Finite Group Databasebeta

← #11753691

Subgroups — #11753691

Order 960.

588 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6773C211yesmaximal, characteristic, complemented
2C2×#6771C211yesmaximal, characteristic, complemented
3#91784C211yesmaximal, characteristic, complemented
4C5×#897C211yesmaximal, characteristic, complemented
5C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
6#91460C211yesmaximal, characteristic, complemented
7#91450C212yesmaximal, complemented
8#91448C212yesmaximal, complemented
9#91420C212yesmaximal, complemented
10#91419C212yesmaximal, complemented
11#91383C211yesmaximal, characteristic, complemented
12#65963—31nomaximal, Hall
13C2×D60C2211yescharacteristic
14C2×D60C2212yes—
15C2×C4×D15C2211yescharacteristic
16C2×C4×C5×D3C2211yescharacteristic
17C2×C5×Dic6C2211yescharacteristic
18C2×C3×C4×D5C2212yes—
19C2×C3×C4×D5C2211yescharacteristic
20C2×#1204C2211yescharacteristic
21C2×#1203C2211yescharacteristic
22C2×#1203C2212yes—
23C2×#1202C2212yes—
24C2×#1202C2211yescharacteristic
25C2×#1201C2211yescharacteristic
26C2×#1200C2212yes—
27#6773—24no—
28#6771—24no—
29C3×C5×C4⋊C4C2211yescharacteristic
30#6714C2212yes—
31C5×(C2×D3)⋊C4C2212yes—
32C5×C4⋊Dic3C2212yes—
33C3×C4⋊Dic5C2211yescharacteristic
34C3×#683C2212yes—
35#6668C2212yes—
36#6667C2212yes—
37#6667C2212yes—
38#5510—51nomaximal, Hall
39C2×#713—31no—
40C2×#709—31no—
41C5×C22⋊Q8—31no—
42#4092—31no—
43#4076—31no—
44#4042—32no—
45#4041—32no—
46#4041—31no—
47D5×C4⋊C4D311yescharacteristic, complemented
48#4030—32no—
49#4030—32no—
50C22×D15C2311yescharacteristic
51C22×D15C2312yes—
52C22×C5×D3C2311yescharacteristic
53C22×C3×D5C2311yescharacteristic
54C2×C3×C4×C5C2312yes—
55C2×C3×C4×C5C2311yescharacteristic
56C2×Dic15C2311yescharacteristic
57D60—22no—
58D60—42no—
59C4×D15—22no—
60C2×C5×Dic3C2311yescharacteristic
61C2×C5×Dic3C2312yes—
62C4×C5×D3—22no—
63C5×Dic6—22no—
64C2×C3×Dic5C2312yes—
65C2×C3×Dic5C2311yescharacteristic
66C3×C4×D5—42no—
67C3×C4×D5D414yescomplemented
68#1204—22no—
69#1203—22no—
70#1203—42no—
71#1202—22no—
72#1202—24no—
73#1201—22no—
74#1200—24no—
75C2×#235—51no—
76C2×#235—51no—
77C2×C3×C4⋊C4—51no—
78#930—52no—
79#930—52no—
80#897—51no—
81#897—52no—
82#897D511yescharacteristic, complemented
83#895—51no—
84#895—51no—
85#895—52no—
86C2×C5×Q8—31no—
87C22×C4×C5—31no—
88C2×C22⋊D5—31no—
89C2×C22⋊D5—31no—
90C2×C22⋊D5—32no—
91#713—64no—
92#709—64no—
93C2×D20—31no—
94C2×D20—32no—
95C2×D20—31no—
96C2×D20—32no—
97C2×C4×D5—31no—
98C2×C4×D5—32no—
99C2×C4×D5C2×D312yes—
100C2×C4×D5C2×D311yescharacteristic
101C2×Dic10—31no—
102C5×C4⋊C4—32no—
103C5×C4⋊C4C2×D311yescharacteristic
104C5×C22⋊C4—32no—
105#685—32no—
106#685—32no—
107#685—32no—
