Finite Group Databasebeta

← #14484724

Subgroups — #14484724

Order 1920.

2480 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D15×#127C211yesmaximal, characteristic
2C5×#5713C211yesmaximal, characteristic, complemented
3C3×#66047C211yesmaximal, characteristic, complemented
4#11754906C214yesmaximal, complemented
5#11754903C214yesmaximal, complemented
6#11754902C214yesmaximal, complemented
7#11754831C214yesmaximal, complemented
8#11754830C214yesmaximal, complemented
9D4×#1200C214yesmaximal, complemented
10#11752662C212yesmaximal, complemented
11C4×D15⋊Q8C212yesmaximal, complemented
12D5×#559—31nomaximal, Hall
13C2×D4×D15C2214yes—
14C2×D4×D15C2212yes—
15C22×#1200C2214yes—
16C2×D15⋊Q8C2212yes—
17C3×C5×#127C2211yescharacteristic
18#91829C2214yes—
19#91829C2212yes—
20#91763C2211yescharacteristic
21C42×D15C2211yescharacteristic
22C5×#936C2214yescomplemented
23C5×#935C2214yescomplemented
24C5×D4×Dic3C2214yescomplemented
25C4×C5×Dic6C2212yescomplemented
26C3×#4082C2214yescomplemented
27C3×#4081C2214yescomplemented
28C3×D4×Dic5C2214yescomplemented
29C3×C4×Dic10C2212yescomplemented
30#91562C2218yescomplemented
31#91561C2218yes—
32#91561C2214yes—
33#91556C2218yescomplemented
34#91552C2218yescomplemented
35#91546C2214yescomplemented
36#91542C2214yescomplemented
37#91526C2218yescomplemented
38#91526C2218yescomplemented
39C4×#1204C2214yescomplemented
40#91437C2212yes—
41#91433C2218yescomplemented
42#91428C2214yescomplemented
43#91418C2214yescomplemented
44#91404C2214yes—
45C4×#1200C2214yes—
46#91375C2214yescomplemented
47#91374C2214yescomplemented
48#91344C2212yescomplemented
49#91331C2212yescomplemented
50#91325C2214yescomplemented
51D3×#559—51nomaximal, Hall
52C5×#559—31no—
53D5×#127—31no—
54#66047D311yescharacteristic, complemented
55#66015—34no—
56D5×#124—34no—
57#65998—34no—
58D5×#123—34no—
59#65919—32no—
60C4×Q8×D5—32no—
61#65893—34no—
62C4×D4×D5—34no—
63C23×D15C2314yes—
64C2×C3×C5×D4C2314yes—
65C2×C3×C5×D4C2312yes—
66C2×#1220C2318yes—
67C2×#1220C2314yes—
68D4×D15—216no—
69D4×D15—44no—
70C2×D60C2314yes—
71C2×D60C2312yes—
72C2×C4×D15C2311yescharacteristic
73C2×C4×D15C2312yes—
74C22×C5×Dic3C2314yes—
75C2×C5×Dic6C2312yes—
76C22×C3×Dic5C2314yes—
77C2×C3×Dic10C2312yes—
78C2×#1204C2314yes—
79C2×#1200—48no—
80C2×#1200C2314yes—
81C2×#1200C2314yes—
82C2×#1200C2318yes—
83D15⋊Q8—28no—
84C3×C42×C5C2311yescharacteristic
85C4×Dic15C2312yes—
86C4×Dic15C2311yescharacteristic
87C5×#217C2318yes—
88C5×#217C2314yes—
89C5×C4⋊Dic3C2312yes—
90C5×Dic3⋊C4C2314yes—
91C4×C5×Dic3C2314yes—
92C3×C22⋊Dic5C2318yes—
93C3×C22⋊Dic5C2314yes—
94C3×C4⋊Dic5C2312yes—
95C3×#683C2314yes—
96C3×C4×Dic5C2314yes—
97Dic3⋊Dic5C2314yes—
98#6669C2314yes—
99#6668C2314yes—
100#6667C2318yes—
101#6667C2318yes—
102#6667C2318yes—
103Dic3×Dic5C2314yes—
104Dic3×Dic5C2314yes—
105C3×#559—51no—
106D3×#127—51no—
107#5713D511yescharacteristic, complemented
