Finite Group Databasebeta

← #14424487

Subgroups — #14424487

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
2C3×#66164C211yesmaximal, characteristic, complemented
3C2×#91312C211yesmaximal, characteristic, complemented
4C22×#6657C211yesmaximal, characteristic, complemented
5C5×#5234C211yesmaximal, characteristic, complemented
6#11748550C214yesmaximal, complemented
7#11748549C214yesmaximal, complemented
8#11748415C211yesmaximal, characteristic, complemented
9#11748411C211yesmaximal, characteristic, 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×Dic30C2211yescharacteristic
20C22×Dic30C2212yescomplemented
21C22×C3×D20C2211yescharacteristic
22C2×C5×#208C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C3×#4093—21no—
25C3×#4086—21no—
26C3×#4083—22no—
27C3×#4076C2214yes—
28C3×#4072C2211yescharacteristic
29#91312—24no—
30C2×#6657—24no—
31C2×#6657C2214yes—
32C2×#6657C2212yes—
33C2×#6653C2212yes—
34C5×#830C2214yescomplemented
35#90974C2212yescomplemented
36#90974C2214yescomplemented
37#90968C2212yescomplemented
38#83390—51nomaximal, Hall
39C2×#4150—31no—
40#66164D311yescharacteristic, complemented
41C2×#4054—31no—
42C22×#677—31no—
43C5×#408—31no—
44#65409—31no—
45#65402—31no—
46#65027—34no—
47#65023—34no—
48C23×C3×D5—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×C3×C22⋊D5—24no—
79C2×C3×D20—22no—
80C2×C3×D20—22no—
81C2×C3×D20—21no—
82C2×C3×D20C2312yes—
83C5×#208—22no—
84C2×C5×C3⋊C8—22no—
85C2×C5×C3⋊C8C2312yes—
86C2×C5×C3⋊C8C2312yes—
87C3×C22⋊Dic5—21no—
88C3×#685—24no—
89C3×C4⋊Dic5C2312yes—
90C3×C4×Dic5—21no—
91#6657—28no—
92#6657—24no—
93#6653—24no—
94C2×#1010—51no—
95C3×#535—51no—
96C22×#214—51no—
97C2×#932—51no—
98#5234D511yescharacteristic, complemented
99#5040—54no—
100#5037—54no—
101#5004—51no—
102#5002—51no—
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×D20C2×D311yescharacteristic
112C22×Dic10—31no—
113C22×Dic10—32no—
114C2×C5×M16—31no—
115C22×C5×C8—31no—
116#4093—21no—
117#4086—21no—
118#4083—22no—
119#4076C2×D314yes—
120#4072C2×D311yescharacteristic
121#4054—64no—
122C2×D40—32no—
123C2×#677—32no—
124C2×#677—34no—
125C2×#677—64no—
126C5×C22⋊C8—34no—
127#3953—32no—
128#3948—32no—
129#3948—34no—
130#3010—151noSylow
131C23×C3×C5C2×D412yes—
132C23×C3×C5C2×D411yescharacteristic
133C22×D15—21no—
134C22×C3×D5—22no—
135C22×C3×D5—42no—
136C22×C3×D5—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—
163C3×C22⋊D5—84no—
164C2×C3×Dic5—22no—
165C3×D20—22no—
166C3×D20—22no—
167C3×D20—42no—
168C5×C3⋊C8—22no—
169C5×C3⋊C8—22no—
170C2×C3×#41C2×D511yescharacteristic
171C22×C3×D4—51no—
172#1010—104no—
173#1010—104no—
174C2×D3×Q8—101no—
175C2×#237—102no—
176C2×#237—101no—
177C2×#235—51no—
178C2×#235—52no—
179C22×Dic6—51no—
180C22×Dic6—52no—
181C3×#127—101no—
182C3×#124—101no—
183C3×#121—54no—
184C3×#120—102no—
185C3×#117—51no—
186C2×#214—52no—
187C2×#214—54no—
188C2×#214—104no—
189#932—104no—
190C2×#213—52no—
191C2×#208C2×D511yescharacteristic
192C22×C3⋊C8C2×D511yescharacteristic
193#830C2×D514yescomplemented
194#810—52no—
195#810—54no—
196#809—52no—
197C23×D5—21no—
198C5×#41—22no—
199C5×#41—22no—
200C2×C5×Q8#6711yescharacteristic
201C2×C5×D4#6712yes—
202C2×C5×D4#6711yescharacteristic
203C22×C4×C5C22×D312yes—
204C22×C4×C5C22×D311yescharacteristic
205C2×C22⋊D5—24no—
206C2×C22⋊D5—62no—
