Group #11943512 — subgroups

Subgroups — C₅×#20792 #11943512

Order 1280.

1118 conjugacy classes of subgroups; only the 622 normal subgroups are shown.

normal subgroups only

This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 622 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	C₂×C₅×#423	C₂	1	6	yes	maximal
2	C₂×C₅×#376	C₂	1	1	yes	maximal, characteristic
3	C₅×#1843	C₂	1	8	yes	maximal, complemented
4	C₂²×C₅×M₁₆	C₂²	1	4	yes	—
5	C₂²×C₄²×C₅	C₂²	1	3	yes	—
6	C₅×#423	—	2	24	no	—
7	C₂×C₅×C₄⋊C₈	C₂²	1	24	yes	—
8	C₅×#376	C₄	1	4	yes	—
9	C₅×#376	C₂²	1	4	yes	—
10	C₂×C₅×#95	C₄	1	4	yes	—
11	#20792	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂³×C₄×C₅	C₂×C₄	1	6	yes	—
13	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
14	C₂×C₅×M₁₆	—	2	24	no	—
15	C₂²×C₅×C₈	C₂³	1	8	yes	—
16	C₂×C₄²×C₅	C₂×C₄	1	6	yes	—
17	C₂×C₄²×C₅	D₄	1	12	yes	—
18	C₂×C₄²×C₅	Q₈	1	12	yes	—
19	C₂×C₄²×C₅	C₂³	1	6	yes	—
20	C₅×C₄⋊C₈	—	2	48	no	—
21	C₅×#95	C₂×C₄	1	16	yes	—
22	C₂×#423	C₂×C₅	1	6	yes	—
23	C₂×#376	C₂×C₅	1	1	yes	characteristic
24	#1843	C₂×C₅	1	8	yes	complemented
25	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₅	—	4	12	no	—
27	C₂²×C₄×C₅	C₄⋊C₄	1	24	yes	—
28	C₂²×C₄×C₅	C₂²×C₄	1	12	yes	—
29	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₅	C₂×D₄	1	6	yes	—
31	C₂²×C₄×C₅	C₂×Q₈	1	6	yes	—
32	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
33	C₅×M₁₆	—	4	16	no	—
34	C₂×C₅×C₈	—	2	24	no	—
35	C₄²×C₅	C₄⋊C₄	1	24	yes	—
36	C₄²×C₅	C₂×D₄	1	12	yes	—
37	C₄²×C₅	C₂×Q₈	1	12	yes	—
38	C₂²×M₁₆	C₂²×C₅	1	4	yes	—
39	C₂²×C₄²	C₂²×C₅	1	3	yes	—
40	#423	—	2	24	no	—
41	C₂×C₄⋊C₈	C₂²×C₅	1	24	yes	—
42	#376	C₄×C₅	1	4	yes	—
43	#376	C₂²×C₅	1	4	yes	—
44	C₂×#95	C₄×C₅	1	4	yes	—
45	C₂³×C₅	—	2	4	no	—
46	C₂³×C₅	C₂×C₄⋊C₄	1	6	yes	—
47	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
48	C₂×C₄×C₅	—	2	24	no	—
49	C₂×C₄×C₅	—	4	24	no	—
50	C₂×C₄×C₅	C₂×C₄⋊C₄	1	24	yes	—
51	C₂×C₄×C₅	C₂×C₄⋊C₄	1	6	yes	—
52	C₂×C₄×C₅	#127	1	4	yes	—
