Finite Group Databasebeta

← #14417730

Subgroups — #14417730

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#520C211yesmaximal, characteristic, complemented
2C2×#91839C211yesmaximal, characteristic
3#11756282C211yesmaximal, characteristic, complemented
4#11751333C211yesmaximal, characteristic, complemented
5#11751131C212yesmaximal, complemented
6C4×#6717C212yesmaximal, complemented
7C4×#6716C212yesmaximal, complemented
8#11751115C212yesmaximal, complemented
9#11751098C211yesmaximal, characteristic, complemented
10#11751067C211yesmaximal, characteristic, complemented
11C2×#91092C211yesmaximal, characteristic, complemented
12#10614289—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×#6817C2211yescharacteristic
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#91839C418yescomplemented
23C2×#6718C2211yescharacteristic
24C2×#6717C2211yescharacteristic
25C2×#6716C2211yescharacteristic
26C2×#6715C2211yescharacteristic
27C2×C4⋊Dic15C2211yescharacteristic
28C2×#6710C2211yescharacteristic
29C22×C3⋊#168C2211yescharacteristic
30#91781—21no—
31C4⋊C4×D15—21no—
32#91770—22no—
33C4×D60C2212yes—
34C4×Dic30C2212yes—
35#91119C2212yes—
36#91116C2212yes—
37#91094C2212yes—
38#91093C2212yes—
39#91092C2212yes—
40#91092C2212yes—
41#91087C2212yes—
42C4×C3⋊#168C2212yes—
43#82558—51nomaximal, Hall
44C5×#520D311yescharacteristic, complemented
45C2×#4096—31no—
46#65857—31no—
47#65521—31no—
48#65319—32no—
49C4×#688—32no—
50C4×#687—32no—
51#65303—32no—
52#65286—31no—
53#65255—31no—
54C2×#3940—31no—
55C3×C5×#41—22no—
56C3×C5×#41C2×C414yescomplemented
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
64C2×#1220—21no—
65C22×Dic15—21no—
66#6817—22no—
67#6817C2×C414yescomplemented
68C2×D60C2311yescharacteristic
69C2×C4×D15—21no—
70C2×C4×D15—22no—
71C2×Dic30C2311yescharacteristic
72C3×C5×C4⋊C4—21no—
73C3×C5×C4⋊C4—22no—
74C3×C5×C4⋊C4D411yescharacteristic
75C3×C5×C4⋊C4D411yescharacteristic
76C3×C5×C4⋊C4C2312yes—
77C3×C5×C22⋊C4—22no—
78C3×C5×C22⋊C4D412yes—
79C3×C42×C5—22no—
80C3×C42×C5C2312yes—
81#6718C2×C414yescomplemented
82#6717C2×C414yescomplemented
83#6716C2×C414yescomplemented
84#6715C2×C414yescomplemented
85#6714—22no—
86C4⋊Dic15—21no—
87C4⋊Dic15C2312yes—
88#6712—22no—
89C4×Dic15—22no—
90#6710—22no—
91C2×C3⋊#168C2×C414yescomplemented
92C2×C3⋊#168C2312yes—
93C2×C3⋊#168C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95C3×#520D511yescharacteristic, complemented
96C2×#950—51no—
97#5523—51no—
98#5232—51no—
99#5030—52no—
100C4×#215—52no—
101C4×#214—52no—
102#5014—52no—
103#4997—51no—
104#4966—51no—
105C2×#808—51no—
