Finite Group Databasebeta

← #14416890

Subgroups — #14416890

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
1C5×#5522C211yesmaximal, characteristic
2C2×Dic3×Dic10C211yesmaximal, characteristic, complemented
3C2×#91309C211yesmaximal, characteristic
4#11751096C211yesmaximal, characteristic, complemented
5C3×#65293C211yesmaximal, characteristic, complemented
6#11748390C211yesmaximal, characteristic
7Dic3×#681C211yesmaximal, characteristic, complemented
8#11747267C212yesmaximal, complemented
9#11747266C212yesmaximal, complemented
10#11747265C212yesmaximal, complemented
11#11747264C212yesmaximal, complemented
12C4×#4097—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×#6710C2211yescharacteristic
18C2×C4×C5×Dic3C2211yescharacteristic
19C5×#893C2211yescharacteristic
20C5×#893C2211yescharacteristic
21C5×#887C2211yescharacteristic
22C5×#887C2211yescharacteristic
23C5×#67⋊C4—21no—
24C5×#67⋊C4—21no—
25C5×#872—21no—
26C42×C5×D3—21no—
27C2×C3×#681C2211yescharacteristic
28C2×#6668—21no—
29C2×Dic3×Dic5—21no—
30Dic3×Dic10—21no—
31Dic3×Dic10—21no—
32Dic3×Dic10C2212yes—
33Dic3×Dic10C2212yes—
34C2×#6661C2212yes—
35#91309C418yescomplemented
36C2×#6656C2212yes—
37#91092C2212yes—
38#91091C2212yes—
39C3×#3942C2212yes—
40C3×#3942C2212yes—
41#90973C2212yes—
42#90967C2212yes—
43#90953C2212yes—
44Dic3×#168C2212yes—
45#78946—51nomaximal, Hall
46C4×C5×#41—31no—
47C2×#4097—31no—
48C2×C4×Dic10—31no—
49#65521—31no—
50#65319—32no—
51C4×#689—32no—
52#65307—32no—
53C4×#687—32no—
54#65293D311yescharacteristic, complemented
55#65284—31no—
56C4×#681—31no—
57C22×C3×C4×C5C2311yescharacteristic
58C22×Dic15—21no—
59C2×C5×#67—21no—
60C22×C5×Dic3D411yescharacteristic
61C22×C5×Dic3D411yescharacteristic
62C5×#235—22no—
63C5×#235C2×C414yes—
64C2×C5×D12C2311yescharacteristic
65C2×C4×C5×D3—21no—
66C2×C4×C5×D3—21no—
67C2×C4×C5×D3—21no—
68C2×C5×Dic6C2311yescharacteristic
69C22×C3×Dic5—21no—
70C2×C3×Dic10—21no—
71C2×C3×Dic10—22no—
72C2×C3×Dic10C2×C414yescomplemented
73C2×C3×Dic10C2312yes—
74C3×C5×C4⋊C4C2311yescharacteristic
75C3×C5×C4⋊C4C2311yescharacteristic
76C3×C5×C22⋊C4—21no—
77C3×C42×C5—21no—
78C4⋊Dic15—21no—
79C4⋊Dic15C2312yes—
80#6710C2×C414yescomplemented
81C2×C3⋊#168C2312yes—
82C5×(C2×D3)⋊C4—21no—
83C5×(C2×D3)⋊C4—21no—
84C5×Dic3⋊C4—21no—
85C5×Dic3⋊C4—21no—
86C4×C5×Dic3—21no—
87C4×C5×Dic3—21no—
88C4×C5×Dic3D411yescharacteristic
89C4×C5×Dic3D411yescharacteristic
90C4×C5×Dic3C2311yescharacteristic
91C4×C5×Dic3C2311yescharacteristic
92C3×#681—22no—
93C2×C3×#168C2312yes—
94#6668—22no—
95#6668—22no—
96Dic3×Dic5—22no—
