Finite Group Databasebeta

← #14430715

Subgroups — #14430715

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
1C2×C5×#890C211yesmaximal, characteristic, complemented
2#11754436C211yesmaximal, characteristic
3#11751067C211yesmaximal, characteristic
4C3×#65253C211yesmaximal, characteristic, complemented
5#11748472C211yesmaximal, characteristic, complemented
6#11748440C211yesmaximal, characteristic, complemented
7#11748394C211yesmaximal, characteristic
8#11747291C212yesmaximal, complemented
9#11747290C212yesmaximal, complemented
10#11747252C212yesmaximal, complemented
11#11747250C212yesmaximal, complemented
12#10614748—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C2×#6710C2211yescharacteristic
16C2×C5×C4⋊Dic3—21no—
17C2×C5×C4⋊Dic3C2211yescharacteristic
18C2×C5×Dic3⋊C4—21no—
19C2×C4×C5×Dic3C2211yescharacteristic
20C5×#890—21no—
21C5×#890—21no—
22C5×#890C2212yes—
23C5×#890C2212yes—
24C3×#4072C2211yescharacteristic
25C2×C3×#681C2211yescharacteristic
26#91556—21no—
27#91556—21no—
28#91428C2211yescharacteristic
29#91428C2211yescharacteristic
30C4×#1200—21no—
31#91386—21no—
32#91340C2211yescharacteristic
33#91340C2211yescharacteristic
34#91094C2212yes—
35#91093C2212yes—
36C3×#3940C2212yes—
37C3×#3939C2212yes—
38#90989C2212yes—
39#90986C2212yes—
40Dic3⋊#168C2212yes—
41Dic3⋊#168C2212yes—
42#90975C2212yes—
43#90969C2212yes—
44#79241—51nomaximal, Hall
45C2×C5×#125—31no—
46C4×#709—31no—
47#65355—32no—
48#65355—32no—
49#65352—32no—
50#65352—32no—
51#65255—31no—
52#65255—31no—
53#65253—31no—
54#65253D311yescharacteristic, complemented
55#65213—31no—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—21no—
59#6817—22no—
60#6817Q814yes—
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×Dic30C2311yescharacteristic
64C22×C5×Dic3—21no—
65C22×C5×Dic3D411yescharacteristic
66C22×C5×Dic3D411yescharacteristic
67C2×#1200—21no—
68C2×#1200—21no—
69C3×C5×C4⋊C4—21no—
70C3×C5×C4⋊C4C2312yes—
71#6710—22no—
72C2×C3⋊#168C2312yes—
73C5×C4⋊Dic3—21no—
74C5×C4⋊Dic3—22no—
75C5×C4⋊Dic3—22no—
76C5×C4⋊Dic3C2312yes—
77C5×Dic3⋊C4—22no—
78C5×Dic3⋊C4—22no—
79C4×C5×Dic3D411yescharacteristic
80C4×C5×Dic3D411yescharacteristic
81C4×C5×Dic3C2311yescharacteristic
82C4×C5×Dic3C2311yescharacteristic
83C3×C22⋊Dic5—21no—
84C3×C4⋊Dic5C2311yescharacteristic
85C3×C4⋊Dic5C2311yescharacteristic
86C3×C4×Dic5—21no—
87C3×#681—22no—
88C2×C3×#168C2312yes—
89#6669—21no—
90#6669—21no—
91#6667—21no—
92#6667—21no—
93Dic3×Dic5—21no—
94Dic3×Dic5—21no—
95#5522—51no—
96C2×#890D511yescharacteristic, complemented
97C3×#428—51no—
98#5133—51no—
99#5118—51no—
100#4995—51no—
101#4966—51no—
102#4891—52no—
103#4877—52no—
104#4871—52no—
105#4857—52no—
106C2×#709—31no—
107C5×#125—32no—
108C5×#125—32no—
109C5×#125—61no—
110C5×#125—61no—
111C2×C5×C4⋊C4—31no—
112C2×C5×C4⋊C4—61no—
113C2×C5×C4⋊C4—61no—
114C2×C5×C4⋊C4C2×D311yescharacteristic
115C2×C42×C5—31no—
116C4×C22⋊D5—61no—
117C4×C22⋊D5—61no—
118#4072C2×D311yescharacteristic
119C2×#681—31no—
120C2×#681C2×D311yescharacteristic
