Finite Group Databasebeta

← #13085933

Subgroups — #13085933

Order 1440.

410 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 102 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×#67155C211yesmaximal, characteristic, complemented
2C2×C5×#626C211yesmaximal, characteristic
3C2×C3×D3×Dic5C211yesmaximal, characteristic, complemented
4(C2×D3)⋊Dic15C211yesmaximal, characteristic, complemented
5Dic3×Dic15C211yesmaximal, characteristic, complemented
6#10623771C211yesmaximal, characteristic, complemented
7C3×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
8Dic5×#67—31nomaximal
9#91435—31nomaximal
10C22×C5×C3⋊D3C2211yescharacteristic
11C22×C3×C5×D3C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C3×Dic15C2211yescharacteristic
14C2×C3×Dic15C2211yescharacteristic
15C2×C3×C5×Dic3C2211yescharacteristic
16C2×C32×Dic5C2211yescharacteristic
17#67155—22no—
18C5×#626C414yescomplemented
19C3×D3×Dic5—22no—
20#63904—51nomaximal, Hall
21C2×C5×#67—31no—
22C2×C5×D12—31no—
23C22×C3×Dic5—31no—
24C2×D3×Dic5—31no—
25C2×D3×Dic5—31no—
26C2×D3×Dic5D311yescharacteristic, complemented
27#6719—31no—
28C4×Dic15—31no—
29C3×C4⋊Dic5—31no—
30Dic3⋊Dic5D311yescharacteristic, complemented
31(C2×D3)⋊Dic5—31no—
32(C2×D3)⋊Dic5—31no—
33(C2×D3)⋊Dic5—31no—
34(C2×D3)⋊Dic5—61no—
35Dic3×Dic5—31no—
36C22×C32×C5C2311yescharacteristic
37C2×C5×C3⋊D3—21no—
38C2×C5×C3⋊D3—21no—
39C2×C5×C3⋊D3C2×C412yescomplemented
40C2×C3×C5×D3—21no—
41C2×C3×C5×D3—21no—
42C2×C3×C5×D3C2×C412yescomplemented
43C3⋊Dic15—21no—
44C3×Dic15—21no—
45C3×Dic15D412yescomplemented
46C3×C5×Dic3C2×C412yescomplemented
47C32×Dic5—21no—
48D4×Dic5—91noHall
49C2×C3×C4×D3—51no—
50C2×#626D511yescharacteristic
51C2×#624—51no—
52#3752—51no—
53C3×Dic3⋊C4—51no—
54(C2×D3)⋊Dic3—51no—
55Dic32—51no—
56C23×C3×C5—31no—
57C22×C5×D3—31no—
58C22×C5×D3—31no—
59C22×C5×D3—61no—
60C22×C5×D3C2×D311yescharacteristic
61C2×C3×C4×C5—31no—
62C2×Dic15—31no—
63C2×Dic15—31no—
64C2×Dic15—61no—
65C2×Dic15C2×D311yescharacteristic
66C2×Dic15C2×D311yescharacteristic
67C5×#67—34no—
68C2×C5×Dic3C2×D311yescharacteristic
69C5×D12—34no—
70C2×C3×Dic5—21no—
71C2×C3×Dic5—31no—
72C2×C3×Dic5—31no—
73C2×C3×Dic5—62no—
74C2×C3×Dic5C2×D311yescharacteristic
75C2×C3×Dic5C2×D311yescharacteristic
76D3×Dic5—22no—
77D3×Dic5—62no—
78D3×Dic5—62no—
79C4×#67—151no—
80#893—151no—
81C2×C32×C5C22×C411yescharacteristic
82C2×C32×C5C2×D411yescharacteristic
83C2×C32×C5#4111yescharacteristic
84C5×C3⋊D3—22no—
85C3×C5×D3—22no—
86C2×C5×D4—91no—
87C22×Dic5—31no—
88C22×Dic5—91no—
89C22⋊Dic5—91no—
90C22⋊Dic5—91no—
91C4⋊Dic5—31no—
92C4×Dic5—91no—
93C22×C3⋊D3C2×D511yescharacteristic
94C22×C3×D3C2×D511yescharacteristic
95C2×C32×C4—51no—
96C2×C3⋊Dic3—51no—
97C2×C3×Dic3—51no—
98C2×C3×Dic3—51no—
99C2×C3×Dic3C2×D511yescharacteristic
100C3×C4×D3—102no—
101#626Dic514yescomplemented
102#624—102no—
