Finite Group Databasebeta

← #13087588

Subgroups — #13087588

Order 1440.

350 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C22×C3⋊Dic15C211yesmaximal, characteristic
2C2×#67153C211yesmaximal, characteristic, complemented
3C3×#6719C211yesmaximal, characteristic
4C3×C5×#217C211yesmaximal, characteristic
5Dic3⋊Dic15C211yesmaximal, characteristic, complemented
6#10623815C211yesmaximal, characteristic, complemented
7#10623814C211yesmaximal, characteristic, complemented
8#91767—31nomaximal
9#91576—31nomaximal
10C23×C32×C5C2211yescharacteristic
11C2×C3⋊Dic15—22no—
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C3⋊Dic15C2211yescharacteristic
14C2×C3×Dic15C2211yescharacteristic
15C2×C3×Dic15C2211yescharacteristic
16C2×C3×C5×Dic3C2211yescharacteristic
17C2×C3×C5×Dic3C2211yescharacteristic
18#67153—22no—
19#63982—51nomaximal, Hall
20C22×Dic15—31no—
21C22×Dic15—31no—
22C22×Dic15—61no—
23C2×Dic30—31no—
24C2×#1204—31no—
25C3×C5×C22⋊C4—31no—
26#6719D311yescharacteristic
27C4⋊Dic15—31no—
28#6712—31no—
29#6712—31no—
30C5×#217D311yescharacteristic
31C3×C22⋊Dic5—31no—
32Dic3⋊Dic5—31no—
33#6669—31no—
34#6668—31no—
35C22×C32×C5—21no—
36C22×C32×C5—21no—
37C22×C32×C5Q812yescomplemented
38C22×C32×C5C2311yescharacteristic
39C3⋊Dic15—21no—
40C3⋊Dic15D412yes—
41C3×Dic15—21no—
42C3×Dic15—21no—
43C3×C5×Dic3—21no—
44C3×C5×Dic3—21no—
45#4024—91noHall
46C22×C3⋊Dic3—51no—
47C2×#627—51no—
48C3×#217—51no—
49C3×#217D511yescharacteristic
50#3724—51no—
51Dic3⋊Dic3—51no—
52Dic3⋊Dic3—51no—
53C23×C3×C5—21no—
54C23×C3×C5C2×D311yescharacteristic
55C23×C3×C5C2×D311yescharacteristic
56C2×C3×C4×C5—31no—
57C2×C3×C4×C5—31no—
58C2×Dic15—31no—
59C2×Dic15—31no—
60C2×Dic15—31no—
61C2×Dic15—31no—
62C2×Dic15—62no—
63C2×Dic15—62no—
64C2×Dic15—61no—
65C2×Dic15—61no—
66C2×Dic15—64no—
67C2×Dic15C2×D311yescharacteristic
68C2×Dic15C2×D311yescharacteristic
69Dic30—62no—
70C2×C5×Dic3C2×D311yescharacteristic
71C2×C5×Dic3C2×D311yescharacteristic
72C2×C3×Dic5—31no—
73C2×C3×Dic5—31no—
74#1204—62no—
75#878—151no—
76#878—151no—
77C2×C32×C5—22no—
78C2×C32×C5C2×D411yescharacteristic
79C2×C32×C5C2×Q811yescharacteristic
80C2×C32×C5#4111yescharacteristic
81C22×Dic5—91no—
82C2×Dic10—91no—
83C5×C22⋊C4—31no—
84C22⋊Dic5—31no—
85C4⋊Dic5—91no—
86#683—91no—
87#683—91no—
88C23×C32C2×D511yescharacteristic
89C2×C3⋊Dic3—51no—
90C2×C3⋊Dic3—51no—
91C2×C3⋊Dic3—102no—
92C2×C3×Dic3—51no—
93C2×C3×Dic3—51no—
94C2×C3×Dic3C2×D511yescharacteristic
95C2×C3×Dic3C2×D511yescharacteristic
96#627—102no—
97C22×C3×C5—22no—
