Finite Group Databasebeta

← #14308904

Subgroups — #14308904

Order 1920.

564 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756278C211yesmaximal, characteristic, complemented
2C3×C5×#418C211yesmaximal, characteristic
3#11751322C211yesmaximal, characteristic
4#11751316C211yesmaximal, characteristic
5#11746376C211yesmaximal, characteristic, complemented
6#11746375C211yesmaximal, characteristic, complemented
7#11746353C211yesmaximal, characteristic, complemented
8#10601106—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×#6719—22no—
13#91815C2211yescharacteristic
14C2×C4⋊Dic15C2211yescharacteristic
15C2×C4×Dic15C2211yescharacteristic
16C2×#6710C2211yescharacteristic
17#91779—21no—
18#91777—21no—
19#91767—22no—
20#91759—21no—
21#91758—21no—
22C3×C5×#102—21no—
23C3×C5×#102—21no—
24#91116—21no—
25#91116—21no—
26#70313—51nomaximal, Hall
27#65853—31no—
28C5×#418D311yescharacteristic
29#65510—31no—
30#65504—31no—
31#64775—31no—
32#64774—31no—
33#64752—31no—
34C24×C3×C5—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4Q812yescomplemented
41C22×C3×C4×C5C2311yescharacteristic
42C22×Dic15—21no—
43C22×Dic15D412yes—
44C2×Dic30—22no—
45C3×C5×M16—21no—
46C3×C5×M16—21no—
47C2×C3×C5×C8—21no—
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C4⋊C4D411yescharacteristic
50C3×C5×C22⋊C4—21no—
51C3×C42×C5—21no—
52#6719—21no—
53#6719—44no—
54C4⋊Dic15—22no—
55C4⋊Dic15—21no—
56C4⋊Dic15—21no—
57C4⋊Dic15D411yescharacteristic
58C4⋊Dic15D411yescharacteristic
59#6712—22no—
60#6712—22no—
61C4×Dic15—21no—
62C4×Dic15—21no—
63C4×Dic15—21no—
64#6710—21no—
65#6710—21no—
66C2×C3⋊#168—21no—
67#5519—51no—
68C3×#418D511yescharacteristic
69#5221—51no—
70#5215—51no—
71#4555—51no—
72#4554—51no—
73#4532—51no—
74C22×C5×D4C2×D311yescharacteristic
75C2×C5×M16C2×D311yescharacteristic
76C5×#117C2×D311yescharacteristic
77C2×C22⋊Dic5—62no—
78#4072—31no—
79C2×C4⋊Dic5—31no—
80C2×C4×Dic5—31no—
81C2×#681—31no—
82#4036—61no—
83#4034—61no—
84#4024—62no—
85#4016—61no—
86#4015—61no—
87C5×#102—21no—
88C5×#102—21no—
89#3964—61no—
90#3964—61no—
91#2027—151noSylow
92C23×C3×C5—22no—
93C23×C3×C5—42no—
94C23×C3×C5—42no—
95C23×C3×C5—41no—
96C23×C3×C5—41no—
97C23×C3×C5C2×D411yescharacteristic
98C3×C5×D4—22no—
99C3×C5×D4—22no—
100C3×C5×D4—41no—
101C3×C5×D4—41no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×Q811yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×Dic15—22no—
111C2×Dic15—21no—
112C2×Dic15—21no—
113C2×Dic15—22no—
114C2×Dic15—41no—
115C2×Dic15—41no—
116C2×Dic15—42no—
117Dic30—82no—
118C3×C5×C8—41no—
119C3⋊#168—41no—
120C22×C3×D4C2×D511yescharacteristic
121C2×C3×M16C2×D511yescharacteristic
122C3×#117C2×D511yescharacteristic
123C2×#217—102no—
124#926—51no—
125C2×C4⋊Dic3—51no—
126C2×C4×Dic3—51no—
127C2×#208—51no—
128#890—101no—
129#888—101no—
130#878—102no—
131#870—101no—
132#869—101no—
133C3×#102—21no—
134C3×#102—21no—
135#832—101no—
136#832—101no—
137C24×C5—21no—
138C2×C5×D4—21no—
139C2×C5×D4—21no—
140C2×C5×D4—21no—
141C2×C5×D4—21no—
142C2×C5×D4—21no—
143C2×C5×D4Dic612yescomplemented
144C22×C4×C5C22×D311yescharacteristic
145C22×Dic5—32no—
146C22×Dic5—61no—
147C2×Dic10—62no—
148C5×M16—21no—
149C5×M16—21no—
150C2×C5×C8—21no—
151C5×C4⋊C4#6711yescharacteristic
152C5×C4⋊C4#6711yescharacteristic
153C5×C22⋊C4—21no—
154C42×C5—21no—
155C22⋊Dic5—61no—
156C22⋊Dic5—124no—
157C4⋊Dic5—31no—
158C4⋊Dic5—31no—
159C4⋊Dic5—62no—
160C4⋊Dic5—61no—
