Finite Group Databasebeta

← #13085880

Subgroups — #13085880

Order 1440.

338 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 98 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×D5×Dic3C211yesmaximal, characteristic
2#10623831C211yesmaximal, characteristic, complemented
3#10623814C211yesmaximal, characteristic, complemented
4Dic3×Dic15C211yesmaximal, characteristic, complemented
5C5×Dic32C211yesmaximal, characteristic, complemented
6#10623770C211yesmaximal, characteristic
7C3×#6665C211yesmaximal, characteristic
8#91393—31nomaximal
9#91357—31nomaximal
10C22×C32×D5C2211yescharacteristic
11C2×C3⋊Dic15C2211yescharacteristic
12C2×C5×C3⋊Dic3C2211yescharacteristic
13C2×C3×Dic15C2211yescharacteristic
14C2×C3×Dic15C2211yescharacteristic
15C2×C3×C5×Dic3C2211yescharacteristic
16C2×C3×C5×Dic3C2211yescharacteristic
17C3×D5×Dic3C414yescomplemented
18#63955—51nomaximal, Hall
19C2×C3×C4×D5—31no—
20C2×D5×Dic3D311yescharacteristic
21#6712—31no—
22C4×Dic15—31no—
23C4×C5×Dic3—31no—
24C4×C5×Dic3—31no—
25C3×#685—31no—
26#6669—31no—
27#6668—31no—
28#6668—31no—
29#6665—31no—
30#6665—31no—
31#6665—61no—
32#6665D311yescharacteristic
33Dic3×Dic5—31no—
34C22×C32×C5C2311yescharacteristic
35C2×C32×D5—21no—
36C2×C32×D5—21no—
37C2×C32×D5C2×C412yes—
38C3⋊Dic15—21no—
39C5×C3⋊Dic3—21no—
40C3×Dic15—21no—
41C3×Dic15C2×C412yes—
42C3×C5×Dic3—21no—
43C3×C5×Dic3C2×C412yes—
44#4018—91noHall
45C22×C3×Dic3—51no—
46#3757—51no—
47C3×#217—51no—
48Dic3⋊Dic3—51no—
49Dic3⋊Dic3—51no—
50Dic32—51no—
51Dic32D511yescharacteristic, complemented
52C22×C3×D5—21no—
53C22×C3×D5C2×D311yescharacteristic
54C22×C3×D5C2×D311yescharacteristic
55C2×C3×C4×C5—31no—
56C2×C3×C4×C5—31no—
57C2×Dic15—31no—
58C2×Dic15—31no—
59C2×Dic15—61no—
60C2×Dic15C2×D311yescharacteristic
61C2×Dic15C2×D311yescharacteristic
62C2×C5×Dic3—31no—
63C2×C5×Dic3—31no—
64C2×C5×Dic3—61no—
65C2×C5×Dic3C2×D311yescharacteristic
66C2×C5×Dic3C2×D311yescharacteristic
67C2×C3×Dic5—31no—
68C2×C3×Dic5—31no—
69C3×C4×D5—34no—
70D5×Dic3Dic314yescomplemented
71#926—151no—
72#877—151no—
73C2×C32×C5C22×C411yescharacteristic
74C2×C32×C5#4111yescharacteristic
75C2×C32×C5#4111yescharacteristic
76C32×D5—22no—
77C2×C4×D5—31no—
78C42×C5—91no—
79#685—31no—
80#685—91no—
81#683—91no—
82#683—91no—
83C4×Dic5—91no—
84C23×C32—51no—
85C2×C3⋊Dic3—51no—
86C2×C3⋊Dic3C2×D511yescharacteristic
87C2×C3×Dic3—51no—
88C2×C3×Dic3—54no—
89C2×C3×Dic3—51no—
90C2×C3×Dic3C2×D511yescharacteristic
91C2×C3×Dic3C2×D511yescharacteristic
92C22×C3×C5—21no—
93C22×C3×C5C22×D311yescharacteristic
94C22×C3×C5C22×D311yescharacteristic
95C2×C3×D5—21no—
96C2×C3×D5—21no—
97C2×C3×D5—21no—
98C2×C3×D5—21no—
99C2×C3×D5—22no—
100C2×C3×D5—41no—
101C2×C3×D5—41no—
102C2×C3×D5C4×D312yes—
103C2×C3×D5C2×Dic312yes—
104C3×C4×C5—32no—
105C3×C4×C5—61no—
106Dic15—21no—
107Dic15—61no—
108Dic15—61no—
109Dic15—121no—
110Dic15C2×Dic312yes—
111C3×Dic5—32no—
112C3×Dic5—61no—
113C5×Dic3—21no—
114C5×Dic3—61no—
115C5×Dic3—61no—
116C5×Dic3—121no—
117C5×Dic3C2×Dic312yes—
118C22×C3×C4—151no—
119C22×Dic3—51no—
120C3×C22⋊C4—151no—
121#217—51no—
122#217—151no—
123#217—151no—
124#217—301no—
125C4⋊Dic3—151no—
126C4⋊Dic3—151no—
127Dic3⋊C4—151no—
128Dic3⋊C4—151no—
129C4×Dic3—31no—
130C4×Dic3—31no—
131C4×Dic3—151no—
132C4×Dic3—151no—
133C32×C5#11711yescharacteristic, complemented, Hall
134C22×D5D3211yescharacteristic
135C2×C4×C5—31no—
136C2×C4×C5—31no—
137C2×C4×C5—91no—
138C2×Dic5—31no—
139C2×Dic5—31no—
140C2×Dic5—91no—
141C4×D5—34no—
142C22×C32—52no—
143C22×C32—101no—
144C22×C32—101no—
