Finite Group Databasebeta

← #11754367

Subgroups — #11754367

Order 960.

580 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6817C211yesmaximal, characteristic, complemented
2C2×D5×Dic6C211yesmaximal, characteristic, complemented
3C5×#924C211yesmaximal, characteristic, complemented
4C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
5#91550C212yesmaximal, complemented
6#91526C212yesmaximal, complemented
7#91450C211yesmaximal, characteristic, complemented
8#91396C212yesmaximal, complemented
9#91377C212yesmaximal, complemented
10#91375C211yesmaximal, characteristic, complemented
11#91333C211yesmaximal, characteristic, complemented
12#65967—31nomaximal, Hall
13C22×C3×C4×C5C2211yescharacteristic
14C2×#1220C2212yes—
15#6817—24no—
16C2×D60C2211yescharacteristic
17C2×C4×D15C2212yes—
18C2×Dic30C2211yescharacteristic
19C2×C5×Dic6C2211yescharacteristic
20C2×C3×C22⋊D5C2211yescharacteristic
21C2×C3×C4×D5C2211yescharacteristic
22C2×#1204C2212yes—
23C2×#1202C2212yes—
24C2×D5×Dic3C2212yes—
25D5×Dic6—24no—
26C5×#217C2212yes—
27C5×C4⋊Dic3C2211yescharacteristic
28C5×Dic3⋊C4C2212yes—
29C3×C22⋊Dic5C2211yescharacteristic
30C3×#685C2211yescharacteristic
31C3×#683C2211yescharacteristic
32C3×C4×Dic5C2211yescharacteristic
33#6669C2212yes—
34#6667C2212yes—
35#6667C2212yes—
36#6667C2212yes—
37Dic3×Dic5C2212yes—
38#5552—51nomaximal, Hall
39C2×Q8×D5—31no—
40C2×#709—31no—
41C5×C22⋊Q8—31no—
42#4093—31no—
43C4×C22⋊D5D311yescharacteristic, complemented
44#4042—32no—
45#4041—31no—
46#4039—32no—
47#4033—31no—
48#4031—32no—
49#4030—32no—
50C23×C3×C5C2311yescharacteristic
51C22×D15C2312yes—
52C22×C3×D5C2311yescharacteristic
53C2×C3×C4×C5—22no—
54C2×C3×C4×C5C2311yescharacteristic
55C2×C3×C4×C5C2311yescharacteristic
56#1220—24no—
57C2×Dic15C2312yes—
58D60—22no—
59C4×D15—24no—
60Dic30D414yescomplemented
61C2×C5×Dic3C2312yes—
62C2×C5×Dic3C2312yes—
63C5×Dic6—22no—
64C3×C22⋊D5—22no—
65C2×C3×Dic5C2311yescharacteristic
66C2×C3×Dic5C2311yescharacteristic
67C2×C3×Dic5C2311yescharacteristic
68C3×C4×D5—22no—
69#1204—24no—
70#1202—24no—
71D5×Dic3—24no—
72C2×#235—51no—
73C22×Dic6—51no—
74C3×C4×D4—51no—
75#939—52no—
76#930—51no—
77#924D511yescharacteristic, complemented
78#896—52no—
79#885—52no—
80#67⋊C4—52no—
81#875—51no—
82C4×Dic6—51no—
83C2×C5×Q8—31no—
84C22×C4×C5C2×D311yescharacteristic
85C2×C22⋊D5—32no—
86C2×C22⋊D5C2×D311yescharacteristic
87Q8×D5—64no—
88#709—64no—
89C2×D20—32no—
90C2×D20—31no—
91C2×C4×D5—32no—
92C2×C4×D5—32no—
93C2×C4×D5C2×D311yescharacteristic
94C2×Dic10—31no—
95C2×Dic10—32no—
96C5×C4⋊C4—32no—
97C5×C4⋊C4—31no—
98C5×C22⋊C4—32no—
99C22⋊Dic5C2×D311yescharacteristic
100#685—32no—
101#685—32no—
102#685—32no—
