Finite Group Databasebeta

← #14495602

Subgroups — #14495602

Order 1920.

1860 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#533C211yesmaximal, characteristic, complemented
2#11756494C214yesmaximal, complemented
3#11756459C211yesmaximal, characteristic, complemented
4#11756458C212yesmaximal, complemented
5#11756445C211yesmaximal, characteristic, complemented
6#11756406C214yesmaximal, complemented
7#11756405C214yesmaximal, complemented
8#11756339C214yesmaximal, complemented
9#11756337C214yesmaximal, complemented
10#11756287C214yesmaximal, complemented
11#11756238C212yesmaximal, complemented
12#10618187—31nomaximal, Hall
13C3×C5×C4⋊Q8C2212yes—
14C3×C5×#125C2211yescharacteristic
15C3×C5×#125C2211yescharacteristic
16C3×C5×C22⋊Q8C2214yes—
17C3×C4×C5×Q8C2214yes—
18C3×C5×#117C2212yes—
19C2×C3×C42×C5C2211yescharacteristic
20#91836C2214yes—
21#91835C2214yes—
22#91835C2214yes—
23#91833C2214yes—
24#91819C2212yes—
25#91818C2214yes—
26C4×#1220C2214yes—
27#91813C2212yes—
28#91787C2214yes—
29#91787C2214yes—
30#91787C2214yes—
31#91786C2214yes—
32#91785C2214yes—
33#91785C2214yes—
34#91785C2214yes—
35#91784C2214yes—
36#91783C2214yes—
37#91783C2214yes—
38#91783C2214yes—
39#91779C2214yes—
40#91778C2214yes—
41#91778C2214yes—
42#91778C2214yes—
43#91777C2214yes—
44#91774C2214yes—
45#91773C2214yes—
46#91772C2214yes—
47#91768C2214yes—
48#91765C2214yes—
49#91764C2212yes—
50C4×D60C2212yes—
51C4×D60C2214yes—
52#91761C2214yes—
53#91761C2214yes—
54C42×D15C2214yes—
55#91759C2212yes—
56C4×Dic30C2212yes—
57C4×Dic30C2214yes—
58#86286—51nomaximal, Hall
59C5×#533D311yescharacteristic, complemented
60#66069—34no—
61#66034—31no—
62#66033—32no—
63C5⋊#564—31no—
64#65981—34no—
65#65980—34no—
66#65914—34no—
67#65912—34no—
68#65862—34no—
69#65813—32no—
70C2×C3×C5×Q8C2314yes—
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2312yes—
73C2×#1220C2314yes—
74C2×D60C2312yes—
75C2×D60C2314yes—
76C2×C4×D15C2314yes—
77C2×C4×D15C2314yes—
78C2×C4×D15C2314yes—
79C2×Dic30C2312yes—
80C2×Dic30C2314yes—
81C3×C5×C4⋊C4C2314yes—
82C3×C5×C4⋊C4C2312yes—
83C3×C5×C4⋊C4C2314yes—
84C3×C5×C4⋊C4C2314yes—
85C3×C5×C4⋊C4C2312yes—
86C3×C5×C22⋊C4C2314yes—
87C3×C42×C5C2314yes—
88C3×C42×C5C2312yes—
89C3×C42×C5C2311yescharacteristic
90C3×C42×C5C2311yescharacteristic
91#6719C2314yes—
92#6714C2314yes—
93#6714C2314yes—
94#6714C2314yes—
95#6714C2314yes—
96#6714C2314yes—
97#6714C2314yes—
98#6714C2314yes—
99#6714C2314yes—
100C4⋊Dic15C2312yes—
