Finite Group Databasebeta

← #14412721

Subgroups — #14412721

Order 1920.

1452 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92101C211yesmaximal, characteristic
2C2×C3×C5×#131C211yesmaximal, characteristic, complemented
3#11756586C211yesmaximal, characteristic, complemented
4#11751234C213yesmaximal, complemented
5#11751221C213yesmaximal, complemented
6#11751214C213yesmaximal, complemented
7C2×#91100C213yesmaximal, complemented
8#10615537—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10#92101—24no—
11#92101C418yescomplemented
12C2×Q8×D15—21no—
13C2×#6819—23no—
14C2×#6817C2213yes—
15C22×Dic30C2213yes—
16C3×C5×#131—24no—
17C2×C3×C5×M16C2213yes—
18C22×C3×C5×C8C2213yes—
19Q8×Dic15—21no—
20D4×Dic15—23no—
21#91815C2213yes—
22C2×C4⋊Dic15C2213yes—
23#91105C2211yescharacteristic
24#91105C2213yes—
25#91100C2213yes—
26#91100C2216yes—
27#91100C2213yes—
28#83806—51nomaximal, Hall
29C2×#4150—31no—
30C2×C5×#131D311yescharacteristic, complemented
31#66161—31no—
32#65422—33no—
33#65409—33no—
34#65402—33no—
35C2×#3948—33no—
36C3×C5×#41C2×C414yes—
37C3×C5×#41D414yes—
38C2×C3×C5×Q8D411yescharacteristic
39C2×C3×C5×D4D413yes—
40C22×C3×C4×C5C2313yes—
41C2×#1220—23no—
42C22×Dic15—23no—
43C22×Dic15—23no—
44Q8×D15—28no—
45#6819—224no—
46#6817—26no—
47#6817C2×C4112yescomplemented
48C2×D60C2311yescharacteristic
49C2×C4×D15—23no—
50C2×Dic30—23no—
51C2×Dic30—26no—
52C2×Dic30C2×C4112yescomplemented
53C2×Dic30C2313yes—
54C3×C5×M16—26no—
55C2×C3×C5×C8—26no—
56C2×C3×C5×C8C2311yescharacteristic
57C2×C3×C5×C8C2313yes—
58#6719—23no—
59C4⋊Dic15—23no—
60C4⋊Dic15C2313yes—
61C4⋊Dic15C2311yescharacteristic
62C4×Dic15—23no—
63C2×#1010—51no—
64C2×C3×#131D511yescharacteristic, complemented
65#5827—51no—
66#5133—53no—
67#5120—53no—
68#5113—53no—
69C2×#816—53no—
70C2×C5×#41C2×D311yescharacteristic
71#4150—38no—
72#4150—64no—
73C2×Q8×D5—61no—
74C2×#711—63no—
75C2×#709—33no—
76C22×Dic10—33no—
77C5×#131—24no—
78C2×C5×M16C2×D313yes—
79C22×C5×C8C2×D313yes—
80Q8×Dic5—61no—
81D4×Dic5—63no—
82#4072—33no—
83C2×C4⋊Dic5—33no—
84#3953—31no—
85#3953—33no—
86#3948—33no—
87#3948—36no—
88#3948—33no—
89#2898—151noSylow
90C23×C3×C5C2×D413yes—
91C22×D15—21no—
92C3×C5×Q8C22⋊C414yes—
93C3×C5×D4C22⋊C4112yes—
94C2×C3×C4×C5C22×C416yes—
95C2×C3×C4×C5C2×D413yes—
96C2×C3×C4×C5C2×D416yes—
97C2×C3×C4×C5C2411yescharacteristic
98#1220—212no—
99C2×Dic15—212no—
100C2×Dic15—23no—
101C2×Dic15—21no—
102C2×Dic15—23no—
103C2×Dic15—83no—
104D60—21no—
105D60C22×C412yes—
106C4×D15—212no—
107Dic30—212no—
108Dic30—23no—
109Dic30C22×C416yes—
110C3×C5×C8—21no—
111C3×C5×C8—23no—
112C2×C3×#41C2×D511yescharacteristic
113#1010—58no—
114#1010—104no—
115C2×D3×Q8—101no—
116C2×#237—103no—
117C2×#235—53no—
118C22×Dic6—53no—
119C3×#131—24no—
120C2×C3×M16C2×D513yes—
121C22×C3×C8C2×D513yes—
122Q8×Dic3—101no—
123D4×Dic3—103no—
124#926—53no—
125C2×C4⋊Dic3—53no—
126#821—53no—
127#821—51no—
128#816—53no—
129#816—56no—
130#816—53no—
131C5×#41C4×D314yes—
