Finite Group Databasebeta

← #14424501

Subgroups — #14424501

Order 1920.

1464 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4150C211yesmaximal, characteristic, complemented
2C2×C5×#949C211yesmaximal, characteristic, complemented
3#11754604C211yesmaximal, characteristic, complemented
4C22×#6656C211yesmaximal, characteristic, complemented
5#11751334C211yesmaximal, characteristic, complemented
6#11749267C214yesmaximal, complemented
7#11749024C214yesmaximal, complemented
8#11748400C211yesmaximal, characteristic, complemented
9#11748343C211yesmaximal, characteristic, complemented
10#10615679—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C22×C5×D12C2211yescharacteristic
13C3×#4150—24no—
14C3×#4150—24no—
15C2×C3×Q8×D5C2212yescomplemented
16C2×C3×#711—22no—
17C2×C3×#711C2212yescomplemented
18C2×C3×#709—21no—
19C2×C3×#709C2211yescharacteristic
20C22×C3×Dic10—21no—
21C22×C3×Dic10C2211yescharacteristic
22#91815C2211yescharacteristic
23C22×C3⋊#168C2211yescharacteristic
24C5×#949—24no—
25C2×C5×#215C2212yes—
26C2×C5×#213C2212yes—
27C2×C5×#208C2211yescharacteristic
28#91568—22no—
29#91463—21no—
30#91449C2214yes—
31#91370—21no—
32C2×#6656—24no—
33C2×#6656C2214yes—
34#91119C2212yescomplemented
35#91116C2212yescomplemented
36#90971C2214yescomplemented
37#90955C2214yescomplemented
38#84113—51nomaximal, Hall
39C2×#4150D311yescharacteristic, complemented
40C2×C5×AGL(1,ℤ/8)—31no—
41#66139—31no—
42C22×#687—31no—
43#65522—31no—
44#65459—34no—
45#65447—34no—
46#65418—31no—
47#65409—31no—
48C23×C5×D3—21no—
49C3×C5×#41—22no—
50C3×C5×#41D414yescomplemented
51C2×C3×C5×Q8C2311yescharacteristic
52C2×C3×C5×D4—21no—
53C2×C3×C5×D4C2311yescharacteristic
54C22×C3×C4×C5—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×C5×D12—22no—
57C2×C5×D12—22no—
58C2×C5×D12—21no—
59C2×C5×D12C2312yes—
60C2×C3×C22⋊D5—22no—
61C2×C3×C22⋊D5D412yes—
62C22×C3×Dic5—21no—
63C22×C3×Dic5—22no—
64C3×Q8×D5—24no—
65C3×Q8×D5—24no—
66C3×#711—216no—
67C3×#711—24no—
68C3×#711—24no—
69C3×#709—28no—
70C3×#709—22no—
71C3×#709—22no—
72C2×C3×D20D411yescharacteristic
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5C2312yes—
75C2×C3×Dic10—28no—
76C2×C3×Dic10—21no—
77C2×C3×Dic10—22no—
78C2×C3×Dic10—22no—
79C2×C3×Dic10D411yescharacteristic
80C2×C3×Dic10D414yescomplemented
81C2×C3×Dic10C2312yes—
82C2×#1201—24no—
83#6719—21no—
84C4⋊Dic15C2312yes—
85C4×Dic15—21no—
86C2×C3⋊#168—22no—
87C2×C3⋊#168C2312yes—
88C5×#215—24no—
89C5×#213—24no—
90C5×#208—22no—
91C2×C5×C3⋊C8C2312yes—
92(C2×D3)⋊Dic5—24no—
93#6656—28no—
94C2×C3×2−1+4—51no—
95#5830—51no—
