Finite Group Databasebeta

← C3×#91771 #13087980

Subgroups — C3×#91771 #13087980

Order 1440.

554 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C23×C3×D15C211yesmaximal, characteristic, complemented
2C2×C3×#1220C211yesmaximal, characteristic, complemented
3C2×C3×D60C212yesmaximal, complemented
4C32×C5×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#6714C212yesmaximal, complemented
6#91771C311yesmaximal, characteristic, direct product factor
7C3×#4028—31nomaximal
8C23×C32×C5C2211yescharacteristic
9C22×C3×D15—22no—
10C22×C3×D15—24no—
11C22×C3×D15C2212yes—
12C22×C3×D15C2211yescharacteristic, complemented
13C2×C32×C4×C5C2212yescomplemented
14C3×#1220—22no—
15C2×C3×Dic15C2211yescharacteristic, complemented
16C3×D60—24no—
17C3×#882—51nomaximal, Hall
18C23×D15C2×C311yescharacteristic, complemented
19C23×C3×D5—31no—
20C2×#1220C2×C311yescharacteristic, complemented
21C2×D60C2×C312yescomplemented
22C2×C3×C22⋊D5—31no—
23C2×C3×D20—32no—
24C3×C5×C22⋊C4—21no—
25C3×C5×C22⋊C4D311yescharacteristic, complemented
26C3×C5×C22⋊C4C2×C311yescharacteristic, complemented
27#6714C2×C312yescomplemented
28C3×#685—32no—
29C22×C32×C5—22no—
30C22×C32×C5D412yescomplemented
31C22×C32×C5C2311yescharacteristic
32C2×C3×D15—28no—
33C2×C3×D15—22no—
34C2×C3×D15—22no—
35C2×C3×D15—22no—
36C2×C3×D15—21no—
37C2×C3×D15D414yescomplemented
38C32×C4×C5—22no—
39C3×Dic15—21no—
40#4028—31noHall
41C23×C3×D3—51no—
42C2×C3×#67—51no—
43C2×C3×D12—52no—
44C32×C22⋊C4D511yescharacteristic, complemented
45C3×(C2×D3)⋊C4—52no—
46C23×C3×C5—21no—
47C23×C3×C5C2×D311yescharacteristic
48C23×C3×C5C22×C311yescharacteristic
49C22×D15—22no—
50C22×D15—24no—
51C22×D15C22×C312yes—
52C22×D15C22×C311yescharacteristic, complemented
53C22×C3×D5—32no—
54C22×C3×D5—31no—
55C22×C3×D5—64no—
56C22×C3×D5—62no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5C2×D312yescomplemented
59C2×C3×C4×C5C22×C312yescomplemented
60#1220—22no—
61C2×Dic15C22×C311yescharacteristic, complemented
62D60—24no—
63C3×C22⋊D5—62no—
64C2×C3×Dic5—31no—
65C3×D20—64no—
66C3×#120—151no—
67#882—51no—
68C2×C32×C5—22no—
69C2×C32×C5C2×D411yescharacteristic
70C2×C32×C5C2×D412yes—
71C3×D15—24no—
72C3×D15—41no—
73C23×D5—31no—
74C2×C22⋊D5—31no—
75C2×D20—32no—
76C5×C22⋊C4C3×D311yescharacteristic, complemented
77#685—32no—
78C23×C32C2×D511yescharacteristic
79C22×C3×D3—52no—
80C22×C3×D3—51no—
81C22×C3×D3—104no—
82C22×C3×D3—102no—
83C2×C32×C4C2×D512yescomplemented
84C3×#67—102no—
85C2×C3×Dic3—51no—
86C3×D12—104no—
87C22×C3×C5—22no—
88C22×C3×C5—22no—
89C22×C3×C5—22no—
90C22×C3×C5—21no—
91C22×C3×C5—42no—
92C22×C3×C5D1212yescomplemented
93C22×C3×C5C3×D412yescomplemented
94C22×C3×C5C22×D311yescharacteristic
95C22×C3×C5C23×C311yescharacteristic
96C2×D15—28no—
