Finite Group Databasebeta

← #14297408

Subgroups — #14297408

Order 1920.

1072 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#1010C211yesmaximal, characteristic
2#11751337C211yesmaximal, characteristic, complemented
3C3×#65525C211yesmaximal, characteristic, complemented
4#11748625C211yesmaximal, characteristic, complemented
5#11748409C211yesmaximal, characteristic, complemented
6#11748407C211yesmaximal, characteristic, complemented
7#11748355C211yesmaximal, characteristic, complemented
8#10602937—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C5×#1010—22no—
11C5×#1010—22no—
12C5×#1010—22no—
13C5×#1010—22no—
14C2×C5×D3×Q8C412yescomplemented
15C2×C5×#237—22no—
16C2×C5×#237C412yescomplemented
17C2×C5×#235—21no—
18C2×C5×#235C2211yescharacteristic
19C22×C5×Dic6—21no—
20C22×C5×Dic6C2211yescharacteristic
21#91815C2211yescharacteristic
22C2×#6710C2211yescharacteristic
23C3×#4072C2211yescharacteristic
24C2×C3×#681C2211yescharacteristic
25#91121—22no—
26C3×#3969—22no—
27#90996—22no—
28#90973—22no—
29#90972—22no—
30#90962—21no—
31#90959—21no—
32#70415—51nomaximal, Hall
33C2×C5×2−1+4—31no—
34#65529—31no—
35#65526—31no—
36#65525—31no—
37#65525D311yescharacteristic, complemented
38#65514—31no—
39#65514—31no—
40C3×C5×#41—21no—
41C3×C5×#41—21no—
42C3×C5×#41D412yes—
43C3×C5×#41D412yes—
44C2×C3×C5×Q8C2×C411yescharacteristic
45C2×C3×C5×D4—21no—
46C2×C3×C5×D4C2×C411yescharacteristic
47C22×C3×C4×C5—21no—
48C22×C3×C4×C5C2311yescharacteristic
49C2×C5×#67—22no—
50C2×C5×#67D412yes—
51C22×C5×Dic3—21no—
52C22×C5×Dic3—22no—
53C5×D3×Q8—24no—
54C5×D3×Q8—24no—
55C5×#237—28no—
56C5×#237—28no—
57C5×#237—24no—
58C5×#237—24no—
59C5×#235—24no—
60C5×#235—24no—
61C5×#235—21no—
62C5×#235—21no—
63C5×#235—21no—
64C5×#235—21no—
65C2×C5×D12D411yescharacteristic
66C2×C4×C5×D3—22no—
67C2×C4×C5×D3C2×C412yes—
68C2×C5×Dic6—24no—
69C2×C5×Dic6—24no—
70C2×C5×Dic6—21no—
71C2×C5×Dic6—21no—
72C2×C5×Dic6—21no—
73C2×C5×Dic6—22no—
74C2×C5×Dic6C2×C412yes—
75C2×C5×Dic6D411yescharacteristic
76C2×C5×Dic6D412yes—
77C2×C5×Dic6D412yes—
78#6719—21no—
79C4⋊Dic15—21no—
80C4×Dic15—21no—
81#6710—21no—
82#6710—21no—
83C2×C3⋊#168—21no—
84C3×C22⋊Dic5—21no—
85C3×C4⋊Dic5—21no—
86C3×C4×Dic5—21no—
87C3×#681—21no—
88C3×#681—21no—
89C2×C3×#168—21no—
90C2×#1010D511yescharacteristic
91C3×#421—51no—
92#5236—51no—
93#5132—51no—
94#5120—51no—
95#5006—51no—
96#5004—51no—
97C5×2−1+4—62no—
98C5×2−1+4—62no—
99C5×2−1+4—62no—
100C5×2−1+4—62no—
101C2×C5×#41—31no—
102C2×C5×#41—32no—
103C2×C5×#41—61no—
104C2×C5×#41—62no—
