Finite Group Databasebeta

← #13087465

Subgroups — #13087465

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⋊D15C211yesmaximal, characteristic, complemented
2C2×#67152C211yesmaximal, characteristic
3C3×#6712C211yesmaximal, characteristic, complemented
4C3×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5Dic3⋊Dic15C211yesmaximal, characteristic, complemented
6#10623813C211yesmaximal, characteristic, complemented
7(C2×D3)⋊Dic15C211yesmaximal, characteristic, complemented
8#91772—31nomaximal
9#91355—31nomaximal
10C22×C3⋊D15C2211yescharacteristic
11C22×C3×C5×D3C2211yescharacteristic
12C2×C32×C4×C5C2211yescharacteristic
13C2×C3⋊Dic15C2211yescharacteristic
14C4×C3⋊D15—22no—
15C2×C3×Dic15C2211yescharacteristic
16C2×C3×Dic15C2211yescharacteristic
17C2×C3×C5×Dic3C2211yescharacteristic
18#67152—22no—
19#63853—51nomaximal, Hall
20C2×#1220—31no—
21C2×C4×D15—31no—
22C2×C4×D15—31no—
23C2×C4×D15—61no—
24C2×#1203—31no—
25C3×C5×C22⋊C4—31no—
26#6719—31no—
27#6714—31no—
28C4⋊Dic15—31no—
29#6712D311yescharacteristic, complemented
30C5×(C2×D3)⋊C4D311yescharacteristic, complemented
31C3×#683—31no—
32Dic3⋊Dic5—31no—
33#6667—31no—
34(C2×D3)⋊Dic5—31no—
35C22×C32×C5C2311yescharacteristic
36C2×C3⋊D15—21no—
37C2×C3⋊D15—21no—
38C2×C3⋊D15D412yes—
39C2×C3×C5×D3—21no—
40C2×C3×C5×D3—21no—
41C2×C3×C5×D3—21no—
42C32×C4×C5—21no—
43C3⋊Dic15—21no—
44C3×Dic15—21no—
45C3×Dic15—21no—
46C3×C5×Dic3—21no—
47#4029—91noHall
48C2×C4×C3⋊D3—51no—
49C2×#626—51no—
50C3×(C2×D3)⋊C4D511yescharacteristic, complemented
51C3×Dic3⋊C4—51no—
52Dic3⋊Dic3—51no—
53#3722—51no—
54(C2×D3)⋊Dic3—51no—
55C23×C3×C5—31no—
56C22×D15—31no—
57C22×D15—31no—
58C22×D15—61no—
59C22×C5×D3C2×D311yescharacteristic
60C2×C3×C4×C5—21no—
61C2×C3×C4×C5—31no—
62C2×C3×C4×C5C2×D311yescharacteristic
63C2×C3×C4×C5C2×D311yescharacteristic
64#1220—62no—
65C2×Dic15—31no—
66C2×Dic15—31no—
67C2×Dic15—61no—
68C2×Dic15C2×D311yescharacteristic
69C2×Dic15C2×D311yescharacteristic
70C4×D15—62no—
71C4×D15—62no—
72C4×D15—64no—
73C2×C5×Dic3C2×D311yescharacteristic
74C2×C3×Dic5—31no—
75C2×C3×Dic5—31no—
76#1203—62no—
77#894—151no—
78#883—151no—
79C2×C32×C5C2×D411yescharacteristic
80C2×C32×C5#4111yescharacteristic
81C2×C32×C5#4111yescharacteristic
82C3⋊D15—22no—
83C3×C5×D3—41no—
84C2×C22⋊D5—91no—
85C2×C4×D5—91no—
86C5×C22⋊C4—31no—
87C22⋊Dic5—91no—
88#685—91no—
89C4⋊Dic5—91no—
90#683—31no—
91C22×C3⋊D3—51no—
92C22×C3×D3C2×D511yescharacteristic
93C2×C32×C4C2×D511yescharacteristic
94C2×C3⋊Dic3—51no—
95C4×C3⋊D3—102no—
96C2×C3×Dic3—51no—
97C2×C3×Dic3—51no—
98C2×C3×Dic3C2×D511yescharacteristic
