Finite Group Databasebeta

← #14297374

Subgroups — #14297374

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×#92101C211yesmaximal, characteristic
2C3×C5×#421C211yesmaximal, characteristic, complemented
3#11751337C211yesmaximal, characteristic, complemented
4#11751233C211yesmaximal, characteristic, complemented
5#11751221C211yesmaximal, characteristic, complemented
6#11751107C211yesmaximal, characteristic, complemented
7#11751105C211yesmaximal, characteristic, complemented
8#10601208—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10#92101—22no—
11#92101—22no—
12#92101—22no—
13#92101—22no—
14C2×Q8×D15C412yescomplemented
15C2×#6819—22no—
16C2×#6819C412yescomplemented
17C2×#6817—21no—
18C2×#6817C2211yescharacteristic
19C22×Dic30—21no—
20C22×Dic30C2211yescharacteristic
21C2×C3×C5×M16C2211yescharacteristic
22C3×C5×#117C2211yescharacteristic
23#91815C2211yescharacteristic
24C2×#6710C2211yescharacteristic
25C3×C5×#104—22no—
26#91121—22no—
27#91108—21no—
28#91107—21no—
29#91100—22no—
30#91094—22no—
31#91090—22no—
32#70415—51nomaximal, Hall
33C2×#4150—31no—
34C5×#421D311yescharacteristic, complemented
35#65525—31no—
36#65421—31no—
37#65409—31no—
38#65295—31no—
39#65293—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×#1220—22no—
50C2×#1220D412yes—
51C22×Dic15—21no—
52C22×Dic15—22no—
53Q8×D15—24no—
54Q8×D15—24no—
55#6819—28no—
56#6819—28no—
57#6819—24no—
58#6819—24no—
59#6817—24no—
60#6817—24no—
61#6817—21no—
62#6817—21no—
63#6817—21no—
64#6817—21no—
65C2×D60D411yescharacteristic
66C2×C4×D15—22no—
67C2×C4×D15C2×C412yes—
68C2×Dic30—24no—
69C2×Dic30—24no—
70C2×Dic30—21no—
71C2×Dic30—21no—
72C2×Dic30—21no—
73C2×Dic30—22no—
74C2×Dic30C2×C412yes—
75C2×Dic30D411yescharacteristic
76C2×Dic30D412yes—
77C2×Dic30D412yes—
78C3×C5×M16—21no—
79C3×C5×M16—21no—
80C2×C3×C5×C8—21no—
81C3×C5×C4⋊C4—21no—
82C3×C5×C22⋊C4—21no—
83C3×C42×C5—21no—
84#6719—21no—
85C4⋊Dic15—21no—
86C4×Dic15—21no—
87#6710—21no—
88#6710—21no—
89C2×C3⋊#168—21no—
90C2×#1010—51no—
91C3×#421D511yescharacteristic, complemented
92#5236—51no—
93#5132—51no—
94#5120—51no—
95#5006—51no—
96#5004—51no—
97C2×C5×#41C2×D311yescharacteristic
98#4150—62no—
99#4150—62no—
100#4150—62no—
101#4150—62no—
102C2×Q8×D5—32no—
103C2×#711—32no—
104C2×#711—62no—
105C2×#709—31no—
106C2×#709—61no—
107C22×Dic10—31no—
108C22×Dic10—61no—
109C2×C5×M16C2×D311yescharacteristic
110C5×#117C2×D311yescharacteristic
111#4072—31no—
112C2×#681—31no—
113C5×#104—22no—
114#3969—62no—
115#3956—61no—
116#3955—61no—
117#3948—62no—
118#3942—62no—
119#3938—62no—
120#1796—151noSylow
121C23×C3×C5—21no—
122C23×C3×C5C2×D411yescharacteristic
123C22×D15C22⋊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×C5—41no—
134C2×C3×C4×C5C22×C411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140#1220—28no—
141#1220—22no—
142#1220—22no—
143C2×Dic15—28no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×Dic15—41no—
148C2×Dic15C22⋊C412yes—
149D60—21no—
150D60—21no—
