Finite Group Databasebeta

← #14416895

Subgroups — #14416895

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×Q8×Dic15C211yesmaximal, characteristic, complemented
2C2×C3×#4088C211yesmaximal, characteristic
3#11754444C211yesmaximal, characteristic
4C5×#5225C211yesmaximal, characteristic, complemented
5#11749264C212yesmaximal, complemented
6#11749263C212yesmaximal, complemented
7#11749241C212yesmaximal, complemented
8#11749239C212yesmaximal, complemented
9#11748460C211yesmaximal, characteristic, complemented
10#11748369C211yesmaximal, characteristic
11#11748328C211yesmaximal, characteristic, complemented
12#10610677—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15Q8×Dic15—21no—
16Q8×Dic15—21no—
17Q8×Dic15C2212yes—
18Q8×Dic15C2212yes—
19C2×C4⋊Dic15—21no—
20C2×C4⋊Dic15C2211yescharacteristic
21C2×C4×Dic15—21no—
22C2×C4×Dic15C2211yescharacteristic
23C5×#926C2211yescharacteristic
24C2×C5×#208C2211yescharacteristic
25C2×C3×#689C2212yes—
26C3×#4088C418yescomplemented
27C2×C3×#688C2212yes—
28C2×C3×#681C2211yescharacteristic
29#91559—21no—
30#91559—21no—
31#91434C2211yescharacteristic
32#91434C2211yescharacteristic
33C4×D5×Dic3—21no—
34#91357—21no—
35#91331C2211yescharacteristic
36#91331C2211yescharacteristic
37C5×#835C2212yes—
38C5×#835C2212yes—
39#90988C2212yes—
40#90985C2212yes—
41#90971C2212yes—
42#90965C2212yes—
43#90954C2212yes—
44#90951C2212yes—
45Dic3×#137—51nomaximal, Hall
46C2×Q8×Dic5—31no—
47C2×#4088D311yescharacteristic
48#65856—31no—
49C5×#419—31no—
50#65422—31no—
51M16×Dic5—31no—
52#65284—31no—
53#65106—32no—
54#65079—32no—
55#65078—32no—
56#65077—32no—
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
63C22×Dic15—21no—
64C22×Dic15D411yescharacteristic
65C22×Dic15D411yescharacteristic
66C2×C3×C22⋊D5—21no—
67C3×#709—22no—
68C3×#709C2×C414yes—
69C2×C3×D20C2311yescharacteristic
70C2×C3×C4×D5—21no—
71C2×C3×Dic10C2311yescharacteristic
72C2×D5×Dic3—21no—
73C2×D5×Dic3—21no—
74C4⋊Dic15—21no—
75C4⋊Dic15—22no—
76C4⋊Dic15—22no—
77C4⋊Dic15C2312yes—
78C4×Dic15—22no—
79C4×Dic15—22no—
80C4×Dic15D411yescharacteristic
81C4×Dic15D411yescharacteristic
82C4×Dic15C2311yescharacteristic
83C4×Dic15C2311yescharacteristic
84C5×#217—21no—
85C5×C4⋊Dic3C2311yescharacteristic
86C5×C4⋊Dic3C2311yescharacteristic
87C4×C5×Dic3—21no—
88C5×#208—22no—
89C2×C5×C3⋊C8C2312yes—
90C3×#689C2×C418yescomplemented
91C3×#688C2×C418yescomplemented
92C3×#681C2×C414yescomplemented
93C2×C3×#168C2312yes—
94#6668—21no—
95#6668—21no—
96#6665—21no—
97#6665—21no—
98Dic3×Dic5—21no—
