Finite Group Databasebeta

← #14430737

Subgroups — #14430737

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
1C5×#5522C211yesmaximal, characteristic
2C2×#91381C211yesmaximal, characteristic, complemented
3#11751096C211yesmaximal, characteristic, complemented
4C3×#65284C211yesmaximal, characteristic, complemented
5#11748440C211yesmaximal, characteristic, complemented
6#11748390C211yesmaximal, characteristic
7#11748384C211yesmaximal, characteristic
8#11747396C212yesmaximal, complemented
9#11747395C212yesmaximal, complemented
10#11747394C212yesmaximal, complemented
11#11747393C212yesmaximal, complemented
12#10614240—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C3×C5×#117C2211yescharacteristic
15C2×C4⋊Dic15C2211yescharacteristic
16C2×#6710C2211yescharacteristic
17C2×C4×C5×Dic3C2211yescharacteristic
18C5×#893C2211yescharacteristic
19C5×#893C2211yescharacteristic
20C5×#887C2211yescharacteristic
21C5×#887C2211yescharacteristic
22C5×#67⋊C4—21no—
23C5×#67⋊C4—21no—
24C5×#872—21no—
25C42×C5×D3—21no—
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C2×C3×#681C2211yescharacteristic
28C2×#6669—21no—
29C2×#6668—21no—
30#91381—21no—
31#91381—21no—
32#91381C2212yes—
33#91381C2212yes—
34#91092C2212yes—
35#91091C2212yes—
36C3×#3940C2212yes—
37C3×#3939C2212yes—
38Dic3⋊#168C2212yes—
39Dic3⋊#168C2212yes—
40#90973C2212yes—
41#90972C2212yes—
42#90967C2212yes—
43#90966C2212yes—
44#79241—51nomaximal, Hall
45C4×C5×#41—31no—
46C2×#4016—31no—
47#65521—31no—
48#65521—31no—
49#65311—32no—
50#65311—32no—
51#65298—32no—
52#65298—32no—
53#65284—31no—
54#65284D311yescharacteristic, complemented
55#65213—31no—
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15—21no—
58C2×C5×#67—21no—
59C22×C5×Dic3D411yescharacteristic
60C22×C5×Dic3D411yescharacteristic
61C5×#235—22no—
62C5×#235Q814yes—
63C2×C5×D12C2311yescharacteristic
64C2×C4×C5×D3—21no—
65C2×C4×C5×D3—21no—
66C2×C4×C5×D3—21no—
67C2×C5×Dic6C2311yescharacteristic
68C22×C3×Dic5—21no—
69C3×C5×C4⋊C4C2311yescharacteristic
70C3×C5×C4⋊C4C2311yescharacteristic
71C3×C5×C22⋊C4—21no—
72C3×C42×C5—21no—
73C4⋊Dic15—21no—
74C4⋊Dic15C2312yes—
75#6710—22no—
76C2×C3⋊#168C2312yes—
77C5×(C2×D3)⋊C4—21no—
78C5×(C2×D3)⋊C4—21no—
79C5×Dic3⋊C4—21no—
80C5×Dic3⋊C4—21no—
81C4×C5×Dic3—21no—
82C4×C5×Dic3—21no—
83C4×C5×Dic3D411yescharacteristic
84C4×C5×Dic3D411yescharacteristic
85C4×C5×Dic3C2311yescharacteristic
86C4×C5×Dic3C2311yescharacteristic
87C3×C4⋊Dic5—21no—
88C3×C4⋊Dic5C2312yes—
89C3×#681—22no—
90C2×C3×#168C2312yes—
91#6669—22no—
92#6669—22no—
93#6668—22no—
94#6668—22no—
95#5522D511yescharacteristic
96C2×#890—51no—
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×C5×#41—31no—
107C4×C5×Q8—31no—
108C4×C5×Q8—31no—
109C4×C5×D4—31no—
110C4×C5×D4—31no—
111C4×C5×D4—61no—
112C4×C5×D4—61no—
113C5×#117—61no—
114C5×#117C2×D311yescharacteristic
115C2×C42×C5—31no—
116C2×C42×C5—61no—