96C2×#949D511yescharacteristic, complemented
97C22×#215—51no—
98#5238—54no—
99#5234—51no—
100#5233—51no—
101#5227—54no—
102#5225—51no—
103C2×C5×#41C2×D311yescharacteristic
104C22×C5×D4—31no—
105#4150—24no—
106#4150—24no—
107C2×Q8×D5C2×D312yescomplemented
108C2×#711—22no—
109C2×#711C2×D312yescomplemented
110C2×#709—21no—
111C2×#709C2×D311yescharacteristic
112C22×Dic10—21no—
113C22×Dic10C2×D311yescharacteristic
114C5×AGL(1,ℤ/8)—64no—
115C2×C5×SD16—32no—
116C2×C5×D8—32no—
117C2×C5×M16—31no—
118#4099—62no—
119#4086—61no—
120#4084—34no—
121#4082—61no—
122C2×#687—34no—
123C2×#687—64no—
124#4072—31no—
125C22×#168—31no—
126#3967—32no—
127#3964—32no—
128#3952—34no—
129#3948—34no—
130#3010—151noSylow
131C23×C3×C5—21no—
132C23×C3×C5C2×D411yescharacteristic
133C22×C5×D3—22no—
134C22×C5×D3—42no—
135C22×C5×D3—82no—
136C22×C3×D5C2×D412yes—
137C3×C5×Q8—21no—
138C3×C5×Q8C2×D412yes—
139C3×C5×D4—24no—
140C3×C5×D4—21no—
141C3×C5×D4C2×D412yes—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—24no—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5C2×D412yes—
147C2×C3×C4×C5C2411yescharacteristic
148C2×Dic15—22no—
149C5×D12—22no—
150C5×D12—22no—
151C5×D12—42no—
152C3×C22⋊D5—28no—
153C3×C22⋊D5—24no—
154C2×C3×Dic5—28no—
155C2×C3×Dic5—24no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5C2×D412yes—
158C3×D20—22no—
159C3×C4×D5—28no—
160C3×C4×D5—22no—
161C3×C4×D5—22no—
162C3×Dic10—28no—
163C3×Dic10—22no—
164C3×Dic10—24no—
165C3×Dic10—22no—
166C3×Dic10C2×D414yes—
167#1201—84no—
168C3⋊#168—22no—
169C5×C3⋊C8—22no—
170C3×2−1+4—104no—
171C3×2−1+4—104no—
172C2×C3×#41—51no—
173C2×C3×#41—52no—
174C2×C3×#41—101no—
175C2×C3×#41—102no—
176C2×C3×#41C2×D511yescharacteristic
177C22×C3×Q8—52no—
178C22×C3×Q8—51no—
179C22×C3×Q8—101no—
180C22×D12C2×D511yescharacteristic
181#949—24no—
182#947—101no—
183C2×#215—54no—
184C2×#215—104no—
185C2×#215C2×D512yes—
186#940—101no—
187#937—102no—
188C2×#213C2×D512yes—
189#930—54no—
190#926—51no—
191C2×#208C2×D511yescharacteristic
192C22×C3⋊C8—51no—
193#835—52no—
194#835—54no—
195#832—52no—
196#830—54no—
197C24×C5—61no—
198C5×#41—22no—
199C5×#41#6714yescomplemented
200C2×C5×Q8C22×D311yescharacteristic
201C2×C5×D4—21no—
202C2×C5×D4—32no—
203C2×C5×D4—62no—
204C2×C5×D4—62no—
205C2×C5×D4—61no—
206C2×C5×D4C22×D311yescharacteristic
207C22×C4×C5—21no—
208C22×C4×C5C22×D311yescharacteristic
209C2×C22⋊D5—22no—
210C2×C22⋊D5—64no—
211C2×C22⋊D5#6712yes—
212C22×Dic5—21no—
213C22×Dic5—22no—
214Q8×D5—24no—
215Q8×D5—24no—
216#711—216no—
217#711—24no—
218#711—24no—
219#709—28no—
220#709—22no—
221#709—22no—
222C2×D20#6711yescharacteristic
