Finite Group Databasebeta

← #14417259

Subgroups — #14417259

Order 1920.

940 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#942C211yesmaximal, characteristic
2C3×#66146C211yesmaximal, characteristic, complemented
3#11754513C211yesmaximal, characteristic
4C2×#91119C211yesmaximal, characteristic, complemented
5#11749247C212yesmaximal, complemented
6Dic5×#216C212yesmaximal, complemented
7#11749223C212yesmaximal, complemented
8Dic5×#215C212yesmaximal, complemented
9#11748455C211yesmaximal, characteristic, complemented
10#11748382C211yesmaximal, characteristic
11#11748320C211yesmaximal, characteristic, complemented
12#10615696—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C2×C4⋊Dic15C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
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—
25C3×#4072—22no—
26C3×#4072C2211yescharacteristic
27C3×#4072C2211yescharacteristic
28#67⋊Dic5—22no—
29D3×C4⋊Dic5—21no—
30Dic5×D12C2212yes—
31#91338—21no—
32Dic5×Dic6C2212yes—
33#91119C2212yes—
34#91119C2212yes—
35#90990C2212yes—
36#90987C2212yes—
37#90972C2211yescharacteristic
38#90972C2211yescharacteristic
39#90966C2211yescharacteristic
40#90966C2211yescharacteristic
41#90952C2212yes—
42Dic5×C3⋊C8C2212yes—
43#82547—51nomaximal, Hall
44C2×C5×#137—31no—
45#66161—31no—
46#66146D311yescharacteristic, complemented
47#65522—31no—
48C2×#3967—31no—
49#65473—32no—
50Q16×Dic5—32no—
51#65453—32no—
52SD16×Dic5—32no—
53#65411—31no—
54#65410—31no—
55C2×C3×C5×Q8—21no—
56C2×C3×C5×Q8—22no—
57C2×C3×C5×Q8C2×C414yescomplemented
58C2×C3×C5×Q8C2312yes—
59C22×C3×C4×C5—21no—
60C22×C3×C4×C5C2311yescharacteristic
61C22×Dic15—21no—
62C2×C5×#67—21no—
63C5×#235—22no—
64C5×#235C2×C414yes—
65C2×C5×D12C2311yescharacteristic
66C2×C4×C5×D3—21no—
67C2×C5×Dic6C2311yescharacteristic
68C2×D3×Dic5—22no—
69C4⋊Dic15—21no—
70C4⋊Dic15C2312yes—
71C2×C3⋊#168—22no—
72C2×C3⋊#168C2311yescharacteristic
73C2×C3⋊#168C2311yescharacteristic
74C5×#216C2×C418yescomplemented
75C5×#215C2×C418yescomplemented
76C5×#208C2×C414yescomplemented
77C2×C5×C3⋊C8C2312yes—
78C3×C22⋊Dic5—21no—
79C3×C22⋊Dic5D412yes—
80C3×C4⋊Dic5—22no—
81C3×C4⋊Dic5—22no—
82C3×C4⋊Dic5D411yescharacteristic
83C3×C4⋊Dic5D411yescharacteristic
84C3×C4⋊Dic5C2311yescharacteristic
85C3×C4⋊Dic5C2311yescharacteristic
86C3×C4×Dic5—21no—
87C3×C4×Dic5—22no—
88C3×C4×Dic5—22no—
89C3×C4×Dic5C2312yes—
90Dic3⋊Dic5—22no—
91(C2×D3)⋊Dic5—22no—
92Dic3×Dic5—22no—
93C3×#519—51no—
94C2×#942D511yescharacteristic
95#5523—51no—
96C2×#835—51no—
97#5030—52no—
98C4×#216—52no—
99#5026—52no—
100C4×#215—52no—
101#5002—51no—
102#4997—51no—
103#4995—51no—
104C2×C5×#41—31no—
105C22×C5×Q8C2×D311yescharacteristic
106C5×#137—38no—
107C2×C5×Q16—32no—
108C2×C5×SD16—32no—
109C2×C5×M16—31no—
110Q8×Dic5—21no—
111Q8×Dic5—21no—
112Q8×Dic5—32no—
113Q8×Dic5C2×D312yes—
114Q8×Dic5C2×D312yes—
115D4×Dic5—32no—
116D4×Dic5—62no—
117#4072—22no—
118#4072—61no—
119#4072C2×D311yescharacteristic
120#4072C2×D311yescharacteristic
