Finite Group Databasebeta

← #14424437

Subgroups — #14424437

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
2#11756589C211yesmaximal, characteristic, complemented
3C2×#91797C211yesmaximal, characteristic, complemented
4C22×#6706C211yesmaximal, characteristic, complemented
5C3×C5×#408C211yesmaximal, characteristic, complemented
6#11751221C211yesmaximal, characteristic, complemented
7#11751214C211yesmaximal, characteristic, complemented
8#11750839C214yesmaximal, complemented
9#11750835C214yesmaximal, complemented
10#10610409—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×D60C2211yescharacteristic
20C22×Dic30C2211yescharacteristic
21C22×Dic30C2212yescomplemented
22C2×C3×C5×M16C2211yescharacteristic
23C22×C3×C5×C8C2211yescharacteristic
24#91836—21no—
25#91829—21no—
26#91826—22no—
27#91819C2214yes—
28#91815C2211yescharacteristic
29#91797—24no—
30C2×D120C2212yes—
31C2×#6706—24no—
32C2×#6706C2214yes—
33C2×#6706C2212yes—
34C3×C5×C22⋊C8C2214yescomplemented
35#91105C2212yescomplemented
36#91100C2212yescomplemented
37#91100C2214yescomplemented
38#78678—51nomaximal, Hall
39C2×#4150—31no—
40#66164—31no—
41C2×#4054—31no—
42C22×#677—31no—
43C5×#408D311yescharacteristic, complemented
44#65409—31no—
45#65402—31no—
46#65027—34no—
47#65023—34no—
48C23×D15—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—
58C2×#1220—24no—
59C22×Dic15—21no—
60C22×Dic15—22no—
61Q8×D15—28no—
62#6819—216no—
63#6819—28no—
64#6817—22no—
65#6817—24no—
66#6817—24no—
67#6817D414yescomplemented
68C2×D60—22no—
69C2×D60—22no—
70C2×D60—21no—
71C2×D60C2312yes—
72C2×D60C2311yescharacteristic
73C2×C4×D15—21no—
74C2×C4×D15—22no—
75C2×Dic30—21no—
76C2×Dic30—22no—
77C2×Dic30—22no—
78C2×Dic30—24no—
79C2×Dic30—24no—
80C2×Dic30D414yescomplemented
81C2×Dic30C2312yes—
82C2×Dic30C2311yescharacteristic
83C3×C5×M16—22no—
84C2×C3×C5×C8—22no—
85C2×C3×C5×C8C2312yes—
86C2×C3×C5×C8C2312yes—
87#6719—21no—
88#6714—24no—
89C4⋊Dic15C2312yes—
90C4×Dic15—21no—
91D120—24no—
92#6706—28no—
93#6706—24no—
94C2×#1010—51no—
95#5830—51no—
96C2×#908—51no—
97C22×#204—51no—
98C3×#408D511yescharacteristic, complemented
99#5120—51no—
100#5113—51no—
101#4738—54no—
102#4734—54no—
103C2×C5×#41C2×D311yescharacteristic
104#4150—64no—
105#4150—64no—
106C2×Q8×D5—61no—
107C2×#711—62no—
108C2×#711—61no—
109C2×#709—31no—
110C2×#709—32no—
111C22×D20—31no—
112C22×Dic10—31no—
113C22×Dic10—32no—
114C2×C5×M16C2×D311yescharacteristic
115C22×C5×C8C2×D311yescharacteristic
116#4093—61no—
117#4086—61no—
118#4083—62no—
119#4076—34no—
120#4072—31no—
121#4054—64no—
122C2×D40—32no—
123C2×#677—32no—
124C2×#677—34no—
125C2×#677—64no—
126C5×C22⋊C8C2×D314yescomplemented
127#3953—32no—
128#3948—32no—
129#3948—34no—
130#3010—151noSylow
131C23×C3×C5C2×D412yes—
132C23×C3×C5C2×D411yescharacteristic
133C22×D15—21no—
134C22×D15—22no—