207C2×C22⋊D5—61no—
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—22no—
218C2×D20—22no—
219C2×D20—21no—
220C2×D20—31no—
221C2×D20C22×D312yes—
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—62no—
231C2×Dic10—61no—
232C5×M16—62no—
233C2×C5×C8—32no—
234C2×C5×C8—32no—
235C2×C5×C8—62no—
236C22⋊Dic5—21no—
237#685—24no—
238C4⋊Dic5C22×D312yes—
239C4×Dic5—21no—
240D40—64no—
241#677—68no—
242#677—64no—
243C2×2−1+4—151no—
244C2×AGL(1,ℤ/8)—151no—
245C22×SD16—151no—
246#535—51no—
247#449—154no—
248#448—154no—
249#419—151no—
250#416—151no—
251#408—31no—
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×C3×D5—42no—
260C2×C3×D5—44no—
261C2×C3×D5—84no—
262C3×C4×C5—22no—
263C3×C4×C5#12012yes—
264C3×C4×C5C22×D411yescharacteristic
265C3×C4×C5C22×D411yescharacteristic
266Dic15—22no—
267Dic15—24no—
268C3×Dic5—42no—
269C24×C3—101no—
270C3×#41—22no—
271C3×#41—22no—
272C2×C3×Q8D2011yescharacteristic
273C2×C3×D4—52no—
274C2×C3×D4—104no—
275C2×C3×D4—101no—
276C2×C3×D4—102no—
277C2×C3×D4—102no—
278C2×C3×D4D2012yes—
279C2×C3×D4D2011yescharacteristic
280C22×C3×C4C22×D512yes—
281C22×C3×C4C22×D511yescharacteristic
282C2×#67—102no—
283C2×#67—101no—
284C22×Dic3—102no—
285C22×Dic3—101no—
286D3×Q8—108no—
287#237—1016no—
288#237—108no—
289#235—54no—
290#235—104no—
291#235—104no—
292#235—102no—
293C2×D12—51no—
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×C4⋊C4—52no—
305C3×C22⋊C4—101no—
306C3×C22⋊C4—104no—
307C3×C42—101no—
308#214—104no—
309#214—108no—
310#213—104no—
311#208—22no—
312C2×C3⋊C8—22no—
313C2×C3⋊C8C22×D512yes—
314C2×C3⋊C8C22×D512yes—
315C23×C5C2×#6712yes—
316C23×C5C2×#6711yescharacteristic
317C22×D5—22no—
318C22×D5—42no—
319C22×D5—61no—
320C22×D5—82no—
321C5×Q8—22no—
322C5×D4—24no—
323C5×D4—22no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5D3×D412yes—
327C2×C4×C5D3×D412yes—
328C2×C4×C5C2×#6712yes—
329C2×C4×C5C2×#6711yescharacteristic
330C2×C4×C5C23×D311yescharacteristic
331C22⋊D5—68no—
332C22⋊D5—64no—
333C22⋊D5—84no—
334C2×Dic5—22no—
335C2×Dic5—68no—
336C2×Dic5—64no—
337C2×Dic5—62no—
338C2×Dic5—61no—
339D20—22no—
340D20—22no—
341D20—32no—
342D20—42no—
343D20—61no—
344C4×D5—68no—
345C4×D5—64no—
346Dic10—34no—
347Dic10—32no—
348Dic10—68no—
349Dic10—64no—
350Dic10—61no—
351Dic10—62no—
352C5×C8—62no—
353C5×C8—62no—
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—51no—
365AGL(1,ℤ/8)—304no—
366C2×SD16—154no—
367C2×SD16—152no—
368C2×SD16—304no—
369C2×D8—152no—
370C2×M16—31no—
371C22×C8—31no—
372#127—101no—
373#124—101no—
374#121—54no—
375#120—102no—
376#117—51no—
377#103—152no—
378#103—154no—
379#102—152no—
380C22⋊C8—34no—
381C2×C3×C5—22no—
382C2×C3×C5—42no—
383C2×C3×C5C2×#12011yescharacteristic
384C2×C3×C5#57712yes—
385D15—42no—
386C3×D5—82no—
387C23×C3—102no—
388C23×C3—202no—
389C23×C3—402no—
390C23×C3C2×D2012yes—
391C23×C3C2×D2011yescharacteristic
392C22×D3—101no—
393C3×Q8—22no—
394C3×D4—24no—
395C3×D4—22no—
396C3×D4—102no—
397C3×D4—102no—
398C3×D4—202no—
399C3×D4—404no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—102no—
403C2×C3×C4C2×D2012yes—
404C2×C3×C4C2×D2011yescharacteristic
405C2×C3×C4D4×D512yes—
406C2×C3×C4D4×D512yes—
407C2×C3×C4C23×D511yescharacteristic
408#67—108no—
409#67—104no—
410C2×Dic3—108no—
411C2×Dic3—102no—
412C2×Dic3—101no—
413C2×Dic3—104no—
414D12—52no—
415D12—101no—
