Finite Group Databasebeta

← C3×C5×#944 #13087952

Subgroups — C3×C5×#944 #13087952

Order 1440.

310 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 148 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×C32×C5×Q8C211yesmaximal, characteristic
2C2×C3×C5×Dic6C211yesmaximal, characteristic
3C3×C5×Dic3⋊C4C214yesmaximal
4C3×C4×C5×Dic3C211yesmaximal, characteristic
5C3×C5×C4⋊Q8—31nomaximal
6C5×#944C311yesmaximal, characteristic, direct product factor
7C32×C5×Q8—22no—
8C2×C32×C4×C5C2212yes—
9C2×C32×C4×C5C2211yescharacteristic
10C2×C3×C5×Dic3C2212yes—
11C2×C3×C5×Dic3C2212yes—
12C3×C5×Dic6—22no—
13C3×#944C511yesmaximal, characteristic, direct product factor, Hall
14C2×C3×C5×Q8—21no—
15C2×C3×C5×Q8—31no—
16C2×C3×C5×Q8D311yescharacteristic
17C2×C3×C5×Q8C2×C311yescharacteristic
18C2×C5×Dic6C2×C311yescharacteristic
19C3×C5×C4⋊C4—34no—
20C3×C42×C5—31no—
21C5×Dic3⋊C4C2×C314yes—
22C4×C5×Dic3C2×C311yescharacteristic
23C22×C32×C5C2311yescharacteristic
24C32×C4×C5—22no—
25C32×C4×C5D412yes—
26C3×C5×Dic3—22no—
27C3×C5×Dic3Q814yescomplemented
28C5×C4⋊Q8—31noHall
29C2×C32×Q8C2×C511yescharacteristic
30C2×C3×Dic6C2×C511yescharacteristic
31C3×Dic3⋊C4C2×C514yes—
32C3×C4×Dic3C2×C511yescharacteristic
33C3×C5×Q8—24no—
34C3×C5×Q8—22no—
35C3×C5×Q8—22no—
36C3×C5×Q8—62no—
37C2×C3×C4×C5—22no—
38C2×C3×C4×C5—21no—
39C2×C3×C4×C5—32no—
40C2×C3×C4×C5—32no—
41C2×C3×C4×C5C2×D312yes—
42C2×C3×C4×C5C2×D311yescharacteristic
43C2×C3×C4×C5C22×C312yes—
44C2×C3×C4×C5C22×C311yescharacteristic
45C2×C5×Dic3C22×C312yes—
46C2×C5×Dic3C22×C312yes—
47C5×Dic6—22no—
48C3×C4⋊Q8—31no—
49#944C3×C511yescharacteristic, direct product factor
50C2×C32×C5C2×D411yescharacteristic
51C2×C32×C5C2×Q812yes—
52C2×C5×Q8—31no—
53C2×C5×Q8C3×D311yescharacteristic
54C5×C4⋊C4—34no—
55C42×C5—31no—
56C32×Q8—22no—
57C2×C32×C4C22×C512yes—
58C2×C32×C4C22×C511yescharacteristic
59C2×C3×Dic3C22×C512yes—
60C2×C3×Dic3C22×C512yes—
61C3×Dic6—22no—
62C22×C3×C5—21no—
63C22×C3×C5C22×D311yescharacteristic
64C22×C3×C5C23×C311yescharacteristic
65C3×C4×C5—24no—
66C3×C4×C5—22no—
67C3×C4×C5—22no—
68C3×C4×C5—22no—
69C3×C4×C5—34no—
70C3×C4×C5—62no—
71C3×C4×C5#6712yes—
72C3×C4×C5C3×D412yes—
73C5×Dic3—22no—
74C5×Dic3C3×Q814yescomplemented
75C2×C3×Q8—21no—
76C2×C3×Q8—31no—
77C2×C3×Q8C5×D311yescharacteristic
78C2×C3×Q8C2×C3×C511yescharacteristic
79C2×Dic6C2×C3×C511yescharacteristic
80C3×C4⋊C4—34no—
81C3×C42—31no—
82Dic3⋊C4C2×C3×C514yes—
83C4×Dic3C2×C3×C511yescharacteristic
84C32×C5C4⋊Q811yescharacteristic, complemented, Hall
85C5×Q8—22no—
86C5×Q8—62no—
87C2×C4×C5—32no—
88C2×C4×C5—32no—
89C2×C4×C5C2×C3×D312yes—
90C2×C4×C5C2×C3×D311yescharacteristic
91C22×C32C23×C511yescharacteristic
92C32×C4—22no—
93C32×C4C5×D412yes—
94C3×Dic3—22no—
95C3×Dic3C5×Q814yescomplemented
