Subgroups — C₂×C₄×C₇×D₁₃ #13089883

Order 1456.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₇×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₇×D₁₃	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₇×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₇×D₁₃	C₄	1	4	yes	direct product factor
7	C₂×C₇×D₁₃	C₂²	1	2	yes	—
8	C₄×C₇×C₁₃	C₂²	1	2	yes	complemented
9	C₇×Dic₁₃	C₂²	1	2	yes	complemented
10	C₂×C₄×D₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₇×C₁₃	C₂×C₄	1	2	yes	complemented
12	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
13	C₇×D₁₃	C₂×C₄	1	4	yes	direct product factor
14	C₂²×C₄×C₇	—	13	1	no	maximal, Hall
15	C₂²×D₁₃	C₂×C₇	1	1	yes	characteristic
16	C₂×C₄×C₁₃	C₂×C₇	1	1	yes	characteristic, complemented
17	C₂×Dic₁₃	C₂×C₇	1	1	yes	characteristic, complemented
18	C₄×D₁₃	C₂×C₇	1	4	yes	direct product factor
19	C₇×C₁₃	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
20	C₂³×C₇	—	13	1	no	—
21	C₂×C₄×C₇	—	13	1	no	—
22	C₂×C₄×C₇	—	13	4	no	—
23	C₂×C₄×C₇	D₁₃	1	1	yes	characteristic, direct product factor
24	C₂²×C₁₃	C₂²×C₇	1	1	yes	characteristic
25	C₂×D₁₃	C₄×C₇	1	4	yes	direct product factor
26	C₂×D₁₃	C₂²×C₇	1	2	yes	—
27	C₄×C₁₃	C₂²×C₇	1	2	yes	complemented
28	Dic₁₃	C₂²×C₇	1	2	yes	complemented
29	C₂²×C₇	—	13	4	no	—
30	C₂²×C₇	—	13	2	no	—
31	C₂²×C₇	C₂×D₁₃	1	1	yes	characteristic
32	C₄×C₇	—	13	2	no	—
33	C₄×C₇	C₂×D₁₃	1	2	yes	direct product factor
34	C₂×C₁₃	C₂×C₄×C₇	1	2	yes	complemented
35	C₂×C₁₃	C₂³×C₇	1	1	yes	characteristic
36	D₁₃	C₂×C₄×C₇	1	4	yes	direct product factor
37	C₂²×C₄	—	13	1	no	Sylow
38	C₂×C₇	—	13	4	no	—
39	C₂×C₇	C₄×D₁₃	1	2	yes	direct product factor
40	C₂×C₇	C₂²×D₁₃	1	1	yes	characteristic
41	C₁₃	C₂²×C₄×C₇	1	1	yes	characteristic, complemented, Sylow
42	C₂³	—	13	1	no	—
43	C₂×C₄	—	13	1	no	—
44	C₂×C₄	—	13	4	no	—
45	C₂×C₄	C₇×D₁₃	1	1	yes	characteristic, direct product factor
46	C₇	C₂×C₄×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
47	C₂²	—	13	4	no	—
48	C₂²	—	13	2	no	—
49	C₂²	C₂×C₇×D₁₃	1	1	yes	characteristic
50	C₄	—	13	2	no	—
51	C₄	C₂×C₇×D₁₃	1	2	yes	direct product factor
52	C₂	—	13	4	no	—
53	C₂	C₄×C₇×D₁₃	1	2	yes	direct product factor
54	C₂	C₂²×C₇×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄×C₇	D₁₃
commutator, hypocenter	C₁₃	C₂²×C₄×C₇
Frattini	C₂	C₂²×C₇×D₁₃
Fitting	C₂×C₄×C₇×C₁₃	C₂
socle	C₂²×C₇×C₁₃	C₂²
prime radical	C₂²×C₇×D₁₃	C₂
cosocle	C₂×C₁₃	C₂³×C₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₄×C₇

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×C₇×Dic₁₃	C₂	semidirect
4. C₄×C₇×D₁₃	C₂	direct (N × H)
6. C₂×C₇×D₁₃	C₄	direct (N × H)
8. C₄×C₇×C₁₃	C₂²	semidirect
9. C₇×Dic₁₃	C₂²	semidirect
10. C₂×C₄×D₁₃	C₇	direct (N × H)
11. C₂×C₇×C₁₃	C₂×C₄	semidirect
13. C₇×D₁₃	C₂×C₄	direct (N × H)
16. C₂×C₄×C₁₃	C₂×C₇	semidirect
17. C₂×Dic₁₃	C₂×C₇	semidirect
18. C₄×D₁₃	C₂×C₇	direct (N × H)
19. C₇×C₁₃	C₂²×C₄	semidirect
23. C₂×C₄×C₇	D₁₃	direct (N × H)
25. C₂×D₁₃	C₄×C₇	direct (N × H)
27. C₄×C₁₃	C₂²×C₇	semidirect
28. Dic₁₃	C₂²×C₇	semidirect
33. C₄×C₇	C₂×D₁₃	direct (N × H)
34. C₂×C₁₃	C₂×C₄×C₇	semidirect
36. D₁₃	C₂×C₄×C₇	direct (N × H)
39. C₂×C₇	C₄×D₁₃	direct (N × H)
41. C₁₃	C₂²×C₄×C₇	semidirect
45. C₂×C₄	C₇×D₁₃	direct (N × H)
46. C₇	C₂×C₄×D₁₃	direct (N × H)
51. C₄	C₂×C₇×D₁₃	direct (N × H)
53. C₂	C₄×C₇×D₁₃	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×C₇×D₁₃	2
C₂×C₄×C₇×C₁₃	2
C₂×C₇×Dic₁₃	2
C₄×C₇×D₁₃	2
C₂×C₄×D₁₃	7
C₂²×C₄×C₇	13

Subgroups — C2×C4×C7×D13 #13089883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₇×D₁₃ #13089883