121C4×D20—31no—
122C4×D20—31no—
123#4018—61no—
124C42×D5—61no—
125C4×Dic10—31no—
126C4×Dic10—31no—
127#3942—32no—
128#3942—32no—
129#3941—32no—
130#3941—32no—
131#3940—32no—
132#3940C2×D312yes—
133#3939—32no—
134#3939C2×D312yes—
135C4⋊#168—32no—
136C4⋊#168—32no—
137#3080—151noSylow
138C23×C3×C5C2×D411yescharacteristic
139C22×D15—21no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—42no—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2×Q812yes—
144C2×C3×C4×C5#4112yes—
145C2×C3×C4×C5C2411yescharacteristic
146#1220—24no—
147C2×Dic15—21no—
148D60—21no—
149D60C2×Q812yes—
150C4×D15—24no—
151Dic30—21no—
152Dic30C2×Q812yes—
153C2×C5×Dic3—22no—
154C2×C5×Dic3—41no—
155C2×C5×Dic3—41no—
156C2×C5×Dic3—42no—
157C2×C5×Dic3C2×D411yescharacteristic
158C2×C5×Dic3C2×D411yescharacteristic
159C2×C5×Dic3C2×D411yescharacteristic
160C2×C5×Dic3C2×D411yescharacteristic
161C2×C3×Dic5—21no—
162C2×C3×Dic5—21no—
163#1200—42no—
164#1200—42no—
165C3⋊#168—22no—
166C3×#168—22no—
167C2×#235—51no—
168C2×C3×M16—51no—
169C3×#117—51no—
170C2×C3×C4⋊C4C2×D511yescharacteristic
171C2×C4⋊Dic3—21no—
172C2×C4⋊Dic3C2×D511yescharacteristic
173C2×Dic3⋊C4—21no—
174C2×C4×Dic3C2×D511yescharacteristic
175C2×#208—51no—
176#893—51no—
177#893—51no—
178#890—21no—
179#890—21no—
180#890C2×D512yes—
181#890C2×D512yes—
182#887—51no—
183#887—51no—
184#67⋊C4—101no—
185#67⋊C4—101no—
186#872—101no—
187C42×D3—101no—
188C3×#107—52no—
189C3×#106—52no—
190#821—52no—
191#816—52no—
192Dic3⋊C8—52no—
193Dic3⋊C8—52no—
194#810—52no—
195#809—52no—
196#808—52no—
197#807—52no—
198C22×C4×C5—21no—
199C22×C4×C5—31no—
200C22×C4×C5—31no—
201C22×C4×C5—61no—
202C22×C4×C5C22×D311yescharacteristic
203C2×C22⋊D5—61no—
204#709—34no—
205#709—62no—
206C2×D20—31no—
207C2×C4×D5—61no—
208C2×C4×D5—61no—
209C2×C4×D5—61no—
210C2×Dic10—31no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—32no—
213C5×C4⋊C4—62no—
214C5×C4⋊C4—62no—
215C5×C4⋊C4—62no—
216C5×C4⋊C4—62no—
217C5×C4⋊C4—61no—
218C5×C4⋊C4C22×D312yes—
219C42×C5—31no—
220C42×C5—31no—
221C42×C5—31no—
222C42×C5—31no—
223C22⋊Dic5—21no—
224#685—61no—
225#685—61no—
226C4⋊Dic5C22×D311yescharacteristic
227C4⋊Dic5C22×D311yescharacteristic
228#683—61no—
229#683—61no—
230C4×Dic5—21no—
231C4×Dic5—61no—
232C4×Dic5—61no—
233#681—22no—
234#681—62no—
235C2×#168—32no—
236C2×#168C22×D312yes—
237C2×#125—31no—
238C4×#41—151no—
239#479—152no—
240#479—152no—
241#478—152no—
242#478—152no—
243#428—51no—
244#428—151no—
245#423—151no—
246#417—151no—
247#417—151no—
248C22×C3×C5—21no—
249C22×C3×C5—21no—
250C22×C3×C5C22⋊Q812yes—
251C22×C3×C5C22×D411yescharacteristic
252C2×D15—22no—
253C2×D15—41no—
254C2×D15—41no—
255C3×C4×C5—42no—
256C3×C4×C5C22⋊Q812yes—
257C3×C4×C5C22×Q811yescharacteristic
258C3×C4×C5C2×#4111yescharacteristic
259Dic15—22no—
260C3×Dic5—41no—
261C3×Dic5—41no—
262C5×Dic3—21no—
263C5×Dic3—21no—
264C5×Dic3—21no—
265C5×Dic3—21no—
266C5×Dic3—42no—
267C22×C3×C4—21no—
268C22×C3×C4C22×D511yescharacteristic
269C2×#67—101no—
270C22×Dic3—21no—
