Finite Group Databasebeta

← #14424505

Subgroups — #14424505

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
2C2×C3×#4095C211yesmaximal, characteristic, complemented
3#11754602C211yesmaximal, characteristic, complemented
4C22×#6657C211yesmaximal, characteristic, complemented
5C5×#5233C211yesmaximal, characteristic, complemented
6#11749286C214yesmaximal, complemented
7#11749042C214yesmaximal, complemented
8#11748417C211yesmaximal, characteristic, complemented
9#11748350C211yesmaximal, characteristic, complemented
10#10610567—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12#92101—24no—
13#92101—24no—
14C2×Q8×D15C2212yescomplemented
15C2×#6819—22no—
16C2×#6819C2212yescomplemented
17C2×#6817—21no—
18C2×#6817C2211yescharacteristic
19C22×Dic30—21no—
20C22×Dic30C2211yescharacteristic
21C22×C3×D20C2211yescharacteristic
22C5×#926C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C3×#4095—24no—
25C2×C3×#688C2212yes—
26C2×C3×#686C2212yes—
27C2×C3×#681C2211yescharacteristic
28#91564—22no—
29#91465C2214yes—
30#91458—21no—
31#91364—21no—
32C2×#6657—24no—
33C2×#6657C2214yes—
34C5×#835C2212yescomplemented
35C5×#832C2212yescomplemented
36#90975C2214yescomplemented
37#90957C2214yescomplemented
38#83948—51nomaximal, Hall
39C2×#4150—31no—
40C2×#4095D311yescharacteristic, complemented
41C22×#677—31no—
42#65859—31no—
43C5×#416—31no—
44#65399—31no—
45#65293—31no—
46#65095—34no—
47#65070—34no—
48C23×C3×D5—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×#1220—22no—
57C2×#1220D412yes—
58C22×Dic15—21no—
59C22×Dic15—22no—
60Q8×D15—24no—
61Q8×D15—24no—
62#6819—216no—
63#6819—24no—
64#6819—24no—
65#6817—28no—
66#6817—22no—
67#6817—22no—
68C2×D60D411yescharacteristic
69C2×C4×D15—22no—
70C2×C4×D15C2312yes—
71C2×Dic30—28no—
72C2×Dic30—21no—
73C2×Dic30—22no—
74C2×Dic30—22no—
75C2×Dic30D411yescharacteristic
76C2×Dic30D414yescomplemented
77C2×Dic30C2312yes—
78C2×C3×D20—22no—
79C2×C3×D20—22no—
80C2×C3×D20—21no—
81C2×C3×D20C2312yes—
82C2×#1202—24no—
83C5×#217—21no—
84C5×C4⋊Dic3C2312yes—
85C4×C5×Dic3—21no—
86C2×C5×C3⋊C8—22no—
87C2×C5×C3⋊C8C2312yes—
88C3×#688—24no—
89C3×#686—24no—
90C3×#681—22no—
91C2×C3×#168C2312yes—
92#6665—24no—
93#6657—28no—
94C2×#1010—51no—
95C2×C3×AGL(1,ℤ/8)—51no—
96#5805—51no—
97C22×#214—51no—
98#5233D511yescharacteristic, complemented
99#5170—54no—
100#5158—54no—
101#5129—51no—
102#5120—51no—
103C2×C5×#41C2×D311yescharacteristic
104#4150—64no—
105#4150—64no—
106C2×Q8×D5—32no—
107C2×#711—32no—
108C2×#711—62no—
109C2×#709—31no—
110C2×#709—61no—
111C22×D20C2×D311yescharacteristic
112C22×Dic10—31no—
113C22×Dic10—61no—
114C22×C5×C8—31no—
115C5×#117—31no—
116#4095—24no—
117C2×#688C2×D312yes—
118C2×#686C2×D312yes—
119C2×#681C2×D311yescharacteristic
120C2×#677—34no—
121C2×#677—64no—
122#4041—34no—
123#4028—62no—
124#4021—61no—
125#4020—61no—
126C5×#103—32no—
127C5×#102—32no—
128#3952—34no—
129#3942—34no—
130#3010—151noSylow
131C23×C3×C5—21no—
132C23×C3×C5C2×D411yescharacteristic
133C22×D15C2×D412yes—
