Group #11933306 — subgroups

Subgroups — C₅×#10586 #11933306

Order 1280.

350 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2845	C₂	1	1	yes	maximal, characteristic
2	C₅×#1836	C₂	1	3	yes	maximal
3	C₅×#1295	C₂	1	3	yes	maximal
4	C₂×C₅×#97	C₂²	1	3	yes	—
5	C₅×#398	—	2	6	no	—
6	C₅×#384	C₂²	1	1	yes	characteristic
7	C₅×#382	C₂²	1	3	yes	—
8	C₅×#340	—	2	6	no	—
9	#10586	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂²×C₅×C₈	—	2	3	no	—
11	C₂×C₅×C₄⋊C₄	—	2	3	no	—
12	C₂×C₅×C₄⋊C₄	—	2	6	no	—
13	C₂×C₅×C₄⋊C₄	D₄	1	6	yes	—
14	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
15	C₅×#97	—	2	3	no	—
16	C₅×#97	Q₈	1	6	yes	—
17	C₅×#95	—	2	2	no	—
18	C₅×#95	—	2	6	no	—
19	#2845	C₂×C₅	1	1	yes	characteristic
20	#1836	C₂×C₅	1	3	yes	—
21	#1295	C₂×C₅	1	3	yes	—
22	C₂²×C₄×C₅	—	2	6	no	—
23	C₂²×C₄×C₅	—	4	1	no	—
24	C₂²×C₄×C₅	C₂×D₄	1	3	yes	—
25	C₂×C₅×C₈	—	2	6	no	—
26	C₂×C₅×C₈	—	4	3	no	—
27	C₂×C₅×C₈	—	4	3	no	—
28	C₅×C₄⋊C₄	—	4	6	no	—
29	C₅×C₄⋊C₄	—	4	6	no	—
30	C₅×C₄⋊C₄	—	8	6	no	—
31	C₄²×C₅	C₂×Q₈	1	3	yes	—
32	C₄²×C₅	#41	1	1	yes	characteristic
33	C₂×#97	C₂²×C₅	1	3	yes	—
34	#398	—	2	6	no	—
35	#384	C₂²×C₅	1	1	yes	characteristic
36	#382	C₂²×C₅	1	3	yes	—
37	#340	—	2	6	no	—
38	C₂³×C₅	#120	1	1	yes	characteristic
39	C₂×C₄×C₅	—	2	3	no	—
40	C₂×C₄×C₅	—	2	3	no	—
41	C₂×C₄×C₅	—	4	6	no	—
42	C₂×C₄×C₅	—	4	6	no	—
43	C₂×C₄×C₅	—	4	6	no	—
44	C₂×C₄×C₅	—	8	3	no	—
45	C₂×C₄×C₅	C₂²⋊Q₈	1	3	yes	—
46	C₂×C₄×C₅	C₄⋊Q₈	1	3	yes	—
47	C₅×C₈	—	4	6	no	—
48	C₂²×C₈	—	2	3	no	—
49	C₂×C₄⋊C₄	—	2	3	no	—
50	C₂×C₄⋊C₄	—	2	6	no	—
51	C₂×C₄⋊C₄	C₅×D₄	1	6	yes	—
52	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
53	#97	—	2	3	no	—
54	#97	C₅×Q₈	1	6	yes	—
55	#95	—	2	2	no	—
56	#95	—	2	6	no	—
57	C₂²×C₅	#395	1	1	yes	characteristic
58	C₂²×C₅	#454	1	3	yes	—
59	C₂²×C₅	#455	1	3	yes	—
60	C₄×C₅	—	2	3	no	—
61	C₄×C₅	—	2	3	no	—
62	C₄×C₅	—	8	6	no	—
63	C₄×C₅	—	16	1	no	—
64	C₂²×C₄	—	2	6	no	—
65	C₂²×C₄	—	4	1	no	—
66	C₂²×C₄	C₂×C₅×D₄	1	3	yes	—
67	C₂×C₈	—	2	6	no	—
68	C₂×C₈	—	4	3	no	—
69	C₂×C₈	—	4	3	no	—
70	C₄⋊C₄	—	4	6	no	—
71	C₄⋊C₄	—	4	6	no	—
72	C₄⋊C₄	—	8	6	no	—
73	C₄²	C₂×C₅×Q₈	1	3	yes	—
74	C₄²	C₅×#41	1	1	yes	characteristic
75	C₂×C₅	#1658	1	1	yes	characteristic
76	C₂×C₅	#1662	1	3	yes	—
77	C₂×C₅	#2061	1	3	yes	—
78	C₂³	C₅×#120	1	1	yes	characteristic
79	C₂×C₄	—	2	3	no	—
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	4	6	no	—
82	C₂×C₄	—	4	6	no	—
83	C₂×C₄	—	4	6	no	—
84	C₂×C₄	—	8	3	no	—
85	C₂×C₄	C₅×C₂²⋊Q₈	1	3	yes	—
86	C₂×C₄	C₅×C₄⋊Q₈	1	3	yes	—
87	C₈	—	4	6	no	—
88	C₅	#10586	1	1	yes	characteristic, direct product factor, Sylow
89	C₂²	C₅×#395	1	1	yes	characteristic
90	C₂²	C₅×#454	1	3	yes	—
91	C₂²	C₅×#455	1	3	yes	—
92	C₄	—	2	3	no	—
93	C₄	—	2	3	no	—
94	C₄	—	8	6	no	—
95	C₄	—	16	1	no	—
96	C₂	C₅×#1658	1	1	yes	characteristic
97	C₂	C₅×#1662	1	3	yes	—
98	C₂	C₅×#2061	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#2845

