Finite Group Databasebeta

← D5×D1815 #49136997

Subgroups — D5×D1815 #49136997

Order 36300.

144 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 40 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⋊D605)C211yesmaximal, characteristic, complemented
2C5×D1815C211yesmaximal, characteristic, complemented
3C3×C5×D5×C121C211yesmaximal, characteristic, complemented
4D5×D605—31nomaximal, Hall
5C3×C52×C121C2211yescharacteristic, complemented, Hall
6C2×D1815—51nomaximal
7D5×D363—51nomaximal
8C5⋊D605—31no—
9C5×D605—31no—
10C5×D5×C121D311yescharacteristic, complemented
11D1815—51no—
12D1815—51no—
13D1815—102no—
14D1815D511yescharacteristic, direct product factor
15C5×D363—51no—
16C3×D5×C121D511yescharacteristic, complemented
17C2×C3×C5×C121—51no—
18D5×D165—111nomaximal
19C52×C121C2×D311yescharacteristic, complemented, Hall
20C2×D605—151no—
21D5×D121—151no—
22C3×C5×C121—22no—
23C3×C5×C121C2×D511yescharacteristic, complemented
24C3×C5×C121C2×D511yescharacteristic, complemented
25C3⋊(C5⋊D55)—111no—
26C5×D165—111no—
27C3×C5×D5×C11D1111yescharacteristic
28C2×D363—251noHall
29C2×C5×C121—51no—
30D605—31no—
31D605—151no—
32D605—151no—
33D605—302no—
34C5×D121—151no—
35D5×C121D1511yescharacteristic, complemented
36D5×D55—331no—
37C3×C52×C11C2×D1111yescharacteristic
38C2×C3×C121—51no—
39D363—51no—
40D363—251no—
41C2×D165—551no—
42D5×D33—551no—
43C5×C121—22no—
44C5×C121D3×D511yescharacteristic, complemented
45C5×C121C2×D1511yescharacteristic, complemented
46C5⋊D55—331no—
47C5×D55—331no—
48C5×D5×C11D3311yescharacteristic
49C2×D121—751noHall
50C3×C121D5211yescharacteristic, complemented, Hall
51C2×C3×C5×C11—51no—
52D165—111no—
53D165—551no—
54D165—551no—
55D165—1102no—
56C5×D33—551no—
57C3×D5×C11D5511yescharacteristic
58D5×D15—1211noHall
59C52×C11C2×D3311yescharacteristic
60C2×C121—51no—
61D121—151no—
62D121—751no—
63C2×D55—1651no—
64D5×D11—1651no—
65C3×C5×C11—22no—
66C3×C5×C11D5×D1111yescharacteristic
67C3×C5×C11C2×D5511yescharacteristic
68C3⋊(C5⋊D5)—1211no—
69C5×D15—1211no—
70C3×C5×D5D12111yescharacteristic, complemented
71C2×D33—2751no—
72C121D5×D1511yescharacteristic, complemented, Sylow
73C2×C5×C11—51no—
74D55—331no—
75D55—3302no—
76D55—1651no—
77D55—1651no—
78C5×D11—1651no—
79D5×C11D16511yescharacteristic
80D52—3631noHall
81C3×C52C2×D12111yescharacteristic, complemented, Hall
82C2×C3×C11—51no—
83D33—2751no—
84D33—551no—
85C2×D15—6051no—
86D3×D5—6051no—
87C5×C11—22no—
88C5×C11D5×D3311yescharacteristic
89C5×C11C2×D16511yescharacteristic
90C5⋊D5—3631no—
91C5×D5—3631no—
92C5×D5D36311yescharacteristic, complemented
93C2×D11—8251no—
94C3×C11D5×D5511yescharacteristic
95C2×C3×C5—51no—
96D15—6051no—
97D15—6051no—
98D15—1211no—
99D15—12102no—
100C3×D5D60511yescharacteristic, complemented
101C5×D3—6051no—
102C52C2×D36311yescharacteristic, complemented, Sylow
103C2×C11—51no—
104D11—8251no—
105D11—1651no—
106C2×D5—18151no—
107C2×D5—18151no—
108C3×C5—22no—
109C3×C5D5×D12111yescharacteristic, complemented
110C3×C5C2×D60511yescharacteristic, complemented
111C2×D3—30251noHall
112C11D5×D16511yescharacteristic
113C2×C5—51no—
114C2×C5—18151no—
115D5—18151no—
116D5—18151no—
117D5—36302no—
118D5—3631no—
119D5D181511yescharacteristic, direct product factor
120C2×C3—51no—
121D3—6051no—
122D3—30251no—
123C5—22no—
124C5D5×D36311yescharacteristic, complemented
125C5C2×D181511yescharacteristic, complemented
126C22—90751noSylow
127C3D5×D60511yescharacteristic, complemented, Sylow
128C2—51no—
129C2—18151no—
130C2—90751no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×C52×C121C22
FrattiniC11D5×D165
socleC3×C52×C11C2×D11
LCSG ▷ C3×C52×C121
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C5⋊D605)C2semidirect
2. C5×D1815C2semidirect
3. C3×C5×D5×C121C2semidirect
5. C3×C52×C121C22semidirect
10. C5×D5×C121D3semidirect
14. D1815D5direct (N × H)
16. C3×D5×C121D5semidirect
19. C52×C121C2×D3semidirect
23. C3×C5×C121C2×D5semidirect
24. C3×C5×C121C2×D5semidirect
35. D5×C121D15semidirect
44. C5×C121D3×D5semidirect
45. C5×C121C2×D15semidirect
50. C3×C121D52semidirect
70. C3×C5×D5D121semidirect
72. C121D5×D15semidirect
81. C3×C52C2×D121semidirect
92. C5×D5D363semidirect
100. C3×D5D605semidirect
102. C52C2×D363semidirect
109. C3×C5D5×D121semidirect
110. C3×C5C2×D605semidirect
119. D5D1815direct (N × H)
124. C5D5×D363semidirect
125. C5C2×D1815semidirect
127. C3D5×D605semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C5⋊D605)2
C5×D18152
C3×C5×D5×C1212
D5×D6053
C2×D18155
D5×D3635
D5×D16511