132C5×#41#6714yes—
133C2×C5×Q8D1211yescharacteristic
134C2×C5×D4D1213yes—
135C22×C4×C5C22×D313yes—
136C2×C22⋊D5—63no—
137C22×Dic5—63no—
138C22×Dic5—63no—
139Q8×D5—68no—
140#711—624no—
141#709—312no—
142#709—66no—
143C2×D20—31no—
144C2×C4×D5—63no—
145C2×Dic10—312no—
146C2×Dic10—33no—
147C2×Dic10—63no—
148C2×Dic10—66no—
149C5×M16—26no—
150C2×C5×C8—26no—
151C2×C5×C8C22×D311yescharacteristic
152C2×C5×C8C22×D313yes—
153C22⋊Dic5—63no—
154C4⋊Dic5—33no—
155C4⋊Dic5—31no—
156C4⋊Dic5—63no—
157C4×Dic5—63no—
158C2×2−1+4—151no—
159C2×#131D1511yescharacteristic, complemented
160#520—151no—
161#419—153no—
162#417—153no—
163#416—153no—
164C2×#103—153no—
165C22×C3×C5—23no—
166C22×C3×C5—23no—
167C22×C3×C5C2×C22⋊C416yes—
168C22×C3×C5C22×D411yescharacteristic
169C2×D15—22no—
170C2×D15—41no—
171C2×D15—41no—
172C3×C4×C5C2×C22⋊C416yes—
173C3×C4×C5C23×C411yescharacteristic
174C3×C4×C5C22×D411yescharacteristic
175Dic15—26no—
176Dic15—43no—
177Dic15—41no—
178C3×#41C4×D514yes—
179C3×#41C22⋊D514yes—
180C2×C3×Q8D2011yescharacteristic
181C2×C3×D4D2013yes—
182C22×C3×C4C22×D513yes—
183C2×#67—103no—
184C22×Dic3—103no—
185C22×Dic3—103no—
186D3×Q8—108no—
187#237—1024no—
188#235—512no—
189#235—106no—
190C2×D12—51no—
191C2×C4×D3—103no—
192C2×Dic6—512no—
193C2×Dic6—53no—
194C2×Dic6—103no—
195C2×Dic6—106no—
196C3×M16—26no—
197C2×C3×C8—26no—
198C2×C3×C8C22×D511yescharacteristic
199C2×C3×C8C22×D513yes—
200#217—103no—
201C4⋊Dic3—53no—
202C4⋊Dic3—51no—
203C4⋊Dic3—103no—
204C4×Dic3—103no—
205C23×C5C2×D1213yes—
206C22×D5—61no—
207C5×Q8(C2×D3)⋊C414yes—
208C5×D4(C2×D3)⋊C4112yes—
209C2×C4×C5C2×C4×D316yes—
210C2×C4×C5C2×D1213yes—
211C2×C4×C5C2×#6716yes—
212C2×C4×C5C23×D311yescharacteristic
213C22⋊D5—612no—
214C2×Dic5—612no—
215C2×Dic5—63no—
216C2×Dic5—61no—
217C2×Dic5—63no—
218C2×Dic5—243no—
219D20—32no—
220D20—61no—
221C4×D5—612no—
222Dic10—36no—
223Dic10—612no—
224Dic10—63no—
225C5×C8—21no—
226C5×C8—23no—
2272−1+4—158no—
2282−1+4—304no—
229C2×#41—153no—
230C2×#41—303no—
231C2×#41C2×D1511yescharacteristic
232C22×Q8—153no—
233C22×Q8—301no—
234#131—24no—
235C2×M16C2×D1513yes—
236C22×C8C2×D1513yes—
237C4×Q8—301no—
238C4×D4—303no—
239#117—153no—
240C2×C4⋊C4—153no—
241#103—153no—
242#103—156no—
243#103—153no—
244#102—151no—
245#102—153no—
246C2×C3×C5—26no—
247C2×C3×C5C22×C22⋊C411yescharacteristic
248C2×C3×C5#57711yescharacteristic
249C2×C3×C5#57811yescharacteristic
250D15—42no—
251C23×C3C2×D2013yes—
252C22×D3—101no—
253C3×Q8#68514yes—
254C3×D4#685112yes—
255C2×C3×C4C2×C4×D516yes—
256C2×C3×C4C2×D2013yes—
257C2×C3×C4C2×C22⋊D516yes—
258C2×C3×C4C23×D511yescharacteristic
259#67—1012no—
260C2×Dic3—103no—
261C2×Dic3—1012no—
262C2×Dic3—101no—
263C2×Dic3—103no—
264C2×Dic3—403no—
265D12—52no—
266D12—101no—
267C4×D3—1012no—
268Dic6—56no—
269Dic6—103no—
270Dic6—1012no—
271C3×C8—21no—
272C3×C8—23no—
273C22×C5—23no—
274C22×C5—23no—
275C22×C5C2×(C2×D3)⋊C416yes—
276C22×C5C22×D1211yescharacteristic
277C2×D5—62no—
278C2×D5—121no—
279C2×D5—121no—
