Finite Group Databasebeta

← #14424484

Subgroups — #14424484

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×#92101C211yesmaximal, characteristic, complemented
2C5×#5830C211yesmaximal, characteristic, complemented
3C22×#6659C211yesmaximal, characteristic, complemented
4C2×#91304C211yesmaximal, characteristic, complemented
5C3×#65523C211yesmaximal, characteristic, complemented
6#11748553C214yesmaximal, complemented
7#11748526C214yesmaximal, complemented
8#11748417C211yesmaximal, characteristic, complemented
9#11748393C211yesmaximal, characteristic, complemented
10#10615121—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12#92101—24no—
13#92101—24no—
14C2×Q8×D15—21no—
15C2×#6819—21no—
16C2×#6819—22no—
17C2×#6817C2211yescharacteristic
18C2×#6817C2212yescomplemented
19C22×Dic30C2211yescharacteristic
20C22×Dic30C2212yescomplemented
21C22×C5×D12C2211yescharacteristic
22C5×#947—21no—
23C5×#940—21no—
24C5×#937—22no—
25C5×#930C2214yes—
26C5×#926C2211yescharacteristic
27C2×C3×#681C2211yescharacteristic
28C22×C3×#168C2211yescharacteristic
29C2×#6659—24no—
30C2×#6659C2212yes—
31C2×#6659C2214yes—
32#91304—24no—
33C2×#6654C2212yes—
34C3×C22⋊#168C2214yescomplemented
35#90975C2212yescomplemented
36#90975C2214yescomplemented
37#90969C2212yescomplemented
38#78678—51nomaximal, Hall
39C2×#4150—31no—
40C5×#535—31no—
41C22×#687—31no—
42C2×#4078—31no—
43#65523D311yescharacteristic, complemented
44#65329—34no—
45#65326—34no—
46#65293—31no—
47#65291—31no—
48C23×C5×D3—21no—
49C3×C5×#41—22no—
50C3×C5×#41—22no—
51C2×C3×C5×Q8D411yescharacteristic
52C2×C3×C5×D4D412yes—
53C2×C3×C5×D4D411yescharacteristic
54C22×C3×C4×C5C2312yes—
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220—21no—
57C2×#1220—22no—
58C22×Dic15—21no—
59C22×Dic15—22no—
60Q8×D15—28no—
61#6819—216no—
62#6819—28no—
63#6817—22no—
64#6817—24no—
65#6817—24no—
66#6817D414yescomplemented
67C2×D60C2311yescharacteristic
68C2×C4×D15—21no—
69C2×C4×D15—22no—
70C2×Dic30—21no—
71C2×Dic30—22no—
72C2×Dic30—22no—
73C2×Dic30—24no—
74C2×Dic30—24no—
75C2×Dic30D414yescomplemented
76C2×Dic30C2312yes—
77C2×Dic30C2311yescharacteristic
78C2×C5×#67—24no—
79C2×C5×D12—22no—
80C2×C5×D12—22no—
81C2×C5×D12—21no—
82C2×C5×D12C2312yes—
83C5×#217—21no—
84C5×(C2×D3)⋊C4—24no—
85C5×C4⋊Dic3C2312yes—
86C4×C5×Dic3—21no—
87C3×#681—22no—
88C2×C3×#168—22no—
89C2×C3×#168C2312yes—
90C2×C3×#168C2312yes—
91#6659—24no—
92#6659—28no—
93#6654—24no—
94C2×#1010—51no—
95#5830D511yescharacteristic, complemented
96C2×#908—51no—
97C22×#204—51no—
98C3×#408—51no—
99#5120—51no—
100#5113—51no—
101#4738—54no—
102#4734—54no—
103C2×C5×#41C2×D311yescharacteristic
104C22×C5×D4—31no—
105#4150—64no—
106#4150—64no—
107C2×Q8×D5—61no—
108C2×#711—62no—
109C2×#711—61no—
110C2×#709—31no—
111C2×#709—32no—
112C22×Dic10—31no—
113C22×Dic10—32no—
114C5×#127—61no—
115C5×#124—61no—
116C5×#121—34no—
117C5×#120—62no—
118C5×#117—31no—
119C2×#687—34no—
120C2×#687—32no—
121C2×#687—64no—
122#4078—64no—
123C2×#686—32no—
124C2×#681C2×D311yescharacteristic
125C22×#168C2×D311yescharacteristic
126C22⋊#168C2×D314yescomplemented
127#3942—32no—
128#3942—34no—
129#3941—32no—
