Finite Group Databasebeta

← #14327585

Subgroups — #14327585

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
2C5×#5212C211yesmaximal, characteristic, complemented
3C2×C3×#3963C211yesmaximal, characteristic, complemented
4#11749494C212yesmaximal
5Dic5×#217C212yesmaximal, complemented
6#11748687C212yesmaximal, complemented
7#11748685C212yesmaximal, complemented
8#11748670C211yesmaximal, characteristic, complemented
9#11748653C211yesmaximal, characteristic, complemented
10#11748621C211yesmaximal, characteristic, complemented
11#11748606C211yesmaximal, characteristic, complemented
12#10605615—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×#1220C2211yescharacteristic
15C22×C4×D15C2211yescharacteristic
16C23×C3×Dic5C2212yes—
17C2×#6719C2211yescharacteristic
18C4×#1220C418yescomplemented
19C2×#6714C2211yescharacteristic
20C2×#6712C2211yescharacteristic
21C2×C4×Dic15C2211yescharacteristic
22C2×C5×#217C2212yes—
23C2×C5×C4⋊Dic3C2212yes—
24C2×#6667C2212yes—
25C2×#6667C2212yes—
26C2×Dic3×Dic5C2212yes—
27C2×Dic3×Dic5C2212yes—
28C5×C3⋊#95C2211yescharacteristic
29C5×C3⋊#95C2211yescharacteristic
30C3×#3963C2211yescharacteristic
31C3×#3963C2211yescharacteristic
32C3×#3963C2212yes—
33#90994C2212yes—
34#90994C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#73336—51nomaximal, Hall
38C2×C4×C22⋊D5—31no—
39C5×#380—31no—
40C2×#3963D311yescharacteristic, complemented
41#65279—32no—
42#65267—32no—
43#65247—32no—
44C22⋊C4×Dic5—32no—
45#64955—31no—
46#64953—31no—
47#64940—31no—
48#64937—31no—
49C24×C3×C5C2311yescharacteristic
50C23×D15C2311yescharacteristic
51C22×C3×C4×C5—42no—
52C22×C3×C4×C5C2×C414yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C2×#1220—22no—
56C2×#1220—22no—
57C2×#1220C2×C414yes—
58C22×Dic15C2311yescharacteristic
59C22×Dic15C2311yescharacteristic
60C22×Dic15C2311yescharacteristic
61C2×C4×D15—42no—
62C2×C4×D15C2×C414yescomplemented
63C22×C5×Dic3C2312yes—
64C22×C5×Dic3C2312yes—
65C22×C3×Dic5—24no—
66C22×C3×Dic5—24no—
67C22×C3×Dic5—42no—
68C22×C3×Dic5C2312yes—
69C22×C3×Dic5C2312yes—
70#6719C2×C414yes—
71#6714C2×C414yescomplemented
72#6712C2×C414yescomplemented
73C4×Dic15C2×C414yescomplemented
74C5×#217—24no—
75C5×C4⋊Dic3—42no—
76#6667—24no—
77#6667—42no—
78Dic3×Dic5—24no—
79Dic3×Dic5—42no—
80C2×C4×#67—51no—
81C2×C3×#95—51no—
82#5213—52no—
83#5212D511yescharacteristic, complemented
84C4×#217—52no—
85#4670—52no—
86#4666—51no—
87#4664—51no—
88#4655—52no—
89#4651—51no—
90#4648—51no—
91C23×C4×C5C2×D311yescharacteristic
92C22×C22⋊D5—31no—
93C23×Dic5C2×D312yes—
94C22×C4×D5—31no—
95C2×C5×C4⋊C4—32no—
96C2×C5×C22⋊C4—32no—
97C2×C22⋊Dic5—31no—
98C4×C22⋊D5—38no—
99C2×#685—31no—
100C2×#685—32no—
101C2×#685—32no—
102C2×#683—31no—
103C2×C4×Dic5—31no—
104C2×C4×Dic5—32no—
105C2×C4×Dic5—32no—
106C5×#95—31no—
107C5×#95—31no—
108#3963—32no—
109#3963—32no—
110#3963—32no—
111#3963—32no—
112#3963C2×D311yescharacteristic
113#3963C2×D311yescharacteristic
114#3963C2×D312yes—
