Finite Group Databasebeta

← #72269601

Subgroups — #72269601

Order 3240.

432 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 19 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
1#13108557C211yesmaximal, characteristic
2#13108537C211yesmaximal, characteristic, complemented
3C5×#66472C211yesmaximal, characteristic, complemented
4C5×C3⋊(C3⋊(C3⋊D3))C2211yescharacteristic
5C32×C3⋊D15C412yescomplemented
6#10620198—51nomaximal, Hall
7D15⋊(C3⋊D3)—64no—
8C34×C5C2×C411yescharacteristic, complemented, Hall
9D5×#157—92nomaximal
10C3⋊D32—51no—
11#66472—51no—
12#66472D511yescharacteristic, complemented
13C5×C3⋊(C3⋊D3)—64no—
14C5×C3⋊(C3⋊D3)—128no—
15C3×C3⋊D15—24no—
16C32×D15—64no—
17(C3⋊D3)⋊D5—188no—
18D5×C3⋊D3—92no—
19#4379—92no—
20#4379—184no—
21C5×#157—92no—
22C5×#157—184no—
23C3⋊(C3⋊(C3⋊D3))C2×D511yescharacteristic
24C32×C3⋊D3—52no—
25C33×C5—24no—
26C33×C5—48no—
27D3×C3⋊D3—304no—
28C3⋊D15#15712yescomplemented
29C5×C3⋊D3—92no—
30C5×C3⋊D3—188no—
31C5×C3⋊D3—184no—
32C5×C3⋊D3—184no—
33C5×C3⋊D3—3616no—
34C5×C3⋊D3—368no—
35C3×D15—616no—
36C32×D5—92no—
37C34C4×D511yescharacteristic, complemented, Sylow
38C2×#157—452no—
39D3×D5—544no—
40C3⋊(C3⋊D3)—64no—
41C3⋊(C3⋊D3)—128no—
42C3×C3⋊D3—104no—
43C32×D3—304no—
44C32×C5—28no—
45C32×C5—24no—
46C32×C5—24no—
47C32×C5—416no—
48C32×C5—48no—
49C32×C5C2×#15712yescomplemented
50C4×D5—811noHall
51C2×C3⋊D3—452no—
52D32—908no—
53#157—92no—
54#157—184no—
55#157—452no—
56#157—904no—
57D15—64no—
58C3×D5—184no—
59C5×D3—544no—
60C5×D3—1088no—
61C33—24no—
62C33—48no—
63C2×D5—811no—
64C4×C5—811no—
65Dic5—811no—
66C2×C32—452no—
67C3⋊D3—52no—
68C3⋊D3—92no—
69C3⋊D3—188no—
70C3⋊D3—184no—
71C3⋊D3—184no—
72C3⋊D3—3616no—
73C3⋊D3—368no—
74C3×D3—3016no—
75C3×C5—24no—
76C3×C5—48no—
77C2×D3—2704no—
78C2×C5—811no—
79D5—92no—
80C32—28no—
81C32—24no—
82C32—24no—
83C32—416no—
84C32—48no—
85C32D5×#15712yescomplemented
86C2×C4—4051noSylow
87C2×C3—904no—
88D3—304no—
89D3—544no—
90D3—1088no—
91C5#1062019811yescharacteristic, complemented, Sylow
92C22—4051no—
93C4—811no—
94C4—4051no—
95C3—24no—
96C3—48no—
97C2—452no—
98C2—811no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC34×C5C2×C4
prime radical#13108557C2
cosocleC5×C3⋊(C3⋊(C3⋊D3))C22
LCSG ▷ C34×C5
UCSC1

Complements

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

NH ≅ G/Ntype
2. #13108537C2semidirect
3. C5×#66472C2semidirect
5. C32×C3⋊D15C4semidirect
8. C34×C5C2×C4semidirect
12. #66472D5semidirect
28. C3⋊D15#157semidirect
37. C34C4×D5semidirect
49. C32×C5C2×#157semidirect
85. C32D5×#157semidirect
91. C5#10620198semidirect

Maximal subgroups

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

subgroupindex
#131085572
#131085372
C5×#664722
#106201985
D5×#1579