Group #18072961 — subgroups

Subgroups — #18072961

Order 4864.

574 conjugacy classes of subgroups; only the 291 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 291 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×Dic₁₉	C₂	1	3	yes	maximal
2	C₁₉⋊#1273	C₂	1	3	yes	maximal
3	C₁₉×#1273	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₁₉⋊C₈	C₂²	1	3	yes	—
5	C₂×C₈×Dic₁₉	C₄	1	6	yes	—
6	C₂×C₈×Dic₁₉	C₄	1	6	yes	—
7	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	—
9	C₂²×C₈×C₁₉	C₂×C₄	1	6	yes	—
10	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
11	C₂×C₄×Dic₁₉	C₂×C₄	1	3	yes	—
12	C₂×C₄×Dic₁₉	C₂×C₄	1	3	yes	—
13	C₂²×C₁₉⋊C₈	C₂×C₄	1	6	yes	—
14	C₄×C₈×C₁₉	—	2	6	no	—
15	C₈×Dic₁₉	—	2	12	no	—
16	C₈×Dic₁₉	C₈	1	24	yes	complemented
17	C₄×C₁₉⋊C₈	—	2	3	no	—
18	C₄×C₁₉⋊C₈	—	2	3	no	—
19	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
20	C₂²×Dic₁₉	C₄²	1	1	yes	characteristic
21	C₂²×Dic₁₉	C₄²	1	3	yes	—
22	C₂×C₈×C₁₉	—	2	6	no	—
23	C₂×C₈×C₁₉	—	2	6	no	—
24	C₂×C₈×C₁₉	C₂×C₈	1	12	yes	—
25	C₄²×C₁₉	#41	1	3	yes	—
26	C₄²×C₁₉	#41	1	1	yes	characteristic
27	C₄×Dic₁₉	C₂×C₈	1	12	yes	—
28	C₄×Dic₁₉	M₁₆	1	12	yes	—
29	C₂×C₁₉⋊C₈	—	2	6	no	—
30	C₂×C₁₉⋊C₈	—	2	6	no	—
31	C₂×C₁₉⋊C₈	C₂×C₈	1	12	yes	—
32	#8131	—	19	1	no	maximal, Sylow
33	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
34	C₂×C₄×C₁₉	#117	1	3	yes	—
35	C₂×C₄×C₁₉	#117	1	3	yes	—
36	C₂×C₄×C₁₉	C₂²×C₈	1	6	yes	—
37	C₂×C₄×C₁₉	C₂×M₁₆	1	6	yes	—
38	C₂×Dic₁₉	C₄×C₈	1	6	yes	—
39	C₂×Dic₁₉	C₄×C₈	1	6	yes	—
40	C₂×Dic₁₉	#97	1	12	yes	—
41	C₈×C₁₉	—	2	12	no	—
42	C₁₉⋊C₈	—	2	12	no	—
43	C₄²×C₈	—	19	3	no	—
44	#1273	—	19	3	no	—
45	#1273	D₁₉	1	1	yes	characteristic
46	C₂²×C₁₉	#376	1	1	yes	characteristic
47	C₂²×C₁₉	C₂×C₄×C₈	1	3	yes	—
48	C₂²×C₁₉	C₂×#97	1	3	yes	—
49	C₄×C₁₉	#431	1	6	yes	—
50	C₄×C₁₉	#431	1	6	yes	—
51	Dic₁₉	C₈²	1	4	yes	—
52	Dic₁₉	#322	1	12	yes	—
53	C₂×C₄×C₈	—	19	6	no	—
54	C₂×C₄×C₈	—	19	6	no	—
55	C₂×C₄×C₈	—	19	3	no	—
56	C₂×C₄×C₈	C₂×D₁₉	1	3	yes	—
57	C₄³	—	19	1	no	—
58	C₂×C₁₉	C₂×C₈²	1	1	yes	characteristic
59	C₂×C₁₉	C₂×#322	1	3	yes	—
60	C₂×C₁₉	#1744	1	3	yes	—
61	C₂²×C₈	—	19	6	no	—
62	C₂²×C₈	C₄×D₁₉	1	6	yes	—
63	C₂×C₄²	—	19	3	no	—
64	C₂×C₄²	—	19	3	no	—
65	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
66	C₄×C₈	—	2	6	no	—
67	C₄×C₈	—	19	24	no	—
68	C₄×C₈	—	38	12	no	—
69	C₄×C₈	—	38	3	no	—
70	C₄×C₈	—	38	3	no	—
71	C₁₉	#8131	1	1	yes	characteristic, complemented, Sylow
72	C₂²×C₄	—	19	1	no	—
73	C₂²×C₄	—	19	3	no	—
74	C₂²×C₄	C₂×C₄×D₁₉	1	3	yes	—
75	C₂×C₈	—	2	6	no	—
76	C₂×C₈	—	2	6	no	—
77	C₂×C₈	—	19	12	no	—
78	C₂×C₈	—	38	6	no	—
79	C₂×C₈	—	38	6	no	—
80	C₂×C₈	C₈×D₁₉	1	12	yes	—
81	C₄²	—	19	12	no	—
82	C₄²	—	19	12	no	—
83	C₄²	#64543	1	3	yes	—
84	C₄²	#64545	1	1	yes	characteristic
85	C₂³	C₄²×D₁₉	1	1	yes	characteristic
86	C₂×C₄	—	19	6	no	—
87	C₂×C₄	—	19	6	no	—
88	C₂×C₄	—	19	12	no	—
89	C₂×C₄	#10597323	1	3	yes	—
90	C₂×C₄	#10597338	1	3	yes	—
91	C₂×C₄	C₂×C₈×D₁₉	1	6	yes	—
92	C₂×C₄	M₁₆×D₁₉	1	6	yes	—
93	C₈	—	2	12	no	—
94	C₈	—	38	12	no	—
95	C₂²	#11926389	1	1	yes	characteristic
96	C₂²	C₄×C₈×D₁₉	1	3	yes	—
97	C₂²	#97×D₁₉	1	3	yes	—
98	C₄	—	19	4	no	—
99	C₄	—	19	12	no	—
100	C₄	#11926594	1	6	yes	—
101	C₄	#11926596	1	6	yes	—
102	C₂	C₈²×D₁₉	1	1	yes	characteristic
103	C₂	D₁₉×#322	1	3	yes	—
104	C₂	#14563379	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₈×Dic₁₉