130#3010—151noSylow
131C23×C3×C5C2×D412yes—
132C23×C3×C5C2×D411yescharacteristic
133C22×D15—21no—
134C22×C5×D3—22no—
135C22×C5×D3—42no—
136C22×C5×D3—82no—
137C3×C5×Q8—22no—
138C3×C5×D4—24no—
139C3×C5×D4—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5C2×D412yes—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D412yes—
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5C2411yescharacteristic
147#1220—28no—
148#1220—24no—
149C2×Dic15—28no—
150C2×Dic15—24no—
151C2×Dic15—22no—
152C2×Dic15—21no—
153D60—21no—
154D60C2×D412yes—
155C4×D15—28no—
156C4×D15—24no—
157Dic30—28no—
158Dic30—24no—
159Dic30—22no—
160Dic30—21no—
161Dic30C2×D412yes—
162Dic30C2×D414yes—
163C5×#67—84no—
164C2×C5×Dic3—22no—
165C5×D12—22no—
166C5×D12—22no—
167C5×D12—42no—
168C3×#168—22no—
169C3×#168—22no—
170C2×C3×#41C2×D511yescharacteristic
171#1010—104no—
172#1010—104no—
173C2×D3×Q8—101no—
174C2×#237—102no—
175C2×#237—101no—
176C2×#235—51no—
177C2×#235—52no—
178C22×D12C2×D511yescharacteristic
179C22×Dic6—51no—
180C22×Dic6—52no—
181C2×C3×M16—51no—
182C22×C3×C8—51no—
183#947—21no—
184#940—21no—
185#937—22no—
186#930C2×D514yes—
187#926C2×D511yescharacteristic
188#908—104no—
189C2×D24—52no—
190C2×#204—54no—
191C2×#204—52no—
192C2×#204—104no—
193C3×C22⋊C8—54no—
194#821—52no—
195#816—54no—
196#816—52no—
197C24×C5—61no—
198C5×#41—22no—
199C5×#41—22no—
200C2×C5×Q8D1211yescharacteristic
201C2×C5×D4—32no—
202C2×C5×D4—64no—
203C2×C5×D4—61no—
204C2×C5×D4—62no—
205C2×C5×D4—62no—
206C2×C5×D4D1212yes—
207C2×C5×D4D1211yescharacteristic
208C22×C4×C5C22×D312yes—
209C22×C4×C5C22×D311yescharacteristic
210C2×C22⋊D5—62no—
211C2×C22⋊D5—61no—
212C22×Dic5—62no—
213C22×Dic5—61no—
214Q8×D5—68no—
215#711—616no—
216#711—68no—
217#709—34no—
218#709—64no—
219#709—64no—
220#709—62no—
221C2×D20—31no—
222C2×C4×D5—62no—
223C2×C4×D5—61no—
224C2×Dic10—34no—
225C2×Dic10—32no—
226C2×Dic10—31no—
227C2×Dic10—64no—
228C2×Dic10—64no—
229C2×Dic10—62no—
230C2×Dic10—61no—
231C2×Dic10—62no—
232C5×C4⋊C4—32no—
233C5×C22⋊C4—61no—
234C5×C22⋊C4—64no—
235C42×C5—61no—
236#687—64no—
237#687—68no—
238#686—64no—
239#681—22no—
240C2×#168—22no—
241C2×#168C22×D312yes—
242C2×#168C22×D312yes—
243C2×2−1+4—151no—
244C2×AGL(1,ℤ/8)—151no—
245C22×SD16—151no—
246#535—31no—
247#449—154no—
248#448—154no—
249#419—151no—
250#416—151no—
251#408—51no—
252C22×C3×C5—22no—
253C22×C3×C5—22no—
254C22×C3×C5—24no—
255C22×C3×C5#12012yes—
256C22×C3×C5C22×D411yescharacteristic
257C2×D15—22no—
258C2×D15—42no—
259C2×C5×D3—42no—
260C2×C5×D3—44no—
261C2×C5×D3—84no—
262C3×C4×C5—22no—
263C3×C4×C5#12012yes—
264C3×C4×C5C22×D411yescharacteristic
265C3×C4×C5C22×D411yescharacteristic
266Dic15—22no—
267Dic15—24no—
268C5×Dic3—42no—
269C23×D3—21no—
270C3×#41—22no—
271C3×#41—22no—
272C2×C3×Q8C22⋊D511yescharacteristic
273C2×C3×D4C22⋊D512yes—
274C2×C3×D4C22⋊D511yescharacteristic
275C22×C3×C4C22×D512yes—
276C22×C3×C4C22×D511yescharacteristic
277C2×#67—24no—
278C2×#67—102no—
279C2×#67—101no—
280C22×Dic3—102no—
281C22×Dic3—101no—
282D3×Q8—108no—
283#237—1016no—
284#237—108no—
285#235—54no—
286#235—104no—
287#235—104no—
288#235—102no—
289C2×D12—22no—