117C2×C4⋊Dic5—31no—
118C2×C4⋊Dic5C2×D311yescharacteristic
119C2×#683—61no—
120C2×#683—61no—
121C2×#681—31no—
122C2×#681C2×D311yescharacteristic
123#4016—32no—
124#4016—32no—
125#4016—61no—
126#4016—61no—
127#3967—32no—
128#3967—32no—
129#3964—32no—
130#3964—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×C5×D3—21no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2×Q812yes—
144C2×C3×C4×C5#4112yes—
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15—22no—
147C2×Dic15—42no—
148C5×#67—24no—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—41no—
151C2×C5×Dic3—41no—
152C2×C5×Dic3C2×D411yescharacteristic
153C2×C5×Dic3C2×D411yescharacteristic
154C2×C5×Dic3C2×D411yescharacteristic
155C2×C5×Dic3C2×D411yescharacteristic
156C5×D12—21no—
157C5×D12C2×Q812yes—
158C4×C5×D3—24no—
159C4×C5×D3—42no—
160C4×C5×D3—42no—
161C5×Dic6—21no—
162C5×Dic6C2×Q812yes—
163C2×C3×Dic5—22no—
164C2×C3×Dic5—42no—
165C3⋊#168—22no—
166C3×#168—22no—
167C2×#235C2×D511yescharacteristic
168C2×C3×M16—51no—
169C3×#117C2×D511yescharacteristic
170C2×C3×C4⋊C4—51no—
171C2×C4⋊Dic3—51no—
172C2×C4⋊Dic3—101no—
173C2×Dic3⋊C4—101no—
174C2×C4×Dic3C2×D511yescharacteristic
175C2×#208—51no—
176#893C2×D511yescharacteristic
177#893C2×D511yescharacteristic
178#890—52no—
179#890—52no—
180#890—101no—
181#890—101no—
182#887C2×D511yescharacteristic
183#887C2×D511yescharacteristic
184#67⋊C4—21no—
185#67⋊C4—21no—
186#872—21no—
187C42×D3—21no—
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—
198C5×#41—34no—
199C5×#41—62no—
200C2×C5×Q8—31no—
201C2×C5×D4—31no—
202C2×C5×D4—61no—
203C22×C4×C5—31no—
204C22×C4×C5—31no—
205C22×C4×C5—61no—
206C22×C4×C5—61no—
207C22×C4×C5—61no—
208C22×C4×C5C22×D311yescharacteristic
209C22×Dic5—21no—
210C22×Dic5—61no—
211C5×C4⋊C4—61no—
212C5×C4⋊C4—61no—
213C5×C4⋊C4C22×D311yescharacteristic
214C5×C4⋊C4C22×D311yescharacteristic
215C5×C22⋊C4—21no—
216C5×C22⋊C4—61no—
217C5×C22⋊C4—61no—
218C42×C5—21no—
219C42×C5—31no—
220C42×C5—31no—
221C42×C5—31no—
222C42×C5—31no—
223C42×C5—61no—
224C42×C5—61no—
225C4⋊Dic5—21no—
226C4⋊Dic5—32no—
227C4⋊Dic5—61no—
228C4⋊Dic5C22×D312yes—
229#683—62no—
230#683—62no—
231#683—62no—
232#683—62no—
233#681—22no—
234#681—62no—
235C2×#168—32no—
236C2×#168C22×D312yes—
237C2×#125—151no—
238C4×#41—31no—
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×C5×D3—22no—
253C2×C5×D3—41no—
254C2×C5×D3—41no—
255C3×C4×C5—41no—
256C3×C4×C5—41no—
257C3×C4×C5C22⋊Q812yes—
258C3×C4×C5C22×Q811yescharacteristic
259C3×C4×C5C2×#4111yescharacteristic
260Dic15—42no—
261C3×Dic5—42no—
262C5×Dic3—22no—
263C5×Dic3—21no—
264C5×Dic3—21no—
265C5×Dic3—21no—
266C5×Dic3—21no—
267C22×C3×C4—101no—
268C22×C3×C4C22×D511yescharacteristic
269C2×#67—21no—
270C22×Dic3—101no—
271C22×Dic3C22⋊D511yescharacteristic
272C22×Dic3C22⋊D511yescharacteristic
273#235—22no—
274#235Dic1014yes—
275C2×D12C22×D511yescharacteristic
