Group #11931522 — subgroups

Subgroups — C₅×#8802 #11931522

Order 1280.

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

normal subgroups only

This group has 258 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×#1745	C₂	1	1	yes	maximal, characteristic
2	C₅×#1281	C₂	1	2	yes	maximal
3	C₅×#1276	C₂	1	2	yes	maximal
4	C₅×#1275	C₂	1	2	yes	maximal
5	C₅×#431	C₂²	1	4	yes	—
6	C₂×C₅×#97	C₂²	1	1	yes	characteristic
7	C₂×C₅×#97	C₂²	1	1	yes	characteristic
8	C₄³×C₅	C₂²	1	1	yes	characteristic
9	C₅×#336	C₄	1	4	yes	—
10	#8802	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
12	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
13	C₂×C₄²×C₅	—	2	2	no	—
14	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
16	C₅×C₄⋊C₈	—	2	4	no	—
17	C₅×C₂²⋊C₈	—	2	4	no	—
18	C₅×#97	—	2	2	no	—
19	C₅×#97	—	2	2	no	—
20	C₄×C₅×C₈	—	2	4	no	—
21	#1745	C₂×C₅	1	1	yes	characteristic
22	#1281	C₂×C₅	1	2	yes	—
23	#1276	C₂×C₅	1	2	yes	—
24	#1275	C₂×C₅	1	2	yes	—
25	C₂²×C₄×C₅	—	2	2	no	—
26	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₄×C₅	#41	1	2	yes	—
28	C₂×C₅×C₈	—	2	2	no	—
29	C₂×C₅×C₈	—	2	2	no	—
30	C₂×C₅×C₈	—	2	4	no	—
31	C₂×C₅×C₈	—	2	4	no	—
32	C₂×C₅×C₈	—	4	4	no	—
33	C₄²×C₅	—	2	4	no	—
34	C₄²×C₅	—	4	4	no	—
35	C₄²×C₅	#41	1	2	yes	—
36	C₄²×C₅	#41	1	2	yes	—
37	#431	C₂²×C₅	1	4	yes	—
38	C₂×#97	C₂²×C₅	1	1	yes	characteristic
39	C₂×#97	C₂²×C₅	1	1	yes	characteristic
40	C₄³	C₂²×C₅	1	1	yes	characteristic
41	#336	C₄×C₅	1	4	yes	—
42	C₂³×C₅	#117	1	1	yes	characteristic
43	C₂×C₄×C₅	—	2	4	no	—
44	C₂×C₄×C₅	—	4	2	no	—
45	C₂×C₄×C₅	—	4	2	no	—
46	C₂×C₄×C₅	—	4	2	no	—
47	C₂×C₄×C₅	#117	1	1	yes	characteristic
48	C₂×C₄×C₅	#117	1	1	yes	characteristic
49	C₂×C₄×C₅	#126	1	4	yes	—
50	C₂×C₄×C₅	#131	1	4	yes	—
51	C₅×C₈	—	4	2	no	—
52	C₅×C₈	—	4	2	no	—
53	C₅×C₈	—	8	4	no	—
54	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
55	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
56	C₂×C₄²	—	2	2	no	—
57	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
58	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
59	C₄⋊C₈	—	2	4	no	—
60	C₂²⋊C₈	—	2	4	no	—
61	#97	—	2	2	no	—
62	#97	—	2	2	no	—
63	C₄×C₈	—	2	4	no	—
64	C₂²×C₅	—	2	2	no	—
65	C₂²×C₅	#383	1	1	yes	characteristic
66	C₂²×C₅	#433	1	2	yes	—
67	C₄×C₅	—	2	4	no	—
68	C₄×C₅	—	4	4	no	—
69	C₄×C₅	#433	1	2	yes	—
70	C₄×C₅	#433	1	2	yes	—
71	C₂²×C₄	—	2	2	no	—
72	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
73	C₂²×C₄	C₅×#41	1	2	yes	—
74	C₂×C₈	—	2	2	no	—
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	—	2	4	no	—
77	C₂×C₈	—	2	4	no	—
78	C₂×C₈	—	4	4	no	—
79	C₄²	—	2	4	no	—
80	C₄²	—	4	4	no	—
81	C₄²	C₅×#41	1	2	yes	—
82	C₄²	C₅×#41	1	2	yes	—
83	C₂×C₅	—	2	2	no	—
84	C₂×C₅	#1840	1	1	yes	characteristic
85	C₂×C₅	#1841	1	2	yes	—
86	C₂³	C₅×#117	1	1	yes	characteristic
87	C₂×C₄	—	2	4	no	—
88	C₂×C₄	—	4	2	no	—
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	—	4	2	no	—
91	C₂×C₄	C₅×#117	1	1	yes	characteristic
92	C₂×C₄	C₅×#117	1	1	yes	characteristic
93	C₂×C₄	C₅×#126	1	4	yes	—
94	C₂×C₄	C₅×#131	1	4	yes	—
95	C₈	—	4	2	no	—
96	C₈	—	4	2	no	—
97	C₈	—	8	4	no	—
98	C₅	#8802	1	1	yes	characteristic, direct product factor, Sylow
99	C₂²	—	2	2	no	—
100	C₂²	C₅×#383	1	1	yes	characteristic
101	C₂²	C₅×#433	1	2	yes	—
102	C₄	—	2	4	no	—
103	C₄	—	4	4	no	—
104	C₄	C₅×#433	1	2	yes	—
105	C₄	C₅×#433	1	2	yes	—
106	C₂	—	2	2	no	—
107	C₂	C₅×#1840	1	1	yes	characteristic
108	C₂	C₅×#1841	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#1745