98C22×C3×C5—22no—
99C22×C3×C5—21no—
100C22×C3×C5—21no—
101C22×C3×C5—21no—
102C22×C3×C5—21no—
103C22×C3×C5—22no—
104C22×C3×C5—21no—
105C22×C3×C5Dic612yescomplemented
106C22×C3×C5Dic612yescomplemented
107C22×C3×C5C22×D311yescharacteristic
108C22×C3×C5C22×D311yescharacteristic
109C3×C4×C5—61no—
110C3×C4×C5—61no—
111Dic15—21no—
112Dic15—21no—
113Dic15—32no—
114Dic15—32no—
115Dic15—62no—
116Dic15—62no—
117Dic15—61no—
118Dic15—61no—
119C3×Dic5—61no—
120C3×Dic5—61no—
121C5×Dic3—21no—
122C5×Dic3—21no—
123C22×Dic3—151no—
124C22×Dic3—151no—
125C22×Dic3—301no—
126C2×Dic6—151no—
127C2×Dic6—151no—
128C3×C22⋊C4—31no—
129C3×C22⋊C4—151no—
130#217—51no—
131#217D1511yescharacteristic
132C4⋊Dic3—151no—
133C4⋊Dic3—151no—
134Dic3⋊C4—151no—
135Dic3⋊C4—151no—
136Dic3⋊C4—151no—
137Dic3⋊C4—151no—
138C32×C5C22⋊Q811yescharacteristic, complemented, Hall
139C23×C5D3211yescharacteristic
140C2×C4×C5—31no—
141C2×C4×C5—31no—
142C2×Dic5—31no—
143C2×Dic5—31no—
144C2×Dic5—91no—
145C2×Dic5—91no—
146C2×Dic5—182no—
147Dic10—182no—
148C22×C32—21no—
149C22×C32—21no—
150C22×C32Dic1012yescomplemented
151C22×C32C22×D511yescharacteristic
152C3⋊Dic3—52no—
153C3⋊Dic3—101no—
154C3×Dic3—21no—
155C3×Dic3—21no—
156C3×Dic3—101no—
157C3×Dic3—101no—
158C22⋊Q8—451noSylow
159C2×C3×C5—24no—
160C2×C3×C5—22no—
161C2×C3×C5—22no—
162C2×C3×C5—21no—
163C2×C3×C5—21no—
164C2×C3×C5—21no—
165C2×C3×C5C2×Dic611yescharacteristic
166C2×C3×C5C2×Dic611yescharacteristic
167C2×C3×C5D3×D411yescharacteristic
168C2×C3×C5D3×D411yescharacteristic
169C2×C3×C5#23711yescharacteristic
170C2×C3×C5#23711yescharacteristic
171C23×C3—21no—
172C23×C3D3×D511yescharacteristic
173C23×C3C2×D1511yescharacteristic
174C2×C3×C4—31no—
175C2×C3×C4—31no—
176C2×C3×C4—151no—
177C2×C3×C4—151no—
178C2×Dic3—51no—
179C2×Dic3—51no—
180C2×Dic3—151no—
181C2×Dic3—151no—
182C2×Dic3—151no—
183C2×Dic3—151no—
184C2×Dic3—301no—
185C2×Dic3—301no—
186C2×Dic3—302no—
187C2×Dic3—302no—
188C2×Dic3—304no—
189C2×Dic3C2×D1511yescharacteristic
190C2×Dic3C2×D1511yescharacteristic
191Dic6—302no—
192Dic6—302no—
193C22×C5—21no—
194C22×C5—21no—
195C22×C5#62712yescomplemented
196C22×C5C2×D3211yescharacteristic
197C4×C5—61no—
198C4×C5—61no—
199Dic5—61no—
200Dic5—61no—
201Dic5—92no—
202Dic5—181no—
203C2×C32—22no—
204C2×C32C2×Dic1011yescharacteristic
205C2×C32D4×D511yescharacteristic
206C2×C32#71111yescharacteristic
207C2×Q8—451no—
208C22×C4—451no—
209C4⋊C4—451no—
210C4⋊C4—451no—
211C4⋊C4—451no—
212C22⋊C4—31no—
213C22⋊C4—151no—
214C3×C5—21no—
215C3×C5#87811yescharacteristic, complemented
