Finite Group Databasebeta

← D5×C13×#64425 #50304203

Subgroups — D5×C13×#64425 #50304203

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
1D5×C13×#3862C211yesmaximal, characteristic, complemented
2C13×C5⋊#64425C211yesmaximal, characteristic, complemented
3C5×C13×#64425C211yesmaximal, characteristic, complemented
4D5×C13×C7⋊D7C311yesmaximal, characteristic, complemented, Hall
5C5×C13×#3862C2211yescharacteristic, complemented, Hall
6C2×C13×#64425—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)—72nomaximal
11C2×C13×#3862—51no—
12C13×#64425—51no—
13C13×#64425D511yescharacteristic, direct product factor
14C5×C72×C13C22×C311yescharacteristic, complemented, Hall
15D5×#64425C1311yesmaximal, characteristic, direct product factor, Hall
16C13×C5⋊AGL(1,𝔽7)—72no—
17D5×C13×ΓL(1,𝔽8)—72no—
18C5×C13×AGL(1,𝔽7)—72no—
19C2×C13×C7⋊D7—51noHall
20C13×#3862C2×D511yescharacteristic, complemented, Hall
21D5×C13×D7—72no—
22D5×C13×D7—212no—
23D5×#3862C2×C1311yescharacteristic, complemented
24C5⋊#64425C2×C1311yescharacteristic, complemented
25C5×#64425C2×C1311yescharacteristic, complemented
26C5×C13×ΓL(1,𝔽8)—72no—
27C2×C72×C13—51no—
28C13×C7⋊D7—51no—
29C13×C7⋊D7C3×D511yescharacteristic, complemented
30C2×C13×AGL(1,𝔽7)—352no—
31D5×C7⋊D7C3×C1311yescharacteristic, complemented, Hall
32C13×D35—72no—
33C13×D35—212no—
34C7×D5×C13—32no—
35C7×D5×C13AGL(1,𝔽7)12yescomplemented
36C5×C13×D7—72no—
37C5×C13×D7—212no—
38C2×C3×D5×C13—491noHall
39C5×#3862C22×C1311yescharacteristic, complemented, Hall
40C72×C13C2×C3×D511yescharacteristic, complemented, Hall
41C2×#64425—51noHall
42C2×C13×ΓL(1,𝔽8)—352no—
43C13×AGL(1,𝔽7)—72no—
44C13×AGL(1,𝔽7)—352no—
45C5⋊(C7⋊D7)C2×C3×C1311yescharacteristic, complemented
46C72×D5C2×C3×C1311yescharacteristic, complemented
47C5×C7⋊D7C2×C3×C1311yescharacteristic, complemented
48C5×C7×C13—32no—
49C5×C7×C13C2×AGL(1,𝔽7)12yescomplemented
50D5×AGL(1,𝔽7)—72no—
51C2×C3×C5×C13—491no—
52C3×D5×C13—491no—
53C3×D5×C13—491no—
54C2×C13×D7—352no—
55C2×C13×D7—1052no—
56C2×#3862—51no—
57#64425—51no—
58#64425D5×C1311yescharacteristic, direct product factor
59C13×ΓL(1,𝔽8)—72no—
60C2×D5×C13—491noHall
61C5×C72C22×C3×C1311yescharacteristic, complemented, Hall
62C5⋊AGL(1,𝔽7)—72no—
63D5×ΓL(1,𝔽8)—72no—
64C5×AGL(1,𝔽7)—72no—
65C2×C7⋊D7—51noHall
66C3×C5×C13—491noHall
67C2×C7×C13—52no—
68C2×C7×C13—152no—
69C13×D7—72no—
70C13×D7—212no—
71C13×D7—352no—
72C13×D7—1052no—
73C22×C3×C13—2451noHall
74#3862C2×D5×C1311yescharacteristic, complemented, Hall
75D5×D7—72no—
76D5×D7—212no—
77C2×C5×C13—491no—
78D5×C13—491no—
79D5×C13#6442511yescharacteristic, direct product factor
80C5×ΓL(1,𝔽8)—72no—
81C2×C72—51no—
82C7⋊D7—51no—
83C7⋊D7C3×D5×C1311yescharacteristic, complemented
