Finite Group Databasebeta

← #13087422

Subgroups — #13087422

Order 1440.

366 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C2×C4⋊(C3⋊D15)C211yesmaximal, characteristic
2C2×#67149C211yesmaximal, characteristic, complemented
3C3×#6712C211yesmaximal, characteristic, complemented
4C3×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
5#10623813C211yesmaximal, characteristic, complemented
6#10623813C211yesmaximal, characteristic, complemented
7#10623813C211yesmaximal, characteristic, complemented
8#91783—31nomaximal
9#91433—31nomaximal
10C22×C3⋊D15C2211yescharacteristic
11C22×C3⋊D15C2211yescharacteristic
12C2×C32×C4×C5C2211yescharacteristic
13C4⋊(C3⋊D15)—22no—
14C2×C3×Dic15C2211yescharacteristic
15C2×C3×Dic15C2211yescharacteristic
16C2×C3×C5×Dic3C2211yescharacteristic
17C2×C3×C5×Dic3C2211yescharacteristic
18#67149—22no—
19#63897—51nomaximal, Hall
20C2×D60—31no—
21C2×D60—31no—
22C2×D60—61no—
23C2×C4×D15—31no—
24C2×#1200—31no—
25C3×C5×C4⋊C4—31no—
26#6714—31no—
27#6714—31no—
28#6714—31no—
29#6712D311yescharacteristic, complemented
30C5×Dic3⋊C4D311yescharacteristic, complemented
31C3×#683—31no—
32#6667—31no—
33#6667—31no—
34#6667—31no—
35C22×C32×C5C2311yescharacteristic
36C2×C3⋊D15—21no—
37C2×C3⋊D15—21no—
38C2×C3⋊D15—21no—
39C2×C3⋊D15—21no—
40C2×C3⋊D15—21no—
41C2×C3⋊D15D412yes—
42C32×C4×C5—21no—
43C3×Dic15—21no—
44C3×Dic15—21no—
45C3×C5×Dic3—21no—
46C3×C5×Dic3—21no—
47#4040—91noHall
48C2×C4⋊(C3⋊D3)—51no—
49C2×#624—51no—
50C3×Dic3⋊C4—51no—
51C3×Dic3⋊C4D511yescharacteristic, complemented
52#3722—51no—
53#3722—51no—
54#3722—51no—
55C22×D15—31no—
56C22×D15—31no—
57C22×D15—31no—
58C22×D15—31no—
59C22×D15—61no—
60C22×D15—61no—
61C2×C3×C4×C5—21no—
62C2×C3×C4×C5—31no—
63C2×C3×C4×C5—31no—
64C2×C3×C4×C5C2×D311yescharacteristic
65C2×C3×C4×C5C2×D311yescharacteristic
66C2×Dic15C2×D311yescharacteristic
67C2×Dic15C2×D311yescharacteristic
68D60—62no—
69D60—62no—
70D60—64no—
71C4×D15—62no—
72C2×C5×Dic3C2×D311yescharacteristic
73C2×C5×Dic3C2×D311yescharacteristic
74C2×C3×Dic5—31no—
75C2×C3×Dic5—31no—
76#1200—62no—
77#894—151no—
78#894—151no—
79C2×C32×C5C2×D411yescharacteristic
80C2×C32×C5#4111yescharacteristic
81C2×C32×C5#4111yescharacteristic
82C3⋊D15—22no—
83C3⋊D15—41no—
84C2×D20—91no—
85C2×C4×D5—91no—
86C5×C4⋊C4—31no—
87#685—91no—
88#685—91no—
89#685—91no—
90#683—31no—
91C22×C3⋊D3—51no—
92C22×C3⋊D3—51no—
93C2×C32×C4C2×D511yescharacteristic
94C4⋊(C3⋊D3)—102no—
95C2×C3×Dic3—51no—
96C2×C3×Dic3—51no—
97C2×C3×Dic3C2×D511yescharacteristic
98C2×C3×Dic3C2×D511yescharacteristic
99#624—102no—
100C22×C3×C5—21no—
101C22×C3×C5C22×D311yescharacteristic
