Finite Group Databasebeta

← #14424493

Subgroups — #14424493

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×#92004C211yesmaximal, characteristic, complemented
2C22×C3×#677C211yesmaximal, characteristic, complemented
3#11754602C211yesmaximal, characteristic, complemented
4C2×#91298C211yesmaximal, characteristic, complemented
5#11751211C211yesmaximal, characteristic, complemented
6C5×#5113C211yesmaximal, characteristic, complemented
7#11748399C211yesmaximal, characteristic, complemented
8#11747891C214yesmaximal, complemented
9#11747889C214yesmaximal, complemented
10#10610567—31nomaximal, Hall
11C2×#6817C2211yescharacteristic
12C2×C5×#235C2211yescharacteristic
13C22×C3×D20C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic
15C2×#6782—22no—
16C2×D15⋊Q8C2212yescomplemented
17C2×#6769—21no—
18#92004—24no—
19#92004—24no—
20C2×#6768C2212yescomplemented
21C2×D3×Dic10—21no—
22C22×C3×C5×C8C2211yescharacteristic
23C2×#6710C2211yescharacteristic
24C5×#926C2211yescharacteristic
25C2×C3×#677—24no—
26C2×C3×#677C2214yes—
27#91564—22no—
28#91465C2214yes—
29#91458—21no—
30#91364—21no—
31C2×#6655C2212yes—
32#91298—24no—
33C2×#6652C2212yes—
34#91104C2214yescomplemented
35C5×#821C2212yescomplemented
36C5×#816C2212yescomplemented
37#90970C2214yescomplemented
38#83860—51nomaximal, Hall
39C2×#4150—31no—
40C2×#4095—31no—
41C22×#677D311yescharacteristic, complemented
42#65859—31no—
43C5×#416—31no—
44#65399—31no—
45#65293—31no—
46#65095—34no—
47#65070—34no—
48C23×C3×D5—21no—
49C22×C3×C4×C5C2311yescharacteristic
50C2×#1220D412yes—
51#6817—22no—
52#6817—22no—
53C2×D60D411yescharacteristic
54C2×C4×D15C2312yes—
55C2×Dic30D411yescharacteristic
56C2×C5×#67—21no—
57C5×#235—22no—
58C5×#235D414yescomplemented
59C2×C5×D12C2311yescharacteristic
60C2×C4×C5×D3—21no—
61C2×C5×Dic6C2311yescharacteristic
62C22×C3×Dic5—21no—
63C2×C3×D20—22no—
64C2×C3×D20—22no—
65C2×C3×D20—21no—
66C2×C3×D20C2312yes—
67C2×C3×Dic10—21no—
68C2×C3×Dic10—22no—
69C2×C3×Dic10D414yescomplemented
70C2×C3×Dic10C2312yes—
71C2×#1204—22no—
72C2×#1203—22no—
73C2×#1202—24no—
74C2×#1200—22no—
75#6782—216no—
76C2×D3×Dic5—22no—
77D15⋊Q8—24no—
78D15⋊Q8—24no—
79#6769—28no—
80#6768—24no—
81#6768—24no—
82D3×Dic10—28no—
83C2×C3×C5×C8—22no—
84C2×C3×C5×C8C2312yes—
85#6710—22no—
86C2×C3⋊#168C2312yes—
87C5×#217—21no—
88C5×C4⋊Dic3C2312yes—
89C4×C5×Dic3—21no—
90C3×#677—28no—
91#6665—24no—
92#6655—24no—
93#6652—24no—
94C2×#1007—51no—
95C22×C3×SD16—51no—
96#5805—51no—
97C2×#932—51no—
98#5225—51no—
99#5172—54no—
100#5170—54no—
101#5113D511yescharacteristic, complemented
102#5110—51no—
103C2×C5×#41—31no—
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—61no—
113C22×Dic10C2×D311yescharacteristic
114C22×C5×C8C2×D311yescharacteristic
115C5×#117—31no—
116#4095—64no—
117C2×#688—32no—
118C2×#686—32no—
119C2×#681—31no—
120C2×#677—24no—
121C2×#677C2×D314yes—
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×C5C2×D411yescharacteristic
132C22×D15C2×D412yes—