106C2×C5×#41C2×D311yescharacteristic
107C2×#709—31no—
108C4×C5×Q8C2×D312yes—
109C4×C5×D4—22no—
110C4×C5×D4C2×D312yes—
111C5×#117—21no—
112C5×#117C2×D311yescharacteristic
113C2×C5×C4⋊C4—21no—
114C2×C5×C4⋊C4C2×D311yescharacteristic
115#4096—38no—
116C2×#689—31no—
117C2×#688—31no—
118C2×#687—31no—
119C2×#686—31no—
120C2×C4⋊Dic5—31no—
121C2×#681—31no—
122C22×#168—31no—
123#4038—61no—
124D5×C4⋊C4—61no—
125#4027—62no—
126C4×D20—32no—
127C4×Dic10—32no—
128#3967—32no—
129#3964—32no—
130#3942—32no—
131#3941—32no—
132#3940—32no—
133#3940—32no—
134#3935—32no—
135C4×#168—32no—
136#2952—151noSylow
137C23×C3×C5—21no—
138C23×C3×C5C2×D411yescharacteristic
139C22×D15—21no—
140C3×C5×Q8—21no—
141C3×C5×Q8C22×C412yes—
142C3×C5×D4—24no—
143C3×C5×D4—21no—
144C3×C5×D4C22×C412yes—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—24no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—82no—
149C2×C3×C4×C5—81no—
150C2×C3×C4×C5C22×C412yes—
151C2×C3×C4×C5C2×D412yes—
152C2×C3×C4×C5C2×D412yes—
153C2×C3×C4×C5C2×D411yescharacteristic
154C2×C3×C4×C5#4112yes—
155C2×C3×C4×C5C2411yescharacteristic
156#1220—24no—
157C2×Dic15—21no—
158C2×Dic15—22no—
159C2×Dic15—81no—
160D60—21no—
161D60C22×C412yes—
162C4×D15—24no—
163C4×D15—82no—
164Dic30—21no—
165Dic30C22×C412yes—
166C3⋊#168—22no—
167C3⋊#168C22×C412yes—
168C3⋊#168C22×C412yes—
169C2×C3×#41C2×D511yescharacteristic
170C2×#235—51no—
171C3×C4×Q8C2×D512yes—
172C3×C4×D4—22no—
173C3×C4×D4C2×D512yes—
174C3×#117—21no—
175C3×#117C2×D511yescharacteristic
176C2×C3×C4⋊C4—21no—
177C2×C3×C4⋊C4C2×D511yescharacteristic
178#950—58no—
179C2×#216—51no—
180C2×#215—51no—
181C2×#214—51no—
182C2×#213—51no—
183C2×C4⋊Dic3—51no—
184C2×#208—51no—
185C22×C3⋊C8—51no—
186#892—101no—
187D3×C4⋊C4—101no—
188#67⋊C4—102no—
189C4×D12—52no—
190C4×Dic6—52no—
191#835—52no—
192#832—52no—
193#810—52no—
194#809—52no—
195#808—52no—
196#808—52no—
197#803—52no—
198C4×C3⋊C8—52no—
199C5×#41—22no—
200C5×#41C4×D314yescomplemented
201C2×C5×Q8C22×D311yescharacteristic
202C2×C5×D4—21no—
203C2×C5×D4C22×D311yescharacteristic
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—22no—
207C22×C4×C5C22×D311yescharacteristic
208C2×C22⋊D5—61no—
209C22×Dic5—61no—
210#709—34no—
211#709—62no—
212C2×D20—31no—
213C2×C4×D5—61no—
214C2×C4×D5—62no—
215C2×Dic10—31no—
216C5×C4⋊C4—21no—
217C5×C4⋊C4—22no—
218C5×C4⋊C4#6711yescharacteristic
219C5×C4⋊C4#6711yescharacteristic
220C5×C4⋊C4C22×D312yes—
221C5×C22⋊C4—22no—
222C5×C22⋊C4#6712yes—
223C42×C5—22no—
224C42×C5C22×D312yes—
225#689—34no—
226#688—34no—
227#687—34no—
228#686—34no—
229#685—62no—
230C4⋊Dic5—32no—