103C22×C3×C5—21no—
104C22×C3×C5—32no—
105C22×C3×C5—61no—
106C22×C3×C5—61no—
107C22×C3×C5C22×D311yescharacteristic
108C22×C3×C5C22×D311yescharacteristic
109C2×C5×D3—21no—
110C2×C5×D3—21no—
111C2×C5×D3—32no—
112C2×C5×D3—32no—
113C2×C5×D3—62no—
114C2×C5×D3—61no—
115C2×C5×D3—61no—
116C2×C5×D3—61no—
117C2×C5×D3—61no—
118C2×C5×D3—121no—
119C2×C5×D3—121no—
120C2×C5×D3C4×D312yescomplemented
121C3×C4×C5—32no—
122Dic15—21no—
123Dic15—61no—
124Dic15—61no—
125Dic15—121no—
126Dic15#6712yescomplemented
127C3×Dic5—21no—
128C3×Dic5—21no—
129C3×Dic5—32no—
130C3×Dic5—41no—
131C3×Dic5—61no—
132C5×Dic3C4×D312yescomplemented
133C22×C3×C4—151no—
134C2×#67—31no—
135C2×D12—31no—
136C2×C4×D3—51no—
137C2×C4×D3—151no—
138C2×C4×D3—151no—
139C3×C4⋊C4—151no—
140#217—151no—
141(C2×D3)⋊C4—151no—
142(C2×D3)⋊C4—151no—
143(C2×D3)⋊C4—151no—
144(C2×D3)⋊C4—301no—
145Dic3⋊C4—51no—
146C4×Dic3—151no—
147C4×Dic3—151no—
148C32×C5C4×D411yescharacteristic, complemented, Hall
149C23×C5—31no—
150C23×C5—91no—
151C5×D4—94no—
152C2×C4×C5—31no—
153C2×Dic5—31no—
154C2×Dic5—31no—
155C2×Dic5—62no—
156C2×Dic5—91no—
157C2×Dic5—182no—
158C2×Dic5D3211yescharacteristic
159C22×C32C22×D511yescharacteristic
160C2×C3⋊D3—21no—
161C2×C3⋊D3—21no—
162C2×C3⋊D3C2×Dic512yescomplemented
163C2×C3×D3—21no—
164C2×C3×D3—21no—
165C2×C3×D3C2×Dic512yescomplemented
166C32×C4—101no—
167C3⋊Dic3—101no—
168C3×Dic3—52no—
169C3×Dic3—101no—
170C3×Dic3C2×Dic512yescomplemented
171C4×D4—451noSylow
172C2×C3×C5—21no—
173C2×C3×C5—21no—
174C2×C3×C5—21no—
175C2×C3×C5—62no—
176C2×C3×C5C2×C4×D311yescharacteristic
177C2×C3×C5C2×C4×D311yescharacteristic
178C2×C3×C5#23511yescharacteristic
179C2×C3×C5D3×D411yescharacteristic
180C2×C3×C5#23911yescharacteristic
181C2×C3×C5C2×#6711yescharacteristic
182C5×D3—22no—
183C5×D3—62no—
184C5×D3—62no—
185C5×D3—122no—
186C23×C3—31no—
187C22×D3—31no—
188C22×D3—31no—
189C22×D3—61no—
190C22×D3D3×D511yescharacteristic
191C2×C3×C4—31no—
192C2×C3×C4—51no—
193C2×C3×C4—51no—
194C2×C3×C4—101no—
195C2×C3×C4—151no—
196C2×C3×C4—151no—
197C2×C3×C4—302no—
198#67—34no—
199C2×Dic3—51no—
200C2×Dic3—51no—
201C2×Dic3—151no—
202C2×Dic3—151no—
203C2×Dic3—301no—
204C2×Dic3D3×D511yescharacteristic
205D12—34no—
206C4×D3—102no—
207C4×D3—302no—
208C4×D3—302no—
209C22×C5—32no—
210C22×C5—61no—
211C22×C5—61no—
212C22×C5—92no—
213C22×C5—181no—
214C22×C5—181no—
215C22×C5C2×D3211yescharacteristic
216C4×C5—32no—
217Dic5—21no—
218Dic5—32no—
219Dic5—61no—
220Dic5—181no—
221C2×C32D4×D511yescharacteristic
222C2×C32#71111yescharacteristic
223C2×C32C22×Dic511yescharacteristic
224C3⋊D3—22no—
225C3×D3—22no—
226C2×D4—91no—
227C22×C4—151no—
228C22×C4—451no—
229C4⋊C4—151no—
230C22⋊C4—451no—
231C22⋊C4—451no—
232C42—451no—
233C3×C5—21no—
234C3×C5#89311yescharacteristic, complemented
235C3×C5C4×#6711yescharacteristic, complemented
236C22×C3—21no—
237C22×C3—32no—
