Finite Group Databasebeta

← #14417791

Subgroups — #14417791

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
1#11756282C211yesmaximal, characteristic, complemented
2C5×#5523C211yesmaximal, characteristic, complemented
3C2×#91303C211yesmaximal, characteristic
4C3×#65286C211yesmaximal, characteristic, complemented
5C2×#90985C211yesmaximal, characteristic, complemented
6#11748394C211yesmaximal, characteristic, complemented
7#11748390C211yesmaximal, characteristic, complemented
8#11747093C212yesmaximal, complemented
9C4×#6660C212yesmaximal, complemented
10C4×#6659C212yesmaximal, complemented
11#11747025C212yesmaximal, complemented
12#10614289—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17#91781—21no—
18C4⋊C4×D15—21no—
19#91770—22no—
20C4×D60C2212yes—
21C4×Dic30C2212yes—
22C2×C5×C4⋊Dic3C2211yescharacteristic
23C5×#892—21no—
24C5×D3×C4⋊C4—21no—
25C5×#67⋊C4—22no—
26C4×C5×D12C2212yes—
27C4×C5×Dic6C2212yes—
28C2×C3×#681C2211yescharacteristic
29C22×C3×#168C2211yescharacteristic
30C2×#6663C2211yescharacteristic
31C2×#6660C2211yescharacteristic
32C2×#6659C2211yescharacteristic
33#91303C418yescomplemented
34C2×#6654C2211yescharacteristic
35C3×#3935C2212yes—
36C3×C4×#168C2212yes—
37#90985C2212yes—
38#90985C2212yes—
39#90975C2212yes—
40#90973C2212yes—
41#90969C2212yes—
42#90967C2212yes—
43#78574—51nomaximal, Hall
44C5×#520—31no—
45C2×#4096—31no—
46#65857—31no—
47#65521—31no—
48#65319—32no—
49C4×#688—32no—
50C4×#687—32no—
51#65303—32no—
52#65286D311yescharacteristic, complemented
53#65255—31no—
54C2×#3940—31no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220—21no—
57C22×Dic15—21no—
58#6817—22no—
59#6817C2×C414yescomplemented
60C2×D60C2311yescharacteristic
61C2×C4×D15—21no—
62C2×C4×D15—22no—
63C2×Dic30C2311yescharacteristic
64C2×C5×#67—21no—
65C22×C5×Dic3—21no—
66C5×#235—22no—
67C5×#235C2×C414yescomplemented
68C2×C5×D12C2311yescharacteristic
69C2×C4×C5×D3—21no—
70C2×C4×C5×D3—22no—
71C2×C5×Dic6C2311yescharacteristic
72C3×C5×C4⋊C4D411yescharacteristic
73C3×C5×C4⋊C4D411yescharacteristic
74C3×C5×C22⋊C4D412yes—
75C3×C42×C5C2312yes—
76#6714—22no—
77C4⋊Dic15—21no—
78C4⋊Dic15C2312yes—
79#6712—22no—
80C4×Dic15—22no—
81C5×(C2×D3)⋊C4—22no—
82C5×C4⋊Dic3—21no—
83C5×C4⋊Dic3C2312yes—
84C5×Dic3⋊C4—22no—
85C4×C5×Dic3—22no—
86C3×#681—22no—
87C2×C3×#168C2×C414yescomplemented
88C2×C3×#168C2312yes—
89C2×C3×#168C2311yescharacteristic
90C2×C3×#168C2311yescharacteristic
91#6663C2×C414yescomplemented
92#6660C2×C414yescomplemented
93#6659C2×C414yescomplemented
94#6654C2×C414yescomplemented
95C2×#904—51no—
96#5523—51no—
97#5523D511yescharacteristic, complemented
98C3×#405—51no—
99#5133—51no—
100#5133—51no—
101C2×#817—51no—
102#4716—52no—
103#4711—52no—
104C4×#204—52no—
105C4×#204—52no—
106C2×C5×#41—31no—
107C2×#709—31no—
108C4×C5×Q8—32no—
109C4×C5×D4—32no—
110C4×C5×D4—62no—
111C5×#117—61no—
112C5×#117C2×D311yescharacteristic
113C2×C5×C4⋊C4—31no—
114C2×C5×C4⋊C4—61no—
115#4096—38no—
116C2×#689—31no—
117C2×#688—31no—
118C2×#687—31no—
119C2×#686—31no—
120C2×C4⋊Dic5—31no—
121C2×#681C2×D311yescharacteristic
