Finite Group Databasebeta

← #13085930

Subgroups — #13085930

Order 1440.

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

normal subgroups only

This group has 402 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×D3×Dic15C211yesmaximal, characteristic, complemented
2C2×C5×#625C211yesmaximal, characteristic
3C2×C3×D3×Dic5C211yesmaximal, characteristic, complemented
4#10623828C211yesmaximal, characteristic, complemented
5(C2×D3)⋊Dic15C211yesmaximal, characteristic, complemented
6#10623775C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
8#67⋊Dic5—31nomaximal
9Dic5×#67—31nomaximal
10C22×C3×C5×D3C2211yescharacteristic
11C22×C3×C5×D3C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C3×Dic15C2211yescharacteristic
15C2×C3×Dic15C2211yescharacteristic
16C2×C32×Dic5C2211yescharacteristic
17D3×Dic15—22no—
18C5×#625C414yescomplemented
19C3×D3×Dic5—22no—
20#63879—51nomaximal, Hall
21C22×Dic15—31no—
22C2×C5×#67—31no—
23C2×C5×#67—31no—
24C22×C3×Dic5—31no—
25C2×D3×Dic5—31no—
26C2×D3×Dic5D311yescharacteristic, complemented
27#6719—31no—
28C3×C22⋊Dic5—31no—
29Dic3⋊Dic5—31no—
30Dic3⋊Dic5—31no—
31Dic3⋊Dic5—61no—
32(C2×D3)⋊Dic5—31no—
33(C2×D3)⋊Dic5D311yescharacteristic, complemented
34Dic3×Dic5—31no—
35Dic3×Dic5—31no—
36C22×C32×C5C2311yescharacteristic
37C2×C3×C5×D3—21no—
38C2×C3×C5×D3—21no—
39C2×C3×C5×D3—21no—
40C2×C3×C5×D3—21no—
41C2×C3×C5×D3C2×C412yescomplemented
42C2×C3×C5×D3C2×C412yescomplemented
43C3⋊Dic15—21no—
44C5×C3⋊Dic3C2×C412yescomplemented
45C3×Dic15—21no—
46C3×Dic15D412yescomplemented
47C32×Dic5—21no—
48D4×Dic5—91noHall
49C2×C3×C4×D3—51no—
50C2×#625D511yescharacteristic
51C2×D3×Dic3—51no—
52#3750—51no—
53C3×(C2×D3)⋊C4—51no—
54(C2×D3)⋊Dic3—51no—
55Dic32—51no—
56C23×C3×C5—31no—
57C23×C3×C5—31no—
58C22×C5×D3C2×D311yescharacteristic
59C22×C5×D3C2×D311yescharacteristic
60C2×Dic15—31no—
61C2×Dic15—31no—
62C2×Dic15—62no—
63C2×Dic15—61no—
64C2×Dic15C2×D311yescharacteristic
65C2×Dic15C2×D311yescharacteristic
66C5×#67—34no—
67C5×#67—34no—
68C2×C5×Dic3—31no—
69C2×C5×Dic3—31no—
70C2×C5×Dic3—61no—
71C2×C3×Dic5—21no—
72C2×C3×Dic5—31no—
73C2×C3×Dic5—31no—
74C2×C3×Dic5—62no—
75C2×C3×Dic5C2×D311yescharacteristic
76C2×C3×Dic5C2×D311yescharacteristic
77D3×Dic5—22no—
78D3×Dic5—62no—
79C4×#67—151no—
80#67⋊C4—151no—
81C2×C32×C5C22×C411yescharacteristic
82C2×C32×C5C2×D411yescharacteristic
83C2×C32×C5#4111yescharacteristic
84C3×C5×D3—22no—
85C3×C5×D3—22no—
86C2×C5×D4—91no—
87C22×Dic5—31no—
88C22×Dic5—91no—
89C22⋊Dic5—31no—
90C22⋊Dic5—91no—
91C4⋊Dic5—91no—
92C4×Dic5—91no—
93C22×C3×D3C2×D511yescharacteristic
94C22×C3×D3C2×D511yescharacteristic
95C2×C32×C4—51no—
96C2×C3⋊Dic3—51no—
97C2×C3⋊Dic3C2×D511yescharacteristic
98C2×C3×Dic3—51no—
99C2×C3×Dic3—51no—
100C3×C4×D3—102no—
101#625Dic514yescomplemented
