Finite Group Databasebeta

← D5×C3⋊#11759816 #44478136

Subgroups — D5×C3⋊#11759816 #44478136

Order 30420.

256 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 38 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
1C3⋊(C5⋊#11759816)C211yesmaximal, characteristic, complemented
2C5×C3⋊#11759816C211yesmaximal, characteristic, complemented
3C3×D5×#92789C211yesmaximal, characteristic, complemented
4D5×C3⋊(C13⋊D13)C311yesmaximal, characteristic, complemented
5D5×#11759816—31nomaximal
6C3×C5×#92789C2211yescharacteristic, complemented, Hall
7C2×C3⋊#11759816—51nomaximal, Hall
8C3⋊(C5⋊(C13⋊D13))C2×C311yescharacteristic, complemented
9C5×C3⋊(C13⋊D13)C2×C311yescharacteristic, complemented
10C3×D5×C132C2×C311yescharacteristic, complemented
11D5×#92789—21no—
12D5×#92789D311yescharacteristic, complemented
13C5⋊#11759816—31no—
14C5×#11759816—31no—
15D5×C13⋊D13—31noHall
16C2×C3×#92789—51no—
17C3⋊#11759816—51no—
18C3⋊#11759816D511yescharacteristic, direct product factor
19C5×#92789—21no—
20C5×#92789C2×D311yescharacteristic, complemented
21C3×C5×C132C22×C311yescharacteristic, complemented
22D5×C3⋊(D13⋊C3)—132nomaximal
23C2×C3⋊(C13⋊D13)—51no—
24C2×#11759816—151no—
25C5⋊(C13⋊D13)—31no—
26D5×C132C3×D311yescharacteristic, complemented
27C5×C13⋊D13—31no—
28C3×#92789C2×D511yescharacteristic, complemented, Hall
29C3⋊(C5⋊(D13⋊C3))—132no—
30C5×C3⋊(D13⋊C3)—132no—
31C3×D5×C13⋊C3—262no—
32C2×C3×C132—51no—
33C3⋊(C13⋊D13)—51no—
34C3⋊(C13⋊D13)C3×D511yescharacteristic, complemented
35C2×#92789—51no—
36C2×#92789—101no—
37#11759816—31no—
38#11759816—151no—
39C5×C132C2×C3×D311yescharacteristic, complemented, Hall
40D5×D39—132no—
41D5×D39—394no—
42D5×D13⋊C3—392no—
43C2×C13⋊D13—151noHall
44C3×C5×C13⋊C3—262no—
45C3×C132C2×C3×D511yescharacteristic, complemented
46#92789—21no—
47#92789D3×D511yescharacteristic, complemented
48C2×C3⋊(D13⋊C3)—652no—
49D195—132no—
50D195—394no—
51C5×D39—132no—
52C5×D39—394no—
53C3×D5×C13—34no—
54C3×D5×C13D13⋊C312yescomplemented
55C5⋊(D13⋊C3)—392no—
56D5×C13⋊C3—262no—
57D5×C13⋊C3—262no—
58C5×D13⋊C3—392no—
59C2×C132—51no—
60C13⋊D13—31no—
61C13⋊D13—151no—
62D5×D13—392no—
63D5×D13—1174no—
64C2×C3×C13⋊C3—1302no—
65C3⋊(D13⋊C3)—132no—
66C3⋊(D13⋊C3)—652no—
67C3×C5×C13—34no—
68C3×C5×C13C2×D13⋊C312yescomplemented
69C5×C13⋊C3—262no—
70C5×C13⋊C3—262no—
71C3×D3×D5—1691noHall
72C132C3×D3×D511yescharacteristic, complemented, Sylow
73C2×D39—652no—
74C2×D39—1954no—
75C2×D13⋊C3—1952no—
76D65—392no—
77D65—1174no—
78C5×D13—392no—
79C5×D13—1174no—
80D5×C13—34no—
81D5×C13C3⋊(D13⋊C3)12yescomplemented
82C3×C13⋊C3—262no—
83C3×D15—1691no—
84C3×C5×D3—1691no—
