Finite Group Databasebeta

← C3×#10599175 #14284700

Subgroups — C3×#10599175 #14284700

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×#66050C211yesmaximal, characteristic
2C3×#65122C212yesmaximal, complemented
3C3×C5×#331C211yesmaximal, characteristic, complemented
4C3×#64764C211yesmaximal, characteristic, complemented
5C3×#64701C212yesmaximal, complemented
6#10599175C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#711C412yes—
8C3×C5×#127C2211yescharacteristic
9C3×#4084—22no—
10C3×#4082C412yes—
11C3×D4×Dic5—22no—
12C3×C42×D5C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14C3×C5×C4⋊C8C2212yes—
15C3×#3952—22no—
16C3×C8×Dic5—22no—
17C3×C4⋊#168C2212yes—
18C3×#1543—51nomaximal, Hall
19#66050C2×C311yescharacteristic
20#65122C2×C312yescomplemented
21C5×#331C2×C311yescharacteristic, complemented
22#64764C2×C311yescharacteristic, complemented
23#64701C2×C312yescomplemented
24C2×C3×C5×D4—22no—
25C2×C3×C5×D4C2×C412yes—
26C2×C3×C22⋊D5—22no—
27C22×C3×Dic5—22no—
28C3×#711—44no—
29C2×C3×C4×D5C2×C411yescharacteristic
30C2×C3×C4×D5D412yes—
31C2×C3×Dic10C2×C412yes—
32C2×C3×C5×C8—22no—
33C3×C42×C5C2311yescharacteristic
34C3×C22⋊Dic5—24no—
35C3×C4⋊Dic5—22no—
36C3×C4×Dic5C2×C411yescharacteristic
37C3×C4×Dic5D412yes—
38C2×C3×#168—22no—
39C3×#532—51no—
40C3×#431—52no—
41C3×#333—52no—
42C3×#331—51no—
43C3×#331D511yescharacteristic, complemented
44C2×#711C3×C412yes—
45C5×#127C22×C311yescharacteristic
46#4084—22no—
47#4082C3×C412yes—
48D4×Dic5—22no—
49C42×D5C22×C311yescharacteristic
50#4015C22×C311yescharacteristic
51C5×C4⋊C8C22×C312yes—
52#3952—22no—
53C8×Dic5—22no—
54C4⋊#168C22×C312yes—
55#1543—51noSylow
56C23×C3×C5—22no—
57C22×C3×D5C22⋊C411yescharacteristic
58C3×C5×D4—42no—
59C3×C5×D4—42no—
60C3×C5×D4—42no—
61C2×C3×C4×C5C22×C411yescharacteristic
62C2×C3×C4×C5C2×D412yes—
63C3×C22⋊D5—44no—
64C2×C3×Dic5—22no—
65C2×C3×Dic5—44no—
66C2×C3×Dic5C22⋊C412yes—
67C2×C3×Dic5C22⋊C411yescharacteristic
68C3×C4×D5—22no—
69C3×C4×D5—22no—
70C3×C4×D5—22no—
71C3×Dic10—42no—
72C3×C5×C8—42no—
73C3×#168—42no—
74C2×C3×#41—52no—
75C3×C4⋊Q8—51no—
76C3×#127C2×D511yescharacteristic
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×D4—22no—
86C2×C5×D4C2×C3×C412yes—
87C2×C22⋊D5—22no—
88C22×Dic5—22no—
89#711—44no—
90C2×C4×D5C2×C3×C411yescharacteristic
91C2×C4×D5C3×D412yes—
92C2×Dic10C2×C3×C412yes—
93C2×C5×C8—22no—
94C42×C5C23×C311yescharacteristic
95C22⋊Dic5—24no—
96C4⋊Dic5—22no—
97C4×Dic5C2×C3×C411yescharacteristic
98C4×Dic5C3×D412yes—
99C2×#168—22no—
100#532—51no—
101#431—52no—
102#333—52no—
103#331—51no—
104#331C3×D511yescharacteristic, complemented
105C22×C3×C5—42no—
106C22×C3×C5—44no—
107C22×C3×C5C2×C22⋊C411yescharacteristic
108C2×C3×D5—21no—
109C2×C3×D5—22no—
110C3×C4×C5—21no—
111C3×C4×C5#13512yes—
112C3×C4×C5#13512yes—
113C3×Dic5—22no—
114C3×Dic5—42no—
115C3×Dic5#10012yes—
116C3×#41—204no—
117C2×C3×Q8—52no—
118C2×C3×D4—22no—
119C2×C3×D4—102no—
120C2×C3×D4C4×D512yes—
121C22×C3×C4—51no—
122C22×C3×C4—52no—
123C22×C3×C4—102no—
124C2×C3×C8—22no—
125C2×C3×C8—102no—
126C3×C4⋊C4—102no—
127C3×C22⋊C4—104no—
128C3×C42—51no—
129C3×C42—52no—