99Dic3×Dic5—21no—
100C2×C3×#137—51no—
101Dic3×#41—51no—
102C2×Q8×Dic3—51no—
103#5232—51no—
104#5225D511yescharacteristic, complemented
105#5184—52no—
106Dic3×Q16—52no—
107#5164—52no—
108Dic3×SD16—52no—
109#5121—51no—
110Dic3×M16—51no—
111C22×C5×Q8C2×D311yescharacteristic
112C2×#709C2×D311yescharacteristic
113C2×C5×M16—31no—
114C5×#117—31no—
115Q8×Dic5—32no—
116Q8×Dic5—32no—
117Q8×Dic5—61no—
118Q8×Dic5—61no—
119C2×#689C2×D312yes—
120#4088Dic318yescomplemented
121C2×#688C2×D312yes—
122C2×C4⋊Dic5—31no—
123C2×C4⋊Dic5—61no—
124C2×C4×Dic5—31no—
125C2×C4×Dic5—61no—
126C2×#681C2×D311yescharacteristic
127#4039—31no—
128#4039—31no—
129#4033—31no—
130#4033—31no—
131#4027—61no—
132#4027—61no—
133#4018—61no—
134C42×D5—61no—
135C5×#103—32no—
136C5×#103—32no—
137#3953—32no—
138#3948—32no—
139#3947—32no—
140C8×Dic5—32no—
141#3940—32no—
142#3939—32no—
143C4×#137—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×C3×D5—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
155C2×Dic15—22no—
156C2×Dic15—22no—
157C2×Dic15—41no—
158C2×Dic15—42no—
159C2×Dic15C2×D411yescharacteristic
160C2×Dic15C2×D411yescharacteristic
161C2×Dic15C2×D411yescharacteristic
162C2×Dic15C2×D411yescharacteristic
163C2×C5×Dic3—21no—
164C2×C5×Dic3—21no—
165C3×C22⋊D5—24no—
166C2×C3×Dic5—21no—
167C3×D20—21no—
168C3×D20C22×C412yes—
169C3×C4×D5—24no—
170C3×Dic10—21no—
171C3×Dic10C22×C412yes—
172D5×Dic3—42no—
173D5×Dic3—42no—
174C3×#168C22×C414yes—
175C5×C3⋊C8—22no—
176C2×C3×#41—51no—
177C22×C3×Q8C2×D511yescharacteristic
178C3×#137—58no—
179C2×C3×Q16—52no—
180C2×C3×SD16—52no—
181C2×C3×M16—51no—
182Q8×Dic3—52no—
183Q8×Dic3—52no—
184Q8×Dic3—51no—
185Q8×Dic3—51no—
186Q8×Dic3—101no—
187Q8×Dic3—101no—
188D4×Dic3—51no—
189D4×Dic3—51no—
190D4×Dic3—101no—
191D4×Dic3—101no—
192#926—101no—
193#926C2×D511yescharacteristic
194C2×C4⋊Dic3—51no—
195C2×C4⋊Dic3—101no—
196C2×C4×Dic3—51no—
197C2×C4×Dic3—101no—
198C2×C4×Dic3—101no—
199C2×#208C2×D511yescharacteristic
200#835—52no—
201#835C2×D512yes—
202#835C2×D512yes—
203#832—52no—
204#818—52no—
205#817—52no—
206#815—52no—
207C8×Dic3—52no—
208C2×C5×Q8—21no—
209C2×C5×Q8—22no—
210C2×C5×Q8C2×Dic314yescomplemented
211C2×C5×Q8C22×D312yes—
212C22×C4×C5—21no—
213C22×C4×C5C22×D311yescharacteristic
214C2×C22⋊D5—21no—
215C22×Dic5—31no—
216C22×Dic5—31no—
217C22×Dic5—61no—
218#709—22no—
219#709C2×Dic314yes—
220C2×D20C22×D311yescharacteristic
221C2×C4×D5—21no—
222C2×C4×D5—61no—
223C2×C4×D5—61no—
224C2×Dic10C22×D311yescharacteristic
225C5×M16—62no—
226C2×C5×C8—32no—