105C2×C5×#41C2×D311yescharacteristic
106C22×C5×Q8—32no—
107C22×C5×Q8—31no—
108C22×C5×Q8—61no—
109#4072—31no—
110#4072C2×D311yescharacteristic
111C2×#681—31no—
112C2×#681C2×D311yescharacteristic
113#3969—22no—
114#3969—62no—
115#3968—61no—
116#3967—62no—
117#3967—62no—
118#3966—62no—
119#3965—61no—
120#1796—151noSylow
121C23×C3×C5—21no—
122C23×C3×C5C2×D411yescharacteristic
123C22×C5×D3C22⋊C412yes—
124C3×C5×Q8—21no—
125C3×C5×Q8C22⋊C412yes—
126C3×C5×D4—22no—
127C3×C5×D4—22no—
128C3×C5×D4—21no—
129C3×C5×D4C22⋊C412yes—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5C22×C411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×Dic15—41no—
140C5×#67—28no—
141C5×#67—22no—
142C5×#67—22no—
143C2×C5×Dic3—28no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3C22⋊C412yes—
148C5×D12—21no—
149C5×D12—21no—
150C4×C5×D3—28no—
151C4×C5×D3—22no—
152C4×C5×D3—22no—
153C5×Dic6—28no—
154C5×Dic6—22no—
155C5×Dic6—21no—
156C5×Dic6—21no—
157C5×Dic6—22no—
158C5×Dic6—22no—
159C5×Dic6C22⋊C414yes—
160C2×C3×Dic5—41no—
161C3⋊#168—41no—
162C3×#168—41no—
163C2×C3×#41C2×D511yescharacteristic
164#1010—22no—
165#1010—22no—
166#1010—22no—
167#1010—22no—
168C2×D3×Q8Dic512yescomplemented
169C2×#237—22no—
170C2×#237Dic512yescomplemented
171C2×#235—21no—
172C2×#235C2×D511yescharacteristic
173C22×Dic6—21no—
174C22×Dic6C2×D511yescharacteristic
175C2×C3×M16—51no—
176C3×#117—51no—
177#926—51no—
178C2×#208—51no—
179C3×#104—102no—
180#837—102no—
181#824—101no—
182#823—101no—
183#816—102no—
184#810—102no—
185#806—102no—
186C5×#41—21no—
187C5×#41—21no—
188C5×#41—64no—
189C5×#41—64no—
190C5×#41—64no—
191C5×#41—68no—
192C5×#41—68no—
193C5×#41—64no—
194C5×#41—61no—
195C5×#41—61no—
196C5×#41—61no—
197C5×#41—61no—
198C5×#41D1212yes—
199C5×#41#6712yes—
200C2×C5×Q8—31no—
201C2×C5×Q8—32no—
202C2×C5×Q8—32no—
203C2×C5×Q8—32no—
204C2×C5×Q8—62no—
205C2×C5×Q8—64no—
206C2×C5×Q8—64no—
207C2×C5×Q8—64no—
208C2×C5×Q8—64no—
209C2×C5×Q8—61no—
210C2×C5×Q8—61no—
211C2×C5×Q8—61no—
212C2×C5×Q8C4×D311yescharacteristic
213C2×C5×D4—21no—
214C2×C5×D4—32no—
215C2×C5×D4—31no—
216C2×C5×D4—62no—
217C2×C5×D4C4×D311yescharacteristic
218C22×C4×C5—21no—
219C22×C4×C5—32no—
220C22×C4×C5—62no—
221C22×C4×C5—62no—
222C22×C4×C5—61no—
223C22×C4×C5C22×D311yescharacteristic
224C22⋊Dic5—21no—
225C22⋊Dic5—61no—
226C4⋊Dic5—21no—
227C4⋊Dic5—61no—
228C4×Dic5—21no—
229C4×Dic5—61no—
230#681—21no—
231#681—21no—
232#681—61no—
233#681—61no—
234C2×#168—21no—
235C2×#168—61no—
236C2×2−1+4—31no—
237#421—51no—
238#421—151no—
239#419—151no—
240#419—151no—
