Group #14278401 — subgroups

Subgroups — C₃×#10598285 #14278401

Order 1920.

184 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 74 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	C₃×C₅×#494	C₂	1	1	yes	maximal, characteristic
2	C₃×#64683	C₂	1	2	yes	maximal
3	#10598285	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₅×Q₁₆	—	2	2	no	—
5	C₃×C₅×C₄⋊Q₈	C₄	1	2	yes	—
6	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₃×#3944	—	2	2	no	—
8	C₃×#1358	—	5	1	no	maximal, Hall
9	C₅×#494	C₂×C₃	1	1	yes	characteristic
10	#64683	C₂×C₃	1	2	yes	—
11	C₂×C₃×C₅×Q₈	—	2	2	no	—
12	C₃×C₅×Q₁₆	—	4	2	no	—
13	C₃×C₅×Q₁₆	—	4	2	no	—
14	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
15	C₃×C₅×C₄⋊C₄	—	4	2	no	—
16	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
17	C₃×#672	—	4	2	no	—
18	C₃×#494	D₅	1	1	yes	characteristic
19	C₃×#364	—	5	2	no	—
20	C₂×C₅×Q₁₆	—	2	2	no	—
21	C₅×C₄⋊Q₈	C₃×C₄	1	2	yes	—
22	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
23	#3944	—	2	2	no	—
24	#1358	—	5	1	no	Sylow
25	C₃×C₅×Q₈	—	4	4	no	—
26	C₂×C₃×C₄×C₅	—	2	1	no	—
27	C₂×C₃×C₄×C₅	—	4	2	no	—
28	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
29	C₃×C₅×C₈	D₈	1	2	yes	—
30	C₃×C₅×C₈	SD₁₆	1	2	yes	—
31	C₂×C₃×Q₁₆	—	2	2	no	—
32	C₃×C₄⋊Q₈	Dic₅	1	2	yes	—
33	C₃×M₃₂	—	10	2	no	—
34	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
35	C₂×C₅×Q₈	—	2	2	no	—
36	C₅×Q₁₆	—	4	2	no	—
37	C₅×Q₁₆	—	4	2	no	—
38	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
39	C₅×C₄⋊C₄	—	4	2	no	—
40	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
41	#672	—	4	2	no	—
42	#494	C₃×D₅	1	1	yes	characteristic
43	#364	—	5	2	no	—
44	C₂²×C₃×C₅	#100	1	1	yes	characteristic
45	C₃×C₄×C₅	—	2	2	no	—
46	C₃×C₄×C₅	—	8	2	no	—
47	C₃×C₄×C₅	#102	1	2	yes	—
48	C₂×C₃×Q₈	—	2	2	no	—
49	C₃×Q₁₆	—	4	2	no	—
50	C₃×Q₁₆	—	4	2	no	—
51	C₂×C₃×C₈	C₂²⋊D₅	1	2	yes	—
52	C₃×C₄⋊C₄	—	4	2	no	—
53	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
54	C₃×C₁₆	—	20	2	no	—
55	C₅×Q₈	—	4	4	no	—
56	C₂×C₄×C₅	—	2	1	no	—
57	C₂×C₄×C₅	—	4	2	no	—
58	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
59	C₅×C₈	C₃×D₈	1	2	yes	—
60	C₅×C₈	C₃×SD₁₆	1	2	yes	—
61	C₂×Q₁₆	—	2	2	no	—
62	C₄⋊Q₈	C₃×Dic₅	1	2	yes	—
63	M₃₂	—	10	2	no	—
64	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
65	C₂×C₃×C₅	—	2	1	no	—
66	C₂×C₃×C₅	#331	1	1	yes	characteristic
67	C₃×Q₈	—	4	4	no	—
68	C₂×C₃×C₄	—	2	1	no	—
69	C₂×C₃×C₄	—	4	2	no	—
70	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
71	C₃×C₈	#686	1	2	yes	—
72	C₃×C₈	#687	1	2	yes	—
73	C₂²×C₅	C₃×#100	1	1	yes	characteristic
74	C₄×C₅	—	2	2	no	—
75	C₄×C₅	—	8	2	no	—
76	C₄×C₅	C₃×#102	1	2	yes	—
77	C₂×Q₈	—	2	2	no	—
78	Q₁₆	—	4	2	no	—
79	Q₁₆	—	4	2	no	—
80	C₂×C₈	C₃×C₂²⋊D₅	1	2	yes	—
81	C₄⋊C₄	—	4	2	no	—
82	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
83	C₁₆	—	20	2	no	—
84	C₃×C₅	#1358	1	1	yes	characteristic, complemented, Hall
85	C₂²×C₃	#3965	1	1	yes	characteristic
86	C₃×C₄	—	2	2	no	—
87	C₃×C₄	—	8	2	no	—
88	C₃×C₄	#3964	1	2	yes	—
89	C₂×C₅	—	2	1	no	—
90	C₂×C₅	C₃×#331	1	1	yes	characteristic
91	Q₈	—	4	4	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	4	2	no	—
94	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
95	C₈	C₃×#686	1	2	yes	—
96	C₈	C₃×#687	1	2	yes	—
97	C₂×C₃	—	2	1	no	—
98	C₂×C₃	#64764	1	1	yes	characteristic
99	C₅	C₃×#1358	1	1	yes	characteristic, complemented, Sylow
100	C₂²	C₃×#3965	1	1	yes	characteristic
101	C₄	—	2	2	no	—
102	C₄	—	8	2	no	—
103	C₄	C₃×#3964	1	2	yes	—
104	C₃	#10598285	1	1	yes	characteristic, direct product factor, Sylow
105	C₂	—	2	1	no	—
106	C₂	C₃×#64764	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅×#494

