Finite Group Databasebeta

← D15×C7⋊D91 #50304449

Subgroups — D15×C7⋊D91 #50304449

Order 38220.

400 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C3×C5×C7⋊D91C211yesmaximal, characteristic, complemented
2C72×C13×D15C211yesmaximal, characteristic, complemented
3C3⋊(C5⋊(C7⋊D91))C211yesmaximal, characteristic, complemented
4D5×C7⋊D91—31nomaximal, Hall
5C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
6D3×C7⋊D91—51nomaximal, Hall
7C5⋊(C7⋊D91)—31no—
8C72×D5×C13—31no—
9C5×C7⋊D91D311yescharacteristic, complemented
10D15×D91—78nomaximal
11C3⋊(C7⋊D91)—51no—
12D3×C72×C13—51no—
13C3×C7⋊D91D511yescharacteristic, complemented
14C5×C72×C13C2×D311yescharacteristic, complemented, Hall
15D15×C7⋊D7—131nomaximal, Hall
16D1365—78no—
17C7×C13×D15D718yescomplemented
18C3×C5×D91—78no—
19C2×C7⋊D91—151noHall
20C3×C72×C13C2×D511yescharacteristic, complemented, Hall
21D5×D91—218no—
22C3⋊(C5⋊(C7⋊D7))—131no—
23C72×D15D1311yescharacteristic, complemented
24C3×C5×C7⋊D7—131no—
25C3×C5×C7×C13C2×D718yescomplemented
26C2×C72×C13—151no—
27C7⋊D91—151no—
28C7⋊D91D1511yescharacteristic, direct product factor
29D3×D91—358no—
30D5×C7⋊D7—391noHall
31D455—218no—
32C7×D5×C13—38no—
33C5×D91—78no—
34D13×D15—491noHall
35C3×C5×C72C2×D1311yescharacteristic, complemented, Hall
36C72×C13C2×D1511yescharacteristic, complemented, Hall
37D3×C7⋊D7—651noHall
38D273—358no—
39D3×C7×C13—58no—
40C3×D91—78no—
41C5⋊(C7⋊D7)—391no—
42C72×D5—31no—
43C5×C7⋊D7—131no—
44C5×C7×C13D3×D718yescomplemented
45D7×D15—918no—
46D195—491no—
47C13×D15C7⋊D711yescharacteristic, complemented
48C3×C5×D13—491no—
49C2×D91—1058no—
50C3⋊(C7⋊D7)—651no—
51D3×C72—51no—
52C3×C7⋊D7—131no—
53C3×C7×C13D5×D718yescomplemented
54D5×D13—1471noHall
55C5×C72D3×D1311yescharacteristic, complemented, Hall
56D105—918no—
57C7×D15D9118yescomplemented
58C3×C5×D7—918no—
59C2×C7⋊D7—1951noHall
60C3×C5×C13C2×C7⋊D711yescharacteristic, complemented, Hall
61C2×C7×C13—158no—
62D91—78no—
63D91—1058no—
64D3×D13—2451noHall
65C3×C72D5×D1311yescharacteristic, complemented, Hall
66D5×D7—2738no—
67D65—1471no—
68C5×D13—491no—
69D5×C13—31no—
70C3×C5×C7C2×D9118yescomplemented
71C2×C72—151no—
72C7⋊D7—131no—
73C7⋊D7—1951no—
74C7×C13D7×D1518yescomplemented
75D3×D7—4558no—
76D39—2451no—
77C3×D13—491no—
78D3×C13—51no—
79D35—2738no—
80C5×D7—918no—
81C7×D5—38no—
82C5×C13D3×C7⋊D711yescharacteristic, complemented, Hall
83C2×D15—6371noHall
84C2×D13—7351noHall
85C72D13×D1511yescharacteristic, complemented, Sylow
86D21—4558no—
87C3×D7—918no—
88D3×C7—58no—
89C3×C13D5×C7⋊D711yescharacteristic, complemented, Hall
90C5×C7D3×D9118yescomplemented
91C2×C3×C5—6371no—
92D15—6371no—
93D15C7⋊D9111yescharacteristic, direct product factor
94C2×D7—13658no—
95C2×C13—151no—
96D13—491no—
97D13—7351no—
98C3×C7D5×D9118yescomplemented
99C2×D5—19111noHall
100C3×C5C2×C7⋊D9111yescharacteristic, complemented, Hall
101C2×C7—158no—
102D7—13658no—
103D7—918no—
104C13D15×C7⋊D711yescharacteristic, complemented, Sylow
105C2×D3—31851noHall
106C2×C5—6371no—
107D5—31no—
108D5—19111no—
109C7D15×D9118yescomplemented
110C2×C3—6371no—
111D3—51no—
112D3—31851no—
113C5D3×C7⋊D9111yescharacteristic, complemented, Sylow
114C22—95551noSylow
115C3D5×C7⋊D9111yescharacteristic, complemented, Sylow
116C2—151no—
117C2—95551no—
118C2—6371no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C72×C13C22
LCSG ▷ C3×C5×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7⋊D91C2semidirect
2. C72×C13×D15C2semidirect
3. C3⋊(C5⋊(C7⋊D91))C2semidirect
5. C3×C5×C72×C13C22semidirect
9. C5×C7⋊D91D3semidirect
13. C3×C7⋊D91D5semidirect
14. C5×C72×C13C2×D3semidirect
17. C7×C13×D15D7semidirect
20. C3×C72×C13C2×D5semidirect
23. C72×D15D13semidirect
25. C3×C5×C7×C13C2×D7semidirect
28. C7⋊D91D15direct (N × H)
35. C3×C5×C72C2×D13semidirect
36. C72×C13C2×D15semidirect
44. C5×C7×C13D3×D7semidirect
47. C13×D15C7⋊D7semidirect
53. C3×C7×C13D5×D7semidirect
55. C5×C72D3×D13semidirect
57. C7×D15D91semidirect
60. C3×C5×C13C2×C7⋊D7semidirect
65. C3×C72D5×D13semidirect
70. C3×C5×C7C2×D91semidirect
74. C7×C13D7×D15semidirect
82. C5×C13D3×C7⋊D7semidirect
85. C72D13×D15semidirect
89. C3×C13D5×C7⋊D7semidirect
90. C5×C7D3×D91semidirect
93. D15C7⋊D91direct (N × H)
98. C3×C7D5×D91semidirect
100. C3×C5C2×C7⋊D91semidirect
104. C13D15×C7⋊D7semidirect
109. C7D15×D91semidirect
113. C5D3×C7⋊D91semidirect
115. C3D5×C7⋊D91semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7⋊D912
C72×C13×D152
C3⋊(C5⋊(C7⋊D91))2
D5×C7⋊D913
D3×C7⋊D915
D15×D917
D15×C7⋊D713