C₂

yes

maximal

C₁₉⋊#1273

C₂

yes

maximal

C₁₉×#1273

C₂

yes

maximal, characteristic

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

C₂×C₈×Dic₁₉

C₄

yes

—

C₂×C₈×Dic₁₉

C₄

yes

—

C₄²×Dic₁₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

—

C₂×C₄×Dic₁₉

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₈×C₁₉

—

C₈×Dic₁₉

—

C₈×Dic₁₉

C₈

yes

complemented

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

—

C₂²×Dic₁₉

C₄²

yes

characteristic

C₂²×Dic₁₉

C₄²

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₈

yes

—

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₄×Dic₁₉

C₂×C₈

yes

—

C₄×Dic₁₉

M₁₆

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₈

yes

—

#8131

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

C₂²×C₈

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×Dic₁₉

C₄×C₈

yes

—

C₂×Dic₁₉

C₄×C₈

yes

—

C₂×Dic₁₉

#97

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₄²×C₈

—

#1273

—

#1273

D₁₉

yes

characteristic

C₂²×C₁₉

#376

yes

characteristic

C₂²×C₁₉

C₂×C₄×C₈

yes

—

C₂²×C₁₉

C₂×#97

yes

—

C₄×C₁₉

#431

yes

—

C₄×C₁₉

#431

yes

—

Dic₁₉

C₈²

yes

—

Dic₁₉

#322

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

C₄³

—

C₂×C₁₉

C₂×C₈²

yes

characteristic

C₂×C₁₉

C₂×#322

yes

—

C₂×C₁₉

#1744

yes

—

C₂²×C₈

—

C₂²×C₈

C₄×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₁₉

#8131

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₄×D₁₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₈×D₁₉

yes

—

C₄²

—

C₄²

—

C₄²

#64543

yes

—

C₄²

#64545

yes

characteristic

C₂³

C₄²×D₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#10597323

yes

—

C₂×C₄

#10597338

yes

—

C₂×C₄

C₂×C₈×D₁₉

yes

—

C₂×C₄

M₁₆×D₁₉

yes

—

C₈

—

C₈

—

C₂²

#11926389

yes

characteristic

C₂²

C₄×C₈×D₁₉

yes

—

C₂²

#97×D₁₉

yes

—

C₄

—

C₄

—

100

C₄

#11926594

yes

—

101

C₄

#11926596

yes

—

102

C₂

C₈²×D₁₉

yes

characteristic

103

C₂

D₁₉×#322

yes

—

104

C₂

#14563379

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₉
commutator	C₂×C₁₉	C₂×C₈²
Fitting	C₁₉×#1273	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1273	D₁₉
hypocenter	C₁₉	#8131
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₁₉

commutator

C₂×C₁₉

C₂×C₈²

Fitting

C₁₉×#1273

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₄²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
16. C₈×Dic₁₉	C₈	semidirect
71. C₁₉	#8131	semidirect

H ≅ G/N

type

16. C₈×Dic₁₉

C₈

semidirect

71. C₁₉

#8131

semidirect

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

subgroup	index
C₄×C₈×Dic₁₉	2
C₁₉⋊#1273	2
C₁₉×#1273	2
#8131	19

subgroup

index

C₄×C₈×Dic₁₉

C₁₉⋊#1273

C₁₉×#1273

#8131

Subgroups — #18072961

Conjugacy classes of subgroups

Complements

Maximal subgroups