Finite Group Databasebeta

← D35×C3⋊D69 #44394652

Subgroups — D35×C3⋊D69 #44394652

Order 28980.

240 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C32×C23×D35C211yesmaximal, characteristic, complemented
2C5×C7×C3⋊D69C211yesmaximal, characteristic, complemented
3C3⋊D2415C211yesmaximal, characteristic, complemented
4D35×D69—34nomaximal
5C32×C5×C7×C23C2211yescharacteristic, complemented, Hall
6D7×C3⋊D69—51nomaximal, Hall
7D2415—34no—
8C5×C7×D69—34no—
9C3×C23×D35D314yescomplemented
10D5×C3⋊D69—71nomaximal, Hall
11D23×D35—91noHall
12C3⋊D483—51no—
13C7×C3⋊D69D511yescharacteristic, complemented
14C32×D7×C23—51no—
15C3×C5×C7×C23C2×D314yescomplemented
16C3⋊D345—71no—
17C5×C3⋊D69D711yescharacteristic, complemented
18C32×D5×C23—71no—
19D7×D69—154no—
20D805—91no—
21C23×D35C3⋊D311yescharacteristic, complemented
22C5×C7×D23—91no—
23C32×C7×C23C2×D511yescharacteristic, complemented, Hall
24D5×D69—214no—
25C3⋊D3×D35—231nomaximal, Hall
26C32×C5×C23C2×D711yescharacteristic, complemented, Hall
27D483—154no—
28C7×D69—34no—
29C3×D7×C23—54no—
30C2×C3⋊D69—351noHall
31C5×C7×C23C2×C3⋊D311yescharacteristic, complemented, Hall
32D345—214no—
33C5×D69—34no—
34C3×D5×C23—74no—
35D7×D23—451noHall
36C3⋊D105—231no—
37C5×C7×C3⋊D3—231no—
38C32×D35D2311yescharacteristic, complemented
39C3×C7×C23D3×D514yescomplemented
40D5×D23—631noHall
41D3×D35—694no—
42C2×C32×C23—351no—
43C3⋊D69—351no—
44C3⋊D69D3511yescharacteristic, direct product factor
45C3×C5×C23D3×D714yescomplemented
46D161—451no—
47C7×D23—91no—
48D7×C23—51no—
49C32×C5×C7C2×D2311yescharacteristic, complemented, Hall
50C2×D69—1054no—
51D7×C3⋊D3—1151noHall
52D115—631no—
53C5×D23—91no—
54D5×C23—71no—
55D105—694no—
56C5×D3×C7—694no—
57C3×D35D6914yescomplemented
58C32×C23C2×D3511yescharacteristic, complemented, Hall
59D5×C3⋊D3—1611noHall
60C7×C23D5×C3⋊D311yescharacteristic, complemented, Hall
61C2×D35—2071noHall
62C2×C3×C23—354no—
63D69—34no—
64D69—1054no—
65C3⋊D21—1151no—
66C7×C3⋊D3—231no—
67C32×D7—51no—
68C5×C23D7×C3⋊D311yescharacteristic, complemented, Hall
69C3×C5×C7C2×D6914yescomplemented
70C2×D23—3151noHall
71C3⋊D15—1611no—
72C5×C3⋊D3—231no—
73C32×D5—71no—
74D3×D7—3454no—
75C2×C5×C7—2071no—
76D35—2071no—
77D35C3⋊D6911yescharacteristic, direct product factor
78C3×C23D3×D3514yescomplemented
79C32×C7D5×D2311yescharacteristic, complemented, Hall
80D3×D5—4834no—
81C2×C23—351no—
82D23—91no—
83D23—3151no—
84C32×C5D7×D2311yescharacteristic, complemented, Hall
85D21—3454no—
86C3×D7—54no—
87D3×C7—694no—
88C2×C3⋊D3—8051noHall
89C5×C7C2×C3⋊D6911yescharacteristic, complemented, Hall
90D15—4834no—
91C3×D5—74no—
92C5×D3—694no—
93C2×D7—10351noHall
94C23C3⋊D3×D3511yescharacteristic, complemented, Sylow
95C3×C7D5×D6914yescomplemented
96C2×D5—14491noHall
97C2×C32—351no—
98C3⋊D3—231no—
99C3⋊D3—8051no—
100C3×C5D7×D6914yescomplemented
101C2×C7—2071no—
102D7—51no—
103D7—10351no—
104C2×D3—24154no—
105C2×C5—2071no—
106D5—71no—
107D5—14491no—
108C32D23×D3511yescharacteristic, complemented, Sylow
109C7D5×C3⋊D6911yescharacteristic, complemented, Sylow
110C2×C3—354no—
111D3—694no—
112D3—24154no—
113C5D7×C3⋊D6911yescharacteristic, complemented, Sylow
114C22—72451noSylow
115C3D35×D6914yescomplemented
116C2—351no—
117C2—72451no—
118C2—2071no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C23C22
LCSG ▷ C32×C5×C7×C23
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C23×D35C2semidirect
2. C5×C7×C3⋊D69C2semidirect
3. C3⋊D2415C2semidirect
5. C32×C5×C7×C23C22semidirect
9. C3×C23×D35D3semidirect
13. C7×C3⋊D69D5semidirect
15. C3×C5×C7×C23C2×D3semidirect
17. C5×C3⋊D69D7semidirect
21. C23×D35C3⋊D3semidirect
23. C32×C7×C23C2×D5semidirect
26. C32×C5×C23C2×D7semidirect
31. C5×C7×C23C2×C3⋊D3semidirect
38. C32×D35D23semidirect
39. C3×C7×C23D3×D5semidirect
44. C3⋊D69D35direct (N × H)
45. C3×C5×C23D3×D7semidirect
49. C32×C5×C7C2×D23semidirect
57. C3×D35D69semidirect
58. C32×C23C2×D35semidirect
60. C7×C23D5×C3⋊D3semidirect
68. C5×C23D7×C3⋊D3semidirect
69. C3×C5×C7C2×D69semidirect
77. D35C3⋊D69direct (N × H)
78. C3×C23D3×D35semidirect
79. C32×C7D5×D23semidirect
84. C32×C5D7×D23semidirect
89. C5×C7C2×C3⋊D69semidirect
94. C23C3⋊D3×D35semidirect
95. C3×C7D5×D69semidirect
100. C3×C5D7×D69semidirect
108. C32D23×D35semidirect
109. C7D5×C3⋊D69semidirect
113. C5D7×C3⋊D69semidirect
115. C3D35×D69semidirect

Maximal subgroups

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

subgroupindex
C32×C23×D352
C5×C7×C3⋊D692
C3⋊D24152
D35×D693
D7×C3⋊D695
D5×C3⋊D697
C3⋊D3×D3523