Finite Group Databasebeta

← D5×C11×D147 #44568407

Subgroups — D5×C11×D147 #44568407

Order 32340.

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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
1C11×D735C211yesmaximal, characteristic, complemented
2C5×C11×D147C211yesmaximal, characteristic, complemented
3C3×D5×C11×C49C211yesmaximal, characteristic, complemented
4D5×C11×D49—31nomaximal, Hall
5C3×C5×C11×C49C2211yescharacteristic, complemented, Hall
6C2×C11×D147—51nomaximal, Hall
7C11×D245—31no—
8D5×C11×C49D311yescharacteristic, complemented
9C5×C11×D49—31no—
10D5×C11×D21—71nomaximal
11C11×D147—51no—
12C11×D147D511yescharacteristic, direct product factor
13C2×C3×C11×C49—51no—
14D5×D147C1111yesmaximal, characteristic, direct product factor, Hall
15C5×C11×C49C2×D311yescharacteristic, complemented, Hall
16C11×D105—71no—
17C5×C11×D21—71no—
18C3×C7×D5×C11D711yescharacteristic
19C2×C11×D49—151noHall
20C3×C11×C49C2×D511yescharacteristic, complemented, Hall
21D5×C11×D7—211no—
22D735C2×C1111yescharacteristic, complemented
23C5×D147C2×C1111yescharacteristic, complemented
24C3×D5×C49C2×C1111yescharacteristic, complemented
25C3×C5×C7×C11C2×D711yescharacteristic
26C2×C11×C49—51no—
27C11×D49—31no—
28C11×D49—151no—
29D5×D49—31noHall
30C2×C11×D21—351no—
31C11×D35—211no—
32C7×D5×C11D2111yescharacteristic
33C5×C11×D7—211no—
34C3×C5×C49C22×C1111yescharacteristic, complemented, Hall
35D3×D5×C11—491noHall
36C2×D147—51noHall
37C11×C49D3×D511yescharacteristic, complemented, Hall
38D245—31no—
39C5×D49—31no—
40D5×C49D3×C1111yescharacteristic, complemented
41C2×C3×C7×C11—51no—
42C11×D21—71no—
43C11×D21—351no—
44D5×D21—71no—
45C5×C7×C11C2×D2111yescharacteristic
46C11×D15—491no—
47C5×D3×C11—491no—
48C3×D5×C11D4911yescharacteristic, complemented
49C2×C11×D7—1051no—
50C2×C3×C49—51no—
51D147—51no—
52D147D5×C1111yescharacteristic, direct product factor
53C5×C49C2×D3×C1111yescharacteristic, complemented, Hall
54C3×C7×C11D5×D711yescharacteristic
55C2×D5×C11—1471noHall
56D105—71no—
57C5×D21—71no—
58C3×C7×D5C11×D711yescharacteristic
59C2×D49—151noHall
60C3×C5×C11C2×D4911yescharacteristic, complemented, Hall
61C2×C7×C11—51no—
62C11×D7—211no—
63C11×D7—1051no—
64C3×C49C2×D5×C1111yescharacteristic, complemented, Hall
65D5×D7—211no—
66C2×D3×C11—2451noHall
67C2×C5×C11—1471no—
68D5×C11—1471no—
69D5×C11D14711yescharacteristic, direct product factor
70C3×C5×C7C2×C11×D711yescharacteristic
71C2×C49—51no—
72D49—31no—
73D49—151no—
74C2×D21—351no—
75C7×C11D5×D2111yescharacteristic
76D35—211no—
77C5×D7—211no—
78C7×D5C11×D2111yescharacteristic
79C2×C3×C11—51no—
80D3×C11—491no—
81D3×C11—2451no—
82D3×D5—491noHall
83C5×C11C2×D14711yescharacteristic, complemented, Hall
84C49D3×D5×C1111yescharacteristic, complemented, Sylow
85C22×C11—7351noHall
86C2×C3×C7—51no—
87D21—71no—
88D21—351no—
89C5×C7C2×C11×D2111yescharacteristic
90C3×C11D5×D4911yescharacteristic, complemented, Hall
91D15—491no—
92C3×D5C11×D4911yescharacteristic, complemented
93C5×D3—491no—
94C2×D7—1051no—
95C2×C11—51no—
96C2×C11—1471no—
97C2×C11—7351no—
98C3×C7D5×C11×D711yescharacteristic
99C2×D5—1471noHall
100C3×C5C2×C11×D4911yescharacteristic, complemented, Hall
101C2×C7—51no—
102D7—211no—
103D7—1051no—
104C2×D3—2451noHall
105C11D5×D14711yescharacteristic, direct product factor, Sylow
106C2×C5—1471no—
107D5—1471no—
108D5C11×D14711yescharacteristic, direct product factor
109C7D5×C11×D2111yescharacteristic
110C2×C3—51no—
111D3—491no—
112D3—2451no—
113C5C2×C11×D14711yescharacteristic, complemented, Sylow
114C22—7351noSylow
115C3D5×C11×D4911yescharacteristic, complemented, Sylow
116C2—51no—
117C2—1471no—
118C2—7351no—
subgroupG/H
center, hypercenterC11D5×D147
commutator, cosocle, hypocenterC3×C5×C49C22×C11
FrattiniC7D5×C11×D21
FittingC3×C5×C11×C49C22
socleC3×C5×C7×C11C2×D7
LCSG ▷ C3×C5×C49
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×D735C2semidirect
2. C5×C11×D147C2semidirect
3. C3×D5×C11×C49C2semidirect
5. C3×C5×C11×C49C22semidirect
8. D5×C11×C49D3semidirect
12. C11×D147D5direct (N × H)
14. D5×D147C11direct (N × H)
15. C5×C11×C49C2×D3semidirect
20. C3×C11×C49C2×D5semidirect
22. D735C2×C11semidirect
23. C5×D147C2×C11semidirect
24. C3×D5×C49C2×C11semidirect
34. C3×C5×C49C22×C11semidirect
37. C11×C49D3×D5semidirect
40. D5×C49D3×C11semidirect
48. C3×D5×C11D49semidirect
52. D147D5×C11direct (N × H)
53. C5×C49C2×D3×C11semidirect
60. C3×C5×C11C2×D49semidirect
64. C3×C49C2×D5×C11semidirect
69. D5×C11D147direct (N × H)
83. C5×C11C2×D147semidirect
84. C49D3×D5×C11semidirect
90. C3×C11D5×D49semidirect
92. C3×D5C11×D49semidirect
100. C3×C5C2×C11×D49semidirect
105. C11D5×D147direct (N × H)
108. D5C11×D147direct (N × H)
113. C5C2×C11×D147semidirect
115. C3D5×C11×D49semidirect

Maximal subgroups

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

subgroupindex
C11×D7352
C5×C11×D1472
C3×D5×C11×C492
D5×C11×D493
C2×C11×D1475
D5×C11×D217
D5×D14711