Group #11935618 — subgroups

Subgroups — C₅×#12898 #11935618

Order 1280.

414 conjugacy classes of subgroups; only the 286 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 286 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×C₄⋊C₁₆	C₂	1	6	yes	maximal
2	C₄²×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×C₁₆	C₂²	1	4	yes	—
4	C₂×C₄×C₅×C₈	C₄	1	3	yes	—
5	C₂×C₄×C₅×C₈	C₂²	1	3	yes	—
6	C₄³×C₅	C₄	1	1	yes	characteristic
7	C₅×C₄⋊C₁₆	—	2	12	no	—
8	#12898	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₂²×C₅×C₈	C₂×C₄	1	3	yes	—
10	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
11	C₂×C₄²×C₅	C₈	1	3	yes	—
12	C₂×C₄²×C₅	C₈	1	1	yes	characteristic
13	C₂×C₄²×C₅	C₂×C₄	1	3	yes	—
14	C₂×C₅×C₁₆	—	2	12	no	—
15	C₄×C₅×C₈	—	2	6	no	—
16	C₄×C₅×C₈	D₄	1	6	yes	—
17	C₄×C₅×C₈	Q₈	1	6	yes	—
18	C₂×C₄⋊C₁₆	C₂×C₅	1	6	yes	—
19	C₄²×C₈	C₂×C₅	1	1	yes	characteristic
20	C₂²×C₄×C₅	C₂×C₈	1	3	yes	—
21	C₂²×C₄×C₅	C₂×C₈	1	3	yes	—
22	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₅×C₈	—	2	6	no	—
24	C₂×C₅×C₈	C₄⋊C₄	1	6	yes	—
25	C₂×C₅×C₈	C₂×D₄	1	3	yes	—
26	C₂×C₅×C₈	C₂×Q₈	1	3	yes	—
27	C₄²×C₅	—	2	6	no	—
28	C₄²×C₅	C₁₆	1	4	yes	complemented
29	C₄²×C₅	C₄⋊C₄	1	6	yes	—
30	C₄²×C₅	M₁₆	1	6	yes	—
31	C₅×C₁₆	—	4	4	no	—
32	C₂²×C₁₆	C₂²×C₅	1	4	yes	—
33	C₂×C₄×C₈	C₄×C₅	1	3	yes	—
34	C₂×C₄×C₈	C₂²×C₅	1	3	yes	—
35	C₄³	C₄×C₅	1	1	yes	characteristic
36	C₄⋊C₁₆	—	2	12	no	—
37	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
38	C₂×C₄×C₅	—	2	6	no	—
39	C₂×C₄×C₅	C₄⋊C₈	1	6	yes	—
40	C₂×C₄×C₅	C₄⋊C₈	1	6	yes	—
41	C₂×C₄×C₅	C₂×C₁₆	1	6	yes	—
42	C₂×C₄×C₅	M₃₂	1	6	yes	—
43	C₂×C₄×C₅	C₂×C₄⋊C₄	1	3	yes	—
44	C₂×C₄×C₅	C₂×M₁₆	1	3	yes	—
45	C₅×C₈	—	2	6	no	—
46	C₅×C₈	#127	1	1	yes	characteristic
47	C₅×C₈	C₄⋊Q₈	1	3	yes	—
48	C₂²×C₈	C₂×C₄×C₅	1	3	yes	—
49	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
50	C₂×C₄²	C₅×C₈	1	3	yes	—
51	C₂×C₄²	C₅×C₈	1	1	yes	characteristic
52	C₂×C₄²	C₂×C₄×C₅	1	3	yes	—
53	C₂×C₁₆	—	2	12	no	—
54	C₄×C₈	—	2	6	no	—
55	C₄×C₈	C₅×D₄	1	6	yes	—
56	C₄×C₈	C₅×Q₈	1	6	yes	—
57	C₂²×C₅	C₂×C₄⋊C₈	1	3	yes	—
58	C₂²×C₅	C₂²×C₁₆	1	1	yes	characteristic
59	C₂²×C₅	C₂×M₃₂	1	3	yes	—
60	C₄×C₅	—	2	6	no	—
61	C₄×C₅	C₄⋊C₁₆	1	12	yes	complemented
62	C₄×C₅	#384	1	1	yes	characteristic
63	C₄×C₅	#423	1	3	yes	—
64	C₂²×C₄	C₂×C₅×C₈	1	3	yes	—
65	C₂²×C₄	C₂×C₅×C₈	1	3	yes	—
66	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
67	C₂×C₈	—	2	6	no	—
68	C₂×C₈	C₅×C₄⋊C₄	1	6	yes	—
69	C₂×C₈	C₂×C₅×D₄	1	3	yes	—
70	C₂×C₈	C₂×C₅×Q₈	1	3	yes	—
71	C₄²	—	2	6	no	—
72	C₄²	C₅×C₁₆	1	4	yes	complemented
73	C₄²	C₅×C₄⋊C₄	1	6	yes	—
74	C₄²	C₅×M₁₆	1	6	yes	—
75	C₁₆	—	4	4	no	—
76	C₂×C₅	#1842	1	1	yes	characteristic
77	C₂×C₅	C₂×C₄⋊C₁₆	1	3	yes	—
78	C₂×C₅	#2150	1	3	yes	—
79	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
80	C₂×C₄	—	2	6	no	—
81	C₂×C₄	C₅×C₄⋊C₈	1	6	yes	—
82	C₂×C₄	C₅×C₄⋊C₈	1	6	yes	—
83	C₂×C₄	C₂×C₅×C₁₆	1	6	yes	—
84	C₂×C₄	C₅×M₃₂	1	6	yes	—
85	C₂×C₄	C₂×C₅×C₄⋊C₄	1	3	yes	—
86	C₂×C₄	C₂×C₅×M₁₆	1	3	yes	—
87	C₈	—	2	6	no	—
88	C₈	C₅×#127	1	1	yes	characteristic
89	C₈	C₅×C₄⋊Q₈	1	3	yes	—
90	C₅	#12898	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²	C₂×C₅×C₄⋊C₈	1	3	yes	—
92	C₂²	C₂²×C₅×C₁₆	1	1	yes	characteristic
93	C₂²	C₂×C₅×M₃₂	1	3	yes	—
94	C₄	—	2	6	no	—
95	C₄	C₅×C₄⋊C₁₆	1	12	yes	complemented
96	C₄	C₅×#384	1	1	yes	characteristic
97	C₄	C₅×#423	1	3	yes	—
98	C₂	C₅×#1842	1	1	yes	characteristic
99	C₂	C₂×C₅×C₄⋊C₁₆	1	3	yes	—
100	C₂	C₅×#2150	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅×C₄⋊C₁₆

