Finite Group Databasebeta

← Dic5×#942 #14416899

Subgroups — Dic5×#942 #14416899

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×C5×#942C211yesmaximal, characteristic
2C2×C3×Q8×Dic5C211yesmaximal, characteristic, complemented
3Dic5×#235C211yesmaximal, characteristic
4#11751326C211yesmaximal, characteristic, complemented
5#11749247C212yesmaximal, complemented
6Dic5×#216C212yesmaximal, complemented
7#11749223C212yesmaximal, complemented
8Dic5×#215C212yesmaximal, complemented
9#11748453C211yesmaximal, characteristic, complemented
10#11748384C211yesmaximal, characteristic
11Dic5×#208C211yesmaximal, characteristic, complemented
12Dic5×#137—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15#91815C2211yescharacteristic
16C2×#6710C2211yescharacteristic
17C2×C5×#216C2212yes—
18C5×#942C418yescomplemented
19C2×C5×#215C2212yes—
20C2×C5×#208C2211yescharacteristic
21C3×Q8×Dic5—21no—
22C3×Q8×Dic5—21no—
23C3×Q8×Dic5C2212yes—
24C3×Q8×Dic5C2212yes—
25C2×C3×C4⋊Dic5—21no—
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C2×C3×C4×Dic5—21no—
28C2×C3×C4×Dic5C2211yescharacteristic
29Dic5×#67—21no—
30Dic5×#67—21no—
31Dic5×D12C2211yescharacteristic
32Dic5×D12C2211yescharacteristic
33C4×D3×Dic5—21no—
34#91371—21no—
35Dic5×Dic6C2211yescharacteristic
36Dic5×Dic6C2211yescharacteristic
37#91119C2212yes—
38#91119C2212yes—
39#90990C2212yes—
40#90987C2212yes—
41#90972C2212yes—
42#90966C2212yes—
43#90952C2212yes—
44Dic5×C3⋊C8C2212yes—
45C4×#942—51nomaximal, Hall
46C2×C5×#137—31no—
47#41×Dic5—31no—
48C2×Q8×Dic5D311yescharacteristic, complemented
49#65521—31no—
50#65514—31no—
51#65473—32no—
52Q16×Dic5—32no—
53#65453—32no—
54SD16×Dic5—32no—
55#65410—31no—
56M16×Dic5—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×C5×#67—21no—
64C5×#235—22no—
65C5×#235C2×C414yes—
66C2×C5×D12C2311yescharacteristic
67C2×C4×C5×D3—21no—
68C2×C5×Dic6C2311yescharacteristic
69C22×C3×Dic5—21no—
70C22×C3×Dic5D411yescharacteristic
71C22×C3×Dic5D411yescharacteristic
72C2×D3×Dic5—21no—
73C2×D3×Dic5—21no—
74#6719—21no—
75C4⋊Dic15C2311yescharacteristic
76C4⋊Dic15C2311yescharacteristic
77C4×Dic15—21no—
78#6710—22no—
79C2×C3⋊#168C2312yes—
80C5×#216C2×C418yescomplemented
81C5×#215C2×C418yescomplemented
82C5×#208C2×C414yescomplemented
83C2×C5×C3⋊C8C2312yes—
84C3×C4⋊Dic5—21no—
85C3×C4⋊Dic5—22no—
86C3×C4⋊Dic5—22no—
87C3×C4⋊Dic5C2312yes—
88C3×C4×Dic5—22no—
89C3×C4×Dic5—22no—
90C3×C4×Dic5D411yescharacteristic
91C3×C4×Dic5D411yescharacteristic
92C3×C4×Dic5C2311yescharacteristic
93C3×C4×Dic5C2311yescharacteristic
94Dic3⋊Dic5—21no—
