Finite Group Databasebeta

← #13087673

Subgroups — #13087673

Order 1440.

338 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 75 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×C3×D60C211yesmaximal, characteristic
2C2×#67154C211yesmaximal, characteristic, complemented
3C5×#3750C211yesmaximal, characteristic, complemented
4C3×#6712C211yesmaximal, characteristic, complemented
5#10623829C211yesmaximal, characteristic, complemented
6#10623829C211yesmaximal, characteristic, complemented
7#10623829C211yesmaximal, characteristic, complemented
8#91433—31nomaximal
9#91407—31nomaximal
10C22×C3×D15C2211yescharacteristic
11C22×C3×D15C2211yescharacteristic
12C2×C32×C4×C5C2211yescharacteristic
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C5×C3⋊Dic3C2211yescharacteristic
15C2×C3×Dic15C2211yescharacteristic
16C2×C3×Dic15C2211yescharacteristic
17C3×D60—22no—
18#67154—22no—
19#63884—51nomaximal, Hall
20C2×D60D311yescharacteristic
21C2×C3×D20—31no—
22C2×#1200—31no—
23C2×D5×Dic3—31no—
24#6712D311yescharacteristic, complemented
25C5×Dic3⋊C4—31no—
26C5×Dic3⋊C4—31no—
27C5×Dic3⋊C4—61no—
28C3×#683—31no—
29#6667—31no—
30#6667—31no—
31#6667—31no—
32#6665—31no—
33#6665—31no—
34#6665—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—
43C5×C3⋊Dic3—21no—
44C5×C3⋊Dic3—21no—
45C3×Dic15—21no—
46C3×Dic15—21no—
47#4040—91noHall
48C2×C3×D12—51no—
49C2×D3×Dic3—51no—
50#3750D511yescharacteristic, complemented
51C3×Dic3⋊C4—51no—
52(C2×D3)⋊Dic3—51no—
53(C2×D3)⋊Dic3—51no—
54(C2×D3)⋊Dic3—51no—
55C22×D15C2×D311yescharacteristic
56C22×D15C2×D311yescharacteristic
57C22×C3×D5—31no—
58C22×C3×D5—31no—
59C2×C3×C4×C5—21no—
60C2×C3×C4×C5C2×D311yescharacteristic
61C2×C3×C4×C5C2×D311yescharacteristic
62C2×Dic15C2×D311yescharacteristic
63C2×Dic15C2×D311yescharacteristic
64D60—22no—
65C2×C5×Dic3—31no—
66C2×C5×Dic3—31no—
67C2×C5×Dic3—31no—
68C2×C5×Dic3—31no—
69C2×C5×Dic3—61no—
70C2×C5×Dic3—61no—
71C2×C3×Dic5—31no—
72C2×C3×Dic5—31no—
73C3×D20—62no—
74#1200—62no—
75D5×Dic3—62no—
76#935—151no—
77#894—151no—
78C2×C32×C5C2×D411yescharacteristic
79C2×C32×C5#4111yescharacteristic
80C2×C32×C5#4111yescharacteristic
81C3×D15—22no—
82C3×D15—41no—
83C2×D20—31no—
84C2×C4×D5—91no—
85C5×C4⋊C4—91no—
86#685—91no—
87#685—91no—
88#685—91no—
89#683—31no—
90C22×C3×D3—51no—
91C22×C3×D3—51no—
92C2×C32×C4C2×D511yescharacteristic
93C2×C3⋊Dic3C2×D511yescharacteristic
94C2×C3⋊Dic3C2×D511yescharacteristic
95C2×C3×Dic3—51no—
96C2×C3×Dic3—51no—
97C3×D12—102no—
98D3×Dic3—102no—
99C22×C3×C5—21no—
100C22×C3×C5C22×D311yescharacteristic
101C22×C3×C5C22×D311yescharacteristic
102C2×D15—21no—
103C2×D15—21no—
104C2×D15—21no—
105C2×D15—21no—
106C2×D15—21no—
107C2×D15#6712yes—
108C2×C3×D5—32no—
109C2×C3×D5—61no—
110C2×C3×D5—61no—
111C2×C3×D5—61no—
112C2×C3×D5—61no—
113C2×C3×D5—61no—
114C3×C4×C5—21no—
115C3×C4×C5—21no—
116C3×C4×C5—41no—
117Dic15—21no—
118Dic15—21no—
119C3×Dic5—61no—
120C3×Dic5—61no—
121C5×Dic3—62no—
122C5×Dic3—61no—
123C5×Dic3—61no—
124C5×Dic3—61no—
125C5×Dic3—61no—
126C5×Dic3—121no—
127C2×C3×D4—151no—
128C22×Dic3—151no—
129C2×D12—51no—
130C2×C4×D3—151no—
131C3×C4⋊C4—151no—
132#217—151no—
133#217—151no—
134#217—151no—
135(C2×D3)⋊C4—151no—
136(C2×D3)⋊C4—151no—
137(C2×D3)⋊C4—151no—
138Dic3⋊C4—31no—
139Dic3⋊C4—31no—
140Dic3⋊C4—51no—
141Dic3⋊C4—61no—
142C32×C5#12311yescharacteristic, complemented, Hall
143C22×D5—31no—
144C22×D5—31no—
145C2×C4×C5—91no—
146C2×C4×C5—91no—
147C2×C4×C5D3211yescharacteristic
148C2×Dic5—31no—
149C2×Dic5—31no—
150D20—62no—
151C4×D5—182no—
152C22×C32C22×D511yescharacteristic
153C2×C3×D3—52no—
154C2×C3×D3—101no—
155C2×C3×D3—101no—
156C2×C3×D3—101no—
157C2×C3×D3—101no—
158C2×C3×D3—101no—
159C32×C4—21no—