280C4×C5C2×(C2×D3)⋊C416yes—
281C4×C5C22×C4×D311yescharacteristic
282C4×C5C22×#6711yescharacteristic
283Dic5—66no—
284Dic5—123no—
285Dic5—121no—
286#41—1512no—
287#41—3024no—
288#41—306no—
289#41C4×D1514yes—
290#41#122014yes—
291C2×Q8—1512no—
292C2×Q8—153no—
293C2×Q8—308no—
294C2×Q8—303no—
295C2×Q8—306no—
296C2×Q8D6011yescharacteristic
297C2×D4—151no—
298C2×D4—303no—
299C2×D4D6013yes—
300C22×C4—303no—
301C22×C4—303no—
302C22×C4—303no—
303C22×C4C22×D1513yes—
304M16—26no—
305C2×C8—26no—
306C2×C8C22×D1511yescharacteristic
307C2×C8C22×D1513yes—
308C4⋊C4—153no—
309C4⋊C4—151no—
310C4⋊C4—303no—
311C22⋊C4—303no—
312C42—303no—
313C3×C5#289811yescharacteristic, complemented, Hall
314C22×C3—23no—
315C22×C3—23no—
316C22×C3C2×#68516yes—
317C22×C3C22×D2011yescharacteristic
318C2×D3—102no—
319C2×D3—201no—
320C2×D3—201no—
321C3×C4C2×#68516yes—
322C3×C4C22×C4×D511yescharacteristic
323C3×C4C22×C22⋊D511yescharacteristic
324Dic3—106no—
325Dic3—203no—
326Dic3—201no—
327C2×C5—26no—
328C2×C5#575111yescharacteristic
329C2×C5#575311yescharacteristic
330C2×C5C22×(C2×D3)⋊C411yescharacteristic
331D5—122no—
332C23—301no—
333C23C2×D6013yes—
334Q8—156no—
335Q8—3012no—
336Q8—303no—
337Q8#671414yes—
338D4—152no—
339D4—3012no—
340D4—301no—
341D4#6714112yes—
342C2×C4—3012no—
343C2×C4—303no—
344C2×C4—3012no—
345C2×C4—301no—
346C2×C4—303no—
347C2×C4—1203no—
348C2×C4C2×C4×D1516yes—
349C2×C4C2×D6013yes—
350C2×C4C2×#122016yes—
351C2×C4C23×D1511yescharacteristic
352C8—21no—
353C8—23no—
354C2×C3—26no—
355C2×C3#6608511yescharacteristic
356C2×C3#6608711yescharacteristic
357C2×C3C22×#68511yescharacteristic
358D3—202no—
359C5#8380611yescharacteristic, complemented, Sylow
360C22—23no—
361C22—23no—
362C22—302no—
363C22—601no—
364C22—601no—
365C22C2×#671416yes—
366C22C22×D6011yescharacteristic
367C4—306no—
368C4—603no—
369C4—601no—
370C4C2×#671416yes—
371C4C22×C4×D1511yescharacteristic
372C4C22×#122011yescharacteristic
373C3#1061553711yescharacteristic, complemented, Sylow
374C2—26no—
375C2—602no—
376C2#1175651011yescharacteristic
377C2#1175651211yescharacteristic
378C2C22×#671411yescharacteristic
subgroupG/H
centerC22C22×D60
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC2×C3×C5×#131C2
socleC22×C3×C5C22×D4
prime radicalC2×#92101C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#131D15
hypocenterC3×C5#2898
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#131C2semidirect
3. #11756586C2semidirect
4. #11751234C2semidirect
5. #11751221C2semidirect
6. #11751214C2semidirect
7. C2×#91100C2semidirect
11. #92101C4semidirect
30. C2×C5×#131D3semidirect
47. #6817C2×C4semidirect
52. C2×Dic30C2×C4semidirect
64. C2×C3×#131D5semidirect
159. C2×#131D15semidirect
313. C3×C5#2898semidirect
359. C5#83806semidirect
373. C3#10615537semidirect

Maximal subgroups

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

subgroupindex
C2×#921012
C2×C3×C5×#1312
#117565862
#117512342
#117512212
#117512142
C2×#911002
#106155373
#838065