151C4×D15—28no—
152C4×D15—22no—
153C4×D15—22no—
154Dic30—28no—
155Dic30—22no—
156Dic30—21no—
157Dic30—21no—
158Dic30—22no—
159Dic30—22no—
160Dic30C22⋊C414yes—
161C3×C5×C8—41no—
162C3⋊#168—41no—
163C2×C3×#41C2×D511yescharacteristic
164#1010—102no—
165#1010—102no—
166#1010—102no—
167#1010—102no—
168C2×D3×Q8—52no—
169C2×#237—52no—
170C2×#237—102no—
171C2×#235—51no—
172C2×#235—101no—
173C22×Dic6—51no—
174C22×Dic6—101no—
175C2×C3×M16C2×D511yescharacteristic
176C3×#117C2×D511yescharacteristic
177#926—51no—
178C2×#208—51no—
179C3×#104—22no—
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×#41D1212yes—
189C5×#41#6712yes—
190C2×C5×Q8C4×D311yescharacteristic
191C2×C5×D4—21no—
192C2×C5×D4C4×D311yescharacteristic
193C22×C4×C5—21no—
194C22×C4×C5C22×D311yescharacteristic
195C2×C22⋊D5—32no—
196C2×C22⋊D5—62no—
197C22×Dic5—62no—
198C22×Dic5—61no—
199Q8×D5—64no—
200Q8×D5—64no—
201#711—64no—
202#711—68no—
203#711—68no—
204#711—64no—
205#709—64no—
206#709—64no—
207#709—61no—
208#709—61no—
209#709—61no—
210#709—61no—
211C2×D20—31no—
212C2×C4×D5—32no—
213C2×C4×D5—62no—
214C2×Dic10—32no—
215C2×Dic10—32no—
216C2×Dic10—32no—
217C2×Dic10—31no—
218C2×Dic10—62no—
219C2×Dic10—64no—
220C2×Dic10—64no—
221C2×Dic10—61no—
222C2×Dic10—61no—
223C2×Dic10—61no—
224C5×M16—21no—
225C5×M16—21no—
226C2×C5×C8—21no—
227C5×C4⋊C4—21no—
228C5×C22⋊C4—21no—
229C42×C5—21no—
230C22⋊Dic5—61no—
231C4⋊Dic5—61no—
232C4×Dic5—61no—
233#681—61no—
234#681—61no—
235C2×#168—61no—
236C2×2−1+4—151no—
237#421—151no—
238#421D1511yescharacteristic, complemented
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×D15—22no—
250C2×D15—42no—
251C3×C4×C5—22no—
252C3×C4×C5—81no—
253C3×C4×C5C2×C22⋊C411yescharacteristic
254C3×C4×C5C2×C22⋊C411yescharacteristic
255C3×C4×C5#12011yescharacteristic
256C3×C4×C5#12011yescharacteristic
257Dic15—22no—
258Dic15—24no—
259Dic15—81no—
260C3×#41—21no—
261C3×#41—21no—
262C3×#41D2012yes—
263C3×#41C22⋊D512yes—
264C2×C3×Q8C4×D511yescharacteristic
265C2×C3×D4—21no—
266C2×C3×D4C4×D511yescharacteristic
267C22×C3×C4—21no—
268C22×C3×C4C22×D511yescharacteristic
269C2×#67—52no—
270C2×#67—102no—
271C22×Dic3—102no—
272C22×Dic3—101no—
273D3×Q8—104no—
274D3×Q8—104no—
275#237—104no—
276#237—108no—
277#237—108no—
278#237—104no—
279#235—104no—
280#235—104no—
281#235—101no—
282#235—101no—
283#235—101no—
284#235—101no—
285C2×D12—51no—
286C2×C4×D3—52no—
287C2×C4×D3—102no—
288C2×Dic6—52no—
289C2×Dic6—52no—
290C2×Dic6—52no—
291C2×Dic6—51no—
292C2×Dic6—102no—
293C2×Dic6—104no—
294C2×Dic6—104no—
295C2×Dic6—101no—
296C2×Dic6—101no—
297C2×Dic6—101no—
298C3×M16—21no—
299C3×M16—21no—
300C2×C3×C8—21no—
301C3×C4⋊C4—21no—
302C3×C22⋊C4—21no—
303C3×C42—21no—
304#217—101no—
305C4⋊Dic3—101no—
306C4×Dic3—101no—
307#208—101no—
308#208—101no—
309C2×C3⋊C8—101no—
310C23×C5—21no—
311C23×C5D3×D411yescharacteristic
312C22×D5—32no—
313C5×Q8—21no—
314C5×Q8(C2×D3)⋊C412yes—
315C5×D4—22no—
316C5×D4—22no—
317C5×D4—21no—
318C5×D4(C2×D3)⋊C412yes—
