Group #11989722 — subgroups

Subgroups — #11989722

Order 1280.

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×Dic₅	C₂	1	3	yes	maximal
2	C₅×#1273	C₂	1	1	yes	maximal, characteristic
3	#10598144	C₂	1	3	yes	maximal
4	C₂×C₄×C₅×C₈	C₂²	1	3	yes	—
5	C₂×C₈×Dic₅	C₄	1	6	yes	—
6	C₂×C₈×Dic₅	C₄	1	6	yes	—
7	C₄²×Dic₅	C₂²	1	1	yes	characteristic
8	C₂×C₄×#168	C₂²	1	3	yes	—
9	#8131	—	5	1	no	maximal, Sylow
10	C₂²×C₅×C₈	C₂×C₄	1	6	yes	—
11	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
12	C₂×C₄×Dic₅	C₂×C₄	1	3	yes	—
13	C₂×C₄×Dic₅	C₂×C₄	1	3	yes	—
14	C₂²×#168	C₂×C₄	1	6	yes	—
15	C₄×C₅×C₈	—	2	6	no	—
16	C₈×Dic₅	—	2	12	no	—
17	C₈×Dic₅	C₈	1	24	yes	complemented
18	C₄×#168	—	2	3	no	—
19	C₄×#168	—	2	3	no	—
20	C₄²×C₈	—	5	3	no	—
21	#1273	—	5	3	no	—
22	#1273	D₅	1	1	yes	characteristic
23	C₂²×C₄×C₅	C₂²×C₄	1	3	yes	—
24	C₂²×Dic₅	C₄²	1	1	yes	characteristic
25	C₂²×Dic₅	C₄²	1	3	yes	—
26	C₂×C₅×C₈	—	2	6	no	—
27	C₂×C₅×C₈	—	2	6	no	—
28	C₂×C₅×C₈	C₂×C₈	1	12	yes	—
29	C₄²×C₅	#41	1	3	yes	—
30	C₄²×C₅	#41	1	1	yes	characteristic
31	C₄×Dic₅	C₂×C₈	1	12	yes	—
32	C₄×Dic₅	M₁₆	1	12	yes	—
33	C₂×#168	—	2	6	no	—
34	C₂×#168	—	2	6	no	—
35	C₂×#168	C₂×C₈	1	12	yes	—
36	C₂×C₄×C₈	—	5	6	no	—
37	C₂×C₄×C₈	—	5	6	no	—
38	C₂×C₄×C₈	—	5	3	no	—
39	C₂×C₄×C₈	C₂×D₅	1	3	yes	—
40	C₄³	—	5	1	no	—
41	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
42	C₂×C₄×C₅	#117	1	3	yes	—
43	C₂×C₄×C₅	#117	1	3	yes	—
44	C₂×C₄×C₅	C₂²×C₈	1	6	yes	—
45	C₂×C₄×C₅	C₂×M₁₆	1	6	yes	—
46	C₂×Dic₅	C₄×C₈	1	6	yes	—
47	C₂×Dic₅	C₄×C₈	1	6	yes	—
48	C₂×Dic₅	#97	1	12	yes	—
49	C₅×C₈	—	2	12	no	—
50	#168	—	2	12	no	—
51	C₂²×C₈	—	5	6	no	—
52	C₂²×C₈	C₄×D₅	1	6	yes	—
53	C₂×C₄²	—	5	3	no	—
54	C₂×C₄²	—	5	3	no	—
55	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
56	C₄×C₈	—	2	6	no	—
57	C₄×C₈	—	5	24	no	—
58	C₄×C₈	—	10	12	no	—
59	C₄×C₈	—	10	3	no	—
60	C₄×C₈	—	10	3	no	—
61	C₂²×C₅	#376	1	1	yes	characteristic
62	C₂²×C₅	C₂×C₄×C₈	1	3	yes	—
63	C₂²×C₅	C₂×#97	1	3	yes	—
64	C₄×C₅	#431	1	6	yes	—
65	C₄×C₅	#431	1	6	yes	—
66	Dic₅	C₈²	1	4	yes	—
67	Dic₅	#322	1	12	yes	—
68	C₂²×C₄	—	5	1	no	—
69	C₂²×C₄	—	5	3	no	—
70	C₂²×C₄	C₂×C₄×D₅	1	3	yes	—
71	C₂×C₈	—	2	6	no	—
72	C₂×C₈	—	2	6	no	—
73	C₂×C₈	—	5	12	no	—
74	C₂×C₈	—	10	6	no	—
75	C₂×C₈	—	10	6	no	—
76	C₂×C₈	C₈×D₅	1	12	yes	—
77	C₄²	—	5	12	no	—
78	C₄²	—	5	12	no	—
79	C₄²	#711	1	3	yes	—
80	C₄²	#713	1	1	yes	characteristic
81	C₂×C₅	C₂×C₈²	1	1	yes	characteristic
82	C₂×C₅	C₂×#322	1	3	yes	—
83	C₂×C₅	#1744	1	3	yes	—
84	C₂³	C₄²×D₅	1	1	yes	characteristic
85	C₂×C₄	—	5	6	no	—
86	C₂×C₄	—	5	6	no	—
87	C₂×C₄	—	5	12	no	—
88	C₂×C₄	#4023	1	3	yes	—
89	C₂×C₄	#4038	1	3	yes	—
90	C₂×C₄	C₂×C₈×D₅	1	6	yes	—
91	C₂×C₄	D₅×M₁₆	1	6	yes	—
92	C₈	—	2	12	no	—
93	C₈	—	10	12	no	—
94	C₅	#8131	1	1	yes	characteristic, complemented, Sylow
95	C₂²	#64937	1	1	yes	characteristic
96	C₂²	C₄×C₈×D₅	1	3	yes	—
97	C₂²	D₅×#97	1	3	yes	—
98	C₄	—	5	4	no	—
99	C₄	—	5	12	no	—
100	C₄	#65007	1	6	yes	—
101	C₄	#65122	1	6	yes	—
102	C₂	C₈²×D₅	1	1	yes	characteristic
103	C₂	D₅×#322	1	3	yes	—
104	C₂	#10599389	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₈×Dic₅

