Finite Group Databasebeta

← #14416896

Subgroups — #14416896

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91831C211yesmaximal, characteristic
2C2×C5×Q8×Dic3C211yesmaximal, characteristic, complemented
3#11754436C211yesmaximal, characteristic
4C3×#65514C211yesmaximal, characteristic, complemented
5#11749260C212yesmaximal, complemented
6#11749257C212yesmaximal, complemented
7#11749235C212yesmaximal, complemented
8#11749232C212yesmaximal, complemented
9#11748472C211yesmaximal, characteristic, complemented
10#11748394C211yesmaximal, characteristic
11Dic3×#681C211yesmaximal, characteristic, complemented
12C4×#4088—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C2×#6718C2212yes—
16#91831C418yescomplemented
17C2×#6717C2212yes—
18C2×#6710C2211yescharacteristic
19C5×Q8×Dic3—21no—
20C5×Q8×Dic3—21no—
21C5×Q8×Dic3C2212yes—
22C5×Q8×Dic3C2212yes—
23C2×C5×C4⋊Dic3—21no—
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C2×C4×C5×Dic3—21no—
26C2×C4×C5×Dic3C2211yescharacteristic
27C3×#4072C2211yescharacteristic
28C2×C3×#681C2211yescharacteristic
29#91556—21no—
30#91556—21no—
31#91428C2211yescharacteristic
32#91428C2211yescharacteristic
33C4×#1200—21no—
34#91386—21no—
35#91340C2211yescharacteristic
36#91340C2211yescharacteristic
37C3×#3967C2212yes—
38C3×#3967C2212yes—
39#90989C2212yes—
40#90986C2212yes—
41#90975C2212yes—
42#90969C2212yes—
43#90953C2212yes—
44Dic3×#168C2212yes—
45#78946—51nomaximal, Hall
46C2×C4×C5×Q8—31no—
47C2×#4088—31no—
48C4×#709—31no—
49#65514D311yescharacteristic, complemented
50#65319—32no—
51C4×#689—32no—
52#65315—32no—
53C4×#688—32no—
54#65255—31no—
55#65253—31no—
56C4×#681—31no—
57C2×C3×C5×Q8—21no—
58C2×C3×C5×Q8—22no—
59C2×C3×C5×Q8C2×C414yescomplemented
60C2×C3×C5×Q8C2312yes—
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—21no—
64#6817—22no—
65#6817C2×C414yes—
66C2×D60C2311yescharacteristic
67C2×C4×D15—21no—
68C2×Dic30C2311yescharacteristic
69C22×C5×Dic3—21no—
70C22×C5×Dic3D411yescharacteristic
71C22×C5×Dic3D411yescharacteristic
72C2×#1200—21no—
73C2×#1200—21no—
74#6718C2×C418yescomplemented
75#6717C2×C418yescomplemented
76#6710C2×C414yescomplemented
77C2×C3⋊#168C2312yes—
78C5×C4⋊Dic3—21no—
79C5×C4⋊Dic3—22no—
80C5×C4⋊Dic3—22no—
81C5×C4⋊Dic3C2312yes—
82C4×C5×Dic3—22no—
83C4×C5×Dic3—22no—
84C4×C5×Dic3D411yescharacteristic
85C4×C5×Dic3D411yescharacteristic
86C4×C5×Dic3C2311yescharacteristic
87C4×C5×Dic3C2311yescharacteristic
88C3×C22⋊Dic5—21no—
89C3×C4⋊Dic5C2311yescharacteristic
90C3×C4⋊Dic5C2311yescharacteristic
91C3×C4×Dic5—21no—
92C3×#681—22no—
93C2×C3×#168C2312yes—
94#6669—21no—
95#6669—21no—
96#6667—21no—
97#6667—21no—
