Finite Group Databasebeta

← #14327503

Subgroups — #14327503

Order 1920.

1176 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1220C211yesmaximal, characteristic
2C3×C5×#381C211yesmaximal, characteristic, complemented
3C4×#6719C211yesmaximal, characteristic, complemented
4#11751057C212yesmaximal
5#11751046C212yesmaximal, complemented
6#11750768C211yesmaximal, characteristic, complemented
7#11750767C212yesmaximal, complemented
8D15×#95C211yesmaximal, characteristic, complemented
9#11750753C212yesmaximal, complemented
10#11750752C211yesmaximal, characteristic, complemented
11#11750749C211yesmaximal, characteristic, complemented
12#10605854—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×#1220C2211yescharacteristic
15C22×C4×D15C2212yes—
16C22×C4×D15C2211yescharacteristic
17C2×C3×C5×C22⋊C4C2212yes—
18C2×#6719C2212yes—
19C2×#6719C2211yescharacteristic
20C4×#1220C418yescomplemented
21C2×#6714C2212yes—
22C2×#6714C2211yescharacteristic
23C2×#6712C2212yes—
24C2×#6712C2211yescharacteristic
25C2×C4×Dic15C2212yes—
26C2×C4×Dic15C2212yes—
27C2×C4×Dic15C2211yescharacteristic
28C3×C5×#95C2211yescharacteristic
29C3×C5×#95C2211yescharacteristic
30C3×C5×#95C2212yes—
31#91115C2212yes—
32#91115C2211yescharacteristic
33#91115C2212yes—
34#91115C2212yes—
35#91115C2211yescharacteristic
36#91115C2212yes—
37#74123—51nomaximal, Hall
38C2×C4×C22⋊D5—31no—
39C5×#381D311yescharacteristic, complemented
40C4×C22⋊Dic5—31no—
41#65245—32no—
42#65234—32no—
43#64956—31no—
44#64955—32no—
45D5×#95—31no—
46#64941—32no—
47#64940—31no—
48#64937—31no—
49C24×C3×C5C2311yescharacteristic
50C23×D15C2311yescharacteristic
51C22×C3×C4×C5—42no—
52C22×C3×C4×C5C2×C414yescomplemented
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2312yes—
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—22no—
58C2×#1220—22no—
59C2×#1220C2×C414yes—
60C22×Dic15C2312yes—
61C22×Dic15C2311yescharacteristic
62C22×Dic15C2311yescharacteristic
63C22×Dic15C2311yescharacteristic
64C22×Dic15C2312yes—
65C2×C4×D15—24no—
66C2×C4×D15—24no—
67C2×C4×D15—42no—
68C2×C4×D15—42no—
69C2×C4×D15C2×C414yes—
70C3×C5×C22⋊C4—42no—
71#6719—24no—
72#6719C2×C414yescomplemented
73#6714—24no—
74#6714C2×C414yes—
75#6712—42no—
76#6712C2×C414yescomplemented
77C4×Dic15—24no—
78C4×Dic15—42no—
79C4×Dic15C2×C414yescomplemented
80C2×C4×#67—51no—
81C3×#381D511yescharacteristic, complemented
82C4×#217—51no—
83#4956—52no—
84#4945—52no—
85#4667—51no—
86#4666—52no—
87D3×#95—51no—
88#4652—52no—
89#4651—51no—
90#4648—51no—
91C23×C4×C5C2×D311yescharacteristic
92C22×C22⋊D5—31no—
93C22×C4×D5—31no—
94C22×C4×D5—32no—
95C2×C5×C22⋊C4C2×D312yes—
96C2×C22⋊Dic5—31no—
97C2×C22⋊Dic5—32no—
98C4×C22⋊D5—38no—
99C2×#685—31no—
100C2×#685—32no—
101C2×#683—31no—
102C2×#683—32no—
103C2×C4×Dic5—31no—
104C2×C4×Dic5—32no—
105C2×C4×Dic5—32no—
106C5×#95C2×D311yescharacteristic
107C5×#95C2×D311yescharacteristic
108C5×#95C2×D312yes—
109#3963—32no—
110#3963—31no—
111#3963—32no—
112#3963—32no—
113#3963—31no—
114#3963—32no—
115#2353—151noSylow
116C23×C3×C5—22no—
