Finite Group Databasebeta

← #14430683

Subgroups — #14430683

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic15C211yesmaximal, characteristic
2C2×#91779C211yesmaximal, characteristic, complemented
3C3×C5×#417C211yesmaximal, characteristic
4#11751333C211yesmaximal, characteristic
5#11751222C211yesmaximal, characteristic, complemented
6#11751219C211yesmaximal, characteristic, complemented
7#11751065C211yesmaximal, characteristic, complemented
8#11750900C212yesmaximal, complemented
9#11750897C212yesmaximal, complemented
10#11750867C212yesmaximal, complemented
11#11750864C212yesmaximal, complemented
12#10610602—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16Q8×Dic15C2211yescharacteristic
17Q8×Dic15C2211yescharacteristic
18D4×Dic15—21no—
19D4×Dic15—21no—
20D4×Dic15C2211yescharacteristic
21D4×Dic15C2211yescharacteristic
22#91815—21no—
23#91815C2211yescharacteristic
24C2×C4⋊Dic15—21no—
25C2×C4⋊Dic15C2211yescharacteristic
26C2×#6712—21no—
27C2×C4×Dic15—21no—
28C2×C4×Dic15C2211yescharacteristic
29C2×#6710C2211yescharacteristic
30#91779—21no—
31#91779—21no—
32#91779C2212yes—
33#91779C2212yes—
34C3×C5×#103C2212yes—
35C3×C5×#102C2212yes—
36#91119C2212yes—
37#91116C2212yes—
38#91102C2212yes—
39#91101C2212yes—
40#91098C2212yes—
41#91098C2212yes—
42#91092C2212yes—
43#91091C2212yes—
44#78871—51nomaximal, Hall
45#41×Dic5—31no—
46C2×#4036—31no—
47C5×#417D311yescharacteristic
48#65521—31no—
49#65410—31no—
50#65407—31no—
51#65253—31no—
52#65088—32no—
53#65085—32no—
54#65055—32no—
55#65052—32no—
56C3×C5×#41—22no—
57C3×C5×#41Q814yes—
58C2×C3×C5×Q8C2311yescharacteristic
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4C2311yescharacteristic
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5C2311yescharacteristic
64C22×Dic15—21no—
65C22×Dic15—21no—
66C22×Dic15—21no—
67C22×Dic15D411yescharacteristic
68C22×Dic15D411yescharacteristic
69C3×C5×M16—22no—
70C2×C3×C5×C8C2312yes—
71C3×C5×C4⋊C4—21no—
72C3×C5×C4⋊C4C2312yes—
73#6719—21no—
74#6719—21no—
75#6719—21no—
76C4⋊Dic15—21no—
77C4⋊Dic15—22no—
78C4⋊Dic15—22no—
79C4⋊Dic15—21no—
80C4⋊Dic15—21no—
81C4⋊Dic15C2312yes—
82C4⋊Dic15C2311yescharacteristic
83C4⋊Dic15C2311yescharacteristic
84#6712—22no—
85#6712—22no—
86C4×Dic15—21no—
87C4×Dic15—21no—
88C4×Dic15—21no—
89C4×Dic15D411yescharacteristic
90C4×Dic15D411yescharacteristic
91C4×Dic15C2311yescharacteristic
92C4×Dic15C2311yescharacteristic
93#6710—22no—
94C2×C3⋊#168C2312yes—
95Dic3×#41—51no—
96C2×#890—51no—
97C3×#417D511yescharacteristic
98#5232—51no—
99#5121—51no—
100#5118—51no—
101#4964—51no—
102#4799—52no—
103#4796—52no—
104#4766—52no—
105#4763—52no—
106C2×C5×#41C2×D311yescharacteristic
107C2×C5×M16C2×D311yescharacteristic
108C2×C5×C4⋊C4C2×D311yescharacteristic
109Q8×Dic5—31no—
110Q8×Dic5—31no—
111D4×Dic5—31no—
112D4×Dic5—31no—
113D4×Dic5—61no—
114D4×Dic5—61no—
115#4072—31no—
116#4072—61no—
117C2×C4⋊Dic5—31no—
118C2×C4⋊Dic5—61no—
119C2×#683—61no—
120C2×C4×Dic5—31no—
121C2×C4×Dic5—61no—
122C2×#681—31no—
123#4036—32no—
124#4036—32no—
125#4036—61no—
