Finite Group Databasebeta

← #14484800

Subgroups — #14484800

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#557C211yesmaximal, characteristic, complemented
2#11756491C213yesmaximal, complemented
3#11756484C213yesmaximal, complemented
4#11756454C216yesmaximal, complemented
5#11756450C216yesmaximal, complemented
6#11756344C213yesmaximal, complemented
7#11756336C211yesmaximal, characteristic, complemented
8#11756335C212yesmaximal, complemented
9C4×#6821C213yesmaximal, complemented
10C4×#6821C212yesmaximal, complemented
11C4×Q8×D15C211yesmaximal, characteristic, complemented
12#10618917—31nomaximal, Hall
13C2×#6821C2212yes—
14C2×#6821C2213yes—
15C2×Q8×D15C2211yescharacteristic
16C3×C5×C4⋊Q8C2213yes—
17C3×C5×#125C2216yes—
18C3×C4×C5×Q8C2211yescharacteristic
19C3×C4×C5×Q8C2212yes—
20C3×C4×C5×Q8C2213yes—
21#91836C2216yes—
22Q8×Dic15C2211yescharacteristic
23Q8×Dic15C2213yes—
24#91787C22112yes—
25#91786C2216yes—
26#91784C2216yes—
27#91784C2216yes—
28#91784C2216yes—
29#91783C22112yes—
30#91782C2213yes—
31#91782C2216yes—
32#91782C2216yes—
33#91782C2216yes—
34#91781C2211yescharacteristic
35#91781C2216yes—
36#91781C2216yes—
37C4⋊C4×D15C2213yes—
38#91776C2213yes—
39#91764C2216yes—
40#91763C2213yes—
41C4×D60C2216yes—
42C4×D60C2213yes—
43C4×D60C2216yes—
44C42×D15C2213yes—
45C42×D15C2216yes—
46C4×Dic30C2213yes—
47#87016—51nomaximal, Hall
48C5×#557D311yescharacteristic, complemented
49#66066—33no—
50#66059—33no—
51#66029—36no—
52#66025—36no—
53#65919—33no—
54#65911—31no—
55#65910—32no—
56C4×#713—32no—
57C4×#713—33no—
58C4×Q8×D5—31no—
59C2×C3×C5×Q8C2313yes—
60C2×C3×C5×Q8C2311yescharacteristic
61#6821—28no—
62#6821—212no—
63Q8×D15—24no—
64C2×D60C2313yes—
65C2×D60C2316yes—
66C2×D60C2316yes—
67C2×D60C2316yes—
68C2×C4×D15C2313yes—
69C2×C4×D15C2316yes—
70C2×C4×D15C2316yes—
71C2×C4×D15C2316yes—
72C2×C4×D15C2313yes—
73C2×C4×D15C2311yescharacteristic
74C2×Dic30C2313yes—
75C3×C5×C4⋊C4C2313yes—
76C3×C5×C4⋊C4C2311yescharacteristic
77C3×C5×C4⋊C4C2316yes—
78C3×C5×C4⋊C4C2316yes—
79C3×C5×C4⋊C4C2316yes—
80C3×C42×C5C2313yes—
81C3×C42×C5C2316yes—
82#6714C2312yes—
83#6714C2316yes—
84#6714C23112yes—
85#6714C2316yes—
86#6714C23112yes—
87C4⋊Dic15C2313yes—
88C4⋊Dic15C2311yescharacteristic
89C4⋊Dic15C2316yes—
90#6712C2316yes—
91C4×Dic15C2313yes—
92C4×Dic15C2313yes—
93C4×Dic15C2312yes—
94C4×Dic15C2313yes—
95C4×Dic15C2316yes—
96C3×#557D511yescharacteristic, complemented
97#5732—53no—
98#5725—53no—
99#5695—56no—
100#5691—56no—
101#5585—53no—
102#5577—51no—
103#5576—52no—
104C4×#239—52no—
105C4×#239—53no—
106C4×D3×Q8—51no—
107C2×#713—33no—
108C2×#713—32no—
109C2×Q8×D5—31no—
110C5×C4⋊Q8C2×D313yes—
111C5×#125C2×D316yes—
112C4×C5×Q8C2×D311yescharacteristic
113C4×C5×Q8C2×D312yes—
114C4×C5×Q8C2×D313yes—
115#4093—36no—
116Q8×Dic5—33no—
117Q8×Dic5—31no—
118#4044—312no—