231C4⋊Dic5—61no—
232#683—62no—
233C4×Dic5—62no—
234#681—62no—
235C2×#168—34no—
236C2×#168—31no—
237C2×#168—31no—
238C2×#168—32no—
239C2×#135—151no—
240#520—151no—
241#520D1511yescharacteristic, complemented
242#442—152no—
243#441—152no—
244C4×SD16—152no—
245C4×SD16—152no—
246C2×#106—151no—
247#417—151no—
248#417—151no—
249#405—151no—
250C22×C3×C5—21no—
251C22×C3×C5—21no—
252C22×C3×C5—22no—
253C22×C3×C5—41no—
254C22×C3×C5—41no—
255C22×C3×C5C4×D412yes—
256C22×C3×C5C22×D411yescharacteristic
257C2×D15—22no—
258C2×D15—41no—
259C2×D15—41no—
260C3×C4×C5—22no—
261C3×C4×C5—22no—
262C3×C4×C5—22no—
263C3×C4×C5—42no—
264C3×C4×C5C4×D412yes—
265C3×C4×C5C23×C411yescharacteristic
266C3×C4×C5C2×#4111yescharacteristic
267Dic15—22no—
268Dic15—42no—
269C3×#41—22no—
270C3×#41C4×D514yescomplemented
271C2×C3×Q8C22×D511yescharacteristic
272C2×C3×D4—21no—
273C2×C3×D4C22×D511yescharacteristic
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—22no—
277C22×C3×C4C22×D511yescharacteristic
278C2×#67—101no—
279C22×Dic3—101no—
280#235—54no—
281#235—102no—
282C2×D12—51no—
283C2×C4×D3—101no—
284C2×C4×D3—102no—
285C2×Dic6—51no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—22no—
288C3×C4⋊C4C22⋊D511yescharacteristic
289C3×C4⋊C4C22⋊D511yescharacteristic
290C3×C4⋊C4C22×D512yes—
291C3×C22⋊C4—22no—
292C3×C22⋊C4C22⋊D512yes—
293C3×C42—22no—
294C3×C42C22×D512yes—
295#216—54no—
296#215—54no—
297#214—54no—
298#213—54no—
299(C2×D3)⋊C4—102no—
300C4⋊Dic3—52no—
301C4⋊Dic3—101no—
302Dic3⋊C4—102no—
303C4×Dic3—102no—
304#208—102no—
305C2×C3⋊C8—54no—
306C2×C3⋊C8—51no—
307C2×C3⋊C8—51no—
308C2×C3⋊C8—52no—
309C23×C5—21no—
310C23×C5C2×#6711yescharacteristic
311C22×D5—61no—
312C5×Q8—21no—
313C5×Q8C2×C4×D312yes—
314C5×D4—24no—
315C5×D4—21no—
316C5×D4C2×C4×D312yes—
317C2×C4×C5—21no—
318C2×C4×C5—24no—
319C2×C4×C5—22no—
320C2×C4×C5—82no—
321C2×C4×C5—81no—
322C2×C4×C5C2×C4×D312yes—
323C2×C4×C5#23512yes—
324C2×C4×C5C2×#6712yes—
325C2×C4×C5C2×#6712yes—
326C2×C4×C5C2×#6711yescharacteristic
327C2×C4×C5C23×D311yescharacteristic
328C22⋊D5—64no—
329C2×Dic5—61no—
330C2×Dic5—62no—
331C2×Dic5—241no—
332D20—32no—
333D20—61no—
334C4×D5—64no—
335C4×D5—242no—
336Dic10—32no—
337Dic10—61no—
338#168—32no—
339#168—32no—
340#168—62no—
341C2×#41—151no—
342C2×#41C2×D1511yescharacteristic
343#135—158no—
344C2×Q16—151no—
345C2×SD16—151no—
346C2×SD16—151no—
347C2×D8—151no—
348C2×M16—151no—
349C22×C8—151no—
350C4×Q8—152no—
351C4×Q8C2×D1512yes—
352C4×D4—22no—
353C4×D4—152no—
354C4×D4—302no—
355C4×D4C2×D1512yes—
356#117—21no—
357#117—301no—
358#117C2×D1511yescharacteristic
359C2×C4⋊C4—21no—
