Finite Group Databasebeta

← D5×C13×#64424 #50304100

Subgroups — D5×C13×#64424 #50304100

Order 38220.

400 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 82 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
1D5×C13×#3861C211yesmaximal, characteristic, complemented
2C13×C5⋊#64424C211yesmaximal, characteristic, complemented
3C5×C13×#64424C211yesmaximal, characteristic, complemented
4D5×C13×C7⋊D7C311yesmaximal, characteristic, complemented, Hall
5C5×C13×#3861C2211yescharacteristic, complemented, Hall
6C2×C13×#64424—51nomaximal, Hall
7C13×C5⋊(C7⋊D7)C2×C311yescharacteristic, complemented
8C72×D5×C13C2×C311yescharacteristic, complemented
9C5×C13×C7⋊D7C2×C311yescharacteristic, complemented
10D5×C13×AGL(1,𝔽7)—78nomaximal
11C2×C13×#3861—51no—
12C13×#64424—51no—
13C13×#64424D511yescharacteristic, direct product factor
14C5×C72×C13C22×C311yescharacteristic, complemented, Hall
15D5×#64424C1311yesmaximal, characteristic, direct product factor, Hall
16C13×C5⋊AGL(1,𝔽7)—78no—
17D5×C13×ΓL(1,𝔽8)—78no—
18C5×C13×AGL(1,𝔽7)—78no—
19C2×C13×C7⋊D7—51noHall
20C13×#3861C2×D511yescharacteristic, complemented, Hall
21D5×C13×D7—78no—
22D5×#3861C2×C1311yescharacteristic, complemented
23C5⋊#64424C2×C1311yescharacteristic, complemented
24C5×#64424C2×C1311yescharacteristic, complemented
25C5×C13×ΓL(1,𝔽8)—78no—
26C2×C72×C13—51no—
27C13×C7⋊D7—51no—
28C13×C7⋊D7C3×D511yescharacteristic, complemented
29C2×C13×AGL(1,𝔽7)—358no—
30D5×C7⋊D7C3×C1311yescharacteristic, complemented, Hall
31C13×D35—78no—
32C7×D5×C13AGL(1,𝔽7)18yescomplemented
33C5×C13×D7—78no—
34C2×C3×D5×C13—491noHall
35C5×#3861C22×C1311yescharacteristic, complemented, Hall
36C72×C13C2×C3×D511yescharacteristic, complemented, Hall
37C2×#64424—51noHall
38C2×C13×ΓL(1,𝔽8)—358no—
39C13×AGL(1,𝔽7)—78no—
40C13×AGL(1,𝔽7)—358no—
41C5⋊(C7⋊D7)C2×C3×C1311yescharacteristic, complemented
42C72×D5C2×C3×C1311yescharacteristic, complemented
43C5×C7⋊D7C2×C3×C1311yescharacteristic, complemented
44C5×C7×C13C2×AGL(1,𝔽7)18yescomplemented
45D5×AGL(1,𝔽7)—78no—
46C2×C3×C5×C13—491no—
47C3×D5×C13—491no—
48C3×D5×C13—491no—
49C2×C13×D7—358no—
50C2×#3861—51no—
51#64424—51no—
52#64424D5×C1311yescharacteristic, direct product factor
53C13×ΓL(1,𝔽8)—78no—
54C2×D5×C13—491noHall
55C5×C72C22×C3×C1311yescharacteristic, complemented, Hall
56C5⋊AGL(1,𝔽7)—78no—
57D5×ΓL(1,𝔽8)—78no—
58C5×AGL(1,𝔽7)—78no—
59C2×C7⋊D7—51noHall
60C3×C5×C13—491noHall
61C2×C7×C13—58no—
62C13×D7—78no—
63C13×D7—358no—
64C22×C3×C13—2451noHall
65#3861C2×D5×C1311yescharacteristic, complemented, Hall
66D5×D7—78no—
67C2×C5×C13—491no—
68D5×C13—491no—
69D5×C13#6442411yescharacteristic, direct product factor
70C5×ΓL(1,𝔽8)—78no—
71C2×C72—51no—
72C7⋊D7—51no—
