Finite Group Databasebeta

← #14424491

Subgroups — #14424491

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#11754600C211yesmaximal, characteristic, complemented
4C2×#91312C211yesmaximal, characteristic, complemented
5#11751214C211yesmaximal, characteristic, complemented
6C5×#5110C211yesmaximal, characteristic, complemented
7#11748400C211yesmaximal, characteristic, complemented
8#11748124C214yesmaximal, complemented
9#11747890C214yesmaximal, complemented
10#10610409—31nomaximal, Hall
11C2×#6817C2211yescharacteristic
12C2×C5×#235C2211yescharacteristic
13C22×C3×D20C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic
15C2×#6782—22no—
16C2×D15⋊Q8—21no—
17C2×#6769C2212yescomplemented
18#92004—24no—
19#92004—24no—
20C2×#6768—21no—
21C2×D3×Dic10C2212yescomplemented
22C22×C3×C5×C8C2211yescharacteristic
23#91815C2211yescharacteristic
24C2×C5×#208C2211yescharacteristic
25C2×C3×#677—24no—
26C2×C3×#677C2214yes—
27#91563—22no—
28#91463—21no—
29#91456C2214yes—
30#91368—21no—
31#91312—24no—
32C2×#6657C2212yes—
33C2×#6653C2212yes—
34#91105C2212yescomplemented
35#91100C2212yescomplemented
36C5×(C2×D3)⋊C8C2214yescomplemented
37#90971C2214yescomplemented
38#83860—51nomaximal, Hall
39C2×#4150—31no—
40#66164—31no—
41C2×#4054—31no—
42C22×#677D311yescharacteristic, complemented
43C5×#408—31no—
44#65409—31no—
45#65402—31no—
46#65027—34no—
47#65023—34no—
48C23×C3×D5—21no—
49C22×C3×C4×C5C2311yescharacteristic
50C2×#1220—21no—
51#6817—22no—
52#6817D414yescomplemented
53C2×D60C2311yescharacteristic
54C2×C4×D15—21no—
55C2×Dic30C2311yescharacteristic
56C2×C5×#67D412yes—
57C5×#235—22no—
58C5×#235—22no—
59C2×C5×D12D411yescharacteristic
60C2×C4×C5×D3C2312yes—
61C2×C5×Dic6D411yescharacteristic
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×#1201—24no—
74C2×#1200—22no—
75#6782—216no—
76C2×D3×Dic5—22no—
77D15⋊Q8—28no—
78#6769—24no—
79#6769—24no—
80#6768—28no—
81D3×Dic10—24no—
82D3×Dic10—24no—
83C2×C3×C5×C8—22no—
84C2×C3×C5×C8C2312yes—
85#6719—21no—
86C4⋊Dic15C2312yes—
87C4×Dic15—21no—
88C5×#208—22no—
89C2×C5×C3⋊C8C2312yes—
90C3×#677—28no—
91#6665—24no—
92#6657—24no—
93#6653—24no—
94C2×#1007—51no—
95C22×C3×SD16—51no—
96#5805—51no—
97C2×#932—51no—
98#5225—51no—
99#5172—54no—
100#5170—54no—
101#5113—51no—
102#5110D511yescharacteristic, complemented
103C2×C5×#41—31no—
104#4150—64no—
105#4150—64no—
106C2×Q8×D5—61no—
107C2×#711—61no—
108C2×#711—62no—
109C2×#709—31no—
110C2×#709—32no—
111C22×D20C2×D311yescharacteristic
112C22×Dic10—32no—
113C22×Dic10C2×D311yescharacteristic
114C2×C5×M16—31no—
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—24no—
124C2×#677—32no—
125C2×#677C2×D314yes—
126C5×C22⋊C8—34no—