102D3×Dic3—102no—
103C22×C3×C5—21no—
104C22×C3×C5—32no—
105C22×C3×C5—32no—
106C22×C3×C5—61no—
107C22×C3×C5—61no—
108C22×C3×C5—61no—
109C22×C3×C5—61no—
110C22×C3×C5C22×D311yescharacteristic
111C22×C3×C5C22×D311yescharacteristic
112C2×C5×D3—21no—
113C2×C5×D3—21no—
114C2×C5×D3—21no—
115C2×C5×D3—21no—
116C2×C5×D3C4×D312yescomplemented
117C2×C5×D3C4×D312yescomplemented
118Dic15—21no—
119Dic15—61no—
120Dic15—61no—
121Dic15—121no—
122Dic15#6712yescomplemented
123C3×Dic5—21no—
124C3×Dic5—21no—
125C3×Dic5—32no—
126C3×Dic5—41no—
127C3×Dic5—61no—
128C5×Dic3—32no—
129C5×Dic3—32no—
130C5×Dic3—62no—
131C22×C3×C4—151no—
132C2×#67—31no—
133C2×#67—31no—
134C22×Dic3—151no—
135C2×C4×D3—51no—
136C2×C4×D3—151no—
137C3×C22⋊C4—151no—
138#217—151no—
139(C2×D3)⋊C4—51no—
140(C2×D3)⋊C4—151no—
141Dic3⋊C4—151no—
142Dic3⋊C4—151no—
143Dic3⋊C4—301no—
144C4×Dic3—151no—
145C4×Dic3—151no—
146C32×C5C4×D411yescharacteristic, complemented, Hall
147C23×C5—31no—
148C23×C5—31no—
149C5×D4—94no—
150C2×C4×C5—91no—
151C2×Dic5—31no—
152C2×Dic5—31no—
153C2×Dic5—62no—
154C2×Dic5—91no—
155C2×Dic5—182no—
156C2×Dic5D3211yescharacteristic
157C22×C32C22×D511yescharacteristic
158C2×C3×D3—21no—
159C2×C3×D3—21no—
160C2×C3×D3—21no—
161C2×C3×D3—21no—
162C2×C3×D3C2×Dic512yescomplemented
163C2×C3×D3C2×Dic512yescomplemented
164C32×C4—101no—
165C3⋊Dic3—101no—
166C3⋊Dic3C2×Dic512yescomplemented
167C3×Dic3—52no—
168C3×Dic3—101no—
169C4×D4—451noSylow
170C2×C3×C5—21no—
171C2×C3×C5—21no—
172C2×C3×C5—21no—
173C2×C3×C5—62no—
174C2×C3×C5—62no—
175C2×C3×C5C2×C4×D311yescharacteristic
176C2×C3×C5C2×C4×D311yescharacteristic
177C2×C3×C5#23511yescharacteristic
178C2×C3×C5D3×D411yescharacteristic
179C2×C3×C5#23711yescharacteristic
180C2×C3×C5C2×#6711yescharacteristic
181C5×D3—22no—
182C5×D3—22no—
183C23×C3—31no—
184C23×C3—31no—
185C22×D3D3×D511yescharacteristic
186C22×D3D3×D511yescharacteristic
187C2×C3×C4—51no—
188C2×C3×C4—51no—
189C2×C3×C4—101no—
190C2×C3×C4—151no—
191C2×C3×C4—151no—
192C2×C3×C4—302no—
193#67—34no—
194#67—34no—
195C2×Dic3—31no—
196C2×Dic3—31no—
197C2×Dic3—51no—
198C2×Dic3—51no—
199C2×Dic3—61no—
200C2×Dic3—151no—
201C2×Dic3—151no—
202C2×Dic3—301no—
203C2×Dic3—302no—
204C4×D3—102no—
205C4×D3—302no—
206C22×C5—32no—
207C22×C5—32no—
208C22×C5—61no—
209C22×C5—61no—
210C22×C5—61no—
211C22×C5—61no—
212C22×C5C2×D3211yescharacteristic
213C4×C5—92no—
214Dic5—21no—
215Dic5—32no—
216Dic5—61no—
217Dic5—181no—
218C2×C32D4×D511yescharacteristic
219C2×C32#71111yescharacteristic
220C2×C32C22×Dic511yescharacteristic
221C3×D3—22no—
222C3×D3—22no—
223C2×D4—91no—
224C22×C4—151no—
225C22×C4—451no—
226C4⋊C4—451no—
227C22⋊C4—151no—
228C22⋊C4—451no—
229C42—451no—
230C3×C5—21no—
231C3×C5#67⋊C411yescharacteristic, complemented
232C3×C5C4×#6711yescharacteristic, complemented