101C4⋊Dic15C2314yes—
102C4⋊Dic15C2312yes—
103C4⋊Dic15C2314yes—
104#6712C2314yes—
105#6712C2314yes—
106#6712C2314yes—
107#6712C2314yes—
108#6712C2314yes—
109#6712C2314yes—
110#6712C2314yes—
111#6712C2314yes—
112C4×Dic15C2314yes—
113C4×Dic15C2314yes—
114C4×Dic15C2314yes—
115C3×#533D511yescharacteristic, complemented
116#5735—54no—
117#5700—51no—
118#5699—52no—
119C3⋊#564—51no—
120#5647—54no—
121#5646—54no—
122#5580—54no—
123#5578—54no—
124#5528—54no—
125#5479—52no—
126C5×C4⋊Q8C2×D312yes—
127C5×#125C2×D311yescharacteristic
128C5×#125C2×D311yescharacteristic
129C5×C22⋊Q8C2×D314yes—
130C4×C5×Q8C2×D314yes—
131C5×#117C2×D312yes—
132C2×C42×C5C2×D311yescharacteristic
133#4093—34no—
134#4092—34no—
135#4092—34no—
136#4090—34no—
137#4076—32no—
138#4075—34no—
139C4×C22⋊D5—34no—
140#4070—32no—
141#4044—34no—
142#4044—34no—
143#4044—34no—
144#4043—34no—
145#4042—34no—
146#4042—34no—
147#4042—34no—
148#4041—34no—
149#4040—34no—
150#4040—34no—
151#4040—34no—
152#4036—34no—
153#4035—34no—
154#4035—34no—
155#4035—34no—
156#4034—34no—
157#4031—34no—
158#4030—34no—
159#4029—34no—
160#4025—34no—
161#4022—34no—
162#4021—32no—
163C4×D20—32no—
164C4×D20—34no—
165#4018—34no—
166#4018—34no—
167C42×D5—34no—
168#4016—32no—
169C4×Dic10—32no—
170C4×Dic10—34no—
171#3531—151noSylow
172C23×C3×C5C2411yescharacteristic
173C22×D15C2414yes—
174C3×C5×Q8—44no—
175C2×C3×C4×C5—22no—
176C2×C3×C4×C5—42no—
177C2×C3×C4×C5C2414yes—
178C2×C3×C4×C5C2414yes—
179C2×C3×C4×C5C2411yescharacteristic
180C2×C3×C4×C5C2412yes—
181C2×C3×C4×C5C2412yes—
182C2×C3×C4×C5C2411yescharacteristic
183#1220—44no—
184C2×Dic15C2414yes—
185C2×Dic15C2414yes—
186C2×Dic15C2414yes—
187D60—42no—
188D60—44no—
189C4×D15—28no—
190C4×D15—44no—
191C4×D15—44no—
192Dic30—42no—
193Dic30—44no—
194C3×C4⋊Q8C2×D512yes—
195C3×#125C2×D511yescharacteristic
196C3×#125C2×D511yescharacteristic
197C3×C22⋊Q8C2×D514yes—
198C3×C4×Q8C2×D514yes—
199C3×#117C2×D512yes—
200C2×C3×C42C2×D511yescharacteristic
201#947—54no—
202#946—54no—
203#946—54no—
204#944—54no—
205#930—52no—
206#929—54no—
207C4×#67—54no—
208#924—52no—
209#898—54no—
210#898—54no—
211#898—54no—
212#897—54no—
213#896—54no—
214#896—54no—
215#896—54no—
216#895—54no—
217#894—54no—
218#894—54no—
219#894—54no—
220#890—54no—
221#889—54no—
222#889—54no—
223#889—54no—
224#888—54no—
225#885—54no—
226#884—54no—
227#883—54no—
228#879—54no—
229#876—54no—
230#875—52no—
231C4×D12—52no—
232C4×D12—54no—
233#872—54no—
234#872—54no—
