Group #11931518 — subgroups

Subgroups — C₅×#8798 #11931518

Order 1280.

220 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 110 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	C₅×#1568	C₂	1	2	yes	maximal
2	C₅×#1452	C₂	1	1	yes	maximal, characteristic
3	C₅×#1287	C₂	1	4	yes	maximal
4	C₅×#432	C₂²	1	4	yes	—
5	C₅×#431	C₂²	1	2	yes	—
6	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₅×#335	—	2	2	no	—
8	C₅×#334	—	2	2	no	—
9	C₅×#322	C₄	1	4	yes	—
10	#8798	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂²×C₅×C₈	Q₈	1	2	yes	—
12	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
13	C₅×C₄⋊C₈	—	2	4	no	—
14	C₅×C₄⋊C₈	—	2	2	no	—
15	C₅×C₂²⋊C₈	—	2	2	no	—
16	C₅×C₂²⋊C₈	—	2	4	no	—
17	C₅×#97	—	2	4	no	—
18	C₄×C₅×C₈	C₂×C₄	1	4	yes	—
19	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
20	C₄×C₅×C₈	D₄	1	1	yes	characteristic
21	C₄×C₅×C₈	D₄	1	1	yes	characteristic
22	#1568	C₂×C₅	1	2	yes	—
23	#1452	C₂×C₅	1	1	yes	characteristic
24	#1287	C₂×C₅	1	4	yes	—
25	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
26	C₂²×C₄×C₅	#41	1	2	yes	—
27	C₂×C₅×C₈	—	2	4	no	—
28	C₂×C₅×C₈	—	4	2	no	—
29	C₂×C₅×C₈	—	4	4	no	—
30	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
31	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
32	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
33	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
34	C₄²×C₅	#41	1	2	yes	—
35	#432	C₂²×C₅	1	4	yes	—
36	#431	C₂²×C₅	1	2	yes	—
37	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
38	#335	—	2	2	no	—
39	#334	—	2	2	no	—
40	#322	C₄×C₅	1	4	yes	—
41	C₂³×C₅	#125	1	1	yes	characteristic
42	C₂×C₄×C₅	—	2	2	no	—
43	C₂×C₄×C₅	—	4	2	no	—
44	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₂×C₄×C₅	#117	1	2	yes	—
46	C₂×C₄×C₅	#124	1	2	yes	—
47	C₂×C₄×C₅	#125	1	1	yes	characteristic
48	C₅×C₈	—	2	2	no	—
49	C₅×C₈	—	2	2	no	—
50	C₅×C₈	—	4	4	no	—
51	C₅×C₈	—	8	4	no	—
52	C₂²×C₈	C₅×Q₈	1	2	yes	—
53	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
54	C₄⋊C₈	—	2	4	no	—
55	C₄⋊C₈	—	2	2	no	—
56	C₂²⋊C₈	—	2	2	no	—
57	C₂²⋊C₈	—	2	4	no	—
58	#97	—	2	4	no	—
59	C₄×C₈	C₂×C₄×C₅	1	4	yes	—
60	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
61	C₄×C₈	C₅×D₄	1	1	yes	characteristic
62	C₄×C₈	C₅×D₄	1	1	yes	characteristic
63	C₂²×C₅	—	2	2	no	—
64	C₂²×C₅	—	2	1	no	—
65	C₂²×C₅	#382	1	1	yes	characteristic
66	C₄×C₅	—	2	2	no	—
67	C₄×C₅	—	2	2	no	—
68	C₄×C₅	—	2	1	no	—
69	C₄×C₅	#430	1	2	yes	—
70	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
71	C₂²×C₄	C₅×#41	1	2	yes	—
72	C₂×C₈	—	2	4	no	—
73	C₂×C₈	—	4	2	no	—
74	C₂×C₈	—	4	4	no	—
75	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
76	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
77	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
78	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
79	C₄²	C₅×#41	1	2	yes	—
80	C₂×C₅	—	4	1	no	—
81	C₂×C₅	#1833	1	2	yes	—
82	C₂×C₅	#1838	1	1	yes	characteristic
83	C₂³	C₅×#125	1	1	yes	characteristic
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	4	2	no	—
86	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄	C₅×#117	1	2	yes	—
88	C₂×C₄	C₅×#124	1	2	yes	—
89	C₂×C₄	C₅×#125	1	1	yes	characteristic
90	C₈	—	2	2	no	—
91	C₈	—	2	2	no	—
92	C₈	—	4	4	no	—
93	C₈	—	8	4	no	—
94	C₅	#8798	1	1	yes	characteristic, direct product factor, Sylow
95	C₂²	—	2	2	no	—
96	C₂²	—	2	1	no	—
97	C₂²	C₅×#382	1	1	yes	characteristic
98	C₄	—	2	2	no	—
99	C₄	—	2	2	no	—
100	C₄	—	2	1	no	—
101	C₄	C₅×#430	1	2	yes	—
102	C₂	—	4	1	no	—
103	C₂	C₅×#1833	1	2	yes	—
104	C₂	C₅×#1838	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#1568