97Dic3×Dic5—22no—
98#6661C2×C418yescomplemented
99#6656C2×C418yescomplemented
100C2×Q8×Dic3—51no—
101C2×#942—51no—
102#5522D511yescharacteristic
103C3×#419—51no—
104#5133—51no—
105Dic3×M16—51no—
106#4995—51no—
107#4817—52no—
108#4790—52no—
109#4789—52no—
110#4788—52no—
111C2×C5×#41—31no—
112C22×Dic10C2×D311yescharacteristic
113C4×C5×Q8—31no—
114C4×C5×Q8—31no—
115C4×C5×D4—31no—
116C4×C5×D4—31no—
117C4×C5×D4—61no—
118C4×C5×D4—61no—
119C5×#117—61no—
120C5×#117C2×D311yescharacteristic
121C2×C42×C5—31no—
122C2×C42×C5—61no—
123#4097—38no—
124C2×#689—32no—
125C2×#687—32no—
126C2×C4⋊Dic5—31no—
127C2×#683—61no—
128C2×C4×Dic5—61no—
129C2×#681—31no—
130C2×#681C2×D311yescharacteristic
131C4×Dic10—32no—
132C4×Dic10—32no—
133C4×Dic10—61no—
134C4×Dic10—61no—
135#3967—32no—
136#3964—32no—
137#3942C2×D312yes—
138#3942C2×D312yes—
139#3940—32no—
140#3939—32no—
141#3935—32no—
142C4×#168—32no—
143C4×#137—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×C5×D3—21no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5C22×C412yes—
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5#4112yes—
151C2×C3×C4×C5C2411yescharacteristic
152C2×Dic15—22no—
153C2×Dic15—42no—
154C5×#67—24no—
155C2×C5×Dic3—21no—
156C2×C5×Dic3—22no—
157C2×C5×Dic3—41no—
158C2×C5×Dic3C2×D411yescharacteristic
159C2×C5×Dic3C2×D411yescharacteristic
160C2×C5×Dic3C2×D411yescharacteristic
161C2×C5×Dic3C2×D411yescharacteristic
162C5×D12—21no—
163C5×D12C22×C412yes—
164C4×C5×D3—24no—
165C4×C5×D3—42no—
166C4×C5×D3—42no—
167C5×Dic6—21no—
168C5×Dic6C22×C412yes—
169C2×C3×Dic5—24no—
170C2×C3×Dic5—22no—
171C3×Dic10—24no—
172C3×Dic10—22no—
173C3×Dic10C22×C414yes—
174C3⋊#168C22×C414yes—
175C3×#168—22no—
176C22×C3×Q8—51no—
177C2×#235C2×D511yescharacteristic
178C2×C3×M16—51no—
179C3×#117C2×D511yescharacteristic
180Q8×Dic3—52no—
181Q8×Dic3—52no—
182Q8×Dic3—101no—
183Q8×Dic3—101no—
184C2×#216—52no—
185#942—58no—
186C2×#215—52no—
187C2×C4⋊Dic3—51no—
188C2×C4⋊Dic3—101no—
189C2×C4×Dic3—101no—
190C2×C4×Dic3C2×D511yescharacteristic
191C2×#208—51no—
192#893C2×D511yescharacteristic
193#893C2×D511yescharacteristic
194#887C2×D511yescharacteristic
195#887C2×D511yescharacteristic
196#67⋊C4—21no—
197#67⋊C4—21no—
198#872—21no—
199C42×D3—21no—
200C3×#103—52no—
201C3×#103—52no—
202#821—52no—
203#816—52no—
204#815—52no—
205C8×Dic3—52no—
206#808—52no—
207#807—52no—
208C5×#41—34no—
209C5×#41—62no—
210C2×C5×Q8—31no—
211C2×C5×D4—31no—
212C2×C5×D4—61no—
213C22×C4×C5—31no—
214C22×C4×C5—31no—
215C22×C4×C5—61no—
216C22×C4×C5—61no—
217C22×C4×C5—61no—