53	C₂×C₄×C₅	C₄⋊Q₈	1	12	yes	—
54	C₂×C₄×C₅	C₂²×D₄	1	3	yes	—
55	C₂×C₄×C₅	C₂²×Q₈	1	3	yes	—
56	C₅×C₈	—	4	8	no	—
57	C₂³×C₄	C₂×C₄×C₅	1	6	yes	—
58	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
59	C₂×M₁₆	—	2	24	no	—
60	C₂²×C₈	C₂³×C₅	1	8	yes	—
61	C₂×C₄²	C₂×C₄×C₅	1	6	yes	—
62	C₂×C₄²	C₅×D₄	1	12	yes	—
63	C₂×C₄²	C₅×Q₈	1	12	yes	—
64	C₂×C₄²	C₂³×C₅	1	6	yes	—
65	C₄⋊C₈	—	2	48	no	—
66	#95	C₂×C₄×C₅	1	16	yes	—
67	C₂²×C₅	—	2	12	no	—
68	C₂²×C₅	#384	1	4	yes	—
69	C₂²×C₅	C₂²×C₄⋊C₄	1	3	yes	—
70	C₂²×C₅	#568	1	4	yes	—
71	C₄×C₅	—	2	24	no	—
72	C₄×C₅	#384	1	4	yes	—
73	C₄×C₅	C₂×#127	1	1	yes	characteristic
74	C₄×C₅	C₂×C₄⋊Q₈	1	3	yes	—
75	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
76	C₂²×C₄	—	4	12	no	—
77	C₂²×C₄	C₅×C₄⋊C₄	1	24	yes	—
78	C₂²×C₄	C₂²×C₄×C₅	1	12	yes	—
79	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
80	C₂²×C₄	C₂×C₅×D₄	1	6	yes	—
81	C₂²×C₄	C₂×C₅×Q₈	1	6	yes	—
82	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
83	M₁₆	—	4	16	no	—
84	C₂×C₈	—	2	24	no	—
85	C₄²	C₅×C₄⋊C₄	1	24	yes	—
86	C₄²	C₂×C₅×D₄	1	12	yes	—
87	C₄²	C₂×C₅×Q₈	1	12	yes	—
88	C₂×C₅	—	2	4	no	—
89	C₂×C₅	C₂×#384	1	1	yes	characteristic
90	C₂×C₅	#2905	1	6	yes	—
91	C₂³	—	2	4	no	—
92	C₂³	C₂×C₅×C₄⋊C₄	1	6	yes	—
93	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
94	C₂×C₄	—	2	24	no	—
95	C₂×C₄	—	4	24	no	—
96	C₂×C₄	C₂×C₅×C₄⋊C₄	1	24	yes	—
97	C₂×C₄	C₂×C₅×C₄⋊C₄	1	6	yes	—
98	C₂×C₄	C₅×#127	1	4	yes	—
99	C₂×C₄	C₅×C₄⋊Q₈	1	12	yes	—
100	C₂×C₄	C₂²×C₅×D₄	1	3	yes	—
101	C₂×C₄	C₂²×C₅×Q₈	1	3	yes	—
102	C₈	—	4	8	no	—
103	C₅	#20792	1	1	yes	characteristic, direct product factor, Sylow
104	C₂²	—	2	12	no	—
105	C₂²	C₅×#384	1	4	yes	—
106	C₂²	C₂²×C₅×C₄⋊C₄	1	3	yes	—
107	C₂²	C₅×#568	1	4	yes	—
108	C₄	—	2	24	no	—
109	C₄	C₅×#384	1	4	yes	—
110	C₄	C₂×C₅×#127	1	1	yes	characteristic
111	C₄	C₂×C₅×C₄⋊Q₈	1	3	yes	—
112	C₂	—	2	4	no	—
113	C₂	C₂×C₅×#384	1	1	yes	characteristic
114	C₂	C₅×#2905	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅×#423

