Finite Group Databasebeta

← #14438690

Subgroups — #14438690

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5832C211yesmaximal, characteristic
2C2×#91381C211yesmaximal, characteristic, complemented
3#11751333C211yesmaximal, characteristic, complemented
4C3×#65521C211yesmaximal, characteristic, complemented
5#11749192C212yesmaximal, complemented
6#11749188C212yesmaximal, complemented
7#11748946C212yesmaximal, complemented
8#11748942C212yesmaximal, complemented
9#11748390C211yesmaximal, characteristic, complemented
10#11748384C211yesmaximal, characteristic, complemented
11Dic3×#681C211yesmaximal, characteristic, complemented
12#10615015—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C2×C4⋊Dic15C2211yescharacteristic
16C2×#6710C2211yescharacteristic
17C5×#947C2211yescharacteristic
18C5×#944C2211yescharacteristic
19C5×#940C2211yescharacteristic
20C5×#939—21no—
21C5×#939—21no—
22C5×#936C2211yescharacteristic
23C4×C5×#67—21no—
24C4×C5×#67—21no—
25C2×C4×C5×Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C2×C3×#681C2211yescharacteristic
28C2×#6669—21no—
29C2×#6668—21no—
30#91381—21no—
31#91381—21no—
32#91381C2212yes—
33#91381C2212yes—
34#91119C2212yes—
35#91116C2212yes—
36C3×#3967C2212yes—
37C3×#3964C2212yes—
38#90973C2212yes—
39#90972C2212yes—
40#90967C2212yes—
41#90966C2212yes—
42#90953C2212yes—
43Dic3×#168C2212yes—
44#78879—51nomaximal, Hall
45C5×#532—31no—
46C2×#4016—31no—
47#65521—31no—
48#65521—31no—
49#65521—31no—
50#65521D311yescharacteristic, complemented
51#65371—32no—
52#65360—32no—
53#65345—32no—
54#65345—32no—
55C4×#681—31no—
56C3×C5×#41—22no—
57C3×C5×#41—22no—
58C2×C3×C5×Q8C2311yescharacteristic
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4C2311yescharacteristic
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C22×Dic15—21no—
64C2×C5×#67—21no—
65C2×C5×#67—21no—
66C2×C5×#67—21no—
67C22×C5×Dic3D411yescharacteristic
68C22×C5×Dic3D411yescharacteristic
69C5×#235—22no—
70C5×#235—22no—
71C2×C5×D12C2311yescharacteristic
72C2×C4×C5×D3—21no—
73C2×C5×Dic6C2311yescharacteristic
74C22×C3×Dic5—21no—
75C4⋊Dic15—21no—
76C4⋊Dic15C2312yes—
77#6710—22no—
78C2×C3⋊#168C2312yes—
79C5×#217—21no—
80C5×#217—21no—
81C5×(C2×D3)⋊C4—21no—
82C5×(C2×D3)⋊C4—21no—
83C5×Dic3⋊C4—21no—
84C5×Dic3⋊C4—21no—
85C4×C5×Dic3D411yescharacteristic
86C4×C5×Dic3D411yescharacteristic
87C4×C5×Dic3C2311yescharacteristic
88C4×C5×Dic3C2311yescharacteristic
89C3×C4⋊Dic5—21no—
90C3×C4⋊Dic5C2312yes—
91C3×#681—22no—
92C2×C3×#168C2312yes—
93#6669—22no—
94#6669—22no—
95#6668—22no—
96#6668—22no—
97#5832D511yescharacteristic
98C2×#890—51no—