271C22×Dic3C22⋊D511yescharacteristic
272C22×Dic3C22⋊D511yescharacteristic
273#235—54no—
274#235—102no—
275C2×D12—51no—
276C2×C4×D3—101no—
277C2×C4×D3—101no—
278C2×C4×D3—101no—
279C2×Dic6—51no—
280C3×M16—102no—
281C2×C3×C8—52no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—51no—
284C3×C4⋊C4—51no—
285C3×C4⋊C4C22×D512yes—
286C3×C22⋊C4—101no—
287C3×C42—101no—
288(C2×D3)⋊C4—101no—
289(C2×D3)⋊C4—101no—
290C4⋊Dic3—21no—
291C4⋊Dic3—22no—
292C4⋊Dic3—22no—
293C4⋊Dic3C22×D512yes—
294Dic3⋊C4—22no—
295Dic3⋊C4—22no—
296Dic3⋊C4—101no—
297Dic3⋊C4—101no—
298C4×Dic3—101no—
299C4×Dic3—101no—
300C4×Dic3C22⋊D511yescharacteristic
301C4×Dic3C22⋊D511yescharacteristic
302C4×Dic3C22×D511yescharacteristic
303C4×Dic3C22×D511yescharacteristic
304#208—102no—
305C2×C3⋊C8—52no—
306C23×C5D3×D411yescharacteristic
307C22×D5—61no—
308C2×C4×C5—22no—
309C2×C4×C5—31no—
310C2×C4×C5—31no—
311C2×C4×C5—31no—
312C2×C4×C5—31no—
313C2×C4×C5—42no—
314C2×C4×C5—62no—
315C2×C4×C5—121no—
316C2×C4×C5—121no—
317C2×C4×C5—122no—
318C2×C4×C5#23512yes—
319C2×C4×C5D3×D411yescharacteristic
320C2×C4×C5D3×Q812yes—
321C2×C4×C5C23×D311yescharacteristic
322C22⋊D5—64no—
323C2×Dic5—21no—
324C2×Dic5—21no—
325C2×Dic5—61no—
326D20—32no—
327D20—61no—
328C4×D5—64no—
329C4×D5—122no—
330C4×D5—122no—
331Dic10—32no—
332Dic10—61no—
333#168—22no—
334#168—62no—
335C2×#41—151no—
336C2×M16—51no—
337C2×M16—151no—
338#125—32no—
339#125—32no—
340#125—61no—
341#125—61no—
342C4×Q8—151no—
343C4×Q8—151no—
344C4×D4—151no—
345C4×D4—151no—
346C4×D4—301no—
347C4×D4—301no—
348#117—51no—
349#117—301no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—61no—
352C2×C4⋊C4—61no—
353C2×C4⋊C4D3×D511yescharacteristic
354C2×C42—31no—
355C2×C42—301no—
356#107—52no—
357#107—152no—
358#106—52no—
359#106—152no—
360C4⋊C8—152no—
361C4⋊C8—152no—
362#103—152no—
363#103—152no—
364#102—152no—
365#102—152no—
366C2×C3×C5—22no—
367C2×C3×C5C2×C22⋊Q811yescharacteristic
368C2×C3×C5#57511yescharacteristic
369C2×C3×C5#57511yescharacteristic
370D15—42no—
371C23×C3C2×C22⋊D511yescharacteristic
372C22×D3—101no—
373C2×C3×C4—22no—
374C2×C3×C4—42no—
375C2×C3×C4—101no—
376C2×C3×C4—101no—
377C2×C3×C4Q8×D512yes—
378C2×C3×C4#71312yes—
379C2×C3×C4C2×C22⋊D511yescharacteristic
380C2×C3×C4C23×D511yescharacteristic
381#67—104no—
382C2×Dic3—22no—
383C2×Dic3—41no—
384C2×Dic3—41no—
385C2×Dic3—42no—
386C2×Dic3—101no—
387C2×Dic3C2×C22⋊D511yescharacteristic
388C2×Dic3C2×C22⋊D511yescharacteristic
389C2×Dic3C2×C22⋊D511yescharacteristic
390C2×Dic3C2×C22⋊D511yescharacteristic
391D12—52no—
392D12—101no—
393C4×D3—104no—
394C4×D3—202no—
395C4×D3—202no—
396Dic6—52no—
397Dic6—101no—
398C3×C8—102no—
399C3⋊C8—102no—
400C22×C5—21no—
401C22×C5—21no—
402C22×C5#89612yes—
403C22×C5C2×D3×D411yescharacteristic
404C2×D5—62no—
405C2×D5—121no—
406C2×D5—121no—
407C4×C5—42no—
408C4×C5—61no—
409C4×C5—61no—
410C4×C5—61no—
411C4×C5—61no—
412C4×C5—122no—
413C4×C5#89612yes—
414C4×C5C2×#23511yescharacteristic
415C4×C5C2×D3×Q811yescharacteristic
416Dic5—41no—
417Dic5—41no—
