Finite Group Databasebeta

← C3×#10599280 #14285334

Subgroups — C3×#10599280 #14285334

Order 1920.

456 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 134 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×D5×C4⋊Q8C211yesmaximal, characteristic
2C3×#65124C212yesmaximal
3C3×C5×#333C211yesmaximal, characteristic, complemented
4C3×#64766C211yesmaximal, characteristic, complemented
5C3×#64701C212yesmaximal, complemented
6#10599280C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×Q8×D5C412yes—
8C3×C5×C4⋊Q8C2211yescharacteristic
9C3×#4090C412yes—
10C3×D5×C4⋊C4—22no—
11C3×#4034—22no—
12C3×C42×D5C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14C3×C5×C4⋊C8C2212yes—
15C3×#3952—22no—
16C3×#3947—22no—
17C3×C4⋊#168C2212yes—
18C3×#1558—51nomaximal, Hall
19D5×C4⋊Q8C2×C311yescharacteristic
20#65124C2×C312yes—
21C5×#333C2×C311yescharacteristic, complemented
22#64766C2×C311yescharacteristic, complemented
23#64701C2×C312yescomplemented
24C2×C3×C5×Q8C2×C412yes—
25C3×Q8×D5—44no—
26C2×C3×C4×D5—22no—
27C2×C3×C4×D5C2×C411yescharacteristic
28C2×C3×C4×D5D412yes—
29C2×C3×Dic10—22no—
30C2×C3×Dic10C2×C412yes—
31C2×C3×C5×C8—22no—
32C3×C5×C4⋊C4—22no—
33C3×C42×C5C2311yescharacteristic
34C3×C4⋊Dic5—22no—
35C3×#683—24no—
36C3×C4×Dic5C2×C411yescharacteristic
37C3×C4×Dic5D412yes—
38C2×C3×#168—22no—
39C2×C3×C4⋊Q8—51no—
40C3×#432—52no—
41C3×#333—51no—
42C3×#333—52no—
43C3×#333D511yescharacteristic, complemented
44C2×Q8×D5C3×C412yes—
45C5×C4⋊Q8C22×C311yescharacteristic
46#4090C3×C412yes—
47D5×C4⋊C4—22no—
48#4034—22no—
49C42×D5C22×C311yescharacteristic
50#4015C22×C311yescharacteristic
51C5×C4⋊C8C22×C312yes—
52#3952—22no—
53#3947—22no—
54C4⋊#168C22×C312yes—
55#1558—51noSylow
56C22×C3×D5C22⋊C411yescharacteristic
57C3×C5×Q8—42no—
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5C22×C411yescharacteristic
60C2×C3×C4×C5C2×D412yes—
61C2×C3×Dic5—22no—
62C2×C3×Dic5C22⋊C412yes—
63C2×C3×Dic5C22⋊C411yescharacteristic
64C3×C4×D5—22no—
65C3×C4×D5—22no—
66C3×C4×D5—22no—
67C3×C4×D5—44no—
68C3×Dic10—44no—
69C3×Dic10—42no—
70C3×C5×C8—42no—
71C3×#168—42no—
72C22×C3×Q8—52no—
73C3×C4⋊Q8—52no—
74C3×C4⋊Q8—51no—
75C3×C4⋊Q8—102no—
76C3×C4⋊Q8C2×D511yescharacteristic
77C2×C3×C4⋊C4—102no—
78C2×C3×C42—51no—
79C3×C4⋊C8—52no—
80C3×C4⋊C8C2×D512yes—
81C3×C22⋊C8—102no—
82C3×#97—102no—
83C2×C5×Q8C2×C3×C412yes—
84Q8×D5—44no—
85C2×C4×D5—22no—
86C2×C4×D5C2×C3×C411yescharacteristic
87C2×C4×D5C3×D412yes—
88C2×Dic10—22no—
89C2×Dic10C2×C3×C412yes—
90C2×C5×C8—22no—
91C5×C4⋊C4—22no—
92C42×C5C23×C311yescharacteristic
93C4⋊Dic5—22no—
94#683—24no—
95C4×Dic5C2×C3×C411yescharacteristic
96C4×Dic5C3×D412yes—
97C2×#168—22no—
98C2×C4⋊Q8—51no—
99#432—52no—
100#333—51no—
101#333—52no—
102#333C3×D511yescharacteristic, complemented
103C22×C3×C5C2×C22⋊C411yescharacteristic
104C2×C3×D5—22no—
105C2×C3×D5#10012yes—
106C3×C4×C5—21no—
107C3×C4×C5—42no—
108C3×C4×C5#13712yes—
109C3×C4×C5#13712yes—
110C3×Dic5—21no—
111C3×Dic5—22no—
112C3×Dic5—42no—
113C2×C3×Q8—52no—
114C2×C3×Q8—102no—
115C2×C3×Q8—204no—
116C2×C3×Q8C4×D512yes—
117C22×C3×C4—51no—
118C22×C3×C4—52no—
119C22×C3×C4—102no—
120C2×C3×C8—22no—
121C2×C3×C8—102no—
122C3×C4⋊C4—22no—
123C3×C4⋊C4—104no—
124C3×C4⋊C4—102no—
125C3×C42—51no—
