Finite Group Databasebeta

← (#11759813⋊C3)⋊D5 #44477889

Subgroups — (#11759813⋊C3)⋊D5 #44477889

Order 30420.

160 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 22 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⋊(#11759813⋊C3)C211yesmaximal, characteristic, complemented
2C5⋊((C13⋊C3)⋊(D13⋊C3))C211yesmaximal, characteristic, complemented
3C5×#11759813⋊C3C211yesmaximal, characteristic, complemented
4#11759813⋊D5C311yesmaximal, characteristic, complemented
5#11759817⋊D5—31nomaximal
6C5×C13⋊C32C2211yescharacteristic, complemented, Hall
7(#11759813⋊C2)⋊C3—51nomaximal, Hall
8C5⋊#11759813C2×C311yescharacteristic, complemented
9C5⋊((C13⋊C3)⋊D13)—21no—
10C5⋊#11759817—31no—
11C5⋊#11759816C2×C311yescharacteristic, complemented
12C5⋊#11759815D311yescharacteristic, complemented
13C5×#11759813C2×C311yescharacteristic, complemented
14C5×#11759817—31no—
15D13×D65—31noHall
16#11759813⋊C3—51no—
17#11759813⋊C3D511yescharacteristic, complemented
18(C13⋊C3)⋊(D13⋊C3)—51no—
19C5×#92789C22×C311yescharacteristic, complemented
20C5×#92788C2×D311yescharacteristic, complemented
21C5×C13×C13⋊C3—21no—
22#11759813⋊C2—51no—
23#11759815⋊C2—151no—
24C5⋊(C13⋊D13)C3×D311yescharacteristic, complemented
25C13×D65—31no—
26C5×C13×D13—31no—
27C13⋊C32C2×D511yescharacteristic, complemented, Hall
28C3×C5⋊(D13⋊C3)—261no—
29(C13⋊C3)⋊D13—101no—
30#11759817—31no—
31#11759817—151no—
32#11759816—51no—
33#11759815—51no—
34#11759813—51no—
35#11759813C3×D511yescharacteristic, complemented
36C5×C132C2×C3×D311yescharacteristic, complemented, Hall
37C2×C5⋊(D13⋊C3)—391no—
38D5×D13⋊C3—391no—
39D132—151noHall
40C3×C5×C13⋊C3—521no—
41#92789C2×C3×D511yescharacteristic, complemented
42#92788D3×D511yescharacteristic, complemented
43C13×C13⋊C3—21no—
44C3×D65—261no—
45C2×C5×C13⋊C3—391no—
46C5⋊(D13⋊C3)—261no—
47C5⋊(D13⋊C3)—261no—
48C5⋊(D13⋊C3)—261no—
49C5⋊(D13⋊C3)—391no—
50C5⋊(D13⋊C3)—391no—
51C5⋊(D13⋊C3)—391no—
52C5⋊(D13⋊C3)—781no—
53D5×C13⋊C3—391no—
54C5×D13⋊C3—781no—
55C13⋊D13—51no—
56C13×D13—31no—
57C13×D13—151no—
58C2×D65—391no—
59D5×D13—391no—
60C3×D13⋊C3—1301no—
61C3×C5×C13—521no—
62C5×C13⋊C3—21no—
63C5×C13⋊C3—521no—
64C5×C13⋊C3—521no—
65C5×C13⋊C3—781no—
66C5×C13⋊C3—1561no—
67C5×C13⋊C3—1561no—
68C3×D3×D5—1691nomaximal, Hall
69C132C3×D3×D511yescharacteristic, complemented, Sylow
70C2×D13⋊C3—1951no—
71C2×D13⋊C3—1951no—
72C2×C5×C13—391no—
73D65—31no—
74D65—261no—
75D65—781no—
76D65—781no—
77D65—781no—
78C5×D13—31no—
79D5×C13—391no—
80C3×C13⋊C3—521no—
81C3×D15—3381no—
82C3×C5×D3—3381no—
83C32×D5—1691no—
84C3×D13—1301no—
85C2×C13⋊C3—391no—
86C2×C13⋊C3—1951no—
87D13⋊C3—781no—
88D13⋊C3—1301no—
89D13⋊C3—1301no—
90D13⋊C3—1301no—
91D13⋊C3—3901no—
92D13⋊C3—3901no—
93D13⋊C3—3901no—
94D13⋊C3—1951no—
95C5×C13—21no—
96C5×C13—61no—
97C5×C13—61no—
98C5×C13—61no—
99C2×C3×D5—5071no—
100D3×D5—1691no—
101C2×D13—1951no—
102C2×D13—1951no—
103C32×C5—6761noHall
104C3×C13—521no—
105C13⋊C3—21no—
106C13⋊C3—521no—
107C13⋊C3—521no—
108C13⋊C3—781no—
109C13⋊C3—1561no—
110C13⋊C3—1561no—
111C2×C3×D3—8451noHall
112C2×C3×C5—10141no—
113D15—3381no—
114C3×D5—3381no—
115C3×D5—1691no—
116C3×D5—1691no—
117C3×D5—10141no—
118C5×D3—3381no—
119C2×C13—391no—
120C2×C13—1951no—
121D13—31no—
122D13—151no—
123D13—1301no—
124D13—3901no—
125D13—3901no—
126D13—3901no—
127C2×D5—5071noHall
128C2×C32—8451no—
129C3×D3—8451no—
130C3×D3—3381no—
131C3×C5—261no—
132C3×C5—6761no—
133C3×C5—6761no—
134C13—21no—
135C13—61no—
136C13—61no—
137C13—61no—
138C22×C3—25351no—
139C2×D3—8451no—
140C2×C5—391no—
141D5—391no—
142D5—1691no—
143C32—3381noSylow
144C2×C3—8451no—
145C2×C3—8451no—
146C2×C3—16901no—
147C2×C3—50701no—
148C2×C3—10141no—
149D3—3381no—
150D3—16901no—
151C5(#11759813⋊C2)⋊C311yescharacteristic, complemented, Sylow
152C22—25351noSylow
153C3—521no—
154C3—6761no—
155C3—6761no—
156C2—391no—
157C2—8451no—
158C2—1951no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenterC5×#92789C22×C3
Fitting, socleC5×C132C2×C3×D3
LCSG ▷ C5×#92789
UCSC1