418Dic5—62no—
419#41—154no—
420#41—302no—
421C2×Q8—151no—
422C2×D4—151no—
423C2×D4—301no—
424C22×C4—21no—
425C22×C4—31no—
426C22×C4—31no—
427C22×C4—61no—
428C22×C4—301no—
429C22×C4—301no—
430C22×C4—301no—
431C22×C4C2×D3×D511yescharacteristic
432M16—102no—
433M16—302no—
434C2×C8—52no—
435C2×C8—152no—
436C4⋊C4—21no—
437C4⋊C4—32no—
438C4⋊C4—51no—
439C4⋊C4—51no—
440C4⋊C4—62no—
441C4⋊C4—62no—
442C4⋊C4—62no—
443C4⋊C4—62no—
444C4⋊C4—61no—
445C4⋊C4—301no—
446C4⋊C4—301no—
447C4⋊C4C2×D3×D512yes—
448C22⋊C4—101no—
449C22⋊C4—301no—
450C22⋊C4—301no—
451C42—31no—
452C42—31no—
453C42—31no—
454C42—31no—
455C42—101no—
456C42—301no—
457C42—301no—
458C3×C5#308011yescharacteristic, complemented, Hall
459C22×C3—21no—
460C22×C3—21no—
461C22×C3#409212yes—
462C22×C3C22×C22⋊D511yescharacteristic
463C2×D3—102no—
464C2×D3—201no—
465C2×D3—201no—
466C3×C4—42no—
467C3×C4—201no—
468C3×C4—201no—
469C3×C4#409212yes—
470C3×C4C2×Q8×D511yescharacteristic
471C3×C4C2×#71311yescharacteristic
472Dic3—21no—
473Dic3—21no—
474Dic3—21no—
475Dic3—21no—
476Dic3—42no—
477Dic3—102no—
478C2×C5—22no—
479C2×C5C2×#89611yescharacteristic
480C2×C5#577311yescharacteristic
481C2×C5#577711yescharacteristic
482D5—122no—
483C23—301no—
484C23D3×C22⋊D511yescharacteristic
485Q8—152no—
486Q8—301no—
487D4—152no—
488D4—304no—
489D4—301no—
490C2×C4—22no—
491C2×C4—31no—
492C2×C4—31no—
493C2×C4—31no—
494C2×C4—31no—
495C2×C4—42no—
496C2×C4—62no—
497C2×C4—101no—
498C2×C4—101no—
499C2×C4—121no—
500C2×C4—121no—
501C2×C4—122no—
502C2×C4—301no—
503C2×C4—304no—
504C2×C4—602no—
505C2×C4—602no—
506C2×C4D15⋊Q812yes—
507C2×C4#677312yes—
508C2×C4D3×C22⋊D511yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—102no—
511C8—302no—
512C2×C3—22no—
513C2×C3C2×#409211yescharacteristic
514C2×C3#6615611yescharacteristic
515C2×C3#6615611yescharacteristic
516D3—202no—
517C5#7924111yescharacteristic, complemented, Sylow
518C22—21no—
519C22—21no—
520C22—302no—
521C22—601no—
522C22—601no—
523C22#9142412yes—
524C22C2×D3×C22⋊D511yescharacteristic
525C4—42no—
526C4—61no—
527C4—61no—
528C4—61no—
529C4—61no—
530C4—122no—
531C4—201no—
532C4—201no—
533C4—302no—
534C4#9142412yes—
535C4C2×D15⋊Q811yescharacteristic
536C4C2×#677311yescharacteristic
537C3#1061474811yescharacteristic, complemented, Sylow
538C2—22no—
539C2—602no—
540C2C2×#9142411yescharacteristic
541C2#1175469611yescharacteristic
542C2#1175509011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3080
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C5×#890C2semidirect
4. C3×#65253C2semidirect
5. #11748472C2semidirect
6. #11748440C2semidirect
8. #11747291C2semidirect
9. #11747290C2semidirect
10. #11747252C2semidirect
11. #11747250C2semidirect
54. #65253D3semidirect
96. C2×#890D5semidirect
458. C3×C5#3080semidirect
517. C5#79241semidirect
537. C3#10614748semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8902
#117544362
#117510672
C3×#652532
#117484722
#117484402
#117483942
#117472912
#117472902
#117472522
#117472502
#106147483
#792415