126C3×C42—52no—
127C3×C42C22×D511yescharacteristic
128C22×D5C3×C22⋊C411yescharacteristic
129C5×Q8—42no—
130C2×C4×C5—22no—
131C2×C4×C5C22×C3×C411yescharacteristic
132C2×C4×C5C2×C3×D412yes—
133C2×Dic5—22no—
134C2×Dic5C3×C22⋊C412yes—
135C2×Dic5C3×C22⋊C411yescharacteristic
136C4×D5—22no—
137C4×D5—22no—
138C4×D5—22no—
139C4×D5—44no—
140Dic10—44no—
141Dic10—42no—
142C5×C8—42no—
143#168—42no—
144C22×Q8—52no—
145C4⋊Q8—52no—
146C4⋊Q8—51no—
147C4⋊Q8—102no—
148C4⋊Q8C2×C3×D511yescharacteristic
149C2×C4⋊C4—102no—
150C2×C42—51no—
151C4⋊C8—52no—
152C4⋊C8C2×C3×D512yes—
153C22⋊C8—102no—
154#97—102no—
155C2×C3×C5C2×#10011yescharacteristic
156C2×C3×C5#41912yes—
157C3×D5—22no—
158C23×C3—51no—
159C3×Q8—42no—
160C3×Q8—202no—
161C3×Q8—204no—
162C2×C3×C4—22no—
163C2×C3×C4—52no—
164C2×C3×C4—51no—
165C2×C3×C4—102no—
166C2×C3×C4—102no—
167C2×C3×C4—102no—
168C2×C3×C4—102no—
169C2×C3×C4—204no—
170C2×C3×C4C2×C4×D511yescharacteristic
171C2×C3×C4D4×D512yes—
172C3×C8—42no—
173C3×C8—202no—
174C22×C5C2×C3×C22⋊C411yescharacteristic
175C2×D5—22no—
176C2×D5C3×#10012yes—
177C4×C5—21no—
178C4×C5—42no—
179C4×C5C3×#13712yes—
180C4×C5C3×#13712yes—
181Dic5—21no—
182Dic5—22no—
183Dic5—42no—
184C2×Q8—52no—
185C2×Q8—102no—
186C2×Q8—204no—
187C2×Q8C3×C4×D512yes—
188C22×C4—51no—
189C22×C4—52no—
190C22×C4—102no—
191C2×C8—22no—
192C2×C8—102no—
193C4⋊C4—22no—
194C4⋊C4—104no—
195C4⋊C4—102no—
196C42—51no—
197C42—52no—
198C42C22×C3×D511yescharacteristic
199C3×C5#155811yescharacteristic, complemented, Hall
200C22×C3—52no—
201C22×C3—102no—
202C22×C3D5×C22⋊C411yescharacteristic
203C3×C4—21no—
204C3×C4—42no—
205C3×C4—101no—
206C3×C4—102no—
207C3×C4—202no—
208C3×C4#406112yes—
209C3×C4#406412yes—
210C2×C5C2×C3×#10011yescharacteristic
211C2×C5C3×#41912yes—
212D5—22no—
213C23—51no—
214Q8—42no—
215Q8—202no—
216Q8—204no—
217C2×C4—22no—
218C2×C4—52no—
219C2×C4—51no—
220C2×C4—102no—
221C2×C4—102no—
222C2×C4—102no—
223C2×C4—102no—
224C2×C4—204no—
225C2×C4C2×C3×C4×D511yescharacteristic
226C2×C4C3×D4×D512yes—
227C8—42no—
228C8—202no—
229C2×C3—102no—
230C2×C3D5×#10011yescharacteristic
231C2×C3#6509112yes—
232C5C3×#155811yescharacteristic, complemented, Sylow
233C22—52no—
234C22—102no—
235C22C3×D5×C22⋊C411yescharacteristic
236C4—21no—
237C4—42no—
238C4—101no—
239C4—102no—
240C4—202no—
241C4C3×#406112yes—
242C4C3×#406412yes—
243C3#1059928011yescharacteristic, direct product factor, Sylow
244C2—102no—
245C2C3×D5×#10011yescharacteristic
246C2C3×#6509112yes—
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#333C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC42×C5C23×C3
hypercenterC3×#333D5
hypocenterC5C3×#1558
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#333

Complements

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

NH ≅ G/Ntype
3. C3×C5×#333C2semidirect
4. C3×#64766C2semidirect
5. C3×#64701C2semidirect
6. #10599280C3direct (N × H)
21. C5×#333C2×C3semidirect
22. #64766C2×C3semidirect
23. #64701C2×C3semidirect
43. C3×#333D5semidirect
102. #333C3×D5semidirect
199. C3×C5#1558semidirect
232. C5C3×#1558semidirect
243. C3#10599280direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×C4⋊Q82
C3×#651242
C3×C5×#3332
C3×#647662
C3×#647012
#105992803
C3×#15585