161C4⋊Dic5—61no—
162#683—62no—
163#683—62no—
164C4×Dic5—61no—
165C4×Dic5—61no—
166C4×Dic5—61no—
167#681—61no—
168#681—61no—
169C2×#168—61no—
170#544—151no—
171#418—151no—
172#418D1511yescharacteristic
173#390—151no—
174#343—151no—
175#339—151no—
176#339—151no—
177C22×C3×C5—21no—
178C22×C3×C5—21no—
179C22×C3×C5—44no—
180C22×C3×C5—42no—
181C22×C3×C5—82no—
182C22×C3×C5—81no—
183C22×C3×C5—81no—
184C22×C3×C5#12011yescharacteristic
185C22×C3×C5C22⋊Q811yescharacteristic
186C22×C3×C5#12411yescharacteristic
187C3×C4×C5—41no—
188C3×C4×C5—41no—
189C3×C4×C5C22⋊Q811yescharacteristic
190C3×C4×C5C22⋊Q811yescharacteristic
191C3×C4×C5#12411yescharacteristic
192C3×C4×C5#12411yescharacteristic
193Dic15—42no—
194Dic15—41no—
195Dic15—42no—
196Dic15—41no—
197C24×C3—21no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—21no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4Dic1012yescomplemented
204C22×C3×C4C22×D511yescharacteristic
205C22×Dic3—52no—
206C22×Dic3—101no—
207C2×Dic6—102no—
208C3×M16—21no—
209C3×M16—21no—
210C2×C3×C8—21no—
211C3×C4⋊C4C22⋊D511yescharacteristic
212C3×C4⋊C4C22⋊D511yescharacteristic
213C3×C22⋊C4—21no—
214C3×C42—21no—
215#217—101no—
216#217—204no—
217C4⋊Dic3—51no—
218C4⋊Dic3—51no—
219C4⋊Dic3—102no—
220C4⋊Dic3—101no—
221C4⋊Dic3—101no—
222Dic3⋊C4—102no—
223Dic3⋊C4—102no—
224C4×Dic3—101no—
225C4×Dic3—101no—
226C4×Dic3—101no—
227#208—101no—
228#208—101no—
229C2×C3⋊C8—101no—
230C23×C5—22no—
231C23×C5—42no—
232C23×C5—42no—
233C23×C5—41no—
234C23×C5—41no—
235C23×C5D3×D411yescharacteristic
236C5×D4—22no—
237C5×D4—22no—
238C5×D4—41no—
239C5×D4—41no—
240C2×C4×C5—21no—
241C2×C4×C5—21no—
242C2×C4×C5C2×Dic611yescharacteristic
243C2×C4×C5#23511yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5#23711yescharacteristic
246C2×C4×C5#23711yescharacteristic
247C2×C4×C5C2×#6711yescharacteristic
248C2×Dic5—62no—
249C2×Dic5—61no—
250C2×Dic5—61no—
251C2×Dic5—62no—
252C2×Dic5—121no—
253C2×Dic5—121no—
254C2×Dic5—122no—
255Dic10—242no—
256C5×C8—41no—
257#168—121no—
258C22×D4C2×D1511yescharacteristic
259C2×M16—151no—
260C2×M16C2×D1511yescharacteristic
261C4⋊Q8—301no—
262C4⋊Q8—301no—
263#125—301no—
264#125—301no—
265C22⋊Q8—302no—
266#117—151no—
267#117C2×D1511yescharacteristic
268C2×C4⋊C4—151no—
269C2×C22⋊C4—302no—
270C2×C42—151no—
271#102—21no—
272#102—21no—
273#102—301no—
274#102—301no—
275C2×C3×C5—21no—
276C2×C3×C5—21no—
277C2×C3×C5—82no—
278C2×C3×C5#39311yescharacteristic
279C2×C3×C5#45311yescharacteristic
280C2×C3×C5#45411yescharacteristic
281C23×C3—22no—
282C23×C3—42no—
283C23×C3—42no—
284C23×C3—41no—
285C23×C3—41no—
286C23×C3D4×D511yescharacteristic
287C3×D4—22no—
288C3×D4—22no—
289C3×D4—41no—
290C3×D4—41no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4C2×Dic1011yescharacteristic
294C2×C3×C4#70911yescharacteristic
295C2×C3×C4D4×D511yescharacteristic
296C2×C3×C4#71111yescharacteristic
297C2×C3×C4#71111yescharacteristic
298C2×C3×C4C2×C22⋊D511yescharacteristic
299C2×Dic3—102no—
300C2×Dic3—101no—
301C2×Dic3—101no—
302C2×Dic3—102no—
303C2×Dic3—201no—
304C2×Dic3—201no—
305C2×Dic3—202no—
306Dic6—402no—
307C3×C8—41no—
308C3⋊C8—201no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5—44no—
312C22×C5—42no—
313C22×C5—82no—
314C22×C5—81no—
315C22×C5—81no—
316C22×C5#87811yescharacteristic
317C22×C5#88511yescharacteristic
318C22×C5#93711yescharacteristic
319C4×C5—41no—
320C4×C5—41no—
321C4×C5#87811yescharacteristic