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#93712yes—
430C22×C5C22×#6711yescharacteristic
431C2×D5—42no—
432C2×D5—44no—
433C2×D5—62no—
434C2×D5—84no—
435C2×D5—122no—
436C4×C5—22no—
437C4×C5#93712yes—
438C4×C5C2×D3×D411yescharacteristic
439C4×C5C2×D3×D411yescharacteristic
440Dic5—42no—
441Dic5—64no—
442Dic5—62no—
443C24—101no—
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#120211yescharacteristic
462C2×D4—52no—
463C2×D4—104no—
464C2×D4—101no—
465C2×D4—102no—
466C2×D4—102no—
467C2×D4—151no—
468C2×D4—302no—
469C2×D4—301no—
470C2×D4#120212yes—
471C2×D4#120211yescharacteristic
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—62no—
482C2×C8—32no—
483C2×C8—32no—
484C2×C8—62no—
485C4⋊C4—52no—
486C22⋊C4—101no—
487C22⋊C4—104no—
488C42—101no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—24no—
493C22×C3—202no—
494C22×C3—204no—
495C22×C3—404no—
496C22×C3#402812yes—
497C22×C3C22×D2011yescharacteristic
498C2×D3—102no—
499C2×D3—202no—
500C3×C4—22no—
501C3×C4—202no—
502C3×C4#402812yes—
503C3×C4C2×D4×D511yescharacteristic
504C3×C4C2×D4×D511yescharacteristic
505Dic3—104no—
506Dic3—102no—
507C2×C5—22no—
508C2×C5—42no—
509C2×C5C2×#93711yescharacteristic
510C2×C5#583612yes—
511D5—82no—
512D5—122no—
513C23—102no—
514C23—202no—
515C23—301no—
516C23—402no—
517C23C2×#120212yes—
518C23C2×#120211yescharacteristic
519Q8—22no—
520Q8—154no—
521Q8—152no—
522Q8—308no—
523Q8—302no—
524Q8—301no—
525Q8—304no—
526D4—24no—
527D4—22no—
528D4—102no—
529D4—102no—
530D4—152no—
531D4—202no—
532D4—308no—
533D4—304no—
534D4—301no—
535D4—404no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—102no—
539C2×C4—308no—
540C2×C4—308no—
541C2×C4—302no—
542C2×C4—301no—
543C2×C4—304no—
544C2×C4—304no—
545C2×C4C2×#120212yes—
546C2×C4C2×#120211yescharacteristic
547C2×C4#679012yes—
548C2×C4#679012yes—
549C2×C4C22×D3×D511yescharacteristic
550C8—62no—
551C8—62no—
552C2×C3—22no—
553C2×C3—42no—
554C2×C3—402no—
555C2×C3C2×#402811yescharacteristic
556C2×C3#6608512yes—
557D3—202no—
558C5#8339011yescharacteristic, complemented, Sylow
559C22—22no—
560C22—24no—
561C22—22no—
562C22—204no—
563C22—202no—
564C22—302no—
565C22—404no—
566C22—602no—
567C22#9157212yes—
568C22C22×#120211yescharacteristic
569C4—22no—
570C4—202no—
571C4—304no—
572C4—302no—
573C4#9157212yes—
574C4C2×#679011yescharacteristic
575C4C2×#679011yescharacteristic
576C3#1061040911yescharacteristic, complemented, Sylow
577C2—22no—
578C2—42no—
579C2—402no—
580C2—602no—
581C2#1175530912yes—
582C2C2×#9157211yescharacteristic
subgroupG/H
centerC22C22×#1202
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. C3×#66164C2semidirect
3. C2×#91312C2semidirect
4. C22×#6657C2semidirect
5. C5×#5234C2semidirect
6. #11748550C2semidirect
7. #11748549C2semidirect
8. #11748415C2semidirect
9. #11748411C2semidirect
18. C2×#6817C22semidirect
20. C22×Dic30C22semidirect
34. C5×#830C22semidirect
35. #90974C22semidirect
36. #90974C22semidirect
37. #90968C22semidirect
40. #66164D3semidirect
66. #6817D4semidirect
75. C2×Dic30D4semidirect
98. #5234D5semidirect
193. #830C2×D5semidirect
489. C3×C5#3010semidirect
558. C5#83390semidirect
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
C3×#661642
C2×#913122
C22×#66572
C5×#52342
#117485502
#117485492
#117484152
#117484112
#106104093
#833905