122C22×#168C2×D311yescharacteristic
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#3935C2×D312yes—
135C4×#168C2×D312yes—
136#2952—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×D15—21no—
139C22×C5×D3—21no—
140C2×C3×C4×C5C22×C412yes—
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2×D412yes—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5#4112yes—
145C2×C3×C4×C5C2411yescharacteristic
146#1220—24no—
147C2×Dic15—21no—
148C2×Dic15—22no—
149C2×Dic15—81no—
150D60—21no—
151D60C22×C412yes—
152C4×D15—24no—
153C4×D15—82no—
154Dic30—21no—
155Dic30C22×C412yes—
156C5×#67—24no—
157C2×C5×Dic3—21no—
158C2×C5×Dic3—22no—
159C2×C5×Dic3—81no—
160C5×D12—21no—
161C5×D12C22×C412yes—
162C4×C5×D3—24no—
163C4×C5×D3—82no—
164C5×Dic6—21no—
165C5×Dic6C22×C412yes—
166C3×#168—22no—
167C3×#168C22×C412yes—
168C3×#168C22×C412yes—
169C2×#235—51no—
170C2×#235C2×D511yescharacteristic
171C2×C3×M16—51no—
172C22×C3×C8—51no—
173C3×#117C2×D511yescharacteristic
174C2×C4⋊Dic3—51no—
175C2×C4⋊Dic3C2×D511yescharacteristic
176C2×Dic12—51no—
177#904—58no—
178C2×D24—51no—
179C2×#204—51no—
180C2×#204—51no—
181#892—21no—
182#892—101no—
183D3×C4⋊C4—21no—
184D3×C4⋊C4—101no—
185#67⋊C4—22no—
186#67⋊C4—102no—
187C4×D12—52no—
188C4×D12C2×D512yes—
189C4×Dic6—52no—
190C4×Dic6C2×D512yes—
191C3×#97—52no—
192C3×C4×C8—52no—
193#821—52no—
194#821—52no—
195#817—52no—
196#817—52no—
197#816—52no—
198#816—52no—
199C5×#41—34no—
200C5×#41—62no—
201C2×C5×Q8—31no—
202C2×C5×D4—31no—
203C2×C5×D4—61no—
204C22×C4×C5—61no—
205C22×C4×C5—61no—
206C22×C4×C5—62no—
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—32no—
217C5×C4⋊C4—61no—
218C5×C4⋊C4—62no—
219C5×C4⋊C4D1211yescharacteristic
220C5×C4⋊C4D1211yescharacteristic
221C5×C22⋊C4—62no—
222C5×C22⋊C4D1212yes—
223C42×C5—62no—
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—22no—
235C2×#168C4×D314yescomplemented
236C2×#168C22×D312yes—
237C2×#168C22×D311yescharacteristic
238C2×#168C22×D311yescharacteristic
239C2×#135—151no—
240#520—31no—
241#520—151no—
242#442—152no—
243#441—152no—
244C4×SD16—152no—
245C4×SD16—152no—
246C2×#106—151no—
247#417—151no—
248#417—151no—
249#405—51no—
250C22×C3×C5—21no—
251C22×C3×C5—21no—
252C22×C3×C5C4×D412yes—
253C22×C3×C5C22×D411yescharacteristic
254C2×D15—22no—
255C2×D15—41no—
256C2×D15—41no—
257C2×C5×D3—22no—
258C2×C5×D3—41no—
259C2×C5×D3—41no—
260C3×C4×C5—22no—
261C3×C4×C5—22no—
262C3×C4×C5C4×D412yes—
263C3×C4×C5C23×C411yescharacteristic
264C3×C4×C5C2×#4111yescharacteristic
265Dic15—22no—
266Dic15—42no—
267C5×Dic3—22no—
268C5×Dic3—42no—
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—21no—
271C2×#67—101no—
272C22×Dic3—21no—
273C22×Dic3—101no—
274#235—22no—
275#235—54no—
276#235—102no—
277#235C4×D514yescomplemented
278C2×D12—51no—
279C2×D12C22×D511yescharacteristic
280C2×C4×D3—21no—
281C2×C4×D3—22no—
282C2×C4×D3—101no—
283C2×C4×D3—102no—
284C2×Dic6—51no—
285C2×Dic6C22×D511yescharacteristic
286C3×M16—102no—
287C2×C3×C8—54no—
288C2×C3×C8—51no—
289C2×C3×C8—51no—
290C2×C3×C8—52no—
291C3×C4⋊C4C22⋊D511yescharacteristic