117C23×C3×C5—21no—
118C23×C3×C5—21no—
119C23×C3×C5—22no—
120C23×C3×C5C22×C412yes—
121C23×C3×C5C2411yescharacteristic
122C22×D15—22no—
123C22×D15—22no—
124C22×D15C22×C412yes—
125C22×D15#4112yes—
126C22×D15#4112yes—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—44no—
136C2×C3×C4×C5C22×C412yes—
137C2×C3×C4×C5C22×C412yes—
138#1220—28no—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15—21no—
142C2×Dic15—21no—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×Dic15—22no—
148C2×Dic15C22×C412yes—
149C2×Dic15C22×C412yes—
150C2×Dic15C22×C412yes—
151C2×Dic15#4114yes—
152C4×D15—44no—
153C4×D15—48no—
154C23×C3×C4C2×D511yescharacteristic
155C22×#67—51no—
156C22×C4×D3—51no—
157C22×C4×D3—52no—
158C2×C3×C22⋊C4C2×D512yes—
159C2×#217—51no—
160C2×#217—52no—
161C4×#67—58no—
162C2×(C2×D3)⋊C4—51no—
163C2×(C2×D3)⋊C4—52no—
164C2×Dic3⋊C4—51no—
165C2×Dic3⋊C4—52no—
166C2×C4×Dic3—51no—
167C2×C4×Dic3—52no—
168C2×C4×Dic3—52no—
169C3×#95C2×D511yescharacteristic
170C3×#95C2×D511yescharacteristic
171C3×#95C2×D512yes—
172C3⋊#95—52no—
173C3⋊#95—51no—
174C3⋊#95—52no—
175C3⋊#95—52no—
176C3⋊#95—51no—
177C3⋊#95—52no—
178C24×C5C22×D311yescharacteristic
179C23×D5—31no—
180C22×C4×C5—42no—
181C22×C4×C5C4×D314yescomplemented
182C22×C4×C5C22×D312yes—
183C22×C4×C5C22×D312yes—
184C22×C4×C5C22×D311yescharacteristic
185C22×C4×C5C22×D311yescharacteristic
186C2×C22⋊D5—34no—
187C2×C22⋊D5—62no—
188C2×C22⋊D5—62no—
189C22×Dic5—32no—
190C22×Dic5—31no—
191C22×Dic5—31no—
192C22×Dic5—31no—
193C22×Dic5—32no—
194C2×C4×D5—34no—
195C2×C4×D5—64no—
196C2×C4×D5—64no—
197C2×C4×D5—122no—
198C2×C4×D5—122no—
199C5×C22⋊C4—42no—
200C22⋊Dic5—34no—
201C22⋊Dic5—64no—
202#685—34no—
203#685—64no—
204#683—34no—
205#683—122no—
206C4×Dic5—34no—
207C4×Dic5—64no—
208C4×Dic5—122no—
209C2×C4×D4—151no—
210#388—152no—
211#387—152no—
212#386—152no—
213#383—151no—
214#381D1511yescharacteristic, complemented
215#380—151no—
216C4×C22⋊C4—151no—
217C4×C22⋊C4—152no—
218#376—151no—
219C2×#95—151no—
220C22×C3×C5—22no—
221C22×C3×C5—22no—
222C22×C3×C5—22no—
223C22×C3×C5—42no—
224C22×C3×C5—42no—
225C22×C3×C5C23×C411yescharacteristic
226C22×C3×C5C2×#4111yescharacteristic
227C22×C3×C5C2×#4111yescharacteristic
228C22×C3×C5C2×#4112yes—
229C22×C3×C5H(5,𝔽2)12yes—
230C2×D15—22no—
231C2×D15—22no—
232C2×D15—24no—
233C2×D15—24no—
234C2×D15#11714yes—
235C3×C4×C5—22no—
236C3×C4×C5—22no—
237C3×C4×C5—42no—
238C3×C4×C5—42no—
239Dic15—22no—
240Dic15—22no—
241Dic15—22no—
242Dic15—24no—
243Dic15—42no—
244C24×C3C22×D511yescharacteristic
245C23×D3—51no—
246C22×C3×C4—42no—
247C22×C3×C4C4×D514yescomplemented
248C22×C3×C4C22×D512yes—
249C22×C3×C4C22×D512yes—
250C22×C3×C4C22×D511yescharacteristic
251C22×C3×C4C22×D511yescharacteristic
252C2×#67—54no—
253C2×#67—102no—
254C2×#67—102no—
255C22×Dic3—51no—
256C22×Dic3—52no—
257C22×Dic3—51no—
258C22×Dic3—51no—
259C22×Dic3—52no—
260C2×C4×D3—54no—
261C2×C4×D3—104no—
262C2×C4×D3—104no—
263C2×C4×D3—202no—
264C2×C4×D3—202no—
265C3×C22⋊C4—42no—
266#217—54no—
267#217—104no—
268(C2×D3)⋊C4—54no—
269(C2×D3)⋊C4—104no—
