Finite Group Databasebeta

← #14299789

Subgroups — #14299789

Order 1920.

572 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#520C211yesmaximal, characteristic
2C2×#91121C211yesmaximal, characteristic
3#11751333C211yesmaximal, characteristic
4#11751096C211yesmaximal, characteristic, complemented
5#11751078C211yesmaximal, characteristic, complemented
6#11746353C211yesmaximal, characteristic, complemented
7#11746351C211yesmaximal, characteristic, complemented
8#10602458—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C3×C4×C5×Q8—21no—
11C3×C4×C5×D4—21no—
12C3×C4×C5×D4—22no—
13C3×C5×#117—21no—
14C3×C5×#117C2211yescharacteristic
15C2×C3×C5×C4⋊C4—21no—
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C4⋊Dic15C2211yescharacteristic
18C2×C4×Dic15C2211yescharacteristic
19C2×#6710C2211yescharacteristic
20C2×#6710C2211yescharacteristic
21#91121C414yescomplemented
22#91119—21no—
23#91116—21no—
24#91115—22no—
25#91092—21no—
26#91091—21no—
27#71665—51nomaximal, Hall
28C5×#520D311yescharacteristic
29C2×#3969—31no—
30#65521—31no—
31#65284—31no—
32#65266—31no—
33#64752—31no—
34#64750—31no—
35C3×C5×#41—21no—
36C3×C5×#41—21no—
37C3×C5×#41C2×C412yes—
38C3×C5×#41Q812yes—
39C2×C3×C5×Q8D411yescharacteristic
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4D411yescharacteristic
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5—22no—
44C22×C3×C4×C5D412yes—
45C22×C3×C4×C5C2311yescharacteristic
46C22×Dic15—21no—
47C22×Dic15—21no—
48C3×C5×C4⋊C4—22no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4D411yescharacteristic
52C3×C5×C4⋊C4D411yescharacteristic
53C3×C5×C22⋊C4—22no—
54C3×C5×C22⋊C4—21no—
55C3×C42×C5—22no—
56C3×C42×C5—21no—
57C4⋊Dic15—21no—
58C4⋊Dic15—21no—
59C4×Dic15—21no—
60C4×Dic15C2×C412yescomplemented
61#6710—21no—
62#6710—21no—
63#6710—21no—
64#6710C2×C412yescomplemented
65C2×C3⋊#168—21no—
66C2×C3⋊#168—21no—
67C3×#520D511yescharacteristic
68C2×#837—51no—
69#5232—51no—
70#4995—51no—
71#4977—51no—
72#4532—51no—
73#4530—51no—
74C2×C5×#41C2×D311yescharacteristic
75C4×C5×Q8—21no—
76C4×C5×D4—21no—
77C4×C5×D4—22no—
78C5×#117—21no—
79C5×#117C2×D311yescharacteristic
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4C2×D311yescharacteristic
82C2×C4⋊Dic5—31no—
83C2×C4×Dic5—31no—
84C2×#681—31no—
85C2×#681—31no—
86#3969—34no—
87#3967—61no—
88#3964—61no—
89#3963—62no—
90#3940—61no—
91#3939—61no—
92#1860—151noSylow
93C23×C3×C5—21no—
94C23×C3×C5C2×D411yescharacteristic
95C3×C5×Q8—21no—
96C3×C5×Q8C4⋊C412yes—
97C3×C5×D4—22no—
98C3×C5×D4—22no—
99C3×C5×D4—21no—
100C3×C5×D4C4⋊C412yes—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—22no—
103C2×C3×C4×C5—22no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—42no—
108C2×C3×C4×C5—82no—
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×Q811yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×Dic15—22no—
116C2×Dic15—41no—
117C2×Dic15—41no—
118C2×Dic15—42no—
119C2×Dic15—41no—
120C3⋊#168—22no—
121C3⋊#168—41no—
122C2×C3×#41C2×D511yescharacteristic
123C3×C4×Q8—21no—
124C3×C4×D4—21no—
125C3×C4×D4—22no—
126C3×#117—21no—
127C3×#117C2×D511yescharacteristic
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4C2×D511yescharacteristic
130C2×C4⋊Dic3—51no—
131C2×C4×Dic3—51no—
132C2×#208—51no—
133C2×#208—51no—
134#837—54no—
135#835—101no—
136#832—101no—
137C3⋊#95—102no—
138#808—101no—
139#807—101no—
140C5×#41—21no—
141C5×#41—21no—
142C5×#41Dic612yes—
143C5×#41C4×D312yes—
144C2×C5×Q8#6711yescharacteristic
145C2×C5×D4—21no—
146C2×C5×D4#6711yescharacteristic
147C22×C4×C5—21no—
148C22×C4×C5—22no—
149C22×C4×C5#6712yes—
150C22×C4×C5C22×D311yescharacteristic
