Group #11931545 — subgroups

Subgroups — C₅×#8825 #11931545

Order 1280.

338 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 198 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×#1848	C₂	1	2	yes	maximal
2	C₅×#1566	C₂	1	4	yes	maximal
3	C₂×C₅×#322	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#108	—	2	4	no	—
5	C₅×#423	C₂²	1	4	yes	—
6	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
8	C₅×#334	—	2	8	no	—
9	C₅×#322	C₄	1	4	yes	—
10	#8825	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂×C₅×M₁₆	—	2	4	no	—
12	C₂²×C₅×C₈	D₄	1	2	yes	—
13	C₂²×C₅×C₈	Q₈	1	4	yes	—
14	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
15	C₅×#108	—	4	8	no	—
16	C₅×C₄⋊C₈	—	2	8	no	—
17	C₄×C₅×C₈	C₂×C₄	1	4	yes	—
18	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
19	C₄×C₅×C₈	D₄	1	4	yes	—
20	C₄×C₅×C₈	Q₈	1	2	yes	—
21	#1848	C₂×C₅	1	2	yes	—
22	#1566	C₂×C₅	1	4	yes	—
23	C₂×#322	C₂×C₅	1	1	yes	characteristic
24	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
25	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
26	C₅×M₁₆	—	4	8	no	—
27	C₂×C₅×C₈	—	4	4	no	—
28	C₂×C₅×C₈	—	4	4	no	—
29	C₂×C₅×C₈	C₄⋊C₄	1	8	yes	—
30	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
31	C₂×C₅×C₈	SD₁₆	1	8	yes	—
32	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
33	C₄²×C₅	C₂×D₄	1	2	yes	—
34	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
35	C₂×#108	—	2	4	no	—
36	#423	C₂²×C₅	1	4	yes	—
37	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
38	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
39	#334	—	2	8	no	—
40	#322	C₄×C₅	1	4	yes	—
41	C₂³×C₅	C₄⋊Q₈	1	1	yes	characteristic
42	C₂×C₄×C₅	—	2	4	no	—
43	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
45	C₂×C₄×C₅	#127	1	1	yes	characteristic
46	C₂×C₄×C₅	C₄⋊Q₈	1	2	yes	—
47	C₂×C₄×C₅	C₂×SD₁₆	1	4	yes	—
48	C₅×C₈	—	2	8	no	—
49	C₅×C₈	—	8	4	no	—
50	C₅×C₈	#106	1	8	yes	—
51	C₂×M₁₆	—	2	4	no	—
52	C₂²×C₈	C₅×D₄	1	2	yes	—
53	C₂²×C₈	C₅×Q₈	1	4	yes	—
54	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
55	#108	—	4	8	no	—
56	C₄⋊C₈	—	2	8	no	—
57	C₄×C₈	C₂×C₄×C₅	1	4	yes	—
58	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
59	C₄×C₈	C₅×D₄	1	4	yes	—
60	C₄×C₈	C₅×Q₈	1	2	yes	—
61	C₂²×C₅	—	2	2	no	—
62	C₂²×C₅	#384	1	1	yes	characteristic
63	C₂²×C₅	#498	1	2	yes	—
64	C₄×C₅	—	2	2	no	—
65	C₄×C₅	C₂×#106	1	2	yes	—
66	C₄×C₅	#430	1	4	yes	—
67	C₄×C₅	#492	1	2	yes	—
68	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
69	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
70	M₁₆	—	4	8	no	—
71	C₂×C₈	—	4	4	no	—
72	C₂×C₈	—	4	4	no	—
73	C₂×C₈	C₅×C₄⋊C₄	1	8	yes	—
74	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
75	C₂×C₈	C₅×SD₁₆	1	8	yes	—
76	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
77	C₄²	C₂×C₅×D₄	1	2	yes	—
78	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
79	C₂×C₅	—	2	2	no	—
80	C₂×C₅	#1844	1	1	yes	characteristic
81	C₂×C₅	#1849	1	2	yes	—
82	C₂³	C₅×C₄⋊Q₈	1	1	yes	characteristic
83	C₂×C₄	—	2	4	no	—
84	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
86	C₂×C₄	C₅×#127	1	1	yes	characteristic
87	C₂×C₄	C₅×C₄⋊Q₈	1	2	yes	—
88	C₂×C₄	C₂×C₅×SD₁₆	1	4	yes	—
89	C₈	—	2	8	no	—
90	C₈	—	8	4	no	—
91	C₈	C₅×#106	1	8	yes	—
92	C₅	#8825	1	1	yes	characteristic, direct product factor, Sylow
93	C₂²	—	2	2	no	—
94	C₂²	C₅×#384	1	1	yes	characteristic
95	C₂²	C₅×#498	1	2	yes	—
96	C₄	—	2	2	no	—
97	C₄	C₂×C₅×#106	1	2	yes	—
98	C₄	C₅×#430	1	4	yes	—
99	C₄	C₅×#492	1	2	yes	—
100	C₂	—	2	2	no	—
101	C₂	C₅×#1844	1	1	yes	characteristic
102	C₂	C₅×#1849	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#1848