99#626—102no—
100C22×C3×C5—21no—
101C22×C3×C5—61no—
102C22×C3×C5—61no—
103C22×C3×C5—61no—
104C22×C3×C5C22×D311yescharacteristic
105C22×C3×C5C22×D311yescharacteristic
106C2×D15—32no—
107C2×D15—32no—
108C2×D15—62no—
109C2×D15—62no—
110C2×D15—62no—
111C2×D15—61no—
112C2×D15—61no—
113C2×D15—61no—
114C2×D15—61no—
115C2×C5×D3—21no—
116C2×C5×D3—21no—
117C2×C5×D3—21no—
118C3×C4×C5—22no—
119C3×C4×C5—21no—
120C3×C4×C5—21no—
121C3×C4×C5—61no—
122Dic15—21no—
123Dic15—21no—
124Dic15—62no—
125Dic15—61no—
126Dic15—61no—
127C3×Dic5—61no—
128C3×Dic5—61no—
129C5×Dic3—21no—
130C2×#67—151no—
131C2×D12—151no—
132C2×C4×D3—151no—
133C2×C4×D3—151no—
134C2×C4×D3—301no—
135C3×C4⋊C4—151no—
136C3×C22⋊C4—31no—
137#217—151no—
138(C2×D3)⋊C4—151no—
139(C2×D3)⋊C4—151no—
140(C2×D3)⋊C4—151no—
141(C2×D3)⋊C4D1511yescharacteristic, complemented
142C4⋊Dic3—151no—
143Dic3⋊C4—51no—
144Dic3⋊C4—151no—
145C32×C5#12311yescharacteristic, complemented, Hall
146C23×C5—31no—
147C22×D5—91no—
148C2×C4×C5—31no—
149C2×C4×C5D3211yescharacteristic
150C22⋊D5—182no—
151C2×Dic5—31no—
152C2×Dic5—31no—
153C2×Dic5—91no—
154C4×D5—182no—
155C22×C32C22×D511yescharacteristic
156C2×C3⋊D3—52no—
157C2×C3⋊D3—101no—
158C2×C3⋊D3—101no—
159C2×C3×D3—21no—
160C2×C3×D3—21no—
161C2×C3×D3—21no—
162C32×C4—21no—
163C3⋊Dic3—101no—
164C3×Dic3—21no—
165C3×Dic3—101no—
166C3×Dic3—101no—
167#123—451noSylow
168C2×C3×C5—21no—
169C2×C3×C5—21no—
170C2×C3×C5—21no—
171C2×C3×C5—121no—
172C2×C3×C5#23511yescharacteristic
173C2×C3×C5#23511yescharacteristic
174C2×C3×C5D3×D411yescharacteristic
175C2×C3×C5D3×D411yescharacteristic
176C2×C3×C5#23711yescharacteristic
177C2×C3×C5#23911yescharacteristic
178D15—64no—
179D15—62no—
180D15—62no—
181C5×D3—41no—
182C23×C3—31no—
183C22×D3—151no—
184C22×D3—151no—
185C22×D3—301no—
186C22×D3C2×D1511yescharacteristic
187C2×C3×C4—21no—
188C2×C3×C4—31no—
189C2×C3×C4—151no—
190C2×C3×C4—151no—
191C2×C3×C4D3×D511yescharacteristic
192C2×C3×C4C2×D1511yescharacteristic
193#67—302no—
194C2×Dic3—51no—
195C2×Dic3—51no—
196C2×Dic3—151no—
197C2×Dic3—151no—
198C2×Dic3—301no—
199C2×Dic3C2×D1511yescharacteristic
200D12—302no—
201C4×D3—302no—
202C4×D3—302no—
203C4×D3—304no—
204C22×C5—61no—
205C22×C5—61no—
206C22×C5—61no—
207C22×C5C2×D3211yescharacteristic
208C2×D5—92no—
209C2×D5—181no—
210C2×D5—181no—
211C4×C5—21no—
212C4×C5—61no—
213Dic5—61no—
214Dic5—61no—
215Dic5—181no—
216C2×C32#70911yescharacteristic
217C2×C32D4×D511yescharacteristic
218C2×C32#71111yescharacteristic
219C3⋊D3—102no—
220C3×D3—41no—
221C2×D4—451no—
222C22×C4—451no—
223C4⋊C4—151no—
224C4⋊C4—451no—
225C22⋊C4—31no—
