Finite Group Databasebeta

← #14417164

Subgroups — #14417164

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
1C3×C5×#520C211yesmaximal, characteristic
2C2×#91840C211yesmaximal, characteristic
3#11756275C211yesmaximal, characteristic, complemented
4#11751334C211yesmaximal, characteristic
5#11751131C212yesmaximal, complemented
6C4×#6718C212yesmaximal, complemented
7#11751119C212yesmaximal, complemented
8C4×#6716C212yesmaximal, complemented
9#11751098C211yesmaximal, characteristic, complemented
10C2×#91094C211yesmaximal, characteristic, complemented
11#11751065C211yesmaximal, characteristic, complemented
12#10614302—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C3×C4×C5×Q8C2212yes—
16C3×C4×C5×D4—22no—
17C3×C4×C5×D4C2212yes—
18C3×C5×#117—21no—
19C3×C5×#117C2211yescharacteristic
20C2×C3×C5×C4⋊C4—21no—
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22#91840C418yescomplemented
23C2×#6718C2212yes—
24C2×#6716C2212yes—
25#91815C2211yescharacteristic
26C2×#6710C2211yescharacteristic
27C22×C3⋊#168C2211yescharacteristic
28#91776—21no—
29#91776—21no—
30#91766—22no—
31C4×Dic30C2212yes—
32C4×Dic30C2212yes—
33#91119C2211yescharacteristic
34#91119C2211yescharacteristic
35#91116C2211yescharacteristic
36#91116C2211yescharacteristic
37#91094C2212yes—
38#91094C2212yes—
39#91092C2212yes—
40#91091C2212yes—
41#91087C2212yes—
42C4×C3⋊#168C2212yes—
43#82571—51nomaximal, Hall
44C5×#520D311yescharacteristic
45C2×#4097—31no—
46#65850—31no—
47#65522—31no—
48#65319—32no—
49C4×#689—32no—
50#65307—32no—
51C4×#687—32no—
52#65286—31no—
53C2×#3942—31no—
54#65253—31no—
55C3×C5×#41—22no—
56C3×C5×#41C2×C414yes—
57C2×C3×C5×Q8C2311yescharacteristic
58C2×C3×C5×D4—21no—
59C2×C3×C5×D4C2311yescharacteristic
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5—22no—
63C22×C3×C4×C5C2311yescharacteristic
64C22×Dic15—21no—
65C2×Dic30—21no—
66C2×Dic30—22no—
67C2×Dic30C2×C414yescomplemented
68C2×Dic30C2312yes—
69C3×C5×C4⋊C4—21no—
70C3×C5×C4⋊C4—22no—
71C3×C5×C4⋊C4D411yescharacteristic
72C3×C5×C4⋊C4D411yescharacteristic
73C3×C5×C4⋊C4C2312yes—
74C3×C5×C22⋊C4—22no—
75C3×C5×C22⋊C4D412yes—
76C3×C42×C5—22no—
77C3×C42×C5C2312yes—
78#6719—21no—
79#6718C2×C418yescomplemented
80#6716C2×C418yescomplemented
81C4⋊Dic15C2311yescharacteristic
82C4⋊Dic15C2311yescharacteristic
83#6712—22no—
84#6712—22no—
85C4×Dic15—22no—
86C4×Dic15—22no—
87C4×Dic15—21no—
88#6710C2×C414yescomplemented
89C2×C3⋊#168—22no—
90C2×C3⋊#168C2311yescharacteristic
91C2×C3⋊#168C2311yescharacteristic
92C2×C3⋊#168C2312yes—
93C3×#520D511yescharacteristic
94C2×#951—51no—
95#5516—51no—
96#5233—51no—
97#5030—52no—
98C4×#216—52no—
99#5018—52no—
100C4×#214—52no—
101#4997—51no—
102C2×#810—51no—
103#4964—51no—
104C2×C5×#41C2×D311yescharacteristic
105C22×Dic10—31no—
106C4×C5×Q8C2×D312yes—
107C4×C5×D4—22no—
108C4×C5×D4C2×D312yes—
109C5×#117—21no—
110C5×#117C2×D311yescharacteristic
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4C2×D311yescharacteristic
113#4097—38no—
114C2×#689—32no—
115C2×#687—32no—
116#4072—31no—
117C2×#681—31no—