99C3×#417—51no—
100#5232—51no—
101#5133—51no—
102Dic3×M16—51no—
103#4966—51no—
104#4800—52no—
105#4797—52no—
106#4768—52no—
107#4764—52no—
108C2×C5×#41—31no—
109C2×C5×#41C2×D311yescharacteristic
110C5×C4⋊Q8—31no—
111C5×#127—31no—
112C5×#124—31no—
113C5×#124—31no—
114C5×#121—61no—
115C5×#121—61no—
116C4×C5×D4—61no—
117C4×C5×D4—61no—
118C2×C42×C5—31no—
119C2×C4⋊Dic5—31no—
120C2×C4⋊Dic5C2×D311yescharacteristic
121C2×#683—61no—
122C2×#683—61no—
123C2×#681—31no—
124C2×#681C2×D311yescharacteristic
125#4016—32no—
126#4016—32no—
127#4016—61no—
128#4016—61no—
129#3967—32no—
130#3967—32no—
131#3967—32no—
132#3967C2×D312yes—
133#3964—32no—
134#3964—32no—
135#3964—32no—
136#3964C2×D312yes—
137#3935—32no—
138C4×#168—32no—
139#3142—151noSylow
140C23×C3×C5—21no—
141C23×C3×C5C2×D411yescharacteristic
142C22×C5×D3—21no—
143C3×C5×Q8—21no—
144C3×C5×Q8—21no—
145C3×C5×D4—21no—
146C3×C5×D4—21no—
147C3×C5×D4—42no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—42no—
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5#4112yes—
152C2×C3×C4×C5#4112yes—
153C2×C3×C4×C5C2411yescharacteristic
154C2×Dic15—22no—
155C2×Dic15—42no—
156C5×#67—42no—
157C5×#67—42no—
158C5×#67—42no—
159C2×C5×Dic3—21no—
160C2×C5×Dic3—41no—
161C2×C5×Dic3—41no—
162C2×C5×Dic3C2×D411yescharacteristic
163C2×C5×Dic3C2×D411yescharacteristic
164C2×C5×Dic3C2×D411yescharacteristic
165C2×C5×Dic3C2×D411yescharacteristic
166C5×D12—21no—
167C5×D12—21no—
168C4×C5×D3—42no—
169C5×Dic6—21no—
170C5×Dic6—21no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—42no—
173C3⋊#168—22no—
174C3×#168—22no—
175C2×C3×#41C2×D511yescharacteristic
176C2×#235C2×D511yescharacteristic
177C2×C3×M16—51no—
178C2×C3×C4⋊C4—51no—
179#947C2×D511yescharacteristic
180#944C2×D511yescharacteristic
181#940C2×D511yescharacteristic
182#939—21no—
183#939—21no—
184#936C2×D511yescharacteristic
185C4×#67—21no—
186C4×#67—21no—
187C2×C4⋊Dic3—51no—
188C2×C4⋊Dic3—101no—
189C2×Dic3⋊C4—101no—
190C2×C4×Dic3C2×D511yescharacteristic
191C2×#208—51no—
192#890—52no—
193#890—52no—
194#890—101no—
195#890—101no—
196C3×#103—52no—
197C3×#102—52no—
198#835—52no—
199#832—52no—
200#821—52no—
201#816—52no—
202#815—52no—
203C8×Dic3—52no—
204#810—52no—
205#809—52no—
206C5×#41—22no—
207C5×#41—22no—
208C5×#41—62no—
209C5×#41—62no—
210C2×C5×Q8—31no—
211C2×C5×Q8C22×D311yescharacteristic
212C2×C5×D4—21no—
213C2×C5×D4—31no—
214C2×C5×D4—61no—
215C2×C5×D4—61no—
216C2×C5×D4—61no—
217C2×C5×D4C22×D311yescharacteristic
218C22×C4×C5—21no—
219C22×C4×C5—31no—
220C22×C4×C5—31no—
221C22×C4×C5—61no—
222C22×C4×C5C22×D311yescharacteristic
