Finite Group Databasebeta

← #14322751

Subgroups — #14322751

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4072C211yesmaximal, characteristic
2#11751313C211yesmaximal, characteristic
3C5×#5212C211yesmaximal, characteristic
4#11749486C212yesmaximal
5#11749485C212yesmaximal
6#11748834C211yesmaximal, characteristic, complemented
7#11748698C212yesmaximal, complemented
8#11748697C212yesmaximal, complemented
9Dic5×C4⋊Dic3C211yesmaximal, characteristic, complemented
10Dic5×C4⋊Dic3C211yesmaximal, characteristic, complemented
11#11748613C211yesmaximal, characteristic, complemented
12#10605599—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C2×#6719C2212yes—
15C2×C4⋊Dic15C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C5×#217C2212yes—
18C2×C5×C4⋊Dic3C2211yescharacteristic
19C2×C5×C4⋊Dic3C2211yescharacteristic
20C2×C3×C22⋊Dic5C2211yescharacteristic
21C2×C3×C22⋊Dic5C2211yescharacteristic
22C3×#4072C418yescomplemented
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C2×C3×C4×Dic5C2211yescharacteristic
26C2×C3×C4×Dic5C2211yescharacteristic
27C2×#6668C2212yes—
28C2×#6668C2212yes—
29C2×Dic3×Dic5C2212yes—
30C2×Dic3×Dic5C2212yes—
31#91115C2212yes—
32C5×C3⋊#95C2212yes—
33#90994C2212yes—
34#90994C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#82231—51nomaximal, Hall
38C2×#4072D311yescharacteristic
39C5×#380—31no—
40#65501—31no—
41#65266—31no—
42#65265—31no—
43C4⋊C4×Dic5—31no—
44C4⋊C4×Dic5—31no—
45#65234—32no—
46#65233—32no—
47#64943—32no—
48#64942—32no—
49C24×C3×C5C2311yescharacteristic
50C22×C3×C4×C5—22no—
51C22×C3×C4×C5—22no—
52C22×C3×C4×C5C2×C414yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2312yes—
57C22×C5×Dic3C2312yes—
58C22×C5×Dic3C2312yes—
59C22×C3×Dic5C2311yescharacteristic
60C22×C3×Dic5C2311yescharacteristic
61C22×C3×Dic5C2311yescharacteristic
62C22×C3×Dic5C2311yescharacteristic
63#6719—42no—
64C4⋊Dic15—22no—
65C4⋊Dic15—22no—
66C5×#217—42no—
67C5×C4⋊Dic3—22no—
68C5×C4⋊Dic3—22no—
69C3×C22⋊Dic5C2×C414yes—
70C3×C22⋊Dic5C2×C414yes—
71C3×C4⋊Dic5C2×C414yes—
72C3×C4⋊Dic5C2×C414yes—
73C3×C4×Dic5C2×C414yes—
74C3×C4×Dic5C2×C414yes—
75#6668—42no—
76#6668—42no—
77Dic3×Dic5—42no—
78Dic3×Dic5—42no—
79C2×C3×#117—51no—
80#5212—51no—
81#5212D511yescharacteristic
82#4980—52no—
83#4980—52no—
84#4951—52no—
85#4951—52no—
86#4936—51no—
87#4935—51no—
88C4×C4⋊Dic3—51no—
89C4×C4⋊Dic3—51no—
90C23×C4×C5C2×D311yescharacteristic
91C2×C5×C4⋊C4—31no—
92C2×C5×C4⋊C4—31no—
93C2×C5×C22⋊C4—32no—
94C2×C22⋊Dic5—32no—
95C2×C22⋊Dic5C2×D311yescharacteristic
96C2×C22⋊Dic5C2×D311yescharacteristic
97#4072Dic318yescomplemented
98C2×C4⋊Dic5—31no—
99C2×C4⋊Dic5—31no—
100C2×C4⋊Dic5C2×D311yescharacteristic
101C2×C4⋊Dic5C2×D311yescharacteristic
102C2×#683—32no—
103C2×#683—32no—
104C2×C4×Dic5—32no—
105C2×C4×Dic5—32no—
106C2×C4×Dic5C2×D311yescharacteristic
107C2×C4×Dic5C2×D311yescharacteristic
108C5×#95—32no—
109#3963—32no—
110#3963—32no—
111#3963—32no—
112#3963—32no—
113#3963—32no—
114#2314—151noSylow
115C23×C3×C5—21no—
116C23×C3×C5—21no—
117C23×C3×C5—21no—
118C23×C3×C5—21no—
119C23×C3×C5—21no—
120C23×C3×C5—21no—
121C23×C3×C5C22×C412yes—
122C23×C3×C5C2411yescharacteristic
123C2×C3×C4×C5—21no—