227C5×C4⋊C4—31no—
228C5×C4⋊C4—31no—
229C5×C22⋊C4—61no—
230C42×C5—61no—
231#689C2×Dic318yescomplemented
232#688C2×Dic318yescomplemented
233#685—61no—
234#685—61no—
235C4⋊Dic5—32no—
236C4⋊Dic5—62no—
237C4⋊Dic5—62no—
238C4⋊Dic5—61no—
239#683—61no—
240#683—61no—
241C4×Dic5—31no—
242C4×Dic5—31no—
243C4×Dic5—31no—
244C4×Dic5—31no—
245C4×Dic5—61no—
246C4×Dic5—61no—
247C4×Dic5—62no—
248C4×Dic5—62no—
249#681C2×Dic314yescomplemented
250C2×#168C22×D312yes—
251C2×#137—51no—
252C4×#41—151no—
253C2×C4×Q8—151no—
254#441—152no—
255#440—152no—
256C4×Q16—152no—
257C4×SD16—152no—
258#428—151no—
259#419—31no—
260#417—151no—
261C4×M16—151no—
262C22×C3×C5—21no—
263C22×C3×C5—21no—
264C22×C3×C5C4×D412yes—
265C22×C3×C5C22×D411yescharacteristic
266C2×C3×D5—22no—
267C2×C3×D5—41no—
268C2×C3×D5—41no—
269C3×C4×C5—24no—
270C3×C4×C5C4×D412yes—
271C3×C4×C5C23×C411yescharacteristic
272C3×C4×C5C2×#4111yescharacteristic
273Dic15—21no—
274Dic15—21no—
275Dic15—21no—
276Dic15—42no—
277Dic15#13712yescomplemented
278C3×Dic5—22no—
279C5×Dic3—41no—
280C5×Dic3—41no—
281C3×#41—54no—
282C3×#41—102no—
283C2×C3×Q8—21no—
284C2×C3×Q8—22no—
285C2×C3×Q8—51no—
286C2×C3×Q8C4×D514yescomplemented
287C2×C3×Q8C22×D512yes—
288C2×C3×D4—51no—
289C2×C3×D4—101no—
290C22×C3×C4—21no—
291C22×C3×C4—101no—
292C22×C3×C4C22×D511yescharacteristic
293C22×Dic3—51no—
294C22×Dic3—51no—
295C22×Dic3—101no—
296C22×Dic3—101no—
297C22×Dic3—101no—
298C3×Q16—58no—
299C3×SD16—58no—
300C3×M16—54no—
301C2×C3×C8—52no—
302#217—21no—
303#217—101no—
304#217—101no—
305C4⋊Dic3—52no—
306C4⋊Dic3—101no—
307C4⋊Dic3—101no—
308C4⋊Dic3—102no—
309C4⋊Dic3—102no—
310C4⋊Dic3—101no—
311C4⋊Dic3C22×D511yescharacteristic
312C4⋊Dic3C22×D511yescharacteristic
313C4×Dic3—21no—
314C4×Dic3—51no—
315C4×Dic3—51no—
316C4×Dic3—51no—
317C4×Dic3—51no—
318C4×Dic3—101no—
319C4×Dic3—101no—
320C4×Dic3—102no—
321C4×Dic3—102no—
322#208—22no—
323C2×C3⋊C8C22×D512yes—
324C23×C5D3×D411yescharacteristic
325C22×D5—21no—
326C5×Q8—24no—
327C5×Q8—22no—
328C5×Q8C22×Dic314yes—
329C2×C4×C5—24no—
330C2×C4×C5—22no—
331C2×C4×C5—61no—
332C2×C4×C5—61no—
333C2×C4×C5D3×D411yescharacteristic
334C2×C4×C5#23712yes—
335C2×C4×C5C22×Dic312yes—
336C2×C4×C5C23×D311yescharacteristic
337C22⋊D5—24no—
338C2×Dic5—21no—
339C2×Dic5—31no—
340C2×Dic5—31no—
341C2×Dic5—31no—
342C2×Dic5—31no—
343C2×Dic5—62no—
344C2×Dic5—62no—
345C2×Dic5—121no—
346C2×Dic5—122no—
347D20—21no—
348D20C22×Dic312yes—
349C4×D5—24no—
350C4×D5—122no—
351C4×D5—122no—
352Dic10—21no—
353Dic10C22×Dic312yes—
354C5×C8—62no—
355#168C22×Dic314yes—
