Finite Group Databasebeta

← #14322969

Subgroups — #14322969

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 544 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
3#11751313C211yesmaximal, characteristic, complemented
4#11751057C212yesmaximal
5#11751045C212yesmaximal, complemented
6#11750769C212yesmaximal, complemented
7#11750767C211yesmaximal, characteristic, complemented
8D15×#95C211yesmaximal, characteristic, complemented
9#11750756C212yesmaximal, complemented
10#11750752C211yesmaximal, characteristic, complemented
11#11750751C211yesmaximal, characteristic, complemented
12#10605851—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×C4⋊Dic15C2212yes—
24C2×#6712C2212yes—
25C2×#6712C2211yescharacteristic
26C2×C4×Dic15C2212yes—
27C2×C4×Dic15C2211yescharacteristic
28C3×C5×#95C2211yescharacteristic
29C3×C5×#95C2211yescharacteristic
30C3×C5×#95C2212yes—
31#91115C2212yes—
32#91115C2211yescharacteristic
33#91115C2212yes—
34#91115C2211yescharacteristic
35#91115C2212yes—
36#91115C2212yes—
37#74120—51nomaximal, Hall
38C2×C4×C22⋊D5—31no—
39C5×#381D311yescharacteristic, complemented
40#65501—31no—
41#65245—32no—
42#65233—32no—
43#64957—32no—
44#64955—31no—
45D5×#95—31no—
46#64944—32no—
47#64940—31no—
48#64939—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—24no—
58C2×#1220C2×C414yes—
59C22×Dic15C2312yes—
60C22×Dic15C2312yes—
61C22×Dic15C2311yescharacteristic
62C22×Dic15C2311yescharacteristic
63C22×Dic15C2311yescharacteristic
64C2×C4×D15—24no—
65C2×C4×D15—42no—
66C2×C4×D15—42no—
67C2×C4×D15—42no—
68C2×C4×D15C2×C414yes—
69C3×C5×C22⋊C4—42no—
70#6719—42no—
71#6719C2×C414yescomplemented
72#6714—24no—
73#6714C2×C414yes—
74C4⋊Dic15—42no—
75#6712—42no—
76#6712C2×C414yescomplemented
77C4×Dic15—42no—
78C4×Dic15C2×C414yescomplemented
79C2×C4×#67—51no—
80C3×#381D511yescharacteristic, complemented
81#5212—51no—
82#4956—52no—
83#4944—52no—
84#4668—52no—
85#4666—51no—
86D3×#95—51no—
87#4655—52no—
88#4651—51no—
89#4650—51no—
90C23×C4×C5C2×D311yescharacteristic
91C22×C22⋊D5—31no—
92C22×C4×D5—31no—
93C22×C4×D5—32no—
94C2×C5×C22⋊C4C2×D312yes—
95C2×C22⋊Dic5—31no—
96C2×C22⋊Dic5—32no—
97C4×C22⋊D5—38no—
98C2×#685—31no—
99C2×#685—32no—
100C2×C4⋊Dic5—32no—
101C2×#683—31no—
102C2×#683—32no—
103C2×C4×Dic5—31no—
104C2×C4×Dic5—32no—
105C5×#95C2×D311yescharacteristic
106C5×#95C2×D311yescharacteristic
107C5×#95C2×D312yes—
108#3963—32no—
109#3963—31no—
110#3963—32no—
111#3963—31no—
112#3963—32no—
113#3963—32no—
114#2318—151noSylow
115C23×C3×C5—22no—
116C23×C3×C5—21no—
117C23×C3×C5—22no—
118C23×C3×C5—21no—
119C23×C3×C5C22×C412yes—
120C23×C3×C5C2411yescharacteristic
121C22×D15—22no—
122C22×D15—21no—
123C22×D15—21no—
124C22×D15C22×C412yes—
125C22×D15#4114yes—
126C2×C3×C4×C5—22no—
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—44no—
135C2×C3×C4×C5C22×C412yes—
136C2×C3×C4×C5C22×C412yes—