C₂

yes

maximal, characteristic

C₅×#1281

C₂

yes

maximal

C₅×#1276

C₂

yes

maximal

C₅×#1275

C₂

yes

maximal

C₅×#431

C₂²

yes

—

C₂×C₅×#97

C₂²

yes

characteristic

C₂×C₅×#97

C₂²

yes

characteristic

C₄³×C₅

C₂²

yes

characteristic

C₅×#336

C₄

yes

—

#8802

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×C₈

C₂×C₄

yes

—

C₂²×C₅×C₈

C₂×C₄

yes

—

C₂×C₄²×C₅

—

C₂×C₄²×C₅

C₂×C₄

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×C₄⋊C₈

—

C₅×C₂²⋊C₈

—

C₅×#97

—

C₅×#97

—

C₄×C₅×C₈

—

#1745

C₂×C₅

yes

characteristic

#1281

C₂×C₅

yes

—

#1276

C₂×C₅

yes

—

#1275

C₂×C₅

yes

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅

#41

yes

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₄²×C₅

—

C₄²×C₅

—

C₄²×C₅

#41

yes

—

C₄²×C₅

#41

yes

—

#431

C₂²×C₅

yes

—

C₂×#97

C₂²×C₅

yes

characteristic

C₂×#97

C₂²×C₅

yes

characteristic

C₄³

C₂²×C₅

yes

characteristic

#336

C₄×C₅

yes

—

C₂³×C₅

#117

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

yes

C₂×C₄×C₅

yes

C₂×C₄×C₅

yes

—

C₂×C₄×C₅

#131

yes

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

—

C₂²×C₈

C₂×C₄×C₅

yes

—

C₂²×C₈

C₂×C₄×C₅

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×C₄×C₅

yes

—

C₂×C₄²

C₂³×C₅

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

—

C₂²×C₅

—

C₂²×C₅

#383

yes

characteristic

C₂²×C₅

#433

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

#433

yes

—

C₄×C₅

#433

yes

—

C₂²×C₄

—

C₂²×C₄

C₂²×C₄×C₅

yes

characteristic

C₂²×C₄

C₅×#41

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

C₅×#41

yes

—

C₄²

C₅×#41

yes

—

C₂×C₅

—

C₂×C₅

#1840

yes

characteristic

C₂×C₅

#1841

yes

—

C₂³

C₅×#117

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

—

C₂×C₄

C₅×#131

yes

—

C₈

—

C₈

—

C₈

—

C₅

#8802

yes

characteristic, direct product factor, Sylow

C₂²

—

100

C₂²

C₅×#383

yes

characteristic

101

C₂²

C₅×#433

yes

—

102

C₄

—

103

C₄

—

104

C₄

C₅×#433

yes

—

105

C₄

C₅×#433

yes

—

106

C₂

—

107

C₂

C₅×#1840

yes

characteristic

108

C₂

C₅×#1841

yes

—

	subgroup	G/H
center	C₂×C₄×C₅	#117
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
socle	C₂²×C₅	#383
prime radical	C₂³×C₅	#117
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×#97 ◁ G

subgroup

G/H

center

C₂×C₄×C₅

#117

commutator

C₂²×C₄

C₂²×C₄×C₅

Frattini, cosocle

C₂×C₄²

C₂³×C₅

C₂²×C₅

C₂³×C₅

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×#97 ◁ G

N	H ≅ G/N	type
10. #8802	C₅	direct (N × H)
98. C₅	#8802	direct (N × H)

H ≅ G/N

type

10. #8802

C₅

direct (N × H)

98. C₅

#8802

direct (N × H)

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

subgroup	index
C₅×#1745	2
C₅×#1281	2
C₅×#1276	2
C₅×#1275	2
#8802	5

subgroup

index

Subgroups — C₅×#8802 #11931522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#8802 #11931522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8802 #11931522