Finite Group Databasebeta

← #13087409

Subgroups — #13087409

Order 1440.

330 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 80 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×#67153C211yesmaximal, characteristic, complemented
2C2×#67149C211yesmaximal, characteristic
3#10623908C211yesmaximal, characteristic
4C3×#6712C211yesmaximal, characteristic, complemented
5C3×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
6#10623814C211yesmaximal, characteristic, complemented
7#10623813C211yesmaximal, characteristic
8#91785—31nomaximal
9#91419—31nomaximal
10C22×C3⋊D15C2211yescharacteristic
11C2×C32×C4×C5C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C3×Dic15C2211yescharacteristic
14C2×C3×Dic15C2211yescharacteristic
15C2×C3×C5×Dic3C2211yescharacteristic
16C2×C3×C5×Dic3C2211yescharacteristic
17#67153—22no—
18#67149—22no—
19#63895—51nomaximal, Hall
20C2×C4×D15—31no—
21C2×Dic30—31no—
22C2×#1204—31no—
23C2×#1200—31no—
24C3×C5×C4⋊C4—31no—
25#6714—31no—
26#6714—31no—
27#6714—31no—
28#6714—61no—
29#6712—31no—
30#6712D311yescharacteristic, complemented
31C5×C4⋊Dic3D311yescharacteristic, complemented
32C3×#683—31no—
33#6668—31no—
34#6667—31no—
35C22×C32×C5C2311yescharacteristic
36C2×C3⋊D15—21no—
37C2×C3⋊D15—21no—
38C2×C3⋊D15Q812yescomplemented
39C32×C4×C5—21no—
40C3⋊Dic15—21no—
41C3×Dic15—21no—
42C3×Dic15D412yes—
43C3×C5×Dic3—21no—
44C3×C5×Dic3—21no—
45#4042—91noHall
46C2×#627—51no—
47C2×#624—51no—
48#3752—51no—
49C3×C4⋊Dic3D511yescharacteristic, complemented
50C3×Dic3⋊C4—51no—
51Dic3⋊Dic3—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—
67Dic30—62no—
68C2×C5×Dic3C2×D311yescharacteristic
69C2×C5×Dic3C2×D311yescharacteristic
70C2×C3×Dic5—31no—
71C2×C3×Dic5—31no—
72#1204—62no—
73#1200—62no—
74#897—151no—
75#896—151no—
76C2×C32×C5C2×D411yescharacteristic
77C2×C32×C5C2×Q811yescharacteristic
78C2×C32×C5#4111yescharacteristic
79C3⋊D15—22no—
80C2×C4×D5—91no—
81C2×Dic10—91no—
82C5×C4⋊C4—31no—
83#685—91no—
84#685—91no—
85#683—31no—
86#683—91no—
87C22×C3⋊D3—51no—
88C2×C32×C4C2×D511yescharacteristic
89C2×C3⋊Dic3—51no—
90C2×C3×Dic3—51no—
91C2×C3×Dic3—51no—
92C2×C3×Dic3C2×D511yescharacteristic
93C2×C3×Dic3C2×D511yescharacteristic
94#627—102no—
95#624—102no—
96C22×C3×C5—21no—
97C22×C3×C5C22×D311yescharacteristic
98C22×C3×C5C22×D311yescharacteristic
99C2×D15—32no—
100C2×D15—32no—
101C2×D15—62no—
102C2×D15—61no—
103C2×D15—61no—
104C2×D15—61no—
105C2×D15—61no—
106C2×D15—121no—
107C2×D15—121no—
108C3×C4×C5—21no—
109C3×C4×C5—21no—
110C3×C4×C5—41no—
111C3×C4×C5—61no—
112C3×C4×C5—61no—
113Dic15—21no—
114Dic15—61no—
115Dic15—61no—
116Dic15—121no—
117Dic15D1212yes—
118C3×Dic5—32no—
119C3×Dic5—61no—
120C5×Dic3—21no—
121C5×Dic3—21no—
122C2×C4×D3—151no—
123C2×C4×D3—151no—
124C2×Dic6—151no—
125C2×Dic6—151no—
126C3×C4⋊C4—31no—
127C3×C4⋊C4—151no—
128(C2×D3)⋊C4—151no—
129(C2×D3)⋊C4—151no—
130(C2×D3)⋊C4—151no—
131(C2×D3)⋊C4—151no—
132(C2×D3)⋊C4—301no—
133C4⋊Dic3—151no—
134C4⋊Dic3D1511yescharacteristic, complemented
135Dic3⋊C4—51no—
136Dic3⋊C4—151no—
137C32×C5C22⋊Q811yescharacteristic, complemented, Hall
138C22×D5—91no—
139C2×C4×C5—31no—
140C2×C4×C5—31no—
141C2×C4×C5D3211yescharacteristic
142C2×Dic5—31no—
143C2×Dic5—31no—
144C2×Dic5—91no—
145C4×D5—182no—
146Dic10—182no—
147C22×C32C22×D511yescharacteristic
148C2×C3⋊D3—52no—
149C2×C3⋊D3—101no—
150C2×C3⋊D3—101no—
151C32×C4—21no—
152C3⋊Dic3—101no—
153C3×Dic3—21no—
154C3×Dic3—21no—
155C3×Dic3—52no—
156C3×Dic3—101no—
