Finite Group Databasebeta

← #13087582

Subgroups — #13087582

Order 1440.

654 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 94 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×#67151C212yesmaximal, complemented
4C3×C5×#217C211yesmaximal, characteristic, complemented
5#10623813C212yesmaximal, complemented
6#91771—31nomaximal
7#91572—31nomaximal
8C23×C32×C5C2211yescharacteristic
9C22×C3⋊D15—22no—
10C22×C3⋊D15—24no—
11C22×C3⋊D15C2212yes—
12C22×C3×D15C2211yescharacteristic, complemented
13C3×#1220—22no—
14C2×C3×Dic15C2211yescharacteristic, complemented
15C2×C3×C5×Dic3C2212yescomplemented
16#67151—24no—
17#63981—51nomaximal, Hall
18C23×D15—31no—
19C23×D15—31no—
20C23×D15—61no—
21C2×#1220D311yescharacteristic, complemented
22C2×D60—32no—
23C2×C3×C22⋊D5—31no—
24C2×#1202—32no—
25C3×C5×C22⋊C4—31no—
26#6714—32no—
27C5×#217D311yescharacteristic, complemented
28#6667—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⋊D15D414yescomplemented
36C2×C3×D15—22no—
37C2×C3×D15—21no—
38C3×Dic15—21no—
39C3×C5×Dic3—22no—
40#4028—91noHall
41C23×C3⋊D3—51no—
42C2×C3×#67—51no—
43C2×#626—52no—
44C3×#217D511yescharacteristic, complemented
45#3722—52no—
46C23×C3×C5—21no—
47C23×C3×C5C2×D311yescharacteristic
48C23×C3×C5C2×D311yescharacteristic
49C22×D15—32no—
50C22×D15—32no—
51C22×D15—64no—
52C22×D15—64no—
53C22×D15—62no—
54C22×D15—68no—
55C22×D15—64no—
56C22×D15—62no—
57C22×D15—62no—
58C22×D15C2×D311yescharacteristic, complemented
59C22×C3×D5—31no—
60C2×C3×C4×C5—32no—
61#1220—22no—
62C2×Dic15C2×D311yescharacteristic, complemented
63D60—64no—
64C2×C5×Dic3C2×D312yescomplemented
65C3×C22⋊D5—62no—
66C2×C3×Dic5—31no—
67#1202—64no—
68#937—151no—
69#882—151no—
70C2×C32×C5—22no—
71C2×C32×C5C2×D411yescharacteristic
72C2×C32×C5C2×D412yes—
73C3⋊D15—24no—
74C3×D15—41no—
75C23×D5—91no—
76C2×C22⋊D5—31no—
77C2×D20—92no—
78C5×C22⋊C4—31no—
79#685—92no—
80C23×C32C2×D511yescharacteristic
81C22×C3⋊D3—52no—
82C22×C3⋊D3—104no—
83C22×C3⋊D3—102no—
84C22×C3×D3—51no—
85C3×#67—102no—
86C2×C3×Dic3—51no—
87C2×C3×Dic3C2×D512yescomplemented
88#626—104no—
89C22×C3×C5—24no—
90C22×C3×C5—22no—
91C22×C3×C5—22no—
92C22×C3×C5—22no—
93C22×C3×C5—21no—
94C22×C3×C5D1212yescomplemented
95C22×C3×C5#6712yescomplemented
96C22×C3×C5C22×D311yescharacteristic
97C22×C3×C5C22×D311yescharacteristic
98C2×D15—22no—
99C2×D15—21no—
100C2×D15—34no—
101C2×D15—34no—
102C2×D15—64no—
103C2×D15—616no—
104C2×D15—68no—
105C2×D15—68no—
106C2×D15—64no—
107C2×D15—64no—
108C2×D15—62no—
109C2×D15—62no—
110C2×D15—62no—
111C2×D15—62no—
112C2×C3×D5—61no—
113C2×C3×D5—62no—
114C3×C4×C5—62no—
115Dic15—21no—
116C3×Dic5—61no—
117C5×Dic3—22no—
118C23×D3—151no—
119C23×D3—151no—
120C23×D3—301no—
121C2×C3×D4—151no—
122C2×#67—51no—
123C2×#67—152no—
124C2×D12—152no—
125C3×C22⋊C4—31no—
126#217D1511yescharacteristic, complemented
127(C2×D3)⋊C4—152no—
128(C2×D3)⋊C4—152no—
129C32×C5#12011yescharacteristic, complemented, Hall
130C23×C5D3211yescharacteristic
131C22×D5—31no—
132C22×D5—92no—
133C22×D5—184no—
134C22×D5—182no—
135C2×C4×C5—32no—
136C22⋊D5—62no—
137C2×Dic5—31no—
138D20—184no—
139C22×C32—22no—
140C22×C32D2012yescomplemented
141C22×C32C22×D511yescharacteristic
142C2×C3⋊D3—54no—
143C2×C3⋊D3—108no—
144C2×C3⋊D3—102no—
145C2×C3⋊D3—102no—
146C2×C3×D3—101no—
147C2×C3×D3—102no—
148C3×Dic3—22no—
149C3×Dic3—101no—
150#120—451noSylow
151C2×C3×C5—24no—
152C2×C3×C5—22no—
153C2×C3×C5—22no—
154C2×C3×C5—21no—
155C2×C3×C5—22no—
156C2×C3×C5C2×D1211yescharacteristic
157C2×C3×C5D3×D412yes—
158C2×C3×C5D3×D412yes—
159C2×C3×C5C2×#6711yescharacteristic
160D15—41no—
161D15—68no—
162D15—64no—
163D15—64no—
164C3×D5—121no—
165C23×C3—21no—