126#4036—61no—
127C5×#103C2×D312yes—
128C5×#102C2×D312yes—
129#3967—32no—
130#3964—32no—
131#3950—32no—
132#3949—32no—
133#3946—32no—
134#3946—32no—
135#3940—32no—
136#3939—32no—
137#3080—151noSylow
138C23×C3×C5—21no—
139C23×C3×C5C2×D411yescharacteristic
140C3×C5×Q8—21no—
141C3×C5×Q8C2×Q812yes—
142C3×C5×D4—24no—
143C3×C5×D4—21no—
144C3×C5×D4C2×Q812yes—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—24no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—42no—
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5C2×Q812yes—
151C2×C3×C4×C5#4112yes—
152C2×C3×C4×C5C2411yescharacteristic
153C2×Dic15—21no—
154C2×Dic15—21no—
155C2×Dic15—22no—
156C2×Dic15—41no—
157C2×Dic15—41no—
158C2×Dic15—42no—
159C2×Dic15—42no—
160C2×Dic15—42no—
161C2×Dic15C2×D411yescharacteristic
162C2×Dic15C2×D411yescharacteristic
163C2×Dic15C2×D411yescharacteristic
164C2×Dic15C2×D411yescharacteristic
165C3×C5×C8—22no—
166C3⋊#168—22no—
167C2×C3×#41C2×D511yescharacteristic
168C2×C3×M16C2×D511yescharacteristic
169C2×C3×C4⋊C4C2×D511yescharacteristic
170Q8×Dic3—51no—
171Q8×Dic3—51no—
172D4×Dic3—51no—
173D4×Dic3—51no—
174D4×Dic3—101no—
175D4×Dic3—101no—
176#926—51no—
177#926—101no—
178C2×C4⋊Dic3—51no—
179C2×C4⋊Dic3—101no—
180C2×Dic3⋊C4—101no—
181C2×C4×Dic3—51no—
182C2×C4×Dic3—101no—
183C2×#208—51no—
184#890—52no—
185#890—52no—
186#890—101no—
187#890—101no—
188C3×#103C2×D512yes—
189C3×#102C2×D512yes—
190#835—52no—
191#832—52no—
192#818—52no—
193#817—52no—
194Dic3⋊C8—52no—
195Dic3⋊C8—52no—
196#808—52no—
197#807—52no—
198C5×#41—22no—
199C5×#41Dic614yes—
200C2×C5×Q8C22×D311yescharacteristic
201C2×C5×D4—21no—
202C2×C5×D4C22×D311yescharacteristic
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5C22×D311yescharacteristic
206C22×Dic5—31no—
207C22×Dic5—31no—
208C22×Dic5—61no—
209C22×Dic5—61no—
210C22×Dic5—61no—
211C5×M16—22no—
212C2×C5×C8C22×D312yes—
213C5×C4⋊C4—21no—
214C5×C4⋊C4C22×D312yes—
215C22⋊Dic5—61no—
216C22⋊Dic5—61no—
217C22⋊Dic5—61no—
218C4⋊Dic5—31no—
219C4⋊Dic5—31no—
220C4⋊Dic5—32no—
221C4⋊Dic5—62no—
222C4⋊Dic5—62no—
223C4⋊Dic5—61no—
224C4⋊Dic5—61no—
225C4⋊Dic5—61no—
226#683—62no—
227#683—62no—
228C4×Dic5—31no—
229C4×Dic5—31no—
230C4×Dic5—31no—
231C4×Dic5—31no—
232C4×Dic5—61no—
233C4×Dic5—61no—
234C4×Dic5—61no—
235#681—62no—
236C2×#168—32no—
237C2×#125—151no—
238C4×#41—151no—
239#479—152no—
240#479—152no—
241#478—152no—
242#478—152no—
243#428—151no—
244#428—151no—
245#423—151no—
246#417—151no—
247#417D1511yescharacteristic
248C22×C3×C5—21no—
249C22×C3×C5—21no—
250C22×C3×C5—22no—
251C22×C3×C5—41no—
252C22×C3×C5—41no—
253C22×C3×C5C22⋊Q812yes—
254C22×C3×C5C22×D411yescharacteristic
255C3×C4×C5—22no—
256C3×C4×C5—42no—
257C3×C4×C5C22⋊Q812yes—
258C3×C4×C5C22×Q811yescharacteristic
259C3×C4×C5C2×#4111yescharacteristic
260Dic15—21no—
261Dic15—21no—
262Dic15—21no—
263Dic15—21no—
264Dic15—41no—
265Dic15—41no—
266Dic15—42no—
267C3×#41—22no—
268C3×#41Dic1014yes—
269C2×C3×Q8C22×D511yescharacteristic
270C2×C3×D4—21no—
271C2×C3×D4C22×D511yescharacteristic
