Finite Group Databasebeta

← C3×#10599275 #14284706

Subgroups — C3×#10599275 #14284706

Order 1920.

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

normal subgroups only

This group has 492 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×#66059C211yesmaximal, characteristic
2C3×#65122C212yesmaximal, complemented
3C3×C5×#333C211yesmaximal, characteristic, complemented
4C3×#64766C211yesmaximal, characteristic, complemented
5C3×#64705C212yesmaximal, complemented
6#10599275C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#713C412yes—
8C3×C5×C4⋊Q8C2211yescharacteristic
9C3×#4093C412yes—
10C3×#4041—22no—
11C3×#4039—22no—
12C3×#4020C2211yescharacteristic
13C3×C42×D5C2211yescharacteristic
14C3×C5×C4⋊C8C2212yes—
15C3×#3952—22no—
16C3×C8×Dic5—22no—
17C3×C4⋊#168C2212yes—
18C3×#1543—51nomaximal, Hall
19#66059C2×C311yescharacteristic
20#65122C2×C312yescomplemented
21C5×#333C2×C311yescharacteristic, complemented
22#64766C2×C311yescharacteristic, complemented
23#64705C2×C312yescomplemented
24C2×C3×C5×Q8C2×C412yes—
25C3×#713—44no—
26C2×C3×D20—22no—
27C2×C3×D20—22no—
28C2×C3×D20C2×C412yes—
29C2×C3×C4×D5—22no—
30C2×C3×C4×D5C2×C411yescharacteristic
31C2×C3×C4×D5D412yes—
32C2×C3×C5×C8—22no—
33C3×C5×C4⋊C4—22no—
34C3×C42×C5C2311yescharacteristic
35C3×#685—24no—
36C3×C4×Dic5C2×C411yescharacteristic
37C3×C4×Dic5D412yes—
38C2×C3×#168—22no—
39C3×#532—51no—
40C3×#431—52no—
41C3×#333—51no—
42C3×#333D511yescharacteristic, complemented
43C3×#331—52no—
44C2×#713C3×C412yes—
45C5×C4⋊Q8C22×C311yescharacteristic
46#4093C3×C412yes—
47#4041—22no—
48#4039—22no—
49#4020C22×C311yescharacteristic
50C42×D5C22×C311yescharacteristic
51C5×C4⋊C8C22×C312yes—
52#3952—22no—
53C8×Dic5—22no—
54C4⋊#168C22×C312yes—
55#1543—51noSylow
56C22×C3×D5—22no—
57C22×C3×D5C22⋊C411yescharacteristic
58C3×C5×Q8—42no—
59C2×C3×C4×C5—22no—
60C2×C3×C4×C5C22×C411yescharacteristic
61C2×C3×C4×C5C2×D412yes—
62C2×C3×Dic5C22⋊C412yes—
63C2×C3×Dic5C22⋊C411yescharacteristic
64C3×D20—42no—
65C3×D20—44no—
66C3×D20—42no—
67C3×D20—42no—
68C3×C4×D5—22no—
69C3×C4×D5—22no—
70C3×C4×D5—22no—
71C3×C4×D5—44no—
72C3×C5×C8—42no—
73C3×#168—42no—
74C2×C3×#41—52no—
75C3×C4⋊Q8C2×D511yescharacteristic
76C3×#127—51no—
77C3×#124—52no—
78C3×#121—102no—
79C3×C4×D4—102no—
80C2×C3×C42—51no—
81C3×C4⋊C8—52no—
82C3×C4⋊C8C2×D512yes—
83C3×C22⋊C8—102no—
84C3×C4×C8—102no—
85C2×C5×Q8C2×C3×C412yes—
86#713—44no—
87C2×D20—22no—
88C2×D20—22no—
89C2×D20C2×C3×C412yes—
90C2×C4×D5—22no—
91C2×C4×D5C2×C3×C411yescharacteristic
92C2×C4×D5C3×D412yes—
93C2×C5×C8—22no—
94C5×C4⋊C4—22no—
95C42×C5C23×C311yescharacteristic
96#685—24no—
97C4×Dic5C2×C3×C411yescharacteristic
98C4×Dic5C3×D412yes—
99C2×#168—22no—
100#532—51no—
101#431—52no—
102#333—51no—
103#333C3×D511yescharacteristic, complemented
104#331—52no—
105C22×C3×C5C2×C22⋊C411yescharacteristic
106C2×C3×D5—21no—
107C2×C3×D5—22no—
108C2×C3×D5—42no—
109C2×C3×D5—44no—
110C3×C4×C5—21no—
111C3×C4×C5—42no—
112C3×C4×C5#13512yes—
113C3×C4×C5#13512yes—
114C3×Dic5—22no—
115C3×Dic5#10012yes—
116C3×#41—204no—
117C2×C3×Q8C4×D512yes—
118C2×C3×D4—52no—
119C2×C3×D4—102no—
120C2×C3×D4—102no—
121C22×C3×C4—51no—
122C22×C3×C4—52no—
123C22×C3×C4—102no—
124C2×C3×C8—22no—
125C2×C3×C8—102no—
126C3×C4⋊C4—22no—
127C3×C22⋊C4—104no—
128C3×C42—51no—
129C3×C42—52no—
130C3×C42C22×D511yescharacteristic