290C2×D12—22no—
291C2×D12—21no—
292C2×D12—51no—
293C2×D12C22×D512yes—
294C2×C4×D3—102no—
295C2×C4×D3—101no—
296C2×Dic6—54no—
297C2×Dic6—52no—
298C2×Dic6—51no—
299C2×Dic6—104no—
300C2×Dic6—104no—
301C2×Dic6—102no—
302C2×Dic6—102no—
303C2×Dic6—101no—
304C3×M16—102no—
305C2×C3×C8—52no—
306C2×C3×C8—52no—
307C2×C3×C8—102no—
308#217—21no—
309(C2×D3)⋊C4—24no—
310C4⋊Dic3C22×D512yes—
311C4×Dic3—21no—
312D24—104no—
313#204—108no—
314#204—104no—
315C23×C5—62no—
316C23×C5—122no—
317C23×C5—242no—
318C23×C5C2×D1212yes—
319C23×C5C2×D1211yescharacteristic
320C22×D5—61no—
321C5×Q8—22no—
322C5×D4—24no—
323C5×D4—22no—
324C5×D4—62no—
325C5×D4—62no—
326C5×D4—122no—
327C5×D4—244no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—62no—
331C2×C4×C5C2×D1212yes—
332C2×C4×C5C2×D1211yescharacteristic
333C2×C4×C5D3×D412yes—
334C2×C4×C5D3×D412yes—
335C2×C4×C5C23×D311yescharacteristic
336C22⋊D5—68no—
337C22⋊D5—64no—
338C2×Dic5—68no—
339C2×Dic5—64no—
340C2×Dic5—62no—
341C2×Dic5—61no—
342D20—32no—
343D20—61no—
344C4×D5—68no—
345C4×D5—64no—
346Dic10—34no—
347Dic10—32no—
348Dic10—68no—
349Dic10—64no—
350Dic10—61no—
351Dic10—62no—
352#168—22no—
353#168—22no—
3542−1+4—304no—
3552−1+4—304no—
356C2×#41—151no—
357C2×#41—152no—
358C2×#41—302no—
359C2×#41—301no—
360C2×#41D3×D511yescharacteristic
361C22×Q8—151no—
362C22×Q8—152no—
363C22×Q8—301no—
364C22×D4—31no—
365AGL(1,ℤ/8)—304no—
366C2×SD16—154no—
367C2×SD16—152no—
368C2×SD16—304no—
369C2×D8—152no—
370C2×M16—51no—
371C22×C8—51no—
372#127—61no—
373#124—61no—
374#121—34no—
375#120—62no—
376#117—31no—
377#103—152no—
378#103—154no—
379#102—152no—
380C22⋊C8—54no—
381C2×C3×C5—22no—
382C2×C3×C5—42no—
383C2×C3×C5C2×#12011yescharacteristic
384C2×C3×C5#57712yes—
385D15—42no—
386C5×D3—82no—
387C23×C3C2×C22⋊D512yes—
388C23×C3C2×C22⋊D511yescharacteristic
389C22×D3—22no—
390C22×D3—42no—
391C22×D3—82no—
392C22×D3—101no—
393C3×Q8—22no—
394C3×D4—24no—
395C3×D4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4D4×D512yes—
399C2×C3×C4D4×D512yes—
400C2×C3×C4C2×C22⋊D512yes—
401C2×C3×C4C2×C22⋊D511yescharacteristic
402C2×C3×C4C23×D511yescharacteristic
403#67—84no—
404#67—108no—
405#67—104no—
406C2×Dic3—22no—
407C2×Dic3—108no—
408C2×Dic3—102no—
409C2×Dic3—101no—
410C2×Dic3—104no—
411D12—22no—
412D12—22no—
413D12—42no—
414D12—52no—
415D12—101no—
416C4×D3—108no—
417C4×D3—104no—
418Dic6—54no—
419Dic6—52no—
420Dic6—108no—
421Dic6—101no—
422Dic6—102no—
423Dic6—104no—
424C3×C8—102no—
425C3×C8—102no—
426C22×C5—22no—
427C22×C5—22no—
428C22×C5—24no—
429C22×C5—122no—
430C22×C5—124no—
431C22×C5—244no—
432C22×C5#88212yes—
433C22×C5C22×D1211yescharacteristic
434C2×D5—62no—
435C2×D5—122no—
436C4×C5—22no—
437C4×C5—122no—
438C4×C5#88212yes—
439C4×C5C2×D3×D411yescharacteristic
440C4×C5C2×D3×D411yescharacteristic
441Dic5—64no—
442Dic5—62no—
443C24—61no—
444#41—22no—
445#41—22no—
446#41—154no—
447#41—304no—
448#41—304no—
449#41—3016no—
450#41—308no—
451#41—302no—
452C2×Q8—154no—
453C2×Q8—152no—
454C2×Q8—151no—
455C2×Q8—304no—
456C2×Q8—304no—
457C2×Q8—308no—
458C2×Q8—302no—
459C2×Q8—301no—
460C2×Q8—302no—
461C2×Q8#120311yescharacteristic
462C2×D4—32no—