292C3×C4⋊C4C22⋊D511yescharacteristic
293C3×C22⋊C4C22⋊D512yes—
294C3×C42C22×D512yes—
295(C2×D3)⋊C4—22no—
296(C2×D3)⋊C4—102no—
297C4⋊Dic3—21no—
298C4⋊Dic3—52no—
299C4⋊Dic3—101no—
300C4⋊Dic3C22×D512yes—
301Dic3⋊C4—22no—
302Dic3⋊C4—102no—
303C4×Dic3—22no—
304C4×Dic3—102no—
305Dic12—54no—
306D24—54no—
307#204—54no—
308#204—54no—
309C23×C5—61no—
310C23×C5C2×D1211yescharacteristic
311C22×D5—61no—
312C5×Q8—32no—
313C5×Q8—61no—
314C5×D4—32no—
315C5×D4—64no—
316C5×D4—61no—
317C2×C4×C5—61no—
318C2×C4×C5—64no—
319C2×C4×C5—62no—
320C2×C4×C5—242no—
321C2×C4×C5—241no—
322C2×C4×C5C2×C4×D312yes—
323C2×C4×C5C2×D1212yes—
324C2×C4×C5C2×D1212yes—
325C2×C4×C5C2×D1211yescharacteristic
326C2×C4×C5#23512yes—
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—22no—
339#168C2×C4×D312yes—
340#168C2×C4×D312yes—
341C2×#41—31no—
342C2×#41—151no—
343#135—158no—
344C2×Q16—151no—
345C2×SD16—151no—
346C2×SD16—151no—
347C2×D8—151no—
348C2×M16—51no—
349C22×C8—51no—
350C4×Q8—32no—
351C4×Q8—152no—
352C4×D4—32no—
353C4×D4—62no—
354C4×D4—152no—
355C4×D4—302no—
356#117—61no—
357#117—301no—
358#117D3×D511yescharacteristic
359C2×C4⋊C4—31no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—151no—
362C2×C4⋊C4—301no—
363#106—152no—
364#106—152no—
365#103—152no—
366#103—152no—
367#102—152no—
368#102—152no—
369#97—52no—
370C4×C8—52no—
371C2×C3×C5—22no—
372C2×C3×C5C2×C4×D411yescharacteristic
373C2×C3×C5#57711yescharacteristic
374C2×C3×C5#57711yescharacteristic
375D15—42no—
376C5×D3—42no—
377C23×C3C2×C22⋊D511yescharacteristic
378C22×D3—21no—
379C22×D3—101no—
380C2×C3×C4C2×C4×D512yes—
381C2×C3×C4#70912yes—
382C2×C3×C4C2×C22⋊D512yes—
383C2×C3×C4C2×C22⋊D512yes—
384C2×C3×C4C2×C22⋊D511yescharacteristic
385C2×C3×C4C23×D511yescharacteristic
386#67—24no—
387#67—104no—
388C2×Dic3—21no—
389C2×Dic3—22no—
390C2×Dic3—81no—
391C2×Dic3—101no—
392C2×Dic3—102no—
393C2×Dic3—401no—
394D12—21no—
395D12—52no—
396D12—101no—
397D12C2×C4×D512yes—
398C4×D3—24no—
399C4×D3—82no—
400C4×D3—104no—
401C4×D3—402no—
402Dic6—21no—
403Dic6—52no—
404Dic6—101no—
405Dic6C2×C4×D512yes—
406C3×C8—52no—
407C3×C8—52no—
408C3×C8—102no—
409C22×C5—21no—
410C22×C5—21no—
411C22×C5—62no—
412C22×C5—121no—
413C22×C5—121no—
414C22×C5C4×D1212yes—
415C22×C5C22×D1211yescharacteristic
416C2×D5—62no—
417C2×D5—121no—
418C2×D5—121no—
419C4×C5—22no—
420C4×C5—22no—
421C4×C5—62no—
422C4×C5—122no—
423C4×C5C4×D1212yes—
424C4×C5C22×C4×D311yescharacteristic
425C4×C5C2×#23511yescharacteristic
426Dic5—62no—
427Dic5—122no—
428#41—34no—
429#41—62no—
430#41—154no—
431#41—302no—
432C2×Q8—31no—
433C2×Q8—151no—
434C2×D4—31no—
435C2×D4—61no—
436C2×D4—151no—
437C2×D4—301no—
438C22×C4—61no—
439C22×C4—61no—
440C22×C4—62no—
441C22×C4—301no—
442C22×C4—301no—
443C22×C4—302no—
444C22×C4C2×D3×D511yescharacteristic
445Q16—154no—
446SD16—154no—
447SD16—154no—
448D8—154no—
449M16—102no—
450C2×C8—54no—
451C2×C8—51no—
452C2×C8—51no—
453C2×C8—52no—
454C4⋊C4—32no—
455C4⋊C4—61no—
456C4⋊C4—62no—
457C4⋊C4—152no—
458C4⋊C4—301no—
459C4⋊C4—302no—
460C4⋊C4#120311yescharacteristic
461C4⋊C4#120311yescharacteristic
462C22⋊C4—62no—