127#3953—32no—
128#3948—34no—
129#3948—32no—
130#3010—151noSylow
131C23×C3×C5C2×D411yescharacteristic
132C22×D15—21no—
133C22×C5×D3C2×D412yes—
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×Dic15—21no—
143C2×Dic15—22no—
144D60—21no—
145D60C2×D412yes—
146C4×D15—24no—
147Dic30—21no—
148Dic30C2×D412yes—
149C5×#67—24no—
150C2×C5×Dic3C2×D412yes—
151C5×D12—22no—
152C4×C5×D3—22no—
153C4×C5×D3—22no—
154C5×Dic6—22no—
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#1201—84no—
166#1200—28no—
167D3×Dic5—28no—
168C3×C5×C8—22no—
169C5×C3⋊C8—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#926—51no—
192C2×#208C2×D511yescharacteristic
193#835—54no—
194#821—52no—
195(C2×D3)⋊C8C2×D514yescomplemented
196#816—52no—
197C23×D5—21no—
198C5×#41—62no—
199C5×#41—62no—
200C2×C5×Q8—31no—
201C2×C5×D4—32no—
202C2×C5×D4—31no—
203C22×C4×C5—32no—
204C22×C4×C5C22×D311yescharacteristic
205C2×C22⋊D5—62no—
206C2×C22⋊D5—61no—
207C2×C22⋊D5—64no—
208C22×Dic5—21no—
209C22×Dic5—62no—
210Q8×D5—68no—
211#711—68no—
212#711—616no—
213#709—34no—
214#709—64no—
215#709—62no—
216#709—64no—
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—21no—
225C2×Dic10—22no—
226C2×Dic10—31no—
227C2×Dic10—64no—
228C2×Dic10—62no—
229C2×Dic10—64no—
230C2×Dic10#6714yescomplemented
231C2×Dic10C22×D312yes—
232C5×M16—62no—
233C2×C5×C8—22no—
234C2×C5×C8—32no—
235C2×C5×C8C22×D312yes—
236C22⋊Dic5—61no—
237#685—64no—
238C4⋊Dic5—32no—
239C4×Dic5—61no—
240D40—64no—
241#677—28no—
242#677—64no—
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—151no—
251#408—31no—
252C22×C3×C5—22no—
253C22×C3×C5#12012yes—
254C22×C3×C5C22×D411yescharacteristic
255C2×D15—22no—
256C2×D15—42no—
257C2×C5×D3—22no—
258C2×C5×D3—24no—
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—
266Dic15—42no—
267C3×Dic5—24no—
268C5×Dic3—22no—
269C24×C3—101no—
270C2×C3×Q8—54no—
271C2×C3×Q8—52no—
272C2×C3×Q8—101no—
273C2×C3×Q8—102no—
274C2×C3×D4—52no—
275C2×C3×D4—101no—
276C2×C3×D4—102no—
277C2×C3×D4—102no—
278C22×C3×C4—101no—
279C22×C3×C4C22×D511yescharacteristic
280C2×#67—101no—
281C2×#67—104no—
282C2×#67D2012yes—
283#239—104no—
284#239—104no—
285#239—108no—
286D3×Q8—108no—
287D3×Q8—104no—
288D3×Q8—104no—
289#235—22no—
290#235—22no—
291#235—54no—
292#235—1016no—
293#235—102no—
294C2×D12—51no—
295C2×D12—102no—
296C2×D12D2011yescharacteristic
297C2×C4×D3—102no—
298C2×C4×D3—101no—
299C2×C4×D3—102no—
300C2×C4×D3C22×D512yes—
301C2×Dic6—51no—
302C2×Dic6—102no—
303C2×Dic6D2011yescharacteristic
304C3×SD16—108no—
305C2×C3×C8—22no—
306C2×C3×C8C22×D512yes—
307#217—101no—
308#217—104no—
309#214—104no—
310#213—104no—
311C4⋊Dic3—52no—
312C4×Dic3—101no—
313#208—22no—
