Finite Group Databasebeta

← #13087569

Subgroups — #13087569

Order 1440.

662 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 106 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
2C2×#67149C212yesmaximal, complemented
3C3×#6719C211yesmaximal, characteristic, complemented
4C3×C5×#217C211yesmaximal, characteristic, complemented
5#10623813C212yesmaximal, complemented
6C22⋊C4×D15—31nomaximal
7#91561—31nomaximal
8C23×C32×C5C2211yescharacteristic
9C22×C3⋊D15—24no—
10C22×C3⋊D15C414yescomplemented
11C22×C3⋊D15C2211yescharacteristic
12C22×C3⋊D15C2211yescharacteristic
13C2×C3×Dic15C2212yescomplemented
14C2×C3×C5×Dic3C2212yescomplemented
15#67149—24no—
16#63974—51nomaximal, Hall
17C23×D15—31no—
18C23×D15—31no—
19C23×D15—61no—
20C2×C4×D15—32no—
21C2×#1200—32no—
22C3×C5×C22⋊C4—31no—
23#6719D311yescharacteristic, complemented
24#6714—32no—
25C5×#217D311yescharacteristic, complemented
26C3×C22⋊Dic5—31no—
27#6667—32no—
28C22×C32×C5—22no—
29C22×C32×C5C2×C412yescomplemented
30C22×C32×C5C2311yescharacteristic
31C2×C3⋊D15—22no—
32C2×C3⋊D15—28no—
33C2×C3⋊D15C2×C412yes—
34C2×C3⋊D15C2×C412yescomplemented
35C2×C3⋊D15D414yes—
36C3×Dic15—22no—
37C3×C5×Dic3—22no—
38D5×C22⋊C4—91noHall
39C23×C3⋊D3—51no—
40C2×#624—52no—
41C3×#217—51no—
42C3×#217D511yescharacteristic, complemented
43#3722—52no—
44C23×C3×C5—21no—
45C23×C3×C5C2×D311yescharacteristic
46C23×C3×C5C2×D311yescharacteristic
47C22×D15—31no—
48C22×D15—31no—
49C22×D15—34no—
50C22×D15—34no—
51C22×D15—31no—
52C22×D15—31no—
53C22×D15—64no—
54C22×D15—64no—
55C22×D15—64no—
56C22×D15—61no—
57C22×D15—61no—
58C22×D15—68no—
59C2×C3×C4×C5—32no—
60C2×Dic15C2×D312yescomplemented
61C4×D15—64no—
62C2×C5×Dic3C2×D312yescomplemented
63C2×C3×Dic5—32no—
64#1200—64no—
65D3×C22⋊C4—151no—
66D3×C22⋊C4—151no—
67C2×C32×C5—22no—
68C2×C32×C5C22×C411yescharacteristic
69C2×C32×C5C2×D412yes—
70C3⋊D15—22no—
71C3⋊D15C22⋊C414yescomplemented
72C23×D5—91no—
73C2×C4×D5—92no—
74C5×C22⋊C4—31no—
75C22⋊Dic5—31no—
76#685—92no—
77C23×C32C2×D511yescharacteristic
78C22×C3⋊D3—51no—
79C22×C3⋊D3—54no—
80C22×C3⋊D3—51no—
81C22×C3⋊D3—104no—
82C2×C3×Dic3—52no—
83C2×C3×Dic3C2×D512yescomplemented
84#624—104no—
85C22×C3×C5—24no—
86C22×C3×C5—22no—
87C22×C3×C5—22no—
88C22×C3×C5—22no—
89C22×C3×C5—21no—
90C22×C3×C5C4×D312yescomplemented
91C22×C3×C5C4×D312yescomplemented
92C22×C3×C5C22×D311yescharacteristic
93C22×C3×C5C22×D311yescharacteristic
94C2×D15—32no—
95C2×D15—32no—
96C2×D15—34no—
97C2×D15—34no—
98C2×D15—32no—