238C22×C3—61no—
239C22×C3—61no—
240C22×C3C2×D3×D511yescharacteristic
241C22×C3C2×D3×D511yescharacteristic
242C2×D3—21no—
243C2×D3—21no—
244C2×D3—32no—
245C2×D3—32no—
246C2×D3—62no—
247C2×D3—61no—
248C2×D3—61no—
249C2×D3—61no—
250C2×D3—61no—
251C2×D3—121no—
252C2×D3—121no—
253C2×D3D3×Dic512yescomplemented
254C3×C4—32no—
255C3×C4—101no—
256C3×C4—101no—
257C3×C4—152no—
258C3×C4—201no—
259C3×C4—301no—
260Dic3—52no—
261Dic3—101no—
262Dic3—301no—
263Dic3—301no—
264Dic3—601no—
265Dic3D3×Dic512yescomplemented
266C2×C5—62no—
267C2×C5—182no—
268C2×C5#379911yescharacteristic
269C2×C5C4×D3211yescharacteristic
270C2×C5D3×#6711yescharacteristic
271C32D4×Dic511yescharacteristic, complemented, Sylow
272C23—31no—
273C23—91no—
274D4—94no—
275C2×C4—31no—
276C2×C4—51no—
277C2×C4—151no—
278C2×C4—151no—
279C2×C4—302no—
280C2×C4—451no—
281C2×C4—902no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—62no—
286C2×C3#676811yescharacteristic
287C2×C3#677711yescharacteristic
288C2×C3C2×D3×Dic511yescharacteristic
289C2×C3C2×D3×Dic511yescharacteristic
290C2×C3#678211yescharacteristic
291C2×C3D5×#6711yescharacteristic
292D3—22no—
293D3—62no—
294D3—62no—
295D3—122no—
296C5#6390411yescharacteristic, complemented, Sylow
297C22—32no—
298C22—61no—
299C22—61no—
300C22—92no—
301C22—181no—
302C22—181no—
303C22D32×D511yescharacteristic
304C4—32no—
305C4—101no—
306C4—152no—
307C4—301no—
308C4—901no—
309C3—21no—
310C3#9143511yescharacteristic, complemented
311C3Dic5×#6711yescharacteristic, complemented
312C2—62no—
313C2—182no—
314C2D32×Dic511yescharacteristic
315C2#1062402811yescharacteristic
316C2#1062405111yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutatorC2×C32×C5C22×C4
Fitting, socle, cosocleC22×C32×C5C23
prime radicalC2×C5×#626C2
hypocenterC32×C5C4×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×#67155C2semidirect
3. C2×C3×D3×Dic5C2semidirect
4. (C2×D3)⋊Dic15C2semidirect
5. Dic3×Dic15C2semidirect
6. #10623771C2semidirect
7. C3×Dic3⋊Dic5C2semidirect
18. C5×#626C4semidirect
26. C2×D3×Dic5D3semidirect
30. Dic3⋊Dic5D3semidirect
39. C2×C5×C3⋊D3C2×C4semidirect
42. C2×C3×C5×D3C2×C4semidirect
45. C3×Dic15D4semidirect
46. C3×C5×Dic3C2×C4semidirect
101. #626Dic5semidirect
120. C2×C5×D3C4×D3semidirect
126. Dic15#67semidirect
132. C5×Dic3C4×D3semidirect
148. C32×C5C4×D4semidirect
162. C2×C3⋊D3C2×Dic5semidirect
165. C2×C3×D3C2×Dic5semidirect
170. C3×Dic3C2×Dic5semidirect
234. C3×C5#893semidirect
235. C3×C5C4×#67semidirect
253. C2×D3D3×Dic5semidirect
265. Dic3D3×Dic5semidirect
271. C32D4×Dic5semidirect
296. C5#63904semidirect
310. C3#91435semidirect
311. C3Dic5×#67semidirect

Maximal subgroups

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

subgroupindex
C2×#671552
C2×C5×#6262
C2×C3×D3×Dic52
(C2×D3)⋊Dic152
Dic3×Dic152
#106237712
C3×Dic3⋊Dic52
Dic5×#673
#914353
#639045