Subgroups — #14269028

Order 1824.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	#11744885	C₂	1	2	yes	maximal, complemented
3	#10597290	—	3	1	no	maximal, Hall
4	C₂³×C₃×C₁₉	C₄	1	2	yes	—
5	C₃×D₄×C₁₉	—	2	2	no	—
6	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₃⋊(C₁₉⋊C₈)	—	2	2	no	—
8	C₂×D₄×C₁₉	D₃	1	1	yes	characteristic
9	#64520	—	3	2	no	—
10	C₂²×C₃×C₁₉	—	2	2	no	—
11	C₂²×C₃×C₁₉	—	4	2	no	—
12	C₂²×C₃×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₃×C₄×C₁₉	D₄	1	2	yes	—
14	C₂³×C₁₉	Dic₃	1	2	yes	—
15	D₄×C₁₉	—	2	2	no	—
16	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
17	C₁₉⋊C₈	—	6	2	no	—
18	C₂×C₃×C₁₉	—	2	1	no	—
19	C₂×C₃×C₁₉	—	4	2	no	—
20	C₂×C₃×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
21	#833	—	19	1	no	maximal, Hall
22	C₂²×C₁₉	—	2	2	no	—
23	C₂²×C₁₉	—	4	2	no	—
24	C₂²×C₁₉	C₂×Dic₃	1	1	yes	characteristic
25	C₄×C₁₉	#67	1	2	yes	—
26	C₃×C₁₉	#100	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×D₄	D₁₉	1	1	yes	characteristic
28	#208	—	19	2	no	—
29	C₂×C₁₉	—	2	1	no	—
30	C₂×C₁₉	—	4	2	no	—
31	C₂×C₁₉	#217	1	1	yes	characteristic
32	#100	—	57	1	no	Sylow
33	C₂³×C₃	Dic₁₉	1	2	yes	—
34	C₃×D₄	—	2	2	no	—
35	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
36	C₃⋊C₈	—	38	2	no	—
37	C₁₉	#833	1	1	yes	characteristic, complemented, Sylow
38	C₂×D₄	D₅₇	1	1	yes	characteristic
39	M₁₆	—	57	2	no	—
40	C₂²×C₃	—	2	2	no	—
41	C₂²×C₃	—	4	2	no	—
42	C₂²×C₃	C₂×Dic₁₉	1	1	yes	characteristic
43	C₃×C₄	C₂²⋊D₁₉	1	2	yes	—
44	C₂³	Dic₅₇	1	2	yes	—
45	D₄	—	2	2	no	—
46	C₂×C₄	C₂×D₅₇	1	1	yes	characteristic
47	C₈	—	114	2	no	—
48	C₂×C₃	—	2	1	no	—
49	C₂×C₃	—	4	2	no	—
50	C₂×C₃	C₂²⋊Dic₁₉	1	1	yes	characteristic
51	C₂²	—	2	2	no	—
52	C₂²	—	4	2	no	—
53	C₂²	C₂×Dic₅₇	1	1	yes	characteristic
54	C₄	#90718	1	2	yes	—
55	C₃	#10597290	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	2	1	no	—
57	C₂	—	4	2	no	—
58	C₂	#11744894	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11744894
commutator	C₂²×C₃×C₁₉	C₂×C₄
Frattini	C₂×C₄	C₂×D₅₇
Fitting, prime radical	C₂×C₃×D₄×C₁₉	C₂
socle	C₂×C₃×C₁₉	C₂²⋊C₄
cosocle	C₂×C₃×C₄×C₁₉	C₂²
hypercenter	C₂×D₄	D₅₇
hypocenter	C₃×C₁₉	#100
LCS	G ▷ C₂²×C₃×C₁₉ ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
2. #11744885	C₂	semidirect
26. C₃×C₁₉	#100	semidirect
37. C₁₉	#833	semidirect
55. C₃	#10597290	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₄×C₁₉	2
#11744885	2
#10597290	3
#833	19