99C2×D15—32no—
100C2×D15—62no—
101C2×D15—62no—
102C2×D15—64no—
103C2×D15—68no—
104C2×D15—68no—
105C2×D15—616no—
106C2×D15—64no—
107C2×D15—62no—
108C2×D15—62no—
109C3×C4×C5—62no—
110Dic15—22no—
111C3×Dic5—62no—
112C5×Dic3—22no—
113C23×D3—151no—
114C23×D3—151no—
115C23×D3—301no—
116C2×C4×D3—152no—
117C2×C4×D3—152no—
118C3×C22⋊C4—31no—
119C3×C22⋊C4—151no—
120#217—51no—
121#217D1511yescharacteristic, complemented
122(C2×D3)⋊C4—152no—
123(C2×D3)⋊C4—152no—
124C32×C5C2×C22⋊C411yescharacteristic, complemented, Hall
125C23×C5D3211yescharacteristic
126C22×D5—91no—
127C22×D5—94no—
128C22×D5—91no—
129C22×D5—184no—
130C2×C4×C5—32no—
131C2×Dic5—32no—
132C4×D5—184no—
133C22×C32—22no—
134C22×C32C4×D512yescomplemented
135C22×C32C22×D511yescharacteristic
136C2×C3⋊D3—52no—
137C2×C3⋊D3—54no—
138C2×C3⋊D3—52no—
139C2×C3⋊D3—108no—
140C2×C3⋊D3—102no—
141C3×Dic3—22no—
142C3×Dic3—102no—
143C2×C22⋊C4—451noSylow
144C2×C3×C5—24no—
145C2×C3×C5—22no—
146C2×C3×C5—22no—
147C2×C3×C5—21no—
148C2×C3×C5—22no—
149C2×C3×C5C2×C4×D311yescharacteristic
150C2×C3×C5C2×C4×D311yescharacteristic
151C2×C3×C5D3×D412yes—
152C2×C3×C5D3×D412yes—
153D15—34no—
154D15—34no—
155D15—64no—
156D15—64no—
157D15—62no—
158D15—62no—
159C23×C3—21no—
160C23×C3D3×D511yescharacteristic
161C23×C3C2×D1511yescharacteristic
162C22×D3—151no—
163C22×D3—151no—
164C22×D3—154no—
165C22×D3—154no—
166C22×D3—151no—
167C22×D3—151no—
168C22×D3—301no—
169C22×D3—304no—
170C22×D3—301no—
171C22×D3—304no—
172C22×D3—304no—
173C22×D3—308no—
174C2×C3×C4—32no—
175C2×C3×C4—152no—
176C2×Dic3—52no—
177C2×Dic3C2×D1512yescomplemented
178C4×D3—304no—
179C4×D3—304no—
180C22×C5—22no—
181C22×C5#62412yescomplemented
182C22×C5C2×D3211yescharacteristic
183C2×D5—92no—
184C2×D5—94no—
185C2×D5—92no—
186C2×D5—188no—
187C2×D5—182no—
188C4×C5—62no—
189Dic5—62no—
190C2×C32—22no—
191C2×C32C2×C4×D511yescharacteristic
192C2×C32D4×D512yes—
193C3⋊D3—54no—
194C3⋊D3—102no—
195C24—451no—
196C22×C4—452no—
197C22⋊C4—31no—
198C22⋊C4—151no—
199C22⋊C4—452no—
200C3×C5—21no—
201C3×C5D3×C22⋊C411yescharacteristic, complemented
202C3×C5D3×C22⋊C411yescharacteristic, complemented
203C22×C3—24no—
204C22×C3—22no—
205C22×C3—22no—
206C22×C3—22no—
207C22×C3—21no—
208C22×C3#120012yescomplemented
209C22×C3C4×D1512yescomplemented
210C22×C3C2×D3×D511yescharacteristic
211C22×C3C22×D1511yescharacteristic
212C2×D3—152no—
213C2×D3—154no—
214C2×D3—152no—
215C2×D3—154no—
216C2×D3—152no—
217C2×D3—152no—
218C2×D3—302no—
219C2×D3—304no—