C₂

yes

maximal

C₅×#1452

C₂

yes

maximal, characteristic

C₅×#1287

C₂

yes

maximal

C₅×#432

C₂²

yes

—

C₅×#431

C₂²

yes

—

C₂×C₄×C₅×C₈

C₂²

yes

—

—

C₄

yes

—

#8798

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×C₈

Q₈

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×C₄⋊C₈

—

C₅×C₄⋊C₈

—

C₅×C₂²⋊C₈

—

C₅×C₂²⋊C₈

—

C₅×#97

—

C₄×C₅×C₈

C₂×C₄

yes

—

C₄×C₅×C₈

C₂×C₄

yes

—

C₄×C₅×C₈

D₄

yes

characteristic

C₄×C₅×C₈

D₄

yes

characteristic

#1568

C₂×C₅

yes

—

#1452

C₂×C₅

yes

characteristic

#1287

C₂×C₅

yes

—

C₂²×C₄×C₅

C₂×Q₈

yes

characteristic

C₂²×C₄×C₅

#41

yes

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

C₄⋊C₄

yes

—

C₂×C₅×C₈

C₄⋊C₄

yes

—

C₄²×C₅

C₂²×C₄

yes

characteristic

C₄²×C₅

C₂×D₄

yes

characteristic

C₄²×C₅

#41

yes

—

#432

C₂²×C₅

yes

—

#431

C₂²×C₅

yes

—

C₂×C₄×C₈

C₂²×C₅

yes

—

—

C₄×C₅

yes

—

C₂³×C₅

#125

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₅

#117

yes

—

C₂×C₄×C₅

#124

yes

—

C₂×C₄×C₅

#125

yes

characteristic

C₅×C₈

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

—

C₂²×C₈

C₅×Q₈

yes

—

C₂×C₄²

C₂³×C₅

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

C₂×C₄×C₅

yes

—

C₄×C₈

C₂×C₄×C₅

yes

—

C₄×C₈

C₅×D₄

yes

characteristic

C₄×C₈

C₅×D₄

yes

characteristic

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

#382

yes

characteristic

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

#430

yes

—

C₂²×C₄

C₂×C₅×Q₈

yes

characteristic

C₂²×C₄

C₅×#41

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₅×C₄⋊C₄

yes

—

C₂×C₈

C₅×C₄⋊C₄

yes

—

C₄²

C₂²×C₄×C₅

yes

characteristic

C₄²

C₂×C₅×D₄

yes

characteristic

C₄²

C₅×#41

yes

—

C₂×C₅

—

C₂×C₅

#1833

yes

—

C₂×C₅

yes

C₂³

yes

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₅×C₄⋊C₄

yes

characteristic

C₂×C₄

C₅×#117

yes

—

C₂×C₄

C₅×#124

yes

—

C₂×C₄

C₅×#125

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₅

#8798

yes

characteristic, direct product factor, Sylow

C₂²

—

C₂²

—

C₂²

C₅×#382

yes

characteristic

C₄

—

C₄

—

100

C₄

—

101

C₄

C₅×#430

yes

—

102

C₂

—

103

C₂

C₅×#1833

yes

—

104

C₂

C₅×#1838

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₅	#382
commutator	C₄²	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂³×C₅	#125
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

subgroup

G/H

center, socle

C₂²×C₅

#382

commutator

C₄²

C₂²×C₄×C₅

Frattini, cosocle

C₂×C₄²

C₂³×C₅

C₂³×C₅

G ▷ C₄² ▷ C₂² ▷ C₁

C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

N	H ≅ G/N	type
10. #8798	C₅	direct (N × H)
94. C₅	#8798	direct (N × H)

H ≅ G/N

type

10. #8798

C₅

direct (N × H)

94. C₅

#8798

direct (N × H)

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

subgroup	index
C₅×#1568	2
C₅×#1452	2
C₅×#1287	2
#8798	5

subgroup

index

Subgroups — C₅×#8798 #11931518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#8798 #11931518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8798 #11931518