Finite Group Databasebeta

← C5×D13×#64425 #50303805

Subgroups — C5×D13×#64425 #50303805

Order 38220.

200 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 46 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×D13×#3862C211yesmaximal, characteristic, complemented
2C5×#16838454C211yesmaximal, characteristic, complemented
3C5×C13×#64425C211yesmaximal, characteristic, complemented
4C5×D13×C7⋊D7C311yesmaximal, characteristic, complemented, Hall
5C5×C13×#3862C2211yescharacteristic, complemented, Hall
6D13×#64425C511yesmaximal, characteristic, direct product factor, Hall
7C5×C7⋊D91C2×C311yescharacteristic, complemented
8C5×C13×C7⋊D7C2×C311yescharacteristic, complemented
9C5×C72×D13C2×C311yescharacteristic, complemented
10C5×D13×AGL(1,𝔽7)—72nomaximal
11D13×#3862C2×C511yescharacteristic, complemented
12#16838454C2×C511yescharacteristic, complemented
13C13×#64425C2×C511yescharacteristic, complemented
14C5×C72×C13C22×C311yescharacteristic, complemented, Hall
15C2×C5×#64425—131nomaximal, Hall
16C5×ΓL(1,𝔽8)⋊D13—72no—
17C5×C13×AGL(1,𝔽7)—72no—
18C5×ΓL(1,𝔽8)×D13—72no—
19D13×C7⋊D7C3×C511yescharacteristic, complemented, Hall
20C13×#3862C22×C511yescharacteristic, complemented, Hall
21C5×D7×D13—72no—
22C5×D7×D13—212no—
23C2×C5×#3862—131no—
24C5×#64425—131no—
25C5×#64425D1311yescharacteristic, direct product factor
26C5×C13×ΓL(1,𝔽8)—72no—
27C7⋊D91C2×C3×C511yescharacteristic, complemented
28C13×C7⋊D7C2×C3×C511yescharacteristic, complemented
29C72×D13C2×C3×C511yescharacteristic, complemented
30D13×AGL(1,𝔽7)—72no—
31C2×C5×C7⋊D7—131noHall
32C5×D91—72no—
33C5×D91—212no—
34C5×C13×D7—72no—
35C5×C13×D7—212no—
36C5×C7×D13—32no—
37C5×C7×D13AGL(1,𝔽7)12yescomplemented
38C2×C3×C5×D13—491noHall
39C5×#3862C2×D1311yescharacteristic, complemented, Hall
40C72×C13C22×C3×C511yescharacteristic, complemented, Hall
41C2×#64425—131noHall
42ΓL(1,𝔽8)⋊D13—72no—
43C13×AGL(1,𝔽7)—72no—
44ΓL(1,𝔽8)×D13—72no—
45C2×C5×C72—131no—
46C5×C7⋊D7—131no—
47C5×C7⋊D7C3×D1311yescharacteristic, complemented
48C5×C7×C13—32no—
49C5×C7×C13C2×AGL(1,𝔽7)12yescomplemented
50C2×C5×AGL(1,𝔽7)—912no—
51C2×C3×C5×C13—491no—
52C3×C5×D13—491no—
53C3×C5×D13—491no—
54D7×D13—72no—
55D7×D13—212no—
56C2×#3862—131no—
57#64425—131no—
58#64425C5×D1311yescharacteristic, direct product factor
59C13×ΓL(1,𝔽8)—72no—
60C2×C5×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—131noHall
66C3×C5×C13—491noHall
67D91—72no—
68D91—212no—
69C7×D13—32no—
70C7×D13C5×AGL(1,𝔽7)12yescomplemented
71C13×D7—72no—
72C13×D7—212no—
73C2×C3×D13—491noHall
74#3862C2×C5×D1311yescharacteristic, complemented, Hall
75C2×C5×D7—2732no—
76C2×C5×D7—912no—
77C2×C5×C13—491no—
78C5×D13—491no—
79C5×D13#6442511yescharacteristic, direct product factor
80C5×ΓL(1,𝔽8)—72no—
81C2×C72—131no—
82C7⋊D7—131no—
83C7⋊D7C3×C5×D1311yescharacteristic, complemented