133C22×C5×D3—21no—
134C22×C3×D5—22no—
135C22×C3×D5—42no—
136C22×C3×D5—82no—
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D412yes—
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2411yescharacteristic
141#1220—24no—
142C2×Dic15C2×D412yes—
143D60—22no—
144C4×D15—22no—
145C4×D15—22no—
146Dic30—22no—
147C5×#67—24no—
148C2×C5×Dic3—21no—
149C2×C5×Dic3—22no—
150C5×D12—21no—
151C5×D12C2×D412yes—
152C4×C5×D3—24no—
153C5×Dic6—21no—
154C5×Dic6C2×D412yes—
155C2×C3×Dic5—24no—
156C2×C3×Dic5—22no—
157C3×D20—22no—
158C3×D20—22no—
159C3×D20—42no—
160C3×Dic10—24no—
161C3×Dic10—22no—
162C3×Dic10C2×D414yes—
163#1204—28no—
164#1203—28no—
165#1202—84no—
166#1200—28no—
167D3×Dic5—28no—
168C3×C5×C8—22no—
169C3⋊#168—22no—
170C22×C3×Q8—51no—
171C22×C3×D4—51no—
172#1007—104no—
173#1007—104no—
174C2×#239—52no—
175C2×#239—101no—
176C2×D3×Q8—52no—
177C2×D3×Q8—101no—
178C2×#235—51no—
179C2×#235—102no—
180C2×#235C2×D511yescharacteristic
181C2×C3×SD16—54no—
182C2×C3×SD16—104no—
183C22×C3×C8C2×D511yescharacteristic
184#953—102no—
185#940—101no—
186#938—54no—
187#936—101no—
188C2×#214—52no—
189#932—104no—
190C2×#213—52no—
191#926C2×D511yescharacteristic
192C2×#208—51no—
193#835—54no—
194#821C2×D512yescomplemented
195(C2×D3)⋊C8—54no—
196#816C2×D512yescomplemented
197C23×D5—21no—
198C5×#41—34no—
199C5×#41—62no—
200C2×C5×Q8—31no—
201C2×C5×D4—31no—
202C2×C5×D4—61no—
203C22×C4×C5—61no—
204C22×C4×C5C22×D311yescharacteristic
205C2×C22⋊D5—32no—
206C2×C22⋊D5—62no—
207C22×Dic5—21no—
208C22×Dic5—62no—
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—21no—
226C2×Dic10—22no—
227C2×Dic10—31no—
228C2×Dic10—68no—
229C2×Dic10—62no—
230C2×Dic10#6714yescomplemented
231C2×Dic10C22×D312yes—
232C2×C5×C8—22no—
233C2×C5×C8C22×D312yes—
234C5×C4⋊C4—32no—
235C5×C22⋊C4—61no—
236C42×C5—61no—
237#688—64no—
238#686—64no—
239#685—64no—
240#681—62no—
241C2×#168—32no—
242#677—28no—
243C2×2−1+4—151no—
244C2×AGL(1,ℤ/8)—151no—
245C22×SD16—51no—
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#12012yes—
254C22×C3×C5C22×D411yescharacteristic
255C2×D15—22no—
256C2×D15—24no—
257C2×C5×D3—22no—
258C2×C5×D3—42no—
259C2×C3×D5—42no—
260C2×C3×D5—44no—
261C2×C3×D5—84no—
262C3×C4×C5#12012yes—
263C3×C4×C5C22×D411yescharacteristic
264C3×C4×C5C22×D411yescharacteristic
265Dic15—22no—
266C3×Dic5—24no—
267C5×Dic3—22no—
268C5×Dic3—42no—
269C24×C3—101no—
270C2×C3×Q8—54no—
271C2×C3×Q8—52no—
272C2×C3×Q8—102no—
273C2×C3×Q8—101no—
274C2×C3×D4—52no—
275C2×C3×D4—102no—
276C2×C3×D4—102no—
277C2×C3×D4—101no—
278C22×C3×C4—101no—
279C22×C3×C4C22×D511yescharacteristic
280C2×#67—21no—
281C2×#67—52no—
282C2×#67—104no—
283#239—108no—
284#239—104no—
285#239—104no—
286D3×Q8—104no—
287D3×Q8—108no—
288D3×Q8—104no—
289#235—22no—
290#235—1016no—
291#235—102no—
292#235—102no—
293#235D2014yescomplemented
294C2×D12—51no—
295C2×D12—102no—
296C2×D12C22×D511yescharacteristic
297C2×C4×D3—21no—
298C2×C4×D3—52no—
299C2×C4×D3—102no—
300C2×C4×D3—102no—
301C2×Dic6—51no—