124C2×C3×C4×C5—21no—
125C2×C3×C4×C5—28no—
126C2×C3×C4×C5C22×C412yes—
127C2×C3×C4×C5C22×C412yes—
128C2×C3×C4×C5#4112yes—
129C2×C3×C4×C5#4112yes—
130C2×Dic15—22no—
131C2×Dic15—22no—
132C2×Dic15—22no—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×C5×Dic3—22no—
137C2×C5×Dic3—22no—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—22no—
141C2×C5×Dic3—22no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—21no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5—21no—
148C2×C3×Dic5—21no—
149C2×C3×Dic5—21no—
150C2×C3×Dic5C22×C412yes—
151C2×C3×Dic5C22×C412yes—
152C2×C3×Dic5C22×C412yes—
153C2×C3×Dic5C22×C412yes—
154C23×C3×C4C2×D511yescharacteristic
155C3×#117—58no—
156C2×C3×C4⋊C4—51no—
157C2×C3×C4⋊C4—51no—
158C2×C3×C22⋊C4—51no—
159C2×C3×C22⋊C4—51no—
160C2×C3×C42—51no—
161C2×C3×C42—51no—
162C2×#217—52no—
163C2×#217C2×D512yes—
164C2×C4⋊Dic3—51no—
165C2×C4⋊Dic3—51no—
166C2×C4⋊Dic3—52no—
167C2×C4⋊Dic3—52no—
168C2×C4⋊Dic3C2×D511yescharacteristic
169C2×C4⋊Dic3C2×D511yescharacteristic
170C2×C4×Dic3—52no—
171C2×C4×Dic3—52no—
172C3⋊#95—52no—
173C3⋊#95—52no—
174C3⋊#95—52no—
175C3⋊#95—52no—
176C3⋊#95—52no—
177C3⋊#95C2×D512yes—
178C24×C5C22×D311yescharacteristic
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5—32no—
182C22×C4×C5—32no—
183C22×C4×C5C2×Dic314yes—
184C22×C4×C5C22×D311yescharacteristic
185C22×C4×C5C22×D311yescharacteristic
186C22×Dic5—32no—
187C22×Dic5—32no—
188C22×Dic5C22×D311yescharacteristic
189C22×Dic5C22×D311yescharacteristic
190C22×Dic5C22×D311yescharacteristic
191C22×Dic5C22×D311yescharacteristic
192C5×C4⋊C4—62no—
193C5×C4⋊C4—62no—
194C5×C22⋊C4—122no—
195C22⋊Dic5—122no—
196C22⋊Dic5C2×Dic314yes—
197C22⋊Dic5C2×Dic314yes—
198C4⋊Dic5—62no—
199C4⋊Dic5—62no—
200C4⋊Dic5C2×Dic314yes—
201C4⋊Dic5C2×Dic314yes—
202#683—122no—
203#683—122no—
204C4×Dic5—122no—
205C4×Dic5—122no—
206C4×Dic5C2×Dic314yes—
207C4×Dic5C2×Dic314yes—
208C2×#117—51no—
209#388—152no—
210#388—152no—
211#387—152no—
212#387—152no—
213#384—151no—
214#382—151no—
215#380—31no—
216#380—151no—
217C4×C4⋊C4—151no—
218C4×C4⋊C4—151no—
219C22×C3×C5—22no—
220C22×C3×C5—22no—
221C22×C3×C5—22no—
222C22×C3×C5—41no—
223C22×C3×C5—41no—
224C22×C3×C5—41no—
225C22×C3×C5—41no—
226C22×C3×C5C23×C411yescharacteristic
227C22×C3×C5C2×#4111yescharacteristic
228C22×C3×C5C2×#4111yescharacteristic
229C22×C3×C5H(5,𝔽2)11yescharacteristic
230C22×C3×C5H(5,𝔽2)11yescharacteristic
231C22×C3×C52−1+411yescharacteristic
232C22×C3×C52−1+411yescharacteristic
233C3×C4×C5—22no—
234C3×C4×C5#11714yes—
235Dic15—42no—
236Dic15—42no—
237C3×Dic5—22no—
238C3×Dic5—22no—
239C3×Dic5—22no—
240C3×Dic5—22no—
241C5×Dic3—42no—
242C5×Dic3—42no—
243C24×C3C22×D511yescharacteristic
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—51no—
247C22×C3×C4—51no—
248C22×C3×C4—51no—
249C22×C3×C4—51no—
250C22×C3×C4C4×D514yes—
251C22×C3×C4C22×D511yescharacteristic
252C22×C3×C4C22×D511yescharacteristic
253C22×Dic3—52no—
254C22×Dic3—52no—
255C22×Dic3C22×D512yes—
256C22×Dic3C22×D512yes—
257C3×C4⋊C4—54no—
258C3×C4⋊C4—54no—
259C3×C22⋊C4—54no—
260C3×C22⋊C4—54no—
261C3×C42—54no—
262C3×C42—54no—
263#217—42no—
264#217—202no—
265C4⋊Dic3—22no—
266C4⋊Dic3—22no—
267C4⋊Dic3—102no—