218C22×C4×C5C22×D311yescharacteristic
219C22×Dic5—21no—
220C22×Dic5—61no—
221C2×Dic10—21no—
222C2×Dic10—22no—
223C2×Dic10C4×D314yescomplemented
224C2×Dic10C22×D312yes—
225C5×C4⋊C4—61no—
226C5×C4⋊C4—61no—
227C5×C4⋊C4C22×D311yescharacteristic
228C5×C4⋊C4C22×D311yescharacteristic
229C5×C22⋊C4—21no—
230C5×C22⋊C4—61no—
231C5×C22⋊C4—61no—
232C42×C5—21no—
233C42×C5—31no—
234C42×C5—31no—
235C42×C5—31no—
236C42×C5—31no—
237C42×C5—61no—
238C42×C5—61no—
239#689—38no—
240#687—38no—
241C4⋊Dic5—32no—
242C4⋊Dic5—61no—
243#683—62no—
244#683—62no—
245C4×Dic5—62no—
246C4×Dic5—62no—
247#681—22no—
248#681—34no—
249C2×#168—32no—
250C2×#168C22×D312yes—
251C2×#137—151no—
252C4×#41—31no—
253C2×C4×Q8—151no—
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×C5×D3—22no—
267C2×C5×D3—41no—
268C2×C5×D3—41no—
269C3×C4×C5—41no—
270C3×C4×C5—41no—
271C3×C4×C5C4×D412yes—
272C3×C4×C5C23×C411yescharacteristic
273C3×C4×C5C2×#4111yescharacteristic
274Dic15—42no—
275C3×Dic5—24no—
276C5×Dic3—22no—
277C5×Dic3—21no—
278C5×Dic3—21no—
279C5×Dic3—21no—
280C5×Dic3#13712yescomplemented
281C2×C3×Q8—54no—
282C2×C3×Q8—52no—
283C2×C3×Q8—102no—
284C2×C3×Q8—101no—
285C22×C3×C4—101no—
286C22×C3×C4C22×D511yescharacteristic
287C2×#67—21no—
288C22×Dic3—101no—
289C22×Dic3C22⋊D511yescharacteristic
290C22×Dic3C22⋊D511yescharacteristic
291#235—22no—
292#235C4×D514yes—
293C2×D12C22×D511yescharacteristic
294C2×C4×D3—21no—
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297C2×Dic6C22×D511yescharacteristic
298C3×M16—102no—
299C2×C3×C8—52no—
300C3×C4⋊C4C22×D511yescharacteristic
301C3×C4⋊C4C22×D511yescharacteristic
302C3×C22⋊C4—21no—
303C3×C42—21no—
304#216—58no—
305#215—58no—
306(C2×D3)⋊C4—21no—
307(C2×D3)⋊C4—21no—
308C4⋊Dic3—52no—
309C4⋊Dic3—101no—
310C4⋊Dic3—102no—
311C4⋊Dic3—102no—
312Dic3⋊C4—21no—
313Dic3⋊C4—21no—
314C4×Dic3—21no—
315C4×Dic3—21no—
316C4×Dic3—102no—
317C4×Dic3—102no—
318C4×Dic3C22⋊D511yescharacteristic
319C4×Dic3C22⋊D511yescharacteristic
320C4×Dic3C22×D511yescharacteristic
321C4×Dic3C22×D511yescharacteristic
322#208—54no—
323C2×C3⋊C8—52no—
324C23×C5—61no—
325C23×C5D3×D411yescharacteristic
326C5×Q8—32no—
327C5×Q8—61no—
328C5×D4—32no—
329C5×D4—64no—
330C5×D4—61no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—31no—
334C2×C4×C5—31no—
335C2×C4×C5—31no—
336C2×C4×C5—31no—
337C2×C4×C5—62no—
338C2×C4×C5—61no—
339C2×C4×C5—64no—
340C2×C4×C5—122no—
341C2×C4×C5—122no—
342C2×C4×C5—121no—
343C2×C4×C5C2×C4×D312yes—
344C2×C4×C5D3×D411yescharacteristic
345C2×C4×C5#23712yes—
346C2×C4×C5C23×D311yescharacteristic
347C2×Dic5—24no—
348C2×Dic5—22no—