135C22×D15—42no—
136C22×D15—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—
149#1220—84no—
150C2×Dic15—28no—
151C2×Dic15—24no—
152C2×Dic15—22no—
153C2×Dic15—21no—
154C2×Dic15—22no—
155D60—21no—
156D60—22no—
157D60—22no—
158D60—42no—
159D60C2×D412yes—
160C4×D15—28no—
161C4×D15—24no—
162Dic30—28no—
163Dic30—24no—
164Dic30—22no—
165Dic30—21no—
166Dic30C2×D412yes—
167Dic30C2×D414yes—
168C3×C5×C8—22no—
169C3×C5×C8—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×D12—51no—
179C22×Dic6—51no—
180C22×Dic6—52no—
181C2×C3×M16C2×D511yescharacteristic
182C22×C3×C8C2×D511yescharacteristic
183#947—101no—
184#940—101no—
185#937—102no—
186#930—54no—
187#926—51no—
188#908—104no—
189C2×D24—52no—
190C2×#204—54no—
191C2×#204—52no—
192C2×#204—104no—
193C3×C22⋊C8C2×D514yescomplemented
194#821—52no—
195#816—54no—
196#816—52no—
197C23×D5—61no—
198C5×#41—22no—
199C5×#41—22no—
200C2×C5×Q8D1211yescharacteristic
201C2×C5×D4D1212yes—
202C2×C5×D4D1211yescharacteristic
203C22×C4×C5C22×D312yes—
204C22×C4×C5C22×D311yescharacteristic
205C2×C22⋊D5—62no—
206C2×C22⋊D5—61no—
207C2×C22⋊D5—64no—
208C22×Dic5—62no—
209C22×Dic5—61no—
210Q8×D5—68no—
211#711—616no—
212#711—68no—
213#709—34no—
214#709—64no—
215#709—64no—
216#709—62no—
217C2×D20—31no—
218C2×D20—32no—
219C2×D20—62no—
220C2×D20—62no—
221C2×D20—61no—
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×M16—22no—
233C2×C5×C8—22no—
234C2×C5×C8C22×D312yes—
235C2×C5×C8C22×D312yes—
236C22⋊Dic5—61no—
237#685—64no—
238C4⋊Dic5—32no—
239C4×Dic5—61no—
240D40—64no—
241#677—68no—
242#677—64no—
243C2×2−1+4—151no—
244C2×AGL(1,ℤ/8)—151no—
245C22×SD16—151no—
246#535—151no—
247#449—154no—
248#448—154no—
249#419—151no—
250#416—151no—
251#408D1511yescharacteristic, complemented
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×D15—42no—
260C2×D15—44no—
261C2×D15—84no—
262C3×C4×C5—22no—
263C3×C4×C5#12012yes—
264C3×C4×C5C22×D411yescharacteristic
265C3×C4×C5C22×D411yescharacteristic
266Dic15—22no—
267Dic15—24no—
268Dic15—42no—
269C23×D3—101no—
270C3×#41—22no—
271C3×#41—22no—
272C2×C3×Q8D2011yescharacteristic
273C2×C3×D4D2012yes—
274C2×C3×D4D2011yescharacteristic
275C22×C3×C4C22×D512yes—
276C22×C3×C4C22×D511yescharacteristic
277C2×#67—102no—
278C2×#67—101no—
279C2×#67—104no—
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—51no—
290C2×D12—52no—
291C2×D12—102no—
292C2×D12—102no—
293C2×D12—101no—
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—101no—
303C2×Dic6—102no—
304C3×M16—22no—
305C2×C3×C8—22no—
306C2×C3×C8C22×D512yes—
307C2×C3×C8C22×D512yes—
308#217—101no—
309(C2×D3)⋊C4—104no—
310C4⋊Dic3—52no—
311C4×Dic3—101no—
312D24—104no—
313#204—108no—
314#204—104no—
315C23×C5C2×D1212yes—
316C23×C5C2×D1211yescharacteristic
317C22×D5—61no—
318C22×D5—62no—
319C22×D5—122no—
320C22×D5—242no—
321C5×Q8—22no—
322C5×D4—24no—
