Finite Group Databasebeta

← C3×#10602666 #14313752

Subgroups — C3×#10602666 #14313752

Order 1920.

460 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 146 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×#536C211yesmaximal, characteristic
2C3×#65526C212yesmaximal
3C3×#64768C214yesmaximal, complemented
4#10602666C311yesmaximal, characteristic, direct product factor, Hall
5C2×C3×C5×#41C2211yescharacteristic
6C22×C3×C5×Q8C411yescharacteristic
7C3×C5×C4⋊Q8C2212yes—
8C3×C5×#124C412yes—
9C3×C5×#123—22no—
10C3×C5×C22⋊Q8—22no—
11C3×C5×#117C411yescharacteristic
12C2×C3×#681—22no—
13C3×#3968C2214yes—
14C3×#3965—22no—
15C3×#2135—51nomaximal, Hall
16C5×#536C2×C311yescharacteristic
17#65526C2×C312yes—
18#64768C2×C314yescomplemented
19C3×C5×#41—42no—
20C2×C3×C5×Q8—21no—
21C2×C3×C5×Q8—42no—
22C2×C3×C5×Q8C2×C412yes—
23C2×C3×C5×Q8C2311yescharacteristic
24C2×C3×C5×D4C2×C411yescharacteristic
25C2×C3×C5×D4D412yes—
26C22×C3×C4×C5—21no—
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×C3×C4×C5D412yes—
29C3×C5×C4⋊C4—21no—
30C3×C5×C4⋊C4—24no—
31C3×C5×C22⋊C4—21no—
32C3×C5×C22⋊C4—24no—
33C3×C42×C5C2×C412yes—
34C3×#681—24no—
35C3×#681—42no—
36C2×C3×#168—42no—
37C3×#536D511yescharacteristic
38C3×#413—52no—
39C3×#356—54no—
40C2×C5×#41C22×C311yescharacteristic
41C22×C5×Q8C3×C411yescharacteristic
42C5×C4⋊Q8C22×C312yes—
43C5×#124C3×C412yes—
44C5×#123—22no—
45C5×C22⋊Q8—22no—
46C5×#117C3×C411yescharacteristic
47C2×#681—22no—
48#3968C22×C314yes—
49#3965—22no—
50#2135—51noSylow
51C23×C3×C5C22⋊C412yes—
52C23×C3×C5C22⋊C411yescharacteristic
53C3×C5×Q8—41no—
54C3×C5×Q8—42no—
55C3×C5×Q8—42no—
56C3×C5×D4—41no—
57C3×C5×D4—42no—
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5—22no—
60C2×C3×C4×C5—22no—
61C2×C3×C4×C5—22no—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—42no—
64C2×C3×C4×C5C22⋊C411yescharacteristic
65C2×C3×C4×C5C22×C411yescharacteristic
66C2×C3×C4×C5C2×D412yes—
67C3×#168—44no—
68C2×C3×#41C2×D511yescharacteristic
69C22×C3×Q8Dic511yescharacteristic
70C2×C3×M16—102no—
71C3×C4⋊Q8C2×D512yes—
72C3×#124Dic512yes—
73C3×#123—22no—
74C3×C22⋊Q8—22no—
75C3×#117Dic511yescharacteristic
76C3×#101—54no—
77C3×#100—102no—
78C5×#41—42no—
79C2×C5×Q8—21no—
80C2×C5×Q8—42no—
81C2×C5×Q8C2×C3×C412yes—
82C2×C5×Q8C23×C311yescharacteristic
83C2×C5×D4C2×C3×C411yescharacteristic
84C2×C5×D4C3×D412yes—
85C22×C4×C5—21no—
86C22×C4×C5C2×C3×C411yescharacteristic
87C22×C4×C5C3×D412yes—
88C5×C4⋊C4—21no—
89C5×C4⋊C4—24no—
90C5×C22⋊C4—21no—
91C5×C22⋊C4—24no—
92C42×C5C2×C3×C412yes—
93#681—24no—
94#681—42no—
95C2×#168—42no—
96#536C3×D511yescharacteristic
97#413—52no—
98#356—54no—
99C22×C3×C5—21no—
100C22×C3×C5—22no—
101C22×C3×C5—42no—
102C22×C3×C5—41no—
103C22×C3×C5C2×C22⋊C411yescharacteristic
104C3×C4×C5—22no—
105C3×C4×C5—21no—
106C3×C4×C5—42no—
107C3×C4×C5—42no—
108C3×C4×C5#9912yes—
109C3×#41—42no—
110C2×C3×Q8—21no—
111C2×C3×Q8—42no—
112C2×C3×Q8C2×Dic512yes—
113C2×C3×Q8C22×D511yescharacteristic
114C2×C3×D4C2×Dic511yescharacteristic
115C2×C3×D4C22⋊D512yes—
116C22×C3×C4—21no—
117C22×C3×C4C2×Dic511yescharacteristic
118C22×C3×C4C22⋊D512yes—
119C3×M16—104no—
120C3×M16—202no—
121C2×C3×C8—202no—
122C3×C4⋊C4—21no—
123C3×C4⋊C4—24no—
124C3×C22⋊C4—21no—
125C3×C22⋊C4—24no—
126C3×C42C2×Dic512yes—
127C23×C5C3×C22⋊C412yes—
128C23×C5C3×C22⋊C411yescharacteristic