121C2×C4⋊Dic5—31no—
122C2×C4⋊Dic5—61no—
123C22×#168—31no—
124#3967—32no—
125#3967—32no—
126#3967—31no—
127#3967—31no—
128#3964—31no—
129#3964—31no—
130#3950—32no—
131#3949—32no—
132#3947—32no—
133C8×Dic5—32no—
134#2947—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×C5×D3—21no—
137C3×C5×Q8—24no—
138C3×C5×Q8—22no—
139C3×C5×Q8C22×C414yes—
140C2×C3×C4×C5—24no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5C22×C412yes—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5#4112yes—
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15—22no—
147C2×Dic15—81no—
148C5×#67—24no—
149C2×C5×Dic3—21no—
150C5×D12—21no—
151C5×D12C22×C412yes—
152C4×C5×D3—24no—
153C5×Dic6—21no—
154C5×Dic6C22×C412yes—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5C2×D412yes—
158C2×C3×Dic5C2×D412yes—
159D3×Dic5—82no—
160C3⋊#168—21no—
161C3⋊#168—21no—
162C5×C3⋊C8C22×C414yes—
163C22×C3×Q8C2×D511yescharacteristic
164C2×#235C2×D511yescharacteristic
165C3×C4×Q8—52no—
166C3×C4×Q8—52no—
167C3×C4×Q8—101no—
168C3×C4×Q8—101no—
169C3×#117—51no—
170C3×#117—51no—
171C3×#117—102no—
172C2×#216C2×D512yes—
173#942Dic518yescomplemented
174C2×#215C2×D512yes—
175C2×C4⋊Dic3—51no—
176C2×#208C2×D511yescharacteristic
177C22×C3⋊C8—51no—
178#892—101no—
179D3×C4⋊C4—101no—
180#67⋊C4—102no—
181C4×D12—52no—
182C4×Dic6—52no—
183#835—52no—
184#835—52no—
185#810—51no—
186#810—51no—
187#809—51no—
188#809—51no—
189#808—52no—
190#807—52no—
191#803—52no—
192C4×C3⋊C8—52no—
193C5×#41—34no—
194C5×#41—62no—
195C2×C5×Q8—22no—
196C2×C5×Q8—21no—
197C2×C5×Q8—31no—
198C2×C5×Q8C4×D314yescomplemented
199C2×C5×Q8C22×D312yes—
200C2×C5×D4—31no—
201C2×C5×D4—61no—
202C22×C4×C5—21no—
203C22×C4×C5—61no—
204C22×C4×C5C22×D311yescharacteristic
205C22×Dic5—61no—
206C22×Dic5—62no—
207C5×Q16—38no—
208C5×SD16—38no—
209C5×M16—34no—
210C2×C5×C8—32no—
211C22⋊Dic5—21no—
212C22⋊Dic5—62no—
213C22⋊Dic5#6712yes—
214C4⋊Dic5—22no—
215C4⋊Dic5—22no—
216C4⋊Dic5—32no—
217C4⋊Dic5—61no—
218C4⋊Dic5—62no—
219C4⋊Dic5#6711yescharacteristic
220C4⋊Dic5#6711yescharacteristic
221C4⋊Dic5C22×D311yescharacteristic
222C4⋊Dic5C22×D311yescharacteristic
223C4×Dic5—21no—
224C4×Dic5—22no—
225C4×Dic5—22no—
226C4×Dic5—62no—
227C4×Dic5C22×D312yes—
228C2×#168—31no—
229C2×#168—31no—
230C2×#168—62no—
231C2×#137—31no—
232#520—151no—
233#519—51no—
234#441—152no—
235#440—152no—
236C4×Q16—152no—
237C4×SD16—152no—
238#428—151no—
239#416—151no—
240C2×#103—151no—
241#405—151no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5C4×D412yes—
245C22×C3×C5C22×D411yescharacteristic
246C2×C5×D3—22no—
247C2×C5×D3—41no—
248C2×C5×D3—41no—
249C3×C4×C5—24no—
250C3×C4×C5C4×D412yes—
251C3×C4×C5C23×C411yescharacteristic
252C3×C4×C5C2×#4111yescharacteristic
253Dic15—42no—
254C3×Dic5—22no—
255C3×Dic5—22no—
256C3×Dic5—41no—
257C3×Dic5—41no—
258C5×Dic3—22no—
259C2×C3×Q8—21no—
260C2×C3×Q8—22no—
261C2×C3×Q8C2×Dic514yescomplemented
262C2×C3×Q8C22×D512yes—
263C22×C3×C4—21no—
264C22×C3×C4C22×D511yescharacteristic
265C2×#67—21no—