349C2×Dic5—62no—
350C2×Dic5—122no—
351Dic10—24no—
352Dic10—22no—
353Dic10C2×C4×D314yes—
354#168—22no—
355#168—34no—
356C2×#41—31no—
357C22×Q8—51no—
358#137—158no—
359C2×Q16—152no—
360C2×SD16—152no—
361C2×M16—51no—
362C2×M16—151no—
363C4×Q8—31no—
364C4×Q8—31no—
365C4×Q8—152no—
366C4×Q8—152no—
367C4×Q8—301no—
368C4×Q8—301no—
369C4×D4—31no—
370C4×D4—31no—
371C4×D4—61no—
372C4×D4—61no—
373#117—61no—
374#117D3×D511yescharacteristic
375C2×C4⋊C4—151no—
376C2×C4⋊C4—301no—
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
392C5×D3—42no—
393C23×C3C2×C22⋊D511yescharacteristic
394C22×D3—21no—
395C3×Q8—54no—
396C3×Q8—102no—
397C3×Q8—104no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—102no—
401C2×C3×C4—104no—
402C2×C3×C4C2×C4×D512yes—
403C2×C3×C4#70912yes—
404C2×C3×C4C2×C22⋊D511yescharacteristic
405C2×C3×C4C23×D511yescharacteristic
406#67—24no—
407C2×Dic3—21no—
408C2×Dic3—22no—
409C2×Dic3—41no—
410C2×Dic3—102no—
411C2×Dic3—202no—
412C2×Dic3C2×C22⋊D511yescharacteristic
413C2×Dic3C2×C22⋊D511yescharacteristic
414C2×Dic3C2×C22⋊D511yescharacteristic
415C2×Dic3C2×C22⋊D511yescharacteristic
416D12—21no—
417D12C2×C4×D512yes—
418C4×D3—24no—
419C4×D3—42no—
420C4×D3—42no—
421Dic6—21no—
422Dic6C2×C4×D512yes—
423C3×C8—102no—
424C3⋊C8—54no—
425C22×C5—21no—
426C22×C5—21no—
427C22×C5—62no—
428C22×C5—121no—
429C22×C5—121no—
430C22×C5#67⋊C412yes—
431C22×C5C2×D3×D411yescharacteristic
432C4×C5—32no—
433C4×C5—41no—
434C4×C5—41no—
435C4×C5—62no—
436C4×C5—61no—
437C4×C5—61no—
438C4×C5—61no—
439C4×C5#67⋊C412yes—
440C4×C5C22×C4×D311yescharacteristic
441C4×C5C2×#23711yescharacteristic
442Dic5—24no—
443Dic5—122no—
444#41—34no—
445#41—62no—
446C2×Q8—31no—
447C2×Q8—54no—
448C2×Q8—52no—
449C2×Q8—102no—
450C2×Q8—101no—
451C2×D4—31no—
452C2×D4—61no—
453C22×C4—31no—
454C22×C4—31no—
455C22×C4—61no—
456C22×C4—61no—
457C22×C4—61no—
458C22×C4—101no—
459C22×C4—301no—
460C22×C4C2×D3×D511yescharacteristic
461Q16—158no—
462SD16—158no—
463M16—102no—
464M16—154no—
465C2×C8—52no—
466C2×C8—152no—
467C4⋊C4—61no—
468C4⋊C4—61no—
469C4⋊C4—152no—
470C4⋊C4—302no—
471C4⋊C4—302no—
472C4⋊C4—301no—
473C4⋊C4C2×D3×D511yescharacteristic
474C4⋊C4C2×D3×D511yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—61no—
477C22⋊C4—61no—
478C42—21no—
479C42—31no—
480C42—31no—
481C42—31no—
482C42—31no—
483C42—61no—
484C42—61no—
485C42—302no—
486C42—302no—
487C3×C5C4×#13711yescharacteristic, complemented, Hall
488C22×C3—21no—
489C22×C3—21no—
490C22×C3C4×C22⋊D512yes—
491C22×C3C22×C22⋊D511yescharacteristic
492C2×D3—22no—
493C2×D3—41no—
494C2×D3—41no—