C₂

yes

maximal, characteristic

C₅×#1836

C₂

yes

maximal

C₅×#1295

C₂

yes

maximal

C₂×C₅×#97

C₂²

yes

—

C₅×#398

—

C₅×#384

C₂²

yes

characteristic

C₅×#382

C₂²

yes

—

C₅×#340

—

#10586

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×C₈

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

D₄

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×#97

—

C₅×#97

Q₈

yes

—

C₅×#95

—

C₅×#95

—

#2845

C₂×C₅

yes

characteristic

#1836

C₂×C₅

yes

—

#1295

C₂×C₅

yes

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂×D₄

yes

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₄²×C₅

C₂×Q₈

yes

—

C₄²×C₅

#41

yes

characteristic

C₂×#97

C₂²×C₅

yes

—

#398

—

#384

C₂²×C₅

yes

characteristic

#382

C₂²×C₅

yes

—

#340

—

C₂³×C₅

#120

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂²⋊Q₈

yes

—

C₂×C₄×C₅

C₄⋊Q₈

yes

—

C₅×C₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₅×D₄

yes

—

C₂×C₄²

C₂³×C₅

yes

characteristic

#97

—

#97

C₅×Q₈

yes

—

#95

—

#95

—

C₂²×C₅

#395

yes

characteristic

C₂²×C₅

#454

yes

—

C₂²×C₅

#455

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₅×D₄

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂×C₅×Q₈

yes

—

C₄²

C₅×#41

yes

C₂×C₅

yes

C₂×C₅

yes

—

C₂×C₅

#2061

yes

—

C₂³

C₅×#120

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₅×C₂²⋊Q₈

yes

—

C₂×C₄

C₅×C₄⋊Q₈

yes

—

C₈

—

C₅

#10586

yes

characteristic, direct product factor, Sylow

C₂²

C₅×#395

yes

characteristic

C₂²

C₅×#454

yes

—

C₂²

C₅×#455

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

C₂

C₅×#1658

yes

characteristic

C₂

C₅×#1662

yes

—

C₂

C₅×#2061

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₅

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₅

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

N	H ≅ G/N	type
9. #10586	C₅	direct (N × H)
88. C₅	#10586	direct (N × H)

H ≅ G/N

type

9. #10586

C₅

direct (N × H)

88. C₅

#10586

direct (N × H)

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

subgroup	index
C₅×#2845	2
C₅×#1836	2
C₅×#1295	2
#10586	5

subgroup

index

Subgroups — C₅×#10586 #11933306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#10586 #11933306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10586 #11933306