Group #11926470 — subgroups

Subgroups — #11926470

Order 1216.

170 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 57 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	C₂×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×(C₂×D₁₉)⋊C₄	C₂	1	2	yes	maximal
3	C₂×(C₂×D₁₉)⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₁₉⋊#95	C₂	1	2	yes	maximal, complemented
5	C₁₉⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₁₉	C₂²	1	2	yes	—
8	C₂²×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₁₉	C₂²	1	2	yes	—
10	C₂²×Dic₁₉	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₁₉	—	2	2	no	—
12	(C₂×D₁₉)⋊C₄	—	2	4	no	—
13	(C₂×D₁₉)⋊C₄	—	2	2	no	—
14	C₂³×C₁₉	C₂³	1	1	yes	characteristic
15	C₂²×D₁₉	—	2	1	no	—
16	C₂²×D₁₉	—	2	2	no	—
17	C₂²×D₁₉	—	2	1	no	—
18	C₂²×D₁₉	—	2	2	no	—
19	C₂²×D₁₉	D₄	1	2	yes	—
20	C₂×C₄×C₁₉	—	2	2	no	—
21	C₂×C₄×C₁₉	—	2	2	no	—
22	C₂×C₄×C₁₉	—	2	2	no	—
23	C₂×C₄×C₁₉	—	2	2	no	—
24	C₂×C₄×C₁₉	D₄	1	2	yes	—
25	C₂×Dic₁₉	—	2	2	no	—
26	C₂×Dic₁₉	—	2	1	no	—
27	C₂×Dic₁₉	—	2	2	no	—
28	C₂×Dic₁₉	—	2	2	no	—
29	C₂×Dic₁₉	—	2	2	no	—
30	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
32	C₂²×C₁₉	#41	1	2	yes	—
33	C₂²×C₁₉	#41	1	1	yes	characteristic
34	C₂²×C₁₉	#41	1	2	yes	—
35	C₂×D₁₉	—	2	2	no	—
36	C₂×D₁₉	—	2	4	no	—
37	C₂×D₁₉	—	4	1	no	—
38	C₂×D₁₉	—	4	1	no	—
39	C₂×D₁₉	—	4	2	no	—
40	C₄×C₁₉	—	2	2	no	—
41	C₄×C₁₉	—	4	2	no	—
42	Dic₁₉	—	4	2	no	—
43	Dic₁₉	—	4	1	no	—
44	#397	—	19	1	no	maximal, Sylow
45	C₂×C₁₉	#121	1	1	yes	characteristic
46	C₂×C₁₉	#123	1	2	yes	—
47	C₂×C₁₉	#123	1	1	yes	characteristic
48	C₂×C₁₉	#124	1	1	yes	characteristic
49	C₂×C₁₉	#126	1	2	yes	—
50	D₁₉	—	4	2	no	—
51	C₂×C₄⋊C₄	D₁₉	1	1	yes	characteristic, complemented
52	C₂×C₂²⋊C₄	—	19	2	no	—
53	C₂×C₂²⋊C₄	—	19	1	no	—
54	#95	—	19	2	no	—
55	#95	—	19	1	no	—
56	C₁₉	#397	1	1	yes	characteristic, complemented, Sylow
57	C₂⁴	—	19	1	no	—
58	C₂²×C₄	—	19	2	no	—
59	C₂²×C₄	—	19	1	no	—
60	C₂²×C₄	C₂×D₁₉	1	2	yes	—
61	C₂²×C₄	C₂×D₁₉	1	1	yes	characteristic
62	C₄⋊C₄	—	2	2	no	—
63	C₂²⋊C₄	—	38	4	no	—
64	C₂²⋊C₄	—	38	2	no	—
65	C₂³	—	19	2	no	—
66	C₂³	—	38	2	no	—
67	C₂³	—	38	1	no	—
68	C₂³	—	38	2	no	—
69	C₂³	—	38	1	no	—
70	C₂³	C₂²×D₁₉	1	1	yes	characteristic
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	2	2	no	—
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	—	38	2	no	—
76	C₂×C₄	—	38	2	no	—
77	C₂×C₄	—	38	2	no	—
78	C₂×C₄	—	38	2	no	—
79	C₂×C₄	—	38	1	no	—
80	C₂×C₄	C₂²⋊D₁₉	1	2	yes	—
81	C₂²	—	38	2	no	—
82	C₂²	—	38	4	no	—
83	C₂²	—	76	1	no	—
84	C₂²	—	76	2	no	—
85	C₂²	—	76	1	no	—
86	C₂²	#64541	1	2	yes	—
87	C₂²	D₄×D₁₉	1	1	yes	characteristic
88	C₂²	#64543	1	1	yes	characteristic
89	C₂²	#64545	1	2	yes	—
90	C₂²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	4	2	no	—
93	C₄	—	76	1	no	—
94	C₄	—	76	2	no	—
95	C₂	—	76	2	no	—
96	C₂	#10597340	1	2	yes	—
97	C₂	#10597344	1	2	yes	—
98	C₂	#10597375	1	1	yes	characteristic
99	C₂	#10597384	1	1	yes	characteristic
100	C₂	#10597393	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊C₄×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂×(C₂×D₁₉)⋊C₄