241#413—151no—
242#410—151no—
243C22×C3×C5—22no—
244C22×C3×C5—41no—
245C22×C3×C5—42no—
246C22×C3×C5C2×C22⋊C411yescharacteristic
247C22×C3×C5#12011yescharacteristic
248C22×C3×C5#12011yescharacteristic
249C2×C5×D3—22no—
250C2×C5×D3—42no—
251C3×C4×C5—22no—
252C3×C4×C5C2×C22⋊C411yescharacteristic
253C3×C4×C5C2×C22⋊C411yescharacteristic
254C3×C4×C5#12011yescharacteristic
255C3×C4×C5#12011yescharacteristic
256Dic15—81no—
257C3×Dic5—81no—
258C5×Dic3—22no—
259C5×Dic3—24no—
260C3×#41—21no—
261C3×#41—21no—
262C3×#41C22⋊D512yes—
263C3×#41C22⋊D512yes—
264C2×C3×Q8C2×Dic511yescharacteristic
265C2×C3×D4—21no—
266C2×C3×D4C2×Dic511yescharacteristic
267C22×C3×C4—21no—
268C22×C3×C4C22×D511yescharacteristic
269C2×#67—22no—
270C2×#67C22⋊D512yes—
271C22×Dic3—21no—
272C22×Dic3—22no—
273D3×Q8—24no—
274D3×Q8—24no—
275#237—28no—
276#237—28no—
277#237—24no—
278#237—24no—
279#235—24no—
280#235—24no—
281#235—21no—
282#235—21no—
283#235—21no—
284#235—21no—
285C2×D12C22⋊D511yescharacteristic
286C2×C4×D3—22no—
287C2×C4×D3C2×Dic512yes—
288C2×Dic6—24no—
289C2×Dic6—24no—
290C2×Dic6—21no—
291C2×Dic6—21no—
292C2×Dic6—21no—
293C2×Dic6—22no—
294C2×Dic6C2×Dic512yes—
295C2×Dic6C22⋊D511yescharacteristic
296C2×Dic6C22⋊D512yes—
297C2×Dic6C22⋊D512yes—
298C3×M16—101no—
299C3×M16—101no—
300C2×C3×C8—101no—
301C3×C4⋊C4—101no—
302C3×C22⋊C4—101no—
303C3×C42—101no—
304#217—101no—
305C4⋊Dic3—101no—
306C4×Dic3—101no—
307#208—101no—
308#208—101no—
309C2×C3⋊C8—101no—
310C23×C5—21no—
311C23×C5—32no—
312C23×C5D3×D411yescharacteristic
313C5×Q8—21no—
314C5×Q8—34no—
315C5×Q8—68no—
316C5×Q8—61no—
317C5×Q8—62no—
318C5×Q8—62no—
319C5×Q8—61no—
320C5×Q8—62no—
321C5×Q8(C2×D3)⋊C412yes—
322C5×D4—22no—
323C5×D4—22no—
324C5×D4—21no—
325C5×D4—68no—
326C5×D4—62no—
327C5×D4—62no—
328C5×D4—61no—
329C5×D4—61no—
330C5×D4(C2×D3)⋊C412yes—
331C2×C4×C5—21no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—32no—
335C2×C4×C5—68no—
336C2×C4×C5—68no—
337C2×C4×C5—62no—
338C2×C4×C5—62no—
339C2×C4×C5—62no—
340C2×C4×C5—62no—
341C2×C4×C5—62no—
342C2×C4×C5C2×C4×D311yescharacteristic
343C2×C4×C5C2×D1211yescharacteristic
344C2×C4×C5D3×D411yescharacteristic
345C2×C4×C5D3×D411yescharacteristic
346C2×C4×C5D3×D411yescharacteristic
347C2×C4×C5C2×#6711yescharacteristic
348C2×Dic5—41no—
349C2×Dic5—121no—
350#168—41no—
351#168—121no—
3522−1+4—62no—
3532−1+4—62no—
3542−1+4—62no—
3552−1+4—62no—
356C2×#41—31no—
357C2×#41—32no—
358C2×#41—61no—
359C2×#41—62no—
360C2×#41D3×D511yescharacteristic
361C22×Q8—32no—
362C22×Q8—31no—
363C22×Q8—61no—
364C2×M16—51no—
