Finite Group Databasebeta

← #14481803

Subgroups — #14481803

Order 1920.

1992 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#533C211yesmaximal, characteristic, complemented
2#11756488C214yesmaximal, complemented
3#11756448C214yesmaximal, complemented
4#11756393C214yesmaximal
5#11756382C214yesmaximal, complemented
6#11756337C218yesmaximal, complemented
7D15×#117C212yesmaximal
8#11756276C212yesmaximal, complemented
9C2×#91761C211yesmaximal, characteristic
10#11756229C211yesmaximal, characteristic, complemented
11#10618175—31nomaximal, Hall
12C22×C4×D15C2211yescharacteristic
13C3×C5×C4⋊Q8C2212yescomplemented
14C3×C5×#125C2212yescomplemented
15C3×C5×C22⋊Q8C2214yes—
16C3×C4×C5×Q8C2214yescomplemented
17C3×C5×#117C2212yes—
18C2×C3×C42×C5C2211yescharacteristic
19#91835C2218yes—
20#91833C2218yescomplemented
21C2×#6714C2212yes—
22#91815C2212yes—
23#91813C2214yes—
24C2×#6712C2212yes—
25C2×C4×Dic15C2211yescharacteristic
26#91786C2218yes—
27#91785C2218yes—
28#91785C2218yes—
29#91781C2214yes—
30C4⋊C4×D15C2214yes—
31#91779C2214yescomplemented
32#91778C2218yescomplemented
33#91778C2218yescomplemented
34#91777C2218yescomplemented
35#91777C2214yescomplemented
36C22⋊C4×D15C2214yes—
37#91767C2218yes—
38#91766C2214yes—
39#91761C2214yes—
40#91761C2214yes—
41#91761C2212yes—
42#91761C2212yes—
43C42×D15C2214yes—
44#91759C2212yescomplemented
45#91758C2212yescomplemented
46C4×Dic30C2214yescomplemented
47C4×Dic30C2218yescomplemented
48#86274—51nomaximal, Hall
49C5×#533D311yescharacteristic, complemented
50#66063—34no—
51#66023—34no—
52#65968—34no—
53#65957—34no—
54#65912—38no—
55D5×#117—32no—
56#65851—32no—
57C2×#4018—31no—
58#65804—31no—
59C23×D15C2311yescharacteristic
60C2×C3×C5×Q8C2314yes—
61C22×C3×C4×C5C2312yes—
62C22×C3×C4×C5C2311yescharacteristic
63C22×Dic15C2312yes—
64C22×Dic15C2311yescharacteristic
65C2×C4×D15Q818yescomplemented
66C2×C4×D15C2318yes—
67C2×C4×D15C2312yes—
68C2×C4×D15C2312yes—
69C2×Dic30C2314yes—
70C2×Dic30C2318yes—
71C3×C5×C4⋊C4C2318yes—
72C3×C5×C4⋊C4C2314yes—
73C3×C5×C4⋊C4C2314yes—
74C3×C5×C22⋊C4C2314yes—
75C3×C42×C5C2314yes—
76C3×C42×C5C2312yes—
77C3×C42×C5C2311yescharacteristic
78C3×C42×C5C2311yescharacteristic
79#6719C2314yes—
80#6714C2314yes—
81#6714C2314yes—
82#6714C2318yes—
83C4⋊Dic15C2314yes—
84C4⋊Dic15C2318yes—
85C4⋊Dic15C2314yes—
86#6712C2318yes—
87#6712C2318yes—
88#6712C2318yes—
89#6712C2314yes—
90#6712C2314yes—
91#6712C2318yes—
92C4×Dic15C2314yes—
93C4×Dic15C2312yes—
94C4×Dic15C2318yes—
95C4×Dic15C2312yes—
96C3×#533D511yescharacteristic, complemented
97#5729—54no—
98#5689—54no—
99#5634—54no—
100#5623—54no—
101#5578—58no—
102D3×#117—52no—
103#5517—52no—
104C2×#872—51no—
105#5470—51no—
106C22×C4×D5—31no—
107C5×C4⋊Q8C2×D312yescomplemented
108C5×#125C2×D312yescomplemented
109C5×C22⋊Q8C2×D314yes—
110C4×C5×Q8C2×D314yescomplemented
111C5×#117C2×D312yes—
112C2×C42×C5C2×D311yescharacteristic
113#4092—38no—
114#4090—38no—
115C2×#685—32no—
116#4072—32no—