108#5681—54no—
109D3×#124—54no—
110#5664—54no—
111D3×#123—54no—
112#5585—52no—
113C4×D3×Q8—52no—
114#5559—54no—
115C4×D3×D4—54no—
116C2×Q8×D5—32no—
117C2×D4×D5—34no—
118C2×D4×D5—32no—
119C22×C4×D5—34no—
120C5×#127C2×D311yescharacteristic
121C5×#124—34no—
122C5×#123—34no—
123C4×C5×Q8—32no—
124C4×C5×D4—34no—
125#4093—34no—
126Q8×Dic5—32no—
127#4086—34no—
128#4086—32no—
129#4082C2×D314yescomplemented
130#4081C2×D314yescomplemented
131D4×Dic5C2×D314yescomplemented
132#4075—34no—
133C4×C22⋊D5—38no—
134#4040—38no—
135#4039—34no—
136D5×C4⋊C4—32no—
137D5×C4⋊C4—34no—
138#4033—32no—
139#4033—34no—
140#4032—34no—
141#4031—38no—
142#4031—38no—
143#4029—38no—
144#4027—38no—
145D5×C22⋊C4—38no—
146D5×C22⋊C4—34no—
147#4021—34no—
148#4020—31no—
149C4×D20—34no—
150C42×D5—31no—
151C42×D5—34no—
152C4×Dic10—34no—
153C4×Dic10C2×D312yescomplemented
154C2×#559—151noSylow
155C23×C3×C5C2414yes—
156C22×D15—216no—
157C22×D15—28no—
158C22×D15C2414yes—
159C22×D15C2411yescharacteristic
160C3×C5×D4—28no—
161C3×C5×D4—42no—
162C2×C3×C4×C5C2411yescharacteristic
163C2×C3×C4×C5C2412yes—
164#1220—216no—
165#1220—44no—
166C2×Dic15C2411yescharacteristic
167C2×Dic15C2412yes—
168D60—28no—
169D60—42no—
170C4×D15—22no—
171C4×D15#4118yes—
172C2×C5×Dic3—44no—
173C2×C5×Dic3C2414yes—
174C2×C5×Dic3C2414yes—
175C5×Dic6—24no—
176C2×C3×Dic5—44no—
177C2×C3×Dic5C2414yes—
178C2×C3×Dic5C2414yes—
179C3×Dic10—24no—
180#1204—28no—
181#1200—28no—
182#1200—28no—
183#1200—48no—
184C2×D3×Q8—52no—
185C2×D3×D4—54no—
186C2×D3×D4—52no—
187C22×C4×D3—54no—
188C3×#127C2×D511yescharacteristic
189C3×#124—54no—
190C3×#123—54no—
191C3×C4×Q8—52no—
192C3×C4×D4—54no—
193#947—54no—
194Q8×Dic3—52no—
195#940—52no—
196#940—54no—
197#936C2×D514yescomplemented
198#935C2×D514yescomplemented
199D4×Dic3C2×D514yescomplemented
200#929—54no—
201C4×#67—58no—
202#894—58no—
203#893—54no—
204D3×C4⋊C4—52no—
205D3×C4⋊C4—54no—
206#887—52no—
207#887—54no—
208#886—54no—
209#885—58no—
210#885—58no—
211#883—58no—
212#67⋊C4—58no—
213D3×C22⋊C4—54no—
214D3×C22⋊C4—58no—
215#875—54no—
216#874—51no—
217C4×D12—54no—
218C42×D3—51no—
219C42×D3—54no—
220C4×Dic6—54no—
221C4×Dic6C2×D512yescomplemented
222C23×D5—34no—
223C2×C5×Q8—32no—
224C2×C5×D4C22×D314yes—
225C2×C5×D4C22×D312yes—
226C22×C4×C5—34no—
227C2×C22⋊D5—38no—
228C2×C22⋊D5—34no—
229C22×Dic5C22×D314yes—
230Q8×D5—68no—
231D4×D5—616no—
232D4×D5—124no—
233C2×D20—34no—
234C2×D20—32no—
235C2×C4×D5—32no—
236C2×C4×D5—31no—
237C2×C4×D5—34no—
238C2×C4×D5—34no—
239C2×C4×D5—38no—
240C2×C4×D5—128no—
241C2×Dic10—34no—
242C2×Dic10C22×D312yes—
243C5×C4⋊C4—32no—
244C5×C4⋊C4—34no—
245C5×C22⋊C4—38no—
246C5×C22⋊C4—34no—
247C42×C5—34no—
248C42×C5C22×D311yescharacteristic
249C22⋊Dic5C22×D318yes—
250C22⋊Dic5C22×D314yes—
251#685—38no—
252#685—38no—
253#685—38no—
254C4⋊Dic5—34no—
255C4⋊Dic5C22×D312yes—
256#683—34no—
257#683—34no—
258#683C22×D314yes—
259C4×Dic5—32no—
260C4×Dic5—31no—