323C5×D4—22no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5C2×D1212yes—
327C2×C4×C5C2×D1211yescharacteristic
328C2×C4×C5D3×D412yes—
329C2×C4×C5D3×D412yes—
330C2×C4×C5C23×D311yescharacteristic
331C22⋊D5—68no—
332C22⋊D5—64no—
333C22⋊D5—244no—
334C2×Dic5—68no—
335C2×Dic5—64no—
336C2×Dic5—62no—
337C2×Dic5—61no—
338C2×Dic5—62no—
339D20—32no—
340D20—61no—
341D20—62no—
342D20—62no—
343D20—122no—
344C4×D5—68no—
345C4×D5—64no—
346Dic10—34no—
347Dic10—32no—
348Dic10—68no—
349Dic10—64no—
350Dic10—61no—
351Dic10—62no—
352C5×C8—22no—
353C5×C8—22no—
3542−1+4—304no—
3552−1+4—304no—
356C2×#41—151no—
357C2×#41—152no—
358C2×#41—302no—
359C2×#41—301no—
360C2×#41C2×D1511yescharacteristic
361C22×Q8—151no—
362C22×Q8—152no—
363C22×Q8—301no—
364C22×D4—151no—
365AGL(1,ℤ/8)—304no—
366C2×SD16—154no—
367C2×SD16—152no—
368C2×SD16—304no—
369C2×D8—152no—
370C2×M16C2×D1511yescharacteristic
371C22×C8C2×D1511yescharacteristic
372#127—301no—
373#124—301no—
374#121—154no—
375#120—302no—
376#117—151no—
377#103—152no—
378#103—154no—
379#102—152no—
380C22⋊C8C2×D1514yescomplemented
381C2×C3×C5—22no—
382C2×C3×C5—42no—
383C2×C3×C5C2×#12011yescharacteristic
384C2×C3×C5#57712yes—
385D15—42no—
386D15—82no—
387C23×C3C2×D2012yes—
388C23×C3C2×D2011yescharacteristic
389C22×D3—101no—
390C22×D3—102no—
391C22×D3—202no—
392C22×D3—402no—
393C3×Q8—22no—
394C3×D4—24no—
395C3×D4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4C2×D2012yes—
399C2×C3×C4C2×D2011yescharacteristic
400C2×C3×C4D4×D512yes—
401C2×C3×C4D4×D512yes—
402C2×C3×C4C23×D511yescharacteristic
403#67—108no—
404#67—104no—
405#67—404no—
406C2×Dic3—108no—
407C2×Dic3—102no—
408C2×Dic3—101no—
409C2×Dic3—104no—
410C2×Dic3—102no—
411D12—52no—
412D12—101no—
413D12—102no—
414D12—102no—
415D12—202no—
416C4×D3—108no—
417C4×D3—104no—
418Dic6—54no—
419Dic6—52no—
420Dic6—108no—
421Dic6—101no—
422Dic6—102no—
423Dic6—104no—
424C3×C8—22no—
425C3×C8—22no—
426C22×C5—22no—
427C22×C5—22no—
428C22×C5—24no—
429C22×C5#88212yes—
430C22×C5C22×D1211yescharacteristic
431C2×D5—62no—
432C2×D5—122no—
433C2×D5—122no—
434C2×D5—124no—
435C2×D5—244no—
436C4×C5—22no—
437C4×C5#88212yes—
438C4×C5C2×D3×D411yescharacteristic
439C4×C5C2×D3×D411yescharacteristic
440Dic5—64no—
441Dic5—62no—
442Dic5—122no—
443C24—301no—
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×Q8D6011yescharacteristic
462C2×D4—151no—
463C2×D4—152no—
464C2×D4—302no—
465C2×D4—301no—
466C2×D4—304no—
467C2×D4—301no—
468C2×D4—302no—
469C2×D4—302no—
470C2×D4D6012yes—
471C2×D4D6011yescharacteristic
472C22×C4—302no—
473C22×C4—301no—
474C22×C4—302no—
475C22×C4—301no—
476C22×C4C22×D1512yes—
477C22×C4C22×D1511yescharacteristic
478SD16—308no—
479SD16—304no—
480D8—304no—
481M16—22no—
482C2×C8—22no—
483C2×C8C22×D1512yes—
484C2×C8C22×D1512yes—
485C4⋊C4—152no—
486C22⋊C4—301no—
487C22⋊C4—304no—