235C42×D3—54no—
236#870—52no—
237C4×Dic6—52no—
238C4×Dic6—54no—
239C2×C5×Q8C22×D314yes—
240C22×C4×C5C22×D311yescharacteristic
241C22×C4×C5C22×D312yes—
242C2×C22⋊D5—34no—
243C2×D20—32no—
244C2×D20—34no—
245C2×C4×D5—34no—
246C2×C4×D5—34no—
247C2×C4×D5—34no—
248C2×Dic10—32no—
249C2×Dic10—34no—
250C5×C4⋊C4C22×D312yes—
251C5×C4⋊C4C22×D312yes—
252C5×C4⋊C4C22×D314yes—
253C5×C4⋊C4C22×D314yes—
254C5×C4⋊C4C22×D314yes—
255C5×C22⋊C4C22×D314yes—
256C42×C5C22×D312yes—
257C42×C5C22×D311yescharacteristic
258C42×C5C22×D311yescharacteristic
259C42×C5C22×D314yes—
260C22⋊Dic5—34no—
261#685—34no—
262#685—34no—
263#685—34no—
264#685—34no—
265#685—34no—
266#685—34no—
267#685—34no—
268#685—34no—
269C4⋊Dic5—32no—
270C4⋊Dic5—34no—
271C4⋊Dic5—32no—
272C4⋊Dic5—34no—
273#683—34no—
274#683—34no—
275#683—34no—
276#683—34no—
277#683—34no—
278#683—34no—
279#683—34no—
280#683—34no—
281C4×Dic5—34no—
282C4×Dic5—34no—
283C4×Dic5—34no—
284#564—151no—
285#563—154no—
286#563—152no—
287#563—154no—
288#562—151no—
289#562—154no—
290#533—154no—
291#533D1511yescharacteristic, complemented
292#529—154no—
293#529—154no—
294#529—152no—
295C22×C3×C5—21no—
296C22×C3×C5—22no—
297C22×C3×C5C2511yescharacteristic
298C2×D15—24no—
299C2×D15—24no—
300C2×D15—24no—
301C3×C4×C5—21no—
302C3×C4×C5—24no—
303C3×C4×C5—22no—
304C3×C4×C5—24no—
305C3×C4×C5—22no—
306C3×C4×C52−1+412yes—
307Dic15—24no—
308Dic15—24no—
309Dic15—24no—
310C2×C3×Q8C22×D514yes—
311C22×C3×C4C22×D511yescharacteristic
312C22×C3×C4C22×D512yes—
313C2×#67—54no—
314C2×D12—52no—
315C2×D12—54no—
316C2×C4×D3—54no—
317C2×C4×D3—54no—
318C2×C4×D3—54no—
319C2×Dic6—52no—
320C2×Dic6—54no—
321C3×C4⋊C4C22×D514yes—
322C3×C4⋊C4C22×D512yes—
323C3×C4⋊C4C22×D514yes—
324C3×C4⋊C4C22×D514yes—
325C3×C4⋊C4C22×D512yes—
326C3×C22⋊C4C22×D514yes—
327C3×C42C22×D514yes—
328C3×C42C22×D512yes—
329C3×C42C22×D511yescharacteristic
330C3×C42C22×D511yescharacteristic
331#217—54no—
332(C2×D3)⋊C4—54no—
333(C2×D3)⋊C4—54no—
334(C2×D3)⋊C4—54no—
335(C2×D3)⋊C4—54no—
336(C2×D3)⋊C4—54no—
337(C2×D3)⋊C4—54no—
338(C2×D3)⋊C4—54no—
339(C2×D3)⋊C4—54no—
340C4⋊Dic3—52no—
341C4⋊Dic3—54no—
342C4⋊Dic3—52no—
343C4⋊Dic3—54no—
344Dic3⋊C4—54no—
345Dic3⋊C4—54no—
346Dic3⋊C4—54no—
347Dic3⋊C4—54no—
348Dic3⋊C4—54no—
349Dic3⋊C4—54no—
350Dic3⋊C4—54no—
351Dic3⋊C4—54no—
352C4×Dic3—54no—
353C4×Dic3—54no—
354C4×Dic3—54no—
355C23×C5C23×D311yescharacteristic
356C22×D5—34no—
357C5×Q8—44no—
358C2×C4×C5—22no—
359C2×C4×C5—42no—
360C2×C4×C5C23×D314yes—