157C22⋊Q8—451noSylow
158C2×C3×C5—21no—
159C2×C3×C5—21no—
160C2×C3×C5—21no—
161C2×C3×C5C2×D1211yescharacteristic
162C2×C3×C5#23511yescharacteristic
163C2×C3×C5D3×D411yescharacteristic
164C2×C3×C5#23711yescharacteristic
165C2×C3×C5D3×Q811yescharacteristic
166C2×C3×C5D3×Q811yescharacteristic
167D15—62no—
168D15—62no—
169D15—122no—
170C22×D3—151no—
171C22×D3—151no—
172C22×D3—301no—
173C2×C3×C4—21no—
174C2×C3×C4—31no—
175C2×C3×C4—31no—
176C2×C3×C4—151no—
177C2×C3×C4—151no—
178C2×C3×C4D3×D511yescharacteristic
179C2×C3×C4C2×D1511yescharacteristic
180C2×Dic3—51no—
181C2×Dic3—51no—
182C2×Dic3—151no—
183C2×Dic3—151no—
184C2×Dic3—301no—
185C2×Dic3C2×D1511yescharacteristic
186C2×Dic3C2×D1511yescharacteristic
187C4×D3—302no—
188C4×D3—302no—
189Dic6—302no—
190Dic6—302no—
191C22×C5C2×D3211yescharacteristic
192C2×D5—92no—
193C2×D5—181no—
194C2×D5—181no—
195C4×C5—21no—
196C4×C5—61no—
197C4×C5—61no—
198Dic5—32no—
199Dic5—61no—
200Dic5—181no—
201C2×C32#70911yescharacteristic
202C2×C32D4×D511yescharacteristic
203C2×C32Q8×D511yescharacteristic
204C3⋊D3—102no—
205C2×Q8—451no—
206C22×C4—451no—
207C4⋊C4—31no—
208C4⋊C4—151no—
209C4⋊C4—451no—
210C22⋊C4—451no—
211C22⋊C4—451no—
212C3×C5—21no—
213C3×C5#89611yescharacteristic, complemented
214C3×C5#89711yescharacteristic, complemented
215C22×C3—21no—
216C22×C3C2×D3×D511yescharacteristic
217C22×C3C22×D1511yescharacteristic
218C2×D3—152no—
219C2×D3—152no—
220C2×D3—302no—
221C2×D3—301no—
222C2×D3—301no—
223C2×D3—301no—
224C2×D3—301no—
225C2×D3—601no—
226C2×D3—601no—
227C3×C4—21no—
228C3×C4—21no—
229C3×C4—41no—
230C3×C4—61no—
231C3×C4—61no—
232C3×C4—152no—
233C3×C4—301no—
234Dic3—21no—
235Dic3—21no—
236Dic3—52no—
237Dic3—101no—
238Dic3—301no—
239Dic3—301no—
240Dic3—601no—
241C2×C5#379711yescharacteristic
242C2×C5D3×D1211yescharacteristic
243C2×C5#380411yescharacteristic
244D5—182no—
245C32#404211yescharacteristic, complemented, Sylow
246C23—451no—
247Q8—902no—
248C2×C4—31no—
249C2×C4—31no—
250C2×C4—151no—
251C2×C4—151no—
252C2×C4—451no—
253C2×C4—902no—
254C2×C4D3×D1511yescharacteristic
255C2×C3—21no—
256C2×C3—21no—
257C2×C3—21no—
258C2×C3D15⋊Q811yescharacteristic
259C2×C3D5×D1211yescharacteristic
260C2×C3#677911yescharacteristic
261C2×C3#681711yescharacteristic
262C2×C3D4×D1511yescharacteristic
263C2×C3Q8×D1511yescharacteristic
264D3—302no—
265D3—302no—
266D3—602no—
267C5#6389511yescharacteristic, complemented, Sylow
268C22—452no—
269C22—901no—
270C22—901no—
271C22C2×D3×D1511yescharacteristic
272C4—21no—
273C4—61no—
274C4—61no—
275C4—152no—
276C4—301no—
277C4—901no—
278C3—21no—
279C3#9141911yescharacteristic, complemented
280C3#9178511yescharacteristic, complemented
281C2—902no—
282C2#1062419811yescharacteristic
283C2D12×D1511yescharacteristic
284C2#1062420711yescharacteristic
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
1. C2×#67153C2semidirect
4. C3×#6712C2semidirect
5. C3×C5×C4⋊Dic3C2semidirect
6. #10623814C2semidirect
30. #6712D3semidirect
31. C5×C4⋊Dic3D3semidirect
38. C2×C3⋊D15Q8semidirect
49. C3×C4⋊Dic3D5semidirect
134. C4⋊Dic3D15semidirect
137. C32×C5C22⋊Q8semidirect
213. C3×C5#896semidirect
214. C3×C5#897semidirect
245. C32#4042semidirect
267. C5#63895semidirect
279. C3#91419semidirect
280. C3#91785semidirect

Maximal subgroups

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

subgroupindex
C2×#671532
C2×#671492
#106239082
C3×#67122
C3×C5×C4⋊Dic32
#106238142
#106238132
#917853
#914193
#638955