223C22×Dic5—21no—
224C22×Dic5—61no—
225C5×C4⋊C4—61no—
226C5×C4⋊C4—61no—
227C5×C22⋊C4—61no—
228C5×C22⋊C4—61no—
229C5×C22⋊C4—61no—
230C5×C22⋊C4—61no—
231C42×C5—31no—
232C42×C5—31no—
233C42×C5—31no—
234C42×C5—31no—
235C4⋊Dic5—21no—
236C4⋊Dic5—32no—
237C4⋊Dic5—61no—
238C4⋊Dic5C22×D312yes—
239#683—62no—
240#683—62no—
241#683—62no—
242#683—62no—
243#681—22no—
244#681—62no—
245C2×#168—32no—
246C2×#168C22×D312yes—
247#532—31no—
248C2×#125—151no—
249#491—152no—
250#490—152no—
251#488—152no—
252#488—152no—
253#417—51no—
254#417—151no—
255#417—151no—
256#417—151no—
257C4×M16—151no—
258C22×C3×C5—21no—
259C22×C3×C5—21no—
260C22×C3×C5—41no—
261C22×C3×C5—41no—
262C22×C3×C5—41no—
263C22×C3×C5#12412yes—
264C22×C3×C5C22×D411yescharacteristic
265C2×C5×D3—41no—
266C2×C5×D3—41no—
267C2×C5×D3—41no—
268C3×C4×C5—41no—
269C3×C4×C5#12412yes—
270C3×C4×C5C2×#4111yescharacteristic
271C3×C4×C5C2×#4111yescharacteristic
272Dic15—42no—
273C3×Dic5—42no—
274C5×Dic3—21no—
275C5×Dic3—21no—
276C5×Dic3—21no—
277C5×Dic3—21no—
278C5×Dic3—41no—
279C3×#41—22no—
280C3×#41—22no—
281C2×C3×Q8C22×D511yescharacteristic
282C2×C3×D4—21no—
283C2×C3×D4C22×D511yescharacteristic
284C22×C3×C4—21no—
285C22×C3×C4—101no—
286C22×C3×C4C22×D511yescharacteristic
287C2×#67—21no—
288C2×#67—21no—
289C2×#67—21no—
290C22×Dic3—101no—
291C22×Dic3C22⋊D511yescharacteristic
292C22×Dic3C22⋊D511yescharacteristic
293#235—22no—
294#235—22no—
295C2×D12C22×D511yescharacteristic
296C2×C4×D3—21no—
297C2×Dic6C22×D511yescharacteristic
298C3×M16—102no—
299C2×C3×C8—52no—
300C3×C4⋊C4—52no—
301C3×C4⋊C4—101no—
302#217—21no—
303#217—21no—
304(C2×D3)⋊C4—21no—
305(C2×D3)⋊C4—21no—
306C4⋊Dic3—52no—
307C4⋊Dic3—101no—
308C4⋊Dic3—102no—
309C4⋊Dic3—102no—
310Dic3⋊C4—21no—
311Dic3⋊C4—21no—
312Dic3⋊C4—102no—
313Dic3⋊C4—102no—
314C4×Dic3C22⋊D511yescharacteristic
315C4×Dic3C22⋊D511yescharacteristic
316C4×Dic3C22×D511yescharacteristic
317C4×Dic3C22×D511yescharacteristic
318#208—102no—
319C2×C3⋊C8—52no—
320C23×C5—21no—
321C23×C5—61no—
322C23×C5D3×D411yescharacteristic
323C5×Q8—21no—
324C5×Q8—21no—
325C5×Q8—61no—
326C5×Q8—61no—
327C5×D4—21no—
328C5×D4—21no—
329C5×D4—42no—
330C5×D4—61no—
331C5×D4—61no—
332C5×D4—122no—
333C5×D4—122no—
334C5×D4—122no—
335C2×C4×C5—21no—
336C2×C4×C5—31no—
337C2×C4×C5—31no—
338C2×C4×C5—31no—
339C2×C4×C5—31no—
340C2×C4×C5—42no—
341C2×C4×C5—61no—
342C2×C4×C5—121no—
343C2×C4×C5—121no—
344C2×C4×C5—122no—
345C2×C4×C5#23512yes—
346C2×C4×C5D3×D411yescharacteristic
347C2×C4×C5#23712yes—
348C2×C4×C5C23×D311yescharacteristic
349C2×Dic5—22no—
350C2×Dic5—42no—
351C2×Dic5—62no—
352C2×Dic5—122no—
353#168—22no—
