Finite Group Databasebeta

← D15×C5⋊(C7⋊D7) #28413547

Subgroups — D15×C5⋊(C7⋊D7) #28413547

Order 14700.

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

normal subgroups only

This group has 480 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⋊(C5⋊(C7⋊D7)))C211yesmaximal, characteristic, complemented
2C5×C72×D15C211yesmaximal, characteristic, complemented
3C3×C5×C5⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
4D5×C5⋊(C7⋊D7)—31nomaximal, Hall
5C3×C52×C72C2211yescharacteristic, complemented, Hall
6D3×C5⋊(C7⋊D7)—51nomaximal
7D15×C7⋊D7—51nomaximal
8C5⋊(C5⋊(C7⋊D7))—31no—
9C5×C5⋊(C7⋊D7)D311yescharacteristic, complemented
10C5×C72×D5—31no—
11D15×D35—78nomaximal
12C3⋊(C5⋊(C7⋊D7))—51no—
13C3⋊(C5⋊(C7⋊D7))—51no—
14C3⋊(C5⋊(C7⋊D7))—102no—
15C72×D15D511yescharacteristic, complemented
16C5×D3×C72—51no—
17C3×C5⋊(C7⋊D7)D511yescharacteristic, complemented
18C3×C5×C7⋊D7—51no—
19C52×C72C2×D311yescharacteristic, complemented, Hall
20C3⋊(C5⋊D35)—78no—
21C5×C7×D15D718yescomplemented
22C3×C5×D35—78no—
23C2×C5⋊(C7⋊D7)—151no—
24D5×C7⋊D7—151no—
25C3×C5×C72—22no—
26C3×C5×C72C2×D511yescharacteristic, complemented
27C3×C5×C72C2×D511yescharacteristic, complemented
28D5×D35—218no—
29D3×C7⋊D7—251noHall
30C3×C52×C7C2×D718yescomplemented
31C2×C5×C72—151no—
32C5⋊(C7⋊D7)—151no—
33C5⋊(C7⋊D7)—151no—
34C5⋊(C7⋊D7)—302no—
35C5⋊(C7⋊D7)D1511yescharacteristic, direct product factor
36C72×D5—31no—
37C5×C7⋊D7—51no—
38D3×D35—358no—
39D7×D15—358no—
40C5⋊D35—218no—
41C5×D35—78no—
42C5×C7×D5—38no—
43D5×D15—491noHall
44C3⋊(C7⋊D7)—251no—
45D3×C72—51no—
46C3×C7⋊D7—51no—
47C5×C72—22no—
48C5×C72D3×D511yescharacteristic, complemented
49C5×C72C2×D1511yescharacteristic, complemented
50D105—358no—
51D105—358no—
52D105—7016no—
53C7×D15D3518yescomplemented
54C5×D3×C7—58no—
55C3×D35—78no—
56C3×C5×D7—358no—
57C2×C7⋊D7—751noHall
58C52×C7D3×D718yescomplemented
59C3⋊(C5⋊D5)—491no—
60C5×D15C7⋊D711yescharacteristic, complemented
61C3×C5×D5—491no—
62C3×C72D5211yescharacteristic, complemented, Hall
63C2×D35—1058no—
64D5×D7—1058no—
65C3×C5×C7—216no—
66C3×C5×C7D5×D718yescomplemented
67C3×C5×C7C2×D3518yescomplemented
68D52—1471noHall
69C2×C72—151no—
70C7⋊D7—51no—
71C7⋊D7—751no—
72D3×D7—1758no—
73C3×C52C2×C7⋊D711yescharacteristic, complemented, Hall
74C2×C5×C7—158no—
75D35—78no—
76D35—1058no—
77D35—1058no—
78D35—21016no—
79C5×D7—358no—
80C7×D5—38no—
81C2×D15—2451no—
82D3×D5—2451no—
83C5⋊D5—1471no—
84C5×D5—31no—
85C5×D5—491no—
86C72D5×D1511yescharacteristic, complemented, Sylow
87D21—1758no—
88C3×D7—358no—
89D3×C7—58no—
90C5×C7—216no—
91C5×C7D7×D1518yescomplemented
92C5×C7D3×D3518yescomplemented
93C2×C3×C5—2451no—
94D15—4902no—
95D15—2451no—
96D15—2451no—
97D15C5⋊(C7⋊D7)11yescharacteristic, direct product factor
98C3×D5—491no—
99C5×D3—51no—
100C2×D7—5258no—
101C52D3×C7⋊D711yescharacteristic, complemented, Sylow
102C3×C7D5×D3518yescomplemented
103C2×D5—7351no—
104C2×D5—7351no—
105C3×C5—22no—
106C3×C5D5×C7⋊D711yescharacteristic, complemented
107C3×C5C2×C5⋊(C7⋊D7)11yescharacteristic, complemented
108C2×C7—158no—
109D7—5258no—
110D7—358no—
111C2×D3—12251noHall
112C2×C5—151no—
113C2×C5—2451no—
114D5—31no—
115D5—491no—
116D5—14702no—
117D5—7351no—
118D5—7351no—
119C7D15×D3518yescomplemented
120C2×C3—2451no—
121D3—51no—
122D3—12251no—
123C5—22no—
124C5D15×C7⋊D711yescharacteristic, complemented
125C5D3×C5⋊(C7⋊D7)11yescharacteristic, complemented
126C22—36751noSylow
127C3D5×C5⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
128C2—151no—
129C2—36751no—
130C2—2451no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C72C22
LCSG ▷ C3×C52×C72
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C5⋊(C5⋊(C7⋊D7)))C2semidirect
2. C5×C72×D15C2semidirect
3. C3×C5×C5⋊(C7⋊D7)C2semidirect
5. C3×C52×C72C22semidirect
9. C5×C5⋊(C7⋊D7)D3semidirect
15. C72×D15D5semidirect
17. C3×C5⋊(C7⋊D7)D5semidirect
19. C52×C72C2×D3semidirect
21. C5×C7×D15D7semidirect
26. C3×C5×C72C2×D5semidirect
27. C3×C5×C72C2×D5semidirect
30. C3×C52×C7C2×D7semidirect
35. C5⋊(C7⋊D7)D15direct (N × H)
48. C5×C72D3×D5semidirect
49. C5×C72C2×D15semidirect
53. C7×D15D35semidirect
58. C52×C7D3×D7semidirect
60. C5×D15C7⋊D7semidirect
62. C3×C72D52semidirect
66. C3×C5×C7D5×D7semidirect
67. C3×C5×C7C2×D35semidirect
73. C3×C52C2×C7⋊D7semidirect
86. C72D5×D15semidirect
91. C5×C7D7×D15semidirect
92. C5×C7D3×D35semidirect
97. D15C5⋊(C7⋊D7)direct (N × H)
101. C52D3×C7⋊D7semidirect
102. C3×C7D5×D35semidirect
106. C3×C5D5×C7⋊D7semidirect
107. C3×C5C2×C5⋊(C7⋊D7)semidirect
119. C7D15×D35semidirect
124. C5D15×C7⋊D7semidirect
125. C5D3×C5⋊(C7⋊D7)semidirect
127. C3D5×C5⋊(C7⋊D7)semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C5⋊(C5⋊(C7⋊D7)))2
C5×C72×D152
C3×C5×C5⋊(C7⋊D7)2
D5×C5⋊(C7⋊D7)3
D3×C5⋊(C7⋊D7)5
D15×C7⋊D75
D15×D357