C₂

yes

maximal

C₂×(C₂×D₁₉)⋊C₄

C₂

yes

maximal, characteristic

C₁₉⋊#95

C₂

yes

maximal, complemented

C₁₉⋊#95

C₂

yes

maximal, characteristic, complemented

C₂³×D₁₉

C₂²

yes

characteristic

C₂²×C₄×C₁₉

C₂²

yes

—

C₂²×C₄×C₁₉

C₂²

yes

characteristic

C₂²×Dic₁₉

C₂²

yes

—

C₂²×Dic₁₉

C₂²

yes

characteristic

C₄⋊C₄×C₁₉

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₂³×C₁₉

C₂³

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

D₄

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂²×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₁₉

#41

yes

—

C₂²×C₁₉

#41

yes

characteristic

C₂²×C₁₉

#41

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

—

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

D₁₉

—

C₂×C₄⋊C₄

D₁₉

yes

characteristic, complemented

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

#95

—

#95

—

C₁₉

#397

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₁₉

yes

—

C₂²×C₄

C₂×D₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂²×D₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊D₁₉

yes

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#64541

yes

—

C₂²

D₄×D₁₉

yes

C₂²

yes

C₂²

yes

—

C₂²

C₂×C₂²⋊D₁₉

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₂

—

C₂

#10597340

yes

—

C₂

#10597344

yes

—

C₂

yes

C₂

yes

100

C₂

#10597393

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂³
Fitting	C₂×C₄⋊C₄×C₁₉	C₂
prime radical	C₂³×D₁₉	C₂²
hypercenter	C₂×C₄⋊C₄	D₁₉
hypocenter	C₁₉	#397
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

subgroup

G/H

center, Frattini

C₂³

C₂²×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂³

Fitting

C₂×C₄⋊C₄×C₁₉

C₂

prime radical

C₂³×D₁₉

C₂²

hypercenter

C₂×C₄⋊C₄

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
1. C₂×C₄⋊C₄×C₁₉	C₂	semidirect
4. C₁₉⋊#95	C₂	semidirect
5. C₁₉⋊#95	C₂	semidirect
51. C₂×C₄⋊C₄	D₁₉	semidirect
56. C₁₉	#397	semidirect

H ≅ G/N

type

1. C₂×C₄⋊C₄×C₁₉

C₂

semidirect

4. C₁₉⋊#95

C₂

semidirect

5. C₁₉⋊#95

C₂

semidirect

51. C₂×C₄⋊C₄

D₁₉

semidirect

56. C₁₉

#397

semidirect

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

subgroup	index
C₂×C₄⋊C₄×C₁₉	2
C₂×(C₂×D₁₉)⋊C₄	2
C₁₉⋊#95	2
#397	19

subgroup

index

C₂×C₄⋊C₄×C₁₉

C₂×(C₂×D₁₉)⋊C₄

C₁₉⋊#95

#397

Subgroups — #11926470

Conjugacy classes of subgroups

Complements

Maximal subgroups