117#4070—34no—
118C2×#683—32no—
119C2×C4×Dic5—31no—
120#4043—38no—
121#4042—38no—
122#4042—38no—
123#4038—34no—
124D5×C4⋊C4—34no—
125#4036—34no—
126#4035—38no—
127#4035—38no—
128#4034—34no—
129#4034—38no—
130D5×C22⋊C4—34no—
131#4024—38no—
132#4023—34no—
133#4018—32no—
134#4018—34no—
135#4018—32no—
136#4018—34no—
137C42×D5—34no—
138#4016—32no—
139#4015—32no—
140C4×Dic10—34no—
141C4×Dic10—38no—
142#3458—151noSylow
143C23×C3×C5C2411yescharacteristic
144C22×D15—42no—
145C22×D15C2×Q814yes—
146C22×D15C2412yes—
147C3×C5×Q8—44no—
148C2×C3×C4×C5—42no—
149C2×C3×C4×C5C2×Q814yes—
150C2×C3×C4×C5C2418yes—
151C2×C3×C4×C5C2412yes—
152C2×C3×C4×C5C2412yes—
153C2×C3×C4×C5C2411yescharacteristic
154C2×C3×C4×C5C2411yescharacteristic
155C2×Dic15—42no—
156C2×Dic15C2×Q814yes—
157C2×Dic15C2414yes—
158C2×Dic15C2418yes—
159C2×Dic15C2412yes—
160C4×D15—48no—
161C4×D15C2×Q818yes—
162C4×D15C2×Q818yes—
163Dic30—44no—
164Dic30—48no—
165C22×C4×D3—51no—
166C3×C4⋊Q8C2×D512yescomplemented
167C3×#125C2×D512yescomplemented
168C3×C22⋊Q8C2×D514yes—
169C3×C4×Q8C2×D514yescomplemented
170C3×#117C2×D512yes—
171C2×C3×C42C2×D511yescharacteristic
172#946—58no—
173#944—58no—
174C2×(C2×D3)⋊C4—52no—
175#926—52no—
176#924—54no—
177C2×Dic3⋊C4—52no—
178C2×C4×Dic3—51no—
179#897—58no—
180#896—58no—
181#896—58no—
182#892—54no—
183D3×C4⋊C4—54no—
184#890—54no—
185#889—58no—
186#889—58no—
187#888—54no—
188#888—58no—
189D3×C22⋊C4—54no—
190#878—58no—
191#877—54no—
192#872—52no—
193#872—52no—
194#872—54no—
195#872—54no—
196C42×D3—54no—
197#870—52no—
198#869—52no—
199C4×Dic6—54no—
200C4×Dic6—58no—
201C23×D5—31no—
202C2×C5×Q8C22×D314yes—
203C22×C4×C5C22×D312yes—
204C22×C4×C5C22×D311yescharacteristic
205C22×Dic5—31no—
206C22×Dic5—32no—
207C2×C4×D5—38no—
208C2×C4×D5—32no—
209C2×C4×D5—32no—
210C2×C4×D5—38no—
211C2×Dic10—34no—
212C2×Dic10—38no—
213C5×C4⋊C4C22×D314yes—
214C5×C4⋊C4C22×D318yes—
215C5×C4⋊C4C22×D314yes—
216C5×C22⋊C4C22×D314yes—
217C42×C5C22×D312yes—
218C42×C5C22×D311yescharacteristic
219C42×C5C22×D311yescharacteristic
220C42×C5C22×D314yes—
221C22⋊Dic5—34no—
222#685—34no—
223#685—34no—
224#685—38no—
225C4⋊Dic5—34no—
226C4⋊Dic5—38no—
227C4⋊Dic5—34no—
228#683—38no—
229#683—38no—
230#683—38no—
231#683—34no—
232#683—34no—
233#683—38no—
234C4×Dic5—34no—
235C4×Dic5—32no—
236C4×Dic5—38no—
237C4×Dic5—32no—
238#544—154no—
239#544—154no—
240#544—154no—
241#543—154no—
242#533—158no—
243#533—152no—
244#533—151no—
245#533D1511yescharacteristic, complemented
246C2×#117—152no—
247C2×#117—151no—
248C22×C3×C5—22no—
249C22×C3×C5C22×Q812yes—
250C22×C3×C5C2511yescharacteristic
251C2×D15—24no—
252C2×D15—44no—
253C2×D15C22×Q814yes—
254C3×C4×C5—22no—
255C3×C4×C5—28no—
256C3×C4×C5—22no—
257C3×C4×C5C22×Q812yes—
258C3×C4×C5C22×Q812yes—
259Dic15—28no—
260Dic15—24no—
261Dic15C22×Q814yes—
262C23×D3—51no—
263C2×C3×Q8C22×D514yes—
264C22×C3×C4C22×D512yes—
265C22×C3×C4C22×D511yescharacteristic
266C22×Dic3—51no—
267C22×Dic3—52no—