C₂

yes

maximal

C₅×#1566

C₂

yes

maximal

C₂×C₅×#322

C₂

yes

maximal, characteristic

C₂×C₅×#108

—

C₅×#423

C₂²

yes

—

C₂×C₄×C₅×C₈

C₂²

yes

characteristic

C₂×C₄×C₅×C₈

C₂²

yes

—

C₅×#334

—

C₅×#322

C₄

yes

—

#8825

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₅×M₁₆

—

C₂²×C₅×C₈

D₄

yes

—

C₂²×C₅×C₈

Q₈

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×#108

—

C₅×C₄⋊C₈

—

C₄×C₅×C₈

C₂×C₄

yes

—

C₄×C₅×C₈

C₂×C₄

yes

—

C₄×C₅×C₈

D₄

yes

—

C₄×C₅×C₈

Q₈

yes

—

#1848

C₂×C₅

yes

—

#1566

C₂×C₅

yes

—

C₂×#322

C₂×C₅

yes

characteristic

C₂²×C₄×C₅

C₂×D₄

yes

characteristic

C₂²×C₄×C₅

C₂×Q₈

yes

—

C₅×M₁₆

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

C₄⋊C₄

yes

—

C₂×C₅×C₈

C₄⋊C₄

yes

—

C₂×C₅×C₈

SD₁₆

yes

—

C₄²×C₅

C₂²×C₄

yes

characteristic

C₄²×C₅

C₂×D₄

yes

—

C₄²×C₅

C₂×Q₈

yes

characteristic

C₂×#108

—

#423

C₂²×C₅

yes

—

C₂×C₄×C₈

C₂²×C₅

yes

—

C₂×C₄×C₈

C₂²×C₅

yes

characteristic

#334

—

#322

C₄×C₅

yes

—

C₂³×C₅

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₅

#127

yes

characteristic

C₂×C₄×C₅

C₄⋊Q₈

yes

—

C₂×C₄×C₅

C₂×SD₁₆

yes

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

#106

yes

—

C₂×M₁₆

—

C₂²×C₈

C₅×D₄

yes

—

C₂²×C₈

C₅×Q₈

yes

—

C₂×C₄²

C₂³×C₅

yes

characteristic

#108

—

C₄⋊C₈

—

C₄×C₈

C₂×C₄×C₅

yes

—

C₄×C₈

C₂×C₄×C₅

yes

—

C₄×C₈

C₅×D₄

yes

—

C₄×C₈

C₅×Q₈

yes

—

C₂²×C₅

—

C₂²×C₅

#384

yes

characteristic

C₂²×C₅

#498

yes

—

C₄×C₅

—

C₄×C₅

C₂×#106

yes

—

C₄×C₅

#430

yes

—

C₄×C₅

#492

yes

—

C₂²×C₄

C₂×C₅×D₄

yes

characteristic

C₂²×C₄

C₂×C₅×Q₈

yes

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₅×C₄⋊C₄

yes

—

C₂×C₈

C₅×C₄⋊C₄

yes

—

C₂×C₈

C₅×SD₁₆

yes

—

C₄²

C₂²×C₄×C₅

yes

characteristic

C₄²

C₂×C₅×D₄

yes

—

C₄²

C₂×C₅×Q₈

yes

characteristic

C₂×C₅

—

C₂×C₅

#1844

yes

characteristic

C₂×C₅

#1849

yes

—

C₂³

C₅×C₄⋊Q₈

yes

characteristic

C₂×C₄

—

C₂×C₄

C₂×C₅×C₄⋊C₄

yes

characteristic

C₂×C₄

C₂×C₅×C₄⋊C₄

yes

—

C₂×C₄

C₅×#127

yes

characteristic

C₂×C₄

C₅×C₄⋊Q₈

yes

—

C₂×C₄

C₂×C₅×SD₁₆

yes

—

C₈

—

C₈

—

C₈

C₅×#106

yes

—

C₅

#8825

yes

characteristic, direct product factor, Sylow

C₂²

—

C₂²

C₅×#384

yes

characteristic

C₂²

C₅×#498

yes

—

C₄

—

C₄

C₂×C₅×#106

yes

—

C₄

C₅×#430

yes

—

C₄

C₅×#492

yes

—

100

C₂

—

101

C₂

C₅×#1844

yes

characteristic

102

C₂

C₅×#1849

yes

—

	subgroup	G/H
center	C₂×C₄×C₅	#127
commutator	C₄²	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
socle	C₂²×C₅	#384
prime radical	C₂³×C₅	C₄⋊Q₈
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ G

subgroup

G/H

center

C₂×C₄×C₅

#127

commutator

C₄²

C₂²×C₄×C₅

Frattini, cosocle

C₂×C₄²

C₂³×C₅

socle

C₂²×C₅

#384

prime radical

C₂³×C₅

C₄⋊Q₈

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ G

N	H ≅ G/N	type
10. #8825	C₅	direct (N × H)
92. C₅	#8825	direct (N × H)

H ≅ G/N

type

10. #8825

C₅

direct (N × H)

92. C₅

#8825

direct (N × H)

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

subgroup	index
C₅×#1848	2
C₅×#1566	2
C₂×C₅×#322	2
#8825	5

subgroup

index

C₅×#1848

C₅×#1566

C₂×C₅×#322

#8825

Subgroups — C₅×#8825 #11931545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#8825 #11931545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8825 #11931545