Finite Group Databasebeta

← #14417170

Subgroups — #14417170

Order 1920.

940 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91798C211yesmaximal, characteristic
2#11756275C211yesmaximal, characteristic, complemented
3#11756263C211yesmaximal, characteristic
4C3×C5×#428C211yesmaximal, characteristic, complemented
5#11751223C211yesmaximal, characteristic, complemented
6#11751103C211yesmaximal, characteristic
7C2×#91094C211yesmaximal, characteristic, complemented
8#11750990C212yesmaximal, complemented
9#11750974C212yesmaximal, complemented
10#11750954C212yesmaximal, complemented
11#11750953C212yesmaximal, complemented
12#10610933—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C2×C3×C5×M16C2211yescharacteristic
16C3×C5×#117C2211yescharacteristic
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C4×#1220—22no—
19#91815C2211yescharacteristic
20C22×C3⋊#168C2211yescharacteristic
21#91798C418yescomplemented
22C2×Dic60C2212yes—
23C2×#6706C2212yes—
24#91782C2212yes—
25#91781—21no—
26C4⋊C4×D15—21no—
27#91776C2212yes—
28#91776C2212yes—
29#91776C2212yes—
30#91766—22no—
31C4×Dic30—21no—
32C4×Dic30—21no—
33C3×C5×#107C2212yes—
34C3×C5×#106C2212yes—
35#91099C2212yes—
36C8×Dic15C2212yes—
37#91094C2212yes—
38#91094C2211yescharacteristic
39#91094C2212yes—
40#91094C2211yescharacteristic
41#91093C2211yescharacteristic
42#91093C2211yescharacteristic
43#79202—51nomaximal, Hall
44C2×#4055—31no—
45#65850—31no—
46#65838—31no—
47C5×#428D311yescharacteristic, complemented
48#65411—31no—
49#65291—31no—
50C2×#3942—31no—
51#65178—32no—
52#65162—32no—
53#65142—32no—
54#65141—32no—
55C22×C3×C4×C5—21no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—21no—
58C22×Dic15—21no—
59#6817—22no—
60#6817C2×C414yes—
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×C4×D15—22no—
64C2×Dic30—21no—
65C2×Dic30—22no—
66C2×Dic30C2×C414yescomplemented
67C2×Dic30C2312yes—
68C2×Dic30C2311yescharacteristic
69C3×C5×M16C2×C414yescomplemented
70C2×C3×C5×C8C2312yes—
71C3×C5×C4⋊C4—21no—
72C3×C5×C4⋊C4C2311yescharacteristic
73C3×C5×C4⋊C4C2311yescharacteristic
74C3×C5×C4⋊C4C2312yes—
75C3×C5×C22⋊C4—21no—
76C3×C42×C5—21no—
77#6719D412yes—
78#6714—22no—
79C4⋊Dic15D411yescharacteristic
80C4⋊Dic15D411yescharacteristic
81#6712—22no—
82#6712—22no—
83#6712—22no—
84C4×Dic15—22no—
85C4×Dic15—22no—
86C4×Dic15—22no—
87C4×Dic15C2312yes—
88C2×C3⋊#168—22no—
89C2×C3⋊#168C2311yescharacteristic
90C2×C3⋊#168C2311yescharacteristic
91Dic60C2×C418yescomplemented
92#6706C2×C418yescomplemented
93C2×#909—51no—
94#5516—51no—
95#5504—51no—
96C3×#428D511yescharacteristic, complemented
97#5122—51no—
98#5002—51no—
99C2×#810—51no—
100#4889—52no—
101#4873—52no—
102#4853—52no—
103#4852—52no—
104C2×#709—31no—
105C22×Dic10—31no—
106C2×C5×M16C2×D311yescharacteristic
107C5×#117C2×D311yescharacteristic
108C2×C5×C4⋊C4C2×D311yescharacteristic
109C4×C22⋊D5—62no—
110#4072—31no—
111C22×#168—31no—
112#4055—38no—
113C2×Dic20—32no—
114C2×#677—32no—
115#4039—32no—
