Finite Group Databasebeta

← D5×#16838454 #50304209

Subgroups — D5×#16838454 #50304209

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
1D5×C13×#3862C211yesmaximal, characteristic, complemented
2C5⋊#16838454C211yesmaximal, characteristic, complemented
3C5×#16838454C211yesmaximal, characteristic, complemented
4D5×C7⋊D91C311yesmaximal, characteristic, complemented, Hall
5C5×C13×#3862C2211yescharacteristic, complemented, Hall
6C2×#16838454—51nomaximal, Hall
7C5⋊(C7⋊D91)C2×C311yescharacteristic, complemented
8C72×D5×C13C2×C311yescharacteristic, complemented
9C5×C7⋊D91C2×C311yescharacteristic, complemented
10D5×ΓL(1,𝔽8)⋊D13—72nomaximal
11C2×C13×#3862—51no—
12#16838454—51no—
13#16838454D511yescharacteristic, direct product factor
14C5×C72×C13C22×C311yescharacteristic, complemented, Hall
15D5×#64425—131nomaximal, Hall
16C5⋊(ΓL(1,𝔽8)⋊D13)—72no—
17D5×C13×ΓL(1,𝔽8)—72no—
18C5×ΓL(1,𝔽8)⋊D13—72no—
19C2×C7⋊D91—51noHall
20C13×#3862C2×D511yescharacteristic, complemented, Hall
21D5×D91—72no—
22D5×D91—212no—
23D5×#3862D1311yescharacteristic, complemented
24C5⋊#64425—131no—
25C5×#64425—131no—
26C5×C13×ΓL(1,𝔽8)—72no—
27C2×C72×C13—51no—
28C7⋊D91—51no—
29C7⋊D91C3×D511yescharacteristic, complemented
30C2×ΓL(1,𝔽8)⋊D13—352no—
31D5×C7⋊D7—131noHall
32D455—72no—
33D455—212no—
34C7×D5×C13—32no—
35C7×D5×C13AGL(1,𝔽7)12yescomplemented
36C5×D91—72no—
37C5×D91—212no—
38C3×D5×D13—491noHall
39C5×#3862C2×D1311yescharacteristic, complemented, Hall
40C72×C13C2×C3×D511yescharacteristic, complemented, Hall
41C2×#64425—651noHall
42C2×C13×ΓL(1,𝔽8)—352no—
43ΓL(1,𝔽8)⋊D13—72no—
44ΓL(1,𝔽8)⋊D13—352no—
45C5⋊(C7⋊D7)—131no—
46C72×D5C3×D1311yescharacteristic, complemented
47C5×C7⋊D7—131no—
48C5×C7×C13—32no—
49C5×C7×C13C2×AGL(1,𝔽7)12yescomplemented
50D5×AGL(1,𝔽7)—912no—
51C3×D65—491no—
52C3×D5×C13—491no—
53C3×C5×D13—491no—
54C2×D91—352no—
55C2×D91—1052no—
56C2×#3862—51no—
57#64425—131no—
58#64425—651no—
59C13×ΓL(1,𝔽8)—72no—
60D5×D13—491noHall
61C5×C72C2×C3×D1311yescharacteristic, complemented, Hall
62C5⋊AGL(1,𝔽7)—912no—
63D5×ΓL(1,𝔽8)—72no—
64C5×AGL(1,𝔽7)—912no—
65C2×C7⋊D7—651noHall
66C3×C5×C13—491noHall
67C2×C7×C13—52no—
68C2×C7×C13—152no—
69D91—72no—
70D91—212no—
71D91—352no—
72D91—1052no—
73C2×C3×D13—2451noHall
74#3862D5×D1311yescharacteristic, complemented, Hall
75D5×D7—2732no—
76D5×D7—912no—
77D65—491no—
78C5×D13—491no—
79D5×C13#6442511yescharacteristic, complemented
80C5×ΓL(1,𝔽8)—72no—