119#4043—36no—
120#4041—36no—
121#4041—36no—
122#4041—36no—
123#4040—312no—
124#4039—36no—
125#4039—36no—
126#4039—33no—
127#4039—36no—
128#4038—36no—
129#4038—31no—
130#4038—36no—
131D5×C4⋊C4—33no—
132#4033—33no—
133#4021—36no—
134#4020—33no—
135C4×D20—33no—
136C4×D20—36no—
137C4×D20—36no—
138C42×D5—33no—
139C42×D5—36no—
140C4×Dic10—33no—
141#3480—151noSylow
142C22×D15C2416yes—
143C22×D15C2411yescharacteristic
144C3×C5×Q8—26no—
145C3×C5×Q8#4114yescomplemented
146C2×C3×C4×C5C2413yes—
147C2×C3×C4×C5C2416yes—
148C2×C3×C4×C5C2412yes—
149C2×C3×C4×C5C2411yescharacteristic
150C2×C3×C4×C5C2413yes—
151C2×Dic15C2413yes—
152C2×Dic15C2412yes—
153C2×Dic15C2413yes—
154C2×Dic15C2411yescharacteristic
155D60—212no—
156D60—212no—
157D60—26no—
158D60—46no—
159C4×D15—26no—
160C4×D15—212no—
161C4×D15—212no—
162C4×D15—46no—
163C4×D15—43no—
164C4×D15#4114yescomplemented
165Dic30—26no—
166C2×#239—53no—
167C2×#239—52no—
168C2×D3×Q8—51no—
169C3×C4⋊Q8C2×D513yes—
170C3×#125C2×D516yes—
171C3×C4×Q8C2×D511yescharacteristic
172C3×C4×Q8C2×D512yes—
173C3×C4×Q8C2×D513yes—
174#947—56no—
175Q8×Dic3—53no—
176Q8×Dic3—51no—
177#898—512no—
178#897—56no—
179#895—56no—
180#895—56no—
181#895—56no—
182#894—512no—
183#893—56no—
184#893—56no—
185#893—56no—
186#893—53no—
187#892—56no—
188#892—56no—
189#892—51no—
190D3×C4⋊C4—53no—
191#887—53no—
192#875—56no—
193#874—53no—
194C4×D12—56no—
195C4×D12—56no—
196C4×D12—53no—
197C42×D3—56no—
198C42×D3—53no—
199C4×Dic6—53no—
200C2×C5×Q8C22×D313yes—
201C2×C5×Q8C22×D311yescharacteristic
202#713—612no—
203#713—68no—
204Q8×D5—64no—
205C2×D20—33no—
206C2×D20—36no—
207C2×D20—36no—
208C2×D20—36no—
209C2×C4×D5—31no—
210C2×C4×D5—33no—
211C2×C4×D5—36no—
212C2×C4×D5—36no—
213C2×C4×D5—36no—
214C2×C4×D5—33no—
215C2×Dic10—33no—
216C5×C4⋊C4C22×D311yescharacteristic
217C5×C4⋊C4C22×D313yes—
218C5×C4⋊C4C22×D316yes—
219C5×C4⋊C4C22×D316yes—
220C5×C4⋊C4C22×D316yes—
221C42×C5C22×D316yes—
222C42×C5C22×D313yes—
223#685—32no—
224#685—36no—
225#685—312no—
226#685—36no—
227#685—312no—
228C4⋊Dic5—33no—
229C4⋊Dic5—31no—
230C4⋊Dic5—36no—
231#683—36no—
232C4×Dic5—33no—
233C4×Dic5—33no—
234C4×Dic5—32no—
235C4×Dic5—33no—
236C4×Dic5—36no—
237#559—153no—
238#557D1511yescharacteristic, complemented
239#556—153no—
240#553—156no—
241#550—151no—
242#548—152no—
243#532—153no—
244#529—156no—
245C4×#41—153no—
246C4×#41—152no—
247C2×C4×Q8—151no—
248C22×C3×C5C2511yescharacteristic
249C2×D15—21no—
250C2×D15—21no—
251C2×D15—26no—
252C2×D15—26no—
253C2×D15—26no—
254C2×D15C2×#4112yes—
255C3×C4×C5—26no—
256C3×C4×C5—22no—
257C3×C4×C5—23no—
258C3×C4×C5C2×#4116yes—
259C3×C4×C5C2×#4112yes—
260Dic15—23no—
261Dic15—22no—
262Dic15—23no—
263Dic15C2×#4112yes—
264C2×C3×Q8C22×D513yes—
265C2×C3×Q8C22×D511yescharacteristic
266#239—1012no—
267#239—108no—
268D3×Q8—104no—
269C2×D12—53no—