C₂

yes

maximal, characteristic

C₃×#64683

C₂

yes

maximal

#10598285

C₃

yes

maximal, characteristic, direct product factor, Hall

C₂×C₃×C₅×Q₁₆

—

C₃×C₅×C₄⋊Q₈

C₄

yes

—

C₃×C₄×C₅×C₈

C₂²

yes

—

—

C₂×C₃

yes

characteristic

#64683

C₂×C₃

yes

—

C₂×C₃×C₅×Q₈

—

C₃×C₅×Q₁₆

—

C₃×C₅×Q₁₆

—

C₂×C₃×C₅×C₈

D₄

yes

—

C₃×C₅×C₄⋊C₄

—

C₃×C₄²×C₅

C₂×C₄

yes

characteristic

C₃×#672

—

C₃×#494

D₅

yes

characteristic

C₃×#364

—

C₂×C₅×Q₁₆

—

C₅×C₄⋊Q₈

C₃×C₄

yes

—

C₄×C₅×C₈

C₂²×C₃

yes

—

—

C₃×C₅×Q₈

—

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

C₂²⋊C₄

yes

characteristic

C₃×C₅×C₈

D₈

yes

—

C₃×C₅×C₈

SD₁₆

yes

—

C₂×C₃×Q₁₆

—

C₃×C₄⋊Q₈

Dic₅

yes

—

C₃×M₃₂

—

C₃×C₄×C₈

C₂×D₅

yes

characteristic

C₂×C₅×Q₈

—

C₅×Q₁₆

—

C₅×Q₁₆

—

C₂×C₅×C₈

C₃×D₄

yes

—

C₅×C₄⋊C₄

—

C₄²×C₅

C₂×C₃×C₄

yes

characteristic

#672

—

#494

C₃×D₅

yes

characteristic

#364

—

C₂²×C₃×C₅

#100

yes

characteristic

C₃×C₄×C₅

—

C₃×C₄×C₅

—

C₃×C₄×C₅

#102

yes

—

C₂×C₃×Q₈

—

C₃×Q₁₆

—

C₃×Q₁₆

—

C₂×C₃×C₈

C₂²⋊D₅

yes

—

C₃×C₄⋊C₄

—

C₃×C₄²

C₂×Dic₅

yes

characteristic

C₃×C₁₆

—

C₅×Q₈

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₃×C₂²⋊C₄

yes

characteristic

C₅×C₈

C₃×D₈

yes

—

C₅×C₈

C₃×SD₁₆

yes

—

C₂×Q₁₆

—

C₄⋊Q₈

C₃×Dic₅

yes

—

M₃₂

—

C₄×C₈

C₂×C₃×D₅

yes

characteristic

C₂×C₃×C₅

—

C₂×C₃×C₅

#331

yes

characteristic

C₃×Q₈

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₂²⋊Dic₅

yes

characteristic

C₃×C₈

#686

yes

—

C₃×C₈

#687

yes

—

C₂²×C₅

C₃×#100

yes

characteristic

C₄×C₅

—

C₄×C₅

—

C₄×C₅

C₃×#102

yes

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

C₂×C₈

C₃×C₂²⋊D₅

yes

—

C₄⋊C₄

—

C₄²

C₂×C₃×Dic₅

yes

characteristic

C₁₆

—

C₃×C₅

#1358

yes

characteristic, complemented, Hall

C₂²×C₃

#3965