116#4038—61no—
117D5×C4⋊C4—61no—
118#4033—32no—
119#4033—32no—
120#4033—32no—
121#4023—62no—
122C4×Dic10—61no—
123C4×Dic10—61no—
124C5×#107C2×D312yes—
125C5×#106C2×D312yes—
126#3947—32no—
127C8×Dic5—32no—
128#3942—31no—
129#3942—31no—
130#3942—32no—
131#3942—32no—
132#3941—31no—
133#3941—31no—
134#2947—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×D15—21no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—81no—
141C2×C3×C4×C5C22×C412yes—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5#4112yes—
144C2×C3×C4×C5C2411yescharacteristic
145#1220—24no—
146C2×Dic15—24no—
147C2×Dic15—22no—
148C2×Dic15—21no—
149C2×Dic15C2×D412yes—
150C2×Dic15C2×D412yes—
151D60—21no—
152D60C22×C412yes—
153C4×D15—24no—
154C4×D15—82no—
155Dic30—24no—
156Dic30—22no—
157Dic30—21no—
158Dic30C22×C414yes—
159Dic30C22×C412yes—
160C3×C5×C8C22×C414yes—
161C3⋊#168—21no—
162C3⋊#168—21no—
163C2×#235—51no—
164C22×Dic6—51no—
165C2×C3×M16C2×D511yescharacteristic
166C3×#117C2×D511yescharacteristic
167C2×C3×C4⋊C4C2×D511yescharacteristic
168C4×#67—102no—
169#926—51no—
170C22×C3⋊C8—51no—
171#909—58no—
172C2×Dic12—52no—
173C2×#204—52no—
174#893—52no—
175#892—101no—
176D3×C4⋊C4—101no—
177#887—52no—
178#887—52no—
179#887—52no—
180#877—102no—
181C4×Dic6—101no—
182C4×Dic6—101no—
183C3×#107C2×D512yes—
184C3×#106C2×D512yes—
185#815—52no—
186C8×Dic3—52no—
187#810—51no—
188#810—52no—
189#810—52no—
190#810—51no—
191#809—51no—
192#809—51no—
193C22×C4×C5—21no—
194C22×C4×C5C22×D311yescharacteristic
195C2×C22⋊D5—61no—
196C22×Dic5—61no—
197#709—34no—
198#709—62no—
199C2×D20—31no—
200C2×C4×D5—61no—
201C2×C4×D5—62no—
202C2×Dic10—34no—
203C2×Dic10—32no—
204C2×Dic10—31no—
205C2×Dic10—61no—
206C2×Dic10—62no—
207C5×M16C4×D314yescomplemented
208C2×C5×C8C22×D312yes—
209C5×C4⋊C4—21no—
210C5×C4⋊C4C22×D312yes—
211C5×C4⋊C4C22×D311yescharacteristic
212C5×C4⋊C4C22×D311yescharacteristic
213C5×C22⋊C4—21no—
214C42×C5—21no—
215C22⋊Dic5—32no—
216#685—62no—
217C4⋊Dic5—31no—
218C4⋊Dic5—31no—
219#683—62no—
220#683—62no—
221#683—62no—
222C4×Dic5—32no—
223C4×Dic5—62no—
224C4×Dic5—62no—
225C4×Dic5—62no—
226C2×#168—31no—
227C2×#168—31no—
228C2×#168—62no—
229Dic20—38no—
230#677—38no—
231C2×#137—151no—
232#520—151no—
233#519—151no—
234#441—152no—
235#440—152no—
236C4×Q16—152no—
237C4×SD16—152no—
238#428D1511yescharacteristic, complemented
239#416—151no—
240C2×#103—151no—
241#405—151no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5C4×D412yes—
245C22×C3×C5C22×D411yescharacteristic
246C2×D15—22no—
247C2×D15—41no—
248C2×D15—41no—
249C3×C4×C5—42no—
250C3×C4×C5—41no—
251C3×C4×C5—41no—
252C3×C4×C5C4×D412yes—
253C3×C4×C5C23×C411yescharacteristic
254C3×C4×C5C2×#4111yescharacteristic
255Dic15—24no—
256Dic15—22no—
257Dic15—22no—
258Dic15—22no—
259C22×C3×C4—21no—
260C22×C3×C4C22×D511yescharacteristic
261C2×#67—101no—
262C22×Dic3—101no—
263#235—54no—
264#235—102no—
265C2×D12—51no—
266C2×C4×D3—101no—
267C2×C4×D3—102no—
268C2×Dic6—54no—
269C2×Dic6—52no—
270C2×Dic6—51no—