96C4⋊Q8—31noSylow
97C2×C3×C5—22no—
98C2×C3×C5—21no—
99C2×C3×C5D3×Q812yes—
100C2×C3×C5C2×#6711yescharacteristic
101C2×C3×C5C2×C3×D411yescharacteristic
102C2×C3×C5C2×C3×Q812yes—
103C3×Q8—24no—
104C3×Q8—22no—
105C3×Q8—22no—
106C3×Q8—62no—
107C2×C3×C4—22no—
108C2×C3×C4—21no—
109C2×C3×C4—32no—
110C2×C3×C4—32no—
111C2×C3×C4C2×C5×D312yes—
112C2×C3×C4C2×C5×D311yescharacteristic
113C2×C3×C4C22×C3×C512yes—
114C2×C3×C4C22×C3×C511yescharacteristic
115C2×Dic3C22×C3×C512yes—
116C2×Dic3C22×C3×C512yes—
117Dic6—22no—
118C22×C5C22×C3×D311yescharacteristic
119C4×C5—22no—
120C4×C5—34no—
121C4×C5—62no—
122C4×C5C3×#6712yes—
123C2×C32C2×C5×D411yescharacteristic
124C2×C32C2×C5×Q812yes—
125C2×Q8—31no—
126C2×Q8C3×C5×D311yescharacteristic
127C4⋊C4—34no—
128C42—31no—
129C3×C5—21no—
130C3×C5#94411yescharacteristic, direct product factor
131C3×C5C3×C4⋊Q811yescharacteristic, complemented
132C22×C3—21no—
133C22×C3C22×C5×D311yescharacteristic
134C22×C3C23×C3×C511yescharacteristic
135C3×C4—24no—
136C3×C4—22no—
137C3×C4—22no—
138C3×C4—22no—
139C3×C4—34no—
140C3×C4—62no—
141C3×C4C5×#6712yes—
142C3×C4C3×C5×D412yes—
143Dic3—22no—
144Dic3C3×C5×Q814yescomplemented
145C2×C5C3×D3×Q812yes—
146C2×C5C2×C3×#6711yescharacteristic
147C32C5×C4⋊Q811yescharacteristic, complemented, Sylow
148Q8—22no—
149Q8—62no—
150C2×C4—32no—
151C2×C4—32no—
152C2×C4C2×C3×C5×D312yes—
153C2×C4C2×C3×C5×D311yescharacteristic
154C2×C3—22no—
155C2×C3—21no—
156C2×C3C5×D3×Q812yes—
157C2×C3C2×C5×#6711yescharacteristic
158C2×C3C2×C3×C5×D411yescharacteristic
159C2×C3C2×C3×C5×Q812yes—
160C5C3×#94411yescharacteristic, direct product factor, Sylow
161C22C22×C3×C5×D311yescharacteristic
162C4—22no—
163C4—34no—
164C4—62no—
165C4C3×C5×#6712yes—
166C3—21no—
167C3C5×#94411yescharacteristic, direct product factor
168C3C3×C5×C4⋊Q811yescharacteristic, complemented
169C2C3×C5×D3×Q812yes—
170C2C2×C3×C5×#6711yescharacteristic
subgroupG/H
centerC22×C3×C5C22×D3
commutator, cosocleC22×C3C23×C3×C5
FrattiniC22C22×C3×C5×D3
FittingC2×C32×C5×Q8C2
socle, prime radicalC22×C32×C5C23
hypercenterC2×C3×C5×Q8D3
hypocenterC3C3×C5×C4⋊Q8
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C5 ◁ C2×C3×C5×Q8

Complements

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

NH ≅ G/Ntype
6. C5×#944C3direct (N × H)
13. C3×#944C5direct (N × H)
27. C3×C5×Dic3Q8semidirect
49. #944C3×C5direct (N × H)
74. C5×Dic3C3×Q8semidirect
84. C32×C5C4⋊Q8semidirect
95. C3×Dic3C5×Q8semidirect
130. C3×C5#944direct (N × H)
131. C3×C5C3×C4⋊Q8semidirect
144. Dic3C3×C5×Q8semidirect
147. C32C5×C4⋊Q8semidirect
160. C5C3×#944direct (N × H)
167. C3C5×#944direct (N × H)
168. C3C3×C5×C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C5×Q82
C2×C3×C5×Dic62
C3×C5×Dic3⋊C42
C3×C4×C5×Dic32
C3×C5×C4⋊Q83
C5×#9443
C3×#9445