266C22×Dic3—101no—
267#235—22no—
268#235C2×Dic514yes—
269C2×D12C22×D511yescharacteristic
270C2×C4×D3—21no—
271C2×C4×D3—102no—
272C2×Dic6C22×D511yescharacteristic
273C3×C4⋊C4—51no—
274C3×C4⋊C4—51no—
275C3×C4⋊C4—51no—
276C3×C4⋊C4—51no—
277C3×C4⋊C4—102no—
278C3×C4⋊C4—102no—
279C3×C22⋊C4—52no—
280C3×C22⋊C4—101no—
281C3×C42—52no—
282C3×C42—102no—
283C3×C42—102no—
284C3×C42—101no—
285#216C2×Dic518yescomplemented
286#215C2×Dic518yescomplemented
287(C2×D3)⋊C4—102no—
288C4⋊Dic3—52no—
289C4⋊Dic3—101no—
290Dic3⋊C4—102no—
291C4×Dic3—102no—
292#208C2×Dic514yescomplemented
293C2×C3⋊C8—51no—
294C2×C3⋊C8—51no—
295C2×C3⋊C8—102no—
296C2×C3⋊C8C22×D512yes—
297C23×C5—61no—
298C23×C5C2×#6711yescharacteristic
299C5×Q8—24no—
300C5×Q8—22no—
301C5×Q8—32no—
302C5×Q8—61no—
303C5×Q8C2×C4×D314yes—
304C5×D4—32no—
305C5×D4—64no—
306C5×D4—61no—
307C2×C4×C5—24no—
308C2×C4×C5—22no—
309C2×C4×C5—61no—
310C2×C4×C5—64no—
311C2×C4×C5C2×C4×D312yes—
312C2×C4×C5#23512yes—
313C2×C4×C5C2×#6711yescharacteristic
314C2×C4×C5C23×D311yescharacteristic
315C2×Dic5—21no—
316C2×Dic5—21no—
317C2×Dic5—62no—
318C2×Dic5—242no—
319C2×Dic5—241no—
320C2×Dic5C2×#6712yes—
321C2×Dic5C2×#6712yes—
322C5×C8—34no—
323#168—61no—
324#168—61no—
325C2×#41—31no—
326C22×Q8D3×D511yescharacteristic
327#137—38no—
328C2×Q16—32no—
329C2×SD16—32no—
330C2×M16—31no—
331C22×C8—151no—
332C4×Q8—52no—
333C4×Q8—52no—
334C4×Q8—101no—
335C4×Q8—101no—
336C4×Q8—152no—
337C4×D4—152no—
338C4×D4—302no—
339#117—51no—
340#117—51no—
341#117—102no—
342#117—301no—
343C2×C4⋊C4—151no—
344C2×C4⋊C4—301no—
345#107—152no—
346#106—152no—
347#103—151no—
348#103—151no—
349#103—152no—
350#103—152no—
351#102—151no—
352#102—151no—
353#97—152no—
354C4×C8—152no—
355C2×C3×C5—22no—
356C2×C3×C5C2×C4×D411yescharacteristic
357C2×C3×C5#57711yescharacteristic
358C2×C3×C5#57811yescharacteristic
359C5×D3—42no—
360C23×C3D4×D511yescharacteristic
361C22×D3—21no—
362C3×Q8—22no—
363C3×Q8—24no—
364C3×Q8C22×Dic514yes—
365C2×C3×C4—22no—
366C2×C3×C4—24no—
367C2×C3×C4—52no—
368C2×C3×C4—52no—
369C2×C3×C4—101no—
370C2×C3×C4—101no—
371C2×C3×C4D4×D511yescharacteristic
372C2×C3×C4#71112yes—
373C2×C3×C4C22×Dic512yes—
374C2×C3×C4C23×D511yescharacteristic
375#67—24no—
376C2×Dic3—21no—
377C2×Dic3—102no—
378C2×Dic3—401no—
379D12—21no—
380D12C22×Dic512yes—
381C4×D3—24no—
382C4×D3—402no—
383Dic6—21no—
384Dic6C22×Dic512yes—
385C3⋊C8—101no—
386C3⋊C8—101no—
387C3⋊C8C22×Dic514yes—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5—62no—
391C22×C5—121no—
392C22×C5—121no—
393C22×C5C4×#6712yes—
394C22×C5C22×#6711yescharacteristic
395C4×C5—24no—
396C4×C5—62no—
397C4×C5C4×#6712yes—
398C4×C5C22×C4×D311yescharacteristic
399C4×C5C2×#23511yescharacteristic
400Dic5—22no—
401Dic5—22no—
402Dic5—41no—
403Dic5—41no—
404Dic5—122no—
405#41—34no—
406#41—62no—
407C2×Q8—22no—
408C2×Q8—21no—
409C2×Q8—31no—
410C2×Q8D3×Dic514yescomplemented
411C2×Q8C2×D3×D512yes—
412C2×D4—31no—
413C2×D4—61no—
414C22×C4—21no—
415C22×C4—61no—
416C22×C4—302no—