261C4×Dic5—34no—
262C4×Dic5—34no—
263C4×Dic5C22×D314yes—
264#559—31no—
265#559—51no—
266#559—154no—
267#559—154no—
268#559—152no—
269#559—154no—
270C2×#127—151no—
271C2×#124—154no—
272C2×#123—154no—
273C2×C4×Q8—152no—
274C2×C4×D4—154no—
275C22×C3×C5—28no—
276C22×C3×C5—24no—
277C22×C3×C5C2511yescharacteristic
278C2×D15—28no—
279C2×D15—24no—
280C2×D15—416no—
281C2×D15C2×#4114yes—
282C2×D15H(5,𝔽2)12yes—
283C3×C4×C5—21no—
284C3×C4×C5C2×#4114yes—
285Dic15—21no—
286Dic15C2×#4114yes—
287C3×Dic5—24no—
288C3×Dic5—24no—
289C5×Dic3—24no—
290C5×Dic3—24no—
291C23×D3—54no—
292C2×C3×Q8—52no—
293C2×C3×D4C22×D514yes—
294C2×C3×D4C22×D512yes—
295C22×C3×C4—54no—
296C2×#67—58no—
297C2×#67—54no—
298C22×Dic3C22×D514yes—
299D3×Q8—108no—
300D3×D4—1016no—
301D3×D4—204no—
302C2×D12—54no—
303C2×D12—52no—
304C2×C4×D3—52no—
305C2×C4×D3—51no—
306C2×C4×D3—54no—
307C2×C4×D3—54no—
308C2×C4×D3—58no—
309C2×C4×D3—208no—
310C2×Dic6—54no—
311C2×Dic6C22×D512yes—
312C3×C4⋊C4—54no—
313C3×C4⋊C4—52no—
314C3×C22⋊C4—58no—
315C3×C22⋊C4—54no—
316C3×C42—54no—
317C3×C42C22×D511yescharacteristic
318#217C22×D518yes—
319#217C22×D514yes—
320(C2×D3)⋊C4—58no—
321(C2×D3)⋊C4—58no—
322(C2×D3)⋊C4—58no—
323C4⋊Dic3—54no—
324C4⋊Dic3C22×D512yes—
325Dic3⋊C4—54no—
326Dic3⋊C4—54no—
327Dic3⋊C4C22×D514yes—
328C4×Dic3—52no—
329C4×Dic3—51no—
330C4×Dic3—54no—
331C4×Dic3—54no—
332C4×Dic3C22×D514yes—
333C23×C5C23×D314yes—
334C22×D5—31no—
335C22×D5—34no—
336C22×D5—68no—
337C22×D5—616no—
338C5×Q8—64no—
339C5×D4—28no—
340C5×D4—42no—
341C2×C4×C5—34no—
342C2×C4×C5—34no—
343C2×C4×C5—124no—
344C2×C4×C5C23×D311yescharacteristic
345C2×C4×C5C23×D312yes—
346C22⋊D5—616no—
347C22⋊D5—124no—
348C2×Dic5—32no—
349C2×Dic5—31no—
350C2×Dic5—44no—
351C2×Dic5C23×D314yes—
352C2×Dic5C23×D314yes—
353D20—68no—
354D20—122no—
355C4×D5—38no—
356C4×D5—68no—
357C4×D5—68no—
358C4×D5—62no—
359C4×D5—128no—
360Dic10—24no—
361Dic10—68no—
362C22×Q8—152no—
363C22×D4—154no—
364C22×D4—152no—
365C23×C4—154no—
366#127—152no—
367#127—154no—
368#127—151no—
369#127D3×D511yescharacteristic
370#124—34no—
371#124—54no—
372#124—154no—
373#124—154no—
374#124—158no—
375#124—158no—
376#123—34no—
377#123—54no—
378#123—158no—
379#123—154no—
380#123—154no—
381#123—158no—
382C4×Q8—32no—
383C4×Q8—52no—
384C4×Q8—154no—
385C4×Q8—154no—
386C4×Q8—152no—
387C4×Q8—152no—
388C4×D4—34no—
389C4×D4—54no—
390C4×D4—154no—
391C4×D4—154no—
392C4×D4—158no—
393C4×D4—158no—
394C2×C4⋊C4—152no—
395C2×C4⋊C4—154no—
396C2×C22⋊C4—158no—
397C2×C22⋊C4—154no—
398C2×C42—154no—
399C2×C42—151no—
400C2×C3×C5—44no—
401C2×C3×C5C22×#4112yes—
402C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
403D15—44no—
404D15#55914yescomplemented
405C23×C3C23×D514yes—
406C22×D3—51no—
407C22×D3—54no—
408C22×D3—108no—
409C22×D3—1016no—
410C3×Q8—104no—
411C3×D4—28no—
412C3×D4—42no—
413C2×C3×C4—54no—
414C2×C3×C4—54no—
415C2×C3×C4—204no—
416C2×C3×C4C23×D511yescharacteristic