463C22⋊C4—302no—
464C22⋊C4#120312yes—
465C42—62no—
466C42—302no—
467C42C2×D3×D512yes—
468C3×C5#295211yescharacteristic, complemented, Hall
469C22×C3—21no—
470C22×C3—21no—
471C22×C3C4×C22⋊D512yes—
472C22×C3C22×C22⋊D511yescharacteristic
473C2×D3—22no—
474C2×D3—41no—
475C2×D3—41no—
476C2×D3—102no—
477C2×D3—201no—
478C2×D3—201no—
479C3×C4—22no—
480C3×C4—22no—
481C3×C4C4×C22⋊D512yes—
482C3×C4C22×C4×D511yescharacteristic
483C3×C4C2×#70911yescharacteristic
484Dic3—22no—
485Dic3—42no—
486Dic3—102no—
487Dic3—202no—
488C2×C5—22no—
489C2×C5—122no—
490C2×C5C2×C4×D1211yescharacteristic
491C2×C5#575111yescharacteristic
492C2×C5#575111yescharacteristic
493D5—122no—
494C23—61no—
495C23—301no—
496C23C2×#120311yescharacteristic
497Q8—32no—
498Q8—61no—
499Q8—152no—
500Q8—301no—
501D4—32no—
502D4—64no—
503D4—61no—
504D4—152no—
505D4—304no—
506D4—301no—
507C2×C4—61no—
508C2×C4—64no—
509C2×C4—62no—
510C2×C4—242no—
511C2×C4—241no—
512C2×C4—301no—
513C2×C4—304no—
514C2×C4—302no—
515C2×C4—1202no—
516C2×C4—1201no—
517C2×C4#677112yes—
518C2×C4C4×D3×D512yes—
519C2×C4C2×#120312yes—
520C2×C4C2×#120312yes—
521C2×C4C2×#120311yescharacteristic
522C2×C4C22×D3×D511yescharacteristic
523C8—52no—
524C8—52no—
525C8—102no—
526C2×C3—22no—
527C2×C3C2×C4×C22⋊D511yescharacteristic
528C2×C3#6617011yescharacteristic
529C2×C3#6617111yescharacteristic
530D3—42no—
531D3—202no—
532C5#7857411yescharacteristic, complemented, Sylow
533C22—21no—
534C22—21no—
535C22—62no—
536C22—121no—
537C22—121no—
538C22—302no—
539C22—601no—
540C22—601no—
541C22C4×#120312yes—
542C22C22×#120311yescharacteristic
543C4—22no—
544C4—22no—
545C4—62no—
546C4—122no—
547C4—302no—
548C4—602no—
549C4C4×#120312yes—
550C4C2×#677111yescharacteristic
551C4C2×C4×D3×D511yescharacteristic
552C3#1061428911yescharacteristic, complemented, Sylow
553C2—22no—
554C2—122no—
555C2—602no—
556C2C2×C4×#120311yescharacteristic
557C2#1175530711yescharacteristic
558C2#1175530811yescharacteristic
subgroupG/H
centerC22C22×#1203
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×#91303C2
cosocleC2×C3×C4×C5C24
hypercenter#117D3×D5
hypocenterC3×C5#2952
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #11756282C2semidirect
2. C5×#5523C2semidirect
4. C3×#65286C2semidirect
5. C2×#90985C2semidirect
6. #11748394C2semidirect
7. #11748390C2semidirect
8. #11747093C2semidirect
9. C4×#6660C2semidirect
10. C4×#6659C2semidirect
11. #11747025C2semidirect
33. #91303C4semidirect
52. #65286D3semidirect
59. #6817C2×C4semidirect
67. C5×#235C2×C4semidirect
87. C2×C3×#168C2×C4semidirect
91. #6663C2×C4semidirect
92. #6660C2×C4semidirect
93. #6659C2×C4semidirect
94. #6654C2×C4semidirect
97. #5523D5semidirect
235. C2×#168C4×D3semidirect
277. #235C4×D5semidirect
468. C3×C5#2952semidirect
532. C5#78574semidirect
552. C3#10614289semidirect

Maximal subgroups

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

subgroupindex
#117562822
C5×#55232
C2×#913032
C3×#652862
C2×#909852
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#117483902
#117470932
C4×#66602
C4×#66592
#117470252
#106142893
#785745