134C22×C3×D5—22no—
135C22×C3×D5—42no—
136C22×C3×D5—82no—
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
148#1220—28no—
149#1220—24no—
150C2×Dic15—28no—
151C2×Dic15—24no—
152C2×Dic15—22no—
153C2×Dic15C2×D412yes—
154D60—22no—
155C4×D15—28no—
156C4×D15—22no—
157C4×D15—22no—
158Dic30—28no—
159Dic30—22no—
160Dic30—24no—
161Dic30—22no—
162Dic30C2×D414yes—
163C2×C5×Dic3—22no—
164C3×D20—22no—
165C3×D20—22no—
166C3×D20—42no—
167#1202—84no—
168C3×#168—22no—
169C5×C3⋊C8—22no—
170C2×C3×#41C2×D511yescharacteristic
171C22×C3×D4—51no—
172#1010—104no—
173#1010—104no—
174C2×D3×Q8—52no—
175C2×#237—52no—
176C2×#237—102no—
177C2×#235—51no—
178C2×#235—101no—
179C22×Dic6—51no—
180C22×Dic6—101no—
181C3×AGL(1,ℤ/8)—104no—
182C2×C3×SD16—52no—
183C2×C3×D8—52no—
184C2×C3×M16—51no—
185#953—102no—
186#940—101no—
187#938—54no—
188#936—101no—
189C2×#214—54no—
190C2×#214—104no—
191#926C2×D511yescharacteristic
192C22×C3⋊C8C2×D511yescharacteristic
193#835C2×D512yescomplemented
194#832C2×D512yescomplemented
195(C2×D3)⋊C8—54no—
196#816—54no—
197C23×D5—21no—
198C5×#41—22no—
199C5×#41#6714yescomplemented
200C2×C5×Q8C22×D311yescharacteristic
201C2×C5×D4—21no—
202C2×C5×D4C22×D311yescharacteristic
203C22×C4×C5—21no—
204C22×C4×C5C22×D311yescharacteristic
205C2×C22⋊D5—32no—
206C2×C22⋊D5—62no—
207C22×Dic5—62no—
208C22×Dic5—61no—
209Q8×D5—64no—
210Q8×D5—64no—
211#711—64no—
212#711—616no—
213#711—64no—
214#709—68no—
215#709—62no—
216#709—62no—
217C2×D20—22no—
218C2×D20—22no—
219C2×D20—21no—
220C2×D20—31no—
221C2×D20—64no—
222C2×D20C22×D312yes—
223C2×C4×D5—32no—
224C2×C4×D5—62no—
225C2×Dic10—34no—
226C2×Dic10—32no—
227C2×Dic10—31no—
228C2×Dic10—62no—
229C2×Dic10—68no—
230C2×Dic10—61no—
231C2×Dic10—62no—
232C2×C5×C8—32no—
233C2×C5×C8—62no—
234C5×C4⋊C4—32no—
235C5×C22⋊C4—61no—
236C42×C5—61no—
237#688—24no—
238#686—24no—
239#685—64no—
240#681—22no—
241C2×#168C22×D312yes—
242#677—68no—
243C2×2−1+4—151no—
244C2×AGL(1,ℤ/8)—51no—
245C22×SD16—151no—
246#535—151no—
247#449—154no—
248#448—154no—
249#419—151no—
250#416—31no—
251#408—151no—
252C22×C3×C5—22no—
253C22×C3×C5—22no—
254C22×C3×C5—42no—
255C22×C3×C5#12012yes—
256C22×C3×C5C22×D411yescharacteristic
257C2×D15—22no—
258C2×D15—24no—
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—
268C5×Dic3—42no—
269C24×C3—101no—
270C3×#41—22no—
271C3×#41D2014yescomplemented
272C2×C3×Q8C22×D511yescharacteristic
273C2×C3×D4—21no—
274C2×C3×D4—52no—
275C2×C3×D4—102no—
276C2×C3×D4—102no—
277C2×C3×D4—101no—
278C2×C3×D4C22×D511yescharacteristic
279C22×C3×C4—21no—
280C22×C3×C4C22×D511yescharacteristic
281C2×#67—52no—
282C2×#67—104no—
283C2×#67—102no—
284C22×Dic3—102no—
285C22×Dic3—101no—
286D3×Q8—104no—
287D3×Q8—104no—
288#237—104no—
289#237—1016no—
290#237—104no—
291#235—108no—
292#235—102no—
293#235—102no—
294C2×D12—51no—
295C2×C4×D3—52no—
296C2×C4×D3—102no—
297C2×Dic6—54no—
298C2×Dic6—52no—
299C2×Dic6—51no—
300C2×Dic6—102no—
301C2×Dic6—108no—
302C2×Dic6—102no—
303C2×Dic6—101no—
304C3×SD16—104no—
305C3×D8—104no—
