Finite Group Databasebeta

← D13×C5⋊#64425 #50304202

Subgroups — D13×C5⋊#64425 #50304202

Order 38220.

200 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 38 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
1C5⋊#16838454C211yesmaximal, characteristic, complemented
2C13×C5⋊#64425C211yesmaximal, characteristic, complemented
3C5×D13×#3862C211yesmaximal, characteristic, complemented
4D13×C5⋊(C7⋊D7)C311yesmaximal, characteristic, complemented, Hall
5C5×C13×#3862C2211yescharacteristic, complemented, Hall
6D13×#64425—51nomaximal, Hall
7C5⋊(C7⋊D91)C2×C311yescharacteristic, complemented
8C13×C5⋊(C7⋊D7)C2×C311yescharacteristic, complemented
9C5×C72×D13C2×C311yescharacteristic, complemented
10D13×C5⋊AGL(1,𝔽7)—72nomaximal
11D13×#3862D511yescharacteristic, complemented
12#16838454—51no—
13C13×#64425—51no—
14C5×C72×C13C22×C311yescharacteristic, complemented, Hall
15C2×C5⋊#64425—131nomaximal, Hall
16C5⋊(ΓL(1,𝔽8)⋊D13)—72no—
17C13×C5⋊AGL(1,𝔽7)—72no—
18C5×ΓL(1,𝔽8)×D13—72no—
19D13×C7⋊D7—51noHall
20C13×#3862C2×D511yescharacteristic, complemented, Hall
21D13×D35—72no—
22D13×D35—212no—
23C2×C5×#3862—131no—
24C5⋊#64425—131no—
25C5⋊#64425D1311yescharacteristic, direct product factor
26C5×C13×ΓL(1,𝔽8)—72no—
27C7⋊D91—51no—
28C13×C7⋊D7—51no—
29C72×D13C3×D511yescharacteristic, complemented
30D13×AGL(1,𝔽7)—352no—
31C2×C5⋊(C7⋊D7)—131noHall
32D455—72no—
33D455—212no—
34C13×D35—72no—
35C13×D35—212no—
36C5×C7×D13—32no—
37C5×C7×D13AGL(1,𝔽7)12yescomplemented
38C3×D5×D13—491noHall
39C5×#3862C2×D1311yescharacteristic, complemented, Hall
40C72×C13C2×C3×D511yescharacteristic, complemented, Hall
41C2×#64425—651noHall
42ΓL(1,𝔽8)⋊D13—352no—
43C13×AGL(1,𝔽7)—352no—
44ΓL(1,𝔽8)×D13—72no—
45C2×C5×C72—131no—
46C5⋊(C7⋊D7)—131no—
47C5⋊(C7⋊D7)C3×D1311yescharacteristic, complemented
48C5×C7×C13—32no—
49C5×C7×C13C2×AGL(1,𝔽7)12yescomplemented
50C2×C5⋊AGL(1,𝔽7)—912no—
51C3×D65—491no—
52C3×D5×C13—491no—
53C3×C5×D13—491no—
54D7×D13—352no—
55D7×D13—1052no—
56C2×#3862—131no—
57#64425—51no—
58#64425—651no—
59C13×ΓL(1,𝔽8)—72no—
60D5×D13—491noHall
61C5×C72C2×C3×D1311yescharacteristic, complemented, Hall
62C2×C5×ΓL(1,𝔽8)—912no—
63C5⋊AGL(1,𝔽7)—72no—
64C5⋊AGL(1,𝔽7)—912no—
65C2×C7⋊D7—651noHall
66C3×C5×C13—491noHall
67D91—352no—
68D91—1052no—
69C7×D13—32no—
70C7×D13C5⋊AGL(1,𝔽7)12yescomplemented
71C13×D7—352no—
72C13×D7—1052no—
73C2×C3×D13—2451noHall
74#3862D5×D1311yescharacteristic, complemented, Hall
75C2×D35—2732no—
76C2×D35—912no—
77D65—491no—