160C3⋊Dic3—21no—
161C3⋊Dic3—21no—
162C3×Dic3—101no—
163C3×Dic3—101no—
164#123—451noSylow
165C2×C3×C5—21no—
166C2×C3×C5—21no—
167C2×C3×C5—21no—
168C2×C3×C5#23511yescharacteristic
169C2×C3×C5D3×D411yescharacteristic
170C2×C3×C5#23711yescharacteristic
171C2×C3×C5#23711yescharacteristic
172C2×C3×C5#23911yescharacteristic
173C2×C3×C5C2×#6711yescharacteristic
174D15—22no—
175D15—41no—
176C3×D5—62no—
177C3×D5—121no—
178C23×C3—151no—
179C23×C3—151no—
180C22×D3—51no—
181C22×D3—51no—
182C3×D4—302no—
183C2×C3×C4—21no—
184C2×C3×C4—151no—
185C2×C3×C4—151no—
186C2×C3×C4D3×D511yescharacteristic
187C2×C3×C4D3×D511yescharacteristic
188C2×Dic3—31no—
189C2×Dic3—31no—
190C2×Dic3—31no—
191C2×Dic3—31no—
192C2×Dic3—51no—
193C2×Dic3—51no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—302no—
197D12—102no—
198C4×D3—302no—
199C22×C5C2×D3211yescharacteristic
200C2×D5—32no—
201C2×D5—61no—
202C2×D5—61no—
203C2×D5—61no—
204C2×D5—61no—
205C2×D5—61no—
206C4×C5—21no—
207C4×C5—181no—
208C4×C5—181no—
209Dic5—61no—
210Dic5—61no—
211C2×C32#70911yescharacteristic
212C2×C32D4×D511yescharacteristic
213C2×C32#71311yescharacteristic
214C3×D3—102no—
215C3×D3—201no—
216C2×D4—151no—
217C22×C4—451no—
218C4⋊C4—91no—
219C4⋊C4—151no—
220C22⋊C4—451no—
221C22⋊C4—451no—
222C22⋊C4—451no—
223C3×C5—21no—
224C3×C5#89411yescharacteristic, complemented
225C3×C5#93511yescharacteristic, complemented
226C22×C3—21no—
227C22×C3—152no—
228C22×C3—301no—
229C22×C3—301no—
230C22×C3—301no—
231C22×C3—301no—
232C22×C3—301no—
233C22×C3C2×D3×D511yescharacteristic
234C22×C3C2×D3×D511yescharacteristic
235C2×D3—52no—
236C2×D3—101no—
237C2×D3—101no—
238C2×D3—101no—
239C2×D3—101no—
240C2×D3—101no—
241C3×C4—21no—
242C3×C4—21no—
243C3×C4—41no—
244C3×C4—301no—
245C3×C4—301no—
246Dic3—62no—
247Dic3—61no—
248Dic3—61no—
249Dic3—61no—
250Dic3—61no—
251Dic3—101no—
252Dic3—101no—
253Dic3—121no—
254C2×C5#379511yescharacteristic
255C2×C5#379611yescharacteristic
256C2×C5D3×#6711yescharacteristic
257D5—62no—
258D5—121no—
259C32#404011yescharacteristic, complemented, Sylow
260C23—151no—
261C23—151no—
262D4—302no—
263C2×C4—91no—
264C2×C4—91no—
265C2×C4—151no—
266C2×C4—151no—
267C2×C4—902no—
268C2×C4(C3⋊D3)⋊D511yescharacteristic
269C2×C3—21no—
270C2×C3—21no—
271C2×C3—21no—
272C2×C3—302no—
273C2×C3—601no—
274C2×C3#676511yescharacteristic
275C2×C3#676611yescharacteristic
276C2×C3#676911yescharacteristic
277C2×C3#677311yescharacteristic
278C2×C3D5×#6711yescharacteristic
279C2×C3#679011yescharacteristic
280D3—102no—
281D3—201no—
282C5#6388411yescharacteristic, complemented, Sylow
283C22—152no—
284C22—301no—
285C22—301no—
286C22—301no—
287C22—301no—
288C22—301no—
289C22C2×(C3⋊D3)⋊D511yescharacteristic
290C4—21no—
291C4—181no—
292C4—181no—
293C4—301no—
294C4—301no—
295C3—21no—
296C3#9140711yescharacteristic, complemented
297C3#9143311yescharacteristic, complemented
298C2—302no—
299C2—601no—
300C2#1062422011yescharacteristic
301C2#1062422111yescharacteristic
302C2#1062423511yescharacteristic
subgroupG/H
center, FrattiniC22C2×(C3⋊D3)⋊D5
commutator, socle, cosocleC22×C32×C5C23
FittingC2×C32×C4×C5C22
prime radicalC2×C3×D60C2
hypercenterC2×C4(C3⋊D3)⋊D5
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×#67154C2semidirect
3. C5×#3750C2semidirect
4. C3×#6712C2semidirect
5. #10623829C2semidirect
6. #10623829C2semidirect
7. #10623829C2semidirect
24. #6712D3semidirect
50. #3750D5semidirect
142. C32×C5#123semidirect
224. C3×C5#894semidirect
225. C3×C5#935semidirect
259. C32#4040semidirect
282. C5#63884semidirect
296. C3#91407semidirect
297. C3#91433semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D602
C2×#671542
C5×#37502
C3×#67122
#106238292
#914333
#914073
#638845