Complements

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

NH ≅ G/Ntype
1. C5⋊(#11759813⋊C3)C2semidirect
2. C5⋊((C13⋊C3)⋊(D13⋊C3))C2semidirect
3. C5×#11759813⋊C3C2semidirect
4. #11759813⋊D5C3semidirect
6. C5×C13⋊C32C22semidirect
8. C5⋊#11759813C2×C3semidirect
11. C5⋊#11759816C2×C3semidirect
12. C5⋊#11759815D3semidirect
13. C5×#11759813C2×C3semidirect
17. #11759813⋊C3D5semidirect
19. C5×#92789C22×C3semidirect
20. C5×#92788C2×D3semidirect
24. C5⋊(C13⋊D13)C3×D3semidirect
27. C13⋊C32C2×D5semidirect
35. #11759813C3×D5semidirect
36. C5×C132C2×C3×D3semidirect
41. #92789C2×C3×D5semidirect
42. #92788D3×D5semidirect
69. C132C3×D3×D5semidirect
151. C5(#11759813⋊C2)⋊C3semidirect

Maximal subgroups

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

subgroupindex
C5⋊(#11759813⋊C3)2
C5⋊((C13⋊C3)⋊(D13⋊C3))2
C5×#11759813⋊C32
#11759813⋊D53
#11759817⋊D53
(#11759813⋊C2)⋊C35
C3×D3×D5169