268C4⋊Dic3—102no—
269C4⋊Dic3—202no—
270C4⋊Dic3—202no—
271C4×Dic3—202no—
272C4×Dic3—202no—
273C23×C5—21no—
274C23×C5—21no—
275C23×C5—21no—
276C23×C5—21no—
277C23×C5—21no—
278C23×C5—21no—
279C23×C5C22×Dic312yes—
280C23×C5C23×D311yescharacteristic
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—28no—
284C2×C4×C5—62no—
285C2×C4×C5—62no—
286C2×C4×C5—62no—
287C2×C4×C5—62no—
288C2×C4×C5—62no—
289C2×C4×C5—62no—
290C2×C4×C5#23512yes—
291C2×C4×C5#23512yes—
292C2×C4×C5C22×Dic312yes—
293C2×C4×C5C22×Dic312yes—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—21no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—62no—
303C2×Dic5—62no—
304C2×Dic5—62no—
305C2×Dic5—62no—
306C2×Dic5—62no—
307C2×Dic5—62no—
308C2×Dic5C22×Dic312yes—
309C2×Dic5C22×Dic312yes—
310C2×Dic5C22×Dic312yes—
311C2×Dic5C22×Dic312yes—
312C23×C4D3×D511yescharacteristic
313#117—58no—
314C2×C4⋊C4—31no—
315C2×C4⋊C4—31no—
316C2×C4⋊C4—51no—
317C2×C4⋊C4—51no—
318C2×C4⋊C4—151no—
319C2×C4⋊C4—151no—
320C2×C4⋊C4—152no—
321C2×C4⋊C4—152no—
322C2×C22⋊C4—32no—
323C2×C22⋊C4—51no—
324C2×C22⋊C4—51no—
325C2×C22⋊C4—152no—
326C2×C42—51no—
327C2×C42—51no—
328C2×C42—152no—
329C2×C42—152no—
330#95—32no—
331#95—152no—
332#95—152no—
333#95—152no—
334#95—152no—
335#95—152no—
336C2×C3×C5—42no—
337C2×C3×C5C2×#11711yescharacteristic
338C2×C3×C5#52011yescharacteristic
339C2×C3×C5#52011yescharacteristic
340C2×C3×C5#54011yescharacteristic
341C2×C3×C5#54111yescharacteristic
342C2×C3×C5#54211yescharacteristic
343C2×C3×C5#54211yescharacteristic
344C23×C3—21no—
345C23×C3—21no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—21no—
350C23×C3C2×C4×D512yes—
351C23×C3C23×D511yescharacteristic
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—28no—
355C2×C3×C4—52no—
356C2×C3×C4—52no—
357C2×C3×C4—52no—
358C2×C3×C4—52no—
359C2×C3×C4—101no—
360C2×C3×C4—101no—
361C2×C3×C4—101no—
362C2×C3×C4—101no—
363C2×C3×C4—101no—
364C2×C3×C4—101no—
365C2×C3×C4—101no—
366C2×C3×C4—101no—
367C2×C3×C4C2×C4×D512yes—
368C2×C3×C4C2×C4×D512yes—
369C2×C3×C4#71112yes—
370C2×C3×C4#71112yes—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—102no—
378C2×Dic3—102no—
379C2×Dic3—102no—
380C2×Dic3—102no—
381C2×Dic3—102no—
382C2×Dic3—102no—
383C22×C5—22no—
384C22×C5—22no—
385C22×C5—22no—
386C22×C5—41no—
387C22×C5—41no—
388C22×C5—41no—
389C22×C5—41no—
390C22×C5C2×#23511yescharacteristic
391C22×C5C2×#23511yescharacteristic
392C22×C5#100911yescharacteristic
393C22×C5#100911yescharacteristic
394C22×C5#101011yescharacteristic
395C22×C5#101011yescharacteristic
396C22×C5C23×Dic311yescharacteristic
397C4×C5—22no—
398C4×C5—122no—
399C4×C5—122no—
400C4×C5#92614yes—
401Dic5—22no—
402Dic5—22no—
403Dic5—22no—
404Dic5—22no—
405Dic5—122no—
406Dic5—122no—
407C24C2×D3×D511yescharacteristic
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—32no—
411C22×C4—32no—
412C22×C4—51no—
413C22×C4—51no—
414C22×C4—51no—
415C22×C4—51no—
416C22×C4—152no—
417C22×C4—152no—
418C22×C4D5×Dic314yes—
419C22×C4C2×D3×D511yescharacteristic
420C22×C4C2×D3×D511yescharacteristic
421C4⋊C4—54no—
422C4⋊C4—54no—
423C4⋊C4—62no—
424C4⋊C4—62no—
425C4⋊C4—302no—
426C4⋊C4—302no—
427C4⋊C4—602no—
428C4⋊C4—602no—