271C2×Dic6—101no—
272C2×Dic6—102no—
273C3×M16C4×D514yescomplemented
274C2×C3×C8C22×D512yes—
275C3×C4⋊C4—21no—
276C3×C4⋊C4C22×D511yescharacteristic
277C3×C4⋊C4C22×D511yescharacteristic
278C3×C4⋊C4C22×D512yes—
279C3×C22⋊C4—21no—
280C3×C42—21no—
281#217—52no—
282(C2×D3)⋊C4—102no—
283C4⋊Dic3—51no—
284C4⋊Dic3—51no—
285Dic3⋊C4—102no—
286Dic3⋊C4—102no—
287Dic3⋊C4—102no—
288C4×Dic3—52no—
289C4×Dic3—102no—
290C4×Dic3—102no—
291C4×Dic3—102no—
292C2×C3⋊C8—51no—
293C2×C3⋊C8—51no—
294C2×C3⋊C8—102no—
295Dic12—58no—
296#204—58no—
297C23×C5D3×D411yescharacteristic
298C22×D5—61no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—22no—
302C2×C4×C5—81no—
303C2×C4×C5C2×C4×D312yes—
304C2×C4×C5D3×D411yescharacteristic
305C2×C4×C5#23912yes—
306C2×C4×C5C23×D311yescharacteristic
307C22⋊D5—64no—
308C2×Dic5—32no—
309C2×Dic5—32no—
310C2×Dic5—64no—
311C2×Dic5—62no—
312C2×Dic5—61no—
313D20—32no—
314D20—61no—
315C4×D5—64no—
316C4×D5—242no—
317Dic10—34no—
318Dic10—32no—
319Dic10—64no—
320Dic10—62no—
321Dic10—61no—
322C5×C8C2×C4×D314yes—
323#168—61no—
324#168—61no—
325C2×#41—151no—
326C22×Q8—151no—
327#137—158no—
328C2×Q16—152no—
329C2×SD16—152no—
330C2×M16C2×D1511yescharacteristic
331C22×C8—151no—
332C4×Q8—152no—
333C4×Q8—152no—
334C4×Q8—152no—
335C4×Q8—301no—
336C4×Q8—301no—
337C4×D4—152no—
338C4×D4—302no—
339#117—151no—
340#117—302no—
341#117—301no—
342#117C2×D1511yescharacteristic
343C2×C4⋊C4—301no—
344C2×C4⋊C4C2×D1511yescharacteristic
345#107C2×D1512yes—
346#106C2×D1512yes—
347#103—152no—
348#103—152no—
349#103—151no—
350#103—151no—
351#102—151no—
352#102—151no—
353#97—152no—
354C4×C8—152no—
355C2×C3×C5—22no—
356C2×C3×C5C2×C4×D411yescharacteristic
357C2×C3×C5#57711yescharacteristic
358C2×C3×C5#57811yescharacteristic
359D15—42no—
360C23×C3D4×D511yescharacteristic
361C22×D3—101no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—22no—
365C2×C3×C4—81no—
366C2×C3×C4C2×C4×D512yes—
367C2×C3×C4D4×D511yescharacteristic
368C2×C3×C4#71312yes—
369C2×C3×C4C23×D511yescharacteristic
370#67—104no—
371C2×Dic3—52no—
372C2×Dic3—52no—
373C2×Dic3—102no—
374C2×Dic3—101no—
375C2×Dic3—104no—
376D12—52no—
377D12—101no—
378C4×D3—104no—
379C4×D3—402no—
380Dic6—54no—
381Dic6—52no—
382Dic6—102no—
383Dic6—101no—
384Dic6—104no—
385C3×C8C2×C4×D514yes—
386C3⋊C8—101no—
387C3⋊C8—101no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5#89312yes—
391C22×C5C2×D3×D411yescharacteristic
392C2×D5—62no—
393C2×D5—121no—
394C2×D5—121no—
395C4×C5—42no—
396C4×C5—41no—
397C4×C5—41no—
398C4×C5#89312yes—
399C4×C5C22×C4×D311yescharacteristic
400C4×C5C2×#23911yescharacteristic
401Dic5—64no—
402Dic5—62no—
403Dic5—62no—
404Dic5—62no—
405#41—154no—
406#41—302no—
407C2×Q8—154no—
408C2×Q8—152no—
409C2×Q8—151no—
410C2×Q8—301no—
411C2×Q8—302no—
412C2×D4—151no—
413C2×D4—301no—
414C22×C4—21no—
415C22×C4—302no—
416C22×C4—301no—
417C22×C4—301no—
418C22×C4C22×D1511yescharacteristic
419Q16—158no—
420SD16—158no—
421M16C4×D1514yescomplemented
422C2×C8—151no—