118C22×#168—31no—
119#4033—61no—
120#4033—61no—
121#4023—62no—
122C4×Dic10—32no—
123C4×Dic10—32no—
124#3967—31no—
125#3967—31no—
126#3964—31no—
127#3964—31no—
128#3942—32no—
129#3942—32no—
130#3940—32no—
131#3939—32no—
132#3935—32no—
133C4×#168—32no—
134#2947—151noSylow
135C23×C3×C5—21no—
136C23×C3×C5C2×D411yescharacteristic
137C3×C5×Q8—21no—
138C3×C5×Q8C22×C412yes—
139C3×C5×D4—24no—
140C3×C5×D4—21no—
141C3×C5×D4C22×C412yes—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—24no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—82no—
146C2×C3×C4×C5—81no—
147C2×C3×C4×C5C22×C412yes—
148C2×C3×C4×C5C2×D412yes—
149C2×C3×C4×C5C2×D412yes—
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5#4112yes—
152C2×C3×C4×C5C2411yescharacteristic
153C2×Dic15—24no—
154C2×Dic15—22no—
155C2×Dic15—21no—
156C2×Dic15—21no—
157Dic30—24no—
158Dic30—22no—
159Dic30C22×C414yes—
160C3⋊#168—21no—
161C3⋊#168—21no—
162C3⋊#168C22×C414yes—
163C2×C3×#41C2×D511yescharacteristic
164C22×Dic6—51no—
165C3×C4×Q8C2×D512yes—
166C3×C4×D4—22no—
167C3×C4×D4C2×D512yes—
168C3×#117—21no—
169C3×#117C2×D511yescharacteristic
170C2×C3×C4⋊C4—21no—
171C2×C3×C4⋊C4C2×D511yescharacteristic
172#951—58no—
173C2×#216—52no—
174C2×#214—52no—
175#926—51no—
176C2×#208—51no—
177C22×C3⋊C8—51no—
178#887—101no—
179#887—101no—
180#877—102no—
181C4×Dic6—52no—
182C4×Dic6—52no—
183#835—51no—
184#835—51no—
185#832—51no—
186#832—51no—
187#810—52no—
188#810—52no—
189#808—52no—
190#807—52no—
191#803—52no—
192C4×C3⋊C8—52no—
193C5×#41—22no—
194C5×#41C4×D314yes—
195C2×C5×Q8C22×D311yescharacteristic
196C2×C5×D4—21no—
197C2×C5×D4C22×D311yescharacteristic
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—22no—
201C22×C4×C5C22×D311yescharacteristic
202C22×Dic5—61no—
203C2×Dic10—34no—
204C2×Dic10—32no—
205C2×Dic10—62no—
206C2×Dic10—61no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—22no—
209C5×C4⋊C4#6711yescharacteristic
210C5×C4⋊C4#6711yescharacteristic
211C5×C4⋊C4C22×D312yes—
212C5×C22⋊C4—22no—
213C5×C22⋊C4#6712yes—
214C42×C5—22no—
215C42×C5C22×D312yes—
216C22⋊Dic5—61no—
217#689—38no—
218#687—38no—
219C4⋊Dic5—31no—
220C4⋊Dic5—31no—
221#683—62no—
222#683—62no—
223C4×Dic5—62no—
224C4×Dic5—62no—
225C4×Dic5—61no—
226#681—34no—
227C2×#168—32no—
228C2×#168—31no—
229C2×#168—31no—
230C2×#168—62no—
231C2×#137—151no—
232#520D1511yescharacteristic
233#519—151no—
234#441—152no—
235#440—152no—
236C4×Q16—152no—
237C4×SD16—152no—
238#428—151no—
239#416—151no—
240C2×#103—151no—
241#405—151no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5—22no—
245C22×C3×C5—41no—
246C22×C3×C5—41no—
247C22×C3×C5C4×D412yes—
248C22×C3×C5C22×D411yescharacteristic
249C3×C4×C5—22no—
250C3×C4×C5—22no—
251C3×C4×C5—22no—
252C3×C4×C5—42no—
253C3×C4×C5C4×D412yes—
254C3×C4×C5C23×C411yescharacteristic
255C3×C4×C5C2×#4111yescharacteristic
256Dic15—24no—
257Dic15—41no—
258Dic15—41no—
259C3×#41—22no—
260C3×#41C4×D514yes—
261C2×C3×Q8C22×D511yescharacteristic
262C2×C3×D4—21no—
263C2×C3×D4C22×D511yescharacteristic
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—22no—
