Subgroups — C₂×D₇×Dic₁₃ #13089872

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×Dic₉₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×Dic₁₃	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	complemented
7	C₂×C₁₃×D₇	C₂²	1	2	yes	—
8	Dic₉₁	C₂²	1	2	yes	complemented
9	C₇×Dic₁₃	C₂²	1	2	yes	complemented
10	C₂²×Dic₁₃	—	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	complemented
14	C₂×C₄×D₇	—	13	1	no	maximal, Hall
15	C₂³×C₁₃	—	7	1	no	—
16	C₂×Dic₁₃	—	7	1	no	—
17	C₂×Dic₁₃	—	7	4	no	—
18	C₂×Dic₁₃	D₇	1	1	yes	characteristic, direct product factor
19	C₇×C₁₃	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
20	C₂²×D₇	D₁₃	1	1	yes	characteristic
21	C₂×C₄×C₇	—	13	1	no	—
22	C₂×Dic₇	—	13	1	no	—
23	C₄×D₇	—	13	4	no	—
24	C₂²×C₁₃	—	7	4	no	—
25	C₂²×C₁₃	—	7	2	no	—
26	C₂²×C₁₃	C₂×D₇	1	1	yes	characteristic
27	Dic₁₃	—	7	2	no	—
28	Dic₁₃	C₂×D₇	1	2	yes	direct product factor
29	C₂²×C₇	C₂×D₁₃	1	1	yes	characteristic
30	C₂×D₇	Dic₁₃	1	4	yes	direct product factor
31	C₂×D₇	C₂×D₁₃	1	2	yes	—
32	C₄×C₇	—	13	2	no	—
33	Dic₇	—	13	2	no	—
34	C₂×C₁₃	—	7	4	no	—
35	C₂×C₁₃	C₄×D₇	1	2	yes	complemented
36	C₂×C₁₃	C₂²×D₇	1	1	yes	characteristic
37	C₂²×C₄	—	91	1	no	Sylow
38	C₂×C₇	C₂×Dic₁₃	1	2	yes	complemented
39	C₂×C₇	C₂²×D₁₃	1	1	yes	characteristic
40	D₇	C₂×Dic₁₃	1	4	yes	direct product factor
41	C₁₃	C₂×C₄×D₇	1	1	yes	characteristic, complemented, Sylow
42	C₂³	—	7	1	no	—
43	C₂×C₄	—	13	1	no	—
44	C₂×C₄	—	91	4	no	—
45	C₂×C₄	—	91	1	no	—
46	C₇	C₂²×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
47	C₂²	—	7	4	no	—
48	C₂²	—	7	2	no	—
49	C₂²	D₇×D₁₃	1	1	yes	characteristic
50	C₄	—	13	2	no	—
51	C₄	—	91	2	no	—
52	C₂	—	7	4	no	—
53	C₂	D₇×Dic₁₃	1	2	yes	direct product factor
54	C₂	C₂×D₇×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₇×D₁₃
commutator, hypocenter	C₇×C₁₃	C₂²×C₄
Frattini	C₂	C₂×D₇×D₁₃
Fitting, socle	C₂²×C₇×C₁₃	C₂²
prime radical	C₂²×C₁₃×D₇	C₂
cosocle	C₂×C₇×C₁₃	C₂³
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₉₁	C₂	semidirect
3. C₂×C₇×Dic₁₃	C₂	semidirect
4. D₇×Dic₁₃	C₂	direct (N × H)
6. C₂×C₁₃×D₇	C₄	semidirect
8. Dic₉₁	C₂²	semidirect
9. C₇×Dic₁₃	C₂²	semidirect
11. C₂×C₇×C₁₃	C₂×C₄	semidirect
13. C₁₃×D₇	C₂×C₄	semidirect
18. C₂×Dic₁₃	D₇	direct (N × H)
19. C₇×C₁₃	C₂²×C₄	semidirect
28. Dic₁₃	C₂×D₇	direct (N × H)
30. C₂×D₇	Dic₁₃	direct (N × H)
35. C₂×C₁₃	C₄×D₇	semidirect
38. C₂×C₇	C₂×Dic₁₃	semidirect
40. D₇	C₂×Dic₁₃	direct (N × H)
41. C₁₃	C₂×C₄×D₇	semidirect
46. C₇	C₂²×Dic₁₃	semidirect
53. C₂	D₇×Dic₁₃	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×Dic₉₁	2
C₂×C₇×Dic₁₃	2
D₇×Dic₁₃	2
C₂²×Dic₁₃	7
C₂×C₄×D₇	13

Subgroups — C2×D7×Dic13 #13089872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₇×Dic₁₃ #13089872