151C22×Dic5—61no—
152C22×Dic5—61no—
153C5×C4⋊C4—22no—
154C5×C4⋊C4—21no—
155C5×C4⋊C4—21no—
156C5×C4⋊C4#6711yescharacteristic
157C5×C4⋊C4#6711yescharacteristic
158C5×C22⋊C4—22no—
159C5×C22⋊C4—21no—
160C42×C5—22no—
161C42×C5—21no—
162C4⋊Dic5—61no—
163C4⋊Dic5—61no—
164C4×Dic5—32no—
165C4×Dic5—61no—
166#681—32no—
167#681—61no—
168#681—61no—
169#681—61no—
170C2×#168—61no—
171C2×#168—61no—
172#520D1511yescharacteristic
173#428—151no—
174C2×#104—151no—
175#417—151no—
176#382—151no—
177#343—151no—
178#339—151no—
179C22×C3×C5—21no—
180C22×C3×C5—21no—
181C22×C3×C5—22no—
182C22×C3×C5—41no—
183C22×C3×C5—41no—
184C22×C3×C5C4×D411yescharacteristic
185C22×C3×C5#12011yescharacteristic
186C22×C3×C5C22⋊Q811yescharacteristic
187C3×C4×C5—22no—
188C3×C4×C5—41no—
189C3×C4×C5—42no—
190C3×C4×C5—41no—
191C3×C4×C5C2×C4⋊C411yescharacteristic
192C3×C4×C5C4×D411yescharacteristic
193C3×C4×C5C22⋊Q811yescharacteristic
194C3×C4×C5#12311yescharacteristic
195Dic15—42no—
196Dic15—81no—
197C3×#41—21no—
198C3×#41—21no—
199C3×#41Dic1012yes—
200C3×#41C4×D512yes—
201C2×C3×Q8C22⋊D511yescharacteristic
202C2×C3×D4—21no—
203C2×C3×D4C22⋊D511yescharacteristic
204C22×C3×C4—21no—
205C22×C3×C4—22no—
206C22×C3×C4C22⋊D512yes—
207C22×C3×C4C22×D511yescharacteristic
208C22×Dic3—101no—
209C22×Dic3—101no—
210C3×C4⋊C4—22no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4C22⋊D511yescharacteristic
214C3×C4⋊C4C22⋊D511yescharacteristic
215C3×C22⋊C4—22no—
216C3×C22⋊C4—21no—
217C3×C42—22no—
218C3×C42—21no—
219C4⋊Dic3—101no—
220C4⋊Dic3—101no—
221C4×Dic3—52no—
222C4×Dic3—101no—
223#208—52no—
224#208—101no—
225#208—101no—
226#208—101no—
227C2×C3⋊C8—101no—
228C2×C3⋊C8—101no—
229C23×C5—21no—
230C23×C5C2×#6711yescharacteristic
231C5×Q8—21no—
232C5×Q8Dic3⋊C412yes—
233C5×D4—22no—
234C5×D4—22no—
235C5×D4—21no—
236C5×D4Dic3⋊C412yes—
237C2×C4×C5—21no—
238C2×C4×C5—22no—
239C2×C4×C5—22no—
240C2×C4×C5—21no—
241C2×C4×C5—22no—
242C2×C4×C5—21no—
243C2×C4×C5—42no—
244C2×C4×C5—82no—
245C2×C4×C5C2×Dic611yescharacteristic
246C2×C4×C5C2×C4×D311yescharacteristic
247C2×C4×C5#23511yescharacteristic
248C2×C4×C5#23511yescharacteristic
249C2×C4×C5C2×#6711yescharacteristic
250C2×C4×C5C2×#6711yescharacteristic
251C2×Dic5—62no—
252C2×Dic5—121no—
253C2×Dic5—121no—
254C2×Dic5—122no—
255C2×Dic5—121no—
256#168—62no—
257#168—121no—
258C2×#41C2×D1511yescharacteristic
259C2×M16—151no—
260C2×M16—151no—
261C4×Q8—21no—
262C4×D4—21no—
263C4×D4—22no—
264#117—21no—
265#117C2×D1511yescharacteristic
266C2×C4⋊C4—21no—
267C2×C4⋊C4—151no—
268C2×C4⋊C4C2×D1511yescharacteristic
269C2×C42—151no—
270#107—301no—
271#106—301no—
272#104—154no—
273#103—301no—
274#102—301no—
275#95—302no—
276C2×C3×C5—21no—
277C2×C3×C5—21no—
278C2×C3×C5—42no—
279C2×C3×C5#38511yescharacteristic
280C2×C3×C5#45411yescharacteristic
281C2×C3×C5#45511yescharacteristic
282C23×C3—21no—
283C23×C3C2×C22⋊D511yescharacteristic
284C3×Q8—21no—
285C3×Q8#68312yes—
286C3×D4—22no—
287C3×D4—22no—
288C3×D4—21no—
289C3×D4#68312yes—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—21no—
294C2×C3×C4—22no—
295C2×C3×C4—21no—
296C2×C3×C4—42no—
297C2×C3×C4—82no—
298C2×C3×C4C2×Dic1011yescharacteristic
299C2×C3×C4C2×C4×D511yescharacteristic
300C2×C3×C4#70911yescharacteristic
301C2×C3×C4#70911yescharacteristic
302C2×C3×C4C2×C22⋊D511yescharacteristic
303C2×C3×C4C2×C22⋊D511yescharacteristic
304C2×Dic3—102no—
305C2×Dic3—201no—
306C2×Dic3—201no—
307C2×Dic3—202no—
308C2×Dic3—201no—
309C3⋊C8—102no—
310C3⋊C8—201no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—22no—
314C22×C5—41no—
315C22×C5—41no—
316C22×C5#92411yescharacteristic
317C22×C5C4×#6711yescharacteristic