361C2×C4×C5C23×D314yes—
362C2×C4×C5C23×D311yescharacteristic
363C2×C4×C5C23×D312yes—
364C2×C4×C5C23×D312yes—
365C2×C4×C5C23×D311yescharacteristic
366C22⋊D5—124no—
367C2×Dic5—34no—
368C2×Dic5—34no—
369C2×Dic5—34no—
370D20—122no—
371D20—124no—
372C4×D5—68no—
373C4×D5—124no—
374C4×D5—124no—
375Dic10—122no—
376Dic10—124no—
377C4⋊Q8—154no—
378C4⋊Q8—154no—
379C4⋊Q8C2×D1512yes—
380#126—154no—
381#126—154no—
382#126—154no—
383#126—154no—
384#126—154no—
385#125—154no—
386#125—154no—
387#125—154no—
388#125—154no—
389#125—152no—
390#125C2×D1511yescharacteristic
391#125C2×D1511yescharacteristic
392#124—154no—
393#124—154no—
394#124—152no—
395#123—154no—
396#123—154no—
397#123—154no—
398#123—154no—
399#123—154no—
400C22⋊Q8—154no—
401C22⋊Q8—154no—
402C22⋊Q8—152no—
403C22⋊Q8—154no—
404C22⋊Q8—154no—
405C22⋊Q8—154no—
406C22⋊Q8—154no—
407C22⋊Q8C2×D1514yes—
408#121—152no—
409#121—154no—
410#121—154no—
411C4×Q8—154no—
412C4×Q8—152no—
413C4×Q8C2×D1514yes—
414C4×D4—154no—
415C4×D4—154no—
416C4×D4—152no—
417#117—154no—
418#117—154no—
419#117C2×D1512yes—
420C2×C42—154no—
421C2×C42C2×D1511yescharacteristic
422C2×C3×C5—41no—
423C2×C3×C5C2×2−1+411yescharacteristic
424C2×C3×C5#58512yes—
425D15—44no—
426C23×C3C23×D511yescharacteristic
427C22×D3—54no—
428C3×Q8—44no—
429C2×C3×C4—22no—
430C2×C3×C4—42no—
431C2×C3×C4C23×D514yes—
432C2×C3×C4C23×D514yes—
433C2×C3×C4C23×D511yescharacteristic
434C2×C3×C4C23×D512yes—
435C2×C3×C4C23×D512yes—
436C2×C3×C4C23×D511yescharacteristic
437#67—204no—
438C2×Dic3—54no—
439C2×Dic3—54no—
440C2×Dic3—54no—
441D12—202no—
442D12—204no—
443C4×D3—108no—
444C4×D3—204no—
445C4×D3—204no—
446Dic6—202no—
447Dic6—204no—
448C22×C5—21no—
449C22×C5—22no—
450C22×C5C24×D311yescharacteristic
451C2×D5—64no—
452C2×D5—64no—
453C2×D5—64no—
454C4×C5—21no—
455C4×C5—24no—
456C4×C5—22no—
457C4×C5—24no—
458C4×C5—22no—
459C4×C5#100712yes—
460Dic5—64no—
461Dic5—64no—
462Dic5—64no—
463C2×Q8—152no—
464C2×Q8—154no—
465C2×Q8C22×D1514yes—
466C2×D4—154no—
467C2×D4—154no—
468C2×D4—152no—
469C22×C4—154no—
470C22×C4—154no—
471C22×C4—154no—
472C22×C4C22×D1511yescharacteristic
473C22×C4C22×D1512yes—
474C4⋊C4—154no—
475C4⋊C4—154no—
476C4⋊C4—154no—
477C4⋊C4—154no—
478C4⋊C4—154no—
479C4⋊C4—154no—
480C4⋊C4—152no—
481C4⋊C4—154no—
482C4⋊C4—152no—
483C4⋊C4—154no—
484C4⋊C4—154no—
485C4⋊C4—154no—
486C4⋊C4C22×D1512yes—
487C4⋊C4C22×D1512yes—
488C4⋊C4C22×D1514yes—
489C4⋊C4C22×D1514yes—
490C4⋊C4C22×D1514yes—