95Dic3⋊Dic5—21no—
96(C2×D3)⋊Dic5—21no—
97(C2×D3)⋊Dic5—21no—
98Dic3×Dic5—21no—
99Dic3×Dic5—21no—
100C2×C3×C4×Q8—51no—
101C2×#942D511yescharacteristic
102C4×#235—51no—
103#5225—51no—
104#5030—52no—
105C4×#216—52no—
106#5026—52no—
107C4×#215—52no—
108#4966—51no—
109#4964—51no—
110C4×#208—51no—
111C2×C5×#41—31no—
112C22×C5×Q8C2×D311yescharacteristic
113C5×#137—38no—
114C2×C5×Q16—32no—
115C2×C5×SD16—32no—
116C2×C5×M16—31no—
117Q8×Dic5—21no—
118Q8×Dic5—21no—
119Q8×Dic5—31no—
120Q8×Dic5—31no—
121Q8×Dic5C2×D312yes—
122Q8×Dic5C2×D312yes—
123D4×Dic5—31no—
124D4×Dic5—31no—
125D4×Dic5—61no—
126D4×Dic5—61no—
127#4072—31no—
128#4072—61no—
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5C2×D311yescharacteristic
131C2×C4×Dic5—21no—
132C2×C4×Dic5—61no—
133C2×C4×Dic5C2×D311yescharacteristic
134C2×#681—31no—
135#3967—32no—
136#3967—32no—
137#3967—32no—
138#3964—32no—
139#3950—32no—
140#3949—32no—
141#3947—32no—
142C8×Dic5—32no—
143C4×#137—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×C5×D3—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—21no—
156C2×Dic15—21no—
157C5×#67—24no—
158C2×C5×Dic3—21no—
159C5×D12—21no—
160C5×D12C22×C412yes—
161C4×C5×D3—24no—
162C5×Dic6—21no—
163C5×Dic6C22×C412yes—
164C2×C3×Dic5—22no—
165C2×C3×Dic5—22no—
166C2×C3×Dic5—41no—
167C2×C3×Dic5—42no—
168C2×C3×Dic5C2×D411yescharacteristic
169C2×C3×Dic5C2×D411yescharacteristic
170C2×C3×Dic5C2×D411yescharacteristic
171C2×C3×Dic5C2×D411yescharacteristic
172D3×Dic5—42no—
173D3×Dic5—42no—
174C3⋊#168—22no—
175C5×C3⋊C8C22×C414yes—
176C22×C3×Q8C2×D511yescharacteristic
177C2×#235C2×D511yescharacteristic
178C3×C4×Q8—52no—
179C3×C4×Q8—52no—
180C3×C4×Q8—101no—
181C3×C4×Q8—101no—
182C2×C3×C4⋊C4—51no—
183C2×C3×C4⋊C4—101no—
184C2×C3×C42—51no—
185C2×C3×C42—101no—
186C2×#216C2×D512yes—
187#942Dic518yesdirect product factor
188C2×#215C2×D512yes—
189C4×#67—101no—
190C4×#67—101no—
191#926—51no—
192C2×#208—51no—
193C2×#208C2×D511yescharacteristic
194C4×D12—51no—
195C4×D12—51no—
196#872—101no—
197C42×D3—101no—
198C4×Dic6—51no—
199C4×Dic6—51no—
200#835—52no—
201#835—52no—
202#810—52no—
203#809—52no—
204#808—52no—
205#807—52no—
206#803—52no—
207C4×C3⋊C8—52no—
208C5×#41—34no—
209C5×#41—62no—
210C2×C5×Q8—22no—
211C2×C5×Q8—21no—
212C2×C5×Q8—31no—
213C2×C5×Q8C4×D314yescomplemented
214C2×C5×Q8C22×D312yes—
215C2×C5×D4—31no—
216C2×C5×D4—61no—
217C22×C4×C5—21no—
218C22×C4×C5—61no—
219C22×C4×C5C22×D311yescharacteristic
220C22×Dic5—21no—
221C22×Dic5—61no—
222C22×Dic5—61no—
223C22×Dic5#6711yescharacteristic
224C22×Dic5#6711yescharacteristic