322C4×C5#88511yescharacteristic
323C4×C5#92411yescharacteristic
324C4×C5#93611yescharacteristic
325Dic5—122no—
326Dic5—121no—
327Dic5—122no—
328Dic5—121no—
329C24—21no—
330C2×Q8—302no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4Dic3012yescomplemented
337C22×C4—152no—
338C22×C4—301no—
339C22×C4C22×D1511yescharacteristic
340M16—21no—
341M16—21no—
342M16—301no—
343M16—301no—
344C2×C8—21no—
345C2×C8—301no—
346C4⋊C4—151no—
347C4⋊C4—151no—
348C4⋊C4—302no—
349C4⋊C4—302no—
350C4⋊C4—302no—
351C4⋊C4—301no—
352C4⋊C4—301no—
353C4⋊C4#122011yescharacteristic
354C4⋊C4#122011yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—301no—
357C22⋊C4—604no—
358C42—21no—
359C42—301no—
360C42—301no—
361C42—301no—
362C3×C5#202711yescharacteristic, complemented, Hall
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—44no—
366C22×C3—42no—
367C22×C3—82no—
368C22×C3—81no—
369C22×C3—81no—
370C22×C3#402411yescharacteristic
371C22×C3#403111yescharacteristic
372C22×C3#408311yescharacteristic
373C3×C4—41no—
374C3×C4—41no—
375C3×C4#402411yescharacteristic
376C3×C4#403111yescharacteristic
377C3×C4#407011yescharacteristic
378C3×C4#408211yescharacteristic
379Dic3—202no—
380Dic3—201no—
381Dic3—202no—
382Dic3—201no—
383C2×C5—21no—
384C2×C5—21no—
385C2×C5—82no—
386C2×C5#494711yescharacteristic
387C2×C5#519811yescharacteristic
388C2×C5#520111yescharacteristic
389C23—22no—
390C23—42no—
391C23—42no—
392C23—41no—
393C23—41no—
394C23D4×D1511yescharacteristic
395Q8—1202no—
396D4—22no—
397D4—22no—
398D4—41no—
399D4—41no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—302no—
403C2×C4—301no—
404C2×C4—301no—
405C2×C4—302no—
406C2×C4—601no—
407C2×C4—601no—
408C2×C4—602no—
409C2×C4C2×Dic3011yescharacteristic
410C2×C4#681711yescharacteristic
411C2×C4D4×D1511yescharacteristic
412C2×C4#681911yescharacteristic
413C2×C4#681911yescharacteristic
414C2×C4C2×#122011yescharacteristic
415C8—41no—
416C8—601no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—82no—
420C2×C3#6523611yescharacteristic
421C2×C3#6548711yescharacteristic
422C2×C3#6549011yescharacteristic
423C5#7031311yescharacteristic, complemented, Sylow
424C22—21no—
425C22—21no—
426C22—44no—
427C22—42no—
428C22—82no—
429C22—81no—
430C22—81no—
431C22#9176711yescharacteristic
432C22#9177411yescharacteristic
433C22#9182611yescharacteristic
434C4—41no—
435C4—41no—
436C4—602no—
437C4—602no—
438C4—601no—
439C4—601no—
440C4#9176711yescharacteristic
441C4#9177411yescharacteristic
442C4#9181311yescharacteristic
443C4#9182511yescharacteristic
444C3#1060110611yescharacteristic, complemented, Sylow
445C2—21no—
446C2—21no—
447C2—82no—
448C2#1175104811yescharacteristic
449C2#1175129911yescharacteristic
450C2#1175130211yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#418C2
socleC22×C3×C5#120
prime radicalC22×C3×C5×D4C22
hypercenter#418D15
hypocenterC3×C5#2027
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #11756278C2semidirect
5. #11746376C2semidirect
6. #11746375C2semidirect
7. #11746353C2semidirect
40. C2×C3×C5×D4Q8semidirect
143. C2×C5×D4Dic6semidirect
203. C2×C3×D4Dic10semidirect
336. C2×D4Dic30semidirect
362. C3×C5#2027semidirect
423. C5#70313semidirect
444. C3#10601106semidirect

Maximal subgroups

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

subgroupindex
#117562782
C3×C5×#4182
#117513222
#117513162
#117463762
#117463752
#117463532
#106011063
#703135