C₂

yes

maximal

C₄²×C₅×C₈

C₂

yes

maximal, characteristic

C₂²×C₅×C₁₆

C₂²

yes

—

C₂×C₄×C₅×C₈

C₄

yes

—

C₂×C₄×C₅×C₈

C₂²

yes

—

C₄³×C₅

C₄

yes

characteristic

C₅×C₄⋊C₁₆

—

#12898

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×C₈

C₂×C₄

yes

—

C₂²×C₅×C₈

C₂³

yes

characteristic

C₂×C₄²×C₅

C₈

yes

—

C₂×C₄²×C₅

C₈

yes

characteristic

C₂×C₄²×C₅

C₂×C₄

yes

—

C₂×C₅×C₁₆

—

C₄×C₅×C₈

—

C₄×C₅×C₈

D₄

yes

—

C₄×C₅×C₈

Q₈

yes

—

C₂×C₄⋊C₁₆

C₂×C₅

yes

—

C₄²×C₈

C₂×C₅

yes

characteristic

C₂²×C₄×C₅

C₂×C₈

yes

—

C₂²×C₄×C₅

C₂×C₈

yes

—

C₂²×C₄×C₅

C₂²×C₄

yes

characteristic

C₂×C₅×C₈

—

C₂×C₅×C₈

C₄⋊C₄

yes

—

C₂×C₅×C₈

C₂×D₄

yes

—

C₂×C₅×C₈

C₂×Q₈

yes

—

C₄²×C₅

—

C₄²×C₅

C₁₆

yes

complemented

C₄²×C₅

C₄⋊C₄

yes

—

C₄²×C₅

M₁₆

yes

—

C₅×C₁₆

—

C₂²×C₁₆

C₂²×C₅

yes

—

C₂×C₄×C₈

C₄×C₅

yes

—

C₂×C₄×C₈

C₂²×C₅

yes

—

C₄³

C₄×C₅

yes

characteristic

C₄⋊C₁₆

—

C₂³×C₅

C₂²×C₈

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

C₄⋊C₈

yes

—

C₂×C₄×C₅

C₄⋊C₈

yes

—

C₂×C₄×C₅

C₂×C₁₆

yes

—

C₂×C₄×C₅

M₃₂

yes

—

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₅

C₂×M₁₆

yes

—

C₅×C₈

—

C₅×C₈

#127

yes

characteristic

C₅×C₈

C₄⋊Q₈

yes

—

C₂²×C₈

C₂×C₄×C₅

yes

—

C₂²×C₈

C₂³×C₅

yes

characteristic

C₂×C₄²

C₅×C₈

yes

—

C₂×C₄²

C₅×C₈

yes

characteristic

C₂×C₄²

C₂×C₄×C₅

yes

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

C₅×D₄

yes

—

C₄×C₈

C₅×Q₈

yes

—

C₂²×C₅

C₂×C₄⋊C₈

yes

—

C₂²×C₅

C₂²×C₁₆

yes

characteristic

C₂²×C₅

C₂×M₃₂

yes

—

C₄×C₅

—

C₄×C₅

C₄⋊C₁₆

yes

C₄×C₅

yes

C₄×C₅

yes

—

C₂²×C₄

C₂×C₅×C₈

yes

—

C₂²×C₄

C₂×C₅×C₈

yes

—

C₂²×C₄

C₂²×C₄×C₅

yes

characteristic

C₂×C₈

—

C₂×C₈

C₅×C₄⋊C₄

yes

—

C₂×C₈

C₂×C₅×D₄

yes

—

C₂×C₈

C₂×C₅×Q₈

yes

—

C₄²

—

C₄²

C₅×C₁₆

yes