223C2×C4×D5—22no—
224C2×C4×D5C22×D312yes—
225C2×Dic10—28no—
226C2×Dic10—21no—
227C2×Dic10—22no—
228C2×Dic10—22no—
229C2×Dic10#6711yescharacteristic
230C2×Dic10#6714yescomplemented
231C2×Dic10C22×D312yes—
232C5×SD16—64no—
233C5×D8—64no—
234C5×M16—62no—
235C2×C5×C8—32no—
236C22⋊Dic5—61no—
237C22⋊Dic5—64no—
238#687—68no—
239C4⋊Dic5—32no—
240C4×Dic5—61no—
241C2×#168—32no—
242C2×#168—62no—
243C2×2−1+4—51no—
244C2×AGL(1,ℤ/8)—31no—
245C22×SD16—151no—
246#535—151no—
247#449—154no—
248#448—154no—
249#419—151no—
250#416—151no—
251#408—151no—
252C22×C3×C5—22no—
253C22×C3×C5—22no—
254C22×C3×C5—42no—
255C22×C3×C5#12012yes—
256C22×C3×C5C22×D411yescharacteristic
257C2×C5×D3—42no—
258C2×C5×D3—44no—
259C2×C5×D3—84no—
260C2×C3×D5—22no—
261C2×C3×D5—24no—
262C3×C4×C5—22no—
263C3×C4×C5#12012yes—
264C3×C4×C5C22×D411yescharacteristic
265C3×C4×C5C22×D411yescharacteristic
266Dic15—42no—
267C3×Dic5—22no—
268C3×Dic5—24no—
269C23×D3—21no—
270C3×#41—22no—
271C3×#41—108no—
272C3×#41—104no—
273C3×#41—1016no—
274C3×#41—104no—
275C3×#41—102no—
276C3×#41—102no—
277C3×#41C22⋊D514yescomplemented
278C2×C3×Q8—51no—
279C2×C3×Q8—54no—
280C2×C3×Q8—52no—
281C2×C3×Q8—102no—
282C2×C3×Q8—108no—
283C2×C3×Q8—104no—
284C2×C3×Q8—104no—
285C2×C3×Q8—101no—
286C2×C3×Q8—102no—
287C2×C3×Q8C22×D511yescharacteristic
288C2×C3×D4—21no—
289C2×C3×D4—52no—
290C2×C3×D4—51no—
291C2×C3×D4—102no—
292C2×C3×D4C22×D511yescharacteristic
293C22×C3×C4—21no—
294C22×C3×C4—52no—
295C22×C3×C4—102no—
296C22×C3×C4—102no—
297C22×C3×C4—101no—
298C22×C3×C4C22×D511yescharacteristic
299C2×#67—104no—
300C2×D12—22no—
301C2×D12—22no—
302C2×D12—21no—
303C2×D12C22×D512yes—
304#217—101no—
305#215—24no—
306#215—108no—
307#213—24no—
308(C2×D3)⋊C4—104no—
309C4⋊Dic3—52no—
310C4×Dic3—101no—
311#208—22no—
312C2×C3⋊C8—52no—
313C2×C3⋊C8—102no—
314C2×C3⋊C8C22×D512yes—
315C23×C5—21no—
316C23×C5—62no—
317C23×C5—122no—
318C23×C5—242no—
319C23×C5C2×#6711yescharacteristic
320C22×D5C2×#6712yes—
321C5×Q8—21no—
322C5×Q8C2×#6712yes—
323C5×D4—24no—
324C5×D4—21no—
325C5×D4—62no—
326C5×D4—62no—
327C5×D4—122no—
328C5×D4C2×#6712yes—
329C2×C4×C5—21no—
330C2×C4×C5—24no—
331C2×C4×C5C2×#6712yes—
332C2×C4×C5C2×#6711yescharacteristic
333C2×C4×C5C2×#6712yes—
334C2×C4×C5C23×D311yescharacteristic
335C22⋊D5—28no—
336C22⋊D5—24no—
337C22⋊D5—244no—
338C2×Dic5—28no—
339C2×Dic5—24no—
340C2×Dic5—22no—
341C2×Dic5—62no—
342C2×Dic5C2×#6712yes—
343D20—22no—
344C4×D5—28no—
345C4×D5—22no—
346C4×D5—22no—
347Dic10—28no—
348Dic10—22no—
349Dic10—24no—
350Dic10—22no—
351Dic10C2×#6714yes—
352C5×C8—62no—
353#168—62no—
3542−1+4—104no—