354#168—62no—
355C2×#41—31no—
356C2×#41D3×D511yescharacteristic
357C2×M16—51no—
358C2×M16—151no—
359C4⋊Q8—31no—
360#127—31no—
361#125—152no—
362#125—152no—
363#125—301no—
364#125—301no—
365#124—31no—
366#124—31no—
367#121—61no—
368#121—61no—
369C4×D4—61no—
370C4×D4—61no—
371C2×C4⋊C4—51no—
372C2×C4⋊C4—151no—
373C2×C4⋊C4—301no—
374C2×C4⋊C4—301no—
375C2×C42—31no—
376#103—52no—
377#103—152no—
378#103—152no—
379#103—152no—
380#102—52no—
381#102—152no—
382#102—152no—
383#102—152no—
384#97—152no—
385C4×C8—152no—
386C2×C3×C5—22no—
387C2×C3×C5—81no—
388C2×C3×C5C2×#12411yescharacteristic
389C2×C3×C5#57511yescharacteristic
390C2×C3×C5#57511yescharacteristic
391C5×D3—81no—
392C23×C3—21no—
393C23×C3C2×C22⋊D511yescharacteristic
394C22×D3—21no—
395C3×Q8—21no—
396C3×Q8—21no—
397C3×D4—21no—
398C3×D4—21no—
399C3×D4—42no—
400C2×C3×C4—21no—
401C2×C3×C4—42no—
402C2×C3×C4—102no—
403C2×C3×C4—202no—
404C2×C3×C4#71112yes—
405C2×C3×C4#71112yes—
406C2×C3×C4C2×C22⋊D511yescharacteristic
407C2×C3×C4C23×D511yescharacteristic
408#67—42no—
409#67—42no—
410#67—42no—
411C2×Dic3—21no—
412C2×Dic3—41no—
413C2×Dic3—41no—
414C2×Dic3—102no—
415C2×Dic3—202no—
416C2×Dic3C2×C22⋊D511yescharacteristic
417C2×Dic3C2×C22⋊D511yescharacteristic
418C2×Dic3C2×C22⋊D511yescharacteristic
419C2×Dic3C2×C22⋊D511yescharacteristic
420D12—21no—
421D12—21no—
422C4×D3—42no—
423Dic6—21no—
424Dic6—21no—
425C3×C8—102no—
426C3⋊C8—102no—
427C22×C5—21no—
428C22×C5—21no—
429C22×C5—41no—
430C22×C5—41no—
431C22×C5—41no—
432C22×C5—121no—
433C22×C5—121no—
434C22×C5—121no—
435C22×C5#88512yes—
436C22×C5C2×D3×D411yescharacteristic
437C4×C5—41no—
438C4×C5—61no—
439C4×C5—61no—
440C4×C5—61no—
441C4×C5—61no—
442C4×C5—121no—
443C4×C5#88512yes—
444C4×C5C2×#23511yescharacteristic
445C4×C5C2×#23711yescharacteristic
446Dic5—42no—
447Dic5—122no—
448#41—22no—
449#41—22no—
450#41—62no—
451#41—62no—
452C2×Q8—31no—
453C2×Q8C2×D3×D511yescharacteristic
454C2×D4—21no—
455C2×D4—31no—
456C2×D4—61no—
457C2×D4—61no—
458C2×D4—61no—
459C2×D4C2×D3×D511yescharacteristic
460C22×C4—21no—
461C22×C4—31no—
462C22×C4—31no—
463C22×C4—61no—
464C22×C4—101no—
465C22×C4—301no—
466C22×C4C2×D3×D511yescharacteristic
467M16—102no—
468M16—302no—
469C2×C8—52no—
470C2×C8—152no—
471C4⋊C4—52no—
472C4⋊C4—61no—
473C4⋊C4—61no—
474C4⋊C4—101no—
475C4⋊C4—152no—
476C4⋊C4—302no—
477C4⋊C4—302no—
478C4⋊C4—302no—
479C4⋊C4—302no—
480C4⋊C4—301no—
481C22⋊C4—61no—
482C22⋊C4—61no—
483C22⋊C4—61no—
484C22⋊C4—61no—
485C42—31no—
486C42—31no—
487C42—31no—
488C42—31no—
489C3×C5#314211yescharacteristic, complemented, Hall
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—41no—