423C2×C8—151no—
424C2×C8—302no—
425C2×C8C22×D1512yes—
426C4⋊C4—21no—
427C4⋊C4—151no—
428C4⋊C4—151no—
429C4⋊C4—302no—
430C4⋊C4—302no—
431C4⋊C4—302no—
432C4⋊C4C22×D1511yescharacteristic
433C4⋊C4C22×D1511yescharacteristic
434C4⋊C4C22×D1512yes—
435C22⋊C4—21no—
436C22⋊C4—152no—
437C22⋊C4—302no—
438C42—21no—
439C42—152no—
440C42—302no—
441C42—302no—
442C42—302no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3#403912yes—
447C22×C3C2×D4×D511yescharacteristic
448C2×D3—102no—
449C2×D3—201no—
450C2×D3—201no—
451C3×C4—42no—
452C3×C4—41no—
453C3×C4—41no—
454C3×C4#403912yes—
455C3×C4C22×C4×D511yescharacteristic
456C3×C4C2×#71311yescharacteristic
457Dic3—104no—
458Dic3—102no—
459Dic3—102no—
460Dic3—102no—
461C2×C5—22no—
462C2×C5C2×#89311yescharacteristic
463C2×C5#577511yescharacteristic
464C2×C5#577911yescharacteristic
465D5—122no—
466C23—301no—
467C23D4×D1511yescharacteristic
468Q8—154no—
469Q8—152no—
470Q8—304no—
471Q8—302no—
472Q8—301no—
473D4—152no—
474D4—304no—
475D4—301no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—81no—
480C2×C4—152no—
481C2×C4—152no—
482C2×C4—304no—
483C2×C4—301no—
484C2×C4—302no—
485C2×C4—304no—
486C2×C4—1202no—
487C2×C4C2×C4×D1512yes—
488C2×C4D4×D1511yescharacteristic
489C2×C4#682112yes—
490C2×C4C23×D1511yescharacteristic
491C8—301no—
492C8—301no—
493C8C2×C4×D1514yes—
494C2×C3—22no—
495C2×C3C2×#403911yescharacteristic
496C2×C3#6610911yescharacteristic
497C2×C3#6611311yescharacteristic
498D3—202no—
499C5#7920211yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—302no—
503C22—601no—
504C22—601no—
505C22#9178212yes—
506C22C2×D4×D1511yescharacteristic
507C4—42no—
508C4—41no—
509C4—41no—
510C4—302no—
511C4—304no—
512C4—302no—
513C4—302no—
514C4#9178212yes—
515C4C22×C4×D1511yescharacteristic
516C4C2×#682111yescharacteristic
517C3#1061093311yescharacteristic, complemented, Sylow
518C2—22no—
519C2—602no—
520C2C2×#9178211yescharacteristic
521C2#1175653411yescharacteristic
522C2#1175653811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#428C2
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
cosocleC2×C3×C4×C5C24
hypercenter#428D15
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #11756275C2semidirect
4. C3×C5×#428C2semidirect
5. #11751223C2semidirect
7. C2×#91094C2semidirect
8. #11750990C2semidirect
9. #11750974C2semidirect
10. #11750954C2semidirect
11. #11750953C2semidirect
21. #91798C4semidirect
47. C5×#428D3semidirect
66. C2×Dic30C2×C4semidirect
69. C3×C5×M16C2×C4semidirect
91. Dic60C2×C4semidirect
92. #6706C2×C4semidirect
96. C3×#428D5semidirect
207. C5×M16C4×D3semidirect
238. #428D15semidirect
273. C3×M16C4×D5semidirect
421. M16C4×D15semidirect
443. C3×C5#2947semidirect
499. C5#79202semidirect
517. C3#10610933semidirect

Maximal subgroups

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

subgroupindex
C2×#917982
#117562752
#117562632
C3×C5×#4282
#117512232
#117511032
C2×#910942
#117509902
#117509742
#117509542
#117509532
#106109333
#792025