225C5×Q16—38no—
226C5×SD16—38no—
227C5×M16—34no—
228C2×C5×C8—32no—
229C22⋊Dic5—61no—
230C22⋊Dic5—61no—
231C22⋊Dic5—61no—
232C4⋊Dic5—21no—
233C4⋊Dic5—22no—
234C4⋊Dic5—22no—
235C4⋊Dic5—31no—
236C4⋊Dic5—31no—
237C4⋊Dic5—61no—
238C4⋊Dic5—61no—
239C4⋊Dic5C22×D312yes—
240C4×Dic5—22no—
241C4×Dic5—22no—
242C4×Dic5—61no—
243C4×Dic5—61no—
244C4×Dic5—61no—
245C4×Dic5#6711yescharacteristic
246C4×Dic5#6711yescharacteristic
247C4×Dic5C22×D311yescharacteristic
248C4×Dic5C22×D311yescharacteristic
249#681—62no—
250C2×#168—32no—
251C2×#137—31no—
252C4×#41—151no—
253C2×C4×Q8—51no—
254#441—152no—
255#440—152no—
256C4×Q16—152no—
257C4×SD16—152no—
258#428—151no—
259#419—151no—
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—24no—
270C3×C4×C5C4×D412yes—
271C3×C4×C5C23×C411yescharacteristic
272C3×C4×C5C2×#4111yescharacteristic
273Dic15—41no—
274Dic15—41no—
275C3×Dic5—21no—
276C3×Dic5—21no—
277C3×Dic5—21no—
278C3×Dic5—42no—
279C3×Dic5#13712yescomplemented
280C5×Dic3—22no—
281C2×C3×Q8—21no—
282C2×C3×Q8—22no—
283C2×C3×Q8C2×Dic514yescomplemented
284C2×C3×Q8C22×D512yes—
285C22×C3×C4—21no—
286C22×C3×C4—51no—
287C22×C3×C4—51no—
288C22×C3×C4—101no—
289C22×C3×C4C22×D511yescharacteristic
290C2×#67—21no—
291#235—22no—
292#235C2×Dic514yes—
293C2×D12C22×D511yescharacteristic
294C2×C4×D3—21no—
295C2×C4×D3—101no—
296C2×C4×D3—101no—
297C2×Dic6C22×D511yescharacteristic
298C3×C4⋊C4—52no—
299C3×C4⋊C4—102no—
300C3×C4⋊C4—102no—
301C3×C4⋊C4—101no—
302C3×C42—51no—
303C3×C42—51no—
304C3×C42—51no—
305C3×C42—51no—
306C3×C42—102no—
307C3×C42—102no—
308#217—101no—
309#216C2×Dic518yescomplemented
310#215C2×Dic518yescomplemented
311(C2×D3)⋊C4—101no—
312(C2×D3)⋊C4—101no—
313C4⋊Dic3—51no—
314C4⋊Dic3—51no—
315Dic3⋊C4—101no—
316Dic3⋊C4—101no—
317C4×Dic3—101no—
318C4×Dic3—101no—
319C4×Dic3—101no—
320#208—102no—
321#208C2×Dic514yescomplemented
322C2×C3⋊C8—52no—
323C2×C3⋊C8C22×D512yes—
324C23×C5—61no—
325C23×C5C2×#6711yescharacteristic
326C5×Q8—24no—
327C5×Q8—22no—
328C5×Q8—32no—
329C5×Q8—61no—
330C5×Q8C2×C4×D314yes—
331C5×D4—32no—
332C5×D4—64no—
333C5×D4—61no—
334C2×C4×C5—24no—
335C2×C4×C5—22no—
336C2×C4×C5—61no—
337C2×C4×C5—64no—
338C2×C4×C5C2×C4×D312yes—
339C2×C4×C5#23512yes—
340C2×C4×C5C2×#6711yescharacteristic
341C2×C4×C5C23×D311yescharacteristic
342C2×Dic5—22no—
343C2×Dic5—22no—
344C2×Dic5—41no—
345C2×Dic5—42no—
346C2×Dic5—61no—
347C2×Dic5—61no—
348C2×Dic5—122no—
349C2×Dic5—122no—
350C2×Dic5C2×#6711yescharacteristic
351C2×Dic5C2×#6711yescharacteristic
352C2×Dic5C2×#6711yescharacteristic
353C2×Dic5C2×#6711yescharacteristic