360C2×C4⋊C4—151no—
361C2×C4⋊C4—301no—
362C2×C4⋊C4C2×D1511yescharacteristic
363#106—152no—
364#106—152no—
365#103—152no—
366#103—152no—
367#102—152no—
368#102—152no—
369#97—152no—
370C4×C8—152no—
371C2×C3×C5—22no—
372C2×C3×C5—42no—
373C2×C3×C5C2×C4×D411yescharacteristic
374C2×C3×C5#57711yescharacteristic
375C2×C3×C5#57711yescharacteristic
376D15—42no—
377C23×C3—21no—
378C23×C3C2×C22⋊D511yescharacteristic
379C22×D3—101no—
380C3×Q8—21no—
381C3×Q8C2×C4×D512yes—
382C3×D4—24no—
383C3×D4—21no—
384C3×D4C2×C4×D512yes—
385C2×C3×C4—21no—
386C2×C3×C4—24no—
387C2×C3×C4—22no—
388C2×C3×C4—82no—
389C2×C3×C4—81no—
390C2×C3×C4C2×C4×D512yes—
391C2×C3×C4#70912yes—
392C2×C3×C4C2×C22⋊D512yes—
393C2×C3×C4C2×C22⋊D512yes—
394C2×C3×C4C2×C22⋊D511yescharacteristic
395C2×C3×C4C23×D511yescharacteristic
396#67—104no—
397C2×Dic3—101no—
398C2×Dic3—102no—
399C2×Dic3—401no—
400D12—52no—
401D12—101no—
402C4×D3—104no—
403C4×D3—402no—
404Dic6—52no—
405Dic6—101no—
406C3⋊C8—52no—
407C3⋊C8—52no—
408C3⋊C8—102no—
409C22×C5—21no—
410C22×C5—21no—
411C22×C5—22no—
412C22×C5—41no—
413C22×C5—41no—
414C22×C5C4×#6712yes—
415C22×C5C22×#6711yescharacteristic
416C2×D5—62no—
417C2×D5—121no—
418C2×D5—121no—
419C4×C5—22no—
420C4×C5—22no—
421C4×C5—22no—
422C4×C5—42no—
423C4×C5C4×#6712yes—
424C4×C5C22×C4×D311yescharacteristic
425C4×C5C2×#23511yescharacteristic
426Dic5—62no—
427Dic5—122no—
428#41—22no—
429#41—154no—
430#41—302no—
431#41C4×D1514yescomplemented
432C2×Q8—151no—
433C2×Q8C22×D1511yescharacteristic
434C2×D4—21no—
435C2×D4—151no—
436C2×D4—301no—
437C2×D4C22×D1511yescharacteristic
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—301no—
442C22×C4—301no—
443C22×C4—302no—
444C22×C4C22×D1511yescharacteristic
445Q16—154no—
446SD16—154no—
447SD16—154no—
448D8—154no—
449M16—302no—
450C2×C8—154no—
451C2×C8—151no—
452C2×C8—151no—
453C2×C8—152no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—152no—
457C4⋊C4—301no—
458C4⋊C4—302no—
459C4⋊C4#122011yescharacteristic
460C4⋊C4#122011yescharacteristic
461C4⋊C4C22×D1512yes—
462C22⋊C4—22no—
463C22⋊C4—302no—
464C22⋊C4#122012yes—
465C42—22no—
466C42—302no—
467C42C22×D1512yes—
468C3×C5#295211yescharacteristic, complemented, Hall
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—22no—
472C22×C3—41no—
473C22×C3—41no—
474C22×C3C4×C22⋊D512yes—
475C22×C3C22×C22⋊D511yescharacteristic
476C2×D3—102no—
477C2×D3—201no—
478C2×D3—201no—
479C3×C4—22no—
480C3×C4—22no—
481C3×C4—22no—
482C3×C4—42no—
483C3×C4C4×C22⋊D512yes—
484C3×C4C22×C4×D511yescharacteristic
485C3×C4C2×#70911yescharacteristic
486Dic3—102no—
487Dic3—202no—