3552−1+4—104no—
356C2×#41—51no—
357C2×#41—52no—
358C2×#41—101no—
359C2×#41—102no—
360C2×#41D3×D511yescharacteristic
361C22×Q8—52no—
362C22×Q8—51no—
363C22×Q8—101no—
364C22×D4—31no—
365AGL(1,ℤ/8)—64no—
366C2×SD16—32no—
367C2×SD16—154no—
368C2×SD16—304no—
369C2×D8—32no—
370C2×M16—31no—
371C22×C8—151no—
372#127—301no—
373#124—301no—
374#121—154no—
375#120—302no—
376#117—151no—
377#103—154no—
378#103—152no—
379#102—152no—
380C22⋊C8—154no—
381C2×C3×C5—22no—
382C2×C3×C5—42no—
383C2×C3×C5C2×#12011yescharacteristic
384C2×C3×C5#57712yes—
385C3×D5—42no—
386C5×D3—82no—
387C23×C3—21no—
388C23×C3—52no—
389C23×C3D4×D511yescharacteristic
390C22×D3—22no—
391C22×D3—42no—
392C22×D3—82no—
393C3×Q8—21no—
394C3×Q8—54no—
395C3×Q8—108no—
396C3×Q8—102no—
397C3×Q8—102no—
398C3×Q8—104no—
399C3×Q8C2×C22⋊D512yes—
400C3×D4—24no—
401C3×D4—21no—
402C3×D4—108no—
403C3×D4—104no—
404C3×D4—102no—
405C3×D4C2×C22⋊D512yes—
406C2×C3×C4—21no—
407C2×C3×C4—24no—
408C2×C3×C4—52no—
409C2×C3×C4—108no—
410C2×C3×C4—108no—
411C2×C3×C4—102no—
412C2×C3×C4—104no—
413C2×C3×C4—102no—
414C2×C3×C4—102no—
415C2×C3×C4D4×D512yes—
416C2×C3×C4D4×D511yescharacteristic
417C2×C3×C4C2×C22⋊D512yes—
418C2×C3×C4C23×D511yescharacteristic
419#67—404no—
420C2×Dic3—102no—
421D12—22no—
422D12—22no—
423D12—42no—
424C3⋊C8—22no—
425C3⋊C8—102no—
426C22×C5—22no—
427C22×C5—22no—
428C22×C5—42no—
429C22×C5—124no—
430C22×C5—122no—
431C22×C5—244no—
432C22×C5#95312yes—
433C22×C5C22×#6711yescharacteristic
434C2×D5—24no—
435C2×D5—22no—
436C4×C5—22no—
437C4×C5#95312yes—
438C4×C5C22×#6711yescharacteristic
439C4×C5C22×#6711yescharacteristic
440Dic5—22no—
441Dic5—24no—
442Dic5—122no—
443C24—61no—
444#41—22no—
445#41—108no—
446#41—104no—
447#41—1016no—
448#41—104no—
449#41—102no—
450#41—102no—
451#41#120114yescomplemented
452C2×Q8—51no—
453C2×Q8—54no—
454C2×Q8—52no—
455C2×Q8—102no—
456C2×Q8—108no—
457C2×Q8—104no—
458C2×Q8—104no—
459C2×Q8—102no—
460C2×Q8—101no—
461C2×Q8C2×D3×D511yescharacteristic
462C2×D4—21no—
463C2×D4—32no—
464C2×D4—52no—
465C2×D4—51no—
466C2×D4—62no—
467C2×D4—62no—
468C2×D4—61no—
469C2×D4—102no—
470C2×D4—304no—
471C2×D4C2×D3×D511yescharacteristic
472C22×C4—21no—
473C22×C4—52no—
474C22×C4—102no—
475C22×C4—102no—
476C22×C4—101no—
477C22×C4C2×D3×D511yescharacteristic
478SD16—64no—
479SD16—308no—
480D8—64no—
481M16—62no—
482C2×C8—32no—
483C2×C8—152no—
484C2×C8—302no—
485C4⋊C4—152no—
486C22⋊C4—304no—
487C22⋊C4—301no—
488C42—301no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—42no—
493C22×C3—104no—
494C22×C3—102no—
495C22×C3#408312yes—
496C22×C3C2×D4×D511yescharacteristic
