Group #18072973 — subgroups

Subgroups — #18072973

Order 4864.

382 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 167 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	#14563380	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	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
6	#11926298	C₄	1	6	yes	—
7	#11926298	C₄	1	6	yes	—
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	C₄×C₁₉⋊C₈	—	2	3	no	—
16	C₄×C₁₉⋊C₈	—	2	3	no	—
17	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
18	C₂²×Dic₁₉	C₄²	1	1	yes	characteristic
19	C₂²×Dic₁₉	C₄²	1	3	yes	—
20	C₂×C₈×C₁₉	—	2	6	no	—
21	C₂×C₈×C₁₉	—	2	6	no	—
22	C₂×C₈×C₁₉	—	2	6	no	—
23	C₄²×C₁₉	#41	1	3	yes	—
24	C₄²×C₁₉	#41	1	1	yes	characteristic
25	C₄×Dic₁₉	—	2	6	no	—
26	C₄×Dic₁₉	—	2	6	no	—
27	C₂×C₁₉⋊C₈	—	2	6	no	—
28	C₂×C₁₉⋊C₈	—	2	6	no	—
29	C₂×C₁₉⋊C₈	—	2	6	no	—
30	#8135	—	19	1	no	maximal, Sylow
31	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
32	C₂×C₄×C₁₉	#117	1	3	yes	—
33	C₂×C₄×C₁₉	#117	1	3	yes	—
34	C₂×C₄×C₁₉	#131	1	6	yes	—
35	C₂×C₄×C₁₉	#131	1	6	yes	—
36	C₂×Dic₁₉	—	2	3	no	—
37	C₂×Dic₁₉	—	2	3	no	—
38	C₂×Dic₁₉	—	2	6	no	—
39	C₈×C₁₉	—	4	6	no	—
40	C₁₉⋊C₈	—	4	6	no	—
41	#1744	—	19	3	no	—
42	#1273	—	19	3	no	—
43	#1273	D₁₉	1	1	yes	characteristic
44	C₂²×C₁₉	#376	1	1	yes	characteristic
45	C₂²×C₁₉	#405	1	3	yes	—
46	C₂²×C₁₉	#405	1	3	yes	—
47	C₄×C₁₉	#433	1	6	yes	—
48	C₄×C₁₉	#433	1	6	yes	—
49	Dic₁₉	—	4	1	no	—
50	Dic₁₉	—	4	3	no	—
51	C₂×C₄×C₈	—	19	3	no	—
52	C₂×C₄×C₈	C₂×D₁₉	1	3	yes	—
53	C₄³	—	19	1	no	—
54	#336	—	19	6	no	—
55	#336	—	19	6	no	—
56	C₂×C₁₉	#1454	1	1	yes	characteristic
57	C₂×C₁₉	#1454	1	3	yes	—
58	C₂×C₁₉	#1746	1	3	yes	—
59	C₂²×C₈	—	19	6	no	—
60	C₂²×C₈	C₄×D₁₉	1	6	yes	—
61	C₂×C₄²	—	19	3	no	—
62	C₂×C₄²	—	19	3	no	—
63	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
64	C₄×C₈	—	2	6	no	—
65	C₄×C₈	—	38	3	no	—
66	C₄×C₈	—	38	3	no	—
67	C₁₉	#8135	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₄	—	19	1	no	—
69	C₂²×C₄	—	19	3	no	—
70	C₂²×C₄	C₂×C₄×D₁₉	1	3	yes	—
71	C₂×C₈	—	2	6	no	—
72	C₂×C₈	—	2	6	no	—
73	C₂×C₈	—	2	6	no	—
74	C₂×C₈	—	38	6	no	—
75	C₂×C₈	—	38	6	no	—
76	C₂×C₈	—	38	6	no	—
77	C₄²	—	38	6	no	—
78	C₄²	—	38	6	no	—
79	C₄²	#64543	1	3	yes	—
80	C₄²	#64545	1	1	yes	characteristic
81	C₂³	C₄²×D₁₉	1	1	yes	characteristic
82	C₂×C₄	—	38	3	no	—
83	C₂×C₄	—	38	3	no	—
84	C₂×C₄	—	38	6	no	—
85	C₂×C₄	#10597323	1	3	yes	—
86	C₂×C₄	#10597338	1	3	yes	—
87	C₂×C₄	#10597347	1	6	yes	—
88	C₂×C₄	#10597353	1	6	yes	—
89	C₈	—	4	6	no	—
90	C₈	—	76	6	no	—
91	C₂²	#11926389	1	1	yes	characteristic
92	C₂²	#11926498	1	3	yes	—
93	C₂²	#11926501	1	3	yes	—
94	C₄	—	76	1	no	—
95	C₄	—	76	3	no	—
96	C₄	#11926602	1	6	yes	—
97	C₄	#11926604	1	6	yes	—
98	C₂	#14561934	1	1	yes	characteristic
99	C₂	#14561936	1	3	yes	—
100	C₂	#14563385	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563380

C₂

yes

maximal

C₁₉⋊#1273

C₂

yes

maximal

C₁₉×#1273

C₂

yes

maximal, characteristic

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

C₄²×Dic₁₉

C₂²

yes

characteristic

#11926298

C₄

yes

—

#11926298

C₄

yes

—

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

—

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

—

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8135

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1744

—

#1273

—

#1273

D₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#405

yes

—

C₄×C₁₉

#433

yes

—

C₄×C₁₉

#433

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

C₄³

—

#336

—

#336

—

C₂×C₁₉

#1454

yes

characteristic

C₂×C₁₉

#1454

yes

—

C₂×C₁₉

#1746

yes

—

C₂²×C₈

—

C₂²×C₈

C₄×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₁₉

#8135

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

—

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

#10597347

yes

—

C₂×C₄

#10597353

yes

—

C₈

—

C₈

—

C₂²

#11926389

yes

characteristic

C₂²

#11926498

yes

—

C₂²

#11926501

yes

—

C₄

—

C₄

—

C₄

#11926602

yes

—

C₄

#11926604

yes

—

C₂

#14561934

yes

characteristic

C₂

#14561936

yes

—

100

C₂

#14563385

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₉
commutator, socle, prime radical	C₂³×C₁₉	C₂×C₄²
Fitting	C₁₉×#1273	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1273	D₁₉
hypocenter	C₁₉	#8135
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₁₉

commutator, socle, prime radical

C₂³×C₁₉

C₂×C₄²

Fitting

C₁₉×#1273

C₂

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
67. C₁₉	#8135	semidirect

H ≅ G/N

type

67. C₁₉

#8135

semidirect

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

subgroup	index
#14563380	2
C₁₉⋊#1273	2
C₁₉×#1273	2
#8135	19

subgroup

index

#14563380

C₁₉⋊#1273

C₁₉×#1273

#8135

Subgroups — #18072973

Conjugacy classes of subgroups

Complements

Maximal subgroups