488C2×C5—22no—
489C2×C5—42no—
490C2×C5C2×C4×#6711yescharacteristic
491C2×C5#583611yescharacteristic
492C2×C5#583711yescharacteristic
493D5—122no—
494C23—21no—
495C23—301no—
496C23C2×#122011yescharacteristic
497Q8—21no—
498Q8—152no—
499Q8—301no—
500Q8C2×C4×D1512yes—
501D4—24no—
502D4—21no—
503D4—152no—
504D4—304no—
505D4—301no—
506D4C2×C4×D1512yes—
507C2×C4—21no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—82no—
511C2×C4—81no—
512C2×C4—301no—
513C2×C4—304no—
514C2×C4—302no—
515C2×C4—1202no—
516C2×C4—1201no—
517C2×C4C2×C4×D1512yes—
518C2×C4#681712yes—
519C2×C4C2×#122012yes—
520C2×C4C2×#122012yes—
521C2×C4C2×#122011yescharacteristic
522C2×C4C23×D1511yescharacteristic
523C8—152no—
524C8—152no—
525C8—302no—
526C2×C3—22no—
527C2×C3—42no—
528C2×C3C2×C4×C22⋊D511yescharacteristic
529C2×C3#6617011yescharacteristic
530C2×C3#6617111yescharacteristic
531D3—202no—
532C5#8255811yescharacteristic, complemented, Sylow
533C22—21no—
534C22—21no—
535C22—22no—
536C22—41no—
537C22—41no—
538C22—302no—
539C22—601no—
540C22—601no—
541C22C4×#122012yes—
542C22C22×#122011yescharacteristic
543C4—22no—
544C4—22no—
545C4—22no—
546C4—42no—
547C4—302no—
548C4—602no—
549C4C4×#122012yes—
550C4C22×C4×D1511yescharacteristic
551C4C2×#681711yescharacteristic
552C3#1061428911yescharacteristic, complemented, Sylow
553C2—22no—
554C2—42no—
555C2—602no—
556C2C2×C4×#122011yescharacteristic
557C2#1175659511yescharacteristic
558C2#1175659611yescharacteristic
subgroupG/H
centerC22C22×#1220
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#520C2
socleC22×C3×C5C22×D4
prime radicalC2×#91839C2
cosocleC2×C3×C4×C5C24
hypercenter#520D15
hypocenterC3×C5#2952
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
1. C3×C5×#520C2semidirect
3. #11756282C2semidirect
4. #11751333C2semidirect
5. #11751131C2semidirect
6. C4×#6717C2semidirect
7. C4×#6716C2semidirect
8. #11751115C2semidirect
9. #11751098C2semidirect
10. #11751067C2semidirect
11. C2×#91092C2semidirect
22. #91839C4semidirect
44. C5×#520D3semidirect
56. C3×C5×#41C2×C4semidirect
67. #6817C2×C4semidirect
81. #6718C2×C4semidirect
82. #6717C2×C4semidirect
83. #6716C2×C4semidirect
84. #6715C2×C4semidirect
91. C2×C3⋊#168C2×C4semidirect
95. C3×#520D5semidirect
200. C5×#41C4×D3semidirect
241. #520D15semidirect
270. C3×#41C4×D5semidirect
431. #41C4×D15semidirect
468. C3×C5#2952semidirect
532. C5#82558semidirect
552. C3#10614289semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5202
C2×#918392
#117562822
#117513332
#117511312
C4×#67172
C4×#67162
#117511152
#117510982
#117510672
C2×#910922
#106142893
#825585