270Dic3⋊C4—54no—
271Dic3⋊C4—202no—
272C4×Dic3—54no—
273C4×Dic3—104no—
274C4×Dic3—202no—
275C23×C5—22no—
276C23×C5—22no—
277C23×C5—21no—
278C23×C5—21no—
279C23×C5C2×C4×D312yes—
280C23×C5C23×D311yescharacteristic
281C22×D5—32no—
282C22×D5—32no—
283C22×D5—32no—
284C22×D5—62no—
285C22×D5—62no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5—22no—
292C2×C4×C5—22no—
293C2×C4×C5—22no—
294C2×C4×C5—44no—
295C2×C4×C5C2×C4×D312yes—
296C2×C4×C5C2×C4×D312yes—
297C22⋊D5—68no—
298C2×Dic5—32no—
299C2×Dic5—32no—
300C2×Dic5—32no—
301C2×Dic5—34no—
302C2×Dic5—62no—
303C2×Dic5—62no—
304C2×Dic5—62no—
305C2×Dic5—62no—
306C2×Dic5—61no—
307C2×Dic5—61no—
308C2×Dic5—62no—
309C2×Dic5—62no—
310C2×Dic5—62no—
311C4×D5—124no—
312C4×D5—128no—
313C22×D4—151no—
314C23×C4—151no—
315C23×C4—152no—
316C23×C4C2×D1511yescharacteristic
317C4×D4—158no—
318C2×C4⋊C4—151no—
319C2×C4⋊C4—152no—
320C2×C22⋊C4—151no—
321C2×C22⋊C4—151no—
322C2×C22⋊C4—152no—
323C2×C22⋊C4—152no—
324C2×C22⋊C4C2×D1512yes—
325C2×C42—151no—
326C2×C42—152no—
327C2×C42—152no—
328#95—151no—
329#95—152no—
330#95—152no—
331#95—151no—
332#95—152no—
333#95—152no—
334#95C2×D1511yescharacteristic
335#95C2×D1511yescharacteristic
336#95C2×D1512yes—
337C2×C3×C5—42no—
338C2×C3×C5C2×#11711yescharacteristic
339C2×C3×C5C4×#4111yescharacteristic
340C2×C3×C5#51811yescharacteristic
341C2×C3×C5#55112yes—
342C2×C3×C5#55312yes—
343D15—24no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3C2×C4×D512yes—
349C23×C3C23×D511yescharacteristic
350C22×D3—52no—
351C22×D3—52no—
352C22×D3—52no—
353C22×D3—102no—
354C22×D3—102no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—44no—
364C2×C3×C4C2×C4×D512yes—
365C2×C3×C4C2×C4×D512yes—
366#67—108no—
367C2×Dic3—52no—
368C2×Dic3—52no—
369C2×Dic3—52no—
370C2×Dic3—54no—
371C2×Dic3—102no—
372C2×Dic3—102no—
373C2×Dic3—102no—
374C2×Dic3—102no—
375C2×Dic3—101no—
376C2×Dic3—101no—
377C2×Dic3—102no—
378C2×Dic3—102no—
379C2×Dic3—102no—
380C4×D3—204no—
381C4×D3—208no—
382C22×C5—22no—
383C22×C5—22no—
384C22×C5—22no—
385C22×C5—42no—
386C22×C5—42no—
387C22×C5C22×C4×D311yescharacteristic
388C22×C5#100412yes—
389C22×C5D3×#4111yescharacteristic
390C22×C5D3×#4112yes—
391C22×C5D3×#4111yescharacteristic
392C2×D5—34no—
393C2×D5—64no—
394C2×D5—64no—
395C2×D5—62no—
396C2×D5—62no—
397C4×C5—22no—
398C4×C5—22no—
399C4×C5—42no—
400C4×C5—42no—
401Dic5—64no—
402Dic5—62no—
403Dic5—62no—
404Dic5—62no—
405Dic5—122no—
406C24—151no—
407C24C22×D1511yescharacteristic
408C2×D4—154no—
409C2×D4—302no—
410C2×D4—302no—
411C22×C4—42no—
412C22×C4—151no—
413C22×C4—152no—
414C22×C4—151no—
415C22×C4—151no—
416C22×C4—154no—
417C22×C4—152no—
418C22×C4—304no—
419C22×C4—304no—
420C22×C4—602no—
421C22×C4—602no—
422C22×C4C4×D1514yescomplemented
423C22×C4C22×D1512yes—
424C22×C4C22×D1512yes—
425C22×C4C22×D1511yescharacteristic
426C22×C4C22×D1511yescharacteristic
427C4⋊C4—154no—
428C4⋊C4—602no—
429C22⋊C4—42no—
430C22⋊C4—154no—
431C22⋊C4—154no—
432C22⋊C4—304no—
433C22⋊C4—304no—
434C42—154no—
435C42—304no—
436C42—602no—
437C3×C5#235311yescharacteristic, complemented, Hall