354C5×C8—34no—
355#168—62no—
356C2×#41—31no—
357C22×Q8D3×D511yescharacteristic
358#137—38no—
359C2×Q16—32no—
360C2×SD16—32no—
361C2×M16—31no—
362C2×M16—151no—
363C4×Q8—52no—
364C4×Q8—52no—
365C4×Q8—101no—
366C4×Q8—101no—
367C4×Q8—151no—
368C4×Q8—151no—
369C4×D4—151no—
370C4×D4—151no—
371C4×D4—301no—
372C4×D4—301no—
373#117—151no—
374#117—301no—
375C2×C4⋊C4—51no—
376C2×C4⋊C4—101no—
377C2×C42—51no—
378C2×C42—101no—
379C2×C42—301no—
380#107—152no—
381#106—152no—
382#103—152no—
383#103—152no—
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×C3D4×D511yescharacteristic
394C22×D3—21no—
395C3×Q8—22no—
396C3×Q8—24no—
397C3×Q8C22×Dic514yes—
398C2×C3×C4—22no—
399C2×C3×C4—24no—
400C2×C3×C4—51no—
401C2×C3×C4—51no—
402C2×C3×C4—51no—
403C2×C3×C4—51no—
404C2×C3×C4—102no—
405C2×C3×C4—102no—
406C2×C3×C4—201no—
407C2×C3×C4—202no—
408C2×C3×C4D4×D511yescharacteristic
409C2×C3×C4#71112yes—
410C2×C3×C4C22×Dic512yes—
411C2×C3×C4C23×D511yescharacteristic
412#67—24no—
413C2×Dic3—21no—
414C2×Dic3—101no—
415C2×Dic3—101no—
416D12—21no—
417D12C22×Dic512yes—
418C4×D3—24no—
419C4×D3—202no—
420C4×D3—202no—
421Dic6—21no—
422Dic6C22×Dic512yes—
423C3⋊C8—102no—
424C3⋊C8C22×Dic514yes—
425C22×C5—21no—
426C22×C5—21no—
427C22×C5—62no—
428C22×C5—121no—
429C22×C5—121no—
430C22×C5C4×#6712yes—
431C22×C5C22×#6711yescharacteristic
432C4×C5—24no—
433C4×C5—62no—
434C4×C5C4×#6712yes—
435C4×C5C22×C4×D311yescharacteristic
436C4×C5C2×#23511yescharacteristic
437Dic5—21no—
438Dic5—21no—
439Dic5—21no—
440Dic5—42no—
441Dic5—121no—
442Dic5—121no—
443Dic5#94212yesdirect product factor
444#41—34no—
445#41—62no—
446C2×Q8—22no—
447C2×Q8—21no—
448C2×Q8—31no—
449C2×Q8D3×Dic514yescomplemented
450C2×Q8C2×D3×D512yes—
451C2×D4—31no—
452C2×D4—61no—
453C22×C4—21no—
454C22×C4—51no—
455C22×C4—51no—
456C22×C4—61no—
457C22×C4—101no—
458C22×C4—301no—
459C22×C4—301no—
460C22×C4C2×D3×D511yescharacteristic
461Q16—38no—
462SD16—38no—
463M16—34no—
464M16—302no—
465C2×C8—32no—
466C2×C8—152no—
467C4⋊C4—52no—
468C4⋊C4—102no—
469C4⋊C4—102no—
470C4⋊C4—101no—
471C4⋊C4—151no—
472C4⋊C4—151no—
473C4⋊C4—301no—
474C4⋊C4—301no—
475C22⋊C4—301no—
476C22⋊C4—301no—
477C22⋊C4—301no—
478C42—51no—
479C42—51no—
480C42—51no—
481C42—51no—
482C42—102no—
483C42—102no—
484C42—301no—
485C42—301no—
486C42—301no—
487C3×C5C4×#13711yescharacteristic, complemented, Hall
488C22×C3—21no—
489C22×C3—21no—
490C22×C3D4×Dic512yes—
491C22×C3C2×D4×D511yescharacteristic
492C2×D3—22no—
493C2×D3—41no—
494C2×D3—41no—
495C3×C4—24no—
496C3×C4—52no—
497C3×C4—101no—
498C3×C4—101no—
499C3×C4—101no—