267C22×C3×C4C22×D511yescharacteristic
268C22×Dic3—101no—
269C2×Dic6—54no—
270C2×Dic6—52no—
271C2×Dic6—102no—
272C2×Dic6—101no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—22no—
275C3×C4⋊C4C22⋊D511yescharacteristic
276C3×C4⋊C4C22⋊D511yescharacteristic
277C3×C4⋊C4C22×D512yes—
278C3×C22⋊C4—22no—
279C3×C22⋊C4C22⋊D512yes—
280C3×C42—22no—
281C3×C42C22×D512yes—
282#217—101no—
283#216—58no—
284#214—58no—
285C4⋊Dic3—51no—
286C4⋊Dic3—51no—
287Dic3⋊C4—102no—
288Dic3⋊C4—102no—
289C4×Dic3—102no—
290C4×Dic3—102no—
291C4×Dic3—101no—
292#208—54no—
293C2×C3⋊C8—52no—
294C2×C3⋊C8—51no—
295C2×C3⋊C8—51no—
296C2×C3⋊C8—102no—
297C23×C5—21no—
298C23×C5C2×#6711yescharacteristic
299C5×Q8—21no—
300C5×Q8C2×C4×D312yes—
301C5×D4—24no—
302C5×D4—21no—
303C5×D4C2×C4×D312yes—
304C2×C4×C5—21no—
305C2×C4×C5—24no—
306C2×C4×C5—22no—
307C2×C4×C5—82no—
308C2×C4×C5—81no—
309C2×C4×C5C2×C4×D312yes—
310C2×C4×C5#23512yes—
311C2×C4×C5C2×#6712yes—
312C2×C4×C5C2×#6712yes—
313C2×C4×C5C2×#6711yescharacteristic
314C2×C4×C5C23×D311yescharacteristic
315C2×Dic5—64no—
316C2×Dic5—62no—
317C2×Dic5—61no—
318C2×Dic5—61no—
319Dic10—34no—
320Dic10—64no—
321Dic10—62no—
322#168—34no—
323#168—61no—
324#168—61no—
325C2×#41C2×D1511yescharacteristic
326C22×Q8—151no—
327#137—158no—
328C2×Q16—152no—
329C2×SD16—152no—
330C2×M16—151no—
331C22×C8—151no—
332C4×Q8—152no—
333C4×Q8—152no—
334C4×Q8—301no—
335C4×Q8—301no—
336C4×Q8C2×D1512yes—
337C4×D4—22no—
338C4×D4C2×D1512yes—
339#117—21no—
340#117—151no—
341#117—302no—
342#117C2×D1511yescharacteristic
343C2×C4⋊C4—21no—
344C2×C4⋊C4C2×D1511yescharacteristic
345#107—152no—
346#106—152no—
347#103—151no—
348#103—151no—
349#103—152no—
350#103—152no—
351#102—151no—
352#102—151no—
353#97—152no—
354C4×C8—152no—
355C2×C3×C5—22no—
356C2×C3×C5—42no—
357C2×C3×C5C2×C4×D411yescharacteristic
358C2×C3×C5#57711yescharacteristic
359C2×C3×C5#57811yescharacteristic
360C23×C3—21no—
361C23×C3C2×C22⋊D511yescharacteristic
362C3×Q8—21no—
363C3×Q8C2×C4×D512yes—
364C3×D4—24no—
365C3×D4—21no—
366C3×D4C2×C4×D512yes—
367C2×C3×C4—21no—
368C2×C3×C4—24no—
369C2×C3×C4—22no—
370C2×C3×C4—82no—
371C2×C3×C4—81no—
372C2×C3×C4C2×C4×D512yes—
373C2×C3×C4#70912yes—
374C2×C3×C4C2×C22⋊D512yes—
375C2×C3×C4C2×C22⋊D512yes—
376C2×C3×C4C2×C22⋊D511yescharacteristic
377C2×C3×C4C23×D511yescharacteristic
378C2×Dic3—102no—
379C2×Dic3—104no—
380C2×Dic3—101no—
381C2×Dic3—101no—
382Dic6—54no—
383Dic6—102no—
384Dic6—104no—
385C3⋊C8—54no—
386C3⋊C8—101no—
387C3⋊C8—101no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5—22no—
391C22×C5—41no—
392C22×C5—41no—
393C22×C5C4×#6712yes—
394C22×C5C22×#6711yescharacteristic
395C4×C5—22no—
396C4×C5—22no—
397C4×C5—22no—
398C4×C5—42no—
399C4×C5C4×#6712yes—
400C4×C5C22×C4×D311yescharacteristic
401C4×C5C2×#23511yescharacteristic
402Dic5—64no—
403Dic5—121no—
404Dic5—121no—
405#41—22no—
406#41C4×D1514yes—
407C2×Q8—154no—
408C2×Q8—152no—
409C2×Q8—302no—
410C2×Q8—301no—
411C2×Q8C22×D1511yescharacteristic
412C2×D4—21no—
413C2×D4C22×D1511yescharacteristic