137#1220—28no—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15—21no—
141C2×Dic15—21no—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×Dic15—22no—
148C2×Dic15C22×C412yes—
149C2×Dic15C22×C412yes—
150C2×Dic15C22×C412yes—
151C4×D15—44no—
152C4×D15—48no—
153C23×C3×C4C2×D511yescharacteristic
154C22×#67—51no—
155C22×C4×D3—51no—
156C22×C4×D3—52no—
157C2×C3×C22⋊C4C2×D512yes—
158C2×#217—51no—
159C2×#217—52no—
160C4×#67—58no—
161C2×(C2×D3)⋊C4—51no—
162C2×(C2×D3)⋊C4—52no—
163C2×C4⋊Dic3—52no—
164C2×Dic3⋊C4—51no—
165C2×Dic3⋊C4—52no—
166C2×C4×Dic3—51no—
167C2×C4×Dic3—52no—
168C3×#95C2×D511yescharacteristic
169C3×#95C2×D511yescharacteristic
170C3×#95C2×D512yes—
171C3⋊#95—52no—
172C3⋊#95—51no—
173C3⋊#95—52no—
174C3⋊#95—51no—
175C3⋊#95—52no—
176C3⋊#95—52no—
177C24×C5C22×D311yescharacteristic
178C23×D5—31no—
179C22×C4×C5—42no—
180C22×C4×C5C4×D314yescomplemented
181C22×C4×C5C22×D312yes—
182C22×C4×C5C22×D312yes—
183C22×C4×C5C22×D311yescharacteristic
184C22×C4×C5C22×D311yescharacteristic
185C2×C22⋊D5—34no—
186C2×C22⋊D5—64no—
187C22×Dic5—31no—
188C22×Dic5—31no—
189C22×Dic5—31no—
190C22×Dic5—32no—
191C22×Dic5—32no—
192C2×C4×D5—34no—
193C2×C4×D5—64no—
194C2×C4×D5—122no—
195C2×C4×D5—122no—
196C2×C4×D5—122no—
197C5×C22⋊C4—42no—
198C22⋊Dic5—34no—
199C22⋊Dic5—122no—
200#685—34no—
201#685—64no—
202C4⋊Dic5—122no—
203#683—34no—
204#683—122no—
205C4×Dic5—34no—
206C4×Dic5—122no—
207C2×C4×D4—151no—
208#388—152no—
209#387—152no—
210#386—152no—
211#385—152no—
212#383—151no—
213#382—151no—
214#381D1511yescharacteristic, complemented
215#380—151no—
216C4×C22⋊C4—151no—
217C2×#95—151no—
218C22×C3×C5—22no—
219C22×C3×C5—22no—
220C22×C3×C5—22no—
221C22×C3×C5—42no—
222C22×C3×C5—42no—
223C22×C3×C5C23×C411yescharacteristic
224C22×C3×C5C2×#4112yes—
225C22×C3×C5H(5,𝔽2)12yes—
226C22×C3×C5H(5,𝔽2)11yescharacteristic
227C22×C3×C52−1+411yescharacteristic
228C2×D15—22no—
229C2×D15—22no—
230C2×D15—24no—
231C2×D15—24no—
232C2×D15#11714yes—
233C3×C4×C5—22no—
234C3×C4×C5—22no—
235C3×C4×C5—42no—
236C3×C4×C5—42no—
237Dic15—22no—
238Dic15—22no—
239Dic15—22no—
240Dic15—42no—
241Dic15—42no—
242C24×C3C22×D511yescharacteristic
243C23×D3—51no—
244C22×C3×C4—42no—
245C22×C3×C4C4×D514yescomplemented
246C22×C3×C4C22×D512yes—
247C22×C3×C4C22×D512yes—
248C22×C3×C4C22×D511yescharacteristic
249C22×C3×C4C22×D511yescharacteristic
250C2×#67—54no—
251C2×#67—104no—
252C22×Dic3—51no—
253C22×Dic3—51no—
254C22×Dic3—51no—
255C22×Dic3—52no—
256C22×Dic3—52no—
257C2×C4×D3—54no—
258C2×C4×D3—104no—
259C2×C4×D3—202no—
260C2×C4×D3—202no—
261C2×C4×D3—202no—
262C3×C22⋊C4—42no—
263#217—54no—
264#217—202no—
265(C2×D3)⋊C4—54no—
266(C2×D3)⋊C4—104no—
267C4⋊Dic3—202no—
268Dic3⋊C4—54no—
269Dic3⋊C4—202no—
270C4×Dic3—54no—
271C4×Dic3—202no—
272C23×C5—22no—
273C23×C5—22no—
274C23×C5—21no—
275C23×C5—21no—
276C23×C5C2×C4×D312yes—
277C23×C5C23×D311yescharacteristic