103#685C2×D311yescharacteristic
104#683—32no—
105#683C2×D311yescharacteristic
106C4×Dic5—32no—
107C4×Dic5C2×D311yescharacteristic
108#548—151noSylow
109C22×C3×C5—21no—
110C22×C3×C5—21no—
111C22×C3×C5—21no—
112C22×C3×C5C2411yescharacteristic
113C2×D15—22no—
114C2×D15—22no—
115C2×D15—22no—
116C2×C3×D5—21no—
117C2×C3×D5—21no—
118C2×C3×D5#4112yescomplemented
119C3×C4×C5—21no—
120C3×C4×C5C2×D412yes—
121Dic15C2×D414yes—
122C3×Dic5—21no—
123C3×Dic5—21no—
124C3×Dic5—21no—
125C5×Dic3—22no—
126C5×Dic3—22no—
127C2×C3×D4—51no—
128C22×C3×C4—51no—
129C22×C3×C4C2×D511yescharacteristic
130C2×#67—52no—
131C2×#67—52no—
132C22×Dic3—52no—
133#235—104no—
134C2×D12—51no—
135C2×C4×D3—52no—
136C2×Dic6—51no—
137C2×Dic6—52no—
138C2×Dic6—104no—
139C2×Dic6C2×D511yescharacteristic
140C3×C4⋊C4—51no—
141C3×C22⋊C4—51no—
142C3×C22⋊C4—51no—
143C3×C42—51no—
144#217C2×D512yes—
145(C2×D3)⋊C4—52no—
146(C2×D3)⋊C4—52no—
147(C2×D3)⋊C4—52no—
148C4⋊Dic3C2×D511yescharacteristic
149Dic3⋊C4—52no—
150Dic3⋊C4C2×D512yes—
151C4×Dic3—52no—
152C23×C5C22×D311yescharacteristic
153C22×D5—32no—
154C22×D5C22×D311yescharacteristic
155C5×Q8—62no—
156C2×C4×C5—22no—
157C2×C4×C5—32no—
158C2×C4×C5—32no—
159C2×C4×C5C22×D311yescharacteristic
160C2×C4×C5C22×D311yescharacteristic
161C22⋊D5—22no—
162C22⋊D5—64no—
163C2×Dic5—32no—
164C2×Dic5C22×D311yescharacteristic
165C2×Dic5C22×D311yescharacteristic
166C2×Dic5C22×D311yescharacteristic
167D20—64no—
168D20—62no—
169C4×D5—22no—
170C4×D5—64no—
171C4×D5—64no—
172Dic10—34no—
173Dic10—64no—
174C2×#41—151no—
175C22×Q8—151no—
176#124—151no—
177#124—152no—
178C22⋊Q8—31no—
179C22⋊Q8—152no—
180#121—152no—
181#121—151no—
182C4×Q8—151no—
183C4×D4—51no—
184C4×D4—152no—
185C2×C3×C5—41no—
186C2×C3×C5C22×D411yescharacteristic
187C2×C3×C5C2×#4111yescharacteristic
188C2×C3×C52−1+411yescharacteristic
189D15—42no—
190C3×D5—22no—
191C23×C3—51no—
192C23×C3C22×D511yescharacteristic
193C22×D3—52no—
194C3×D4—102no—
195C2×C3×C4—22no—
196C2×C3×C4—51no—
197C2×C3×C4—51no—
198C2×C3×C4—51no—
199C2×C3×C4—102no—
200C2×C3×C4C22×D511yescharacteristic
201C2×C3×C4C22×D511yescharacteristic
202#67—104no—
203#67—104no—
204C2×Dic3—52no—
205C2×Dic3—104no—
206C2×Dic3C22×D512yes—
207C2×Dic3C22×D512yes—
208D12—102no—
209C4×D3—104no—
210Dic6—22no—
211Dic6—54no—
212Dic6—104no—
213C22×C5—21no—
214C22×C5—21no—
215C22×C5—21no—
216C22×C5C23×D311yescharacteristic
217C2×D5—21no—
218C2×D5—21no—
219C2×D5—62no—
220C2×D5—62no—
221C2×D5—62no—
222C2×D5#23512yescomplemented
223C4×C5—21no—
224C4×C5—62no—
225C4×C5—62no—
226C4×C5D3×D412yes—
227Dic5—21no—
228Dic5—21no—
229Dic5—21no—
230Dic5—34no—
231#41—304no—
232C2×Q8—31no—
233C2×Q8—152no—
234C2×Q8—151no—
235C2×Q8—304no—
236C2×D4—51no—