102C22×C3×C5C22×D311yescharacteristic
103C2×D15—32no—
104C2×D15—32no—
105C2×D15—62no—
106C2×D15—61no—
107C2×D15—61no—
108C2×D15—61no—
109C2×D15—61no—
110C2×D15—62no—
111C2×D15—61no—
112C2×D15—61no—
113C2×D15—61no—
114C2×D15—61no—
115C2×D15—61no—
116C2×D15—61no—
117C2×D15—121no—
118C2×D15—121no—
119C2×D15—121no—
120C2×D15—121no—
121C3×C4×C5—22no—
122C3×C4×C5—21no—
123C3×C4×C5—21no—
124C3×C4×C5—61no—
125C3×C4×C5—61no—
126Dic15—21no—
127Dic15—21no—
128C3×Dic5—61no—
129C3×Dic5—61no—
130C5×Dic3—21no—
131C5×Dic3—21no—
132C2×D12—151no—
133C2×D12—151no—
134C2×D12—301no—
135C2×C4×D3—151no—
136C2×C4×D3—151no—
137C3×C4⋊C4—31no—
138C3×C4⋊C4—151no—
139(C2×D3)⋊C4—151no—
140(C2×D3)⋊C4—151no—
141(C2×D3)⋊C4—151no—
142(C2×D3)⋊C4—151no—
143(C2×D3)⋊C4—151no—
144(C2×D3)⋊C4—151no—
145Dic3⋊C4—51no—
146Dic3⋊C4D1511yescharacteristic, complemented
147C32×C5#12311yescharacteristic, complemented, Hall
148C22×D5—91no—
149C22×D5—91no—
150C2×C4×C5—31no—
151C2×C4×C5—31no—
152C2×C4×C5D3211yescharacteristic
153C2×Dic5—31no—
154C2×Dic5—31no—
155D20—182no—
156C4×D5—182no—
157C22×C32C22×D511yescharacteristic
158C2×C3⋊D3—52no—
159C2×C3⋊D3—101no—
160C2×C3⋊D3—101no—
161C2×C3⋊D3—101no—
162C2×C3⋊D3—101no—
163C2×C3⋊D3—101no—
164C32×C4—21no—
165C3×Dic3—21no—
166C3×Dic3—21no—
167C3×Dic3—101no—
168C3×Dic3—101no—
169#123—451noSylow
170C2×C3×C5—21no—
171C2×C3×C5—21no—
172C2×C3×C5—21no—
173C2×C3×C5#23511yescharacteristic
174C2×C3×C5#23511yescharacteristic
175C2×C3×C5D3×D411yescharacteristic
176C2×C3×C5D3×D411yescharacteristic
177C2×C3×C5#23911yescharacteristic
178C2×C3×C5#23911yescharacteristic
179D15—62no—
180D15—62no—
181D15—122no—
182D15—122no—
183D15—121no—
184D15—121no—
185C22×D3—151no—
186C22×D3—151no—
187C22×D3—151no—
188C22×D3—151no—
189C22×D3—301no—
190C22×D3—301no—
191C2×C3×C4—21no—
192C2×C3×C4—31no—
193C2×C3×C4—31no—
194C2×C3×C4—151no—
195C2×C3×C4—151no—
196C2×C3×C4D3×D511yescharacteristic
197C2×C3×C4C2×D1511yescharacteristic
198C2×Dic3—51no—
199C2×Dic3—51no—
200C2×Dic3C2×D1511yescharacteristic
201C2×Dic3C2×D1511yescharacteristic
202D12—302no—
203D12—302no—
204D12—304no—
205C4×D3—302no—
206C4×D3—302no—
207C22×C5C2×D3211yescharacteristic
208C2×D5—92no—
209C2×D5—181no—
210C2×D5—181no—
211C2×D5—181no—
212C2×D5—181no—
213C2×D5—181no—
214C4×C5—21no—
215C4×C5—61no—
216C4×C5—61no—
217Dic5—61no—
218Dic5—61no—
219C2×C32#70911yescharacteristic
220C2×C32D4×D511yescharacteristic
221C2×C32#71311yescharacteristic
222C3⋊D3—102no—
223C3⋊D3—201no—
224C2×D4—451no—
225C22×C4—451no—
226C4⋊C4—31no—
227C4⋊C4—151no—
228C22⋊C4—451no—
229C22⋊C4—451no—
230C22⋊C4—451no—
