Subgroups — (C₂×D₁₉)⋊C₁₆ #11926323

Order 1216.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₁₉	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₉	C₂²	1	1	yes	characteristic
6	C₂×C₁₉⋊C₈	C₄	1	1	yes	characteristic
7	C₈×D₁₉	—	2	1	no	—
8	C₈×D₁₉	—	2	1	no	—
9	C₁₆×C₁₉	—	2	1	no	—
10	C₁₉⋊C₁₆	—	2	1	no	—
11	C₂²×D₁₉	C₈	1	1	yes	characteristic
12	C₂×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₁₉	C₈	1	1	yes	characteristic
14	C₄×D₁₉	—	2	1	no	—
15	C₄×D₁₉	—	2	1	no	—
16	C₈×C₁₉	D₄	1	1	yes	characteristic
17	C₈×C₁₉	D₄	1	1	yes	characteristic
18	C₁₉⋊C₈	—	2	1	no	—
19	C₂²×C₁₉	C₂×C₈	1	1	yes	characteristic
20	C₂×D₁₉	—	2	1	no	—
21	C₂×D₁₉	—	2	1	no	—
22	C₂×D₁₉	C₁₆	1	2	yes	complemented
23	C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₄×C₁₉	M₁₆	1	1	yes	characteristic
25	Dic₁₉	—	2	1	no	—
26	C₂²⋊C₁₆	—	19	1	no	maximal, Sylow
27	C₂×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
28	C₂×C₁₉	C₂×C₁₆	1	1	yes	characteristic
29	C₂×C₁₉	M₃₂	1	1	yes	characteristic
30	D₁₉	—	2	2	no	—
31	C₂²×C₈	—	19	1	no	—
32	C₂×C₁₆	—	19	1	no	—
33	C₂×C₁₆	D₁₉	1	1	yes	characteristic, complemented
34	C₁₉	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
35	C₂²×C₄	—	19	1	no	—
36	C₂×C₈	—	19	1	no	—
37	C₂×C₈	—	38	1	no	—
38	C₂×C₈	—	38	1	no	—
39	C₂×C₈	C₂×D₁₉	1	1	yes	characteristic
40	C₁₆	—	2	1	no	—
41	C₁₆	—	38	1	no	—
42	C₂³	—	19	1	no	—
43	C₂×C₄	—	19	1	no	—
44	C₂×C₄	—	38	1	no	—
45	C₂×C₄	—	38	1	no	—
46	C₂×C₄	C₄×D₁₉	1	1	yes	characteristic
47	C₈	—	38	1	no	—
48	C₈	D₇₆	1	1	yes	characteristic
49	C₈	C₂²⋊D₁₉	1	1	yes	characteristic
50	C₂²	—	19	2	no	—
51	C₂²	—	38	1	no	—
52	C₂²	—	38	1	no	—
53	C₂²	C₈×D₁₉	1	1	yes	characteristic
54	C₄	—	38	1	no	—
55	C₄	#64515	1	1	yes	characteristic
56	C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
57	C₂	—	38	2	no	—
58	C₂	C₁₆×D₁₉	1	1	yes	characteristic
59	C₂	#10597255	1	1	yes	characteristic
60	C₂	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₁₉
commutator	C₂×C₁₉	C₂×C₁₆
Fitting	C₂×C₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂×C₈
prime radical	C₂²×D₁₉	C₈
cosocle	C₂×C₈×C₁₉	C₂²
hypercenter	C₂×C₁₆	D₁₉
hypocenter	C₁₉	C₂²⋊C₁₆
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₆×C₁₉	C₂	semidirect
3. C₂×C₁₉⋊C₁₆	C₂	semidirect
22. C₂×D₁₉	C₁₆	semidirect
33. C₂×C₁₆	D₁₉	semidirect
34. C₁₉	C₂²⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₁₉	2
C₂×C₁₆×C₁₉	2
C₂×C₁₉⋊C₁₆	2
C₂²⋊C₁₆	19

Subgroups — (C2×D19)⋊C16 #11926323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×D₁₉)⋊C₁₆ #11926323