314C2×C3⋊C8C22×D512yes—
315C23×C5—32no—
316C23×C5D3×D411yescharacteristic
317C22×D5—22no—
318C22×D5—42no—
319C22×D5—61no—
320C22×D5—82no—
321C5×Q8—62no—
322C5×D4—64no—
323C5×D4—62no—
324C2×C4×C5—32no—
325C2×C4×C5—62no—
326C2×C4×C5—62no—
327C2×C4×C5D3×D411yescharacteristic
328C2×C4×C5D3×D412yes—
329C2×C4×C5C2×#6712yes—
330C2×C4×C5C23×D311yescharacteristic
331C22⋊D5—68no—
332C22⋊D5—64no—
333C22⋊D5—244no—
334C2×Dic5—24no—
335C2×Dic5—22no—
336C2×Dic5—68no—
337C2×Dic5—61no—
338C2×Dic5—62no—
339D20—22no—
340D20—22no—
341D20—32no—
342D20—42no—
343D20—61no—
344C4×D5—68no—
345C4×D5—64no—
346Dic10—24no—
347Dic10—22no—
348Dic10—32no—
349Dic10—68no—
350Dic10—61no—
351Dic10C2×#6714yes—
352C5×C8—22no—
353C5×C8—62no—
3542−1+4—304no—
3552−1+4—304no—
356C2×#41—31no—
357C2×#41—152no—
358C2×#41—151no—
359C2×#41—302no—
360C2×#41—301no—
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—31no—
371C22×C8D3×D511yescharacteristic
372#127—301no—
373#124—301no—
374#121—154no—
375#120—302no—
376#117—151no—
377#103—154no—
378#103—152no—
379#102—152no—
380C22⋊C8—34no—
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×C3C2×D2011yescharacteristic
391C22×D3—101no—
392C22×D3C2×D2012yes—
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×D2011yescharacteristic
402C2×C3×C4D4×D512yes—
403C2×C3×C4D4×D512yes—
404C2×C3×C4C23×D511yescharacteristic
405#67—24no—
406#67—104no—
407#67—404no—
408C2×Dic3—101no—
409C2×Dic3—102no—
410C2×Dic3C2×D2012yes—
411D12—22no—
412D12—52no—
413D12—108no—
414D12—101no—
415C4×D3—22no—
416C4×D3—22no—
417C4×D3—108no—
418C4×D3—108no—
419C4×D3—104no—
420Dic6—22no—
421Dic6—52no—
422Dic6—108no—
423Dic6—101no—
424C3×C8—22no—
425C3⋊C8—22no—
426C22×C5—22no—
427C22×C5—64no—
428C22×C5—62no—
429C22×C5#93712yes—
430C22×C5C2×D3×D411yescharacteristic
431C2×D5—44no—
432C2×D5—42no—
433C2×D5—62no—
434C2×D5—84no—
435C2×D5—122no—
436C4×C5—62no—
437C4×C5#93712yes—
438C4×C5C2×D3×D411yescharacteristic
439C4×C5C22×#6711yescharacteristic
440Dic5—24no—
441Dic5—62no—
442Dic5—122no—
443C24—101no—
444#41—62no—
445#41—62no—
446#41—154no—
447#41—304no—
448#41—304no—
449#41—3016no—
450#41—308no—
451#41—302no—
452C2×Q8—31no—
453C2×Q8—54no—
454C2×Q8—52no—
455C2×Q8—101no—
456C2×Q8—102no—
457C2×Q8—151no—
458C2×Q8—302no—
459C2×Q8—304no—
460C2×Q8—304no—
461C2×Q8—308no—
462C2×D4—32no—
463C2×D4—31no—
464C2×D4—52no—
465C2×D4—101no—
466C2×D4—102no—
467C2×D4—102no—
468C2×D4—151no—
469C2×D4—302no—
470C2×D4—301no—
471C2×D4—304no—
472C22×C4—32no—
473C22×C4—101no—
474C22×C4—302no—
475C22×C4—302no—
476C22×C4—301no—
477C22×C4C2×D3×D511yescharacteristic
478SD16—108no—
479SD16—304no—
480D8—304no—
481M16—62no—
482C2×C8—22no—