73C7⋊D7C3×D5×C1311yescharacteristic, complemented
74C7×C13D5×AGL(1,𝔽7)18yescomplemented
75C2×AGL(1,𝔽7)—358no—
76C2×C3×C13—491no—
77C2×C3×C13—2451no—
78C2×C3×C13—2451no—
79D35—78no—
80C5×D7—78no—
81C7×D5C13×AGL(1,𝔽7)18yescomplemented
82C5×C13C2×#6442411yescharacteristic, complemented, Hall
83C2×C3×D5—491noHall
84C22×C13—2451noHall
85C72C2×C3×D5×C1311yescharacteristic, complemented, Sylow
86C2×ΓL(1,𝔽8)—358no—
87AGL(1,𝔽7)—78no—
88AGL(1,𝔽7)—358no—
89C3×C13—491noHall
90C5×C7C2×C13×AGL(1,𝔽7)18yescomplemented
91C2×C3×C5—491no—
92C3×D5—491no—
93C3×D5—491no—
94C2×D7—358no—
95C2×C13—51no—
96C2×C13—491no—
97C2×C13—2451no—
98ΓL(1,𝔽8)—78no—
99C2×D5—491noHall
100C3×C5—491noHall
101C2×C7—58no—
102D7—78no—
103D7—358no—
104C13D5×#6442411yescharacteristic, direct product factor, Sylow
105C22×C3—2451noHall
106C2×C5—491no—
107D5—491no—
108D5C13×#6442411yescharacteristic, direct product factor
109C7D5×C13×AGL(1,𝔽7)18yescomplemented
110C2×C3—491no—
111C2×C3—2451no—
112C2×C3—2451no—
113C5C2×C13×#6442411yescharacteristic, complemented, Sylow
114C22—2451noSylow
115C3—491noSylow
116C2—51no—
117C2—491no—
118C2—2451no—
subgroupG/H
center, hypercenterC13D5×#64424
commutator, cosocle, hypocenterC5×C72C22×C3×C13
FrattiniC1G
Fitting, socleC5×C72×C13C22×C3
LCSG ▷ C5×C72
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
1. D5×C13×#3861C2semidirect
2. C13×C5⋊#64424C2semidirect
3. C5×C13×#64424C2semidirect
4. D5×C13×C7⋊D7C3semidirect
5. C5×C13×#3861C22semidirect
7. C13×C5⋊(C7⋊D7)C2×C3semidirect
8. C72×D5×C13C2×C3semidirect
9. C5×C13×C7⋊D7C2×C3semidirect
13. C13×#64424D5direct (N × H)
14. C5×C72×C13C22×C3semidirect
15. D5×#64424C13direct (N × H)
20. C13×#3861C2×D5semidirect
22. D5×#3861C2×C13semidirect
23. C5⋊#64424C2×C13semidirect
24. C5×#64424C2×C13semidirect
28. C13×C7⋊D7C3×D5semidirect
30. D5×C7⋊D7C3×C13semidirect
32. C7×D5×C13AGL(1,𝔽7)semidirect
35. C5×#3861C22×C13semidirect
36. C72×C13C2×C3×D5semidirect
41. C5⋊(C7⋊D7)C2×C3×C13semidirect
42. C72×D5C2×C3×C13semidirect
43. C5×C7⋊D7C2×C3×C13semidirect
44. C5×C7×C13C2×AGL(1,𝔽7)semidirect
52. #64424D5×C13direct (N × H)
55. C5×C72C22×C3×C13semidirect
65. #3861C2×D5×C13semidirect
69. D5×C13#64424direct (N × H)
73. C7⋊D7C3×D5×C13semidirect
74. C7×C13D5×AGL(1,𝔽7)semidirect
81. C7×D5C13×AGL(1,𝔽7)semidirect
82. C5×C13C2×#64424semidirect
85. C72C2×C3×D5×C13semidirect
90. C5×C7C2×C13×AGL(1,𝔽7)semidirect
104. C13D5×#64424direct (N × H)
108. D5C13×#64424direct (N × H)
109. C7D5×C13×AGL(1,𝔽7)semidirect
113. C5C2×C13×#64424semidirect

Maximal subgroups

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

subgroupindex
D5×C13×#38612
C13×C5⋊#644242
C5×C13×#644242
D5×C13×C7⋊D73
C2×C13×#644245
D5×C13×AGL(1,𝔽7)7
D5×#6442413