Subgroups — D₈×D₁₃ #88164

Order 416.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×D₁₃	C₂	1	2	yes	maximal, complemented
2	C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#6104	C₂	1	2	yes	maximal, complemented
4	D₁₀₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₃	—	2	2	no	—
7	D₄×C₁₃	C₂²	1	2	yes	complemented
8	C₂²⋊D₁₃	—	2	2	no	—
9	D₅₂	C₂²	1	2	yes	complemented
10	C₄×D₁₃	C₂²	1	1	yes	characteristic
11	C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
12	#1055	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₁₃	—	2	2	no	—
14	C₂×D₁₃	—	2	2	no	—
15	C₂×D₁₃	—	4	4	no	—
16	C₂×D₁₃	D₄	1	1	yes	characteristic
17	C₄×C₁₃	C₂³	1	1	yes	characteristic
18	Dic₁₃	D₄	1	1	yes	characteristic
19	C₂×D₈	—	13	1	no	maximal, Sylow
20	C₂×C₁₃	—	4	2	no	—
21	C₂×C₁₃	C₂×D₄	1	1	yes	characteristic
22	D₁₃	—	4	2	no	—
23	D₁₃	D₈	1	2	yes	direct product factor
24	C₂×D₄	—	13	2	no	—
25	D₈	—	13	2	no	—
26	D₈	—	13	1	no	—
27	D₈	D₁₃	1	1	yes	characteristic, direct product factor
28	C₂×C₈	—	13	1	no	—
29	C₁₃	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
30	C₂³	—	26	2	no	—
31	D₄	—	13	2	no	—
32	D₄	—	26	2	no	—
33	D₄	C₂×D₁₃	1	2	yes	complemented
34	C₂×C₄	—	13	1	no	—
35	C₈	—	13	1	no	—
36	C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
37	C₂²	—	2	2	no	—
38	C₂²	—	13	1	no	—
39	C₂²	—	26	2	no	—
40	C₂²	—	52	4	no	—
41	C₄	—	13	1	no	—
42	C₄	C₂²×D₁₃	1	1	yes	characteristic
43	C₂	—	4	2	no	—
44	C₂	—	13	2	no	—
45	C₂	—	52	2	no	—
46	C₂	D₄×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₁₃
commutator, cosocle	C₄×C₁₃	C₂³
Frattini	C₄	C₂²×D₁₃
Fitting	C₁₃×D₈	C₂
socle	C₂×C₁₃	C₂×D₄
hypercenter	D₈	D₁₃
hypocenter	C₁₃	C₂×D₈
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. D₄×D₁₃	C₂	semidirect
2. C₁₃×D₈	C₂	semidirect
3. #6104	C₂	semidirect
4. D₁₀₄	C₂	semidirect
5. C₈×D₁₃	C₂	semidirect
7. D₄×C₁₃	C₂²	semidirect
9. D₅₂	C₂²	semidirect
11. C₈×C₁₃	C₂²	semidirect
12. #1055	C₂²	semidirect
23. D₁₃	D₈	direct (N × H)
27. D₈	D₁₃	direct (N × H)
29. C₁₃	C₂×D₈	semidirect
33. D₄	C₂×D₁₃	semidirect
36. C₈	C₂×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
D₄×D₁₃	2
C₁₃×D₈	2
#6104	2
D₁₀₄	2
C₈×D₁₃	2
C₂×D₈	13

Subgroups — D8×D13 #88164

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×D₁₃ #88164