268C2×C4×D3—58no—
269C2×C4×D3—52no—
270C2×C4×D3—52no—
271C2×C4×D3—58no—
272C2×Dic6—54no—
273C2×Dic6—58no—
274C3×C4⋊C4C22×D518yes—
275C3×C4⋊C4C22×D514yes—
276C3×C4⋊C4C22×D514yes—
277C3×C22⋊C4C22×D514yes—
278C3×C42C22×D514yes—
279C3×C42C22×D512yes—
280C3×C42C22×D511yescharacteristic
281C3×C42C22×D511yescharacteristic
282#217—54no—
283(C2×D3)⋊C4—54no—
284(C2×D3)⋊C4—54no—
285(C2×D3)⋊C4—58no—
286C4⋊Dic3—54no—
287C4⋊Dic3—58no—
288C4⋊Dic3—54no—
289Dic3⋊C4—58no—
290Dic3⋊C4—58no—
291Dic3⋊C4—58no—
292Dic3⋊C4—54no—
293Dic3⋊C4—54no—
294Dic3⋊C4—58no—
295C4×Dic3—54no—
296C4×Dic3—52no—
297C4×Dic3—58no—
298C4×Dic3—52no—
299C23×C5C23×D311yescharacteristic
300C22×D5—32no—
301C22×D5—34no—
302C22×D5—122no—
303C5×Q8—44no—
304C2×C4×C5—42no—
305C2×C4×C5D3×Q814yes—
306C2×C4×C5C23×D318yes—
307C2×C4×C5C23×D312yes—
308C2×C4×C5C23×D312yes—
309C2×C4×C5C23×D311yescharacteristic
310C2×C4×C5C23×D311yescharacteristic
311C2×Dic5—34no—
312C2×Dic5—32no—
313C2×Dic5—34no—
314C2×Dic5—38no—
315C2×Dic5—122no—
316C4×D5—38no—
317C4×D5—38no—
318C4×D5—128no—
319Dic10—124no—
320Dic10—128no—
321C23×C4—151no—
322C4⋊Q8—158no—
323C4⋊Q8—158no—
324C4⋊Q8—154no—
325C4⋊Q8—152no—
326C4⋊Q8C2×D1512yescomplemented
327#125—158no—
328#125—158no—
329#125—154no—
330#125—152no—
331#125C2×D1512yescomplemented
332C22⋊Q8—158no—
333C22⋊Q8—154no—
334C22⋊Q8—158no—
335C22⋊Q8—158no—
336C22⋊Q8—158no—
337C22⋊Q8—158no—
338C22⋊Q8C2×D1514yes—
339C4×Q8—158no—
340C4×Q8—154no—
341C4×Q8C2×D1514yescomplemented
342#117—152no—
343#117—154no—
344#117—154no—
345#117—154no—
346#117—154no—
347#117—152no—
348#117—152no—
349#117C2×D1512yes—
350C2×C4⋊C4—152no—
351C2×C4⋊C4—154no—
352C2×C22⋊C4—152no—
353C2×C22⋊C4—154no—
354C2×C42—151no—
355C2×C42—154no—
356C2×C42C2×D1511yescharacteristic
357C2×C3×C5—22no—
358C2×C3×C5C23×Q811yescharacteristic
359C2×C3×C5#58512yes—
360D15—24no—
361C23×C3C23×D511yescharacteristic
362C22×D3—52no—
363C22×D3—54no—
364C22×D3—202no—
365C3×Q8—44no—
366C2×C3×C4—42no—
367C2×C3×C4Q8×D514yes—
368C2×C3×C4C23×D518yes—
369C2×C3×C4C23×D512yes—
370C2×C3×C4C23×D512yes—
371C2×C3×C4C23×D511yescharacteristic
372C2×C3×C4C23×D511yescharacteristic
373C2×Dic3—54no—
374C2×Dic3—52no—
375C2×Dic3—54no—
376C2×Dic3—58no—
377C2×Dic3—202no—
378C4×D3—58no—
379C4×D3—58no—
380C4×D3—208no—
381Dic6—204no—
382Dic6—208no—
383C22×C5—22no—
384C22×C5C2×D3×Q812yes—
385C22×C5C24×D311yescharacteristic
386C2×D5—34no—
387C2×D5—64no—
388C2×D5—124no—
389C4×C5—22no—
390C4×C5—28no—
391C4×C5—22no—
392C4×C5C2×D3×Q812yes—
393C4×C5C2×D3×Q812yes—
394Dic5—34no—
395Dic5—68no—
396Dic5—64no—
397C24—151no—
398C2×Q8—158no—
399C2×Q8—154no—
400C2×Q8C22×D1514yes—
401C22×C4—151no—
402C22×C4—158no—
403C22×C4—152no—
404C22×C4—152no—
405C22×C4—152no—
406C22×C4—158no—
407C22×C4C22×D1512yes—
408C22×C4C22×D1511yescharacteristic
409C4⋊C4—158no—
410C4⋊C4—154no—
411C4⋊C4—154no—
412C4⋊C4—154no—
413C4⋊C4—158no—
414C4⋊C4—158no—
415C4⋊C4—158no—
416C4⋊C4—158no—
417C4⋊C4—154no—
418C4⋊C4C22×D1514yes—