108C4⋊Dic5C2×D311yescharacteristic
109#683—32no—
110#683C2×D312yes—
111#537—151noSylow
112C22×C3×C5C2411yescharacteristic
113C2×D15—22no—
114C2×D15—21no—
115C2×D15—22no—
116C2×D15—21no—
117C2×D15—21no—
118C2×D15—22no—
119C2×C5×D3—21no—
120C2×C5×D3—21no—
121C2×C5×D3—21no—
122C2×C3×D5—21no—
123C2×C3×D5—21no—
124C2×C3×D5C2×D412yes—
125C3×C4×C5—22no—
126C3×C4×C5C2×D412yes—
127Dic15—21no—
128C3×Dic5—22no—
129C3×Dic5C2×D412yes—
130C5×Dic3—22no—
131C5×Dic3—21no—
132C22×C3×C4—51no—
133C22×C3×C4—52no—
134C2×#67—51no—
135C2×#67—52no—
136C2×#67—51no—
137#235—104no—
138#235—104no—
139C2×D12—51no—
140C2×D12—51no—
141C2×D12—52no—
142C2×D12—52no—
143C2×C4×D3—51no—
144C2×C4×D3—52no—
145C2×C4×D3C2×D511yescharacteristic
146C2×Dic6—51no—
147C2×Dic6C2×D511yescharacteristic
148C3×C4⋊C4—52no—
149C3×C4⋊C4—51no—
150C3×C4⋊C4C2×D511yescharacteristic
151(C2×D3)⋊C4—52no—
152(C2×D3)⋊C4—52no—
153(C2×D3)⋊C4—52no—
154(C2×D3)⋊C4C2×D512yes—
155C4⋊Dic3—52no—
156C4⋊Dic3C2×D512yes—
157C23×C5—31no—
158C22×D5—32no—
159C22×D5—31no—
160C22×D5C22×D311yescharacteristic
161C5×Q8—62no—
162C2×C4×C5—32no—
163C2×C4×C5—31no—
164C2×C4×C5—62no—
165C2×C4×C5C22×D312yes—
166C2×C4×C5C22×D311yescharacteristic
167C22⋊D5—62no—
168C22⋊D5—62no—
169C22⋊D5—122no—
170C2×Dic5—31no—
171C2×Dic5C22×D312yes—
172C2×Dic5C22×D311yescharacteristic
173D20—62no—
174D20—64no—
175D20—62no—
176D20—122no—
177C4×D5—42no—
178C4×D5—62no—
179C4×D5—64no—
180C4×D5D1214yescomplemented
181Dic10—62no—
182C2×#41—151no—
183C2×#41—151no—
184C22⋊Q8—31no—
185C22⋊Q8—152no—
186C22⋊Q8—151no—
187#121—152no—
188#121—152no—
189#121—152no—
190#121—151no—
191#121—151no—
192C2×C4⋊C4—51no—
193C2×C3×C5C22×D411yescharacteristic
194C2×C3×C5H(5,𝔽2)11yescharacteristic
195C2×C3×C52−1+411yescharacteristic
196D15—42no—
197D15—41no—
198C3×D5—22no—
199C5×D3—41no—
200C23×C3—51no—
201C22×D3—52no—
202C22×D3—51no—
203C22×D3C22×D511yescharacteristic
204C2×C3×C4—51no—
205C2×C3×C4—54no—
206C2×C3×C4—52no—
207C2×C3×C4—202no—
208C2×C3×C4C22×D512yes—
209C2×C3×C4C22×D511yescharacteristic
210#67—104no—
211#67—102no—
212#67—102no—
213C2×Dic3—51no—
214C2×Dic3C22×D512yes—
215C2×Dic3C22×D511yescharacteristic
216D12—102no—
217D12—102no—
218D12—202no—
219D12—202no—
220C4×D3—22no—
221C4×D3—104no—
222C4×D3—102no—
223Dic6—22no—
224Dic6—102no—
225C22×C5—61no—
226C22×C5—61no—
227C22×C5—61no—
228C22×C5C23×D311yescharacteristic
229C2×D5—21no—
230C2×D5—21no—
231C2×D5—62no—
232C2×D5—61no—
233C2×D5—61no—
234C2×D5—62no—
235C2×D5—62no—
236C2×D5—61no—
237C2×D5C2×D1212yes—
238C4×C5—22no—
239C4×C5—61no—
240C4×C5—62no—
241C4×C5C2×D1212yes—
242Dic5—22no—
243Dic5—61no—
244Dic5C2×D1212yes—
245#41—304no—
246#41—304no—
247C2×Q8—31no—
248C2×Q8—151no—
249C2×D4—152no—