306C3×M16—102no—
307C2×C3×C8—52no—
308#217—21no—
309#217—104no—
310#214—108no—
311C4⋊Dic3C22×D512yes—
312C4×Dic3—21no—
313C2×C3⋊C8—22no—
314C2×C3⋊C8C22×D512yes—
315C23×C5—21no—
316C23×C5D3×D411yescharacteristic
317C22×D5—22no—
318C22×D5—32no—
319C22×D5—42no—
320C22×D5—82no—
321C5×Q8—21no—
322C5×Q8C2×#6712yes—
323C5×D4—24no—
324C5×D4—21no—
325C5×D4C2×#6712yes—
326C2×C4×C5—21no—
327C2×C4×C5—24no—
328C2×C4×C5—62no—
329C2×C4×C5D3×D411yescharacteristic
330C2×C4×C5D3×D412yes—
331C2×C4×C5C2×#6712yes—
332C2×C4×C5C23×D311yescharacteristic
333C22⋊D5—68no—
334C22⋊D5—64no—
335C2×Dic5—32no—
336C2×Dic5—68no—
337C2×Dic5—64no—
338C2×Dic5—62no—
339D20—22no—
340D20—22no—
341D20—42no—
342D20—62no—
343D20—244no—
344C4×D5—68no—
345C4×D5—62no—
346C4×D5—62no—
347Dic10—34no—
348Dic10—68no—
349Dic10—64no—
350Dic10—62no—
351Dic10—62no—
352C5×C8—62no—
353#168—22no—
3542−1+4—304no—
3552−1+4—304no—
356C2×#41—151no—
357C2×#41—152no—
358C2×#41—301no—
359C2×#41—302no—
360C2×#41D3×D511yescharacteristic
361C22×Q8—152no—
362C22×Q8—151no—
363C22×Q8—301no—
364C22×D4—51no—
365AGL(1,ℤ/8)—104no—
366C2×SD16—52no—
367C2×SD16—154no—
368C2×SD16—304no—
369C2×D8—52no—
370C2×M16—51no—
371C22×C8—31no—
372#127—301no—
373#124—301no—
374#121—154no—
375#120—302no—
376#117—31no—
377#103—32no—
378#103—154no—
379#102—32no—
380C22⋊C8—154no—
381C2×C3×C5—22no—
382C2×C3×C5—42no—
383C2×C3×C5C2×#12011yescharacteristic
384C2×C3×C5#57712yes—
385D15—42no—
386C3×D5—82no—
387C23×C3—21no—
388C23×C3—102no—
389C23×C3—202no—
390C23×C3—402no—
391C23×C3D4×D511yescharacteristic
392C22×D3—52no—
393C3×Q8—21no—
394C3×Q8C2×D2012yes—
395C3×D4—24no—
396C3×D4—21no—
397C3×D4—102no—
398C3×D4—102no—
399C3×D4—202no—
400C3×D4C2×D2012yes—
401C2×C3×C4—21no—
402C2×C3×C4—24no—
403C2×C3×C4C2×D2012yes—
404C2×C3×C4D4×D512yes—
405C2×C3×C4D4×D511yescharacteristic
406C2×C3×C4C23×D511yescharacteristic
407#67—108no—
408#67—104no—
409#67—404no—
410C2×Dic3—22no—
411C2×Dic3—52no—
412C2×Dic3—108no—
413C2×Dic3—102no—
414C2×Dic3—104no—
415D12—102no—
416C4×D3—108no—
417C4×D3—102no—
418C4×D3—102no—
419Dic6—54no—
420Dic6—108no—
421Dic6—102no—
422Dic6—104no—
423Dic6—102no—
424C3×C8—102no—
425C3⋊C8—22no—
426C22×C5—22no—
427C22×C5—22no—
428C22×C5—42no—
429C22×C5#93712yes—
430C22×C5C2×D3×D411yescharacteristic
431C2×D5—44no—
432C2×D5—42no—
433C2×D5—64no—
434C2×D5—62no—
435C2×D5—84no—
436C4×C5—22no—
437C4×C5—122no—
438C4×C5#93712yes—
439C4×C5C2×D3×D411yescharacteristic
440C4×C5C22×#6711yescharacteristic
441Dic5—64no—
442Dic5—62no—
443C24—101no—
444#41—22no—
445#41—308no—
446#41—304no—
447#41—3016no—
448#41—304no—
449#41—302no—
450#41—302no—
451#41#120214yescomplemented
452C2×Q8—151no—
453C2×Q8—154no—
454C2×Q8—152no—
455C2×Q8—302no—
456C2×Q8—308no—
457C2×Q8—304no—
458C2×Q8—304no—
459C2×Q8—302no—
460C2×Q8—301no—
461C2×Q8C2×D3×D511yescharacteristic
462C2×D4—21no—
463C2×D4—52no—
464C2×D4—102no—
465C2×D4—102no—
466C2×D4—101no—
467C2×D4—152no—
468C2×D4—151no—
469C2×D4—304no—
470C2×D4—302no—
471C2×D4C2×D3×D511yescharacteristic
