Finite Group Databasebeta

← C3×D5×D28 #13132643

Subgroups — C3×D5×D28 #13132643

Order 1680.

216 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C2×C3×D5×D7C212yesmaximal, complemented
2C3×D140C211yesmaximal, characteristic, complemented
3C3×C4×C7×D5C211yesmaximal, characteristic, complemented
4C3×C5×D28C211yesmaximal, characteristic, complemented
5C3×#63306C212yesmaximal, complemented
6D5×D28C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×D35C2212yescomplemented
8C2×C3×C7×D5C2211yescharacteristic
9C2×C3×C5×D7C2212yescomplemented
10C3×D5×D7—24no—
11C3×C4×C5×C7C2211yescharacteristic, complemented
12C3×C7×Dic5C2211yescharacteristic, complemented
13C2×C3×D28—51nomaximal, Hall
14C2×D5×D7C2×C312yescomplemented
15D140C2×C311yescharacteristic, complemented
16C4×C7×D5C2×C311yescharacteristic, complemented
17C5×D28C2×C311yescharacteristic, complemented
18#63306C2×C312yescomplemented
19C3×D4×D5—71nomaximal, Hall
20C2×C3×C5×C7C2311yescharacteristic
21C3×D35—22no—
22C3×C7×D5D412yescomplemented
23C3×C5×D7—22no—
24C22×C3×D7—52no—
25C2×C3×C4×C7—51no—
26C3×D28—52no—
27C3×D28—51no—
28C3×D28D511yescharacteristic, direct product factor
29C2×D35C22×C312yescomplemented
30C2×C7×D5C22×C311yescharacteristic
31C2×C5×D7C22×C312yescomplemented
32D5×D7—24no—
33C4×C5×C7C22×C311yescharacteristic, complemented
34C7×Dic5C22×C311yescharacteristic, complemented
35C22×C3×D5—72no—
36C3×C5×D4—71no—
37C3×C22⋊D5—72no—
38C3×D20—71no—
39C3×C4×D5D711yescharacteristic, complemented
40C2×D28—51noHall
41C3×C5×C7C2×D411yescharacteristic, complemented, Hall
42C22×C3×C7—51no—
43C2×C3×D7—52no—
44C2×C3×D7—104no—
45C2×C3×D7C2×D512yescomplemented
46C3×C4×C7—51no—
47C3×C4×C7C2×D511yescharacteristic, complemented
48D4×D5—71noHall
49C2×C5×C7C23×C311yescharacteristic
50D35—22no—
51C5×D7—22no—
52C7×D5C3×D412yescomplemented
53C22×C3×C5—72no—
54C2×C3×D5—72no—
55C2×C3×D5—144no—
56C2×C3×D5C2×D711yescharacteristic
57C3×C4×C5C2×D711yescharacteristic, complemented
58C3×Dic5C2×D711yescharacteristic, complemented
59C22×D7—52no—
60C2×C4×C7—51no—
61D28—52no—
62D28—51no—
63D28C3×D511yescharacteristic, direct product factor
64C2×C3×D4—351noHall
65C2×C3×C7—52no—
66C2×C3×C7C22×D511yescharacteristic
67C3×D7—22no—
68C3×D7—102no—
69C22×D5—72no—
70C5×D4—71no—
71C22⋊D5—72no—
72D20—71no—
73C4×D5C3×D711yescharacteristic, complemented
74C5×C7C2×C3×D411yescharacteristic, complemented, Hall
75C2×C3×C5—142no—
76C2×C3×C5C22×D711yescharacteristic
77C3×D5—142no—
78C3×D5D2812yesdirect product factor
79C22×C7—51no—
80C2×D7—52no—
81C2×D7—104no—
82C2×D7C2×C3×D512yescomplemented
83C4×C7—51no—
84C4×C7C2×C3×D511yescharacteristic, complemented
85C23×C3—352no—
86C3×D4—71no—
87C3×D4—352no—