495C3×C4—41no—
496C3×C4—41no—
497C3×C4—104no—
498C3×C4C4×C22⋊D512yes—
499C3×C4C22×C4×D511yescharacteristic
500C3×C4C2×#70911yescharacteristic
501Dic3—22no—
502Dic3—21no—
503Dic3—21no—
504Dic3—21no—
505Dic3—202no—
506Dic3#409712yescomplemented
507C2×C5—22no—
508C2×C5—122no—
509C2×C5C2×#67⋊C411yescharacteristic
510C2×C5D3×#13711yescharacteristic
511C2×C5#577711yescharacteristic
512C23—61no—
513C23D3×C22⋊D511yescharacteristic
514Q8—32no—
515Q8—54no—
516Q8—61no—
517Q8—104no—
518Q8—102no—
519D4—32no—
520D4—64no—
521D4—61no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—31no—
525C2×C4—31no—
526C2×C4—31no—
527C2×C4—31no—
528C2×C4—62no—
529C2×C4—61no—
530C2×C4—64no—
531C2×C4—104no—
532C2×C4—102no—
533C2×C4—122no—
534C2×C4—122no—
535C2×C4—121no—
536C2×C4—302no—
537C2×C4—602no—
538C2×C4#676512yes—
539C2×C4C4×D3×D512yes—
540C2×C4D3×C22⋊D511yescharacteristic
541C2×C4C22×D3×D511yescharacteristic
542C8—102no—
543C8—154no—
544C2×C3—22no—
545C2×C3C2×C4×C22⋊D511yescharacteristic
546C2×C3#6615611yescharacteristic
547C2×C3C2×#409711yescharacteristic
548D3—42no—
549C5#7894611yescharacteristic, complemented, Sylow
550C22—21no—
551C22—21no—
552C22—62no—
553C22—121no—
554C22—121no—
555C22#9144112yes—
556C22C2×D3×C22⋊D511yescharacteristic
557C4—32no—
558C4—41no—
559C4—41no—
560C4—62no—
561C4—61no—
562C4—61no—
563C4—61no—
564C4—104no—
565C4—602no—
566C4#9144112yes—
567C4C2×#676511yescharacteristic
568C4C2×C4×D3×D511yescharacteristic
569C3C4×#409711yescharacteristic, complemented, Sylow
570C2—22no—
571C2—122no—
572C2C2×#9144111yescharacteristic
573C2D3×#409711yescharacteristic
574C2#1175534811yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#235C22
cosocleC2×C3×C4×C5C24
hypercenter#117D3×D5
hypocenterC3×C5C4×#137
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×Dic10C2semidirect
4. #11751096C2semidirect
5. C3×#65293C2semidirect
7. Dic3×#681C2semidirect
8. #11747267C2semidirect
9. #11747266C2semidirect
10. #11747265C2semidirect
11. #11747264C2semidirect
35. #91309C4semidirect
54. #65293D3semidirect
72. C2×C3×Dic10C2×C4semidirect
80. #6710C2×C4semidirect
98. #6661C2×C4semidirect
99. #6656C2×C4semidirect
223. C2×Dic10C4×D3semidirect
280. C5×Dic3#137semidirect
487. C3×C5C4×#137semidirect
506. Dic3#4097semidirect
549. C5#78946semidirect
569. C3C4×#4097semidirect

Maximal subgroups

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

subgroupindex
C5×#55222
C2×Dic3×Dic102
C2×#913092
#117510962
C3×#652932
#117483902
Dic3×#6812
#117472672
#117472662
#117472652
#117472642
C4×#40973
#789465