231C3×C5—21no—
232C3×C5#89411yescharacteristic, complemented
233C3×C5#89411yescharacteristic, complemented
234C22×C3—21no—
235C22×C3C2×D3×D511yescharacteristic
236C22×C3C22×D1511yescharacteristic
237C2×D3—152no—
238C2×D3—152no—
239C2×D3—302no—
240C2×D3—301no—
241C2×D3—301no—
242C2×D3—301no—
243C2×D3—301no—
244C2×D3—302no—
245C2×D3—301no—
246C2×D3—301no—
247C2×D3—301no—
248C2×D3—301no—
249C2×D3—301no—
250C2×D3—301no—
251C2×D3—601no—
252C2×D3—601no—
253C2×D3—601no—
254C2×D3—601no—
255C3×C4—22no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—61no—
259C3×C4—61no—
260C3×C4—301no—
261C3×C4—301no—
262Dic3—21no—
263Dic3—21no—
264Dic3—101no—
265Dic3—101no—
266C2×C5#379911yescharacteristic
267C2×C5#379911yescharacteristic
268C2×C5#381111yescharacteristic
269D5—182no—
270D5—361no—
271C32#404011yescharacteristic, complemented, Sylow
272C23—451no—
273C23—451no—
274D4—902no—
275C2×C4—31no—
276C2×C4—31no—
277C2×C4—151no—
278C2×C4—151no—
279C2×C4—902no—
280C2×C4D3×D1511yescharacteristic
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3#676911yescharacteristic
285C2×C3#677311yescharacteristic
286C2×C3#679011yescharacteristic
287C2×C3#681711yescharacteristic
288C2×C3D4×D1511yescharacteristic
289C2×C3#682111yescharacteristic
290D3—302no—
291D3—302no—
292D3—602no—
293D3—602no—
294D3—601no—
295D3—601no—
296C5#6389711yescharacteristic, complemented, Sylow
297C22—452no—
298C22—901no—
299C22—901no—
300C22—901no—
301C22—901no—
302C22—901no—
303C22C2×D3×D1511yescharacteristic
304C4—21no—
305C4—61no—
306C4—61no—
307C4—301no—
308C4—301no—
309C3—21no—
310C3#9143311yescharacteristic, complemented
311C3#9178311yescharacteristic, complemented
312C2—902no—
313C2—1801no—
314C2#1062419711yescharacteristic
315C2#1062420111yescharacteristic
316C2#1062421811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D15
commutator, socle, cosocleC22×C32×C5C23
FittingC2×C32×C4×C5C22
prime radicalC2×C4⋊(C3⋊D15)C2
hypercenterC2×C4D3×D15
hypocenterC32×C5#123
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×#67149C2semidirect
3. C3×#6712C2semidirect
4. C3×C5×Dic3⋊C4C2semidirect
5. #10623813C2semidirect
6. #10623813C2semidirect
7. #10623813C2semidirect
29. #6712D3semidirect
30. C5×Dic3⋊C4D3semidirect
51. C3×Dic3⋊C4D5semidirect
146. Dic3⋊C4D15semidirect
147. C32×C5#123semidirect
232. C3×C5#894semidirect
233. C3×C5#894semidirect
271. C32#4040semidirect
296. C5#63897semidirect
310. C3#91433semidirect
311. C3#91783semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊(C3⋊D15)2
C2×#671492
C3×#67122
C3×C5×Dic3⋊C42
#106238132
#917833
#914333
#638975