302C2×Dic6—102no—
303C2×Dic6C22×D511yescharacteristic
304C3×SD16—108no—
305C2×C3×C8—22no—
306C2×C3×C8C22×D512yes—
307#217—21no—
308#217—104no—
309#214—104no—
310#213—104no—
311C4⋊Dic3C22×D512yes—
312C4×Dic3—21no—
313#208—102no—
314C2×C3⋊C8—52no—
315C23×C5—61no—
316C23×C5D3×D411yescharacteristic
317C22×D5—22no—
318C22×D5—32no—
319C22×D5—42no—
320C22×D5—82no—
321C5×Q8—32no—
322C5×Q8—61no—
323C5×D4—32no—
324C5×D4—64no—
325C5×D4—61no—
326C2×C4×C5—61no—
327C2×C4×C5—64no—
328C2×C4×C5—62no—
329C2×C4×C5D3×D412yes—
330C2×C4×C5D3×D411yescharacteristic
331C2×C4×C5C2×#6712yes—
332C2×C4×C5C23×D311yescharacteristic
333C22⋊D5—68no—
334C22⋊D5—64no—
335C2×Dic5—24no—
336C2×Dic5—22no—
337C2×Dic5—32no—
338C2×Dic5—68no—
339D20—22no—
340D20—22no—
341D20—42no—
342D20—62no—
343D20—244no—
344C4×D5—68no—
345C4×D5—62no—
346C4×D5—62no—
347Dic10—24no—
348Dic10—22no—
349Dic10—68no—
350Dic10—62no—
351Dic10C2×#6714yes—
352C5×C8—22no—
353#168—62no—
3542−1+4—304no—
3552−1+4—304no—
356C2×#41—31no—
357C2×#41—151no—
358C2×#41—152no—
359C2×#41—301no—
360C2×#41—302no—
361C22×Q8—51no—
362C22×Q8—152no—
363C22×Q8—301no—
364C22×D4—51no—
365AGL(1,ℤ/8)—304no—
366C2×SD16—54no—
367C2×SD16—104no—
368C2×SD16—152no—
369C2×D8—152no—
370C2×M16—151no—
371C22×C8D3×D511yescharacteristic
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×C5C2×#12011yescharacteristic
383C2×C3×C5#57712yes—
384D15—42no—
385C3×D5—82no—
386C5×D3—42no—
387C23×C3—102no—
388C23×C3—202no—
389C23×C3—402no—
390C23×C3D4×D511yescharacteristic
391C22×D3—21no—
392C22×D3—52no—
393C3×Q8—54no—
394C3×Q8—102no—
395C3×Q8—104no—
396C3×D4—102no—
397C3×D4—102no—
398C3×D4—202no—
399C2×C3×C4—102no—
400C2×C3×C4—104no—
401C2×C3×C4C2×D2012yes—
402C2×C3×C4D4×D511yescharacteristic
403C2×C3×C4D4×D512yes—
404C2×C3×C4C23×D511yescharacteristic
405#67—24no—
406#67—104no—
407#67—404no—
408C2×Dic3—21no—
409C2×Dic3—22no—
410C2×Dic3—52no—
411D12—21no—
412D12—108no—
413D12—102no—
414D12C2×D2012yes—
415C4×D3—24no—
416C4×D3—108no—
417C4×D3—108no—
418C4×D3—102no—
419C4×D3—102no—
420Dic6—21no—
421Dic6—108no—
422Dic6—102no—
423Dic6C2×D2012yes—
424C3×C8—22no—
425C3⋊C8—102no—
426C22×C5—22no—
427C22×C5—62no—
428C22×C5—122no—
429C22×C5#93712yes—
430C22×C5C2×D3×D411yescharacteristic
431C2×D5—44no—
432C2×D5—42no—
433C2×D5—64no—
434C2×D5—62no—
435C2×D5—84no—
436C4×C5—62no—
437C4×C5—122no—
438C4×C5#93712yes—
439C4×C5C2×D3×D411yescharacteristic
440C4×C5C22×#6711yescharacteristic
441Dic5—24no—
442Dic5—62no—
443C24—101no—
444#41—34no—
445#41—62no—
446#41—308no—
447#41—3016no—
448#41—304no—
449#41—304no—
450#41—302no—
451#41—302no—
452C2×Q8—31no—
453C2×Q8—54no—
454C2×Q8—52no—
455C2×Q8—102no—
456C2×Q8—101no—
457C2×Q8—151no—
458C2×Q8—302no—
459C2×Q8—308no—
460C2×Q8—304no—
461C2×Q8—304no—
462C2×D4—31no—
463C2×D4—52no—
464C2×D4—61no—
465C2×D4—102no—
466C2×D4—101no—
467C2×D4—102no—
468C2×D4—152no—
469C2×D4—151no—
470C2×D4—304no—
471C2×D4—302no—
472C22×C4—61no—
473C22×C4—101no—
474C22×C4—152no—
475C22×C4—302no—
