Subgroups — M₁₆×D₁₃ #88160

Order 416.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#6099	C₂	1	1	yes	maximal, characteristic, complemented
4	#6094	C₂	1	2	yes	maximal, complemented
5	C₈×D₁₃	C₂	1	2	yes	maximal, complemented
6	C₂²×D₁₃	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×Dic₁₃	C₄	1	1	yes	characteristic
9	C₄×D₁₃	C₄	1	1	yes	characteristic
10	C₄×D₁₃	C₄	1	1	yes	characteristic
11	C₄×D₁₃	C₂²	1	1	yes	characteristic
12	C₄×D₁₃	C₂²	1	1	yes	characteristic
13	C₈×C₁₃	C₂²	1	2	yes	complemented
14	#1055	C₂²	1	2	yes	complemented
15	C₂²×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×D₁₃	—	2	2	no	—
17	C₂×D₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×D₁₃	C₂×C₄	1	1	yes	characteristic
19	C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₄×C₁₃	C₂³	1	1	yes	characteristic
21	Dic₁₃	C₂×C₄	1	1	yes	characteristic
22	Dic₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂×M₁₆	—	13	1	no	maximal, Sylow
24	C₂×C₁₃	—	2	1	no	—
25	C₂×C₁₃	C₂²×C₄	1	1	yes	characteristic
26	D₁₃	—	2	1	no	—
27	D₁₃	M₁₆	1	2	yes	direct product factor
28	C₂²×C₄	—	13	1	no	—
29	M₁₆	—	13	1	no	—
30	M₁₆	—	13	2	no	—
31	M₁₆	D₁₃	1	1	yes	characteristic, direct product factor
32	C₂×C₈	—	13	2	no	—
33	C₁₃	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₂³	—	13	1	no	—
35	C₂×C₄	—	13	1	no	—
36	C₂×C₄	—	13	1	no	—
37	C₂×C₄	—	13	1	no	—
38	C₂×C₄	—	13	1	no	—
39	C₂×C₄	—	13	1	no	—
40	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
41	C₈	—	13	2	no	—
42	C₈	C₂×D₁₃	1	2	yes	complemented
43	C₂²	—	13	1	no	—
44	C₂²	—	13	1	no	—
45	C₂²	—	26	2	no	—
46	C₂²	C₄×D₁₃	1	1	yes	characteristic
47	C₄	—	13	1	no	—
48	C₄	—	13	1	no	—
49	C₄	C₄×D₁₃	1	1	yes	characteristic
50	C₄	C₂²×D₁₃	1	1	yes	characteristic
51	C₂	—	2	1	no	—
52	C₂	—	13	2	no	—
53	C₂	—	26	1	no	—
54	C₂	C₂×C₄×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×D₁₃
commutator, socle	C₂×C₁₃	C₂²×C₄
Fitting	C₁₃×M₁₆	C₂
prime radical	C₂²×D₁₃	C₄
cosocle	C₄×C₁₃	C₂³
hypercenter	M₁₆	D₁₃
hypocenter	C₁₃	C₂×M₁₆
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. C₁₃×M₁₆	C₂	semidirect
3. #6099	C₂	semidirect
4. #6094	C₂	semidirect
5. C₈×D₁₃	C₂	semidirect
13. C₈×C₁₃	C₂²	semidirect
14. #1055	C₂²	semidirect
27. D₁₃	M₁₆	direct (N × H)
31. M₁₆	D₁₃	direct (N × H)
33. C₁₃	C₂×M₁₆	semidirect
42. 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
C₂×C₄×D₁₃	2
C₁₃×M₁₆	2
#6099	2
#6094	2
C₈×D₁₃	2
C₂×M₁₆	13

Subgroups — M16×D13 #88160

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×D₁₃ #88160