C₂

yes

maximal

C₅×#1273

C₂

yes

maximal, characteristic

#10598144

C₂

yes

maximal

C₂×C₄×C₅×C₈

C₂²

yes

—

C₂×C₈×Dic₅

C₄

yes

—

C₂×C₈×Dic₅

C₄

yes

—

C₄²×Dic₅

C₂²

yes

characteristic

C₂×C₄×#168

C₂²

yes

—

#8131

—

maximal, Sylow

C₂²×C₅×C₈

C₂×C₄

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₂×C₄×Dic₅

C₂×C₄

yes

—

C₂×C₄×Dic₅

C₂×C₄

yes

—

C₂²×#168

C₂×C₄

yes

—

C₄×C₅×C₈

—

C₈×Dic₅

—

C₈×Dic₅

C₈

yes

complemented

C₄×#168

—

C₄×#168

—

C₄²×C₈

—

#1273

—

#1273

D₅

yes

characteristic

C₂²×C₄×C₅

C₂²×C₄

yes

—

C₂²×Dic₅

C₄²

yes

characteristic

C₂²×Dic₅

C₄²

yes

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

C₂×C₈

yes

—

C₄²×C₅

#41

yes

—

C₄²×C₅

#41

yes

characteristic

C₄×Dic₅

C₂×C₈

yes

—

C₄×Dic₅

M₁₆

yes

—

C₂×#168

—

C₂×#168

—

C₂×#168

C₂×C₈

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₅

yes

—

C₄³

—

C₂³×C₅

C₂×C₄²

yes

characteristic

C₂×C₄×C₅

#117

yes

—

C₂×C₄×C₅

#117

yes

—

C₂×C₄×C₅

C₂²×C₈

yes

—

C₂×C₄×C₅

C₂×M₁₆

yes

—

C₂×Dic₅

C₄×C₈

yes

—

C₂×Dic₅

C₄×C₈

yes

—

C₂×Dic₅

#97

yes

—

C₅×C₈

—

#168

—

C₂²×C₈

—

C₂²×C₈

C₄×D₅

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₅

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₅

#376

yes

characteristic

C₂²×C₅

C₂×C₄×C₈

yes

—

C₂²×C₅

C₂×#97

yes

—

C₄×C₅

#431

yes

—

C₄×C₅

#431

yes

—

Dic₅

C₈²

yes

—

Dic₅

#322

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₄×D₅

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₈×D₅

yes

—

C₄²

—

C₄²

—

C₄²

#711

yes

—

C₄²

#713

yes

characteristic

C₂×C₅

C₂×C₈²

yes

characteristic

C₂×C₅

C₂×#322

yes

—

C₂×C₅

#1744

yes

—

C₂³

C₄²×D₅

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#4023

yes

—

C₂×C₄

#4038

yes

—

C₂×C₄

C₂×C₈×D₅

yes

—

C₂×C₄

D₅×M₁₆

yes

—

C₈

—

C₈

—

C₅

#8131

yes

characteristic, complemented, Sylow

C₂²

#64937

yes

characteristic

C₂²

C₄×C₈×D₅

yes

—

C₂²

D₅×#97

yes

—

C₄

—

C₄

—

100

C₄

#65007

yes

—

101

C₄

#65122

yes

—

102

C₂

C₈²×D₅

yes

characteristic

103

C₂

D₅×#322

yes

—

104

C₂

#10599389

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₅
commutator	C₂×C₅	C₂×C₈²
Fitting	C₅×#1273	C₂
socle, prime radical	C₂³×C₅	C₂×C₄²
cosocle	C₂×C₄²×C₅	C₂³
hypercenter	#1273	D₅
hypocenter	C₅	#8131
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₅

commutator

C₂×C₅

C₂×C₈²

Fitting

C₅×#1273

C₂

socle, prime radical

C₂³×C₅

C₂×C₄²

cosocle

C₂×C₄²×C₅

C₂³

D₅

C₅

G ▷ C₂×C₅ ▷ C₅

C₁ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
17. C₈×Dic₅	C₈	semidirect
94. C₅	#8131	semidirect

H ≅ G/N

type

17. C₈×Dic₅

C₈

semidirect

94. C₅

#8131

semidirect

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

subgroup	index
C₄×C₈×Dic₅	2
C₅×#1273	2
#10598144	2
#8131	5

subgroup

index

C₄×C₈×Dic₅

C₅×#1273

#10598144

#8131

Subgroups — #11989722

Conjugacy classes of subgroups

Complements

Maximal subgroups