78C5×D13#6442511yescharacteristic, complemented
79D5×C13—491no—
80C5×ΓL(1,𝔽8)—72no—
81C2×C72—131no—
82C7⋊D7—51no—
83C7⋊D7—651no—
84C7×C13—32no—
85C7×C13C2×C5⋊AGL(1,𝔽7)12yescomplemented
86C2×AGL(1,𝔽7)—4552no—
87C2×C3×C13—2451no—
88C3×D13—491no—
89C3×D13—2451no—
90C2×C5×C7—132no—
91C2×C5×C7—392no—
92D35—72no—
93D35—2732no—
94D35—212no—
95D35—912no—
96C5×C13C2×#6442511yescharacteristic, complemented, Hall
97C2×C3×D5—6371noHall
98C2×D13—2451noHall
99C72C3×D5×D1311yescharacteristic, complemented, Sylow
100C2×ΓL(1,𝔽8)—912no—
101AGL(1,𝔽7)—352no—
102AGL(1,𝔽7)—4552no—
103C3×C13—491noHall
104C5×C7—32no—
105C5×C7D13×AGL(1,𝔽7)12yescomplemented
106C2×C3×C5—6371no—
107C3×D5—491no—
108C3×D5—6371no—
109C2×D7—13652no—
110C2×D7—4552no—
111C2×C13—2451no—
112D13—2451no—
113D13C5⋊#6442511yescharacteristic, direct product factor
114ΓL(1,𝔽8)—72no—
115C2×D5—6371noHall
116C3×C5—491noHall
117C2×C7—132no—
118C2×C7—392no—
119D7—352no—
120D7—13652no—
121D7—1052no—
122D7—4552no—
123C13C2×C5⋊#6442511yescharacteristic, complemented, Sylow
124C22×C3—31851noHall
125C2×C5—131no—
126D5—491no—
127D5—6371no—
128C7—32no—
129C7D13×C5⋊AGL(1,𝔽7)12yescomplemented
130C2×C3—31851no—
131C2×C3—6371no—
132C2×C3—2451no—
133C5D13×#6442511yescharacteristic, complemented, Sylow
134C22—31851noSylow
135C3—491noSylow
136C2—131no—
137C2—31851no—
138C2—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. C5⋊#16838454C2semidirect
2. C13×C5⋊#64425C2semidirect
3. C5×D13×#3862C2semidirect
4. D13×C5⋊(C7⋊D7)C3semidirect
5. C5×C13×#3862C22semidirect
7. C5⋊(C7⋊D91)C2×C3semidirect
8. C13×C5⋊(C7⋊D7)C2×C3semidirect
9. C5×C72×D13C2×C3semidirect
11. D13×#3862D5semidirect
14. C5×C72×C13C22×C3semidirect
20. C13×#3862C2×D5semidirect
25. C5⋊#64425D13direct (N × H)
29. C72×D13C3×D5semidirect
37. C5×C7×D13AGL(1,𝔽7)semidirect
39. C5×#3862C2×D13semidirect
40. C72×C13C2×C3×D5semidirect
47. C5⋊(C7⋊D7)C3×D13semidirect
49. C5×C7×C13C2×AGL(1,𝔽7)semidirect
61. C5×C72C2×C3×D13semidirect
70. C7×D13C5⋊AGL(1,𝔽7)semidirect
74. #3862D5×D13semidirect
78. C5×D13#64425semidirect
85. C7×C13C2×C5⋊AGL(1,𝔽7)semidirect
96. C5×C13C2×#64425semidirect
99. C72C3×D5×D13semidirect
105. C5×C7D13×AGL(1,𝔽7)semidirect
113. D13C5⋊#64425direct (N × H)
123. C13C2×C5⋊#64425semidirect
129. C7D13×C5⋊AGL(1,𝔽7)semidirect
133. C5D13×#64425semidirect

Maximal subgroups

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

subgroupindex
C5⋊#168384542
C13×C5⋊#644252
C5×D13×#38622
D13×C5⋊(C7⋊D7)3
D13×#644255
D13×C5⋊AGL(1,𝔽7)7
C2×C5⋊#6442513