Group #11933332 — subgroups

Subgroups — C₅×#10612 #11933332

Order 1280.

328 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 98 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×#1574	C₂	1	3	yes	maximal, complemented
2	C₅×#1545	C₂	1	3	yes	maximal
3	C₅×#1309	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#127	C₂²	1	1	yes	characteristic
5	C₅×#431	C₂²	1	3	yes	—
6	C₅×#423	C₂²	1	3	yes	—
7	C₅×#335	—	2	3	no	—
8	C₅×#334	—	2	3	no	—
9	C₅×#331	—	2	3	no	—
10	C₅×#331	—	2	3	no	—
11	#10612	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂²×C₅×D₄	—	2	3	no	—
13	C₂×C₅×M₁₆	—	2	3	no	—
14	C₅×#127	—	2	3	no	—
15	C₅×#127	Q₈	1	2	yes	—
16	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
17	C₅×C₄⋊C₈	—	2	3	no	—
18	C₅×C₄⋊C₈	—	2	3	no	—
19	C₅×C₄⋊C₈	D₄	1	3	yes	—
20	C₅×C₄⋊C₈	D₄	1	3	yes	—
21	C₅×C₂²⋊C₈	—	2	3	no	—
22	C₄×C₅×C₈	—	2	3	no	—
23	#1574	C₂×C₅	1	3	yes	complemented
24	#1545	C₂×C₅	1	3	yes	—
25	#1309	C₂×C₅	1	1	yes	characteristic, complemented
26	C₂⁴×C₅	—	4	1	no	—
27	C₂×C₅×D₄	—	2	6	no	—
28	C₂×C₅×D₄	—	4	3	no	—
29	C₂×C₅×D₄	—	8	3	no	—
30	C₂×C₅×D₄	—	8	3	no	—
31	C₂²×C₄×C₅	#41	1	3	yes	—
32	C₅×M₁₆	—	8	3	no	—
33	C₂×C₅×C₈	—	2	3	no	—
34	C₂×C₅×C₈	—	2	3	no	—
35	C₂×C₅×C₈	—	4	3	no	—
36	C₄²×C₅	C₂×D₄	1	3	yes	—
37	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
38	C₂×#127	C₂²×C₅	1	1	yes	characteristic
39	#431	C₂²×C₅	1	3	yes	—
40	#423	C₂²×C₅	1	3	yes	—
41	#335	—	2	3	no	—
42	#334	—	2	3	no	—
43	#331	—	2	3	no	—
44	#331	—	2	3	no	—
45	C₂³×C₅	—	4	2	no	—
46	C₂³×C₅	—	8	6	no	—
47	C₂³×C₅	#126	1	1	yes	characteristic
48	C₅×D₄	—	8	6	no	—
49	C₅×D₄	—	8	3	no	—
50	C₅×D₄	—	8	3	no	—
51	C₂×C₄×C₅	—	2	3	no	—
52	C₂×C₄×C₅	—	2	3	no	—
53	C₂×C₄×C₅	#121	1	3	yes	—
54	C₂×C₄×C₅	C₂²⋊Q₈	1	3	yes	—
55	C₅×C₈	—	4	3	no	—
56	C₅×C₈	—	4	3	no	—
57	C₅×C₈	—	8	3	no	—
58	C₂²×D₄	—	2	3	no	—
59	C₂×M₁₆	—	2	3	no	—
60	#127	—	2	3	no	—
61	#127	C₅×Q₈	1	2	yes	—
62	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
63	C₄⋊C₈	—	2	3	no	—
64	C₄⋊C₈	—	2	3	no	—
65	C₄⋊C₈	C₅×D₄	1	3	yes	—
66	C₄⋊C₈	C₅×D₄	1	3	yes	—
67	C₂²⋊C₈	—	2	3	no	—
68	C₄×C₈	—	2	3	no	—
69	C₂²×C₅	—	2	3	no	—
70	C₂²×C₅	—	8	6	no	—
71	C₂²×C₅	—	16	4	no	—
72	C₂²×C₅	#396	1	1	yes	characteristic
73	C₄×C₅	—	2	3	no	—
74	C₄×C₅	#471	1	3	yes	—
75	C₄×C₅	#472	1	3	yes	—
76	C₂⁴	—	4	1	no	—
77	C₂×D₄	—	2	6	no	—
78	C₂×D₄	—	4	3	no	—
79	C₂×D₄	—	8	3	no	—
80	C₂×D₄	—	8	3	no	—
81	C₂²×C₄	C₅×#41	1	3	yes	—
82	M₁₆	—	8	3	no	—
83	C₂×C₈	—	2	3	no	—
84	C₂×C₈	—	2	3	no	—
85	C₂×C₈	—	4	3	no	—
86	C₄²	C₂×C₅×D₄	1	3	yes	—
87	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
88	C₂×C₅	—	4	1	no	—
89	C₂×C₅	—	16	2	no	—
90	C₂×C₅	#2063	1	3	yes	—
91	C₂³	—	4	2	no	—
92	C₂³	—	8	6	no	—
93	C₂³	C₅×#126	1	1	yes	characteristic
94	D₄	—	8	6	no	—
95	D₄	—	8	3	no	—
96	D₄	—	8	3	no	—
97	C₂×C₄	—	2	3	no	—
98	C₂×C₄	—	2	3	no	—
99	C₂×C₄	C₅×#121	1	3	yes	—
100	C₂×C₄	C₅×C₂²⋊Q₈	1	3	yes	—
101	C₈	—	4	3	no	—
102	C₈	—	4	3	no	—
103	C₈	—	8	3	no	—
104	C₅	#10612	1	1	yes	characteristic, direct product factor, Sylow
105	C₂²	—	2	3	no	—
106	C₂²	—	8	6	no	—
107	C₂²	—	16	4	no	—
108	C₂²	C₅×#396	1	1	yes	characteristic
109	C₄	—	2	3	no	—
110	C₄	C₅×#471	1	3	yes	—
111	C₄	C₅×#472	1	3	yes	—
112	C₂	—	4	1	no	—
113	C₂	—	16	2	no	—
114	C₂	C₅×#2063	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#1574