97C2×D15—22no—
98C2×D15—22no—
99C2×D15—22no—
100C2×D15—21no—
101C2×D15C3×D414yescomplemented
102C2×C3×D5—34no—
103C2×C3×D5—68no—
104C2×C3×D5—62no—
105C2×C3×D5—62no—
106C2×C3×D5—61no—
107C2×C3×D5—62no—
108C3×C4×C5—22no—
109C3×C4×C5—22no—
110C3×C4×C5—42no—
111Dic15—21no—
112C3×Dic5—61no—
113C24×C3—151no—
114C23×D3—51no—
115C2×C3×D4—151no—
116C2×C3×D4—152no—
117C2×#67—51no—
118C2×D12—52no—
119C3×C22⋊C4—21no—
120C3×C22⋊C4—152no—
121C3×C22⋊C4C3×D511yescharacteristic, complemented
122C3×C22⋊C4D1511yescharacteristic, complemented
123(C2×D3)⋊C4—52no—
124C32×C5#12011yescharacteristic, complemented, Hall
125C23×C5C2×C3×D311yescharacteristic
126C22×D5—32no—
127C22×D5—31no—
128C22×D5—64no—
129C22×D5—62no—
130C2×C4×C5C2×C3×D312yescomplemented
131C22⋊D5—62no—
132C2×Dic5—31no—
133D20—64no—
134C22×C32—22no—
135C22×C32D2012yescomplemented
136C22×C32C22×D511yescharacteristic
137C2×C3×D3—54no—
138C2×C3×D3—108no—
139C2×C3×D3—102no—
140C2×C3×D3—102no—
141C2×C3×D3—101no—
142C2×C3×D3—102no—
143C32×C4—22no—
144C3×Dic3—101no—
145#120—151noSylow
146C2×C3×C5—22no—
147C2×C3×C5—22no—
148C2×C3×C5—21no—
149C2×C3×C5—22no—
150C2×C3×C5—42no—
151C2×C3×C5C2×D1211yescharacteristic
152C2×C3×C5D3×D412yes—
153C2×C3×C5C2×C3×D411yescharacteristic
154C2×C3×C5C2×C3×D412yes—
155D15—24no—
156D15—41no—
157C3×D5—64no—
158C3×D5—121no—
159C23×C3—21no—
160C23×C3—152no—
161C23×C3—151no—
162C23×C3—304no—
163C23×C3—302no—
164C23×C3C2×C3×D511yescharacteristic
165C23×C3C2×D1511yescharacteristic
166C22×D3—52no—
167C22×D3—51no—
168C22×D3—104no—
169C22×D3—102no—
170C3×D4—304no—
171C3×D4—302no—
172C2×C3×C4—22no—
173C2×C3×C4—151no—
174C2×C3×C4C2×C3×D512yescomplemented
175C2×C3×C4C2×D1512yescomplemented
176#67—102no—
177C2×Dic3—51no—
178D12—104no—
179C22×C5—22no—
180C22×C5C3×D1212yescomplemented
181C22×C5C22×C3×D311yescharacteristic
182C2×D5—34no—
183C2×D5—68no—
184C2×D5—62no—
185C2×D5—62no—
186C2×D5—61no—
187C2×D5—62no—
188C4×C5—22no—
189Dic5—61no—
190C2×C32—22no—
191C2×C32C2×D2011yescharacteristic
192C2×C32D4×D512yes—
193C3×D3—104no—
194C3×D3—201no—
195C24—151no—
196C2×D4—151no—
197C2×D4—152no—
198C22⋊C4—152no—
199C22⋊C4C3×D1511yescharacteristic, complemented
200C3×C5—21no—
201C3×C5#88211yescharacteristic, complemented
202C3×C5C3×#12011yescharacteristic, complemented
203C22×C3—22no—
204C22×C3—22no—
205C22×C3—22no—
206C22×C3—21no—
207C22×C3—42no—
208C22×C3—154no—
209C22×C3—308no—
210C22×C3—302no—
211C22×C3—302no—
212C22×C3—301no—
213C22×C3—302no—
214C22×C3C3×D2012yescomplemented
215C22×C3D6012yescomplemented
216C22×C3C22×C3×D511yescharacteristic
217C22×C3C22×D1511yescharacteristic
218C2×D3—54no—
219C2×D3—108no—
220C2×D3—102no—
221C2×D3—102no—
222C2×D3—101no—
223C2×D3—102no—
224C3×C4—22no—