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4C22×D511yescharacteristic
275C22×Dic3—51no—
276C22×Dic3—51no—
277C22×Dic3—101no—
278C22×Dic3—101no—
279C22×Dic3—101no—
280C3×M16—22no—
281C2×C3×C8C22×D512yes—
282C3×C4⋊C4—21no—
283C3×C4⋊C4C22×D512yes—
284#217—101no—
285#217—101no—
286#217—101no—
287C4⋊Dic3—51no—
288C4⋊Dic3—51no—
289C4⋊Dic3—52no—
290C4⋊Dic3—102no—
291C4⋊Dic3—102no—
292C4⋊Dic3—101no—
293C4⋊Dic3—101no—
294C4⋊Dic3—101no—
295Dic3⋊C4—102no—
296Dic3⋊C4—102no—
297C4×Dic3—51no—
298C4×Dic3—51no—
299C4×Dic3—51no—
300C4×Dic3—51no—
301C4×Dic3—101no—
302C4×Dic3—101no—
303C4×Dic3—101no—
304#208—102no—
305C2×C3⋊C8—52no—
306C23×C5—21no—
307C23×C5D3×D411yescharacteristic
308C5×Q8—21no—
309C5×Q8C2×Dic612yes—
310C5×D4—24no—
311C5×D4—21no—
312C5×D4C2×Dic612yes—
313C2×C4×C5—21no—
314C2×C4×C5—24no—
315C2×C4×C5—22no—
316C2×C4×C5—42no—
317C2×C4×C5C2×Dic612yes—
318C2×C4×C5D3×D411yescharacteristic
319C2×C4×C5#23712yes—
320C2×C4×C5C23×D311yescharacteristic
321C2×Dic5—31no—
322C2×Dic5—31no—
323C2×Dic5—31no—
324C2×Dic5—31no—
325C2×Dic5—61no—
326C2×Dic5—61no—
327C2×Dic5—62no—
328C2×Dic5—121no—
329C2×Dic5—121no—
330C2×Dic5—122no—
331C2×Dic5—122no—
332C2×Dic5—122no—
333C5×C8—22no—
334#168—62no—
335C2×#41C2×D1511yescharacteristic
336C2×M16—151no—
337C2×M16C2×D1511yescharacteristic
338#125—152no—
339#125—152no—
340#125—301no—
341#125—301no—
342C4×Q8—151no—
343C4×Q8—151no—
344C4×D4—151no—
345C4×D4—151no—
346C4×D4—301no—
347C4×D4—301no—
348#117—151no—
349#117—301no—
350C2×C4⋊C4—151no—
351C2×C4⋊C4—301no—
352C2×C4⋊C4—301no—
353C2×C4⋊C4C2×D1511yescharacteristic
354C2×C42—151no—
355C2×C42—301no—
356#107—152no—
357#107—152no—
358#106—152no—
359#106—152no—
360C4⋊C8—152no—
361C4⋊C8—152no—
362#103—152no—
363#103C2×D1512yes—
364#102—152no—
365#102C2×D1512yes—
366C2×C3×C5—22no—
367C2×C3×C5—42no—
368C2×C3×C5C2×C22⋊Q811yescharacteristic
369C2×C3×C5#57511yescharacteristic
370C2×C3×C5#57511yescharacteristic
371C23×C3—21no—
372C23×C3D4×D511yescharacteristic
373C3×Q8—21no—
374C3×Q8C2×Dic1012yes—
375C3×D4—24no—
376C3×D4—21no—
377C3×D4C2×Dic1012yes—
378C2×C3×C4—21no—
379C2×C3×C4—24no—
380C2×C3×C4—22no—
381C2×C3×C4—42no—
382C2×C3×C4C2×Dic1012yes—
383C2×C3×C4D4×D511yescharacteristic
384C2×C3×C4#71112yes—
385C2×C3×C4C23×D511yescharacteristic
386C2×Dic3—51no—
387C2×Dic3—51no—
388C2×Dic3—51no—
389C2×Dic3—51no—
390C2×Dic3—101no—
391C2×Dic3—101no—
392C2×Dic3—102no—
393C2×Dic3—201no—
394C2×Dic3—201no—
395C2×Dic3—202no—
396C2×Dic3—202no—
397C2×Dic3—202no—
398C3×C8—22no—
399C3⋊C8—102no—
400C22×C5—21no—
401C22×C5—21no—
402C22×C5—22no—
403C22×C5—41no—
404C22×C5—41no—
405C22×C5#87812yes—
406C22×C5C2×D3×D411yescharacteristic
407C4×C5—22no—
408C4×C5—42no—
409C4×C5#87812yes—
410C4×C5C22×Dic611yescharacteristic
411C4×C5C2×#23711yescharacteristic
412Dic5—61no—
413Dic5—61no—
414Dic5—61no—
415Dic5—61no—
416Dic5—121no—
417Dic5—121no—
418Dic5—122no—
419#41—22no—
420#41Dic3014yes—
421C2×Q8C22×D1511yescharacteristic
422C2×D4—21no—
423C2×D4C22×D1511yescharacteristic
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—151no—