237C2×D4—152no—
238C2×D4—152no—
239C2×D4—151no—
240C22×C4—51no—
241C22×C4—152no—
242C22×C4—152no—
243C22×C4D3×D511yescharacteristic
244C4⋊C4—32no—
245C4⋊C4—31no—
246C4⋊C4—51no—
247C4⋊C4—152no—
248C22⋊C4—32no—
249C22⋊C4—51no—
250C22⋊C4—51no—
251C22⋊C4—152no—
252C22⋊C4—152no—
253C22⋊C4—152no—
254C42—51no—
255C42—152no—
256C3×C5#54811yescharacteristic, complemented, Hall
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—52no—
261C22×C3—101no—
262C22×C3—101no—
263C22×C3C23×D511yescharacteristic
264C2×D3—102no—
265C2×D3—102no—
266C2×D3—102no—
267C3×C4—21no—
268C3×C4—101no—
269C3×C4—101no—
270C3×C4—101no—
271C3×C4D4×D512yes—
272Dic3—22no—
273Dic3—22no—
274Dic3—54no—
275C2×C5—41no—
276C2×C5C2×#23511yescharacteristic
277C2×C5C2×D3×D411yescharacteristic
278C2×C5#101011yescharacteristic
279D5—22no—
280D5—122no—
281C23—51no—
282C23—152no—
283C23C2×D3×D511yescharacteristic
284Q8—62no—
285Q8—154no—
286Q8—304no—
287D4—102no—
288D4—304no—
289D4—304no—
290D4—302no—
291C2×C4—22no—
292C2×C4—32no—
293C2×C4—32no—
294C2×C4—51no—
295C2×C4—51no—
296C2×C4—51no—
297C2×C4—102no—
298C2×C4—152no—
299C2×C4—304no—
300C2×C4—304no—
301C2×C4C2×D3×D511yescharacteristic
302C2×C4C2×D3×D511yescharacteristic
303C2×C3—41no—
304C2×C3—102no—
305C2×C3C2×D4×D511yescharacteristic
306C2×C3#414711yescharacteristic
307C2×C3D5×#4111yescharacteristic
308D3—202no—
309C5#555211yescharacteristic, complemented, Sylow
310C22—21no—
311C22—21no—
312C22—21no—
313C22—52no—
314C22—101no—
315C22—101no—
316C22—302no—
317C22—302no—
318C22—302no—
319C22C22×D3×D511yescharacteristic
320C4—21no—
321C4—62no—
322C4—62no—
323C4—101no—
324C4—101no—
325C4—101no—
326C4—154no—
327C4#679012yes—
328C3#6596711yescharacteristic, complemented, Sylow
329C2—41no—
330C2—102no—
331C2—602no—
332C2#9200011yescharacteristic
333C2D5×#23511yescharacteristic
334C2C2×#679011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC22×C3×C4×C5C22
hypercenterC22×C4D3×D5
hypocenterC3×C5#548
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#6817C2semidirect
2. C2×D5×Dic6C2semidirect
3. C5×#924C2semidirect
4. C3×C4×C22⋊D5C2semidirect
5. #91550C2semidirect
6. #91526C2semidirect
7. #91450C2semidirect
8. #91396C2semidirect
9. #91377C2semidirect
10. #91375C2semidirect
11. #91333C2semidirect
43. C4×C22⋊D5D3semidirect
60. Dic30D4semidirect
77. #924D5semidirect
118. C2×C3×D5#41semidirect
222. C2×D5#235semidirect
256. C3×C5#548semidirect
309. C5#5552semidirect
328. C3#65967semidirect

Maximal subgroups

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

subgroupindex
C2×#68172
C2×D5×Dic62
C5×#9242
C3×C4×C22⋊D52
#915502
#915262
#914502
#913962
#913772
#913752
#913332
#659673
#55525