Finite Group Databasebeta

← C3×C5×#1297 #14274331

Subgroups — C3×C5×#1297 #14274331

Order 1920.

492 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 144 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
1C3×C5×#407C211yesmaximal, characteristic
2C3×C4×C5×C22⋊C4C212yesmaximal
3C5×#1297C311yesmaximal, characteristic, direct product factor, Hall
4C23×C3×C4×C5C2211yescharacteristic
5C2×C3×C5×M16C412yescomplemented
6C2×C3×C5×C22⋊C4—22no—
7C2×C3×C42×C5—22no—
8C3×C5×C22⋊C8—22no—
9C3×C5×#95C414yescomplemented
10C3×#1297C511yesmaximal, characteristic, direct product factor, Hall
11C5×#407C2×C311yescharacteristic
12C4×C5×C22⋊C4C2×C312yes—
13C24×C3×C5D411yescharacteristic
14C22×C3×C4×C5—24no—
15C22×C3×C4×C5—42no—
16C22×C3×C4×C5C2×C411yescharacteristic
17C22×C3×C4×C5C2×C412yes—
18C22×C3×C4×C5D412yes—
19C22×C3×C4×C5Q811yescharacteristic
20C3×C5×M16—42no—
21C2×C3×C5×C8—22no—
22C3×C5×C22⋊C4—28no—
23C3×C42×C5—44no—
24C3×#407C2×C511yescharacteristic
25C3×C4×C22⋊C4C2×C512yes—
26C23×C4×C5C22×C311yescharacteristic
27C2×C5×M16C3×C412yescomplemented
28C2×C5×C22⋊C4—22no—
29C2×C42×C5—22no—
30C5×C22⋊C8—22no—
31C5×#95C3×C414yescomplemented
32#1297C3×C511yescharacteristic, direct product factor, Sylow
33C23×C3×C5—24no—
34C23×C3×C5—41no—
35C23×C3×C5C22⋊C412yes—
36C23×C3×C5C4⋊C411yescharacteristic
37C2×C3×C4×C5—24no—
38C2×C3×C4×C5—22no—
39C2×C3×C4×C5—28no—
40C2×C3×C4×C5—42no—
41C2×C3×C4×C5—41no—
42C2×C3×C4×C5—44no—
43C2×C3×C4×C5—44no—
44C2×C3×C4×C5C4211yescharacteristic
45C2×C3×C4×C5C22⋊C411yescharacteristic
46C2×C3×C4×C5C4⋊C412yes—
47C3×C5×C8—42no—
48C23×C3×C4C22×C511yescharacteristic
49C2×C3×M16C4×C512yescomplemented
50C2×C3×C22⋊C4—22no—
51C2×C3×C42—22no—
52C3×C22⋊C8—22no—
53C3×#95C4×C514yescomplemented
54C24×C5C3×D411yescharacteristic
55C22×C4×C5—24no—
56C22×C4×C5—42no—
57C22×C4×C5C2×C3×C411yescharacteristic
58C22×C4×C5C2×C3×C412yes—
59C22×C4×C5C3×D412yes—
60C22×C4×C5C3×Q811yescharacteristic
61C5×M16—42no—
62C2×C5×C8—22no—
63C5×C22⋊C4—28no—
64C42×C5—44no—
65#407C2×C3×C511yescharacteristic
66C4×C22⋊C4C2×C3×C512yes—
67C22×C3×C5—22no—
68C22×C3×C5—22no—
69C22×C3×C5—22no—
70C22×C3×C5—21no—
71C22×C3×C5—44no—
72C22×C3×C5#9511yescharacteristic
73C22×C3×C5#10414yes—
74C3×C4×C5—21no—
75C3×C4×C5—22no—
76C3×C4×C5—48no—
77C3×C4×C5#9912yes—
78C24×C3C5×D411yescharacteristic
79C22×C3×C4—24no—
80C22×C3×C4—42no—
81C22×C3×C4C2×C4×C511yescharacteristic
82C22×C3×C4C2×C4×C512yes—
83C22×C3×C4C5×D412yes—
84C22×C3×C4C5×Q811yescharacteristic
85C3×M16—42no—
86C2×C3×C8—22no—
87C3×C22⋊C4—28no—
88C3×C42—44no—
89C23×C5—24no—
90C23×C5—41no—
91C23×C5C3×C22⋊C412yes—
92C23×C5C3×C4⋊C411yescharacteristic
93C2×C4×C5—24no—
94C2×C4×C5—22no—
95C2×C4×C5—28no—
96C2×C4×C5—42no—
97C2×C4×C5—41no—
98C2×C4×C5—44no—
99C2×C4×C5—44no—
100C2×C4×C5C3×C4211yescharacteristic
101C2×C4×C5C3×C22⋊C411yescharacteristic
102C2×C4×C5C3×C4⋊C412yes—
103C5×C8—42no—
104C23×C4C22×C3×C511yescharacteristic