417C2×C3×C4C23×D512yes—
418#67—1016no—
419#67—204no—
420C2×Dic3—44no—
421C2×Dic3—52no—
422C2×Dic3—51no—
423C2×Dic3C23×D514yes—
424C2×Dic3C23×D514yes—
425D12—108no—
426D12—202no—
427C4×D3—58no—
428C4×D3—108no—
429C4×D3—108no—
430C4×D3—102no—
431C4×D3—208no—
432Dic6—24no—
433Dic6—108no—
434C22×C5—28no—
435C22×C5—24no—
436C22×C5C24×D311yescharacteristic
437C2×D5—34no—
438C2×D5—32no—
439C2×D5—68no—
440C2×D5—64no—
441C2×D5—1216no—
442C4×C5—21no—
443C4×C5—64no—
444C4×C5—64no—
445C4×C5D3×#4114yes—
446Dic5—24no—
447Dic5—24no—
448Dic5—34no—
449Dic5—61no—
450C24—154no—
451C2×Q8—32no—
452C2×Q8—52no—
453C2×Q8—154no—
454C2×Q8—308no—
455C2×D4—158no—
456C2×D4—154no—
457C2×D4—154no—
458C2×D4—152no—
459C2×D4—3016no—
460C2×D4—604no—
461C2×D4C2×D3×D514yes—
462C2×D4C2×D3×D512yes—
463C22×C4—34no—
464C22×C4—54no—
465C22×C4—154no—
466C22×C4—154no—
467C22×C4—158no—
468C22×C4—152no—
469C22×C4—151no—
470C22×C4—608no—
471C4⋊C4—32no—
472C4⋊C4—34no—
473C4⋊C4—52no—
474C4⋊C4—54no—
475C4⋊C4—154no—
476C4⋊C4—154no—
477C4⋊C4—154no—
478C22⋊C4—38no—
479C22⋊C4—34no—
480C22⋊C4—58no—
481C22⋊C4—54no—
482C22⋊C4—158no—
483C22⋊C4—158no—
484C22⋊C4—158no—
485C42—34no—
486C42—54no—
487C42—154no—
488C42—154no—
489C42—151no—
490C42—152no—
491C42C2×D3×D511yescharacteristic
492C3×C5C2×#55911yescharacteristic, complemented, Hall
493C22×C3—28no—
494C22×C3—24no—
495C22×C3C24×D511yescharacteristic
496C2×D3—54no—
497C2×D3—52no—
498C2×D3—108no—
499C2×D3—104no—
500C2×D3—2016no—
501C3×C4—21no—
502C3×C4—104no—
503C3×C4—104no—
504C3×C4D5×#4114yes—
505Dic3—24no—
506Dic3—24no—
507Dic3—54no—
508Dic3—101no—
509C2×C5—44no—
510C2×C5C2×D3×#4112yes—
511C2×C5D3×H(5,𝔽2)11yescharacteristic
512D5—34no—
513D5—124no—
514C23—151no—
515C23—154no—
516C23—308no—
517C23—3016no—
518C23C22×D3×D514yes—
519Q8—64no—
520Q8—104no—
521Q8—308no—
522D4—28no—
523D4—42no—
524D4—3016no—
525D4—308no—
526D4—602no—
527D4—604no—
528C2×C4—34no—
529C2×C4—34no—
530C2×C4—54no—
531C2×C4—54no—
532C2×C4—124no—
533C2×C4—152no—
534C2×C4—158no—
535C2×C4—151no—
536C2×C4—204no—
537C2×C4—302no—
538C2×C4—308no—
539C2×C4—308no—
540C2×C4—608no—
541C2×C4C22×D3×D511yescharacteristic
542C2×C4C22×D3×D512yes—
543C2×C3—44no—
544C2×C3C2×D5×#4112yes—
545C2×C3D5×H(5,𝔽2)11yescharacteristic
546D3—54no—
547D3—204no—
548C5D3×#55911yescharacteristic, complemented, Sylow
549C22—28no—
550C22—24no—
551C22—154no—
552C22—152no—
553C22—308no—
554C22—304no—
555C22—6016no—
556C22C23×D3×D511yescharacteristic
557C4—21no—
558C4—64no—
559C4—64no—
560C4—104no—
561C4—104no—
562C4—154no—
563C4—301no—
564C4#9202414yes—
565C3D5×#55911yescharacteristic, complemented, Sylow
566C2—44no—
567C2—154no—
568C2—604no—
569C2C2×#9202412yes—
570C2#1175703011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C5×#127C22
prime radicalD15×#127C2
hypercenter#127D3×D5
hypocenterC3×C5C2×#559
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #127

