Group #11986947 — subgroups

Subgroups — #11986947

Order 1280.

126 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 45 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	#10599859	C₂	1	1	yes	maximal, characteristic
2	C₅×#1373	C₂	1	1	yes	maximal, characteristic
3	#10598001	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₄₀	—	2	1	no	—
5	C₂×Dic₄₀	C₄	1	2	yes	—
6	#64988	—	2	1	no	—
7	C₅×#364	—	2	1	no	—
8	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
9	#64719	—	2	1	no	—
10	#7449	—	5	1	no	maximal, Sylow
11	C₂×Dic₂₀	—	2	2	no	—
12	C₂×Dic₂₀	—	4	1	no	—
13	#4015	—	4	1	no	—
14	C₅×M₃₂	—	4	1	no	—
15	C₂×C₅×C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₂×C₅×C₁₆	D₄	1	1	yes	characteristic
17	C₄×C₅×C₈	D₄	1	1	yes	characteristic
18	Dic₄₀	—	4	2	no	—
19	Dic₄₀	—	4	1	no	—
20	Dic₄₀	—	4	1	no	—
21	#3926	—	4	1	no	—
22	#2247	—	5	1	no	—
23	#1422	—	5	1	no	—
24	#1373	D₅	1	1	yes	characteristic
25	C₂×Dic₁₀	—	4	2	no	—
26	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₅×C₈	D₈	1	1	yes	characteristic
28	C₄²×C₅	SD₁₆	1	1	yes	characteristic
29	C₄⋊Dic₅	—	8	2	no	—
30	Dic₂₀	—	4	2	no	—
31	Dic₂₀	—	4	2	no	—
32	Dic₂₀	—	8	1	no	—
33	Dic₂₀	—	8	1	no	—
34	C₅×C₁₆	—	2	1	no	—
35	C₅×C₁₆	—	8	1	no	—
36	C₅×C₁₆	D₈	1	1	yes	characteristic
37	C₅×C₁₆	SD₁₆	1	1	yes	characteristic
38	C₂×Q₃₂	—	5	2	no	—
39	C₂×Q₃₂	—	10	1	no	—
40	#494	—	10	1	no	—
41	M₆₄	—	10	1	no	—
42	#364	—	2	1	no	—
43	C₄×C₁₆	C₂×D₅	1	1	yes	characteristic
44	C₂×C₄×C₅	—	2	1	no	—
45	C₂×C₄×C₅	#102	1	1	yes	characteristic
46	C₂×Dic₅	—	8	2	no	—
47	Dic₁₀	—	8	2	no	—
48	Dic₁₀	—	8	2	no	—
49	C₅×C₈	#100	1	1	yes	characteristic
50	C₅×C₈	#102	1	1	yes	characteristic
51	C₅×C₈	D₁₆	1	1	yes	characteristic
52	C₅×C₈	SD₃₂	1	1	yes	characteristic
53	C₂×Q₁₆	—	10	2	no	—
54	C₂×Q₁₆	—	20	1	no	—
55	C₄⋊Q₈	—	20	1	no	—
56	Q₃₂	—	20	2	no	—
57	Q₃₂	—	20	1	no	—
58	Q₃₂	—	20	1	no	—
59	M₃₂	—	4	1	no	—
60	C₂×C₁₆	C₄×D₅	1	1	yes	characteristic
61	C₂×C₁₆	D₂₀	1	1	yes	characteristic
62	C₄×C₈	C₂²⋊D₅	1	1	yes	characteristic
63	C₃₂	—	20	1	no	—
64	C₂²×C₅	#361	1	1	yes	characteristic
65	C₄×C₅	—	2	2	no	—
66	C₄×C₅	#331	1	1	yes	characteristic
67	C₄×C₅	#357	1	1	yes	characteristic
68	Dic₅	—	16	2	no	—
69	C₂×Q₈	—	20	2	no	—
70	Q₁₆	—	20	2	no	—
71	Q₁₆	—	20	2	no	—
72	Q₁₆	—	40	1	no	—
73	Q₁₆	—	40	1	no	—
74	C₂×C₈	#685	1	1	yes	characteristic
75	C₂×C₈	#686	1	1	yes	characteristic
76	C₄⋊C₄	—	40	2	no	—
77	C₄²	#688	1	1	yes	characteristic
78	C₁₆	—	2	1	no	—
79	C₁₆	—	8	1	no	—
80	C₁₆	#677	1	1	yes	characteristic
81	C₁₆	D₄₀	1	1	yes	characteristic
82	C₂×C₅	—	2	1	no	—
83	C₂×C₅	#1361	1	1	yes	characteristic
84	Q₈	—	40	2	no	—
85	Q₈	—	40	2	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	40	2	no	—
88	C₂×C₄	#3941	1	1	yes	characteristic
89	C₈	#3953	1	1	yes	characteristic
90	C₈	#3955	1	1	yes	characteristic
91	C₈	#3958	1	1	yes	characteristic
92	C₈	#3960	1	1	yes	characteristic
93	C₅	#7449	1	1	yes	characteristic, complemented, Sylow
94	C₂²	#64715	1	1	yes	characteristic
95	C₄	—	2	2	no	—
96	C₄	—	80	2	no	—
97	C₄	#64705	1	1	yes	characteristic
98	C₄	#64711	1	1	yes	characteristic
99	C₂	—	2	1	no	—
100	C₂	#10597964	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10599859