98Dic3×Dic5—21no—
99Dic3×Dic5—21no—
100C2×Q8×Dic3D511yescharacteristic, complemented
101C2×#942—51no—
102#5522—51no—
103C3×#419—51no—
104#5133—51no—
105Dic3×M16—51no—
106#4995—51no—
107#4817—52no—
108#4790—52no—
109#4789—52no—
110#4788—52no—
111C22×C5×Q8C2×D311yescharacteristic
112C2×#709—31no—
113C4×C5×Q8—32no—
114C4×C5×Q8—32no—
115C4×C5×Q8—61no—
116C4×C5×Q8—61no—
117C2×C5×C4⋊C4—31no—
118C2×C5×C4⋊C4—61no—
119C2×C42×C5—31no—
120C2×C42×C5—61no—
121C2×#689—32no—
122#4088—38no—
123C2×#688—32no—
124C4×C22⋊D5—61no—
125C4×C22⋊D5—61no—
126#4072C2×D311yescharacteristic
127C2×#681—31no—
128C2×#681C2×D311yescharacteristic
129C4×D20—31no—
130C4×D20—31no—
131#4018—61no—
132C42×D5—61no—
133C4×Dic10—31no—
134C4×Dic10—31no—
135#3967C2×D312yes—
136#3967C2×D312yes—
137#3942—32no—
138#3941—32no—
139#3940—32no—
140#3939—32no—
141#3935—32no—
142C4×#168—32no—
143C4×#137—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—21no—
146C3×C5×Q8—24no—
147C3×C5×Q8—22no—
148C3×C5×Q8C22×C414yes—
149C2×C3×C4×C5—24no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5C22×C412yes—
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5#4112yes—
154C2×C3×C4×C5C2411yescharacteristic
155#1220—24no—
156C2×Dic15—21no—
157D60—21no—
158D60C22×C412yes—
159C4×D15—24no—
160Dic30—21no—
161Dic30C22×C412yes—
162C2×C5×Dic3—22no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—41no—
165C2×C5×Dic3—42no—
166C2×C5×Dic3C2×D411yescharacteristic
167C2×C5×Dic3C2×D411yescharacteristic
168C2×C5×Dic3C2×D411yescharacteristic
169C2×C5×Dic3C2×D411yescharacteristic
170C2×C3×Dic5—21no—
171C2×C3×Dic5—21no—
172#1200—42no—
173#1200—42no—
174C3⋊#168C22×C414yes—
175C3×#168—22no—
176C22×C3×Q8C2×D511yescharacteristic
177C2×#235—51no—
178C2×C3×M16—51no—
179C3×#117—51no—
180Q8×Dic3—21no—
181Q8×Dic3—21no—
182Q8×Dic3C2×D512yes—
183Q8×Dic3C2×D512yes—
184C2×#216—52no—
185#942—58no—
186C2×#215—52no—
187C2×C4⋊Dic3—21no—
188C2×C4⋊Dic3C2×D511yescharacteristic
189C2×C4×Dic3—21no—
190C2×C4×Dic3C2×D511yescharacteristic
191C2×#208—51no—
192#893—51no—
193#893—51no—
194#887—51no—
195#887—51no—
196#67⋊C4—101no—
197#67⋊C4—101no—
198#872—101no—
199C42×D3—101no—
200C3×#103—52no—
201C3×#103—52no—
202#821—52no—
203#816—52no—
204#815—52no—
205C8×Dic3—52no—
206#808—52no—
207#807—52no—
208C2×C5×Q8—21no—
209C2×C5×Q8—22no—
210C2×C5×Q8C4×D314yescomplemented
211C2×C5×Q8C22×D312yes—
212C22×C4×C5—21no—
213C22×C4×C5—31no—
214C22×C4×C5—31no—
215C22×C4×C5—61no—
216C22×C4×C5C22×D311yescharacteristic
217C2×C22⋊D5—61no—
218#709—34no—
219#709—62no—
220C2×D20—31no—
221C2×C4×D5—61no—
222C2×C4×D5—61no—
223C2×C4×D5—61no—
224C2×Dic10—31no—
225C5×C4⋊C4—32no—
226C5×C4⋊C4—62no—
