Finite Group Databasebeta

← C3×C5×C3⋊#10625194 #45686408

Subgroups — C3×C5×C3⋊#10625194 #45686408

Order 33300.

160 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 52 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×C52×D37C211yesmaximal, characteristic
2C5×C3⋊#10625194C311yesmaximal, characteristic, direct product factor
3C3×C5×#10625194—31nomaximal
4C32×C52×C37C411yescharacteristic, complemented, Hall
5C3×C3⋊#10625194C511yesmaximal, characteristic, direct product factor
6C3×C5×C3⋊#3866—51nomaximal
7C3×C52×D37—21no—
8C3×C52×D37D311yescharacteristic
9C3×C52×D37C2×C311yescharacteristic
10C5×#10625194—31noHall
11C32×C5×D37—22no—
12C32×C5×D37D511yescharacteristic
13C32×C5×D37C2×C511yescharacteristic
14C3×C52×C37—21no—
15C3×C52×C37Dic311yescharacteristic, complemented
16C3×C52×C37C3×C411yescharacteristic, complemented
17C3⋊#10625194C3×C511yescharacteristic, direct product factor
18C5×C3⋊#3866—51no—
19C3×#10625194—31no—
20C3×C5×#3866—151no—
21C52×D37C3×D311yescharacteristic
22C32×C5×C37—22no—
23C32×C5×C37Dic511yescharacteristic, complemented
24C32×C5×C37C4×C511yescharacteristic, complemented
25C3×C3⋊#3866—51noHall
26C3×C5×D37—24no—
27C3×C5×D37—21no—
28C3×C5×D37—21no—
29C3×C5×D37—22no—
30C3×C5×D37—22no—
31C3×C5×D37C5×D311yescharacteristic
32C3×C5×D37C3×D511yescharacteristic
33C3×C5×D37D1511yescharacteristic
34C3×C5×D37C2×C3×C511yescharacteristic
35C52×C37C3×Dic311yescharacteristic, complemented, Hall
36C3×C5×Dic15—371nomaximal, Hall
37#10625194—31no—
38C5×#3866—151no—
39C32×D37C5×D511yescharacteristic
40C3×C5×C37—24no—
41C3×C5×C37—22no—
42C3×C5×C37—22no—
43C3×C5×C37—21no—
44C3×C5×C37—21no—
45C3×C5×C37C5×Dic311yescharacteristic, complemented
46C3×C5×C37C3×Dic511yescharacteristic, complemented
47C3×C5×C37Dic1511yescharacteristic, complemented
48C3×C5×C37C3×C4×C511yescharacteristic, complemented
49C2×C32×C52—371no—
50C3⋊#3866—51no—
51C3×#3866—151no—
52C5×D37—22no—
53C5×D37C3×C5×D311yescharacteristic
54C5×D37C3×D1511yescharacteristic
55C32×C37C5×Dic511yescharacteristic, complemented, Hall
56C5×Dic15—371no—
57C3×C5×Dic5—1111no—
58C32×C52#386611yescharacteristic, complemented, Hall
59C3×D37—21no—
60C3×D37C3×C5×D511yescharacteristic
61C3×D37C5×D1511yescharacteristic
62C5×C37—22no—
63C5×C37C3×C5×Dic311yescharacteristic, complemented
64C5×C37C3×Dic1511yescharacteristic, complemented
65C3×Dic15—371no—
66C3×C5×Dic3—1851no—
67C2×C3×C52—371no—
68C2×C3×C52—371no—
69C2×C3×C52—741no—
70#3866—151noHall
71C3×C37—21no—
72C3×C37C3×C5×Dic511yescharacteristic, complemented
73C3×C37C5×Dic1511yescharacteristic, complemented
74C5×Dic5—1111noHall
75C2×C32×C5—371no—
76C2×C32×C5—371no—
77C2×C32×C5—742no—
78C3×C52—21no—
79C3×C52C3×#386611yescharacteristic, complemented
80C3×C52C3⋊#386611yescharacteristic, complemented
81D37C3×C5×D1511yescharacteristic