270C2×D12—56no—
271C2×D12—56no—
272C2×D12—56no—
273C2×C4×D3—51no—
274C2×C4×D3—53no—
275C2×C4×D3—56no—
276C2×C4×D3—56no—
277C2×C4×D3—56no—
278C2×C4×D3—53no—
279C2×Dic6—53no—
280C3×C4⋊C4C22×D513yes—
281C3×C4⋊C4C22×D511yescharacteristic
282C3×C4⋊C4C22×D516yes—
283C3×C4⋊C4C22×D516yes—
284C3×C4⋊C4C22×D516yes—
285C3×C42C22×D513yes—
286C3×C42C22×D516yes—
287(C2×D3)⋊C4—52no—
288(C2×D3)⋊C4—56no—
289(C2×D3)⋊C4—512no—
290(C2×D3)⋊C4—56no—
291(C2×D3)⋊C4—512no—
292C4⋊Dic3—53no—
293C4⋊Dic3—51no—
294C4⋊Dic3—56no—
295Dic3⋊C4—56no—
296C4×Dic3—53no—
297C4×Dic3—53no—
298C4×Dic3—52no—
299C4×Dic3—53no—
300C4×Dic3—56no—
301C22×D5—31no—
302C22×D5—36no—
303C5×Q8—26no—
304C5×Q8#23914yescomplemented
305C2×C4×C5C23×D313yes—
306C2×C4×C5C23×D316yes—
307C2×C4×C5C23×D312yes—
308C2×C4×C5C23×D313yes—
309C2×C4×C5C23×D311yescharacteristic
310C2×Dic5—31no—
311C2×Dic5—33no—
312C2×Dic5—32no—
313C2×Dic5—33no—
314D20—612no—
315D20—612no—
316D20—66no—
317D20—126no—
318C4×D5—34no—
319C4×D5—612no—
320C4×D5—66no—
321C4×D5—612no—
322C4×D5—126no—
323C4×D5—123no—
324Dic10—66no—
325C2×#41—153no—
326C2×#41—152no—
327C22×Q8—151no—
328C4⋊Q8C2×D1513yes—
329#127—153no—
330#126—1512no—
331#125C2×D1516yes—
332#124—156no—
333#124—156no—
334#123—1512no—
335C22⋊Q8—156no—
336#121—156no—
337#121—156no—
338#121—156no—
339C4×Q8—151no—
340C4×Q8—153no—
341C4×Q8—153no—
342C4×Q8—153no—
343C4×Q8C2×D1511yescharacteristic
344C4×Q8C2×D1512yes—
345C4×Q8C2×D1513yes—
346C4×D4—156no—
347C4×D4—156no—
348C4×D4—153no—
349C4×D4—156no—
350C4×D4—156no—
351C4×D4—153no—
352C4×D4—156no—
353#117—151no—
354#117—156no—
355#117—156no—
356C2×C4⋊C4—153no—
357C2×C42—153no—
358C2×C42—156no—
359C2×C3×C5C22×#4111yescharacteristic
360C2×C3×C5C22×#4111yescharacteristic
361C2×C3×C5#58511yescharacteristic
362D15—22no—
363D15—46no—
364C22×D3—51no—
365C22×D3—56no—
366C3×Q8—26no—
367C3×Q8#71314yescomplemented
368C2×C3×C4C23×D513yes—
369C2×C3×C4C23×D516yes—
370C2×C3×C4C23×D512yes—
371C2×C3×C4C23×D513yes—
372C2×C3×C4C23×D511yescharacteristic
373C2×Dic3—51no—
374C2×Dic3—53no—
375C2×Dic3—52no—
376C2×Dic3—53no—
377D12—1012no—
378D12—1012no—
379D12—106no—
380D12—206no—
381C4×D3—54no—
382C4×D3—1012no—
383C4×D3—106no—
384C4×D3—1012no—
385C4×D3—206no—
386C4×D3—203no—
387Dic6—106no—
388C22×C5C24×D311yescharacteristic
389C2×D5—32no—
390C2×D5—61no—
391C2×D5—61no—
392C2×D5—66no—
393C2×D5—66no—
394C2×D5—66no—
395C4×C5—26no—
396C4×C5—22no—
397C4×C5—23no—
398C4×C5C2×#23916yes—
399C4×C5D3×#4112yes—
400Dic5—32no—
401Dic5—63no—
402Dic5—62no—
403Dic5—63no—
404#41—3012no—
405#41—308no—
406C2×Q8—153no—
407C2×Q8—304no—
408C2×Q8C22×D1513yes—
409C2×Q8C22×D1511yescharacteristic
410C2×D4—156no—
411C2×D4—156no—
412C2×D4—153no—
413C2×D4—156no—
414C22×C4—151no—
415C22×C4—153no—
416C22×C4—156no—
417C22×C4—156no—
418C22×C4—153no—
419C22×C4—156no—
420C4⋊C4—153no—
