Subgroups — SD₁₆×D₁₃ #88167

Order 416.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#6106	C₂	1	1	yes	maximal, characteristic, complemented
5	#6105	C₂	1	1	yes	maximal, characteristic, complemented
6	#6095	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₁₃	—	2	1	no	—
9	Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
10	D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²⋊D₁₃	—	2	1	no	—
12	D₅₂	C₂²	1	1	yes	characteristic
13	C₄×D₁₃	—	2	1	no	—
14	C₄×D₁₃	C₂²	1	1	yes	characteristic
15	Dic₂₆	—	2	1	no	—
16	Dic₂₆	C₂²	1	1	yes	characteristic, complemented
17	C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
18	#1055	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₁₃	—	2	1	no	—
20	C₂×D₁₃	—	2	1	no	—
21	C₂×D₁₃	—	4	2	no	—
22	C₂×D₁₃	D₄	1	1	yes	characteristic
23	C₄×C₁₃	—	2	1	no	—
24	C₄×C₁₃	C₂³	1	1	yes	characteristic
25	Dic₁₃	—	2	1	no	—
26	Dic₁₃	D₄	1	1	yes	characteristic
27	C₂×SD₁₆	—	13	1	no	maximal, Sylow
28	C₂×C₁₃	—	4	1	no	—
29	C₂×C₁₃	C₂×D₄	1	1	yes	characteristic
30	D₁₃	—	4	1	no	—
31	D₁₃	SD₁₆	1	2	yes	direct product factor
32	C₂×Q₈	—	13	1	no	—
33	C₂×D₄	—	13	1	no	—
34	SD₁₆	—	13	1	no	—
35	SD₁₆	—	13	1	no	—
36	SD₁₆	—	13	1	no	—
37	SD₁₆	D₁₃	1	1	yes	characteristic, direct product factor
38	C₂×C₈	—	13	1	no	—
39	C₁₃	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
40	C₂³	—	26	1	no	—
41	Q₈	—	13	1	no	—
42	Q₈	—	26	1	no	—
43	Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
44	D₄	—	13	1	no	—
45	D₄	—	26	1	no	—
46	D₄	C₂×D₁₃	1	1	yes	characteristic
47	C₂×C₄	—	13	1	no	—
48	C₂×C₄	—	26	1	no	—
49	C₈	—	13	1	no	—
50	C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
51	C₂²	—	2	1	no	—
52	C₂²	—	13	1	no	—
53	C₂²	—	26	1	no	—
54	C₂²	—	52	2	no	—
55	C₄	—	2	1	no	—
56	C₄	—	13	1	no	—
57	C₄	—	26	1	no	—
58	C₄	C₂²×D₁₃	1	1	yes	characteristic
59	C₂	—	4	1	no	—
60	C₂	—	13	2	no	—
61	C₂	—	52	1	no	—
62	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×SD₁₆	C₂
socle	C₂×C₁₃	C₂×D₄
prime radical	D₄×D₁₃	C₂
hypercenter	SD₁₆	D₁₃
hypocenter	C₁₃	C₂×SD₁₆
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

Complements

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

N	H ≅ G/N	type
1. Q₈×D₁₃	C₂	semidirect
3. C₁₃×SD₁₆	C₂	semidirect
4. #6106	C₂	semidirect
5. #6105	C₂	semidirect
6. #6095	C₂	semidirect
7. C₈×D₁₃	C₂	semidirect
9. Q₈×C₁₃	C₂²	semidirect
16. Dic₂₆	C₂²	semidirect
17. C₈×C₁₃	C₂²	semidirect
18. #1055	C₂²	semidirect
31. D₁₃	SD₁₆	direct (N × H)
37. SD₁₆	D₁₃	direct (N × H)
39. C₁₃	C₂×SD₁₆	semidirect
43. Q₈	C₂×D₁₃	semidirect
50. 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
Q₈×D₁₃	2
D₄×D₁₃	2
C₁₃×SD₁₆	2
#6106	2
#6105	2
#6095	2
C₈×D₁₃	2
C₂×SD₁₆	13

Subgroups — SD16×D13 #88167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₁₆×D₁₃ #88167