500C3×C4—202no—
501C3×C4D4×Dic512yes—
502C3×C4C2×#71111yescharacteristic
503C3×C4C23×Dic511yescharacteristic
504Dic3—22no—
505Dic3—201no—
506Dic3—201no—
507C2×C5—22no—
508C2×C5—122no—
509C2×C5C2×C4×#6711yescharacteristic
510C2×C5C2×#94211yescharacteristic
511C2×C5#582211yescharacteristic
512C23—61no—
513C23D5×#6711yescharacteristic
514Q8—22no—
515Q8—24no—
516Q8—32no—
517Q8—61no—
518Q8C2×D3×Dic514yes—
519D4—32no—
520D4—64no—
521D4—61no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—51no—
525C2×C4—51no—
526C2×C4—51no—
527C2×C4—51no—
528C2×C4—61no—
529C2×C4—64no—
530C2×C4—102no—
531C2×C4—102no—
532C2×C4—201no—
533C2×C4—202no—
534C2×C4—301no—
535C2×C4—301no—
536C2×C4—602no—
537C2×C4—602no—
538C2×C4C2×D3×Dic512yes—
539C2×C4#678212yes—
540C2×C4D5×#6711yescharacteristic
541C2×C4C22×D3×D511yescharacteristic
542C8—34no—
543C8—302no—
544C2×C3—22no—
545C2×C3D5×#13711yescharacteristic
546C2×C3#6611111yescharacteristic
547C2×C3C2×D4×Dic511yescharacteristic
548D3—42no—
549C5C4×#94211yescharacteristic, complemented, Sylow
550C22—21no—
551C22—21no—
552C22—62no—
553C22—121no—
554C22—121no—
555C22Dic5×#6712yes—
556C22C2×D5×#6711yescharacteristic
557C4—24no—
558C4—52no—
559C4—62no—
560C4—101no—
561C4—101no—
562C4—101no—
563C4—202no—
564C4—601no—
565C4—601no—
566C4Dic5×#6712yes—
567C4C22×D3×Dic511yescharacteristic
568C4C2×#678211yescharacteristic
569C3Dic5×#13711yescharacteristic, complemented, Sylow
570C2—22no—
571C2—122no—
572C2D5×#94211yescharacteristic
573C2#1175508411yescharacteristic
574C2C2×Dic5×#6711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#235C22
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×C3×Q8×Dic5C2semidirect
4. #11751326C2semidirect
5. #11749247C2semidirect
6. Dic5×#216C2semidirect
7. #11749223C2semidirect
8. Dic5×#215C2semidirect
9. #11748453C2semidirect
11. Dic5×#208C2semidirect
18. C5×#942C4semidirect
48. C2×Q8×Dic5D3semidirect
59. C2×C3×C5×Q8C2×C4semidirect
80. C5×#216C2×C4semidirect
81. C5×#215C2×C4semidirect
82. C5×#208C2×C4semidirect
187. #942Dic5direct (N × H)
213. C2×C5×Q8C4×D3semidirect
279. C3×Dic5#137semidirect
283. C2×C3×Q8C2×Dic5semidirect
309. #216C2×Dic5semidirect
310. #215C2×Dic5semidirect
321. #208C2×Dic5semidirect
443. Dic5#942direct (N × H)
449. C2×Q8D3×Dic5semidirect
487. C3×C5C4×#137semidirect
549. C5C4×#942semidirect
569. C3Dic5×#137semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9422
C2×C3×Q8×Dic52
Dic5×#2352
#117513262
#117492472
Dic5×#2162
#117492232
Dic5×#2152
#117484532
#117483842
Dic5×#2082
Dic5×#1373
C4×#9425