463C2×D4—64no—
464C2×D4—61no—
465C2×D4—62no—
466C2×D4—62no—
467C2×D4—151no—
468C2×D4—302no—
469C2×D4—301no—
470C2×D4#120312yes—
471C2×D4#120311yescharacteristic
472C22×C4—302no—
473C22×C4—301no—
474C22×C4—302no—
475C22×C4—301no—
476C22×C4C2×D3×D512yes—
477C22×C4C2×D3×D511yescharacteristic
478SD16—308no—
479SD16—304no—
480D8—304no—
481M16—102no—
482C2×C8—52no—
483C2×C8—52no—
484C2×C8—102no—
485C4⋊C4—32no—
486C22⋊C4—61no—
487C22⋊C4—64no—
488C42—61no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—24no—
493C22×C3#408312yes—
494C22×C3C22×C22⋊D511yescharacteristic
495C2×D3—42no—
496C2×D3—44no—
497C2×D3—84no—
498C2×D3—102no—
499C2×D3—202no—
500C3×C4—22no—
501C3×C4#408312yes—
502C3×C4C2×D4×D511yescharacteristic
503C3×C4C2×D4×D511yescharacteristic
504Dic3—42no—
505Dic3—104no—
506Dic3—102no—
507C2×C5—22no—
508C2×C5—42no—
509C2×C5—242no—
510C2×C5C2×#88211yescharacteristic
511C2×C5#575112yes—
512D5—122no—
513C23—62no—
514C23—122no—
515C23—242no—
516C23—301no—
517C23C2×#120312yes—
518C23C2×#120311yescharacteristic
519Q8—22no—
520Q8—154no—
521Q8—152no—
522Q8—308no—
523Q8—302no—
524Q8—301no—
525Q8—304no—
526D4—24no—
527D4—22no—
528D4—62no—
529D4—62no—
530D4—122no—
531D4—152no—
532D4—244no—
533D4—308no—
534D4—304no—
535D4—301no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—62no—
539C2×C4—308no—
540C2×C4—308no—
541C2×C4—302no—
542C2×C4—301no—
543C2×C4—304no—
544C2×C4—304no—
545C2×C4C2×#120312yes—
546C2×C4C2×#120311yescharacteristic
547C2×C4#679012yes—
548C2×C4#679012yes—
549C2×C4C22×D3×D511yescharacteristic
550C8—102no—
551C8—102no—
552C2×C3—22no—
553C2×C3—42no—
554C2×C3C2×#408311yescharacteristic
555C2×C3#6617012yes—
556D3—82no—
557D3—202no—
558C5#7867811yescharacteristic, complemented, Sylow
559C22—22no—
560C22—24no—
561C22—22no—
562C22—124no—
563C22—122no—
564C22—244no—
565C22—302no—
566C22—602no—
567C22#9157312yes—
568C22C22×#120311yescharacteristic
569C4—22no—
570C4—122no—
571C4—304no—
572C4—302no—
573C4#9157312yes—
574C4C2×#679011yescharacteristic
575C4C2×#679011yescharacteristic
576C3#1061512111yescharacteristic, complemented, Sylow
577C2—22no—
578C2—42no—
579C2—242no—
580C2—602no—
581C2#1175530712yes—
582C2C2×#9157311yescharacteristic
subgroupG/H
centerC22C22×#1203
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 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#92101C2semidirect
2. C5×#5830C2semidirect
3. C22×#6659C2semidirect
4. C2×#91304C2semidirect
5. C3×#65523C2semidirect
6. #11748553C2semidirect
7. #11748526C2semidirect
8. #11748417C2semidirect
9. #11748393C2semidirect
18. C2×#6817C22semidirect
20. C22×Dic30C22semidirect
34. C3×C22⋊#168C22semidirect
35. #90975C22semidirect
36. #90975C22semidirect
37. #90969C22semidirect
43. #65523D3semidirect
66. #6817D4semidirect
75. C2×Dic30D4semidirect
95. #5830D5semidirect
126. C22⋊#168C2×D3semidirect
489. C3×C5#3010semidirect
558. C5#78678semidirect
576. C3#10615121semidirect

Maximal subgroups

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

subgroupindex
C2×#921012
C5×#58302
C22×#66592
C2×#913042
C3×#655232
#117485532
#117485262
#117484172
#117483932
#106151213
#786785