yes

characteristic

C₃×C₄

—

C₃×C₄

—

C₃×C₄

#3964

yes

—

C₂×C₅

—

C₂×C₅

C₃×#331

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₃×C₂²⋊Dic₅

yes

characteristic

C₈

C₃×#686

yes

—

C₈

C₃×#687

yes

—

C₂×C₃

—

C₂×C₃

#64764

yes

characteristic

C₅

C₃×#1358

yes

characteristic, complemented, Sylow

100

C₂²

C₃×#3965

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

C₃×#3964

yes

—

104

C₃

#10598285

yes

characteristic, direct product factor, Sylow

105

C₂

—

106

C₂

C₃×#64764

yes

characteristic

	subgroup	G/H
center	C₂×C₃	#64764
commutator	C₄²×C₅	C₂×C₃×C₄
Frattini	C₄×C₈	C₂×C₃×D₅
Fitting	C₃×C₅×#494	C₂
socle	C₂×C₃×C₅	#331
prime radical	C₂²×C₃×C₅	#100
cosocle	C₄×C₅×C₈	C₂²×C₃
hypercenter	C₃×#494	D₅
hypocenter	C₅	C₃×#1358
LCS	G ▷ C₄²×C₅ ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×C₄×C₈ ◁ C₃×#494

subgroup

G/H

center

C₂×C₃

#64764

commutator

C₄²×C₅

C₂×C₃×C₄

Frattini

C₄×C₈

C₂×C₃×D₅

Fitting

C₃×C₅×#494

C₂

C₂×C₃×C₅

C₂²×C₃×C₅

C₄×C₅×C₈

C₂²×C₃

D₅

C₅

G ▷ C₄²×C₅ ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅

UCS

C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×C₄×C₈ ◁ C₃×#494

N	H ≅ G/N	type
3. #10598285	C₃	direct (N × H)
84. C₃×C₅	#1358	semidirect
99. C₅	C₃×#1358	semidirect
104. C₃	#10598285	direct (N × H)

H ≅ G/N

type

3. #10598285

C₃

direct (N × H)

84. C₃×C₅

#1358

semidirect

99. C₅

C₃×#1358

semidirect

104. C₃

#10598285

direct (N × H)

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

subgroup	index
C₃×C₅×#494	2
C₃×#64683	2
#10598285	3
C₃×#1358	5

subgroup

index

C₃×C₅×#494

C₃×#64683

#10598285

C₃×#1358

Subgroups — C₃×#10598285 #14278401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×#10598285 #14278401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10598285 #14278401