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×Dic6C22×D511yescharacteristic
280C3×M16—102no—
281C2×C3×C8—52no—
282C3×C4⋊C4—52no—
283C3×C4⋊C4—101no—
284C3×C4⋊C4C22×D511yescharacteristic
285C3×C4⋊C4C22×D511yescharacteristic
286C3×C22⋊C4—21no—
287C3×C42—21no—
288(C2×D3)⋊C4—21no—
289(C2×D3)⋊C4—21no—
290C4⋊Dic3—52no—
291C4⋊Dic3—101no—
292C4⋊Dic3—102no—
293C4⋊Dic3—102no—
294Dic3⋊C4—21no—
295Dic3⋊C4—21no—
296Dic3⋊C4—102no—
297Dic3⋊C4—102no—
298C4×Dic3—21no—
299C4×Dic3—21no—
300C4×Dic3C22⋊D511yescharacteristic
301C4×Dic3C22⋊D511yescharacteristic
302C4×Dic3C22×D511yescharacteristic
303C4×Dic3C22×D511yescharacteristic
304#208—102no—
305C2×C3⋊C8—52no—
306C23×C5—61no—
307C23×C5D3×D411yescharacteristic
308C5×Q8—32no—
309C5×Q8—61no—
310C5×D4—32no—
311C5×D4—64no—
312C5×D4—61no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—31no—
316C2×C4×C5—31no—
317C2×C4×C5—31no—
318C2×C4×C5—31no—
319C2×C4×C5—61no—
320C2×C4×C5—64no—
321C2×C4×C5—122no—
322C2×C4×C5—122no—
323C2×C4×C5—121no—
324C2×C4×C5—121no—
325C2×C4×C5#23512yes—
326C2×C4×C5D3×D411yescharacteristic
327C2×C4×C5D3×Q812yes—
328C2×C4×C5C23×D311yescharacteristic
329C2×Dic5—22no—
330C2×Dic5—42no—
331C2×Dic5—62no—
332C2×Dic5—122no—
333#168—22no—
334#168—62no—
335C2×#41—31no—
336C2×M16—51no—
337C2×M16—151no—
338#125—152no—
339#125—152no—
340#125—301no—
341#125—301no—
342C4×Q8—31no—
343C4×Q8—31no—
344C4×D4—31no—
345C4×D4—31no—
346C4×D4—61no—
347C4×D4—61no—
348#117—61no—
349#117D3×D511yescharacteristic
350C2×C4⋊C4—51no—
351C2×C4⋊C4—151no—
352C2×C4⋊C4—301no—
353C2×C4⋊C4—301no—
354C2×C42—31no—
355C2×C42—61no—
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
370C5×D3—42no—
371C23×C3C2×C22⋊D511yescharacteristic
372C22×D3—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—102no—
376C2×C3×C4—202no—
377C2×C3×C4C2×Dic1012yes—
378C2×C3×C4#70912yes—
379C2×C3×C4C2×C22⋊D511yescharacteristic
380C2×C3×C4C23×D511yescharacteristic
381#67—24no—
382C2×Dic3—21no—
383C2×Dic3—41no—
384C2×Dic3—41no—
385C2×Dic3—102no—
386C2×Dic3—202no—
387C2×Dic3C2×C22⋊D511yescharacteristic
388C2×Dic3C2×C22⋊D511yescharacteristic
389C2×Dic3C2×C22⋊D511yescharacteristic
390C2×Dic3C2×C22⋊D511yescharacteristic
391D12—21no—
392D12C2×Dic1012yes—
393C4×D3—24no—
394C4×D3—42no—
395C4×D3—42no—
396Dic6—21no—
397Dic6C2×Dic1012yes—
398C3×C8—102no—
399C3⋊C8—102no—
400C22×C5—21no—
401C22×C5—21no—
402C22×C5—62no—
403C22×C5—121no—
404C22×C5—121no—
405C22×C5#89612yes—
406C22×C5C2×D3×D411yescharacteristic
407C4×C5—41no—
408C4×C5—41no—
409C4×C5—62no—
410C4×C5—61no—
411C4×C5—61no—
412C4×C5—61no—
413C4×C5—61no—
414C4×C5#89612yes—
415C4×C5C2×#23511yescharacteristic
416C4×C5C2×D3×Q811yescharacteristic
417Dic5—42no—
418Dic5—122no—
419#41—34no—
420#41—62no—
421C2×Q8—31no—
422C2×D4—31no—
423C2×D4—61no—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—61no—
427C22×C4—61no—
428C22×C4—61no—
429C22×C4—101no—
430C22×C4—301no—
431C22×C4C2×D3×D511yescharacteristic