318C22×C5#95311yescharacteristic
319C4×C5—22no—
320C4×C5—42no—
321C4×C5—41no—
322C4×C5—41no—
323C4×C5C2×Dic3⋊C411yescharacteristic
324C4×C5#92411yescharacteristic
325C4×C5C4×#6711yescharacteristic
326C4×C5#92911yescharacteristic
327Dic5—122no—
328Dic5—241no—
329#41—21no—
330#41—21no—
331#41Dic3012yes—
332#41C4×D1512yes—
333C2×Q8#122011yescharacteristic
334C2×D4—21no—
335C2×D4#122011yescharacteristic
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—301no—
339C22×C4—301no—
340C22×C4#122012yes—
341C22×C4C22×D1511yescharacteristic
342M16—152no—
343M16—301no—
344M16—301no—
345M16—301no—
346C2×C8—301no—
347C2×C8—301no—
348C4⋊C4—22no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—301no—
352C4⋊C4—301no—
353C4⋊C4#122011yescharacteristic
354C4⋊C4#122011yescharacteristic
355C22⋊C4—22no—
356C22⋊C4—21no—
357C42—22no—
358C42—21no—
359C42—152no—
360C42—301no—
361C3×C5#186011yescharacteristic, complemented, Hall
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—22no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3#407011yescharacteristic
368C22×C3C4×C22⋊D511yescharacteristic
369C22×C3#409911yescharacteristic
370C3×C4—22no—
371C3×C4—42no—
372C3×C4—41no—
373C3×C4—41no—
374C3×C4C2×#68311yescharacteristic
375C3×C4#407011yescharacteristic
376C3×C4C4×C22⋊D511yescharacteristic
377C3×C4#407511yescharacteristic
378Dic3—202no—
379Dic3—401no—
380C2×C5—21no—
381C2×C5—21no—
382C2×C5—42no—
383C2×C5#521011yescharacteristic
384C2×C5#524211yescharacteristic
385C2×C5#524511yescharacteristic
386C23—21no—
387C23C2×#122011yescharacteristic
388Q8—21no—
389Q8#671212yes—
390D4—22no—
391D4—22no—
392D4—21no—
393D4#671212yes—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—21no—
398C2×C4—22no—
399C2×C4—21no—
400C2×C4—42no—
401C2×C4—82no—
402C2×C4—302no—
403C2×C4—601no—
404C2×C4—601no—
405C2×C4—602no—
406C2×C4—601no—
407C2×C4C2×Dic3011yescharacteristic
408C2×C4C2×C4×D1511yescharacteristic
409C2×C4#681711yescharacteristic
410C2×C4#681711yescharacteristic
411C2×C4C2×#122011yescharacteristic
412C2×C4C2×#122011yescharacteristic
413C8—302no—
414C8—601no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—42no—
418C2×C3#6549911yescharacteristic
419C2×C3#6553111yescharacteristic
420C2×C3#6553411yescharacteristic
421C5#7166511yescharacteristic, complemented, Sylow
422C22—21no—
423C22—21no—
424C22—22no—
425C22—41no—
426C22—41no—
427C22#9181311yescharacteristic
428C22C4×#122011yescharacteristic
429C22#9184211yescharacteristic
430C4—22no—
431C4—42no—
432C4—41no—
433C4—41no—
434C4—602no—
435C4—1201no—
436C4C2×#671211yescharacteristic
437C4#9181311yescharacteristic
438C4C4×#122011yescharacteristic
439C4#9181811yescharacteristic
440C3#1060245811yescharacteristic, complemented, Sylow
441C2—21no—
442C2—21no—
443C2—42no—
444C2#1175131111yescharacteristic
445C2#1175134311yescharacteristic
446C2#1175134611yescharacteristic
subgroupG/H
centerC22#91842
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#520C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×#41C22
cosocleC22×C3×C4×C5C23
hypercenter#520D15
hypocenterC3×C5#1860
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #520

Complements

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

NH ≅ G/Ntype
4. #11751096C2semidirect
5. #11751078C2semidirect
6. #11746353C2semidirect
7. #11746351C2semidirect
21. #91121C4semidirect
60. C4×Dic15C2×C4semidirect
64. #6710C2×C4semidirect
361. C3×C5#1860semidirect
421. C5#71665semidirect
440. C3#10602458semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5202
C2×#911212
#117513332
#117510962
#117510782
#117463532
#117463512
#106024583
#716655