115#2353—151noSylow
116C23×C3×C5—22no—
117C23×C3×C5—22no—
118C23×C3×C5C22×C412yes—
119C23×C3×C5#4112yes—
120C23×C3×C5#4112yes—
121C23×C3×C5C2411yescharacteristic
122C22×D15—22no—
123C22×D15—21no—
124C22×D15—21no—
125C22×D15—22no—
126C22×D15C22×C412yes—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—44no—
130C2×C3×C4×C5C22×C412yes—
131C2×C3×C4×C5C22×C412yes—
132#1220—28no—
133C2×Dic15—22no—
134C2×Dic15—21no—
135C2×Dic15—21no—
136C2×Dic15—22no—
137C2×Dic15C22×C412yes—
138C2×Dic15C22×C412yes—
139C2×Dic15C22×C412yes—
140C4×D15—44no—
141C2×C5×Dic3—22no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—22no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—48no—
153C2×C3×Dic5#4114yes—
154C23×C3×C4—52no—
155C23×C3×C4C2×D511yescharacteristic
156C22×#67—51no—
157C22×C4×D3—51no—
158C2×#217—51no—
159C2×#217C2×D512yes—
160C4×#67—58no—
161C2×(C2×D3)⋊C4—51no—
162C2×(C2×D3)⋊C4—52no—
163C2×(C2×D3)⋊C4—52no—
164C2×C4⋊Dic3C2×D512yes—
165C2×Dic3⋊C4—51no—
166C2×C4×Dic3—51no—
167C2×C4×Dic3—52no—
168C2×C4×Dic3—52no—
169C3×#95—51no—
170C3×#95—51no—
171C3×#95—52no—
172C3⋊#95—52no—
173C3⋊#95—52no—
174C3⋊#95—52no—
175C3⋊#95—52no—
176C3⋊#95C2×D511yescharacteristic
177C3⋊#95C2×D511yescharacteristic
178C24×C5C22×D311yescharacteristic
179C23×D5—31no—
180C22×C4×C5—32no—
181C22×C4×C5—32no—
182C22×C4×C5—42no—
183C22×C4×C5C4×D314yes—
184C22×C4×C5C22×D311yescharacteristic
185C22×C4×C5C22×D311yescharacteristic
186C2×C22⋊D5—34no—
187C2×C22⋊D5—62no—
188C2×C22⋊D5—62no—
189C22×Dic5—24no—
190C22×Dic5—24no—
191C22×Dic5—31no—
192C22×Dic5—31no—
193C22×Dic5—31no—
194C22×Dic5—42no—
195C22×Dic5C22×D312yes—
196C22×Dic5C22×D312yes—
197C2×C4×D5—34no—
198C2×C4×D5—122no—
199C5×C4⋊C4—122no—
200C5×C22⋊C4—64no—
201C22⋊Dic5—34no—
202#685—34no—
203#685—64no—
204#685—122no—
205#683—34no—
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#381—151no—
215#380—31no—
216C4×C22⋊C4—151no—
217C4×C22⋊C4—152no—
218#376—151no—
219C2×#95—51no—
220C22×C3×C5—22no—
221C22×C3×C5—22no—
222C22×C3×C5—24no—
223C22×C3×C5—24no—
224C22×C3×C5#11714yes—
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—22no—
233C2×D15—42no—
234C2×D15—42no—
235C3×C4×C5—22no—
236C3×C4×C5—22no—
237Dic15—22no—
238Dic15—22no—
239Dic15—22no—
240C3×Dic5—24no—
241C3×Dic5—42no—
242C5×Dic3—42no—
243C5×Dic3—42no—
244C24×C3C22×D511yescharacteristic
245C23×D3—51no—
246C22×C3×C4—42no—
247C22×C3×C4—52no—
248C22×C3×C4—52no—
249C22×C3×C4—104no—
250C22×C3×C4—104no—
251C22×C3×C4—202no—
252C22×C3×C4C4×D514yes—
253C22×C3×C4C22×D511yescharacteristic
254C22×C3×C4C22×D511yescharacteristic
255C2×#67—54no—
256C2×#67—102no—
257C2×#67—102no—
258C22×Dic3—51no—
259C22×Dic3—51no—
260C22×Dic3—51no—
261C22×Dic3C22×D512yes—
262C22×Dic3C22×D512yes—
263C2×C4×D3—54no—
264C2×C4×D3—202no—
265#217—24no—
266#217—54no—
267(C2×D3)⋊C4—54no—
268(C2×D3)⋊C4—104no—
269(C2×D3)⋊C4—202no—
270C4⋊Dic3—42no—
271Dic3⋊C4—54no—
272C4×Dic3—54no—
273C4×Dic3—104no—
274C4×Dic3—202no—
275C23×C5—22no—