105C2×M16C3×C4×C512yescomplemented
106C2×C22⋊C4—22no—
107C2×C42—22no—
108C22⋊C8—22no—
109#95C3×C4×C514yescomplemented
110C2×C3×C5—24no—
111C2×C3×C5—41no—
112C2×C3×C5#33912yes—
113C2×C3×C5#34211yescharacteristic
114C23×C3—24no—
115C23×C3—41no—
116C23×C3C5×C22⋊C412yes—
117C23×C3C5×C4⋊C411yescharacteristic
118C2×C3×C4—24no—
119C2×C3×C4—22no—
120C2×C3×C4—28no—
121C2×C3×C4—42no—
122C2×C3×C4—41no—
123C2×C3×C4—44no—
124C2×C3×C4—44no—
125C2×C3×C4C42×C511yescharacteristic
126C2×C3×C4C5×C22⋊C411yescharacteristic
127C2×C3×C4C5×C4⋊C412yes—
128C3×C8—42no—
129C22×C5—22no—
130C22×C5—22no—
131C22×C5—22no—
132C22×C5—21no—
133C22×C5—44no—
134C22×C5C3×#9511yescharacteristic
135C22×C5C3×#10414yes—
136C4×C5—21no—
137C4×C5—22no—
138C4×C5—48no—
139C4×C5C3×#9912yes—
140C24C3×C5×D411yescharacteristic
141C22×C4—24no—
142C22×C4—42no—
143C22×C4C2×C3×C4×C511yescharacteristic
144C22×C4C2×C3×C4×C512yes—
145C22×C4C3×C5×D412yes—
146C22×C4C3×C5×Q811yescharacteristic
147M16—42no—
148C2×C8—22no—
149C22⋊C4—28no—
150C42—44no—
151C3×C5#129711yescharacteristic, direct product factor, Hall
152C22×C3—22no—
153C22×C3—22no—
154C22×C3—22no—
155C22×C3—21no—
156C22×C3—44no—
157C22×C3C5×#9511yescharacteristic
158C22×C3C5×#10414yes—
159C3×C4—21no—
160C3×C4—22no—
161C3×C4—48no—
162C3×C4C5×#9912yes—
163C2×C5—24no—
164C2×C5—41no—
165C2×C5C3×#33912yes—
166C2×C5C3×#34211yescharacteristic
167C23—24no—
168C23—41no—
169C23C3×C5×C22⋊C412yes—
170C23C3×C5×C4⋊C411yescharacteristic
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—28no—
174C2×C4—42no—
175C2×C4—41no—
176C2×C4—44no—
177C2×C4—44no—
178C2×C4C3×C42×C511yescharacteristic
179C2×C4C3×C5×C22⋊C411yescharacteristic
180C2×C4C3×C5×C4⋊C412yes—
181C8—42no—
182C2×C3—24no—
183C2×C3—41no—
184C2×C3C5×#33912yes—
185C2×C3C5×#34211yescharacteristic
186C5C3×#129711yescharacteristic, direct product factor, Sylow
187C22—22no—
188C22—22no—
189C22—22no—
190C22—21no—
191C22—44no—
192C22C3×C5×#9511yescharacteristic
193C22C3×C5×#10414yes—
194C4—21no—
195C4—22no—
196C4—48no—
197C4C3×C5×#9912yes—
198C3C5×#129711yescharacteristic, direct product factor, Sylow
199C2—24no—
200C2—41no—
201C2C3×C5×#33912yes—
202C2C3×C5×#34211yescharacteristic
subgroupG/H
centerC2×C3×C4×C5C22⋊C4
commutatorC2×C4C3×C42×C5
Frattini, cosocleC23×C4C22×C3×C5
socleC22×C3×C5#95
prime radicalC24×C3×C5D4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C3×C4×C5 ◁ C23×C3×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1297C3direct (N × H)
5. C2×C3×C5×M16C4semidirect
9. C3×C5×#95C4semidirect
10. C3×#1297C5direct (N × H)
27. C2×C5×M16C3×C4semidirect
31. C5×#95C3×C4semidirect
32. #1297C3×C5direct (N × H)
49. C2×C3×M16C4×C5semidirect
53. C3×#95C4×C5semidirect
105. C2×M16C3×C4×C5semidirect
109. #95C3×C4×C5semidirect
151. C3×C5#1297direct (N × H)
186. C5C3×#1297direct (N × H)
198. C3C5×#1297direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4072
C3×C4×C5×C22⋊C42
C5×#12973
C3×#12975