497C2×D3—44no—
498C2×D3—42no—
499C2×D3—84no—
500C3×C4—22no—
501C3×C4—102no—
502C3×C4—104no—
503C3×C4#408312yes—
504C3×C4C2×D4×D511yescharacteristic
505C3×C4C22×C22⋊D511yescharacteristic
506Dic3—202no—
507C2×C5—22no—
508C2×C5—42no—
509C2×C5—242no—
510C2×C5#583712yes—
511C2×C5C2×#95311yescharacteristic
512D5—42no—
513C23—21no—
514C23—52no—
515C23—62no—
516C23—122no—
517C23—242no—
518C23D5×#6711yescharacteristic
519Q8—21no—
520Q8—54no—
521Q8—108no—
522Q8—102no—
523Q8—102no—
524Q8—104no—
525Q8C2×#120112yes—
526D4—24no—
527D4—21no—
528D4—62no—
529D4—62no—
530D4—108no—
531D4—104no—
532D4—102no—
533D4—122no—
534D4—1204no—
535D4C2×#120112yes—
536C2×C4—21no—
537C2×C4—24no—
538C2×C4—52no—
539C2×C4—108no—
540C2×C4—108no—
541C2×C4—102no—
542C2×C4—104no—
543C2×C4—102no—
544C2×C4—102no—
545C2×C4—302no—
546C2×C4C2×#120112yes—
547C2×C4D5×#6712yes—
548C2×C4D5×#6711yescharacteristic
549C2×C4C22×D3×D511yescharacteristic
550C8—62no—
551C8—302no—
552C2×C3—22no—
553C2×C3—42no—
554C2×C3—202no—
555C2×C3#6610912yes—
556C2×C3C2×#408311yescharacteristic
557D3—82no—
558C5#8411311yescharacteristic, complemented, Sylow
559C22—22no—
560C22—22no—
561C22—42no—
562C22—104no—
563C22—102no—
564C22—124no—
565C22—122no—
566C22—244no—
567C22#9156312yes—
568C22C2×D5×#6711yescharacteristic
569C4—22no—
570C4—102no—
571C4—104no—
572C4—602no—
573C4#9156312yes—
574C4C22×#120111yescharacteristic
575C4C2×D5×#6711yescharacteristic
576C3#1061567911yescharacteristic, complemented, Sylow
577C2—22no—
578C2—42no—
579C2—202no—
580C2—242no—
581C2#1175531712yes—
582C2C2×#9156311yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3010
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
1. C2×C3×#4150C2semidirect
2. C2×C5×#949C2semidirect
3. #11754604C2semidirect
4. C22×#6656C2semidirect
5. #11751334C2semidirect
6. #11749267C2semidirect
7. #11749024C2semidirect
8. #11748400C2semidirect
9. #11748343C2semidirect
15. C2×C3×Q8×D5C22semidirect
17. C2×C3×#711C22semidirect
34. #91119C22semidirect
35. #91116C22semidirect
36. #90971C22semidirect
37. #90955C22semidirect
39. C2×#4150D3semidirect
50. C3×C5×#41D4semidirect
80. C2×C3×Dic10D4semidirect
96. C2×#949D5semidirect
107. C2×Q8×D5C2×D3semidirect
109. C2×#711C2×D3semidirect
199. C5×#41#67semidirect
230. C2×Dic10#67semidirect
277. C3×#41C22⋊D5semidirect
451. #41#1201semidirect
489. C3×C5#3010semidirect
558. C5#84113semidirect
576. C3#10615679semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41502
C2×C5×#9492
#117546042
C22×#66562
#117513342
#117492672
#117490242
#117484002
#117483432
#106156793
#841135