276C23×C5—22no—
277C23×C5C2×C4×D312yes—
278C23×C5#23712yes—
279C23×C5#23912yes—
280C23×C5C23×D311yescharacteristic
281C22×D5—32no—
282C22×D5—62no—
283C22×D5—61no—
284C22×D5—62no—
285C22×D5—61no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—44no—
289C2×C4×C5—62no—
290C2×C4×C5—62no—
291C2×C4×C5—62no—
292C2×C4×C5—62no—
293C2×C4×C5—62no—
294C2×C4×C5—62no—
295C2×C4×C5C2×C4×D312yes—
296C2×C4×C5C2×C4×D312yes—
297C22⋊D5—68no—
298C2×Dic5—22no—
299C2×Dic5—22no—
300C2×Dic5—22no—
301C2×Dic5—22no—
302C2×Dic5—22no—
303C2×Dic5—32no—
304C2×Dic5—32no—
305C2×Dic5—32no—
306C2×Dic5—48no—
307C2×Dic5—62no—
308C2×Dic5—61no—
309C2×Dic5—62no—
310C2×Dic5—61no—
311C2×Dic5#23514yes—
312C4×D5—124no—
313C22×D4—151no—
314C23×C4—52no—
315C23×C4—151no—
316C23×C4D3×D511yescharacteristic
317C4×D4—158no—
318C2×C4⋊C4—32no—
319C2×C4⋊C4—151no—
320C2×C22⋊C4—32no—
321C2×C22⋊C4—151no—
322C2×C22⋊C4—151no—
323C2×C22⋊C4—152no—
324C2×C22⋊C4—152no—
325C2×C42—151no—
326C2×C42—152no—
327C2×C42—152no—
328#95—31no—
329#95—31no—
330#95—51no—
331#95—51no—
332#95—52no—
333#95—152no—
334#95—152no—
335#95—152no—
336#95—152no—
337C2×C3×C5—24no—
338C2×C3×C5C2×#11711yescharacteristic
339C2×C3×C5C4×#4111yescharacteristic
340C2×C3×C5#51811yescharacteristic
341C2×C3×C5#55112yes—
342C2×C3×C5#55312yes—
343D15—42no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3C2×C4×D512yes—
347C23×C3#71112yes—
348C23×C3#71312yes—
349C23×C3C23×D511yescharacteristic
350C22×D3—52no—
351C22×D3—101no—
352C22×D3—102no—
353C22×D3—101no—
354C22×D3—102no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—44no—
358C2×C3×C4—54no—
359C2×C3×C4—102no—
360C2×C3×C4—102no—
361C2×C3×C4—102no—
362C2×C3×C4—102no—
363C2×C3×C4—102no—
364C2×C3×C4—208no—
365C2×C3×C4C2×C4×D512yes—
366C2×C3×C4C2×C4×D512yes—
367#67—108no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—52no—
375C2×Dic3—52no—
376C2×Dic3—52no—
377C2×Dic3—101no—
378C2×Dic3—102no—
379C2×Dic3—101no—
380C2×Dic3—102no—
381C4×D3—204no—
382C22×C5—22no—
383C22×C5—22no—
384C22×C5—24no—
385C22×C5—24no—
386C22×C5#89214yes—
387C22×C5C22×C4×D311yescharacteristic
388C22×C5C2×#23512yes—
389C22×C5C2×#23711yescharacteristic
390C22×C5#100412yes—
391C22×C5C2×#23911yescharacteristic
392C2×D5—62no—
393C2×D5—62no—
394C2×D5—62no—
395C2×D5—122no—
396C2×D5—122no—
397C4×C5—22no—
398C4×C5—22no—
399C4×C5—122no—
400C4×C5—122no—
401Dic5—24no—
402Dic5—42no—
403Dic5—62no—
404Dic5—62no—
405Dic5—62no—
406C24—151no—
407C24C2×D3×D511yescharacteristic
408C2×D4—154no—
409C2×D4—302no—
410C2×D4—302no—
411C22×C4—32no—
412C22×C4—32no—
413C22×C4—42no—
414C22×C4—52no—
415C22×C4—52no—
416C22×C4—104no—
417C22×C4—104no—
418C22×C4—151no—
419C22×C4—151no—
420C22×C4—151no—
421C22×C4—154no—
422C22×C4—202no—
423C22×C4—602no—
424C22×C4#120014yes—
425C22×C4C2×D3×D511yescharacteristic
426C22×C4C2×D3×D511yescharacteristic
427C4⋊C4—122no—
428C4⋊C4—154no—
429C22⋊C4—64no—
430C22⋊C4—154no—
431C22⋊C4—154no—
432C22⋊C4—304no—
433C22⋊C4—602no—
