Finite Group Databasebeta

← #13087481

Subgroups — #13087481

Order 1440.

350 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 78 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
2C2×#67153C211yesmaximal, characteristic, complemented
3C3×#6712C211yesmaximal, characteristic, complemented
4C3×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
5#10623815C211yesmaximal, characteristic, complemented
6#10623813C211yesmaximal, characteristic
7#10623813C211yesmaximal, characteristic
8#91785—31nomaximal
9#91377—31nomaximal
10C22×C3⋊D15C2211yescharacteristic
11C2×C32×C4×C5C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C4×C3⋊D15—22no—
14C2×C3×Dic15C2211yescharacteristic
15C2×C3×Dic15C2211yescharacteristic
16C2×C3×C5×Dic3C2211yescharacteristic
17C2×C3×C5×Dic3C2211yescharacteristic
18#67153—22no—
19#63865—51nomaximal, Hall
20C2×C4×D15—31no—
21C2×C4×D15—31no—
22C2×C4×D15—61no—
23C2×Dic30—31no—
24C2×#1204—31no—
25C3×C5×C4⋊C4—31no—
26#6714—31no—
27#6714—31no—
28#6712—31no—
29#6712D311yescharacteristic, complemented
30C5×Dic3⋊C4D311yescharacteristic, complemented
31C3×#683—31no—
32#6669—31no—
33#6667—31no—
34#6667—31no—
35C22×C32×C5C2311yescharacteristic
36C2×C3⋊D15—21no—
37C2×C3⋊D15—21no—
38C2×C3⋊D15Q812yescomplemented
39C32×C4×C5—21no—
40C3⋊Dic15D412yes—
41C3×Dic15—21no—
42C3×Dic15—21no—
43C3×C5×Dic3—21no—
44C3×C5×Dic3—21no—
45#4042—91noHall
46C2×C4×C3⋊D3—51no—
47C2×#627—51no—
48C3×Dic3⋊C4—51no—
49C3×Dic3⋊C4D511yescharacteristic, complemented
50#3724—51no—
51#3722—51no—
52#3722—51no—
53C22×D15—31no—
54C22×D15—31no—
55C22×D15—61no—
56C2×C3×C4×C5—21no—
57C2×C3×C4×C5—31no—
58C2×C3×C4×C5—31no—
59C2×C3×C4×C5C2×D311yescharacteristic
60C2×C3×C4×C5C2×D311yescharacteristic
61C2×Dic15—31no—
62C2×Dic15—31no—
63C2×Dic15—61no—
64C2×Dic15C2×D311yescharacteristic
65C2×Dic15C2×D311yescharacteristic
66C4×D15—62no—
67C4×D15—62no—
68C4×D15—64no—
69Dic30—62no—
70C2×C5×Dic3C2×D311yescharacteristic
71C2×C5×Dic3C2×D311yescharacteristic
72C2×C3×Dic5—31no—
73C2×C3×Dic5—31no—
74#1204—62no—
75#896—151no—
76#896—151no—
77C2×C32×C5C2×D411yescharacteristic
78C2×C32×C5C2×Q811yescharacteristic
79C2×C32×C5#4111yescharacteristic
80C3⋊D15—22no—
81C2×C4×D5—91no—
82C2×Dic10—91no—
83C5×C4⋊C4—31no—
84#685—91no—
85#685—91no—
86#683—31no—
87#683—91no—
88C22×C3⋊D3—51no—
89C2×C32×C4C2×D511yescharacteristic
90C2×C3⋊Dic3—51no—
91C4×C3⋊D3—102no—
92C2×C3×Dic3—51no—
93C2×C3×Dic3—51no—
94C2×C3×Dic3C2×D511yescharacteristic
95C2×C3×Dic3C2×D511yescharacteristic
96#627—102no—
97C22×C3×C5—21no—
98C22×C3×C5C22×D311yescharacteristic
99C22×C3×C5C22×D311yescharacteristic
100C2×D15—32no—
101C2×D15—32no—
102C2×D15—62no—
103C2×D15—62no—
104C2×D15—62no—
105C2×D15—61no—
106C2×D15—61no—
107C2×D15—61no—
108C2×D15—61no—
109C3×C4×C5—22no—
110C3×C4×C5—21no—
111C3×C4×C5—21no—
112C3×C4×C5—61no—
113C3×C4×C5—61no—
114Dic15—21no—
115Dic15—21no—
116Dic15—32no—
117Dic15—32no—
118Dic15—62no—
119C3×Dic5—61no—
120C3×Dic5—61no—
121C5×Dic3—21no—
122C5×Dic3—21no—
123C2×C4×D3—151no—
124C2×C4×D3—151no—
125C2×C4×D3—301no—
126C2×Dic6—151no—
127C2×Dic6—151no—
128C3×C4⋊C4—31no—
129C3×C4⋊C4—151no—
130(C2×D3)⋊C4—151no—
131(C2×D3)⋊C4—151no—
132(C2×D3)⋊C4—151no—
133(C2×D3)⋊C4—151no—
134Dic3⋊C4—51no—
135Dic3⋊C4—151no—
136Dic3⋊C4—151no—
137Dic3⋊C4D1511yescharacteristic, complemented
138C32×C5C22⋊Q811yescharacteristic, complemented, Hall
139C22×D5—91no—
140C2×C4×C5—31no—
141C2×C4×C5—31no—
142C2×C4×C5D3211yescharacteristic
143C2×Dic5—31no—
144C2×Dic5—31no—
145C2×Dic5—91no—
146C4×D5—182no—
147Dic10—182no—
148C22×C32C22×D511yescharacteristic
149C2×C3⋊D3—52no—
150C2×C3⋊D3—101no—
151C2×C3⋊D3—101no—
152C32×C4—21no—
153C3⋊Dic3—52no—