491C22⋊C4—154no—
492C22⋊C4—154no—
493C22⋊C4—154no—
494C22⋊C4—154no—
495C22⋊C4—154no—
496C22⋊C4—154no—
497C22⋊C4—154no—
498C22⋊C4—154no—
499C22⋊C4—154no—
500C22⋊C4C22×D1514yes—
501C42—154no—
502C42—154no—
503C42—154no—
504C42C22×D1511yescharacteristic
505C42C22×D1511yescharacteristic
506C42C22×D1514yes—
507C42C22×D1512yes—
508C3×C5#353111yescharacteristic, complemented, Hall
509C22×C3—21no—
510C22×C3—22no—
511C22×C3C24×D511yescharacteristic
512C2×D3—104no—
513C2×D3—104no—
514C2×D3—104no—
515C3×C4—21no—
516C3×C4—24no—
517C3×C4—22no—
518C3×C4—24no—
519C3×C4—22no—
520C3×C4#414712yes—
521Dic3—104no—
522Dic3—104no—
523Dic3—104no—
524C2×C5—41no—
525C2×C5C2×#100711yescharacteristic
526C2×C5#596412yes—
527D5—124no—
528C23—154no—
529C23C23×D1511yescharacteristic
530Q8—44no—
531Q8—602no—
532Q8—604no—
533D4—602no—
534D4—604no—
535D4—604no—
536C2×C4—22no—
537C2×C4—42no—
538C2×C4—154no—
539C2×C4—154no—
540C2×C4—154no—
541C2×C4—308no—
542C2×C4—604no—
543C2×C4—604no—
544C2×C4C23×D1514yes—
545C2×C4C23×D1514yes—
546C2×C4C23×D1511yescharacteristic
547C2×C4C23×D1512yes—
548C2×C4C23×D1512yes—
549C2×C4C23×D1511yescharacteristic
550C2×C3—41no—
551C2×C3C2×#414711yescharacteristic
552C2×C3#6628312yes—
553D3—204no—
554C5#8628611yescharacteristic, complemented, Sylow
555C22—21no—
556C22—22no—
557C22—304no—
558C22—304no—
559C22—304no—
560C22C24×D1511yescharacteristic
561C4—21no—
562C4—22no—
563C4—22no—
564C4—24no—
565C4—24no—
566C4—304no—
567C4—304no—
568C4—304no—
569C4#9209812yes—
570C3#1061818711yescharacteristic, complemented, Sylow
571C2—41no—
572C2—604no—
573C2C2×#9209811yescharacteristic
574C2#1175714612yes—
subgroupG/H
centerC2×C4C23×D15
commutator, socle, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC3×C5×#533C2
hypercenter#533D15
hypocenterC3×C5#3531
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C3×C5×#533C2semidirect
2. #11756494C2semidirect
3. #11756459C2semidirect
4. #11756458C2semidirect
5. #11756445C2semidirect
6. #11756406C2semidirect
7. #11756405C2semidirect
8. #11756339C2semidirect
9. #11756337C2semidirect
10. #11756287C2semidirect
11. #11756238C2semidirect
59. C5×#533D3semidirect
115. C3×#533D5semidirect
291. #533D15semidirect
508. C3×C5#3531semidirect
554. C5#86286semidirect
570. C3#10618187semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5332
#117564942
#117564592
#117564582
#117564452
#117564062
#117564052
#117563392
#117563372
#117562872
#117562382
#106181873
#862865