421C4⋊C4—156no—
422C4⋊C4—151no—
423C4⋊C4—156no—
424C4⋊C4C22×D1513yes—
425C4⋊C4C22×D1511yescharacteristic
426C4⋊C4C22×D1516yes—
427C4⋊C4C22×D1516yes—
428C4⋊C4C22×D1516yes—
429C22⋊C4—152no—
430C22⋊C4—156no—
431C22⋊C4—1512no—
432C22⋊C4—156no—
433C22⋊C4—1512no—
434C42—152no—
435C42—153no—
436C42—153no—
437C42—156no—
438C42—153no—
439C42C22×D1516yes—
440C42C22×D1513yes—
441C3×C5#348011yescharacteristic, complemented, Hall
442C22×C3C24×D511yescharacteristic
443C2×D3—52no—
444C2×D3—101no—
445C2×D3—101no—
446C2×D3—106no—
447C2×D3—106no—
448C2×D3—106no—
449C3×C4—26no—
450C3×C4—22no—
451C3×C4—23no—
452C3×C4C2×#71316yes—
453C3×C4D5×#4112yes—
454Dic3—52no—
455Dic3—103no—
456Dic3—102no—
457Dic3—103no—
458C2×C5C22×#23911yescharacteristic
459C2×C5C2×D3×#4111yescharacteristic
460C2×C5#596811yescharacteristic
461D5—62no—
462D5—126no—
463C23—151no—
464C23—156no—
465Q8—26no—
466Q8—306no—
467Q8#682114yescomplemented
468D4—3012no—
469D4—3012no—
470D4—306no—
471D4—606no—
472C2×C4—151no—
473C2×C4—154no—
474C2×C4—152no—
475C2×C4—153no—
476C2×C4—153no—
477C2×C4—3012no—
478C2×C4—306no—
479C2×C4—3012no—
480C2×C4—606no—
481C2×C4—603no—
482C2×C4C23×D1512yes—
483C2×C4C23×D1516yes—
484C2×C4C23×D1513yes—
485C2×C4C23×D1513yes—
486C2×C4C23×D1511yescharacteristic
487C2×C3C22×#71311yescharacteristic
488C2×C3C2×D5×#4111yescharacteristic
489C2×C3#6628711yescharacteristic
490D3—102no—
491D3—206no—
492C5#8701611yescharacteristic, complemented, Sylow
493C22—152no—
494C22—301no—
495C22—301no—
496C22—306no—
497C22—306no—
498C22—306no—
499C22C24×D1511yescharacteristic
500C4—26no—
501C4—22no—
502C4—23no—
503C4—152no—
504C4—302no—
505C4—303no—
506C4—303no—
507C4C2×#682116yes—
508C4#41×D1512yes—
509C3#1061891711yescharacteristic, complemented, Sylow
510C2—302no—
511C2—606no—
512C2C22×#682111yescharacteristic
513C2C2×#41×D1511yescharacteristic
514C2#1175715011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D15
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C5×#557C2
hypercenter#557D15
hypocenterC3×C5#3480
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C3×C5×#557C2semidirect
2. #11756491C2semidirect
3. #11756484C2semidirect
4. #11756454C2semidirect
5. #11756450C2semidirect
6. #11756344C2semidirect
7. #11756336C2semidirect
8. #11756335C2semidirect
9. C4×#6821C2semidirect
10. C4×#6821C2semidirect
11. C4×Q8×D15C2semidirect
48. C5×#557D3semidirect
96. C3×#557D5semidirect
145. C3×C5×Q8#41semidirect
164. C4×D15#41semidirect
238. #557D15semidirect
304. C5×Q8#239semidirect
367. C3×Q8#713semidirect
441. C3×C5#3480semidirect
467. Q8#6821semidirect
492. C5#87016semidirect
509. C3#10618917semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5572
#117564912
#117564842
#117564542
#117564502
#117563442
#117563362
#117563352
C4×#68212
C4×Q8×D152
#106189173
#870165