130C3×C42C22×D511yescharacteristic
131C23×C5—22no—
132C22×D5C3×C22⋊C411yescharacteristic
133C5×D4—42no—
134C5×D4—42no—
135C5×D4—42no—
136C2×C4×C5C22×C3×C411yescharacteristic
137C2×C4×C5C2×C3×D412yes—
138C22⋊D5—44no—
139C2×Dic5—22no—
140C2×Dic5—44no—
141C2×Dic5C3×C22⋊C412yes—
142C2×Dic5C3×C22⋊C411yescharacteristic
143C4×D5—22no—
144C4×D5—22no—
145C4×D5—22no—
146Dic10—42no—
147C5×C8—42no—
148#168—42no—
149C2×#41—52no—
150C4⋊Q8—51no—
151#127C2×C3×D511yescharacteristic
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×C5—82no—
161C2×C3×C5C2×#10011yescharacteristic
162C2×C3×C5#41612yes—
163C3×D5—41no—
164C23×C3—22no—
165C23×C3—51no—
166C3×Q8—202no—
167C3×D4—42no—
168C3×D4—42no—
169C3×D4—42no—
170C3×D4—204no—
171C2×C3×C4—51no—
172C2×C3×C4—52no—
173C2×C3×C4—102no—
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×C5—42no—
183C22×C5—44no—
184C22×C5C2×C3×C22⋊C411yescharacteristic
185C2×D5—21no—
186C2×D5—22no—
187C4×C5—21no—
188C4×C5C3×#13512yes—
189C4×C5C3×#13512yes—
190Dic5—22no—
191Dic5—42no—
192Dic5C3×#10012yes—
193#41—204no—
194C2×Q8—52no—
195C2×D4—22no—
196C2×D4—102no—
197C2×D4C3×C4×D512yes—
198C22×C4—51no—
199C22×C4—52no—
200C22×C4—102no—
201C2×C8—22no—
202C2×C8—102no—
203C4⋊C4—102no—
204C22⋊C4—104no—
205C42—51no—
206C42—52no—
207C42C22×C3×D511yescharacteristic
208C3×C5#154311yescharacteristic, complemented, Hall
209C22×C3—42no—
210C22×C3—44no—
211C22×C3—101no—
212C22×C3—102no—
213C22×C3D5×C22⋊C411yescharacteristic
214C3×C4—21no—
215C3×C4—52no—
216C3×C4—102no—
217C3×C4—202no—
218C3×C4#405812yes—
219C3×C4#406212yes—
220C2×C5—82no—
221C2×C5C2×C3×#10011yescharacteristic
222C2×C5C3×#41612yes—
223D5—41no—
224C23—22no—
225C23—51no—
226Q8—202no—
227D4—42no—
228D4—42no—
229D4—42no—
230D4—204no—
231C2×C4—51no—
232C2×C4—52no—
233C2×C4—102no—
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—82no—
243C2×C3—201no—
244C2×C3D5×#10011yescharacteristic
245C2×C3#6506112yes—
246C5C3×#154311yescharacteristic, complemented, Sylow
247C22—42no—
248C22—44no—
249C22—101no—
250C22—102no—
251C22C3×D5×C22⋊C411yescharacteristic
252C4—21no—
253C4—52no—
254C4—102no—
255C4—202no—
256C4C3×#405812yes—
257C4C3×#406212yes—
258C3#1059917511yescharacteristic, direct product factor, Sylow
259C2—82no—
260C2—201no—
261C2C3×D5×#10011yescharacteristic
262C2C3×#6506112yes—
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#331C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66050C2
cosocleC42×C5C23×C3
hypercenterC3×#331D5
hypocenterC5C3×#1543
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#331

Complements

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

NH ≅ G/Ntype
2. C3×#65122C2semidirect
3. C3×C5×#331C2semidirect
4. C3×#64764C2semidirect
5. C3×#64701C2semidirect
6. #10599175C3direct (N × H)
20. #65122C2×C3semidirect
21. C5×#331C2×C3semidirect
22. #64764C2×C3semidirect
23. #64701C2×C3semidirect
43. C3×#331D5semidirect
104. #331C3×D5semidirect
208. C3×C5#1543semidirect
246. C5C3×#1543semidirect
258. C3#10599175direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660502
C3×#651222
C3×C5×#3312
C3×#647642
C3×#647012
#105991753
C3×#15435