Finite Group Databasebeta

← C5×D15×D49 #28412979

Subgroups — C5×D15×D49 #28412979

Order 14700.

144 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 42 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×D735C211yesmaximal, characteristic, complemented
2C5×D15×C49C211yesmaximal, characteristic, complemented
3C3×C52×D49C211yesmaximal, characteristic, complemented
4C5×D5×D49—31nomaximal, Hall
5C3×C52×C49C2211yescharacteristic, complemented, Hall
6D15×D49C511yesmaximal, characteristic, direct product factor
7C5×D3×D49—51nomaximal
8C5×D245—31no—
9C5×D5×C49—31no—
10C52×D49D311yescharacteristic, complemented
11C5×D7×D15—71nomaximal
12D735C2×C511yescharacteristic, complemented
13D15×C49C2×C511yescharacteristic, complemented
14C5×D147—51no—
15C5×D3×C49—51no—
16C3×C5×D49—22no—
17C3×C5×D49D511yescharacteristic, complemented
18C3×C5×D49C2×C511yescharacteristic, complemented
19C52×C49C2×D311yescharacteristic, complemented, Hall
20C5×D105—71no—
21C5×C7×D15D711yescharacteristic
22C3×C52×D7—71no—
23C2×C5×D49—151no—
24D5×D49—31no—
25C3×C5×C49—22no—
26C3×C5×C49C2×D511yescharacteristic, complemented
27C3×C5×C49C22×C511yescharacteristic, complemented
28C5×D5×D7—211no—
29D3×D49—51noHall
30C3×C52×C7C2×D711yescharacteristic
31C2×C5×C49—151no—
32D245—31no—
33C5×D49—22no—
34C5×D49—151no—
35C5×D49C5×D311yescharacteristic, complemented
36C5×D49D1511yescharacteristic, direct product factor
37D5×C49—31no—
38D7×D15—71no—
39C5×D3×D7—351no—
40C5×D35—211no—
41C5×C7×D5—31no—
42C52×D7—71no—
43C2×C5×D15—491noHall
44D147—51no—
45C3×D49C5×D511yescharacteristic, complemented
46D3×C49—51no—
47C5×C49—22no—
48C5×C49C2×C5×D311yescharacteristic, complemented
49C5×C49C2×D1511yescharacteristic, complemented
50D105—71no—
51C7×D15C5×D711yescharacteristic
52C5×D21—351no—
53C5×D3×C7—51no—
54C3×C5×D7—71no—
55C3×C5×D7—71no—
56C3×C5×D7—142no—
57C2×D49—151noHall
58C52×C7D3×D711yescharacteristic
59C2×C3×C52—491no—
60C5×D15—491no—
61C5×D15D4911yescharacteristic, direct product factor
62C3×C49C2×C5×D511yescharacteristic, complemented, Hall
63C2×C5×D7—1051no—
64D5×D7—211no—
65C3×C5×C7—22no—
66C3×C5×C7D5×D711yescharacteristic
67C3×C5×C7C2×C5×D711yescharacteristic
68C2×C5×D5—1471noHall
69C2×C49—151no—
70D49—151no—
71D49C5×D1511yescharacteristic, direct product factor
72D3×D7—351no—
73C3×C52C2×D4911yescharacteristic, complemented, Hall
74C2×C5×C7—151no—
75D35—211no—
76C5×D7—71no—
77C5×D7—71no—
78C5×D7—142no—
79C5×D7—1051no—
80C7×D5—31no—
81C2×D15—491no—
82C2×C5×D3—2451no—
83C2×C52—491no—
84C5×D5—31no—
85C5×D5—1471no—
86C49C2×C5×D1511yescharacteristic, complemented, Sylow
87D21—351no—
88C3×D7—71no—
89D3×C7—51no—
90C5×C7—22no—
91C5×C7C5×D3×D711yescharacteristic
92C5×C7D7×D1511yescharacteristic
93C2×C3×C5—491no—
94C2×C3×C5—491no—
95C2×C3×C5—982no—
96D15—491no—
97D15C5×D4911yescharacteristic, direct product factor
98C5×D3—51no—
99C5×D3—2451no—
100C2×D7—1051no—
101C52D3×D4911yescharacteristic, complemented, Sylow
102C3×C7C5×D5×D711yescharacteristic
103C22×C5—7351no—
104C2×D5—1471no—
105C3×C5—22no—
106C3×C5D5×D4911yescharacteristic, complemented
107C3×C5C2×C5×D4911yescharacteristic, complemented
108C2×C7—151no—
109D7—71no—
110D7—1051no—
111C2×D3—2451noHall
112C2×C5—151no—
113C2×C5—491no—
114C2×C5—491no—
115C2×C5—982no—
116C2×C5—7351no—
117D5—31no—
118D5—1471no—
119C7C5×D7×D1511yescharacteristic
120C2×C3—491no—
121D3—51no—
122D3—2451no—
123C5—22no—
124C5C5×D3×D4911yescharacteristic, complemented
125C5D15×D4911yescharacteristic, direct product factor
126C22—7351noSylow
127C3C5×D5×D4911yescharacteristic, complemented, Sylow
128C2—151no—
129C2—491no—
130C2—7351no—
subgroupG/H
center, hypercenterC5D15×D49
commutator, cosocle, hypocenterC3×C5×C49C22×C5
FrattiniC7C5×D7×D15
FittingC3×C52×C49C22
socleC3×C52×C7C2×D7
LCSG ▷ C3×C5×C49
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×D735C2semidirect
2. C5×D15×C49C2semidirect
3. C3×C52×D49C2semidirect
5. C3×C52×C49C22semidirect
6. D15×D49C5direct (N × H)
10. C52×D49D3semidirect
12. D735C2×C5semidirect
13. D15×C49C2×C5semidirect
17. C3×C5×D49D5semidirect
18. C3×C5×D49C2×C5semidirect
19. C52×C49C2×D3semidirect
26. C3×C5×C49C2×D5semidirect
27. C3×C5×C49C22×C5semidirect
35. C5×D49C5×D3semidirect
36. C5×D49D15direct (N × H)
45. C3×D49C5×D5semidirect
48. C5×C49C2×C5×D3semidirect
49. C5×C49C2×D15semidirect
61. C5×D15D49direct (N × H)
62. C3×C49C2×C5×D5semidirect
71. D49C5×D15direct (N × H)
73. C3×C52C2×D49semidirect
86. C49C2×C5×D15semidirect
97. D15C5×D49direct (N × H)
101. C52D3×D49semidirect
106. C3×C5D5×D49semidirect
107. C3×C5C2×C5×D49semidirect
124. C5C5×D3×D49semidirect
125. C5D15×D49direct (N × H)
127. C3C5×D5×D49semidirect

Maximal subgroups

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

subgroupindex
C5×D7352
C5×D15×C492
C3×C52×D492
C5×D5×D493
D15×D495
C5×D3×D495
C5×D7×D157