C₂

yes

maximal

C₂×C₅×#376

C₂

yes

maximal, characteristic

C₅×#1843

C₂

yes

maximal, complemented

C₂²×C₅×M₁₆

C₂²

yes

—

C₂²×C₄²×C₅

C₂²

yes

—

C₅×#423

—

C₂×C₅×C₄⋊C₈

C₂²

yes

—

C₅×#376

C₄

yes

—

C₅×#376

C₂²

yes

—

C₂×C₅×#95

C₄

yes

—

#20792

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₄×C₅

C₂×C₄

yes

—

C₂³×C₄×C₅

C₂³

yes

characteristic

C₂×C₅×M₁₆

—

C₂²×C₅×C₈

C₂³

yes

—

C₂×C₄²×C₅

C₂×C₄

yes

—

C₂×C₄²×C₅

D₄

yes

—

C₂×C₄²×C₅

Q₈

yes

—

C₂×C₄²×C₅

C₂³

yes

—

C₅×C₄⋊C₈

—

C₅×#95

C₂×C₄

yes

—

C₂×#423

C₂×C₅

yes

—

C₂×#376

C₂×C₅

yes

characteristic

#1843

C₂×C₅

yes

complemented

C₂⁴×C₅

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₄⋊C₄

yes

—

C₂²×C₄×C₅

C₂²×C₄

yes

—

C₂²×C₄×C₅

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅

C₂×D₄

yes

—

C₂²×C₄×C₅

C₂×Q₈

yes

—

C₂²×C₄×C₅

C₂⁴

yes

characteristic

C₅×M₁₆

—

C₂×C₅×C₈

—

C₄²×C₅

C₄⋊C₄

yes

—

C₄²×C₅

C₂×D₄

yes

—

C₄²×C₅

C₂×Q₈

yes

—

C₂²×M₁₆

C₂²×C₅

yes

—

C₂²×C₄²

C₂²×C₅

yes

—

#423

—

C₂×C₄⋊C₈

C₂²×C₅

yes

—

#376

C₄×C₅

yes

—

#376

C₂²×C₅

yes

—

C₂×#95

C₄×C₅

yes

—

C₂³×C₅

—

C₂³×C₅

C₂×C₄⋊C₄

yes

—

C₂³×C₅

C₂³×C₄

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₅

#127

yes

—

C₂×C₄×C₅

C₄⋊Q₈

yes

—

C₂×C₄×C₅

C₂²×D₄

yes

—

C₂×C₄×C₅

C₂²×Q₈

yes

—

C₅×C₈

—

C₂³×C₄

C₂×C₄×C₅

yes

—

C₂³×C₄

C₂³×C₅

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

C₂³×C₅

yes

—

C₂×C₄²

C₂×C₄×C₅

yes

—

C₂×C₄²

C₅×D₄

yes

—

C₂×C₄²

C₅×Q₈

yes

—

C₂×C₄²

C₂³×C₅

yes

—

C₄⋊C₈

—

#95

C₂×C₄×C₅

yes

—

C₂²×C₅

—

C₂²×C₅

#384

yes

—

C₂²×C₅

C₂²×C₄⋊C₄

yes

—

C₂²×C₅

#568

yes

—

C₄×C₅

—

C₄×C₅

#384

yes

—

C₄×C₅

C₂×#127

yes

characteristic

C₄×C₅

C₂×C₄⋊Q₈

yes

—

C₂⁴

C₂²×C₄×C₅

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₅×C₄⋊C₄

yes

—

C₂²×C₄

C₂²×C₄×C₅

yes

—

C₂²×C₄

C₂²×C₄×C₅

yes

characteristic

C₂²×C₄

C₂×C₅×D₄

yes

—

C₂²×C₄

C₂×C₅×Q₈

yes

—

C₂²×C₄

C₂⁴×C₅

yes

characteristic

M₁₆

—

C₂×C₈

—

C₄²

C₅×C₄⋊C₄

yes

—

C₄²

C₂×C₅×D₄

yes

—

C₄²

C₂×C₅×Q₈

yes

—

C₂×C₅

—

C₂×C₅

C₂×#384

yes

characteristic

C₂×C₅

#2905

yes

—

C₂³

—

C₂³

C₂×C₅×C₄⋊C₄

yes

—

C₂³

C₂³×C₄×C₅

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₅×C₄⋊C₄

yes

—

C₂×C₄

C₂×C₅×C₄⋊C₄

yes

—

C₂×C₄

C₅×#127

yes

—

C₂×C₄

C₅×C₄⋊Q₈

yes

—

100

C₂×C₄

C₂²×C₅×D₄

yes

—

101

C₂×C₄

C₂²×C₅×Q₈

yes

—

102

C₈

—

103

C₅

#20792

yes

characteristic, direct product factor, Sylow

104

C₂²

—

105

C₂²

C₅×#384

yes

—

106

C₂²

C₂²×C₅×C₄⋊C₄

yes

—

107

C₂²

C₅×#568

yes

—

108

C₄

—

109

C₄

C₅×#384

yes

—

110

C₄

C₂×C₅×#127

yes

characteristic

111

C₄

C₂×C₅×C₄⋊Q₈

yes

—

112

C₂

—

113

C₂

C₂×C₅×#384

yes

characteristic

114

C₂

C₅×#2905

yes

—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂³	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂⁴×C₅	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

subgroup

G/H

center

C₂²×C₄×C₅

C₂⁴

commutator

C₂³

C₂³×C₄×C₅

Frattini, cosocle

C₂²×C₄

C₂⁴×C₅

socle

C₂³×C₅

C₂³×C₄

prime radical

C₂⁴×C₅

C₂²×C₄

LCS

G ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂²×C₄×C₅ ◁ G

N	H ≅ G/N	type
3. C₅×#1843	C₂	semidirect
11. #20792	C₅	direct (N × H)
24. #1843	C₂×C₅	semidirect
103. C₅	#20792	direct (N × H)

H ≅ G/N

type

3. C₅×#1843

C₂

semidirect

11. #20792

C₅

direct (N × H)

24. #1843

C₂×C₅

semidirect

103. C₅

#20792

direct (N × H)

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

subgroup	index
C₂×C₅×#423	2
C₂×C₅×#376	2
C₅×#1843	2
#20792	5

subgroup

index

C₂×C₅×#423

C₂×C₅×#376

C₅×#1843

#20792

Subgroups — C₅×#20792 #11943512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#20792 #11943512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20792 #11943512