278C22×D5—32no—
279C22×D5—34no—
280C22×D5—62no—
281C22×D5—61no—
282C22×D5—61no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5—44no—
292C2×C4×C5C2×C4×D312yes—
293C2×C4×C5C2×C4×D312yes—
294C22⋊D5—68no—
295C2×Dic5—32no—
296C2×Dic5—32no—
297C2×Dic5—32no—
298C2×Dic5—62no—
299C2×Dic5—62no—
300C2×Dic5—61no—
301C2×Dic5—61no—
302C2×Dic5—62no—
303C2×Dic5—62no—
304C2×Dic5—62no—
305C2×Dic5—62no—
306C2×Dic5—62no—
307C2×Dic5—62no—
308C4×D5—124no—
309C4×D5—128no—
310C22×D4—151no—
311C23×C4—151no—
312C23×C4—152no—
313C23×C4C2×D1511yescharacteristic
314C4×D4—158no—
315C2×C4⋊C4—151no—
316C2×C4⋊C4—152no—
317C2×C4⋊C4—152no—
318C2×C22⋊C4—151no—
319C2×C22⋊C4—151no—
320C2×C22⋊C4—152no—
321C2×C22⋊C4—152no—
322C2×C22⋊C4C2×D1512yes—
323C2×C42—151no—
324C2×C42—152no—
325#95—151no—
326#95—152no—
327#95—151no—
328#95—152no—
329#95—152no—
330#95—152no—
331#95C2×D1511yescharacteristic
332#95C2×D1511yescharacteristic
333#95C2×D1512yes—
334C2×C3×C5—42no—
335C2×C3×C5C2×#11711yescharacteristic
336C2×C3×C5#51811yescharacteristic
337C2×C3×C5#52011yescharacteristic
338C2×C3×C5#53812yes—
339C2×C3×C5#53912yes—
340D15—24no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3C2×C4×D512yes—
346C23×C3C23×D511yescharacteristic
347C22×D3—52no—
348C22×D3—54no—
349C22×D3—102no—
350C22×D3—101no—
351C22×D3—101no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—44no—
361C2×C3×C4C2×C4×D512yes—
362C2×C3×C4C2×C4×D512yes—
363#67—108no—
364C2×Dic3—52no—
365C2×Dic3—52no—
366C2×Dic3—52no—
367C2×Dic3—102no—
368C2×Dic3—102no—
369C2×Dic3—101no—
370C2×Dic3—101no—
371C2×Dic3—102no—
372C2×Dic3—102no—
373C2×Dic3—102no—
374C2×Dic3—102no—
375C2×Dic3—102no—
376C2×Dic3—102no—
377C4×D3—204no—
378C4×D3—208no—
379C22×C5—22no—
380C22×C5—22no—
381C22×C5—22no—
382C22×C5—42no—
383C22×C5—42no—
384C22×C5C22×C4×D311yescharacteristic
385C22×C5#100412yes—
386C22×C5D3×#4112yes—
387C22×C5#100911yescharacteristic
388C22×C5#101011yescharacteristic
389C2×D5—34no—
390C2×D5—64no—
391C2×D5—64no—
392C2×D5—62no—
393C2×D5—62no—
394C4×C5—22no—
395C4×C5—22no—
396C4×C5—42no—
397C4×C5—42no—
398Dic5—62no—
399Dic5—62no—
400Dic5—62no—
401Dic5—122no—
402Dic5—122no—
403C24—151no—
404C24C22×D1511yescharacteristic
405C2×D4—154no—
406C2×D4—304no—
407C22×C4—42no—
408C22×C4—151no—
409C22×C4—151no—
410C22×C4—151no—
411C22×C4—154no—
412C22×C4—152no—
413C22×C4—152no—
414C22×C4—304no—
415C22×C4—602no—
416C22×C4—602no—
417C22×C4—602no—
418C22×C4C4×D1514yescomplemented
419C22×C4C22×D1512yes—
420C22×C4C22×D1512yes—
421C22×C4C22×D1511yescharacteristic
422C22×C4C22×D1511yescharacteristic
423C4⋊C4—154no—
424C4⋊C4—602no—
425C4⋊C4—602no—
426C22⋊C4—42no—
427C22⋊C4—154no—
428C22⋊C4—154no—
429C22⋊C4—304no—
430C22⋊C4—602no—
431C42—154no—
432C42—602no—
433C3×C5#231811yescharacteristic, complemented, Hall
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3C22×C4×D511yescharacteristic
