Finite Group Databasebeta

← #15690146⋊D5 #44477697

Subgroups — #15690146⋊D5 #44477697

Order 30420.

120 conjugacy classes of subgroups; only the 17 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 17 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5⋊#15690146C211yesmaximal, characteristic, complemented
2C5⋊#15690149C211yesmaximal, characteristic, complemented
3C5×#15690146C211yesmaximal, characteristic, complemented
4D39⋊D65—31nomaximal
5C5×#13095201C2211yescharacteristic, complemented, Hall
6#15690146⋊C2—51nomaximal, Hall
7C13×D195—31no—
8C5×C13×D39—31no—
9C3×C5⋊(C13⋊D13)D311yescharacteristic
10D13×D65—91noHall
11#15690149—51no—
12#15690146—51no—
13#15690146D511yescharacteristic, complemented
14C3×C5×C132C2×D311yescharacteristic
15D39⋊D13—151no—
16C5⋊(C13⋊D13)D911yescharacteristic, complemented
17C13×D65—91no—
18C5×C13×D13—91no—
19#13095201C2×D511yescharacteristic, complemented, Hall
20C5⋊(D13⋊C9)—261no—
21C13×D39—31no—
22C13×D39—151no—
23C3×C13⋊D13—51no—
24C5×C132C2×D911yescharacteristic, complemented, Hall
25D15⋊D13—391no—
26D3×D65—391no—
27D132—451noHall
28C5×C13⋊C9—521no—
29C3×C132D3×D511yescharacteristic
30D195—31no—
31C13×D15—391no—
32C5×D39—31no—
33C5×D3×C13—391no—
34C3×D65—261no—
35C3×D65—391no—
36C3×D65—781no—
37C3×D65—781no—
38C13⋊D13—51no—
39C13×D13—91no—
40C13×D13—451no—
41C2×D65—1171no—
42D5×D13—1171no—
43D13⋊C9—1301no—
44C3×C5×C13—21no—
45C3×C5×C13—31no—
46C3×C5×C13—61no—
47C3×C5×C13—61no—
48D5×D9—1691nomaximal, Hall
49C132D5×D911yescharacteristic, complemented, Sylow
50D3×D13—1951no—
51D3×D13—1951no—
52C2×C5×C13—1171no—
53D65—91no—
54D65—261no—
55D65—781no—
56D65—781no—
57D65—781no—
58C5×D13—91no—
59D5×C13—1171no—
60C13⋊C9—521no—
61D45—3381no—
62C9×D5—1691no—
63C5×D9—3381no—
64D39—31no—
65D39—151no—
66C3×D13—1301no—
67C3×D13—3901no—
68C3×D13—3901no—
69C3×D13—3901no—
70D3×C13—391no—
71D3×C13—1951no—
72C5×C13—21no—
73C5×C13—61no—
74C5×C13—61no—
75C5×C13—61no—
76D3×D5—5071no—
77C2×D13—5851no—
78C2×D13—5851no—
79C5×C9—6761noHall
80C3×C13—21no—
81C3×C13—61no—
82C3×C13—61no—
83C3×C13—61no—
84C2×D9—8451noHall
85D15—391no—
86C3×D5—1691no—
87C5×D3—391no—
88C2×C13—5851no—
89C2×C13—1171no—
90D13—91no—
91D13—451no—
92D13—1301no—
93D13—3901no—
94D13—1951no—
95D13—1951no—
96C2×D5—15211noHall
97C2×C9—8451no—
98D9—3381no—
99D9—16901no—
100C3×C5#11759813⋊C211yescharacteristic
101C13—21no—
102C13—31no—
103C13—31no—
104C13—61no—
105C2×D3—25351no—
106C2×C5—1171no—
107D5—1171no—
108D5—1691no—
109C9—3381noSylow
110C2×C3—8451no—
111D3—391no—
112D3—1951no—
113C5#15690146⋊C211yescharacteristic, complemented, Sylow
114C22—76051noSylow
115C3#11759813⋊D511yescharacteristic
116C2—5851no—
117C2—8451no—
118C2—1171no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC5×#13095201C22
FrattiniC3#11759813⋊D5
Fitting, socleC3×C5×C132C2×D3
LCSG ▷ C5×#13095201
UCSC1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C5⋊#15690146C2semidirect
2. C5⋊#15690149C2semidirect
3. C5×#15690146C2semidirect
5. C5×#13095201C22semidirect
13. #15690146D5semidirect
16. C5⋊(C13⋊D13)D9semidirect
19. #13095201C2×D5semidirect
24. C5×C132C2×D9semidirect
49. C132D5×D9semidirect
113. C5#15690146⋊C2semidirect

Maximal subgroups

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

subgroupindex
C5⋊#156901462
C5⋊#156901492
C5×#156901462
D39⋊D653
#15690146⋊C25
D5×D9169