220C2×D3—302no—
221C2×D3—308no—
222C2×D3—308no—
223C2×D3—3016no—
224C2×D3—304no—
225C2×D3—302no—
226C2×D3—302no—
227C3×C4—62no—
228C3×C4—302no—
229Dic3—22no—
230Dic3—102no—
231C2×C5—22no—
232C2×C5C2×#62411yescharacteristic
233C2×C5#381112yes—
234D5—94no—
235D5—182no—
236C32D5×C22⋊C411yescharacteristic, complemented, Sylow
237C23—451no—
238C23—454no—
239C23—451no—
240C23—904no—
241C23D3×D1511yescharacteristic
242C2×C4—32no—
243C2×C4—152no—
244C2×C4—904no—
245C2×C3—24no—
246C2×C3—22no—
247C2×C3—22no—
248C2×C3—21no—
249C2×C3—22no—
250C2×C3C2×#120011yescharacteristic
251C2×C3#679012yes—
252C2×C3C2×C4×D1511yescharacteristic
253C2×C3D4×D1512yes—
254D3—154no—
255D3—154no—
256D3—304no—
257D3—304no—
258D3—302no—
259D3—302no—
260C5#6397411yescharacteristic, complemented, Sylow
261C22—22no—
262C22—452no—
263C22—454no—
264C22—452no—
265C22—908no—
266C22—902no—
267C22#6714912yescomplemented
268C22C2×D3×D1511yescharacteristic
269C4—62no—
270C4—302no—
271C3—21no—
272C3#9156111yescharacteristic, complemented
273C3C22⋊C4×D1511yescharacteristic, complemented
274C2—22no—
275C2—454no—
276C2—902no—
277C2C2×#6714911yescharacteristic
278C2#1062421812yes—
subgroupG/H
center, FrattiniC22C2×D3×D15
commutatorC2×C32×C5C22×C4
FittingC23×C32×C5C22
socle, cosocleC22×C32×C5C23
prime radicalC23×C3⋊D15C2
hypercenterC23D3×D15
hypocenterC32×C5C2×C22⋊C4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×#67149C2semidirect
3. C3×#6719C2semidirect
4. C3×C5×#217C2semidirect
5. #10623813C2semidirect
10. C22×C3⋊D15C4semidirect
13. C2×C3×Dic15C22semidirect
14. C2×C3×C5×Dic3C22semidirect
23. #6719D3semidirect
25. C5×#217D3semidirect
29. C22×C32×C5C2×C4semidirect
34. C2×C3⋊D15C2×C4semidirect
42. C3×#217D5semidirect
60. C2×Dic15C2×D3semidirect
62. C2×C5×Dic3C2×D3semidirect
71. C3⋊D15C22⋊C4semidirect
83. C2×C3×Dic3C2×D5semidirect
90. C22×C3×C5C4×D3semidirect
91. C22×C3×C5C4×D3semidirect
121. #217D15semidirect
124. C32×C5C2×C22⋊C4semidirect
134. C22×C32C4×D5semidirect
177. C2×Dic3C2×D15semidirect
181. C22×C5#624semidirect
201. C3×C5D3×C22⋊C4semidirect
202. C3×C5D3×C22⋊C4semidirect
208. C22×C3#1200semidirect
209. C22×C3C4×D15semidirect
236. C32D5×C22⋊C4semidirect
260. C5#63974semidirect
267. C22#67149semidirect
272. C3#91561semidirect
273. C3C22⋊C4×D15semidirect

Maximal subgroups

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

subgroupindex
C23×C3⋊D152
C2×#671492
C3×#67192
C3×C5×#2172
#106238132
C22⋊C4×D153
#915613
#639745