356C2×#41—51no—
357C22×Q8D3×D511yescharacteristic
358#137—58no—
359C2×Q16—52no—
360C2×SD16—52no—
361C2×M16—31no—
362C2×M16—51no—
363C4×Q8—151no—
364C4×Q8—151no—
365C4×Q8—152no—
366C4×Q8—152no—
367C4×Q8—301no—
368C4×Q8—301no—
369C4×D4—151no—
370C4×D4—151no—
371C4×D4—301no—
372C4×D4—301no—
373#117—31no—
374#117—301no—
375C2×C4⋊C4—151no—
376C2×C4⋊C4—301no—
377C2×C42—151no—
378C2×C42—301no—
379C2×C42—301no—
380#107—152no—
381#106—152no—
382#103—32no—
383#103—32no—
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
392C3×D5—42no—
393C23×C3—101no—
394C23×C3D4×D511yescharacteristic
395C3×Q8—22no—
396C3×Q8—24no—
397C3×Q8—52no—
398C3×Q8—101no—
399C3×Q8C2×C4×D514yes—
400C3×D4—52no—
401C3×D4—104no—
402C3×D4—101no—
403C2×C3×C4—22no—
404C2×C3×C4—24no—
405C2×C3×C4—101no—
406C2×C3×C4—104no—
407C2×C3×C4C2×C4×D512yes—
408C2×C3×C4D4×D511yescharacteristic
409C2×C3×C4#71112yes—
410C2×C3×C4C23×D511yescharacteristic
411C2×Dic3—21no—
412C2×Dic3—21no—
413C2×Dic3—51no—
414C2×Dic3—51no—
415C2×Dic3—51no—
416C2×Dic3—51no—
417C2×Dic3—102no—
418C2×Dic3—102no—
419C2×Dic3—202no—
420C2×Dic3—202no—
421C2×Dic3—201no—
422C2×Dic3—202no—
423C3×C8—54no—
424C3⋊C8—22no—
425C22×C5—21no—
426C22×C5—21no—
427C22×C5D4×Dic312yes—
428C22×C5C2×D3×D411yescharacteristic
429C2×D5—22no—
430C2×D5—41no—
431C2×D5—41no—
432C4×C5—24no—
433C4×C5—121no—
434C4×C5—121no—
435C4×C5D4×Dic312yes—
436C4×C5C2×#23711yescharacteristic
437C4×C5C23×Dic311yescharacteristic
438Dic5—22no—
439Dic5—32no—
440Dic5—61no—
441Dic5—61no—
442Dic5—61no—
443Dic5—122no—
444#41—54no—
445#41—102no—
446C2×Q8—22no—
447C2×Q8—21no—
448C2×Q8—51no—
449C2×Q8D5×Dic314yescomplemented
450C2×Q8C2×D3×D512yes—
451C2×D4—51no—
452C2×D4—101no—
453C22×C4—21no—
454C22×C4—101no—
455C22×C4—151no—
456C22×C4—151no—
457C22×C4—301no—
458C22×C4—301no—
459C22×C4—301no—
460C22×C4C2×D3×D511yescharacteristic
461Q16—58no—
462SD16—58no—
463M16—54no—
464M16—62no—
465C2×C8—32no—
466C2×C8—52no—
467C4⋊C4—31no—
468C4⋊C4—31no—
469C4⋊C4—152no—
470C4⋊C4—302no—
471C4⋊C4—302no—
472C4⋊C4—301no—
473C4⋊C4—301no—
474C4⋊C4—301no—
475C22⋊C4—61no—
476C22⋊C4—301no—
477C22⋊C4—301no—
478C42—61no—
479C42—151no—
480C42—151no—
481C42—151no—
482C42—151no—
483C42—302no—
484C42—302no—
485C42—301no—
486C42—301no—
487C3×C5C4×#13711yescharacteristic, complemented, Hall
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—102no—
491C22×C3—201no—
492C22×C3—201no—
493C22×C3#402712yes—
494C22×C3C2×D4×D511yescharacteristic
495C3×C4—24no—
496C3×C4—102no—
497C3×C4#402712yes—