85C32×D5—3381no—
86C2×C3×C13—52no—
87C2×C3×C13—154no—
88D39—132no—
89D39—394no—
90D39—652no—
91D39—1954no—
92C2×C13⋊C3—1302no—
93C2×C13⋊C3—1302no—
94D13⋊C3—392no—
95D13⋊C3—1952no—
96C5×C13—34no—
97C5×C13C2×C3⋊(D13⋊C3)12yescomplemented
98C2×C3×D5—5071no—
99D3×D5—1691no—
100C2×D13—5854no—
101C2×D13—1952no—
102C32×C5—3381noHall
103C3×C13—34no—
104C3×C13D5×D13⋊C312yescomplemented
105C13⋊C3—262no—
106C13⋊C3—262no—
107C2×C3×D3—8451noHall
108C2×C3×C5—5071no—
109D15—1691no—
110C3×D5—3381no—
111C3×D5—3381no—
112C3×D5—5071no—
113C3×D5#1175981611yescharacteristic, complemented
114C5×D3—1691no—
115C2×C13—52no—
116C2×C13—154no—
117D13—392no—
118D13—5854no—
119D13—1174no—
120D13—1952no—
121C2×D5—5071noHall
122C2×C32—16901no—
123C3×D3—8451no—
124C3×D3—1691no—
125C3×C5—3381no—
126C3×C5—3381no—
127C3×C5C2×#1175981611yescharacteristic, complemented
128C13—34no—
129C13D5×C3⋊(D13⋊C3)12yescomplemented
130C22×C3—25351no—
131C2×D3—8451no—
132C2×C5—5071no—
133D5—5071no—
134D5C3⋊#1175981611yescharacteristic, direct product factor
135C32—3381noSylow
136C2×C3—51no—
137C2×C3—16901no—
138C2×C3—16901no—
139C2×C3—25351no—
140C2×C3—5071no—
141D3—8451no—
142D3—1691no—
143C5C2×C3⋊#1175981611yescharacteristic, complemented, Sylow
144C22—25351noSylow
145C3—3381no—
146C3—3381no—
147C3D5×#1175981611yescharacteristic, complemented
148C2—51no—
149C2—25351no—
150C2—5071no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C132C22×C3
LCSG ▷ C3×C5×C132
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C5⋊#11759816)C2semidirect
2. C5×C3⋊#11759816C2semidirect
3. C3×D5×#92789C2semidirect
4. D5×C3⋊(C13⋊D13)C3semidirect
6. C3×C5×#92789C22semidirect
8. C3⋊(C5⋊(C13⋊D13))C2×C3semidirect
9. C5×C3⋊(C13⋊D13)C2×C3semidirect
10. C3×D5×C132C2×C3semidirect
12. D5×#92789D3semidirect
18. C3⋊#11759816D5direct (N × H)
20. C5×#92789C2×D3semidirect
21. C3×C5×C132C22×C3semidirect
26. D5×C132C3×D3semidirect
28. C3×#92789C2×D5semidirect
34. C3⋊(C13⋊D13)C3×D5semidirect
39. C5×C132C2×C3×D3semidirect
45. C3×C132C2×C3×D5semidirect
47. #92789D3×D5semidirect
54. C3×D5×C13D13⋊C3semidirect
68. C3×C5×C13C2×D13⋊C3semidirect
72. C132C3×D3×D5semidirect
81. D5×C13C3⋊(D13⋊C3)semidirect
97. C5×C13C2×C3⋊(D13⋊C3)semidirect
104. C3×C13D5×D13⋊C3semidirect
113. C3×D5#11759816semidirect
127. C3×C5C2×#11759816semidirect
129. C13D5×C3⋊(D13⋊C3)semidirect
134. D5C3⋊#11759816direct (N × H)
143. C5C2×C3⋊#11759816semidirect
147. C3D5×#11759816semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C5⋊#11759816)2
C5×C3⋊#117598162
C3×D5×#927892
D5×C3⋊(C13⋊D13)3
D5×#117598163
C2×C3⋊#117598165
D5×C3⋊(D13⋊C3)13