C₂

yes

maximal, complemented

C₅×#1545

C₂

yes

maximal

C₅×#1309

C₂

yes

maximal, characteristic, complemented

C₂×C₅×#127

C₂²

yes

characteristic

C₅×#431

C₂²

yes

—

C₅×#423

C₂²

yes

—

—

—

—

—

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×D₄

—

C₂×C₅×M₁₆

—

C₅×#127

—

C₅×#127

Q₈

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×C₄⋊C₈

—

C₅×C₄⋊C₈

—

C₅×C₄⋊C₈

D₄

yes

—

C₅×C₄⋊C₈

D₄

yes

—

C₅×C₂²⋊C₈

—

C₄×C₅×C₈

—

#1574

C₂×C₅

yes

complemented

#1545

C₂×C₅

yes

—

#1309

C₂×C₅

yes

characteristic, complemented

C₂⁴×C₅

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂²×C₄×C₅

#41

yes

—

C₅×M₁₆

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₄²×C₅

C₂×D₄

yes

—

C₄²×C₅

C₂×Q₈

yes

characteristic

C₂×#127

C₂²×C₅

yes

characteristic

#431

C₂²×C₅

yes

—

#423

C₂²×C₅

yes

—

—

—

—

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

#126

yes

characteristic

C₅×D₄

—

C₅×D₄

—

C₅×D₄

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

#121

yes

—

C₂×C₄×C₅

C₂²⋊Q₈

yes

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

—

C₂²×D₄

—

C₂×M₁₆

—

#127

—

#127

C₅×Q₈

yes

—

C₂×C₄²

C₂³×C₅

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₅×D₄

yes

—

C₄⋊C₈

C₅×D₄

yes

—

C₂²⋊C₈

—

C₄×C₈

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

#396

yes

characteristic

C₄×C₅

—

C₄×C₅

#471

yes

—

C₄×C₅

#472

yes

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

C₅×#41

yes

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

C₂×C₅×D₄

yes

—

C₄²

C₂×C₅×Q₈

yes

characteristic

C₂×C₅

—

C₂×C₅

—

C₂×C₅

#2063

yes

—

C₂³

—

C₂³

—

C₂³

C₅×#126

yes

characteristic

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₅×#121

yes

—

100

C₂×C₄

C₅×C₂²⋊Q₈

yes

—

101

C₈

—

102

C₈

—

103

C₈

—

104

C₅

#10612

yes

characteristic, direct product factor, Sylow

105

C₂²

—

106

C₂²

—

107

C₂²

—

108

C₂²

C₅×#396

yes

characteristic

109

C₄

—

110

C₄

C₅×#471

yes

—

111

C₄

C₅×#472

yes

—

112

C₂

—

113

C₂

—

114

C₂

C₅×#2063

yes

—

	subgroup	G/H
center, socle	C₂²×C₅	#396
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂×C₅×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

subgroup

G/H

center, socle

C₂²×C₅

#396

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₅

prime radical

C₂×C₅×#127

C₂²

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

N	H ≅ G/N	type
1. C₅×#1574	C₂	semidirect
3. C₅×#1309	C₂	semidirect
11. #10612	C₅	direct (N × H)
23. #1574	C₂×C₅	semidirect
25. #1309	C₂×C₅	semidirect
104. C₅	#10612	direct (N × H)

H ≅ G/N

type

1. C₅×#1574

C₂

semidirect

3. C₅×#1309

C₂

semidirect

11. #10612

C₅

direct (N × H)

23. #1574

C₂×C₅

semidirect

25. #1309

C₂×C₅

semidirect

104. C₅

#10612

direct (N × H)

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

subgroup	index
C₅×#1574	2
C₅×#1545	2
C₅×#1309	2
#10612	5

subgroup

index

Subgroups — C₅×#10612 #11933332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#10612 #11933332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10612 #11933332