233C22×C3—21no—
234C22×C3—32no—
235C22×C3—32no—
236C22×C3—61no—
237C22×C3—61no—
238C22×C3—61no—
239C22×C3—61no—
240C22×C3C2×D3×D511yescharacteristic
241C22×C3C2×D3×D511yescharacteristic
242C2×D3—21no—
243C2×D3—21no—
244C2×D3—21no—
245C2×D3—21no—
246C2×D3D3×Dic512yescomplemented
247C2×D3D3×Dic512yescomplemented
248C3×C4—101no—
249C3×C4—101no—
250C3×C4—152no—
251C3×C4—201no—
252C3×C4—301no—
253Dic3—32no—
254Dic3—32no—
255Dic3—52no—
256Dic3—62no—
257Dic3—101no—
258Dic3—301no—
259Dic3—301no—
260Dic3—601no—
261C2×C5—62no—
262C2×C5—62no—
263C2×C5#379511yescharacteristic
264C2×C5C4×D3211yescharacteristic
265C2×C5D3×#6711yescharacteristic
266C32D4×Dic511yescharacteristic, complemented, Sylow
267C23—31no—
268C23—31no—
269D4—94no—
270C2×C4—51no—
271C2×C4—91no—
272C2×C4—151no—
273C2×C4—151no—
274C2×C4—302no—
275C2×C4—451no—
276C2×C4—902no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—62no—
281C2×C3—62no—
282C2×C3#678011yescharacteristic
283C2×C3C2×D3×Dic511yescharacteristic
284C2×C3C2×D3×Dic511yescharacteristic
285C2×C3#678211yescharacteristic
286C2×C3D5×#6711yescharacteristic
287C2×C3#679011yescharacteristic
288D3—22no—
289D3—22no—
290C5#6387911yescharacteristic, complemented, Sylow
291C22—32no—
292C22—32no—
293C22—61no—
294C22—61no—
295C22—61no—
296C22—61no—
297C22D32×D511yescharacteristic
298C4—92no—
299C4—101no—
300C4—152no—
301C4—301no—
302C4—901no—
303C3—21no—
304C3Dic5×#6711yescharacteristic, complemented
305C3#67⋊Dic511yescharacteristic, complemented
306C2—62no—
307C2—62no—
308C2D32×Dic511yescharacteristic
309C2#1062402711yescharacteristic
310C2#1062405011yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutatorC2×C32×C5C22×C4
Fitting, socle, cosocleC22×C32×C5C23
prime radicalC2×C5×#625C2
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×D3×Dic15C2semidirect
3. C2×C3×D3×Dic5C2semidirect
4. #10623828C2semidirect
5. (C2×D3)⋊Dic15C2semidirect
6. #10623775C2semidirect
7. C3×(C2×D3)⋊Dic5C2semidirect
18. C5×#625C4semidirect
26. C2×D3×Dic5D3semidirect
33. (C2×D3)⋊Dic5D3semidirect
41. C2×C3×C5×D3C2×C4semidirect
42. C2×C3×C5×D3C2×C4semidirect
44. C5×C3⋊Dic3C2×C4semidirect
46. C3×Dic15D4semidirect
101. #625Dic5semidirect
116. C2×C5×D3C4×D3semidirect
117. C2×C5×D3C4×D3semidirect
122. Dic15#67semidirect
146. C32×C5C4×D4semidirect
162. C2×C3×D3C2×Dic5semidirect
163. C2×C3×D3C2×Dic5semidirect
166. C3⋊Dic3C2×Dic5semidirect
231. C3×C5#67⋊C4semidirect
232. C3×C5C4×#67semidirect
246. C2×D3D3×Dic5semidirect
247. C2×D3D3×Dic5semidirect
266. C32D4×Dic5semidirect
290. C5#63879semidirect
304. C3Dic5×#67semidirect
305. C3#67⋊Dic5semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic152
C2×C5×#6252
C2×C3×D3×Dic52
#106238282
(C2×D3)⋊Dic152
#106237752
C3×(C2×D3)⋊Dic52
#67⋊Dic53
Dic5×#673
#638795