427C22×C4—151no—
428C22×C4—301no—
429C22×C4—301no—
430C22×C4—301no—
431C22×C4C22×D1511yescharacteristic
432M16—22no—
433M16—302no—
434C2×C8—152no—
435C2×C8C22×D1512yes—
436C4⋊C4—21no—
437C4⋊C4—152no—
438C4⋊C4—151no—
439C4⋊C4—151no—
440C4⋊C4—302no—
441C4⋊C4—302no—
442C4⋊C4—302no—
443C4⋊C4—302no—
444C4⋊C4—301no—
445C4⋊C4—301no—
446C4⋊C4—301no—
447C4⋊C4C22×D1512yes—
448C22⋊C4—301no—
449C22⋊C4—301no—
450C22⋊C4—301no—
451C42—151no—
452C42—151no—
453C42—151no—
454C42—151no—
455C42—301no—
456C42—301no—
457C42—301no—
458C3×C5#308011yescharacteristic, complemented, Hall
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—22no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3#402412yes—
465C22×C3C2×D4×D511yescharacteristic
466C3×C4—22no—
467C3×C4—42no—
468C3×C4#402412yes—
469C3×C4C22×Dic1011yescharacteristic
470C3×C4C2×#71111yescharacteristic
471Dic3—101no—
472Dic3—101no—
473Dic3—101no—
474Dic3—101no—
475Dic3—201no—
476Dic3—201no—
477Dic3—202no—
478C2×C5—22no—
479C2×C5—42no—
480C2×C5C2×#87811yescharacteristic
481C2×C5#577311yescharacteristic
482C2×C5#577711yescharacteristic
483C23—21no—
484C23D4×D1511yescharacteristic
485Q8—21no—
486Q8C2×Dic3012yes—
487D4—24no—
488D4—21no—
489D4C2×Dic3012yes—
490C2×C4—21no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—42no—
494C2×C4—151no—
495C2×C4—151no—
496C2×C4—151no—
497C2×C4—151no—
498C2×C4—301no—
499C2×C4—301no—
500C2×C4—302no—
501C2×C4—601no—
502C2×C4—601no—
503C2×C4—602no—
504C2×C4—602no—
505C2×C4—602no—
506C2×C4C2×Dic3012yes—
507C2×C4D4×D1511yescharacteristic
508C2×C4#681912yes—
509C2×C4C23×D1511yescharacteristic
510C8—22no—
511C8—302no—
512C2×C3—22no—
513C2×C3—42no—
514C2×C3C2×#402411yescharacteristic
515C2×C3#6610711yescharacteristic
516C2×C3#6611111yescharacteristic
517C5#7887111yescharacteristic, complemented, Sylow
518C22—21no—
519C22—21no—
520C22—22no—
521C22—41no—
522C22—41no—
523C22#9176712yes—
524C22C2×D4×D1511yescharacteristic
525C4—22no—
526C4—42no—
527C4—301no—
528C4—301no—
529C4—301no—
530C4—301no—
531C4—601no—
532C4—601no—
533C4—602no—
534C4#9176712yes—
535C4C22×Dic3011yescharacteristic
536C4C2×#681911yescharacteristic
537C3#1061060211yescharacteristic, complemented, Sylow
538C2—22no—
539C2—42no—
540C2C2×#9176711yescharacteristic
541C2#1175653211yescharacteristic
542C2#1175653611yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#417C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×C5×#41C22
hypercenter#417D15
hypocenterC3×C5#3080
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#91779C2semidirect
5. #11751222C2semidirect
6. #11751219C2semidirect
7. #11751065C2semidirect
8. #11750900C2semidirect
9. #11750897C2semidirect
10. #11750867C2semidirect
11. #11750864C2semidirect
458. C3×C5#3080semidirect
517. C5#78871semidirect
537. C3#10610602semidirect

Maximal subgroups

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

subgroupindex
#41×Dic152
C2×#917792
C3×C5×#4172
#117513332
#117512222
#117512192
#117510652
#117509002
#117508972
#117508672
#117508642
#106106023
#788715