129C5×Q8—41no—
130C5×Q8—42no—
131C5×Q8—42no—
132C5×D4—41no—
133C5×D4—42no—
134C2×C4×C5—22no—
135C2×C4×C5—22no—
136C2×C4×C5—22no—
137C2×C4×C5—22no—
138C2×C4×C5—22no—
139C2×C4×C5—42no—
140C2×C4×C5C3×C22⋊C411yescharacteristic
141C2×C4×C5C22×C3×C411yescharacteristic
142C2×C4×C5C2×C3×D412yes—
143#168—44no—
144C2×#41C2×C3×D511yescharacteristic
145C22×Q8C3×Dic511yescharacteristic
146C2×M16—102no—
147C4⋊Q8C2×C3×D512yes—
148#124C3×Dic512yes—
149#123—22no—
150C22⋊Q8—22no—
151#117C3×Dic511yescharacteristic
152#101—54no—
153#100—102no—
154C2×C3×C5—21no—
155C2×C3×C5—41no—
156C2×C3×C5—42no—
157C2×C3×C5C2×#9911yescharacteristic
158C23×C3C22⋊Dic512yes—
159C23×C3C22⋊Dic511yescharacteristic
160C3×Q8—41no—
161C3×Q8—42no—
162C3×Q8—42no—
163C3×D4—41no—
164C3×D4—42no—
165C2×C3×C4—22no—
166C2×C3×C4—22no—
167C2×C3×C4—22no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×C3×C4—42no—
171C2×C3×C4C22⋊Dic511yescharacteristic
172C2×C3×C4C22×Dic511yescharacteristic
173C2×C3×C4C2×C22⋊D512yes—
174C3×C8—204no—
175C22×C5—21no—
176C22×C5—22no—
177C22×C5—42no—
178C22×C5—41no—
179C22×C5C2×C3×C22⋊C411yescharacteristic
180C4×C5—22no—
181C4×C5—21no—
182C4×C5—42no—
183C4×C5—42no—
184C4×C5C3×#9912yes—
185#41—42no—
186C2×Q8—21no—
187C2×Q8—42no—
188C2×Q8C2×C3×Dic512yes—
189C2×Q8C22×C3×D511yescharacteristic
190C2×D4C2×C3×Dic511yescharacteristic
191C2×D4C3×C22⋊D512yes—
192C22×C4—21no—
193C22×C4C2×C3×Dic511yescharacteristic
194C22×C4C3×C22⋊D512yes—
195M16—104no—
196M16—202no—
197C2×C8—202no—
198C4⋊C4—21no—
199C4⋊C4—24no—
200C22⋊C4—21no—
201C22⋊C4—24no—
202C42C2×C3×Dic512yes—
203C3×C5#213511yescharacteristic, complemented, Hall
204C22×C3—21no—
205C22×C3—22no—
206C22×C3—42no—
207C22×C3—41no—
208C22×C3C2×C22⋊Dic511yescharacteristic
209C3×C4—22no—
210C3×C4—21no—
211C3×C4—42no—
212C3×C4—42no—
213C3×C4#396612yes—
214C2×C5—21no—
215C2×C5—41no—
216C2×C5—42no—
217C2×C5C2×C3×#9911yescharacteristic
218C23C3×C22⋊Dic512yes—
219C23C3×C22⋊Dic511yescharacteristic
220Q8—41no—
221Q8—42no—
222Q8—42no—
223D4—41no—
224D4—42no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—42no—
231C2×C4C3×C22⋊Dic511yescharacteristic
232C2×C4C22×C3×Dic511yescharacteristic
233C2×C4C2×C3×C22⋊D512yes—
234C8—204no—
235C2×C3—21no—
236C2×C3—41no—
237C2×C3—42no—
238C2×C3C2×#396611yescharacteristic
239C5C3×#213511yescharacteristic, complemented, Sylow
240C22—21no—
241C22—22no—
242C22—42no—
243C22—41no—
244C22C2×C3×C22⋊Dic511yescharacteristic
245C4—22no—
246C4—21no—
247C4—42no—
248C4—42no—
249C4C3×#396612yes—
250C3#1060266611yescharacteristic, direct product factor, Sylow
251C2—21no—
252C2—41no—
253C2—42no—
254C2C2×C3×#396611yescharacteristic
subgroupG/H
centerC2×C3C2×#3966
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×Q8C22×C3×D5
FittingC3×C5×#536C2
socleC2×C3×C5C2×#99
prime radicalC2×C3×C5×#41C22
cosocleC2×C5×Q8C23×C3
hypercenterC3×#536D5
hypocenterC5C3×#2135
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×#41 ◁ C3×#536

Complements

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

NH ≅ G/Ntype
3. C3×#64768C2semidirect
4. #10602666C3direct (N × H)
18. #64768C2×C3semidirect
203. C3×C5#2135semidirect
239. C5C3×#2135semidirect
250. C3#10602666direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5362
C3×#655262
C3×#647682
#106026663
C3×#21355