319C2×C4×C5—21no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—41no—
323C2×C4×C5C2×C4×D311yescharacteristic
324C2×C4×C5C2×D1211yescharacteristic
325C2×C4×C5D3×D411yescharacteristic
326C2×C4×C5D3×D411yescharacteristic
327C2×C4×C5D3×D411yescharacteristic
328C2×C4×C5C2×#6711yescharacteristic
329C22⋊D5—68no—
330C22⋊D5—62no—
331C22⋊D5—62no—
332C2×Dic5—32no—
333C2×Dic5—68no—
334C2×Dic5—62no—
335C2×Dic5—62no—
336C2×Dic5—62no—
337C2×Dic5—121no—
338D20—61no—
339D20—61no—
340C4×D5—68no—
341C4×D5—62no—
342C4×D5—62no—
343Dic10—34no—
344Dic10—68no—
345Dic10—62no—
346Dic10—61no—
347Dic10—62no—
348Dic10—62no—
349Dic10—61no—
350C5×C8—41no—
351#168—121no—
3522−1+4—302no—
3532−1+4—302no—
3542−1+4—302no—
3552−1+4—302no—
356C2×#41—151no—
357C2×#41—152no—
358C2×#41—301no—
359C2×#41—302no—
360C2×#41C2×D1511yescharacteristic
361C22×Q8—152no—
362C22×Q8—151no—
363C22×Q8—301no—
364C2×M16—151no—
365C2×M16C2×D1511yescharacteristic
366#117—151no—
367#117C2×D1511yescharacteristic
368#104—22no—
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
380D15—42no—
381C23×C3—21no—
382C23×C3D4×D511yescharacteristic
383C22×D3—52no—
384C3×Q8—21no—
385C3×Q8#68512yes—
386C3×D4—22no—
387C3×D4—22no—
388C3×D4—21no—
389C3×D4#68512yes—
390C2×C3×C4—21no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—41no—
394C2×C3×C4C2×C4×D511yescharacteristic
395C2×C3×C4C2×D2011yescharacteristic
396C2×C3×C4D4×D511yescharacteristic
397C2×C3×C4D4×D511yescharacteristic
398C2×C3×C4D4×D511yescharacteristic
399C2×C3×C4C2×C22⋊D511yescharacteristic
400#67—108no—
401#67—102no—
402#67—102no—
403C2×Dic3—52no—
404C2×Dic3—108no—
405C2×Dic3—102no—
406C2×Dic3—102no—
407C2×Dic3—102no—
408C2×Dic3—201no—
409D12—101no—
410D12—101no—
411C4×D3—108no—
412C4×D3—102no—
413C4×D3—102no—
414Dic6—54no—
415Dic6—108no—
416Dic6—102no—
417Dic6—101no—
418Dic6—102no—
419Dic6—102no—
420Dic6—101no—
421C3×C8—41no—
422C3⋊C8—201no—
423C22×C5—22no—
424C22×C5—41no—
425C22×C5—42no—
426C22×C5D3×C22⋊C411yescharacteristic
427C22×C5#88211yescharacteristic
428C22×C5#93711yescharacteristic
429C2×D5—62no—
430C2×D5—122no—
431C4×C5—22no—
432C4×C5—81no—
433C4×C5D3×C22⋊C411yescharacteristic
434C4×C5#88211yescharacteristic
435C4×C5C2×(C2×D3)⋊C411yescharacteristic
436C4×C5#93711yescharacteristic
437Dic5—64no—
438Dic5—62no—
439Dic5—241no—
440#41—21no—
441#41—21no—
442#41—304no—
443#41—304no—
444#41—304no—
445#41—308no—
446#41—308no—
447#41—304no—
448#41—301no—
449#41—301no—
450#41—301no—
451#41—301no—
452#41D6012yes—
453#41#122012yes—
454C2×Q8—151no—
455C2×Q8—152no—
456C2×Q8—152no—
457C2×Q8—152no—
458C2×Q8—302no—
459C2×Q8—304no—
460C2×Q8—304no—
461C2×Q8—304no—
462C2×Q8—304no—
463C2×Q8—301no—
464C2×Q8—301no—
465C2×Q8—301no—
466C2×Q8C4×D1511yescharacteristic
467C2×D4—21no—
468C2×D4—152no—
469C2×D4—151no—
470C2×D4—302no—
471C2×D4C4×D1511yescharacteristic
472C22×C4—21no—
473C22×C4—152no—
474C22×C4—302no—
475C22×C4—302no—
476C22×C4—301no—
477C22×C4C22×D1511yescharacteristic