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—22no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3C22×C4×D511yescharacteristic
444C22×C3#414412yes—
445C22×C3D5×#4111yescharacteristic
446C22×C3D5×#4111yescharacteristic
447C22×C3D5×#4112yes—
448C2×D3—54no—
449C2×D3—102no—
450C2×D3—102no—
451C2×D3—104no—
452C2×D3—104no—
453C3×C4—22no—
454C3×C4—22no—
455C3×C4—42no—
456C3×C4—42no—
457Dic3—102no—
458Dic3—102no—
459Dic3—102no—
460Dic3—104no—
461Dic3—202no—
462C2×C5—42no—
463C2×C5#548611yescharacteristic
464C2×C5D3×#11711yescharacteristic
465C2×C5#552211yescharacteristic
466C2×C5#565912yes—
467C2×C5#566112yes—
468D5—64no—
469C23—22no—
470C23—22no—
471C23—21no—
472C23—21no—
473C23—152no—
474C23—152no—
475C23—152no—
476C23—302no—
477C23—302no—
478C23C2×C4×D1512yes—
479C23C23×D1511yescharacteristic
480D4—308no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—44no—
490C2×C4—152no—
491C2×C4—152no—
492C2×C4—152no—
493C2×C4—154no—
494C2×C4—302no—
495C2×C4—302no—
496C2×C4—302no—
497C2×C4—302no—
498C2×C4—301no—
499C2×C4—301no—
500C2×C4—302no—
501C2×C4—302no—
502C2×C4—302no—
503C2×C4—604no—
504C2×C4—608no—
505C2×C4C2×C4×D1512yes—
506C2×C4C2×C4×D1512yes—
507C2×C3—42no—
508C2×C3#6582011yescharacteristic
509C2×C3D5×#11711yescharacteristic
510C2×C3#6585611yescharacteristic
511C2×C3#6599312yes—
512C2×C3#6599512yes—
513D3—104no—
514C5#7412311yescharacteristic, complemented, Sylow
515C22—22no—
516C22—22no—
517C22—22no—
518C22—42no—
519C22—42no—
520C22—154no—
521C22—304no—
522C22—304no—
523C22—302no—
524C22—302no—
525C22C22×C4×D1511yescharacteristic
526C22#9209512yes—
527C22#41×D1511yescharacteristic
528C22#41×D1512yes—
529C22#41×D1511yescharacteristic
530C4—22no—
531C4—22no—
532C4—42no—
533C4—42no—
534C4—304no—
535C4—302no—
536C4—302no—
537C4—302no—
538C4—602no—
539C3#1060585411yescharacteristic, complemented, Sylow
540C2—42no—
541C2—304no—
542C2#1175624511yescharacteristic
543C2D15×#11711yescharacteristic
544C2#1175628111yescharacteristic
545C2#1175641812yes—
546C2#1175642012yes—
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#381C2
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenter#381D15
hypocenterC3×C5#2353
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C3×C5×#381C2semidirect
3. C4×#6719C2semidirect
5. #11751046C2semidirect
6. #11750768C2semidirect
7. #11750767C2semidirect
8. D15×#95C2semidirect
9. #11750753C2semidirect
10. #11750752C2semidirect
11. #11750749C2semidirect
20. C4×#1220C4semidirect
39. C5×#381D3semidirect
52. C22×C3×C4×C5C2×C4semidirect
72. #6719C2×C4semidirect
76. #6712C2×C4semidirect
79. C4×Dic15C2×C4semidirect
81. C3×#381D5semidirect
181. C22×C4×C5C4×D3semidirect
214. #381D15semidirect
247. C22×C3×C4C4×D5semidirect
422. C22×C4C4×D15semidirect
437. C3×C5#2353semidirect
514. C5#74123semidirect
539. C3#10605854semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12202
C3×C5×#3812
C4×#67192
#117510572
#117510462
#117507682
#117507672
D15×#952
#117507532
#117507522
#117507492
#106058543
#741235