88C3×D4—351no—
89C2×C3×C4—51no—
90C3×C7D4×D511yescharacteristic, complemented, Hall
91C22×C5—72no—
92C2×D5—72no—
93C2×D5—144no—
94C2×D5C2×C3×D711yescharacteristic
95C4×C5C2×C3×D711yescharacteristic, complemented
96Dic5C2×C3×D711yescharacteristic, complemented
97C2×D4—351noSylow
98C3×C5C2×D2811yescharacteristic, complemented, Hall
99C2×C7—52no—
100C2×C7C22×C3×D511yescharacteristic
101D7—22no—
102D7—102no—
103C22×C3—51no—
104C22×C3—72no—
105C22×C3—352no—
106C22×C3—704no—
107C3×C4—51no—
108C3×C4D5×D711yescharacteristic, complemented
109C2×C5—142no—
110C2×C5C22×C3×D711yescharacteristic
111D5—142no—
112D5C3×D2812yesdirect product factor
113C23—352no—
114D4—71no—
115D4—352no—
116D4—351no—
117C2×C4—51no—
118C7C3×D4×D511yescharacteristic, complemented, Sylow
119C2×C3—52no—
120C2×C3—142no—
121C2×C3—702no—
122C2×C3C2×D5×D711yescharacteristic
123C5C2×C3×D2811yescharacteristic, complemented, Sylow
124C22—51no—
125C22—72no—
126C22—352no—
127C22—704no—
128C4—51no—
129C4C3×D5×D711yescharacteristic, complemented
130C3D5×D2811yescharacteristic, direct product factor, Sylow
131C2—52no—
132C2—142no—
133C2—702no—
134C2C2×C3×D5×D711yescharacteristic
subgroupG/H
centerC2×C3C2×D5×D7
commutator, cosocleC2×C5×C7C23×C3
FrattiniC2C2×C3×D5×D7
FittingC3×C4×C5×C7C22
socleC2×C3×C5×C7C23
hypercenterC3×C4D5×D7
hypocenterC5×C7C2×C3×D4
LCSG ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D5×D7C2semidirect
2. C3×D140C2semidirect
3. C3×C4×C7×D5C2semidirect
4. C3×C5×D28C2semidirect
5. C3×#63306C2semidirect
6. D5×D28C3direct (N × H)
7. C2×C3×D35C22semidirect
9. C2×C3×C5×D7C22semidirect
11. C3×C4×C5×C7C22semidirect
12. C3×C7×Dic5C22semidirect
14. C2×D5×D7C2×C3semidirect
15. D140C2×C3semidirect
16. C4×C7×D5C2×C3semidirect
17. C5×D28C2×C3semidirect
18. #63306C2×C3semidirect
22. C3×C7×D5D4semidirect
28. C3×D28D5direct (N × H)
29. C2×D35C22×C3semidirect
31. C2×C5×D7C22×C3semidirect
33. C4×C5×C7C22×C3semidirect
34. C7×Dic5C22×C3semidirect
39. C3×C4×D5D7semidirect
41. C3×C5×C7C2×D4semidirect
45. C2×C3×D7C2×D5semidirect
47. C3×C4×C7C2×D5semidirect
52. C7×D5C3×D4semidirect
57. C3×C4×C5C2×D7semidirect
58. C3×Dic5C2×D7semidirect
63. D28C3×D5direct (N × H)
73. C4×D5C3×D7semidirect
74. C5×C7C2×C3×D4semidirect
78. C3×D5D28direct (N × H)
82. C2×D7C2×C3×D5semidirect
84. C4×C7C2×C3×D5semidirect
90. C3×C7D4×D5semidirect
95. C4×C5C2×C3×D7semidirect
96. Dic5C2×C3×D7semidirect
98. C3×C5C2×D28semidirect
108. C3×C4D5×D7semidirect
112. D5C3×D28direct (N × H)
118. C7C3×D4×D5semidirect
123. C5C2×C3×D28semidirect
129. C4C3×D5×D7semidirect
130. C3D5×D28direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×D72
C3×D1402
C3×C4×C7×D52
C3×C5×D282
C3×#633062
D5×D283
C2×C3×D285
C3×D4×D57