226C22⋊C4—451no—
227C22⋊C4—451no—
228C3×C5—21no—
229C3×C5#88311yescharacteristic, complemented
230C3×C5#89411yescharacteristic, complemented
231C22×C3—21no—
232C22×C3—61no—
233C22×C3—61no—
234C22×C3—61no—
235C22×C3C2×D3×D511yescharacteristic
236C22×C3C22×D1511yescharacteristic
237C2×D3—21no—
238C2×D3—21no—
239C2×D3—21no—
240C2×D3—152no—
241C2×D3—152no—
242C2×D3—302no—
243C2×D3—302no—
244C2×D3—302no—
245C2×D3—301no—
246C2×D3—301no—
247C2×D3—301no—
248C2×D3—301no—
249C3×C4—22no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—61no—
253C3×C4—301no—
254C3×C4—301no—
255Dic3—21no—
256Dic3—101no—
257Dic3—101no—
258Dic3—302no—
259Dic3—301no—
260Dic3—301no—
261C2×C5—121no—
262C2×C5#379611yescharacteristic
263C2×C5#379811yescharacteristic
264C2×C5#381111yescharacteristic
265D5—182no—
266C32#402911yescharacteristic, complemented, Sylow
267C23—31no—
268C23—451no—
269D4—902no—
270C2×C4—31no—
271C2×C4—151no—
272C2×C4—151no—
273C2×C4—451no—
274C2×C4—902no—
275C2×C4D3×D1511yescharacteristic
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—121no—
280C2×C3#676811yescharacteristic
281C2×C3#677111yescharacteristic
282C2×C3#679011yescharacteristic
283C2×C3#681711yescharacteristic
284C2×C3D4×D1511yescharacteristic
285C2×C3#681911yescharacteristic
286D3—41no—
287D3—304no—
288D3—302no—
289D3—302no—
290C5#6385311yescharacteristic, complemented, Sylow
291C22—61no—
292C22—61no—
293C22—61no—
294C22—452no—
295C22—901no—
296C22—901no—
297C22C2×D3×D1511yescharacteristic
298C4—21no—
299C4—61no—
300C4—301no—
301C4—301no—
302C4—901no—
303C3—21no—
304C3#9135511yescharacteristic, complemented
305C3#9177211yescharacteristic, complemented
306C2—121no—
307C2—902no—
308C2#1062419611yescharacteristic
309C2#1062419911yescharacteristic
310C2#1062421811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D15
commutator, socle, cosocleC22×C32×C5C23
FittingC2×C32×C4×C5C22
prime radicalC2×#67152C2
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
1. C2×C4×C3⋊D15C2semidirect
3. C3×#6712C2semidirect
4. C3×C5×(C2×D3)⋊C4C2semidirect
5. Dic3⋊Dic15C2semidirect
6. #10623813C2semidirect
7. (C2×D3)⋊Dic15C2semidirect
29. #6712D3semidirect
30. C5×(C2×D3)⋊C4D3semidirect
50. C3×(C2×D3)⋊C4D5semidirect
141. (C2×D3)⋊C4D15semidirect
145. C32×C5#123semidirect
229. C3×C5#883semidirect
230. C3×C5#894semidirect
266. C32#4029semidirect
290. C5#63853semidirect
304. C3#91355semidirect
305. C3#91772semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊D152
C2×#671522
C3×#67122
C3×C5×(C2×D3)⋊C42
Dic3⋊Dic152
#106238132
(C2×D3)⋊Dic152
#917723
#913553
#638535