432M16—102no—
433M16—302no—
434C2×C8—52no—
435C2×C8—152no—
436C4⋊C4—52no—
437C4⋊C4—61no—
438C4⋊C4—61no—
439C4⋊C4—101no—
440C4⋊C4—152no—
441C4⋊C4—302no—
442C4⋊C4—302no—
443C4⋊C4—302no—
444C4⋊C4—302no—
445C4⋊C4—301no—
446C4⋊C4C2×D3×D511yescharacteristic
447C4⋊C4C2×D3×D511yescharacteristic
448C22⋊C4—21no—
449C22⋊C4—61no—
450C22⋊C4—61no—
451C42—21no—
452C42—31no—
453C42—31no—
454C42—31no—
455C42—31no—
456C42—61no—
457C42—61no—
458C3×C5#308011yescharacteristic, complemented, Hall
459C22×C3—21no—
460C22×C3—21no—
461C22×C3#407012yes—
462C22×C3C22×C22⋊D511yescharacteristic
463C2×D3—22no—
464C2×D3—41no—
465C2×D3—41no—
466C3×C4—41no—
467C3×C4—41no—
468C3×C4—202no—
469C3×C4#407012yes—
470C3×C4C22×Dic1011yescharacteristic
471C3×C4C2×#70911yescharacteristic
472Dic3—22no—
473Dic3—21no—
474Dic3—21no—
475Dic3—21no—
476Dic3—21no—
477Dic3—202no—
478C2×C5—22no—
479C2×C5—122no—
480C2×C5C2×#89611yescharacteristic
481C2×C5#577311yescharacteristic
482C2×C5#577711yescharacteristic
483C23—61no—
484C23D3×C22⋊D511yescharacteristic
485Q8—32no—
486Q8—61no—
487D4—32no—
488D4—64no—
489D4—61no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—31no—
493C2×C4—31no—
494C2×C4—31no—
495C2×C4—31no—
496C2×C4—61no—
497C2×C4—64no—
498C2×C4—102no—
499C2×C4—122no—
500C2×C4—122no—
501C2×C4—121no—
502C2×C4—121no—
503C2×C4—202no—
504C2×C4—302no—
505C2×C4—602no—
506C2×C4D3×Dic1012yes—
507C2×C4#677112yes—
508C2×C4D3×C22⋊D511yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—102no—
511C8—302no—
512C2×C3—22no—
513C2×C3C2×#407011yescharacteristic
514C2×C3#6615611yescharacteristic
515C2×C3#6615611yescharacteristic
516D3—42no—
517C5#7924111yescharacteristic, complemented, Sylow
518C22—21no—
519C22—21no—
520C22—62no—
521C22—121no—
522C22—121no—
523C22#9135212yes—
524C22C2×D3×C22⋊D511yescharacteristic
525C4—41no—
526C4—41no—
527C4—61no—
528C4—61no—
529C4—61no—
530C4—61no—
531C4—62no—
532C4—202no—
533C4—602no—
534C4#9135212yes—
535C4C2×D3×Dic1011yescharacteristic
536C4C2×#677111yescharacteristic
537C3#1061424011yescharacteristic, complemented, Sylow
538C2—22no—
539C2—122no—
540C2C2×#9135211yescharacteristic
541C2#1175534511yescharacteristic
542C2#1175534811yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#235C22
hypercenter#117D3×D5
hypocenterC3×C5#3080
LCSG ▷ C2×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×#91381C2semidirect
3. #11751096C2semidirect
4. C3×#65284C2semidirect
5. #11748440C2semidirect
8. #11747396C2semidirect
9. #11747395C2semidirect
10. #11747394C2semidirect
11. #11747393C2semidirect
54. #65284D3semidirect
458. C3×C5#3080semidirect
517. C5#79241semidirect
537. C3#10614240semidirect

Maximal subgroups

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

subgroupindex
C5×#55222
C2×#913812
#117510962
C3×#652842
#117484402
#117483902
#117483842
#117473962
#117473952
#117473942
#117473932
#106142403
#792415