216C3×C5#87811yescharacteristic, complemented
217C22×C3—22no—
218C22×C3—22no—
219C22×C3—21no—
220C22×C3—21no—
221C22×C3—21no—
222C22×C3—21no—
223C22×C3—22no—
224C22×C3—21no—
225C22×C3#120412yescomplemented
226C22×C3Dic3012yescomplemented
227C22×C3C2×D3×D511yescharacteristic
228C22×C3C22×D1511yescharacteristic
229C3×C4—61no—
230C3×C4—61no—
231C3×C4—301no—
232C3×C4—301no—
233Dic3—21no—
234Dic3—21no—
235Dic3—101no—
236Dic3—101no—
237Dic3—152no—
238Dic3—152no—
239Dic3—302no—
240Dic3—302no—
241Dic3—301no—
242Dic3—301no—
243C2×C5—22no—
244C2×C5#380511yescharacteristic
245C2×C5C2×#62711yescharacteristic
246C2×C5#381111yescharacteristic
247C32#402411yescharacteristic, complemented, Sylow
248C23D3×D1511yescharacteristic
249Q8—902no—
250C2×C4—31no—
251C2×C4—31no—
252C2×C4—151no—
253C2×C4—151no—
254C2×C4—451no—
255C2×C4—451no—
256C2×C4—902no—
257C2×C3—24no—
258C2×C3—22no—
259C2×C3—22no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—21no—
263C2×C3#678011yescharacteristic
264C2×C3C2×#120411yescharacteristic
265C2×C3#679011yescharacteristic
266C2×C3C2×Dic3011yescharacteristic
267C2×C3D4×D1511yescharacteristic
268C2×C3#681911yescharacteristic
269C5#6398211yescharacteristic, complemented, Sylow
270C22—21no—
271C22—21no—
272C22#6715312yescomplemented
273C22C2×D3×D1511yescharacteristic
274C4—61no—
275C4—61no—
276C4—301no—
277C4—301no—
278C4—452no—
279C4—901no—
280C3—21no—
281C3#9157611yescharacteristic, complemented
282C3#9176711yescharacteristic, complemented
283C2—22no—
284C2#1062420811yescharacteristic
285C2C2×#6715311yescharacteristic
286C2#1062421811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D15
commutator, socle, cosocleC22×C32×C5C23
Fitting, prime radicalC23×C32×C5C22
hypercenterC23D3×D15
hypocenterC32×C5C22⋊Q8
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×#67153C2semidirect
5. Dic3⋊Dic15C2semidirect
6. #10623815C2semidirect
7. #10623814C2semidirect
37. C22×C32×C5Q8semidirect
105. C22×C3×C5Dic6semidirect
106. C22×C3×C5Dic6semidirect
138. C32×C5C22⋊Q8semidirect
150. C22×C32Dic10semidirect
195. C22×C5#627semidirect
215. C3×C5#878semidirect
216. C3×C5#878semidirect
225. C22×C3#1204semidirect
226. C22×C3Dic30semidirect
247. C32#4024semidirect
269. C5#63982semidirect
272. C22#67153semidirect
281. C3#91576semidirect
282. C3#91767semidirect

Maximal subgroups

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

subgroupindex
C22×C3⋊Dic152
C2×#671532
C3×#67192
C3×C5×#2172
Dic3⋊Dic152
#106238152
#106238142
#917673
#915763
#639825