227C5×C4⋊C4—62no—
228C5×C4⋊C4—61no—
229C42×C5—31no—
230C42×C5—31no—
231C42×C5—31no—
232C42×C5—31no—
233C42×C5—62no—
234C42×C5—62no—
235C22⋊Dic5—21no—
236#689—38no—
237#688—38no—
238#685—61no—
239#685—61no—
240C4⋊Dic5C22×D311yescharacteristic
241C4⋊Dic5C22×D311yescharacteristic
242#683—61no—
243#683—61no—
244C4×Dic5—21no—
245C4×Dic5—61no—
246C4×Dic5—61no—
247#681—22no—
248#681—34no—
249C2×#168—32no—
250C2×#168C22×D312yes—
251C2×#137—151no—
252C4×#41—151no—
253C2×C4×Q8—31no—
254#441—152no—
255#440—152no—
256C4×Q16—152no—
257C4×SD16—152no—
258#428—151no—
259#419—51no—
260#417—151no—
261C4×M16—151no—
262C22×C3×C5—21no—
263C22×C3×C5—21no—
264C22×C3×C5C4×D412yes—
265C22×C3×C5C22×D411yescharacteristic
266C2×D15—22no—
267C2×D15—41no—
268C2×D15—41no—
269C3×C4×C5—24no—
270C3×C4×C5C4×D412yes—
271C3×C4×C5C23×C411yescharacteristic
272C3×C4×C5C2×#4111yescharacteristic
273Dic15—22no—
274C3×Dic5—41no—
275C3×Dic5—41no—
276C5×Dic3—21no—
277C5×Dic3—21no—
278C5×Dic3—21no—
279C5×Dic3—42no—
280C5×Dic3#13712yescomplemented
281C2×C3×Q8—22no—
282C2×C3×Q8—21no—
283C2×C3×Q8C4×D514yescomplemented
284C2×C3×Q8C22×D512yes—
285C22×C3×C4—21no—
286C22×C3×C4C22×D511yescharacteristic
287C2×#67—101no—
288C22×Dic3—21no—
289C22×Dic3C22⋊D511yescharacteristic
290C22×Dic3C22⋊D511yescharacteristic
291#235—54no—
292#235—102no—
293C2×D12—51no—
294C2×C4×D3—101no—
295C2×C4×D3—101no—
296C2×C4×D3—101no—
297C2×Dic6—51no—
298C3×M16—102no—
299C2×C3×C8—52no—
300C3×C4⋊C4—51no—
301C3×C4⋊C4—51no—
302C3×C22⋊C4—101no—
303C3×C42—101no—
304#216—58no—
305#215—58no—
306(C2×D3)⋊C4—101no—
307(C2×D3)⋊C4—101no—
308C4⋊Dic3—21no—
309C4⋊Dic3—22no—
310C4⋊Dic3—22no—
311C4⋊Dic3C22×D512yes—
312Dic3⋊C4—101no—
313Dic3⋊C4—101no—
314C4×Dic3—22no—
315C4×Dic3—22no—
316C4×Dic3—101no—
317C4×Dic3—101no—
318C4×Dic3C22⋊D511yescharacteristic
319C4×Dic3C22⋊D511yescharacteristic
320C4×Dic3C22×D511yescharacteristic
321C4×Dic3C22×D511yescharacteristic
322#208—54no—
323C2×C3⋊C8—52no—
324C23×C5D3×D411yescharacteristic
325C22×D5—61no—
326C5×Q8—24no—
327C5×Q8—22no—
328C5×Q8C2×C4×D314yes—
329C2×C4×C5—24no—
330C2×C4×C5—22no—
331C2×C4×C5—31no—
332C2×C4×C5—31no—
333C2×C4×C5—31no—
334C2×C4×C5—31no—
335C2×C4×C5—62no—
336C2×C4×C5—62no—
337C2×C4×C5—121no—
338C2×C4×C5—122no—
339C2×C4×C5C2×C4×D312yes—
340C2×C4×C5D3×D411yescharacteristic
341C2×C4×C5#23712yes—
342C2×C4×C5C23×D311yescharacteristic
343C22⋊D5—64no—
344C2×Dic5—21no—
345C2×Dic5—21no—
346C2×Dic5—61no—
347D20—32no—
348D20—61no—
349C4×D5—64no—
350C4×D5—122no—
351C4×D5—122no—
352Dic10—32no—
353Dic10—61no—
354#168—22no—
355#168—34no—
356C2×#41—151no—
357C22×Q8D3×D511yescharacteristic
358#137—158no—