84C7×C13—32no—
85C7×C13C2×C5×AGL(1,𝔽7)12yescomplemented
86C2×AGL(1,𝔽7)—912no—
87C2×C3×C13—491no—
88C3×D13—491no—
89C3×D13—491no—
90C2×C5×C7—132no—
91C2×C5×C7—392no—
92C5×D7—72no—
93C5×D7—2732no—
94C5×D7—212no—
95C5×D7—912no—
96C5×C13C2×#6442511yescharacteristic, complemented, Hall
97C22×C3×C5—6371noHall
98C2×D13—491noHall
99C72C2×C3×C5×D1311yescharacteristic, complemented, Sylow
100C2×ΓL(1,𝔽8)—912no—
101AGL(1,𝔽7)—72no—
102AGL(1,𝔽7)—912no—
103C3×C13—491noHall
104C5×C7—32no—
105C5×C7D13×AGL(1,𝔽7)12yescomplemented
106C2×C3×C5—491no—
107C2×C3×C5—6371no—
108C2×C3×C5—6371no—
109C2×D7—2732no—
110C2×D7—912no—
111C2×C13—491no—
112D13—491no—
113D13C5×#6442511yescharacteristic, direct product factor
114ΓL(1,𝔽8)—72no—
115C22×C5—6371noHall
116C3×C5—491noHall
117C2×C7—132no—
118C2×C7—392no—
119D7—72no—
120D7—2732no—
121D7—212no—
122D7—912no—
123C13C2×C5×#6442511yescharacteristic, complemented, Sylow
124C22×C3—6371noHall
125C2×C5—131no—
126C2×C5—491no—
127C2×C5—6371no—
128C7—32no—
129C7C5×D13×AGL(1,𝔽7)12yescomplemented
130C2×C3—491no—
131C2×C3—6371no—
132C2×C3—6371no—
133C5D13×#6442511yescharacteristic, direct product factor, Sylow
134C22—6371noSylow
135C3—491noSylow
136C2—131no—
137C2—491no—
138C2—6371no—
subgroupG/H
center, hypercenterC5D13×#64425
commutator, cosocle, hypocenterC72×C13C22×C3×C5
FrattiniC1G
Fitting, socleC5×C72×C13C22×C3
LCSG ▷ C72×C13
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×D13×#3862C2semidirect
2. C5×#16838454C2semidirect
3. C5×C13×#64425C2semidirect
4. C5×D13×C7⋊D7C3semidirect
5. C5×C13×#3862C22semidirect
6. D13×#64425C5direct (N × H)
7. C5×C7⋊D91C2×C3semidirect
8. C5×C13×C7⋊D7C2×C3semidirect
9. C5×C72×D13C2×C3semidirect
11. D13×#3862C2×C5semidirect
12. #16838454C2×C5semidirect
13. C13×#64425C2×C5semidirect
14. C5×C72×C13C22×C3semidirect
19. D13×C7⋊D7C3×C5semidirect
20. C13×#3862C22×C5semidirect
25. C5×#64425D13direct (N × H)
27. C7⋊D91C2×C3×C5semidirect
28. C13×C7⋊D7C2×C3×C5semidirect
29. C72×D13C2×C3×C5semidirect
37. C5×C7×D13AGL(1,𝔽7)semidirect
39. C5×#3862C2×D13semidirect
40. C72×C13C22×C3×C5semidirect
47. C5×C7⋊D7C3×D13semidirect
49. C5×C7×C13C2×AGL(1,𝔽7)semidirect
58. #64425C5×D13direct (N × H)
61. C5×C72C2×C3×D13semidirect
70. C7×D13C5×AGL(1,𝔽7)semidirect
74. #3862C2×C5×D13semidirect
79. C5×D13#64425direct (N × H)
83. C7⋊D7C3×C5×D13semidirect
85. C7×C13C2×C5×AGL(1,𝔽7)semidirect
96. C5×C13C2×#64425semidirect
99. C72C2×C3×C5×D13semidirect
105. C5×C7D13×AGL(1,𝔽7)semidirect
113. D13C5×#64425direct (N × H)
123. C13C2×C5×#64425semidirect
129. C7C5×D13×AGL(1,𝔽7)semidirect
133. C5D13×#64425direct (N × H)

Maximal subgroups

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

subgroupindex
C5×D13×#38622
C5×#168384542
C5×C13×#644252
C5×D13×C7⋊D73
D13×#644255
C5×D13×AGL(1,𝔽7)7
C2×C5×#6442513