365C2×M16—151no—
366#117—51no—
367#117—151no—
368#104—102no—
369#104—302no—
370#103—302no—
371#103—302no—
372#101—301no—
373#100—301no—
374#99—302no—
375C2×C3×C5—21no—
376C2×C3×C5—21no—
377C2×C3×C5—21no—
378C2×C3×C5—42no—
379C2×C3×C5#37911yescharacteristic
380C5×D3—42no—
381C23×C3—21no—
382C23×C3C2×C22⋊D511yescharacteristic
383C22×D3C22⋊Dic512yes—
384C3×Q8—21no—
385C3×Q8C22⋊Dic512yes—
386C3×D4—22no—
387C3×D4—22no—
388C3×D4—21no—
389C3×D4C22⋊Dic512yes—
390C2×C3×C4—21no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—201no—
394C2×C3×C4C22×Dic511yescharacteristic
395C2×C3×C4C2×C22⋊D511yescharacteristic
396C2×C3×C4C2×C22⋊D511yescharacteristic
397C2×C3×C4C2×C22⋊D511yescharacteristic
398C2×C3×C4C2×C22⋊D511yescharacteristic
399C2×C3×C4C2×C22⋊D511yescharacteristic
400#67—28no—
401#67—22no—
402#67—22no—
403C2×Dic3—28no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—201no—
408C2×Dic3C22⋊Dic512yes—
409D12—21no—
410D12—21no—
411C4×D3—28no—
412C4×D3—22no—
413C4×D3—22no—
414Dic6—28no—
415Dic6—22no—
416Dic6—21no—
417Dic6—22no—
418Dic6—21no—
419Dic6—22no—
420Dic6C22⋊Dic514yes—
421C3×C8—201no—
422C3⋊C8—201no—
423C22×C5—22no—
424C22×C5—41no—
425C22×C5—42no—
426C22×C5—62no—
427C22×C5—122no—
428C22×C5D3×C22⋊C411yescharacteristic
429C22×C5#88211yescharacteristic
430C22×C5#93711yescharacteristic
431C4×C5—22no—
432C4×C5—62no—
433C4×C5—64no—
434C4×C5D3×C22⋊C411yescharacteristic
435C4×C5#88211yescharacteristic
436C4×C5C2×(C2×D3)⋊C411yescharacteristic
437C4×C5#93711yescharacteristic
438Dic5—81no—
439Dic5—241no—
440#41—21no—
441#41—21no—
442#41—64no—
443#41—64no—
444#41—64no—
445#41—68no—
446#41—68no—
447#41—64no—
448#41—61no—
449#41—61no—
450#41—61no—
451#41—61no—
452#41#120112yes—
453#41#120312yes—
454C2×Q8—31no—
455C2×Q8—32no—
456C2×Q8—32no—
457C2×Q8—32no—
458C2×Q8—62no—
459C2×Q8—64no—
460C2×Q8—64no—
461C2×Q8—64no—
462C2×Q8—64no—
463C2×Q8—61no—
464C2×Q8—61no—
465C2×Q8—61no—
466C2×Q8D3×Dic511yescharacteristic
467C2×D4—21no—
468C2×D4—32no—
469C2×D4—31no—
470C2×D4—62no—
471C2×D4D3×Dic511yescharacteristic
472C22×C4—21no—
473C22×C4—32no—
474C22×C4—62no—
475C22×C4—62no—
476C22×C4—61no—
477C22×C4C2×D3×D511yescharacteristic
478M16—101no—
479M16—101no—
480M16—301no—
481M16—301no—
482C2×C8—101no—
483C2×C8—301no—
484C4⋊C4—101no—
485C4⋊C4—301no—
486C22⋊C4—101no—
487C22⋊C4—301no—
488C42—101no—
489C42—301no—
490C3×C5#179611yescharacteristic, complemented, Hall
491C22×C3—22no—
492C22×C3—41no—
493C22×C3—42no—
494C22×C3C2×C22⋊Dic511yescharacteristic
495C22×C3#409911yescharacteristic