225C3×C4—22no—
226C3×C4—42no—
227C3×C4—301no—
228Dic3—101no—
229C2×C5—22no—
230C2×C5C2×C3×D1211yescharacteristic
231C2×C5C3×D3×D412yes—
232D5—64no—
233D5—121no—
234C32#402811yescharacteristic, complemented, Sylow
235C23—152no—
236C23—151no—
237C23—304no—
238C23—302no—
239C23C2×C3×D1511yescharacteristic
240D4—304no—
241D4—302no—
242C2×C4—151no—
243C2×C4C2×C3×D1512yescomplemented
244C2×C3—22no—
245C2×C3—22no—
246C2×C3—21no—
247C2×C3—22no—
248C2×C3—42no—
249C2×C3—304no—
250C2×C3—601no—
251C2×C3C2×C3×D2011yescharacteristic
252C2×C3C3×D4×D512yes—
253C2×C3C2×D6011yescharacteristic
254C2×C3D4×D1512yes—
255D3—104no—
256D3—201no—
257C5C3×#88211yescharacteristic, complemented, Sylow
258C22—22no—
259C22—154no—
260C22—308no—
261C22—302no—
262C22—302no—
263C22—301no—
264C22—302no—
265C22C3×D6012yescomplemented
266C22C22×C3×D1511yescharacteristic
267C4—22no—
268C4—301no—
269C3—21no—
270C3C3×#402811yescharacteristic, complemented
271C3#9177111yescharacteristic, direct product factor
272C2—22no—
273C2—304no—
274C2—601no—
275C2C2×C3×D6011yescharacteristic
276C2C3×D4×D1512yes—
subgroupG/H
centerC22×C3C22×D15
commutator, cosocleC22×C3×C5C23×C3
FrattiniC22C22×C3×D15
FittingC32×C5×C22⋊C4C2
socleC22×C32×C5C23
hypercenterC3×C22⋊C4D15
hypocenterC3×C5C3×#120
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C3×D15C2semidirect
2. C2×C3×#1220C2semidirect
3. C2×C3×D60C2semidirect
4. C32×C5×C22⋊C4C2semidirect
5. C3×#6714C2semidirect
6. #91771C3direct (N × H)
12. C22×C3×D15C22semidirect
13. C2×C32×C4×C5C22semidirect
15. C2×C3×Dic15C22semidirect
18. C23×D15C2×C3semidirect
20. C2×#1220C2×C3semidirect
21. C2×D60C2×C3semidirect
25. C3×C5×C22⋊C4D3semidirect
26. C3×C5×C22⋊C4C2×C3semidirect
27. #6714C2×C3semidirect
30. C22×C32×C5D4semidirect
37. C2×C3×D15D4semidirect
44. C32×C22⋊C4D5semidirect
52. C22×D15C22×C3semidirect
58. C2×C3×C4×C5C2×D3semidirect
59. C2×C3×C4×C5C22×C3semidirect
61. C2×Dic15C22×C3semidirect
76. C5×C22⋊C4C3×D3semidirect
83. C2×C32×C4C2×D5semidirect
92. C22×C3×C5D12semidirect
93. C22×C3×C5C3×D4semidirect
101. C2×D15C3×D4semidirect
121. C3×C22⋊C4C3×D5semidirect
122. C3×C22⋊C4D15semidirect
124. C32×C5#120semidirect
130. C2×C4×C5C2×C3×D3semidirect
135. C22×C32D20semidirect
174. C2×C3×C4C2×C3×D5semidirect
175. C2×C3×C4C2×D15semidirect
180. C22×C5C3×D12semidirect
199. C22⋊C4C3×D15semidirect
201. C3×C5#882semidirect
202. C3×C5C3×#120semidirect
214. C22×C3C3×D20semidirect
215. C22×C3D60semidirect
234. C32#4028semidirect
243. C2×C4C2×C3×D15semidirect
257. C5C3×#882semidirect
265. C22C3×D60semidirect
270. C3C3×#4028semidirect
271. C3#91771direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×D152
C2×C3×#12202
C2×C3×D602
C32×C5×C22⋊C42
C3×#67142
#917713
C3×#40283
C3×#8825