84C7×C13—32no—
85C7×C13D5×AGL(1,𝔽7)12yescomplemented
86C2×AGL(1,𝔽7)—352no—
87C2×C3×C13—491no—
88C2×C3×C13—2451no—
89C2×C3×C13—2451no—
90D35—72no—
91D35—212no—
92C5×D7—72no—
93C5×D7—212no—
94C7×D5—32no—
95C7×D5C13×AGL(1,𝔽7)12yescomplemented
96C5×C13C2×#6442511yescharacteristic, complemented, Hall
97C2×C3×D5—491noHall
98C22×C13—2451noHall
99C72C2×C3×D5×C1311yescharacteristic, complemented, Sylow
100C2×ΓL(1,𝔽8)—352no—
101AGL(1,𝔽7)—72no—
102AGL(1,𝔽7)—352no—
103C3×C13—491noHall
104C5×C7—32no—
105C5×C7C2×C13×AGL(1,𝔽7)12yescomplemented
106C2×C3×C5—491no—
107C3×D5—491no—
108C3×D5—491no—
109C2×D7—352no—
110C2×D7—1052no—
111C2×C13—51no—
112C2×C13—491no—
113C2×C13—2451no—
114ΓL(1,𝔽8)—72no—
115C2×D5—491noHall
116C3×C5—491noHall
117C2×C7—52no—
118C2×C7—152no—
119D7—72no—
120D7—212no—
121D7—352no—
122D7—1052no—
123C13D5×#6442511yescharacteristic, direct product factor, Sylow
124C22×C3—2451noHall
125C2×C5—491no—
126D5—491no—
127D5C13×#6442511yescharacteristic, direct product factor
128C7—32no—
129C7D5×C13×AGL(1,𝔽7)12yescomplemented
130C2×C3—491no—
131C2×C3—2451no—
132C2×C3—2451no—
133C5C2×C13×#6442511yescharacteristic, complemented, Sylow
134C22—2451noSylow
135C3—491noSylow
136C2—51no—
137C2—491no—
138C2—2451no—
subgroupG/H
center, hypercenterC13D5×#64425
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×#3862C2semidirect
2. C13×C5⋊#64425C2semidirect
3. C5×C13×#64425C2semidirect
4. D5×C13×C7⋊D7C3semidirect
5. C5×C13×#3862C22semidirect
7. C13×C5⋊(C7⋊D7)C2×C3semidirect
8. C72×D5×C13C2×C3semidirect
9. C5×C13×C7⋊D7C2×C3semidirect
13. C13×#64425D5direct (N × H)
14. C5×C72×C13C22×C3semidirect
15. D5×#64425C13direct (N × H)
20. C13×#3862C2×D5semidirect
23. D5×#3862C2×C13semidirect
24. C5⋊#64425C2×C13semidirect
25. C5×#64425C2×C13semidirect
29. C13×C7⋊D7C3×D5semidirect
31. D5×C7⋊D7C3×C13semidirect
35. C7×D5×C13AGL(1,𝔽7)semidirect
39. C5×#3862C22×C13semidirect
40. C72×C13C2×C3×D5semidirect
45. C5⋊(C7⋊D7)C2×C3×C13semidirect
46. C72×D5C2×C3×C13semidirect
47. C5×C7⋊D7C2×C3×C13semidirect
49. C5×C7×C13C2×AGL(1,𝔽7)semidirect
58. #64425D5×C13direct (N × H)
61. C5×C72C22×C3×C13semidirect
74. #3862C2×D5×C13semidirect
79. D5×C13#64425direct (N × H)
83. C7⋊D7C3×D5×C13semidirect
85. C7×C13D5×AGL(1,𝔽7)semidirect
95. C7×D5C13×AGL(1,𝔽7)semidirect
96. C5×C13C2×#64425semidirect
99. C72C2×C3×D5×C13semidirect
105. C5×C7C2×C13×AGL(1,𝔽7)semidirect
123. C13D5×#64425direct (N × H)
127. D5C13×#64425direct (N × H)
129. C7D5×C13×AGL(1,𝔽7)semidirect
133. C5C2×C13×#64425semidirect

Maximal subgroups

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

subgroupindex
D5×C13×#38622
C13×C5⋊#644252
C5×C13×#644252
D5×C13×C7⋊D73
C2×C13×#644255
D5×C13×AGL(1,𝔽7)7
D5×#6442513