496C22×C3#409911yescharacteristic
497C2×D3—22no—
498C2×D3—42no—
499C3×C4—22no—
500C3×C4—401no—
501C3×C4C2×C22⋊Dic511yescharacteristic
502C3×C4C2×C22⋊Dic511yescharacteristic
503C3×C4#409911yescharacteristic
504C3×C4#409911yescharacteristic
505Dic3—22no—
506Dic3—24no—
507Dic3—401no—
508C2×C5—21no—
509C2×C5—21no—
510C2×C5—21no—
511C2×C5—42no—
512C2×C5—122no—
513C2×C5#495511yescharacteristic
514C23—21no—
515C23—32no—
516C23D3×C22⋊D511yescharacteristic
517Q8—21no—
518Q8—34no—
519Q8—68no—
520Q8—62no—
521Q8—61no—
522Q8—62no—
523Q8—61no—
524Q8—62no—
525Q8(C2×D3)⋊Dic512yes—
526D4—22no—
527D4—22no—
528D4—21no—
529D4—68no—
530D4—62no—
531D4—62no—
532D4—61no—
533D4—61no—
534D4(C2×D3)⋊Dic512yes—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—32no—
539C2×C4—68no—
540C2×C4—68no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—201no—
547C2×C4—601no—
548C2×C4C2×D3×Dic511yescharacteristic
549C2×C4C2×#120111yescharacteristic
550C2×C4C2×#120311yescharacteristic
551C2×C4D3×C22⋊D511yescharacteristic
552C2×C4D3×C22⋊D511yescharacteristic
553C2×C4D3×C22⋊D511yescharacteristic
554C8—201no—
555C8—601no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—42no—
560C2×C3#6553611yescharacteristic
561D3—42no—
562C5#7041511yescharacteristic, complemented, Sylow
563C22—22no—
564C22—41no—
565C22—42no—
566C22—62no—
567C22—122no—
568C22D3×C22⋊Dic511yescharacteristic
569C22#9156811yescharacteristic
570C22#9157011yescharacteristic
571C4—22no—
572C4—62no—
573C4—64no—
574C4—401no—
575C4—1201no—
576C4C2×(C2×D3)⋊Dic511yescharacteristic
577C4D3×C22⋊Dic511yescharacteristic
578C4#9156811yescharacteristic
579C4#9157011yescharacteristic
580C3#1060293711yescharacteristic, complemented, Sylow
581C2—21no—
582C2—21no—
583C2—21no—
584C2—42no—
585C2—122no—
586C2#1174949611yescharacteristic
subgroupG/H
centerC2#11749496
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5#379
prime radicalC2×C5×#1010C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1796
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11751337C2semidirect
3. C3×#65525C2semidirect
4. #11748625C2semidirect
5. #11748409C2semidirect
6. #11748407C2semidirect
7. #11748355C2semidirect
14. C2×C5×D3×Q8C4semidirect
16. C2×C5×#237C4semidirect
37. #65525D3semidirect
168. C2×D3×Q8Dic5semidirect
170. C2×#237Dic5semidirect
490. C3×C5#1796semidirect
562. C5#70415semidirect
580. C3#10602937semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10102
#117513372
C3×#655252
#117486252
#117484092
#117484072
#117483552
#106029373
#704155