154C3×Dic3—21no—
155C3×Dic3—21no—
156C3×Dic3—101no—
157C3×Dic3—101no—
158C22⋊Q8—451noSylow
159C2×C3×C5—21no—
160C2×C3×C5—21no—
161C2×C3×C5—21no—
162C2×C3×C5#23511yescharacteristic
163C2×C3×C5#23511yescharacteristic
164C2×C3×C5D3×D411yescharacteristic
165C2×C3×C5D3×D411yescharacteristic
166C2×C3×C5D3×Q811yescharacteristic
167C2×C3×C5D3×Q811yescharacteristic
168D15—64no—
169D15—62no—
170D15—62no—
171C22×D3—151no—
172C22×D3—151no—
173C22×D3—301no—
174C2×C3×C4—21no—
175C2×C3×C4—31no—
176C2×C3×C4—31no—
177C2×C3×C4—151no—
178C2×C3×C4—151no—
179C2×C3×C4D3×D511yescharacteristic
180C2×C3×C4C2×D1511yescharacteristic
181C2×Dic3—51no—
182C2×Dic3—51no—
183C2×Dic3—151no—
184C2×Dic3—151no—
185C2×Dic3—301no—
186C2×Dic3C2×D1511yescharacteristic
187C2×Dic3C2×D1511yescharacteristic
188C4×D3—302no—
189C4×D3—302no—
190C4×D3—304no—
191Dic6—302no—
192Dic6—302no—
193C22×C5C2×D3211yescharacteristic
194C2×D5—92no—
195C2×D5—181no—
196C2×D5—181no—
197C4×C5—21no—
198C4×C5—61no—
199C4×C5—61no—
200Dic5—61no—
201Dic5—61no—
202Dic5—92no—
203C2×C32#70911yescharacteristic
204C2×C32D4×D511yescharacteristic
205C2×C32Q8×D511yescharacteristic
206C3⋊D3—102no—
207C2×Q8—451no—
208C22×C4—451no—
209C4⋊C4—31no—
210C4⋊C4—151no—
211C4⋊C4—451no—
212C22⋊C4—451no—
213C22⋊C4—451no—
214C3×C5—21no—
215C3×C5#89611yescharacteristic, complemented
216C3×C5#89611yescharacteristic, complemented
217C22×C3—21no—
218C22×C3C2×D3×D511yescharacteristic
219C22×C3C22×D1511yescharacteristic
220C2×D3—152no—
221C2×D3—152no—
222C2×D3—302no—
223C2×D3—302no—
224C2×D3—302no—
225C2×D3—301no—
226C2×D3—301no—
227C2×D3—301no—
228C2×D3—301no—
229C3×C4—22no—
230C3×C4—21no—
231C3×C4—21no—
232C3×C4—61no—
233C3×C4—61no—
234C3×C4—301no—
235C3×C4—301no—
236Dic3—21no—
237Dic3—21no—
238Dic3—101no—
239Dic3—101no—
240Dic3—152no—
241Dic3—152no—
242Dic3—302no—
243C2×C5#379711yescharacteristic
244C2×C5#379811yescharacteristic
245C2×C5#381111yescharacteristic
246D5—182no—
247C32#404211yescharacteristic, complemented, Sylow
248C23—451no—
249Q8—902no—
250C2×C4—31no—
251C2×C4—31no—
252C2×C4—151no—
253C2×C4—151no—
254C2×C4—451no—
255C2×C4—902no—
256C2×C4D3×D1511yescharacteristic
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—21no—
260C2×C3D15⋊Q811yescharacteristic
261C2×C3#677111yescharacteristic
262C2×C3#679011yescharacteristic
263C2×C3#681711yescharacteristic
264C2×C3D4×D1511yescharacteristic
265C2×C3Q8×D1511yescharacteristic
266D3—304no—
267D3—302no—
268D3—302no—
269C5#6386511yescharacteristic, complemented, Sylow
270C22—452no—
271C22—901no—
272C22—901no—
273C22C2×D3×D1511yescharacteristic
274C4—21no—
275C4—61no—
276C4—61no—
277C4—301no—
278C4—301no—
279C4—452no—
280C3—21no—
281C3#9137711yescharacteristic, complemented
282C3#9178511yescharacteristic, complemented
283C2—902no—
284C2#1062419811yescharacteristic
285C2#1062419911yescharacteristic
286C2#1062421811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D15
commutator, socle, cosocleC22×C32×C5C23
FittingC2×C32×C4×C5C22
prime radicalC22×C3⋊D15C22
hypercenterC2×C4D3×D15
hypocenterC32×C5C22⋊Q8
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×#67153C2semidirect
3. C3×#6712C2semidirect
4. C3×C5×Dic3⋊C4C2semidirect
5. #10623815C2semidirect
29. #6712D3semidirect
30. C5×Dic3⋊C4D3semidirect
38. C2×C3⋊D15Q8semidirect
49. C3×Dic3⋊C4D5semidirect
137. Dic3⋊C4D15semidirect
138. C32×C5C22⋊Q8semidirect
215. C3×C5#896semidirect
216. C3×C5#896semidirect
247. C32#4042semidirect
269. C5#63865semidirect
281. C3#91377semidirect
282. C3#91785semidirect

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×#671532
C3×#67122
C3×C5×Dic3⋊C42
#106238152
#106238132
#917853
#913773
#638655