419C4⋊C4C22×D1514yes—
420C4⋊C4C22×D1518yes—
421C22⋊C4—154no—
422C22⋊C4—158no—
423C22⋊C4—154no—
424C22⋊C4—154no—
425C22⋊C4C22×D1514yes—
426C42—158no—
427C42—152no—
428C42—152no—
429C42—154no—
430C42C22×D1511yescharacteristic
431C42C22×D1511yescharacteristic
432C42C22×D1514yes—
433C42C22×D1512yes—
434C3×C5#345811yescharacteristic, complemented, Hall
435C22×C3—22no—
436C22×C3C2×Q8×D512yes—
437C22×C3C24×D511yescharacteristic
438C2×D3—54no—
439C2×D3—104no—
440C2×D3—204no—
441C3×C4—22no—
442C3×C4—28no—
443C3×C4—22no—
444C3×C4C2×Q8×D512yes—
445C3×C4C2×Q8×D512yes—
446Dic3—54no—
447Dic3—108no—
448Dic3—104no—
449C2×C5—22no—
450C2×C5C22×D3×Q811yescharacteristic
451C2×C5#596412yes—
452D5—64no—
453C23—152no—
454C23—154no—
455C23—602no—
456C23C23×D1511yescharacteristic
457Q8—44no—
458Q8—604no—
459Q8—608no—
460C2×C4—42no—
461C2×C4—154no—
462C2×C4—152no—
463C2×C4—158no—
464C2×C4—158no—
465C2×C4—158no—
466C2×C4—154no—
467C2×C4—608no—
468C2×C4—602no—
469C2×C4Q8×D1514yes—
470C2×C4C23×D1518yes—
471C2×C4C23×D1512yes—
472C2×C4C23×D1512yes—
473C2×C4C23×D1511yescharacteristic
474C2×C4C23×D1511yescharacteristic
475C2×C3—22no—
476C2×C3C22×Q8×D511yescharacteristic
477C2×C3#6628312yes—
478D3—104no—
479C5#8627411yescharacteristic, complemented, Sylow
480C22—22no—
481C22—154no—
482C22—304no—
483C22—604no—
484C22C2×Q8×D1512yes—
485C22C24×D1511yescharacteristic
486C4—22no—
487C4—22no—
488C4—28no—
489C4—154no—
490C4—308no—
491C4—304no—
492C4C2×Q8×D1512yes—
493C4C2×Q8×D1512yes—
494C3#1061817511yescharacteristic, complemented, Sylow
495C2—22no—
496C2—304no—
497C2C22×Q8×D1511yescharacteristic
498C2#1175714612yes—
subgroupG/H
centerC2×C4C23×D15
commutator, socle, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC3×C5×#533C2
prime radicalC23×D15C23
hypercenter#533D15
hypocenterC3×C5#3458
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. #11756488C2semidirect
3. #11756448C2semidirect
5. #11756382C2semidirect
6. #11756337C2semidirect
8. #11756276C2semidirect
10. #11756229C2semidirect
13. C3×C5×C4⋊Q8C22semidirect
14. C3×C5×#125C22semidirect
16. C3×C4×C5×Q8C22semidirect
20. #91833C22semidirect
31. #91779C22semidirect
32. #91778C22semidirect
33. #91778C22semidirect
34. #91777C22semidirect
35. #91777C22semidirect
44. #91759C22semidirect
45. #91758C22semidirect
46. C4×Dic30C22semidirect
47. C4×Dic30C22semidirect
49. C5×#533D3semidirect
65. C2×C4×D15Q8semidirect
96. C3×#533D5semidirect
107. C5×C4⋊Q8C2×D3semidirect
108. C5×#125C2×D3semidirect
110. C4×C5×Q8C2×D3semidirect
166. C3×C4⋊Q8C2×D5semidirect
167. C3×#125C2×D5semidirect
169. C3×C4×Q8C2×D5semidirect
245. #533D15semidirect
326. C4⋊Q8C2×D15semidirect
331. #125C2×D15semidirect
341. C4×Q8C2×D15semidirect
434. C3×C5#3458semidirect
479. C5#86274semidirect
494. C3#10618175semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5332
#117564882
#117564482
#117563932
#117563822
#117563372
D15×#1172
#117562762
C2×#917612
#117562292
#106181753
#862745