145C22×C32C22×D511yescharacteristic
146C3⋊Dic3—21no—
147C3⋊Dic3—101no—
148C3×Dic3—21no—
149C3×Dic3—52no—
150C3×Dic3—101no—
151C3×Dic3C4×D512yes—
152#117—451noSylow
153C2×C3×C5—21no—
154C2×C3×C5—21no—
155C2×C3×C5—21no—
156C2×C3×C5C2×C4×D311yescharacteristic
157C2×C3×C5#23511yescharacteristic
158C2×C3×C5#23511yescharacteristic
159C2×C3×C5#23711yescharacteristic
160C2×C3×C5#23711yescharacteristic
161C2×C3×C5C22×Dic311yescharacteristic
162C3×D5—22no—
163C3×D5—22no—
164C3×D5—42no—
165C23×C3—51no—
166C23×C3—51no—
167C23×C3—101no—
168C2×C3×C4—31no—
169C2×C3×C4—31no—
170C2×C3×C4—154no—
171C2×C3×C4—151no—
172C2×C3×C4—151no—
173C2×Dic3—31no—
174C2×Dic3—31no—
175C2×Dic3—51no—
176C2×Dic3—54no—
177C2×Dic3—51no—
178C2×Dic3—61no—
179C2×Dic3—151no—
180C2×Dic3—151no—
181C2×Dic3—301no—
182C2×Dic3D3×D511yescharacteristic
183C2×Dic3D3×D511yescharacteristic
184C22×C5C2×D3211yescharacteristic
185C2×D5—21no—
186C2×D5—21no—
187C2×D5D3×Dic312yes—
188C4×C5—32no—
189C4×C5—61no—
190C4×C5—181no—
191Dic5—32no—
192Dic5—61no—
193Dic5—181no—
194C2×C32—102no—
195C2×C32C2×C4×D511yescharacteristic
196C2×C32#70911yescharacteristic
197C2×C32#70911yescharacteristic
198C22×C4—151no—
199C4⋊C4—451no—
200C4⋊C4—451no—
201C22⋊C4—151no—
202C22⋊C4—451no—
203C42—91no—
204C42—451no—
205C3×C5—21no—
206C3×C5#87711yescharacteristic, complemented
207C3×C5#92611yescharacteristic, complemented
208C22×C3—21no—
209C22×C3—52no—
210C22×C3—52no—
211C22×C3—102no—
212C22×C3—101no—
213C22×C3—101no—
214C22×C3—101no—
215C22×C3—101no—
216C22×C3—201no—
217C22×C3—201no—
218C22×C3C2×D3×D511yescharacteristic
219C22×C3C2×D3×D511yescharacteristic
220C3×C4—32no—
221C3×C4—61no—
222C3×C4—152no—
223C3×C4—301no—
224Dic3—21no—
225Dic3—52no—
226Dic3—61no—
227Dic3—61no—
228Dic3—101no—
229Dic3—121no—
230Dic3—301no—
231Dic3—301no—
232Dic3—601no—
233Dic3D5×Dic312yes—
234C2×C5C2×D3×Dic311yescharacteristic
235C2×C5#380411yescharacteristic
236C2×C5#380411yescharacteristic
237D5—22no—
238C32#401811yescharacteristic, complemented, Sylow
239C23—51no—
240C2×C4—31no—
241C2×C4—31no—
242C2×C4—91no—
243C2×C4—154no—
244C2×C4—151no—
245C2×C4—151no—
246C2×C4—451no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—102no—
251C2×C3—102no—
252C2×C3—202no—
253C2×C3#676511yescharacteristic
254C2×C3#677111yescharacteristic
255C2×C3#677111yescharacteristic
256C2×C3C4×D3×D511yescharacteristic
257C2×C3C2×D5×Dic311yescharacteristic
258C2×C3#677911yescharacteristic
259C5#6395511yescharacteristic, complemented, Sylow
260C22—52no—
261C22—101no—
262C22—101no—
263C22D32×D511yescharacteristic
264C4—32no—
265C4—61no—
266C4—152no—
267C4—181no—
268C4—301no—
269C4—901no—
270C3—21no—
271C3#9135711yescharacteristic, complemented
272C3#9139311yescharacteristic, complemented
273C2—102no—
274C2D3×D5×Dic311yescharacteristic
275C2#1062404111yescharacteristic
276C2#1062404211yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutatorC2×C32×C5C22×C4
Fitting, socle, cosocleC22×C32×C5C23
prime radicalC22×C32×D5C22
hypocenterC32×C5#117
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #10623831C2semidirect
3. #10623814C2semidirect
4. Dic3×Dic15C2semidirect
5. C5×Dic32C2semidirect
17. C3×D5×Dic3C4semidirect
51. Dic32D5semidirect
70. D5×Dic3Dic3semidirect
133. C32×C5#117semidirect
206. C3×C5#877semidirect
207. C3×C5#926semidirect
238. C32#4018semidirect
259. C5#63955semidirect
271. C3#91357semidirect
272. C3#91393semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×Dic32
#106238312
#106238142
Dic3×Dic152
C5×Dic322
#106237702
C3×#66652
#913933
#913573
#639555