complemented

C₄²

C₅×C₄⋊C₄

yes

—

C₄²

C₅×M₁₆

yes

—

C₁₆

—

C₂×C₅

#1842

yes

characteristic

C₂×C₅

C₂×C₄⋊C₁₆

yes

—

C₂×C₅

#2150

yes

—

C₂³

C₂²×C₅×C₈

yes

characteristic

C₂×C₄

—

C₂×C₄

C₅×C₄⋊C₈

yes

—

C₂×C₄

C₅×C₄⋊C₈

yes

—

C₂×C₄

C₂×C₅×C₁₆

yes

—

C₂×C₄

C₅×M₃₂

yes

—

C₂×C₄

C₂×C₅×C₄⋊C₄

yes

—

C₂×C₄

C₂×C₅×M₁₆

yes

—

C₈

—

C₈

C₅×#127

yes

characteristic

C₈

C₅×C₄⋊Q₈

yes

—

C₅

#12898

yes

characteristic, direct product factor, Sylow

C₂²

C₂×C₅×C₄⋊C₈

yes

—

C₂²

C₂²×C₅×C₁₆

yes

characteristic

C₂²

C₂×C₅×M₃₂

yes

—

C₄

—

C₄

C₅×C₄⋊C₁₆

yes

C₄

yes

C₄

yes

—

C₂

C₅×#1842

yes

characteristic

C₂

C₂×C₅×C₄⋊C₁₆

yes

—

100

C₂

C₅×#2150

yes

—

	subgroup	G/H
center	C₂²×C₅×C₈	C₂³
commutator	C₂²	C₂²×C₅×C₁₆
Frattini, cosocle	C₂²×C₈	C₂³×C₅
socle, prime radical	C₂³×C₅	C₂²×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅×C₈ ◁ G

subgroup

G/H

center

C₂²×C₅×C₈

C₂³

commutator

C₂²

C₂²×C₅×C₁₆

Frattini, cosocle

C₂²×C₈

C₂³×C₅

socle, prime radical

C₂³×C₅

C₂²×C₈

LCS

G ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₅×C₈ ◁ G

N	H ≅ G/N	type
8. #12898	C₅	direct (N × H)
28. C₄²×C₅	C₁₆	semidirect
61. C₄×C₅	C₄⋊C₁₆	semidirect
72. C₄²	C₅×C₁₆	semidirect
90. C₅	#12898	direct (N × H)
95. C₄	C₅×C₄⋊C₁₆	semidirect

H ≅ G/N

type

8. #12898

C₅

direct (N × H)

28. C₄²×C₅

C₁₆

semidirect

61. C₄×C₅

C₄⋊C₁₆

semidirect

72. C₄²

C₅×C₁₆

semidirect

90. C₅

#12898

direct (N × H)

95. C₄

C₅×C₄⋊C₁₆

semidirect

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

subgroup	index
C₂×C₅×C₄⋊C₁₆	2
C₄²×C₅×C₈	2
#12898	5

subgroup

index

C₂×C₅×C₄⋊C₁₆

C₄²×C₅×C₈

#12898

Subgroups — C₅×#12898 #11935618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#12898 #11935618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#12898 #11935618