Subgroups — #11926939

Order 1216.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#124	C₂	1	1	yes	maximal, characteristic
2	C₂×#64528	C₂	1	2	yes	maximal, complemented
3	C₂×#64526	C₂	1	2	yes	maximal
4	#10597315	C₂	1	1	yes	maximal, characteristic, complemented
5	#10597260	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×D₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×Dic₃₈	C₂²	1	2	yes	—
9	C₂²⋊C₄×C₁₉	—	2	2	no	—
10	C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	#64528	—	2	4	no	—
12	#64526	—	2	4	no	—
13	C₄⋊Dic₁₉	—	2	2	no	—
14	C₂×C₁₉⋊C₈	C₂²	1	2	yes	—
15	C₂³×C₁₉	—	2	1	no	—
16	Q₈×C₁₉	—	2	2	no	—
17	D₄×C₁₉	—	2	2	no	—
18	C₂×C₄×C₁₉	—	2	1	no	—
19	C₂×C₄×C₁₉	D₄	1	2	yes	—
20	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×Dic₁₉	—	2	2	no	—
22	Dic₃₈	—	2	2	no	—
23	Dic₃₈	—	2	2	no	—
24	C₁₉⋊C₈	D₄	1	4	yes	—
25	C₂²×C₁₉	—	4	1	no	—
26	C₂²×C₁₉	—	4	2	no	—
27	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
28	C₄×C₁₉	—	2	2	no	—
29	C₄×C₁₉	—	4	1	no	—
30	C₄×C₁₉	C₂×D₄	1	2	yes	—
31	Dic₁₉	—	4	2	no	—
32	#497	—	19	1	no	maximal, Sylow
33	C₂×C₁₉	—	8	1	no	—
34	C₂×C₁₉	#127	1	1	yes	characteristic
35	C₂×C₁₉	#137	1	2	yes	—
36	C₂×Q₁₆	—	19	2	no	—
37	C₂×SD₁₆	—	19	2	no	—
38	C₄⋊Q₈	—	19	1	no	—
39	#124	D₁₉	1	1	yes	characteristic
40	#97	—	19	1	no	—
41	C₁₉	#497	1	1	yes	characteristic, complemented, Sylow
42	C₂×Q₈	—	19	2	no	—
43	C₂×Q₈	C₂×D₁₉	1	1	yes	characteristic
44	C₂×D₄	C₂×D₁₉	1	1	yes	characteristic
45	Q₁₆	—	38	4	no	—
46	SD₁₆	—	38	4	no	—
47	C₂×C₈	—	19	2	no	—
48	C₄⋊C₄	—	38	2	no	—
49	C₂²⋊C₄	—	2	2	no	—
50	C₄²	C₂×D₁₉	1	1	yes	characteristic
51	C₂³	—	2	1	no	—
52	Q₈	—	2	2	no	—
53	Q₈	—	38	2	no	—
54	Q₈	—	38	2	no	—
55	D₄	—	2	2	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	38	2	no	—
58	C₂×C₄	C₂²⋊D₁₉	1	2	yes	—
59	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
60	C₈	—	19	4	no	—
61	C₂²	—	4	1	no	—
62	C₂²	—	4	2	no	—
63	C₂²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	4	1	no	—
66	C₄	—	76	2	no	—
67	C₄	D₄×D₁₉	1	2	yes	—
68	C₂	—	8	1	no	—
69	C₂	#10597386	1	1	yes	characteristic
70	C₂	#10597397	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₁₉×#124	C₂
socle	C₂²×C₁₉	C₂×D₄
prime radical	C₂×D₄×C₁₉	C₂²
hypercenter	#124	D₁₉
hypocenter	C₁₉	#497
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #124

Complements

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

N	H ≅ G/N	type
2. C₂×#64528	C₂	semidirect
4. #10597315	C₂	semidirect
5. #10597260	C₂	semidirect
41. C₁₉	#497	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#124	2
C₂×#64528	2
C₂×#64526	2
#10597315	2
#10597260	2
#497	19