Finite Group Databasebeta

← D4×D105 #13132894

Subgroups — D4×D105 #13132894

Order 1680.

216 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C22×D105C212yesmaximal, complemented
2C3×C5×C7×D4C211yesmaximal, characteristic, complemented
3#11719828C212yesmaximal, complemented
4D420C211yesmaximal, characteristic, complemented
5C4×D105C211yesmaximal, characteristic, complemented
6D4×D35—31nomaximal, Hall
7C22×C3×C5×C7C2212yescomplemented
8C2×D105—24no—
9C2×D105C2211yescharacteristic
10C2×D105C2212yescomplemented
11C3×C4×C5×C7C2211yescharacteristic, complemented
12Dic105C2211yescharacteristic, complemented
13D4×D21—51nomaximal, Hall
14C22×D35—32no—
15C5×C7×D4D311yescharacteristic, complemented
16C22⋊D35—32no—
17D140—31no—
18C4×D35—31no—
19D4×D15—71nomaximal, Hall
20C2×C3×C5×C7—22no—
21C2×C3×C5×C7C2311yescharacteristic
22D105—22no—
23D105D412yesdirect product factor
24C22×D21—52no—
25C3×C7×D4D511yescharacteristic, complemented
26#4268—52no—
27D84—51no—
28C4×D21—51no—
29C22×C5×C7C2×D312yescomplemented
30C2×D35—31no—
31C2×D35—32no—
32C2×D35—64no—
33C4×C5×C7C2×D311yescharacteristic, complemented
34Dic35—31no—
35C22×D15—72no—
36C3×C5×D4D711yescharacteristic, complemented
37#1220—72no—
38D60—71no—
39C4×D15—71no—
40D4×D7—151noHall
41C3×C5×C7C2×D411yescharacteristic, complemented, Hall
42C22×C3×C7C2×D512yescomplemented
43C2×D21—51no—
44C2×D21—52no—
45C2×D21—104no—
46C3×C4×C7C2×D511yescharacteristic, complemented
47Dic21—51no—
48D4×D5—211noHall
49C2×C5×C7—22no—
50C2×C5×C7C22×D311yescharacteristic
51D35—32no—
52D35—62no—
53C22×C3×C5C2×D712yescomplemented
54C2×D15—71no—
55C2×D15—72no—
56C2×D15—144no—
57C3×C4×C5C2×D711yescharacteristic, complemented
58Dic15—71no—
59C22×D7—152no—
60C7×D4D1511yescharacteristic, complemented
61C22⋊D7—152no—
62D28—151no—
63C4×D7—151no—
64D3×D4—351noHall
65C2×C3×C7—22no—
66C2×C3×C7C22×D511yescharacteristic
67D21—52no—
68D21—102no—
69C22×D5—212no—
70C5×D4D2111yescharacteristic, complemented
71C22⋊D5—212no—
72D20—211no—
73C4×D5—211no—
74C5×C7D3×D411yescharacteristic, complemented, Hall
75C2×C3×C5—22no—
76C2×C3×C5C22×D711yescharacteristic
77D15—72no—
78D15—142no—
79C22×C7C2×D1512yescomplemented
80C2×D7—151no—
81C2×D7—152no—
82C2×D7—304no—
83C4×C7C2×D1511yescharacteristic, complemented
84Dic7—151no—
85C22×D3—352no—
86C3×D4D3511yescharacteristic, complemented
87#67—352no—
88D12—351no—
89C4×D3—351no—
90C3×C7D4×D511yescharacteristic, complemented, Hall
91C22×C5C2×D2112yescomplemented
92C2×D5—211no—
93C2×D5—212no—
94C2×D5—424no—
95C4×C5C2×D2111yescharacteristic, complemented
96Dic5—211no—
97C2×D4—1051noSylow
98C3×C5D4×D711yescharacteristic, complemented, Hall
99C2×C7—22no—
100C2×C7C22×D1511yescharacteristic
101D7—152no—
102D7—302no—
103C22×C3C2×D3512yescomplemented
104C2×D3—351no—
105C2×D3—352no—
106C2×D3—704no—
107C3×C4C2×D3511yescharacteristic, complemented
108Dic3—351no—
109C2×C5—22no—
110C2×C5C22×D2111yescharacteristic
111D5—212no—
112D5—422no—
113C23—1052no—
114D4—1052no—
115D4—1051no—
116D4D10511yescharacteristic, direct product factor
117C2×C4—1051no—
118C7D4×D1511yescharacteristic, complemented, Sylow
119C2×C3—22no—
120C2×C3C22×D3511yescharacteristic
121D3—352no—
122D3—702no—
123C5D4×D2111yescharacteristic, complemented, Sylow
124C22—1051no—
125C22—1052no—
126C22—2104no—
127C22C2×D10512yescomplemented
128C4—1051no—
129C4C2×D10511yescharacteristic, complemented
130C3D4×D3511yescharacteristic, complemented, Sylow
131C2—22no—
132C2—1052no—
133C2—2102no—
134C2C22×D10511yescharacteristic
subgroupG/H
center, FrattiniC2C22×D105
commutator, socle, cosocleC2×C3×C5×C7C23
FittingC3×C5×C7×D4C2
hypercenterD4D105
hypocenterC3×C5×C7C2×D4
LCSG ▷ C2×C3×C5×C7 ▷ C3×C5×C7
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C22×D105C2semidirect
2. C3×C5×C7×D4C2semidirect
3. #11719828C2semidirect
4. D420C2semidirect
5. C4×D105C2semidirect
7. C22×C3×C5×C7C22semidirect
10. C2×D105C22semidirect
11. C3×C4×C5×C7C22semidirect
12. Dic105C22semidirect
15. C5×C7×D4D3semidirect
23. D105D4direct (N × H)
25. C3×C7×D4D5semidirect
29. C22×C5×C7C2×D3semidirect
33. C4×C5×C7C2×D3semidirect
36. C3×C5×D4D7semidirect
41. C3×C5×C7C2×D4semidirect
42. C22×C3×C7C2×D5semidirect
46. C3×C4×C7C2×D5semidirect
53. C22×C3×C5C2×D7semidirect
57. C3×C4×C5C2×D7semidirect
60. C7×D4D15semidirect
70. C5×D4D21semidirect
74. C5×C7D3×D4semidirect
79. C22×C7C2×D15semidirect
83. C4×C7C2×D15semidirect
86. C3×D4D35semidirect
90. C3×C7D4×D5semidirect
91. C22×C5C2×D21semidirect
95. C4×C5C2×D21semidirect
98. C3×C5D4×D7semidirect
103. C22×C3C2×D35semidirect
107. C3×C4C2×D35semidirect
116. D4D105direct (N × H)
118. C7D4×D15semidirect
123. C5D4×D21semidirect
127. C22C2×D105semidirect
129. C4C2×D105semidirect
130. C3D4×D35semidirect

Maximal subgroups

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

subgroupindex
C22×D1052
C3×C5×C7×D42
#117198282
D4202
C4×D1052
D4×D353
D4×D215
D4×D157