359C2×Q16—152no—
360C2×SD16—152no—
361C2×M16—51no—
362C2×M16—151no—
363C4×Q8—32no—
364C4×Q8—32no—
365C4×Q8—61no—
366C4×Q8—61no—
367C4×Q8—151no—
368C4×Q8—151no—
369C4×D4—151no—
370C4×D4—151no—
371C4×D4—301no—
372C4×D4—301no—
373#117—51no—
374#117—301no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—61no—
377C2×C42—31no—
378C2×C42—61no—
379C2×C42—301no—
380#107—152no—
381#106—152no—
382#103—52no—
383#103—52no—
384#103—152no—
385#102—152no—
386#97—152no—
387C4×C8—152no—
388C2×C3×C5—22no—
389C2×C3×C5C2×C4×D411yescharacteristic
390C2×C3×C5C2×#13711yescharacteristic
391C2×C3×C5#57511yescharacteristic
392D15—42no—
393C23×C3C2×C22⋊D511yescharacteristic
394C22×D3—101no—
395C3×Q8—22no—
396C3×Q8—24no—
397C3×Q8C2×C4×D514yes—
398C2×C3×C4—22no—
399C2×C3×C4—24no—
400C2×C3×C4—101no—
401C2×C3×C4—101no—
402C2×C3×C4C2×C4×D512yes—
403C2×C3×C4#70912yes—
404C2×C3×C4C2×C22⋊D511yescharacteristic
405C2×C3×C4C23×D511yescharacteristic
406#67—104no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—41no—
410C2×Dic3—42no—
411C2×Dic3—101no—
412C2×Dic3C2×C22⋊D511yescharacteristic
413C2×Dic3C2×C22⋊D511yescharacteristic
414C2×Dic3C2×C22⋊D511yescharacteristic
415C2×Dic3C2×C22⋊D511yescharacteristic
416D12—52no—
417D12—101no—
418C4×D3—104no—
419C4×D3—202no—
420C4×D3—202no—
421Dic6—52no—
422Dic6—101no—
423C3×C8—102no—
424C3⋊C8—54no—
425C22×C5—21no—
426C22×C5—21no—
427C22×C5#67⋊C412yes—
428C22×C5C2×D3×D411yescharacteristic
429C2×D5—62no—
430C2×D5—121no—
431C2×D5—121no—
432C4×C5—24no—
433C4×C5—32no—
434C4×C5—61no—
435C4×C5—61no—
436C4×C5—61no—
437C4×C5—122no—
438C4×C5#67⋊C412yes—
439C4×C5C22×C4×D311yescharacteristic
440C4×C5C2×#23711yescharacteristic
441Dic5—41no—
442Dic5—41no—
443Dic5—62no—
444#41—154no—
445#41—302no—
446C2×Q8—22no—
447C2×Q8—21no—
448C2×Q8—151no—
449C2×Q8#120014yescomplemented
450C2×Q8C2×D3×D512yes—
451C2×D4—151no—
452C2×D4—301no—
453C22×C4—21no—
454C22×C4—31no—
455C22×C4—31no—
456C22×C4—61no—
457C22×C4—301no—
458C22×C4—301no—
459C22×C4—301no—
460C22×C4C2×D3×D511yescharacteristic
461Q16—158no—
462SD16—158no—
463M16—102no—
464M16—154no—
465C2×C8—52no—
466C2×C8—152no—
467C4⋊C4—32no—
468C4⋊C4—51no—
469C4⋊C4—51no—
470C4⋊C4—62no—
471C4⋊C4—62no—
472C4⋊C4—61no—
473C4⋊C4—301no—
474C4⋊C4—301no—
475C22⋊C4—101no—
476C22⋊C4—301no—
477C22⋊C4—301no—
478C42—31no—
479C42—31no—
480C42—31no—
481C42—31no—
482C42—62no—
483C42—62no—
484C42—101no—
485C42—301no—
486C42—301no—
487C3×C5C4×#13711yescharacteristic, complemented, Hall
488C22×C3—21no—
489C22×C3—21no—
490C22×C3C4×C22⋊D512yes—
491C22×C3C22×C22⋊D511yescharacteristic
492C2×D3—102no—
493C2×D3—201no—
494C2×D3—201no—
495C3×C4—24no—
