D₇	C₂×C₄×C₁₃	1	4	yes	direct product factor
41	C₁₃	C₂×C₄×D₇	1	1	yes	characteristic, direct product factor, Sylow
42	C₂³	—	7	1	no	—
43	C₂×C₄	—	7	1	no	—
44	C₂×C₄	—	7	4	no	—
45	C₂×C₄	C₁₃×D₇	1	1	yes	characteristic, direct product factor
46	C₇	C₂²×C₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
47	C₂²	—	7	4	no	—
48	C₂²	—	7	2	no	—
49	C₂²	C₂×C₁₃×D₇	1	1	yes	characteristic
50	C₄	—	7	2	no	—
51	C₄	C₂×C₁₃×D₇	1	2	yes	direct product factor
52	C₂	—	7	4	no	—
53	C₂	C₄×C₁₃×D₇	1	2	yes	direct product factor
54	C₂	C₂²×C₁₃×D₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄×C₁₃	D₇
commutator, hypocenter	C₇	C₂²×C₄×C₁₃
Frattini	C₂	C₂²×C₁₃×D₇
Fitting	C₂×C₄×C₇×C₁₃	C₂
socle	C₂²×C₇×C₁₃	C₂²
prime radical	C₂²×C₁₃×D₇	C₂
cosocle	C₂×C₇	C₂³×C₁₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₄×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₇×C₁₃	C₂	semidirect
3. C₂×C₁₃×Dic₇	C₂	semidirect
4. C₄×C₁₃×D₇	C₂	direct (N × H)
6. C₂×C₁₃×D₇	C₄	direct (N × H)
8. C₄×C₇×C₁₃	C₂²	semidirect
9. C₁₃×Dic₇	C₂²	semidirect
11. C₂×C₇×C₁₃	C₂×C₄	semidirect
13. C₁₃×D₇	C₂×C₄	direct (N × H)
14. C₂×C₄×D₇	C₁₃	direct (N × H)
18. C₂×C₄×C₁₃	D₇	direct (N × H)
19. C₇×C₁₃	C₂²×C₄	semidirect
21. C₂×C₄×C₇	C₂×C₁₃	semidirect
22. C₂×Dic₇	C₂×C₁₃	semidirect
23. C₄×D₇	C₂×C₁₃	direct (N × H)
28. C₄×C₁₃	C₂×D₇	direct (N × H)
30. C₂×D₇	C₄×C₁₃	direct (N × H)
32. C₄×C₇	C₂²×C₁₃	semidirect
33. Dic₇	C₂²×C₁₃	semidirect
35. C₂×C₁₃	C₄×D₇	direct (N × H)
38. C₂×C₇	C₂×C₄×C₁₃	semidirect
40. D₇	C₂×C₄×C₁₃	direct (N × H)
41. C₁₃	C₂×C₄×D₇	direct (N × H)
45. C₂×C₄	C₁₃×D₇	direct (N × H)
46. C₇	C₂²×C₄×C₁₃	semidirect
51. C₄	C₂×C₁₃×D₇	direct (N × H)
53. C₂	C₄×C₁₃×D₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×D₇	2
C₂×C₄×C₇×C₁₃	2
C₂×C₁₃×Dic₇	2
C₄×C₁₃×D₇	2
C₂²×C₄×C₁₃	7
C₂×C₄×D₇	13

Subgroups — C2×C4×C13×D7 #13089893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₁₃×D₇ #13089893