131C22×D5—22no—
132C22×D5C3×C22⋊C411yescharacteristic
133C5×Q8—42no—
134C2×C4×C5—22no—
135C2×C4×C5C22×C3×C411yescharacteristic
136C2×C4×C5C2×C3×D412yes—
137C2×Dic5C3×C22⋊C412yes—
138C2×Dic5C3×C22⋊C411yescharacteristic
139D20—42no—
140D20—44no—
141D20—42no—
142D20—42no—
143C4×D5—22no—
144C4×D5—22no—
145C4×D5—22no—
146C4×D5—44no—
147C5×C8—42no—
148#168—42no—
149C2×#41—52no—
150C4⋊Q8C2×C3×D511yescharacteristic
151#127—51no—
152#124—52no—
153#121—102no—
154C4×D4—102no—
155C2×C42—51no—
156C4⋊C8—52no—
157C4⋊C8C2×C3×D512yes—
158C22⋊C8—102no—
159C4×C8—102no—
160C2×C3×C5C2×#10011yescharacteristic
161C2×C3×C5#41612yes—
162C3×D5—41no—
163C3×D5—82no—
164C23×C3—51no—
165C23×C3—102no—
166C3×Q8—42no—
167C3×D4—202no—
168C3×D4—204no—
169C3×D4—202no—
170C3×D4—202no—
171C2×C3×C4—22no—
172C2×C3×C4—51no—
173C2×C3×C4—52no—
174C2×C3×C4—102no—
175C2×C3×C4—102no—
176C2×C3×C4—102no—
177C2×C3×C4—204no—
178C2×C3×C4C2×C4×D511yescharacteristic
179C2×C3×C4D4×D512yes—
180C3×C8—42no—
181C3×C8—202no—
182C22×C5C2×C3×C22⋊C411yescharacteristic
183C2×D5—21no—
184C2×D5—22no—
185C2×D5—42no—
186C2×D5—44no—
187C4×C5—21no—
188C4×C5—42no—
189C4×C5C3×#13512yes—
190C4×C5C3×#13512yes—
191Dic5—22no—
192Dic5C3×#10012yes—
193#41—204no—
194C2×Q8C3×C4×D512yes—
195C2×D4—52no—
196C2×D4—102no—
197C2×D4—102no—
198C22×C4—51no—
199C22×C4—52no—
200C22×C4—102no—
201C2×C8—22no—
202C2×C8—102no—
203C4⋊C4—22no—
204C22⋊C4—104no—
205C42—51no—
206C42—52no—
207C42C22×C3×D511yescharacteristic
208C3×C5#154311yescharacteristic, complemented, Hall
209C22×C3—101no—
210C22×C3—102no—
211C22×C3—202no—
212C22×C3—204no—
213C22×C3D5×C22⋊C411yescharacteristic
214C3×C4—21no—
215C3×C4—42no—
216C3×C4—52no—
217C3×C4—102no—
218C3×C4#406212yes—
219C3×C4#406512yes—
220C2×C5C2×C3×#10011yescharacteristic
221C2×C5C3×#41612yes—
222D5—41no—
223D5—82no—
224C23—51no—
225C23—102no—
226Q8—42no—
227D4—202no—
228D4—204no—
229D4—202no—
230D4—202no—
231C2×C4—22no—
232C2×C4—51no—
233C2×C4—52no—
234C2×C4—102no—
235C2×C4—102no—
236C2×C4—102no—
237C2×C4—204no—
238C2×C4C2×C3×C4×D511yescharacteristic
239C2×C4C3×D4×D512yes—
240C8—42no—
241C8—202no—
242C2×C3—201no—
243C2×C3—402no—
244C2×C3D5×#10011yescharacteristic
245C2×C3#6509312yes—
246C5C3×#154311yescharacteristic, complemented, Sylow
247C22—101no—
248C22—102no—
249C22—202no—
250C22—204no—
251C22C3×D5×C22⋊C411yescharacteristic
252C4—21no—
253C4—42no—
254C4—52no—
255C4—102no—
256C4C3×#406212yes—
257C4C3×#406512yes—
258C3#1059927511yescharacteristic, direct product factor, Sylow
259C2—201no—
260C2—402no—
261C2C3×D5×#10011yescharacteristic
262C2C3×#6509312yes—
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#333C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66059C2
cosocleC42×C5C23×C3
hypercenterC3×#333D5
hypocenterC5C3×#1543
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
2. C3×#65122C2semidirect
3. C3×C5×#333C2semidirect
4. C3×#64766C2semidirect
5. C3×#64705C2semidirect
6. #10599275C3direct (N × H)
20. #65122C2×C3semidirect
21. C5×#333C2×C3semidirect
22. #64766C2×C3semidirect
23. #64705C2×C3semidirect
42. C3×#333D5semidirect
103. #333C3×D5semidirect
208. C3×C5#1543semidirect
246. C5C3×#1543semidirect
258. C3#10599275direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660592
C3×#651222
C3×C5×#3332
C3×#647662
C3×#647052
#105992753
C3×#15435