498C3×C4C22×C4×D511yescharacteristic
499C3×C4C2×#71111yescharacteristic
500Dic3—41no—
501Dic3—41no—
502Dic3—52no—
503Dic3—101no—
504Dic3—101no—
505Dic3—101no—
506Dic3—202no—
507C2×C5—22no—
508C2×C5D3×#13711yescharacteristic
509C2×C5#577711yescharacteristic
510C2×C5C2×D4×Dic311yescharacteristic
511D5—42no—
512C23—101no—
513C23#679011yescharacteristic
514Q8—22no—
515Q8—24no—
516Q8—52no—
517Q8—101no—
518Q8C2×D5×Dic314yes—
519D4—52no—
520D4—104no—
521D4—101no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—61no—
525C2×C4—61no—
526C2×C4—101no—
527C2×C4—104no—
528C2×C4—151no—
529C2×C4—151no—
530C2×C4—151no—
531C2×C4—151no—
532C2×C4—302no—
533C2×C4—302no—
534C2×C4—602no—
535C2×C4—602no—
536C2×C4—601no—
537C2×C4—602no—
538C2×C4C2×D5×Dic312yes—
539C2×C4#678012yes—
540C2×C4#679011yescharacteristic
541C2×C4C22×D3×D511yescharacteristic
542C8—54no—
543C8—62no—
544C2×C3—22no—
545C2×C3—202no—
546C2×C3C2×#402711yescharacteristic
547C2×C3D5×#13711yescharacteristic
548C2×C3#6611111yescharacteristic
549C5Dic3×#13711yescharacteristic, complemented, Sylow
550C22—21no—
551C22—21no—
552C22—102no—
553C22—201no—
554C22—201no—
555C22#9155912yes—
556C22C2×#679011yescharacteristic
557C4—24no—
558C4—102no—
559C4—121no—
560C4—121no—
561C4—152no—
562C4—301no—
563C4—301no—
564C4—301no—
565C4—602no—
566C4#9155912yes—
567C4C22×D5×Dic311yescharacteristic
568C4C2×#678011yescharacteristic
569C3#1061067711yescharacteristic, complemented, Sylow
570C2—22no—
571C2—202no—
572C2#1175509511yescharacteristic
573C2#1175509611yescharacteristic
574C2C2×#9155911yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
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
1. C2×Q8×Dic15C2semidirect
4. C5×#5225C2semidirect
5. #11749264C2semidirect
6. #11749263C2semidirect
7. #11749241C2semidirect
8. #11749239C2semidirect
9. #11748460C2semidirect
11. #11748328C2semidirect
26. C3×#4088C4semidirect
59. C2×C3×C5×Q8C2×C4semidirect
90. C3×#689C2×C4semidirect
91. C3×#688C2×C4semidirect
92. C3×#681C2×C4semidirect
104. #5225D5semidirect
120. #4088Dic3semidirect
210. C2×C5×Q8C2×Dic3semidirect
231. #689C2×Dic3semidirect
232. #688C2×Dic3semidirect
249. #681C2×Dic3semidirect
277. Dic15#137semidirect
286. C2×C3×Q8C4×D5semidirect
449. C2×Q8D5×Dic3semidirect
487. C3×C5C4×#137semidirect
549. C5Dic3×#137semidirect
569. C3#10610677semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic152
C2×C3×#40882
#117544442
C5×#52252
#117492642
#117492632
#117492412
#117492392
#117484602
#117483692
#117483282
#106106773
Dic3×#1375