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—301no—
418C22×C4C22×D1511yescharacteristic
419Q16—158no—
420SD16—158no—
421M16—154no—
422C2×C8—152no—
423C2×C8—151no—
424C2×C8—151no—
425C2×C8—302no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—151no—
429C4⋊C4—151no—
430C4⋊C4—302no—
431C4⋊C4—302no—
432C4⋊C4#122011yescharacteristic
433C4⋊C4#122011yescharacteristic
434C4⋊C4C22×D1512yes—
435C22⋊C4—22no—
436C22⋊C4—301no—
437C22⋊C4#122012yes—
438C42—22no—
439C42—301no—
440C42—302no—
441C42—302no—
442C42C22×D1512yes—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—22no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3C4×C22⋊D512yes—
450C22×C3C22×C22⋊D511yescharacteristic
451C3×C4—22no—
452C3×C4—22no—
453C3×C4—22no—
454C3×C4—42no—
455C3×C4C4×C22⋊D512yes—
456C3×C4C22×C4×D511yescharacteristic
457C3×C4C2×#70911yescharacteristic
458Dic3—104no—
459Dic3—201no—
460Dic3—201no—
461C2×C5—22no—
462C2×C5—42no—
463C2×C5C2×C4×#6711yescharacteristic
464C2×C5#583611yescharacteristic
465C2×C5#583811yescharacteristic
466C23—21no—
467C23C2×#122011yescharacteristic
468Q8—21no—
469Q8—154no—
470Q8—304no—
471Q8—302no—
472Q8C2×C4×D1512yes—
473D4—24no—
474D4—21no—
475D4C2×C4×D1512yes—
476C2×C4—21no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—82no—
480C2×C4—81no—
481C2×C4—304no—
482C2×C4—302no—
483C2×C4—301no—
484C2×C4—301no—
485C2×C4C2×C4×D1512yes—
486C2×C4#681712yes—
487C2×C4C2×#122012yes—
488C2×C4C2×#122012yes—
489C2×C4C2×#122011yescharacteristic
490C2×C4C23×D1511yescharacteristic
491C8—154no—
492C8—301no—
493C8—301no—
494C2×C3—22no—
495C2×C3—42no—
496C2×C3C2×C4×C22⋊D511yescharacteristic
497C2×C3#6617011yescharacteristic
498C2×C3#6617211yescharacteristic
499C5#8257111yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—22no—
503C22—41no—
504C22—41no—
505C22C4×#122012yes—
506C22C22×#122011yescharacteristic
507C4—22no—
508C4—22no—
509C4—22no—
510C4—42no—
511C4—304no—
512C4—601no—
513C4—601no—
514C4C4×#122012yes—
515C4C22×C4×D1511yescharacteristic
516C4C2×#681711yescharacteristic
517C3#1061430211yescharacteristic, complemented, Sylow
518C2—22no—
519C2—42no—
520C2C2×C4×#122011yescharacteristic
521C2#1175659511yescharacteristic
522C2#1175659711yescharacteristic
subgroupG/H
centerC22C22×#1220
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#520C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×C5×#41C22
cosocleC2×C3×C4×C5C24
hypercenter#520D15
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
3. #11756275C2semidirect
5. #11751131C2semidirect
6. C4×#6718C2semidirect
7. #11751119C2semidirect
8. C4×#6716C2semidirect
9. #11751098C2semidirect
10. C2×#91094C2semidirect
11. #11751065C2semidirect
22. #91840C4semidirect
67. C2×Dic30C2×C4semidirect
79. #6718C2×C4semidirect
80. #6716C2×C4semidirect
88. #6710C2×C4semidirect
443. C3×C5#2947semidirect
499. C5#82571semidirect
517. C3#10614302semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5202
C2×#918402
#117562752
#117513342
#117511312
C4×#67182
#117511192
C4×#67162
#117510982
C2×#910942
#117510652
#106143023
#825715