82C3×C4×C5—5551no—
83Dic15—371no—
84C3×Dic5—1111no—
85C5×Dic3—1851no—
86C2×C52—371no—
87C32×C5—22no—
88C32×C5C5×#386611yescharacteristic, complemented
89C32×C5#1062519411yescharacteristic, complemented
90C37C3×C5×Dic1511yescharacteristic, complemented, Sylow
91C3×Dic3—1851noHall
92C2×C3×C5—371no—
93C2×C3×C5—371no—
94C2×C3×C5—371no—
95C2×C3×C5—371no—
96C2×C3×C5—742no—
97C2×C3×C5—742no—
98C2×C3×C5—741no—
99C2×C3×C5—741no—
100C2×C3×C5—744no—
101C52C3×C3⋊#386611yescharacteristic, complemented, Sylow
102C4×C5—5551no—
103Dic5—1111no—
104C2×C32—371no—
105C3×C5—24no—
106C3×C5—21no—
107C3×C5—21no—
108C3×C5—22no—
109C3×C5—22no—
110C3×C5C3×C5×#386611yescharacteristic, complemented
111C3×C5C3×#1062519411yescharacteristic, complemented
112C3×C5C5×C3⋊#386611yescharacteristic, complemented
113C3×C5C3⋊#1062519411yescharacteristic, direct product factor
114C3×C4—5551no—
115Dic3—1851no—
116C2×C5—371no—
117C2×C5—371no—
118C2×C5—742no—
119C32C5×#1062519411yescharacteristic, complemented, Sylow
120C2×C3—371no—
121C2×C3—371no—
122C2×C3—741no—
123C5—22no—
124C5C3×C5×C3⋊#386611yescharacteristic, complemented
125C5C3×C3⋊#1062519411yescharacteristic, direct product factor
126C4—5551noSylow
127C3—21no—
128C3C3×C5×#1062519411yescharacteristic, complemented
129C3C5×C3⋊#1062519411yescharacteristic, direct product factor
130C2—371no—
subgroupG/H
center, hypercenterC3×C5C3⋊#10625194
commutator, hypocenterC3×C5×C37C3×C4×C5
FrattiniC1G
Fitting, socleC32×C52×C37C4
prime radicalC32×C52×D37C2
cosocleC3×C5×D37C2×C3×C5
LCSG ▷ C3×C5×C37
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
2. C5×C3⋊#10625194C3direct (N × H)
4. C32×C52×C37C4semidirect
5. C3×C3⋊#10625194C5direct (N × H)
15. C3×C52×C37Dic3semidirect
16. C3×C52×C37C3×C4semidirect
17. C3⋊#10625194C3×C5direct (N × H)
23. C32×C5×C37Dic5semidirect
24. C32×C5×C37C4×C5semidirect
35. C52×C37C3×Dic3semidirect
45. C3×C5×C37C5×Dic3semidirect
46. C3×C5×C37C3×Dic5semidirect
47. C3×C5×C37Dic15semidirect
48. C3×C5×C37C3×C4×C5semidirect
55. C32×C37C5×Dic5semidirect
58. C32×C52#3866semidirect
63. C5×C37C3×C5×Dic3semidirect
64. C5×C37C3×Dic15semidirect
72. C3×C37C3×C5×Dic5semidirect
73. C3×C37C5×Dic15semidirect
79. C3×C52C3×#3866semidirect
80. C3×C52C3⋊#3866semidirect
88. C32×C5C5×#3866semidirect
89. C32×C5#10625194semidirect
90. C37C3×C5×Dic15semidirect
101. C52C3×C3⋊#3866semidirect
110. C3×C5C3×C5×#3866semidirect
111. C3×C5C3×#10625194semidirect
112. C3×C5C5×C3⋊#3866semidirect
113. C3×C5C3⋊#10625194direct (N × H)
119. C32C5×#10625194semidirect
124. C5C3×C5×C3⋊#3866semidirect
125. C5C3×C3⋊#10625194direct (N × H)
128. C3C3×C5×#10625194semidirect
129. C3C5×C3⋊#10625194direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C52×D372
C5×C3⋊#106251943
C3×C5×#106251943
C3×C3⋊#106251945
C3×C5×C3⋊#38665
C3×C5×Dic1537