Finite Group Databasebeta

← #13132698

Subgroups — #13132698

Order 1680.

216 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 52 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
1C2×D7×D15C212yesmaximal, complemented
2C4×D105C211yesmaximal, characteristic, complemented
3C7×D60C211yesmaximal, characteristic, complemented
4C3×C5×D28C211yesmaximal, characteristic, complemented
5#11719757C212yesmaximal, complemented
6#10587950—31nomaximal, Hall
7C2×D105C2211yescharacteristic
8C2×C7×D15C2212yescomplemented
9C2×C3×C5×D7C2212yescomplemented
10D7×D15—24no—
11C3×C4×C5×C7C2211yescharacteristic, complemented
12Dic105C2211yescharacteristic, complemented
13#66681—51nomaximal, Hall
14C2×D5×D7—32no—
15C4×D35—31no—
16C7×D20—31no—
17C5×D28D311yescharacteristic, complemented
18#63305—32no—
19D4×D15—71nomaximal, Hall
20C2×C3×C5×C7C2311yescharacteristic
21D105D412yescomplemented
22C7×D15—22no—
23C3×C5×D7—22no—
24C2×D3×D7—52no—
25C4×D21—51no—
26C7×D12—51no—
27C3×D28D511yescharacteristic, complemented
28#4245—52no—
29C2×D35—31no—
30C2×C7×D5—32no—
31C2×C5×D7C2×D312yescomplemented
32D5×D7—64no—
33C4×C5×C7C2×D311yescharacteristic, complemented
34Dic35—31no—
35C22×D15—72no—
36C3×C5×D4—71no—
37#1220—72no—
38D60D711yescharacteristic, complemented
39C4×D15—71no—
40D4×D7—151noHall
41C3×C5×C7C2×D411yescharacteristic, complemented, Hall
42C2×D21—51no—
43C2×D3×C7—52no—
44C2×C3×D7C2×D512yescomplemented
45D3×D7—104no—
46C3×C4×C7C2×D511yescharacteristic, complemented
47Dic21—51no—
48D4×D5—211noHall
49C2×C5×C7C22×D311yescharacteristic
50D35—32no—
51C5×D7—22no—
52C7×D5—62no—
53C22×C3×C5—72no—
54C2×D15—71no—
55C2×D15—144no—
56C2×D15C2×D712yescomplemented
57C3×C4×C5C2×D711yescharacteristic, complemented
58Dic15—71no—
59C22×D7—152no—
60C7×D4—151no—
61C22⋊D7—152no—
62D28D1511yescharacteristic, complemented
63C4×D7—151no—
64D3×D4—351noHall
65C2×C3×C7C22×D511yescharacteristic
66D21—52no—
67C3×D7—22no—
68D3×C7—102no—
69C22×D5—212no—
70C5×D4—71no—
71C22⋊D5—212no—
72D20—31no—
73C4×D5—211no—
74C5×C7D3×D411yescharacteristic, complemented, Hall
75C2×C3×C5—142no—
76C2×C3×C5C22×D711yescharacteristic
77D15—22no—
78D15—72no—
79C22×C7—152no—
80C2×D7—151no—
81C2×D7—304no—
82C2×D7C2×D1512yescomplemented
83C4×C7C2×D1511yescharacteristic, complemented
84Dic7—151no—
85C22×D3—352no—
86C3×D4—71no—
87#67—352no—
88D12—51no—
89C4×D3—351no—
90C3×C7D4×D511yescharacteristic, complemented, Hall
91C22×C5—72no—
92C2×D5—32no—
93C2×D5—211no—
94C2×D5—424no—
95C4×C5D3×D711yescharacteristic, complemented
96Dic5—211no—
97C2×D4—1051noSylow
98C3×C5D4×D711yescharacteristic, complemented, Hall
99C2×C7—302no—
100C2×C7C22×D1511yescharacteristic
101D7—22no—
102D7—152no—
103C22×C3—72no—
104C2×D3—52no—
105C2×D3—351no—
106C2×D3—704no—
107C3×C4D5×D711yescharacteristic, complemented
108Dic3—351no—
109C2×C5—142no—
110C2×C5C2×D3×D711yescharacteristic
111D5—62no—
112D5—212no—
113C23—1052no—
114D4—71no—
115D4—151no—
116D4—1052no—
117C2×C4—1051no—
118C7D4×D1511yescharacteristic, complemented, Sylow
119C2×C3—142no—
120C2×C3C2×D5×D711yescharacteristic
121D3—102no—
122D3—352no—
123C5#6668111yescharacteristic, complemented, Sylow
124C22—72no—
125C22—152no—
126C22—1051no—
127C22—2104no—
128C4—1051no—
129C4D7×D1511yescharacteristic, complemented
130C3#1058795011yescharacteristic, complemented, Sylow
131C2—142no—
132C2—302no—
133C2—1052no—
134C2C2×D7×D1511yescharacteristic
subgroupG/H
center, FrattiniC2C2×D7×D15
commutator, socle, cosocleC2×C3×C5×C7C23
FittingC3×C4×C5×C7C22
hypercenterC4D7×D15
hypocenterC3×C5×C7C2×D4
LCSG ▷ C2×C3×C5×C7 ▷ C3×C5×C7
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×D7×D15C2semidirect
2. C4×D105C2semidirect
3. C7×D60C2semidirect
4. C3×C5×D28C2semidirect
5. #11719757C2semidirect
8. C2×C7×D15C22semidirect
9. C2×C3×C5×D7C22semidirect
11. C3×C4×C5×C7C22semidirect
12. Dic105C22semidirect
17. C5×D28D3semidirect
21. D105D4semidirect
27. C3×D28D5semidirect
31. C2×C5×D7C2×D3semidirect
33. C4×C5×C7C2×D3semidirect
38. D60D7semidirect
41. C3×C5×C7C2×D4semidirect
44. C2×C3×D7C2×D5semidirect
46. C3×C4×C7C2×D5semidirect
56. C2×D15C2×D7semidirect
57. C3×C4×C5C2×D7semidirect
62. D28D15semidirect
74. C5×C7D3×D4semidirect
82. C2×D7C2×D15semidirect
83. C4×C7C2×D15semidirect
90. C3×C7D4×D5semidirect
95. C4×C5D3×D7semidirect
98. C3×C5D4×D7semidirect
107. C3×C4D5×D7semidirect
118. C7D4×D15semidirect
123. C5#66681semidirect
129. C4D7×D15semidirect
130. C3#10587950semidirect

Maximal subgroups

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

subgroupindex
C2×D7×D152
C4×D1052
C7×D602
C3×C5×D282
#117197572
#105879503
#666815
D4×D157