478M16—21no—
479M16—21no—
480M16—301no—
481M16—301no—
482C2×C8—21no—
483C2×C8—301no—
484C4⋊C4—21no—
485C4⋊C4—301no—
486C22⋊C4—21no—
487C22⋊C4—301no—
488C42—21no—
489C42—301no—
490C3×C5#179611yescharacteristic, complemented, Hall
491C22×C3—22no—
492C22×C3—41no—
493C22×C3—42no—
494C22×C3D5×C22⋊C411yescharacteristic
495C22×C3#402811yescharacteristic
496C22×C3#408311yescharacteristic
497C2×D3—102no—
498C2×D3—202no—
499C3×C4—22no—
500C3×C4—81no—
501C3×C4D5×C22⋊C411yescharacteristic
502C3×C4#402811yescharacteristic
503C3×C4C2×#68511yescharacteristic
504C3×C4#408311yescharacteristic
505Dic3—104no—
506Dic3—102no—
507Dic3—401no—
508C2×C5—21no—
509C2×C5—21no—
510C2×C5—21no—
511C2×C5—42no—
512C2×C5#495511yescharacteristic
513D5—122no—
514C23—21no—
515C23—152no—
516C23D4×D1511yescharacteristic
517Q8—21no—
518Q8—154no—
519Q8—308no—
520Q8—301no—
521Q8—302no—
522Q8—302no—
523Q8—301no—
524Q8—302no—
525Q8#671412yes—
526D4—22no—
527D4—22no—
528D4—21no—
529D4—308no—
530D4—302no—
531D4—302no—
532D4—301no—
533D4—301no—
534D4#671412yes—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—41no—
539C2×C4—152no—
540C2×C4—308no—
541C2×C4—308no—
542C2×C4—302no—
543C2×C4—302no—
544C2×C4—302no—
545C2×C4—302no—
546C2×C4—302no—
547C2×C4—601no—
548C2×C4C2×C4×D1511yescharacteristic
549C2×C4C2×D6011yescharacteristic
550C2×C4D4×D1511yescharacteristic
551C2×C4D4×D1511yescharacteristic
552C2×C4D4×D1511yescharacteristic
553C2×C4C2×#122011yescharacteristic
554C8—41no—
555C8—601no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—42no—
560C2×C3#6524411yescharacteristic
561D3—202no—
562C5#7041511yescharacteristic, complemented, Sylow
563C22—22no—
564C22—41no—
565C22—42no—
566C22—302no—
567C22—602no—
568C22C22⋊C4×D1511yescharacteristic
569C22#9177111yescharacteristic
570C22#9182611yescharacteristic
571C4—22no—
572C4—81no—
573C4—302no—
574C4—304no—
575C4—1201no—
576C4C22⋊C4×D1511yescharacteristic
577C4#9177111yescharacteristic
578C4C2×#671411yescharacteristic
579C4#9182611yescharacteristic
580C3#1060120811yescharacteristic, complemented, Sylow
581C2—21no—
582C2—21no—
583C2—21no—
584C2—42no—
585C2—602no—
586C2#1175105611yescharacteristic
subgroupG/H
centerC2#11751056
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#421C2
socleC2×C3×C5#379
prime radicalC2×#92101C2
cosocleC22×C3×C4×C5C23
hypercenter#421D15
hypocenterC3×C5#1796
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. C3×C5×#421C2semidirect
3. #11751337C2semidirect
4. #11751233C2semidirect
5. #11751221C2semidirect
6. #11751107C2semidirect
7. #11751105C2semidirect
14. C2×Q8×D15C4semidirect
16. C2×#6819C4semidirect
34. C5×#421D3semidirect
91. C3×#421D5semidirect
238. #421D15semidirect
490. C3×C5#1796semidirect
562. C5#70415semidirect
580. C3#10601208semidirect

Maximal subgroups

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

subgroupindex
C2×#921012
C3×C5×#4212
#117513372
#117512332
#117512212
#117511072
#117511052
#106012083
#704155