C₂

yes

maximal, characteristic

C₅×#1373

C₂

yes

maximal, characteristic

#10598001

C₂

yes

maximal, characteristic

C₂×Dic₄₀

—

C₂×Dic₄₀

C₄

yes

—

#64988

—

C₅×#364

—

C₄×C₅×C₁₆

C₂²

yes

—

—

C₂×Dic₂₀

—

C₂×Dic₂₀

—

#4015

—

C₅×M₃₂

—

C₂×C₅×C₁₆

C₂×C₄

yes

characteristic

C₂×C₅×C₁₆

D₄

yes

characteristic

C₄×C₅×C₈

D₄

yes

characteristic

Dic₄₀

—

Dic₄₀

—

Dic₄₀

—

—

—

—

D₅

yes

characteristic

C₂×Dic₁₀

—

C₂×C₅×C₈

C₂²⋊C₄

yes

characteristic

C₂×C₅×C₈

D₈

yes

characteristic

C₄²×C₅

SD₁₆

yes

characteristic

C₄⋊Dic₅

—

Dic₂₀

—

Dic₂₀

—

Dic₂₀

—

Dic₂₀

—

C₅×C₁₆

—

C₅×C₁₆

—

C₅×C₁₆

D₈

yes

characteristic

C₅×C₁₆

SD₁₆

yes

characteristic

C₂×Q₃₂

—

C₂×Q₃₂

—

#494

—

M₆₄

—

#364

—

C₄×C₁₆

C₂×D₅

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

#102

yes

characteristic

C₂×Dic₅

—

Dic₁₀

—

Dic₁₀

—

C₅×C₈

yes

C₅×C₈

yes

C₅×C₈

D₁₆

yes

characteristic

C₅×C₈

SD₃₂

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

Q₃₂

—

Q₃₂

—

Q₃₂

—

M₃₂

—

C₂×C₁₆

C₄×D₅

yes

characteristic

C₂×C₁₆

D₂₀

yes

characteristic

C₄×C₈

C₂²⋊D₅

yes

characteristic

C₃₂

—

C₂²×C₅

#361

yes

characteristic

C₄×C₅

—

C₄×C₅

yes

C₄×C₅

yes

Dic₅

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₄²

#688

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

#677

yes

characteristic

C₁₆

D₄₀

yes

characteristic

C₂×C₅

—

C₂×C₅

#1361

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₈

yes

C₈

yes

C₈

yes

C₈

yes

C₅

yes

characteristic, complemented, Sylow

C₂²

#64715

yes

characteristic

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

100

C₂

#10597964

yes

characteristic

	subgroup	G/H
center	C₂	#10597964
commutator	C₂×C₅×C₁₆	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₅
Fitting	C₅×#1373	C₂
socle	C₂×C₅	#1361
prime radical	C₂²×C₅	#361
cosocle	C₄×C₅×C₁₆	C₂²
hypercenter	#1373	D₅
hypocenter	C₅	#7449
LCS	G ▷ C₂×C₅×C₁₆ ▷ C₂×C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1373

subgroup

G/H

center

C₂

#10597964

commutator

C₂×C₅×C₁₆

C₂×C₄

Frattini

C₄×C₁₆

C₂×D₅

C₂

C₂×C₅

C₂²×C₅

C₄×C₅×C₁₆

C₂²

D₅

C₅

G ▷ C₂×C₅×C₁₆ ▷ C₂×C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1373

N	H ≅ G/N	type
93. C₅	#7449	semidirect

H ≅ G/N

type

93. C₅

#7449

semidirect

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

subgroup	index
#10599859	2
C₅×#1373	2
#10598001	2
#7449	5

subgroup

index

Subgroups — #11986947

Conjugacy classes of subgroups

Complements

Maximal subgroups