417C22×C4—301no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—38no—
420SD16—38no—
421M16—34no—
422C2×C8—32no—
423C2×C8—151no—
424C2×C8—151no—
425C2×C8—302no—
426C4⋊C4—51no—
427C4⋊C4—51no—
428C4⋊C4—51no—
429C4⋊C4—51no—
430C4⋊C4—102no—
431C4⋊C4—102no—
432C4⋊C4—152no—
433C4⋊C4—302no—
434C4⋊C4—301no—
435C22⋊C4—52no—
436C22⋊C4—101no—
437C22⋊C4—302no—
438C42—52no—
439C42—102no—
440C42—102no—
441C42—101no—
442C42—302no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3D4×Dic512yes—
447C22×C3C2×D4×D511yescharacteristic
448C2×D3—22no—
449C2×D3—41no—
450C2×D3—41no—
451C3×C4—24no—
452C3×C4—102no—
453C3×C4—102no—
454C3×C4—201no—
455C3×C4—201no—
456C3×C4D4×Dic512yes—
457C3×C4C2×#71111yescharacteristic
458C3×C4C23×Dic511yescharacteristic
459Dic3—22no—
460Dic3—202no—
461C2×C5—22no—
462C2×C5—122no—
463C2×C5C2×C4×#6711yescharacteristic
464C2×C5#583711yescharacteristic
465C2×C5#583811yescharacteristic
466C23—61no—
467C23D5×#6711yescharacteristic
468Q8—22no—
469Q8—24no—
470Q8—32no—
471Q8—61no—
472Q8C2×D3×Dic514yes—
473D4—32no—
474D4—64no—
475D4—61no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—52no—
479C2×C4—52no—
480C2×C4—61no—
481C2×C4—64no—
482C2×C4—101no—
483C2×C4—101no—
484C2×C4—302no—
485C2×C4—1202no—
486C2×C4—1201no—
487C2×C4C2×D3×Dic512yes—
488C2×C4#678212yes—
489C2×C4D5×#6711yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—34no—
492C8—301no—
493C8—301no—
494C2×C3—22no—
495C2×C3#6611211yescharacteristic
496C2×C3#6611311yescharacteristic
497C2×C3C2×D4×Dic511yescharacteristic
498D3—42no—
499C5#8254711yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—62no—
503C22—121no—
504C22—121no—
505C22Dic5×#6712yes—
506C22C2×D5×#6711yescharacteristic
507C4—24no—
508C4—62no—
509C4—102no—
510C4—102no—
511C4—201no—
512C4—201no—
513C4—602no—
514C4Dic5×#6712yes—
515C4C22×D3×Dic511yescharacteristic
516C4C2×#678211yescharacteristic
517C3#1061569611yescharacteristic, complemented, Sylow
518C2—22no—
519C2—122no—
520C2#1175508611yescharacteristic
521C2#1175510211yescharacteristic
522C2C2×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×C5#2947
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. C3×#66146C2semidirect
4. C2×#91119C2semidirect
5. #11749247C2semidirect
6. Dic5×#216C2semidirect
7. #11749223C2semidirect
8. Dic5×#215C2semidirect
9. #11748455C2semidirect
11. #11748320C2semidirect
18. C5×#942C4semidirect
46. #66146D3semidirect
57. C2×C3×C5×Q8C2×C4semidirect
74. C5×#216C2×C4semidirect
75. C5×#215C2×C4semidirect
76. C5×#208C2×C4semidirect
173. #942Dic5semidirect
198. C2×C5×Q8C4×D3semidirect
261. C2×C3×Q8C2×Dic5semidirect
285. #216C2×Dic5semidirect
286. #215C2×Dic5semidirect
292. #208C2×Dic5semidirect
410. C2×Q8D3×Dic5semidirect
443. C3×C5#2947semidirect
499. C5#82547semidirect
517. C3#10615696semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9422
C3×#661462
#117545132
C2×#911192
#117492472
Dic5×#2162
#117492232
Dic5×#2152
#117484552
#117483822
#117483202
#106156963
#825475