440C22×C3#414412yes—
441C22×C3D5×#4112yes—
442C22×C3#414911yescharacteristic
443C22×C3#415011yescharacteristic
444C2×D3—54no—
445C2×D3—102no—
446C2×D3—102no—
447C2×D3—104no—
448C2×D3—104no—
449C3×C4—22no—
450C3×C4—22no—
451C3×C4—42no—
452C3×C4—42no—
453Dic3—102no—
454Dic3—102no—
455Dic3—102no—
456Dic3—202no—
457Dic3—202no—
458C2×C5—42no—
459C2×C5#548611yescharacteristic
460C2×C5D3×#11711yescharacteristic
461C2×C5#552311yescharacteristic
462C2×C5#565712yes—
463C2×C5#566012yes—
464D5—64no—
465C23—22no—
466C23—22no—
467C23—21no—
468C23—21no—
469C23—152no—
470C23—154no—
471C23—302no—
472C23—301no—
473C23—301no—
474C23C2×C4×D1512yes—
475C23C23×D1511yescharacteristic
476D4—308no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—44no—
486C2×C4—152no—
487C2×C4—152no—
488C2×C4—152no—
489C2×C4—302no—
490C2×C4—302no—
491C2×C4—301no—
492C2×C4—301no—
493C2×C4—302no—
494C2×C4—302no—
495C2×C4—302no—
496C2×C4—302no—
497C2×C4—302no—
498C2×C4—302no—
499C2×C4—604no—
500C2×C4—608no—
501C2×C4C2×C4×D1512yes—
502C2×C4C2×C4×D1512yes—
503C2×C3—42no—
504C2×C3#6582011yescharacteristic
505C2×C3D5×#11711yescharacteristic
506C2×C3#6585711yescharacteristic
507C2×C3#6599112yes—
508C2×C3#6599412yes—
509D3—104no—
510C5#7412011yescharacteristic, complemented, Sylow
511C22—22no—
512C22—22no—
513C22—22no—
514C22—42no—
515C22—42no—
516C22—154no—
517C22—304no—
518C22—304no—
519C22—302no—
520C22—302no—
521C22C22×C4×D1511yescharacteristic
522C22#9209512yes—
523C22#41×D1512yes—
524C22#9210011yescharacteristic
525C22#9210111yescharacteristic
526C4—22no—
527C4—22no—
528C4—42no—
529C4—42no—
530C4—302no—
531C4—302no—
532C4—302no—
533C4—602no—
534C4—602no—
535C3#1060585111yescharacteristic, complemented, Sylow
536C2—42no—
537C2—304no—
538C2#1175624511yescharacteristic
539C2D15×#11711yescharacteristic
540C2#1175628211yescharacteristic
541C2#1175641612yes—
542C2#1175641912yes—
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#381C2
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenter#381D15
hypocenterC3×C5#2318
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. #11751313C2semidirect
5. #11751045C2semidirect
6. #11750769C2semidirect
7. #11750767C2semidirect
8. D15×#95C2semidirect
9. #11750756C2semidirect
10. #11750752C2semidirect
11. #11750751C2semidirect
20. C4×#1220C4semidirect
39. C5×#381D3semidirect
52. C22×C3×C4×C5C2×C4semidirect
71. #6719C2×C4semidirect
76. #6712C2×C4semidirect
78. C4×Dic15C2×C4semidirect
80. C3×#381D5semidirect
180. C22×C4×C5C4×D3semidirect
214. #381D15semidirect
245. C22×C3×C4C4×D5semidirect
418. C22×C4C4×D15semidirect
433. C3×C5#2318semidirect
510. C5#74120semidirect
535. C3#10605851semidirect

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
#117513132
#117510572
#117510452
#117507692
#117507672
D15×#952
#117507562
#117507522
#117507512
#106058513
#741205