Group #11931535 — subgroups

Subgroups — C₅×#8815 #11931535

Order 1280.

422 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 238 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×#1844	C₂	1	2	yes	maximal
2	C₅×#1834	C₂	1	4	yes	maximal
3	C₂×C₅×C₈²	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#106	—	2	4	no	—
5	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
6	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₅×#384	C₂²	1	4	yes	—
8	C₅×#340	—	2	8	no	—
9	C₅×C₈²	C₄	1	4	yes	complemented
10	#8815	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂²×C₅×C₈	D₄	1	4	yes	—
12	C₂²×C₅×C₈	D₄	1	2	yes	—
13	C₂×C₅×C₄⋊C₄	—	2	8	no	—
14	C₂×C₅×C₄⋊C₄	—	2	4	no	—
15	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
16	C₅×#106	—	4	8	no	—
17	C₄×C₅×C₈	C₂×C₄	1	4	yes	—
18	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
19	C₄×C₅×C₈	Q₈	1	4	yes	—
20	C₄×C₅×C₈	Q₈	1	2	yes	—
21	#1844	C₂×C₅	1	2	yes	—
22	#1834	C₂×C₅	1	4	yes	—
23	C₂×C₈²	C₂×C₅	1	1	yes	characteristic
24	C₂²×C₄×C₅	—	4	4	no	—
25	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
26	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
27	C₂×C₅×C₈	—	2	8	no	—
28	C₂×C₅×C₈	C₄⋊C₄	1	8	yes	—
29	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
30	C₂×C₅×C₈	SD₁₆	1	8	yes	—
31	C₅×C₄⋊C₄	—	4	8	no	—
32	C₅×C₄⋊C₄	—	4	16	no	—
33	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
34	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
35	C₄²×C₅	C₂×Q₈	1	2	yes	—
36	C₂×#106	—	2	4	no	—
37	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
38	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
39	#384	C₂²×C₅	1	4	yes	—
40	#340	—	2	8	no	—
41	C₈²	C₄×C₅	1	4	yes	complemented
42	C₂³×C₅	#127	1	1	yes	characteristic
43	C₂×C₄×C₅	—	8	4	no	—
44	C₂×C₄×C₅	—	8	8	no	—
45	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
47	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
48	C₂×C₄×C₅	C₄⋊Q₈	1	2	yes	—
49	C₂×C₄×C₅	C₂×SD₁₆	1	4	yes	—
50	C₂×C₄×C₅	#135	1	8	yes	—
51	C₅×C₈	—	2	8	no	—
52	C₅×C₈	#106	1	8	yes	—
53	C₂²×C₈	C₅×D₄	1	4	yes	—
54	C₂²×C₈	C₅×D₄	1	2	yes	—
55	C₂×C₄⋊C₄	—	2	8	no	—
56	C₂×C₄⋊C₄	—	2	4	no	—
57	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
58	#106	—	4	8	no	—
59	C₄×C₈	C₂×C₄×C₅	1	4	yes	—
60	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
61	C₄×C₈	C₅×Q₈	1	4	yes	—
62	C₄×C₈	C₅×Q₈	1	2	yes	—
63	C₂²×C₅	#384	1	1	yes	characteristic
64	C₂²×C₅	#492	1	2	yes	—
65	C₂²×C₅	#495	1	4	yes	—
66	C₄×C₅	—	16	4	no	—
67	C₄×C₅	C₂×#106	1	2	yes	—
68	C₄×C₅	#427	1	4	yes	—
69	C₄×C₅	#498	1	2	yes	—
70	C₄×C₅	#499	1	4	yes	—
71	C₂²×C₄	—	4	4	no	—
72	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
73	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
74	C₂×C₈	—	2	8	no	—
75	C₂×C₈	C₅×C₄⋊C₄	1	8	yes	—
76	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
77	C₂×C₈	C₅×SD₁₆	1	8	yes	—
78	C₄⋊C₄	—	4	8	no	—
79	C₄⋊C₄	—	4	16	no	—
80	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
81	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
82	C₄²	C₂×C₅×Q₈	1	2	yes	—
83	C₂×C₅	#1708	1	4	yes	—
84	C₂×C₅	#1844	1	1	yes	characteristic
85	C₂×C₅	#1846	1	2	yes	—
86	C₂³	C₅×#127	1	1	yes	characteristic
87	C₂×C₄	—	8	4	no	—
88	C₂×C₄	—	8	8	no	—
89	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
90	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
91	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
92	C₂×C₄	C₅×C₄⋊Q₈	1	2	yes	—
93	C₂×C₄	C₂×C₅×SD₁₆	1	4	yes	—
94	C₂×C₄	C₅×#135	1	8	yes	—
95	C₈	—	2	8	no	—
96	C₈	C₅×#106	1	8	yes	—
97	C₅	#8815	1	1	yes	characteristic, direct product factor, Sylow
98	C₂²	C₅×#384	1	1	yes	characteristic
99	C₂²	C₅×#492	1	2	yes	—
100	C₂²	C₅×#495	1	4	yes	—
101	C₄	—	16	4	no	—
102	C₄	C₂×C₅×#106	1	2	yes	—
103	C₄	C₅×#427	1	4	yes	—
104	C₄	C₅×#498	1	2	yes	—
105	C₄	C₅×#499	1	4	yes	—
106	C₂	C₅×#1708	1	4	yes	—
107	C₂	C₅×#1844	1	1	yes	characteristic
108	C₂	C₅×#1846	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#1844

