Subgroups — #14563780

Order 2432.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926299	C₂	1	6	yes	maximal
2	C₁₉×#376	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×C₁₉	C₂²	1	3	yes	—
4	C₂²×C₁₉⋊C₈	C₂²	1	4	yes	—
5	C₁₉×#95	C₄	1	4	yes	—
6	C₂²×C₄×C₁₉	C₂×C₄	1	6	yes	—
7	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
8	C₄²×C₁₉	—	2	6	no	—
9	C₂×C₁₉⋊C₈	—	2	12	no	—
10	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₉	—	2	6	no	—
12	C₂×C₄×C₁₉	—	2	12	no	—
13	C₂×C₄×C₁₉	#41	1	6	yes	—
14	C₁₉⋊C₈	—	4	4	no	—
15	#1840	—	19	1	no	maximal, Sylow
16	C₂²×C₁₉	#117	1	3	yes	—
17	C₂²×C₁₉	#131	1	4	yes	—
18	C₄×C₁₉	—	4	6	no	—
19	C₄×C₁₉	#126	1	4	yes	—
20	#376	D₁₉	1	1	yes	characteristic
21	#336	—	19	6	no	—
22	C₂×C₁₉	#383	1	1	yes	characteristic
23	C₂×C₁₉	#433	1	6	yes	—
24	C₂²×C₈	—	19	4	no	—
25	C₂×C₄²	C₂×D₁₉	1	3	yes	—
26	#95	Dic₁₉	1	4	yes	—
27	C₁₉	#1840	1	1	yes	characteristic, complemented, Sylow
28	C₂²×C₄	C₂×Dic₁₉	1	6	yes	—
29	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
30	C₂×C₈	—	38	12	no	—
31	C₄²	—	2	6	no	—
32	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
33	C₂×C₄	—	2	12	no	—
34	C₂×C₄	—	2	6	no	—
35	C₂×C₄	#64541	1	6	yes	—
36	C₈	—	76	4	no	—
37	C₂²	#10597372	1	3	yes	—
38	C₂²	#10597394	1	4	yes	—
39	C₄	—	4	6	no	—
40	C₄	#10597322	1	4	yes	—
41	C₂	#11926412	1	1	yes	characteristic
42	C₂	#11926605	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₉
commutator, socle, prime radical	C₂³×C₁₉	C₂²×C₄
Fitting	C₁₉×#376	C₂
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#376	D₁₉
hypocenter	C₁₉	#1840
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ #376

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

N	H ≅ G/N	type
27. C₁₉	#1840	semidirect

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