472C22×C4—21no—
473C22×C4—152no—
474C22×C4—302no—
475C22×C4—302no—
476C22×C4—301no—
477C22×C4C2×D3×D511yescharacteristic
478SD16—104no—
479SD16—308no—
480D8—104no—
481M16—102no—
482C2×C8—32no—
483C2×C8—52no—
484C2×C8—62no—
485C4⋊C4—32no—
486C22⋊C4—61no—
487C22⋊C4—304no—
488C42—61no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—42no—
493C22×C3—202no—
494C22×C3—204no—
495C22×C3—404no—
496C22×C3#402812yes—
497C22×C3C2×D4×D511yescharacteristic
498C2×D3—102no—
499C2×D3—104no—
500C3×C4—22no—
501C3×C4#402812yes—
502C3×C4C22×D2011yescharacteristic
503C3×C4C2×D4×D511yescharacteristic
504Dic3—42no—
505Dic3—104no—
506Dic3—102no—
507C2×C5—22no—
508C2×C5—42no—
509C2×C5#577512yes—
510C2×C5C2×#93711yescharacteristic
511D5—82no—
512D5—122no—
513C23—21no—
514C23—102no—
515C23—152no—
516C23—202no—
517C23—402no—
518C23#679011yescharacteristic
519Q8—21no—
520Q8—154no—
521Q8—308no—
522Q8—302no—
523Q8—302no—
524Q8—304no—
525Q8C2×#120212yes—
526D4—24no—
527D4—21no—
528D4—102no—
529D4—102no—
530D4—202no—
531D4—308no—
532D4—304no—
533D4—302no—
534D4—1204no—
535D4C2×#120212yes—
536C2×C4—21no—
537C2×C4—24no—
538C2×C4—62no—
539C2×C4—152no—
540C2×C4—308no—
541C2×C4—308no—
542C2×C4—302no—
543C2×C4—304no—
544C2×C4—302no—
545C2×C4—302no—
546C2×C4C2×#120212yes—
547C2×C4#679012yes—
548C2×C4#679011yescharacteristic
549C2×C4C22×D3×D511yescharacteristic
550C8—62no—
551C8—102no—
552C2×C3—22no—
553C2×C3—42no—
554C2×C3—402no—
555C2×C3C2×#402811yescharacteristic
556C2×C3#6610412yes—
557D3—202no—
558C5#8394811yescharacteristic, complemented, Sylow
559C22—22no—
560C22—22no—
561C22—42no—
562C22—204no—
563C22—202no—
564C22—304no—
565C22—302no—
566C22—404no—
567C22#9157212yes—
568C22C2×#679011yescharacteristic
569C4—22no—
570C4—122no—
571C4—302no—
572C4—304no—
573C4#9157212yes—
574C4C22×#120211yescharacteristic
575C4C2×#679011yescharacteristic
576C3#1061056711yescharacteristic, complemented, Sylow
577C2—22no—
578C2—42no—
579C2—402no—
580C2—602no—
581C2#1175533112yes—
582C2C2×#9157211yescharacteristic
subgroupG/H
centerC22C2×#6790
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×#92101C2semidirect
2. C2×C3×#4095C2semidirect
3. #11754602C2semidirect
4. C22×#6657C2semidirect
5. C5×#5233C2semidirect
6. #11749286C2semidirect
7. #11749042C2semidirect
8. #11748417C2semidirect
9. #11748350C2semidirect
14. C2×Q8×D15C22semidirect
16. C2×#6819C22semidirect
34. C5×#835C22semidirect
35. C5×#832C22semidirect
36. #90975C22semidirect
37. #90957C22semidirect
40. C2×#4095D3semidirect
50. C3×C5×#41D4semidirect
76. C2×Dic30D4semidirect
98. #5233D5semidirect
193. #835C2×D5semidirect
194. #832C2×D5semidirect
199. C5×#41#67semidirect
271. C3×#41D20semidirect
451. #41#1202semidirect
489. C3×C5#3010semidirect
558. C5#83948semidirect
576. C3#10610567semidirect

Maximal subgroups

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

subgroupindex
C2×#921012
C2×C3×#40952
#117546022
C22×#66572
C5×#52332
#117492862
#117490422
#117484172
#117483502
#106105673
#839485