483C2×C8—32no—
484C2×C8C2×D3×D512yes—
485C4⋊C4—152no—
486C22⋊C4—304no—
487C22⋊C4—301no—
488C42—301no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—202no—
492C22×C3—204no—
493C22×C3—404no—
494C22×C3#402812yes—
495C22×C3C22×D2011yescharacteristic
496C2×D3—22no—
497C2×D3—24no—
498C2×D3—102no—
499C2×D3—202no—
500C3×C4—104no—
501C3×C4#402812yes—
502C3×C4C2×D4×D511yescharacteristic
503C3×C4C2×D4×D511yescharacteristic
504Dic3—22no—
505Dic3—102no—
506Dic3—202no—
507C2×C5—22no—
508C2×C5—122no—
509C2×C5#576212yes—
510C2×C5C2×#93711yescharacteristic
511D5—82no—
512D5—122no—
513C23—32no—
514C23—102no—
515C23—202no—
516C23—301no—
517C23—402no—
518C23D3×D2011yescharacteristic
519Q8—54no—
520Q8—62no—
521Q8—104no—
522Q8—102no—
523Q8—152no—
524Q8—308no—
525Q8—301no—
526D4—64no—
527D4—62no—
528D4—102no—
529D4—102no—
530D4—152no—
531D4—202no—
532D4—308no—
533D4—304no—
534D4—301no—
535D4—1204no—
536C2×C4—32no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—104no—
540C2×C4—102no—
541C2×C4—308no—
542C2×C4—308no—
543C2×C4—301no—
544C2×C4—304no—
545C2×C4—302no—
546C2×C4D3×D2011yescharacteristic
547C2×C4#677712yes—
548C2×C4D5×#6712yes—
549C2×C4C22×D3×D511yescharacteristic
550C8—22no—
551C8—62no—
552C2×C3—22no—
553C2×C3—402no—
554C2×C3C2×#402811yescharacteristic
555C2×C3#6608512yes—
556D3—42no—
557D3—202no—
558C5#8386011yescharacteristic, complemented, Sylow
559C22—22no—
560C22—62no—
561C22—64no—
562C22—202no—
563C22—204no—
564C22—302no—
565C22—404no—
566C22—602no—
567C22#9147412yes—
568C22C2×D3×D2011yescharacteristic
569C4—62no—
570C4—104no—
571C4—302no—
572C4—602no—
573C4#9147412yes—
574C4C2×#677711yescharacteristic
575C4C2×D5×#6711yescharacteristic
576C3#1061040911yescharacteristic, complemented, Sylow
577C2—22no—
578C2—122no—
579C2—402no—
580C2—602no—
581C2#1175397012yes—
582C2C2×#9147411yescharacteristic
subgroupG/H
centerC22C2×D3×D20
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. #11754600C2semidirect
4. C2×#91312C2semidirect
5. #11751214C2semidirect
6. C5×#5110C2semidirect
7. #11748400C2semidirect
8. #11748124C2semidirect
9. #11747890C2semidirect
17. C2×#6769C22semidirect
21. C2×D3×Dic10C22semidirect
34. #91105C22semidirect
35. #91100C22semidirect
36. C5×(C2×D3)⋊C8C22semidirect
37. #90971C22semidirect
42. C22×#677D3semidirect
52. #6817D4semidirect
69. C2×C3×Dic10D4semidirect
102. #5110D5semidirect
195. (C2×D3)⋊C8C2×D5semidirect
230. C2×Dic10#67semidirect
489. C3×C5#3010semidirect
558. C5#83860semidirect
576. C3#10610409semidirect

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
#117546002
C2×#913122
#117512142
C5×#51102
#117484002
#117481242
#117478902
#106104093
#838605