Finite Group Databasebeta

← D5×#16838448 #50304107

Subgroups — D5×#16838448 #50304107

Order 38220.

400 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 75 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×#14274263C211yesmaximal, characteristic, complemented
2C5⋊#16838448C211yesmaximal, characteristic, complemented
3C5×#16838448C211yesmaximal, characteristic, complemented
4D5×C13×C7⋊D7C311yesmaximal, characteristic, complemented, Hall
5C5×#14274263C2211yescharacteristic, complemented, Hall
6C2×#16838448—51nomaximal, Hall
7C13×C5⋊(C7⋊D7)C2×C311yescharacteristic, complemented
8C72×D5×C13C2×C311yescharacteristic, complemented
9C5×C13×C7⋊D7C2×C311yescharacteristic, complemented
10D5×#10587720—78nomaximal
11C2×#14274263—51no—
12#16838448—51no—
13#16838448D511yescharacteristic, direct product factor
14C5×C72×C13C22×C311yescharacteristic, complemented, Hall
15D5×#64424—131nomaximal, Hall
16C5⋊#10587720—78no—
17D5×#63270—78no—
18C5×#10587720—78no—
19C2×C13×C7⋊D7—51noHall
20#14274263C2×D511yescharacteristic, complemented, Hall
21D5×C13×D7—78no—
22D5×#3861—131no—
23C5⋊#64424—131no—
24C5×#64424—131no—
25C5×#63270—78no—
26C2×C72×C13—51no—
27C13×C7⋊D7—51no—
28C13×C7⋊D7C3×D511yescharacteristic, complemented
29C2×#10587720—358no—
30D5×C7⋊D7C13⋊C311yescharacteristic, complemented, Hall
31C13×D35—78no—
32C7×D5×C13AGL(1,𝔽7)18yescomplemented
33C5×C13×D7—78no—
34C2×D5×C13⋊C3—491noHall
35C5×#3861—131noHall
36C72×C13C2×C3×D511yescharacteristic, complemented, Hall
37C2×#64424—651noHall
38C2×#63270—358no—
39#10587720—78no—
40#10587720—358no—
41C5⋊(C7⋊D7)C2×C13⋊C311yescharacteristic, complemented
42C72×D5C2×C13⋊C311yescharacteristic, complemented
43C5×C7⋊D7C2×C13⋊C311yescharacteristic, complemented
44C5×C7×C13C2×AGL(1,𝔽7)18yescomplemented
45D5×AGL(1,𝔽7)—918no—
46C2×C5×C13⋊C3—491no—
47D5×C13⋊C3—491no—
48D5×C13⋊C3—491no—
49C2×C13×D7—358no—
50C2×#3861—651no—
51#64424—131no—
52#64424—651no—
53#63270—78no—
54C2×D5×C13—491noHall
55C5×C72C22×C13⋊C311yescharacteristic, complemented, Hall
56C5⋊AGL(1,𝔽7)—918no—
57D5×ΓL(1,𝔽8)—918no—
58C5×AGL(1,𝔽7)—918no—
59C2×C7⋊D7—51noHall
60C5×C13⋊C3—491noHall
61C2×C7×C13—58no—
62C13×D7—78no—
63C13×D7—358no—
64C22×C13⋊C3—2451noHall
65#3861—131noHall
66D5×D7—78no—
67C2×C5×C13—491no—
68D5×C13—491no—
69D5×C13#6442411yescharacteristic, complemented
70C5×ΓL(1,𝔽8)—918no—
71C2×C72—51no—
72C7⋊D7—51no—
73C7⋊D7D5×C13⋊C311yescharacteristic, complemented
74C7×C13D5×AGL(1,𝔽7)18yescomplemented
75C2×AGL(1,𝔽7)—4558no—
76C2×C13⋊C3—491no—
77C2×C13⋊C3—2451no—
78C2×C13⋊C3—2451no—
79D35—78no—
80C5×D7—78no—
81C7×D5#1058772018yescomplemented
82C5×C13C2×#6442411yescharacteristic, complemented, Hall
83C2×C3×D5—6371noHall
84C22×C13—2451noHall
85C72C2×D5×C13⋊C311yescharacteristic, complemented, Sylow
86C2×ΓL(1,𝔽8)—4558no—
87AGL(1,𝔽7)—918no—
88AGL(1,𝔽7)—4558no—
89C13⋊C3—491noHall
90C5×C7C2×#1058772018yescomplemented
91C2×C3×C5—6371no—
92C3×D5—6371no—
93C3×D5—6371no—
94C2×D7—358no—
95C2×C13—51no—
96C2×C13—491no—
97C2×C13—2451no—
98ΓL(1,𝔽8)—918no—
99C2×D5—491noHall
100C3×C5—6371noHall
101C2×C7—58no—
102D7—78no—
103D7—358no—
104C13D5×#6442411yescharacteristic, complemented, Sylow
105C22×C3—31851noHall
106C2×C5—491no—
107D5—491no—
108D5#1683844811yescharacteristic, direct product factor
109C7D5×#1058772018yescomplemented
110C2×C3—31851no—
111C2×C3—31851no—
112C2×C3—6371no—
113C5C2×#1683844811yescharacteristic, complemented, Sylow
114C22—2451noSylow
115C3—6371noSylow
116C2—51no—
117C2—491no—
118C2—2451no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C72×C13C22×C3
LCSG ▷ C5×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. D5×#14274263C2semidirect
2. C5⋊#16838448C2semidirect
3. C5×#16838448C2semidirect
4. D5×C13×C7⋊D7C3semidirect
5. C5×#14274263C22semidirect
7. C13×C5⋊(C7⋊D7)C2×C3semidirect
8. C72×D5×C13C2×C3semidirect
9. C5×C13×C7⋊D7C2×C3semidirect
13. #16838448D5direct (N × H)
14. C5×C72×C13C22×C3semidirect
20. #14274263C2×D5semidirect
28. C13×C7⋊D7C3×D5semidirect
30. D5×C7⋊D7C13⋊C3semidirect
32. C7×D5×C13AGL(1,𝔽7)semidirect
36. C72×C13C2×C3×D5semidirect
41. C5⋊(C7⋊D7)C2×C13⋊C3semidirect
42. C72×D5C2×C13⋊C3semidirect
43. C5×C7⋊D7C2×C13⋊C3semidirect
44. C5×C7×C13C2×AGL(1,𝔽7)semidirect
55. C5×C72C22×C13⋊C3semidirect
69. D5×C13#64424semidirect
73. C7⋊D7D5×C13⋊C3semidirect
74. C7×C13D5×AGL(1,𝔽7)semidirect
81. C7×D5#10587720semidirect
82. C5×C13C2×#64424semidirect
85. C72C2×D5×C13⋊C3semidirect
90. C5×C7C2×#10587720semidirect
104. C13D5×#64424semidirect
108. D5#16838448direct (N × H)
109. C7D5×#10587720semidirect
113. C5C2×#16838448semidirect

Maximal subgroups

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

subgroupindex
D5×#142742632
C5⋊#168384482
C5×#168384482
D5×C13×C7⋊D73
C2×#168384485
D5×#105877207
D5×#6442413