488C42—301no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—24no—
493C22×C3#402812yes—
494C22×C3C22×D2011yescharacteristic
495C2×D3—102no—
496C2×D3—202no—
497C2×D3—202no—
498C2×D3—204no—
499C2×D3—404no—
500C3×C4—22no—
501C3×C4#402812yes—
502C3×C4C2×D4×D511yescharacteristic
503C3×C4C2×D4×D511yescharacteristic
504Dic3—104no—
505Dic3—102no—
506Dic3—202no—
507C2×C5—22no—
508C2×C5—42no—
509C2×C5C2×#88211yescharacteristic
510C2×C5#575112yes—
511D5—122no—
512D5—242no—
513C23—301no—
514C23—302no—
515C23—602no—
516C23—1202no—
517C23C2×D6012yes—
518C23C2×D6011yescharacteristic
519Q8—22no—
520Q8—154no—
521Q8—152no—
522Q8—308no—
523Q8—304no—
524Q8—302no—
525Q8—301no—
526D4—24no—
527D4—22no—
528D4—152no—
529D4—308no—
530D4—304no—
531D4—301no—
532D4—302no—
533D4—302no—
534D4—602no—
535D4—1204no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—308no—
539C2×C4—308no—
540C2×C4—304no—
541C2×C4—302no—
542C2×C4—301no—
543C2×C4—304no—
544C2×C4—302no—
545C2×C4C2×D6012yes—
546C2×C4C2×D6011yescharacteristic
547C2×C4D4×D1512yes—
548C2×C4D4×D1512yes—
549C2×C4C23×D1511yescharacteristic
550C8—22no—
551C8—22no—
552C2×C3—22no—
553C2×C3—42no—
554C2×C3C2×#402811yescharacteristic
555C2×C3#6608512yes—
556D3—202no—
557D3—402no—
558C5#7867811yescharacteristic, complemented, Sylow
559C22—22no—
560C22—22no—
561C22—24no—
562C22—302no—
563C22—602no—
564C22—602no—
565C22—604no—
566C22—1204no—
567C22#9177112yes—
568C22C22×D6011yescharacteristic
569C4—22no—
570C4—304no—
571C4—302no—
572C4—602no—
573C4#9177112yes—
574C4C2×D4×D1511yescharacteristic
575C4C2×D4×D1511yescharacteristic
576C3#1061040911yescharacteristic, complemented, Sylow
577C2—22no—
578C2—42no—
579C2—602no—
580C2—1202no—
581C2C2×#9177111yescharacteristic
582C2#1175651012yes—
subgroupG/H
centerC22C22×D60
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#408C2
socleC22×C3×C5C22×D4
hypercenter#408D15
hypocenterC3×C5#3010
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C2×#92101C2semidirect
2. #11756589C2semidirect
3. C2×#91797C2semidirect
4. C22×#6706C2semidirect
5. C3×C5×#408C2semidirect
6. #11751221C2semidirect
7. #11751214C2semidirect
8. #11750839C2semidirect
9. #11750835C2semidirect
18. C2×#6817C22semidirect
21. C22×Dic30C22semidirect
34. C3×C5×C22⋊C8C22semidirect
35. #91105C22semidirect
36. #91100C22semidirect
37. #91100C22semidirect
43. C5×#408D3semidirect
67. #6817D4semidirect
80. C2×Dic30D4semidirect
98. C3×#408D5semidirect
126. C5×C22⋊C8C2×D3semidirect
193. C3×C22⋊C8C2×D5semidirect
251. #408D15semidirect
380. C22⋊C8C2×D15semidirect
489. C3×C5#3010semidirect
558. C5#78678semidirect
576. C3#10610409semidirect

Maximal subgroups

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

subgroupindex
C2×#921012
#117565892
C2×#917972
C22×#67062
C3×C5×#4082
#117512212
#117512142
#117508392
#117508352
#106104093
#786785