476C22×C4—302no—
477C22×C4C2×D3×D511yescharacteristic
478SD16—108no—
479SD16—304no—
480D8—304no—
481M16—302no—
482C2×C8—22no—
483C2×C8—152no—
484C2×C8C2×D3×D512yes—
485C4⋊C4—32no—
486C22⋊C4—61no—
487C22⋊C4—304no—
488C42—61no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—202no—
492C22×C3—204no—
493C22×C3—404no—
494C22×C3#402812yes—
495C22×C3C2×D4×D511yescharacteristic
496C2×D3—22no—
497C2×D3—42no—
498C2×D3—102no—
499C2×D3—104no—
500C3×C4—104no—
501C3×C4#402812yes—
502C3×C4C22×D2011yescharacteristic
503C3×C4C2×D4×D511yescharacteristic
504Dic3—22no—
505Dic3—42no—
506Dic3—102no—
507C2×C5—22no—
508C2×C5—122no—
509C2×C5#576212yes—
510C2×C5C2×#93711yescharacteristic
511D5—82no—
512D5—122no—
513C23—61no—
514C23—102no—
515C23—152no—
516C23—202no—
517C23—402no—
518C23#677711yescharacteristic
519Q8—32no—
520Q8—54no—
521Q8—61no—
522Q8—104no—
523Q8—102no—
524Q8—308no—
525Q8—302no—
526D4—32no—
527D4—64no—
528D4—61no—
529D4—102no—
530D4—102no—
531D4—202no—
532D4—308no—
533D4—304no—
534D4—302no—
535D4—1204no—
536C2×C4—61no—
537C2×C4—64no—
538C2×C4—62no—
539C2×C4—104no—
540C2×C4—102no—
541C2×C4—152no—
542C2×C4—308no—
543C2×C4—308no—
544C2×C4—302no—
545C2×C4—302no—
546C2×C4D3×D2012yes—
547C2×C4#677711yescharacteristic
548C2×C4D5×#6712yes—
549C2×C4C22×D3×D511yescharacteristic
550C8—22no—
551C8—302no—
552C2×C3—22no—
553C2×C3—402no—
554C2×C3C2×#402811yescharacteristic
555C2×C3#6610412yes—
556D3—42no—
557D3—202no—
558C5#8386011yescharacteristic, complemented, Sylow
559C22—22no—
560C22—62no—
561C22—122no—
562C22—202no—
563C22—204no—
564C22—302no—
565C22—304no—
566C22—404no—
567C22#9147412yes—
568C22C2×#677711yescharacteristic
569C4—62no—
570C4—104no—
571C4—122no—
572C4—302no—
573C4#9147412yes—
574C4C2×D3×D2011yescharacteristic
575C4C2×D5×#6711yescharacteristic
576C3#1061056711yescharacteristic, complemented, Sylow
577C2—22no—
578C2—122no—
579C2—402no—
580C2—602no—
581C2#1175398012yes—
582C2C2×#9147411yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
hypercenterC22×C8D3×D5
hypocenterC3×C5#3010
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#92004C2semidirect
2. C22×C3×#677C2semidirect
3. #11754602C2semidirect
4. C2×#91298C2semidirect
5. #11751211C2semidirect
6. C5×#5113C2semidirect
7. #11748399C2semidirect
8. #11747891C2semidirect
9. #11747889C2semidirect
16. C2×D15⋊Q8C22semidirect
20. C2×#6768C22semidirect
34. #91104C22semidirect
35. C5×#821C22semidirect
36. C5×#816C22semidirect
37. #90970C22semidirect
41. C22×#677D3semidirect
58. C5×#235D4semidirect
69. C2×C3×Dic10D4semidirect
101. #5113D5semidirect
194. #821C2×D5semidirect
196. #816C2×D5semidirect
230. C2×Dic10#67semidirect
293. #235D20semidirect
489. C3×C5#3010semidirect
558. C5#83860semidirect
576. C3#10610567semidirect

Maximal subgroups

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

subgroupindex
C2×#920042
C22×C3×#6772
#117546022
C2×#912982
#117512112
C5×#51132
#117483992
#117478912
#117478892
#106105673
#838605