493C22×C3—41no—
494C22×C3—41no—
495C22×C3#408212yes—
496C22×C3C22×C22⋊D511yescharacteristic
497C2×D3—41no—
498C2×D3—41no—
499C2×D3—41no—
500C3×C4—41no—
501C3×C4—202no—
502C3×C4#408212yes—
503C3×C4C2×#71111yescharacteristic
504C3×C4C2×#71111yescharacteristic
505Dic3—21no—
506Dic3—21no—
507Dic3—21no—
508Dic3—21no—
509Dic3—41no—
510Dic3—202no—
511C2×C5—22no—
512C2×C5—81no—
513C2×C5—241no—
514C2×C5C2×#88511yescharacteristic
515C2×C5#577311yescharacteristic
516C2×C5#577711yescharacteristic
517C23—21no—
518C23—61no—
519C23D3×C22⋊D511yescharacteristic
520Q8—21no—
521Q8—21no—
522Q8—61no—
523Q8—61no—
524D4—21no—
525D4—21no—
526D4—42no—
527D4—61no—
528D4—61no—
529D4—122no—
530D4—122no—
531D4—122no—
532C2×C4—21no—
533C2×C4—31no—
534C2×C4—31no—
535C2×C4—31no—
536C2×C4—31no—
537C2×C4—42no—
538C2×C4—61no—
539C2×C4—102no—
540C2×C4—121no—
541C2×C4—121no—
542C2×C4—122no—
543C2×C4—202no—
544C2×C4—302no—
545C2×C4—602no—
546C2×C4#678012yes—
547C2×C4#678212yes—
548C2×C4D3×C22⋊D511yescharacteristic
549C2×C4C22×D3×D511yescharacteristic
550C8—102no—
551C8—302no—
552C2×C3—22no—
553C2×C3—81no—
554C2×C3C2×#408211yescharacteristic
555C2×C3#6615611yescharacteristic
556C2×C3#6615611yescharacteristic
557D3—81no—
558C5#7887911yescharacteristic, complemented, Sylow
559C22—21no—
560C22—21no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—121no—
565C22—121no—
566C22—121no—
567C22#9152512yes—
568C22C2×D3×C22⋊D511yescharacteristic
569C4—41no—
570C4—61no—
571C4—61no—
572C4—61no—
573C4—61no—
574C4—121no—
575C4—202no—
576C4—602no—
577C4#9152512yes—
578C4C2×#678011yescharacteristic
579C4C2×#678211yescharacteristic
580C3#1061501511yescharacteristic, complemented, Sylow
581C2—22no—
582C2—81no—
583C2—241no—
584C2#1175534511yescharacteristic
585C2#1175534811yescharacteristic
586C2C2×#9152511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC5×#5832C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3142
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#91381C2semidirect
3. #11751333C2semidirect
4. C3×#65521C2semidirect
5. #11749192C2semidirect
6. #11749188C2semidirect
7. #11748946C2semidirect
8. #11748942C2semidirect
9. #11748390C2semidirect
10. #11748384C2semidirect
11. Dic3×#681C2semidirect
50. #65521D3semidirect
489. C3×C5#3142semidirect
558. C5#78879semidirect
580. C3#10615015semidirect

Maximal subgroups

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

subgroupindex
C5×#58322
C2×#913812
#117513332
C3×#655212
#117491922
#117491882
#117489462
#117489422
#117483902
#117483842
Dic3×#6812
#106150153
#788795