496C3×C4—201no—
497C3×C4—201no—
498C3×C4C4×C22⋊D512yes—
499C3×C4C22×C4×D511yescharacteristic
500C3×C4C2×#70911yescharacteristic
501Dic3—21no—
502Dic3—21no—
503Dic3—21no—
504Dic3—42no—
505Dic3—102no—
506Dic3#408812yescomplemented
507C2×C5—22no—
508C2×C5C2×#67⋊C411yescharacteristic
509C2×C5D3×#13711yescharacteristic
510C2×C5#577711yescharacteristic
511D5—122no—
512C23—301no—
513C23D3×C22⋊D511yescharacteristic
514Q8—22no—
515Q8—24no—
516Q8—152no—
517Q8—301no—
518Q8C2×#120014yes—
519D4—152no—
520D4—304no—
521D4—301no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—31no—
525C2×C4—31no—
526C2×C4—31no—
527C2×C4—31no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—101no—
531C2×C4—101no—
532C2×C4—121no—
533C2×C4—122no—
534C2×C4—301no—
535C2×C4—304no—
536C2×C4—602no—
537C2×C4—602no—
538C2×C4#677912yes—
539C2×C4C2×#120012yes—
540C2×C4D3×C22⋊D511yescharacteristic
541C2×C4C22×D3×D511yescharacteristic
542C8—102no—
543C8—154no—
544C2×C3—22no—
545C2×C3C2×C4×C22⋊D511yescharacteristic
546C2×C3C2×#408811yescharacteristic
547C2×C3#6615611yescharacteristic
548D3—202no—
549C5#7894611yescharacteristic, complemented, Sylow
550C22—21no—
551C22—21no—
552C22—302no—
553C22—601no—
554C22—601no—
555C22#9155612yes—
556C22C2×D3×C22⋊D511yescharacteristic
557C4—24no—
558C4—32no—
559C4—61no—
560C4—61no—
561C4—61no—
562C4—122no—
563C4—201no—
564C4—201no—
565C4—302no—
566C4#9155612yes—
567C4C2×#677911yescharacteristic
568C4C22×#120011yescharacteristic
569C3C4×#408811yescharacteristic, complemented, Sylow
570C2—22no—
571C2—602no—
572C2D3×#408811yescharacteristic
573C2#1175509011yescharacteristic
574C2C2×#9155611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
cosocleC2×C3×C4×C5C24
hypercenterC22×Q8D3×D5
hypocenterC3×C5C4×#137
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C5×Q8×Dic3C2semidirect
4. C3×#65514C2semidirect
5. #11749260C2semidirect
6. #11749257C2semidirect
7. #11749235C2semidirect
8. #11749232C2semidirect
9. #11748472C2semidirect
11. Dic3×#681C2semidirect
16. #91831C4semidirect
49. #65514D3semidirect
59. C2×C3×C5×Q8C2×C4semidirect
74. #6718C2×C4semidirect
75. #6717C2×C4semidirect
76. #6710C2×C4semidirect
100. C2×Q8×Dic3D5semidirect
210. C2×C5×Q8C4×D3semidirect
280. C5×Dic3#137semidirect
283. C2×C3×Q8C4×D5semidirect
449. C2×Q8#1200semidirect
487. C3×C5C4×#137semidirect
506. Dic3#4088semidirect
549. C5#78946semidirect
569. C3C4×#4088semidirect

Maximal subgroups

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

subgroupindex
C2×#918312
C2×C5×Q8×Dic32
#117544362
C3×#655142
#117492602
#117492572
#117492352
#117492322
#117484722
#117483942
Dic3×#6812
C4×#40883
#789465