C₂

yes

maximal

C₅×#1834

C₂

yes

maximal

C₂×C₅×C₈²

C₂

yes

maximal, characteristic

C₂×C₅×#106

—

C₂×C₄×C₅×C₈

C₂²

yes

—

C₂×C₄×C₅×C₈

C₂²

yes

characteristic

C₅×#384

C₂²

yes

—

C₅×#340

—

C₅×C₈²

C₄

yes

complemented

#8815

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×C₈

D₄

yes

—

C₂²×C₅×C₈

D₄

yes

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×#106

—

C₄×C₅×C₈

C₂×C₄

yes

—

C₄×C₅×C₈

C₂×C₄

yes

—

C₄×C₅×C₈

Q₈

yes

—

C₄×C₅×C₈

Q₈

yes

—

#1844

C₂×C₅

yes

—

#1834

C₂×C₅

yes

—

C₂×C₈²

C₂×C₅

yes

characteristic

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂×D₄

yes

characteristic

C₂²×C₄×C₅

C₂×D₄

yes

—

C₂×C₅×C₈

—

C₂×C₅×C₈

C₄⋊C₄

yes

—

C₂×C₅×C₈

C₄⋊C₄

yes

—

C₂×C₅×C₈

SD₁₆

yes

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₄²×C₅

C₂²×C₄

yes

characteristic

C₄²×C₅

C₂×Q₈

yes

characteristic

C₄²×C₅

C₂×Q₈

yes

—

C₂×#106

—

C₂×C₄×C₈

C₂²×C₅

yes

—

C₂×C₄×C₈

C₂²×C₅

yes

characteristic

#384

C₂²×C₅

yes

—

#340

—

C₈²

C₄×C₅

yes

complemented

C₂³×C₅

#127

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₅

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₅

C₄⋊Q₈

yes

—

C₂×C₄×C₅

C₂×SD₁₆

yes

—

C₂×C₄×C₅

#135

yes

—

C₅×C₈

—

C₅×C₈

#106

yes

—

C₂²×C₈

C₅×D₄

yes

—

C₂²×C₈

C₅×D₄

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂³×C₅

yes

characteristic

#106

—

C₄×C₈

C₂×C₄×C₅

yes

—

C₄×C₈

C₂×C₄×C₅

yes

—

C₄×C₈

C₅×Q₈

yes

—

C₄×C₈

C₅×Q₈

yes

—

C₂²×C₅

#384

yes

characteristic

C₂²×C₅

#492

yes

—

C₂²×C₅

#495

yes

—

C₄×C₅

—

C₄×C₅

C₂×#106

yes

—

C₄×C₅

#427

yes

—

C₄×C₅

#498

yes

—

C₄×C₅

#499

yes

—

C₂²×C₄

—

C₂²×C₄

C₂×C₅×D₄

yes

characteristic

C₂²×C₄

C₂×C₅×D₄

yes

—

C₂×C₈

—

C₂×C₈

C₅×C₄⋊C₄

yes

—

C₂×C₈

C₅×C₄⋊C₄

yes

—

C₂×C₈

C₅×SD₁₆

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²×C₄×C₅

yes

characteristic

C₄²

C₂×C₅×Q₈

yes

characteristic

C₄²

C₂×C₅×Q₈

yes

—

C₂×C₅

#1708

yes

—

C₂×C₅

#1844

yes

characteristic

C₂×C₅

#1846

yes

—

C₂³

C₅×#127

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₅×C₄⋊C₄

yes

characteristic

C₂×C₄

C₂×C₅×C₄⋊C₄

yes

—

C₂×C₄

C₅×C₄⋊Q₈

yes

characteristic

C₂×C₄

C₅×C₄⋊Q₈

yes

—

C₂×C₄

C₂×C₅×SD₁₆

yes

—

C₂×C₄

C₅×#135

yes

—

C₈

—

C₈

C₅×#106

yes

—

C₅

#8815

yes

characteristic, direct product factor, Sylow

C₂²

C₅×#384

yes

characteristic

C₂²

C₅×#492

yes

—

100

C₂²

C₅×#495

yes

—

101

C₄

—

102

C₄

C₂×C₅×#106

yes

—

103

C₄

C₅×#427

yes

—

104

C₄

C₅×#498

yes

—

105

C₄

C₅×#499

yes

—

106

C₂

C₅×#1708

yes

—

107

C₂

C₅×#1844

yes

characteristic

108

C₂

C₅×#1846

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	#127
commutator	C₄²	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₅

#127

commutator

C₄²

C₂²×C₄×C₅

Frattini, cosocle

C₂×C₄²

C₂³×C₅

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

N	H ≅ G/N	type
9. C₅×C₈²	C₄	semidirect
10. #8815	C₅	direct (N × H)
41. C₈²	C₄×C₅	semidirect
97. C₅	#8815	direct (N × H)

H ≅ G/N

type

9. C₅×C₈²

C₄

semidirect

10. #8815

C₅

direct (N × H)

41. C₈²

C₄×C₅

semidirect

97. C₅

#8815

direct (N × H)

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

subgroup	index
C₅×#1844	2
C₅×#1834	2
C₂×C₅×C₈²	2
#8815	5

subgroup

index

C₅×#1844

C₅×#1834

C₂×C₅×C₈²

#8815

Subgroups — C₅×#8815 #11931535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#8815 #11931535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8815 #11931535