Complements

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

NH ≅ G/Ntype
2. C5×#5713C2semidirect
3. C3×#66047C2semidirect
4. #11754906C2semidirect
5. #11754903C2semidirect
6. #11754902C2semidirect
7. #11754831C2semidirect
8. #11754830C2semidirect
9. D4×#1200C2semidirect
10. #11752662C2semidirect
11. C4×D15⋊Q8C2semidirect
22. C5×#936C22semidirect
23. C5×#935C22semidirect
24. C5×D4×Dic3C22semidirect
25. C4×C5×Dic6C22semidirect
26. C3×#4082C22semidirect
27. C3×#4081C22semidirect
28. C3×D4×Dic5C22semidirect
29. C3×C4×Dic10C22semidirect
30. #91562C22semidirect
33. #91556C22semidirect
34. #91552C22semidirect
35. #91546C22semidirect
36. #91542C22semidirect
37. #91526C22semidirect
38. #91526C22semidirect
39. C4×#1204C22semidirect
41. #91433C22semidirect
42. #91428C22semidirect
43. #91418C22semidirect
46. #91375C22semidirect
47. #91374C22semidirect
48. #91344C22semidirect
49. #91331C22semidirect
50. #91325C22semidirect
54. #66047D3semidirect
107. #5713D5semidirect
129. #4082C2×D3semidirect
130. #4081C2×D3semidirect
131. D4×Dic5C2×D3semidirect
153. C4×Dic10C2×D3semidirect
197. #936C2×D5semidirect
198. #935C2×D5semidirect
199. D4×Dic3C2×D5semidirect
221. C4×Dic6C2×D5semidirect
404. D15#559semidirect
492. C3×C5C2×#559semidirect
548. C5D3×#559semidirect
565. C3D5×#559semidirect

Maximal subgroups

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

subgroupindex
D15×#1272
C5×#57132
C3×#660472
#117549062
#117549032
#117549022
#117548312
#117548302
D4×#12002
#117526622
C4×D15⋊Q82
D5×#5593
D3×#5595