429C22⋊C4—54no—
430C22⋊C4—54no—
431C22⋊C4—122no—
432C22⋊C4—602no—
433C42—54no—
434C42—54no—
435C42—602no—
436C42—602no—
437C3×C5#231411yescharacteristic, complemented, Hall
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—22no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3C22×C4×D511yescharacteristic
446C22×C3C2×#71111yescharacteristic
447C22×C3C2×#71111yescharacteristic
448C22×C3#414411yescharacteristic
449C22×C3#414711yescharacteristic
450C22×C3#414911yescharacteristic
451C22×C3#415011yescharacteristic
452C3×C4—22no—
453C3×C4—102no—
454C3×C4—102no—
455C3×C4—102no—
456C3×C4—102no—
457C3×C4#402314yes—
458Dic3—42no—
459Dic3—42no—
460Dic3—202no—
461Dic3—202no—
462C2×C5—42no—
463C2×C5#551811yescharacteristic
464C2×C5#553411yescharacteristic
465C2×C5#553411yescharacteristic
466C2×C5#553511yescharacteristic
467C2×C5C2×#92611yescharacteristic
468C2×C5#582711yescharacteristic
469C2×C5#582711yescharacteristic
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23C2×D5×Dic312yes—
477C23C22×D3×D511yescharacteristic
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—28no—
481C2×C4—52no—
482C2×C4—52no—
483C2×C4—52no—
484C2×C4—52no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—101no—
492C2×C4—101no—
493C2×C4—101no—
494C2×C4—101no—
495C2×C4—101no—
496C2×C4—101no—
497C2×C4—101no—
498C2×C4—101no—
499C2×C4—302no—
500C2×C4—302no—
501C2×C4—302no—
502C2×C4—302no—
503C2×C4—302no—
504C2×C4—302no—
505C2×C4C2×D5×Dic312yes—
506C2×C4C2×D5×Dic312yes—
507C2×C4#678212yes—
508C2×C4#678212yes—
509C2×C3—42no—
510C2×C3C2×#402311yescharacteristic
511C2×C3#6583811yescharacteristic
512C2×C3#6585711yescharacteristic
513C2×C3#6593711yescharacteristic
514C2×C3#6595311yescharacteristic
515C2×C3#6595911yescharacteristic
516C2×C3#6597711yescharacteristic
517C5#8223111yescharacteristic, complemented, Sylow
518C22—22no—
519C22—22no—
520C22—22no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22#9200011yescharacteristic
526C22#9200111yescharacteristic
527C22#9201811yescharacteristic
528C22#9201911yescharacteristic
529C22C22×D5×Dic311yescharacteristic
530C22C2×#678211yescharacteristic
531C22C2×#678211yescharacteristic
532C4—22no—
533C4—102no—
534C4—102no—
535C4—102no—
536C4—102no—
537C4—122no—
538C4—122no—
539C4—602no—
540C4—602no—
541C4#9152814yes—
542C3#1060559911yescharacteristic, complemented, Sylow
543C2—42no—
544C2#1175418411yescharacteristic
545C2#1175421211yescharacteristic
546C2#1175449911yescharacteristic
547C2#1175450411yescharacteristic
548C2#1175450711yescharacteristic
549C2#1175450911yescharacteristic
550C2C2×#9152811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#2314
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. #11748834C2semidirect
7. #11748698C2semidirect
8. #11748697C2semidirect
9. Dic5×C4⋊Dic3C2semidirect
10. Dic5×C4⋊Dic3C2semidirect
11. #11748613C2semidirect
22. C3×#4072C4semidirect
97. #4072Dic3semidirect
437. C3×C5#2314semidirect
517. C5#82231semidirect
542. C3#10605599semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40722
#117513132
C5×#52122
#117494862
#117494852
#117488342
#117486982
#117486972
Dic5×C4⋊Dic32
#117486132
#106055993
#822315