434C42—154no—
435C42—304no—
436C42—602no—
437C3×C5#235311yescharacteristic, complemented, Hall
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—24no—
441C22×C3—24no—
442C22×C3#403814yes—
443C22×C3C22×C4×D511yescharacteristic
444C22×C3C2×#71111yescharacteristic
445C22×C3#414412yes—
446C22×C3C2×#71311yescharacteristic
447C22×C3D5×#4112yes—
448C2×D3—102no—
449C2×D3—102no—
450C2×D3—102no—
451C2×D3—202no—
452C2×D3—202no—
453C3×C4—22no—
454C3×C4—22no—
455C3×C4—104no—
456C3×C4—202no—
457Dic3—42no—
458Dic3—42no—
459Dic3—102no—
460Dic3—102no—
461Dic3—102no—
462C2×C5—24no—
463C2×C5C4×#23511yescharacteristic
464C2×C5#548611yescharacteristic
465C2×C5#549512yes—
466C2×C5C2×#89211yescharacteristic
467C2×C5#551412yes—
468D5—122no—
469C23—22no—
470C23—22no—
471C23—152no—
472C23—301no—
473C23—301no—
474C23—302no—
475C23—302no—
476C23#676612yes—
477C23#676812yes—
478C23C2×#120012yes—
479C23C22×D3×D511yescharacteristic
480D4—308no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—44no—
484C2×C4—54no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—102no—
492C2×C4—102no—
493C2×C4—102no—
494C2×C4—102no—
495C2×C4—102no—
496C2×C4—152no—
497C2×C4—152no—
498C2×C4—152no—
499C2×C4—208no—
500C2×C4—301no—
501C2×C4—301no—
502C2×C4—302no—
503C2×C4—302no—
504C2×C4—604no—
505C2×C4C2×#120012yes—
506C2×C4C2×#120012yes—
507C2×C3—24no—
508C2×C3#6582011yescharacteristic
509C2×C3C2×#403811yescharacteristic
510C2×C3#6585611yescharacteristic
511C2×C3#6593512yes—
512C2×C3#6597112yes—
513D3—202no—
514C5#7333611yescharacteristic, complemented, Sylow
515C22—22no—
516C22—24no—
517C22—24no—
518C22—22no—
519C22—302no—
520C22—302no—
521C22—302no—
522C22—602no—
523C22—602no—
524C22#9134714yes—
525C22C2×#676611yescharacteristic
526C22C2×#676811yescharacteristic
527C22D5×#23512yes—
528C22C22×#120011yescharacteristic
529C22#9204912yes—
530C4—22no—
531C4—22no—
532C4—104no—
533C4—122no—
534C4—122no—
535C4—202no—
536C4—302no—
537C4—302no—
538C4—302no—
539C3#1060561511yescharacteristic, complemented, Sylow
540C2—24no—
541C2—602no—
542C2C2×#9134711yescharacteristic
543C2#1175440212yes—
544C2#1175441312yes—
545C2#1175441411yescharacteristic
546C2#1175541311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2353
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C5×#5212C2semidirect
3. C2×C3×#3963C2semidirect
5. Dic5×#217C2semidirect
6. #11748687C2semidirect
7. #11748685C2semidirect
8. #11748670C2semidirect
9. #11748653C2semidirect
10. #11748621C2semidirect
11. #11748606C2semidirect
18. C4×#1220C4semidirect
40. C2×#3963D3semidirect
62. C2×C4×D15C2×C4semidirect
71. #6714C2×C4semidirect
72. #6712C2×C4semidirect
73. C4×Dic15C2×C4semidirect
83. #5212D5semidirect
437. C3×C5#2353semidirect
514. C5#73336semidirect
539. C3#10605615semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12202
C5×#52122
C2×C3×#39632
#117494942
Dic5×#2172
#117486872
#117486852
#117486702
#117486532
#117486212
#117486062
#106056153
#733365