81C2×C72—51no—
82C7⋊D7—131no—
83C7⋊D7—651no—
84C7×C13—32no—
85C7×C13D5×AGL(1,𝔽7)12yescomplemented
86C2×AGL(1,𝔽7)—4552no—
87C2×C3×C13—2451no—
88C3×D13—491no—
89C3×D13—2451no—
90D35—2732no—
91D35—912no—
92C5×D7—2732no—
93C5×D7—912no—
94C7×D5—32no—
95C7×D5ΓL(1,𝔽8)⋊D1312yescomplemented
96C5×C13C2×#6442511yescharacteristic, complemented, Hall
97C2×C3×D5—6371noHall
98C2×D13—2451noHall
99C72C3×D5×D1311yescharacteristic, complemented, Sylow
100C2×ΓL(1,𝔽8)—352no—
101AGL(1,𝔽7)—912no—
102AGL(1,𝔽7)—4552no—
103C3×C13—491noHall
104C5×C7—32no—
105C5×C7C2×ΓL(1,𝔽8)⋊D1312yescomplemented
106C2×C3×C5—6371no—
107C3×D5—491no—
108C3×D5—6371no—
109C2×D7—13652no—
110C2×D7—4552no—
111C2×C13—51no—
112D13—491no—
113D13—2451no—
114ΓL(1,𝔽8)—72no—
115C2×D5—6371noHall
116C3×C5—491noHall
117C2×C7—52no—
118C2×C7—152no—
119D7—2732no—
120D7—13652no—
121D7—912no—
122D7—4552no—
123C13D5×#6442511yescharacteristic, complemented, Sylow
124C22×C3—31851noHall
125C2×C5—6371no—
126D5—6371no—
127D5#1683845411yescharacteristic, direct product factor
128C7—32no—
129C7D5×ΓL(1,𝔽8)⋊D1312yescomplemented
130C2×C3—31851no—
131C2×C3—6371no—
132C2×C3—2451no—
133C5C2×#1683845411yescharacteristic, complemented, Sylow
134C22—31851noSylow
135C3—491noSylow
136C2—51no—
137C2—31851no—
138C2—6371no—
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×C13×#3862C2semidirect
2. C5⋊#16838454C2semidirect
3. C5×#16838454C2semidirect
4. D5×C7⋊D91C3semidirect
5. C5×C13×#3862C22semidirect
7. C5⋊(C7⋊D91)C2×C3semidirect
8. C72×D5×C13C2×C3semidirect
9. C5×C7⋊D91C2×C3semidirect
13. #16838454D5direct (N × H)
14. C5×C72×C13C22×C3semidirect
20. C13×#3862C2×D5semidirect
23. D5×#3862D13semidirect
29. C7⋊D91C3×D5semidirect
35. C7×D5×C13AGL(1,𝔽7)semidirect
39. C5×#3862C2×D13semidirect
40. C72×C13C2×C3×D5semidirect
46. C72×D5C3×D13semidirect
49. C5×C7×C13C2×AGL(1,𝔽7)semidirect
61. C5×C72C2×C3×D13semidirect
74. #3862D5×D13semidirect
79. D5×C13#64425semidirect
85. C7×C13D5×AGL(1,𝔽7)semidirect
95. C7×D5ΓL(1,𝔽8)⋊D13semidirect
96. C5×C13C2×#64425semidirect
99. C72C3×D5×D13semidirect
105. C5×C7C2×ΓL(1,𝔽8)⋊D13semidirect
123. C13D5×#64425semidirect
127. D5#16838454direct (N × H)
129. C7D5×ΓL(1,𝔽8)⋊D13semidirect
133. C5C2×#16838454semidirect

Maximal subgroups

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

subgroupindex
D5×C13×#38622
C5⋊#168384542
C5×#168384542
D5×C7⋊D913
C2×#168384545
D5×ΓL(1,𝔽8)⋊D137
D5×#6442513