166C23×C3—151no—
167C23×C3D3×D511yescharacteristic
168C23×C3C2×D1511yescharacteristic
169C22×D3—51no—
170C22×D3—152no—
171C22×D3—152no—
172C22×D3—302no—
173C22×D3—304no—
174C22×D3—304no—
175C22×D3—308no—
176C22×D3—304no—
177C22×D3—302no—
178C22×D3—302no—
179C3×D4—302no—
180C2×C3×C4—32no—
181C2×C3×C4—151no—
182#67—102no—
183#67—304no—
184C2×Dic3—51no—
185C2×Dic3C2×D1512yescomplemented
186D12—304no—
187C22×C5—22no—
188C22×C5#62612yescomplemented
189C22×C5C2×D3211yescharacteristic
190C2×D5—61no—
191C2×D5—62no—
192C2×D5—94no—
193C2×D5—188no—
194C2×D5—182no—
195C2×D5—182no—
196C4×C5—62no—
197Dic5—61no—
198C2×C32—22no—
199C2×C32C2×D2011yescharacteristic
200C2×C32D4×D512yes—
201C3⋊D3—104no—
202C3×D3—201no—
203C24—451no—
204C2×D4—151no—
205C2×D4—452no—
206C22⋊C4—31no—
207C22⋊C4—452no—
208C3×C5—21no—
209C3×C5#88211yescharacteristic, complemented
210C3×C5#93711yescharacteristic, complemented
211C22×C3—24no—
212C22×C3—22no—
213C22×C3—22no—
214C22×C3—22no—
215C22×C3—21no—
216C22×C3—301no—
217C22×C3—302no—
218C22×C3#120212yescomplemented
219C22×C3D6012yescomplemented
220C22×C3C2×D3×D511yescharacteristic
221C22×C3C22×D1511yescharacteristic
222C2×D3—101no—
223C2×D3—102no—
224C2×D3—154no—
225C2×D3—154no—
226C2×D3—304no—
227C2×D3—3016no—
228C2×D3—308no—
229C2×D3—308no—
230C2×D3—304no—
231C2×D3—304no—
232C2×D3—302no—
233C2×D3—302no—
234C2×D3—302no—
235C2×D3—302no—
236C3×C4—62no—
237C3×C4—301no—
238Dic3—22no—
239Dic3—101no—
240C2×C5—22no—
241C2×C5C2×#62611yescharacteristic
242C2×C5#381112yes—
243D5—121no—
244D5—184no—
245C32#402811yescharacteristic, complemented, Sylow
246C23—151no—
247C23—452no—
248C23—904no—
249C23—902no—
250C23D3×D1511yescharacteristic
251D4—302no—
252D4—904no—
253C2×C4—32no—
254C2×C4—151no—
255C2×C3—24no—
256C2×C3—22no—
257C2×C3—22no—
258C2×C3—21no—
259C2×C3—22no—
260C2×C3—601no—
261C2×C3C2×#120211yescharacteristic
262C2×C3#679012yes—
263C2×C3C2×D6011yescharacteristic
264C2×C3D4×D1512yes—
265D3—201no—
266D3—308no—
267D3—304no—
268D3—304no—
269C5#6398111yescharacteristic, complemented, Sylow
270C22—22no—
271C22—301no—
272C22—302no—
273C22—454no—
274C22—908no—
275C22—902no—
276C22—902no—
277C22#6715112yescomplemented
278C22C2×D3×D1511yescharacteristic
279C4—62no—
280C4—301no—
281C3—21no—
282C3#9157211yescharacteristic, complemented
283C3#9177111yescharacteristic, complemented
284C2—22no—
285C2—601no—
286C2—904no—
287C2C2×#6715111yescharacteristic
288C2#1062421812yes—
subgroupG/H
center, FrattiniC22C2×D3×D15
commutator, socle, cosocleC22×C32×C5C23
FittingC23×C32×C5C22
hypercenterC23D3×D15
hypocenterC32×C5#120
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C23×C3⋊D15C2semidirect
2. C2×C3×#1220C2semidirect
3. C2×#67151C2semidirect
4. C3×C5×#217C2semidirect
5. #10623813C2semidirect
12. C22×C3×D15C22semidirect
14. C2×C3×Dic15C22semidirect
15. C2×C3×C5×Dic3C22semidirect
21. C2×#1220D3semidirect
27. C5×#217D3semidirect
30. C22×C32×C5D4semidirect
35. C2×C3⋊D15D4semidirect
44. C3×#217D5semidirect
58. C22×D15C2×D3semidirect
62. C2×Dic15C2×D3semidirect
64. C2×C5×Dic3C2×D3semidirect
87. C2×C3×Dic3C2×D5semidirect
94. C22×C3×C5D12semidirect
95. C22×C3×C5#67semidirect
126. #217D15semidirect
129. C32×C5#120semidirect
140. C22×C32D20semidirect
185. C2×Dic3C2×D15semidirect
188. C22×C5#626semidirect
209. C3×C5#882semidirect
210. C3×C5#937semidirect
218. C22×C3#1202semidirect
219. C22×C3D60semidirect
245. C32#4028semidirect
269. C5#63981semidirect
277. C22#67151semidirect
282. C3#91572semidirect
283. C3#91771semidirect

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×#671512
C3×C5×#2172
#106238132
#917713
#915723
#639815