250C2×D4—151no—
251C2×D4—151no—
252C2×D4—152no—
253C2×D4—151no—
254C2×D4—151no—
255C2×D4—152no—
256C22×C4—31no—
257C22×C4—51no—
258C22×C4—52no—
259C22×C4—152no—
260C22×C4—151no—
261C4⋊C4—32no—
262C4⋊C4—52no—
263C4⋊C4—51no—
264C4⋊C4—152no—
265C4⋊C4D3×D511yescharacteristic
266C22⋊C4—32no—
267C22⋊C4—152no—
268C22⋊C4—152no—
269C22⋊C4—152no—
270C3×C5#53711yescharacteristic, complemented, Hall
271C22×C3—52no—
272C22×C3—101no—
273C22×C3—101no—
274C22×C3C23×D511yescharacteristic
275C2×D3—21no—
276C2×D3—21no—
277C2×D3—21no—
278C2×D3—102no—
279C2×D3—101no—
280C2×D3—101no—
281C2×D3—102no—
282C2×D3—102no—
283C2×D3—101no—
284C3×C4—22no—
285C3×C4—52no—
286C3×C4—102no—
287C3×C4D4×D512yes—
288Dic3—22no—
289Dic3—21no—
290Dic3—101no—
291C2×C5—121no—
292C2×C5C22×D1211yescharacteristic
293C2×C5#100411yescharacteristic
294C2×C5#100711yescharacteristic
295D5—22no—
296D5—122no—
297D5—121no—
298C23—31no—
299C23—51no—
300C23—151no—
301C23—152no—
302Q8—62no—
303Q8—302no—
304D4—302no—
305D4—302no—
306D4—304no—
307D4—302no—
308D4—302no—
309D4—602no—
310D4—602no—
311C2×C4—32no—
312C2×C4—31no—
313C2×C4—51no—
314C2×C4—54no—
315C2×C4—52no—
316C2×C4—62no—
317C2×C4—151no—
318C2×C4—202no—
319C2×C4—304no—
320C2×C4—302no—
321C2×C4C2×D3×D512yes—
322C2×C4C2×D3×D511yescharacteristic
323C2×C3—102no—
324C2×C3C2×D4×D511yescharacteristic
325C2×C3#414711yescharacteristic
326C2×C3#414911yescharacteristic
327D3—41no—
328D3—202no—
329D3—201no—
330C5#551011yescharacteristic, complemented, Sylow
331C22—52no—
332C22—61no—
333C22—61no—
334C22—61no—
335C22—101no—
336C22—101no—
337C22—302no—
338C22—301no—
339C22—301no—
340C22—302no—
341C22—301no—
342C22—302no—
343C22C22×D3×D511yescharacteristic
344C4—22no—
345C4—52no—
346C4—61no—
347C4—62no—
348C4—102no—
349C4—301no—
350C4D5×D1212yes—
351C3#6596311yescharacteristic, complemented, Sylow
352C2—102no—
353C2—121no—
354C2—602no—
355C2—601no—
356C2C2×D5×D1211yescharacteristic
357C2#9202611yescharacteristic
358C2#9202911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#537
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#6773C2semidirect
2. C2×#6771C2semidirect
3. #91784C2semidirect
4. C5×#897C2semidirect
5. C3×D5×C4⋊C4C2semidirect
6. #91460C2semidirect
7. #91450C2semidirect
8. #91448C2semidirect
9. #91420C2semidirect
10. #91419C2semidirect
11. #91383C2semidirect
47. D5×C4⋊C4D3semidirect
67. C3×C4×D5D4semidirect
82. #897D5semidirect
180. C4×D5D12semidirect
270. C3×C5#537semidirect
330. C5#5510semidirect
351. C3#65963semidirect

Maximal subgroups

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

subgroupindex
C2×#67732
C2×#67712
#917842
C5×#8972
C3×D5×C4⋊C42
#914602
#914502
#914482
#914202
#914192
#913832
#659633
#55105