Finite Group Databasebeta

← #14326601

Subgroups — #14326601

Order 1920.

1208 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91815C211yesmaximal, characteristic
2C22×C3×#683C211yesmaximal, characteristic
3C2×#91528C211yesmaximal, characteristic
4C5×#5211C211yesmaximal, characteristic
5#11749506C211yesmaximal, characteristic
6Dic5×#217C211yesmaximal, characteristic
7#11749471C211yesmaximal, characteristic
8#11748691C212yesmaximal, complemented
9#11748680C212yesmaximal, complemented
10#11748637C212yesmaximal, complemented
11#11748601C212yesmaximal, complemented
12#10605791—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×C3×Dic5C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C2×#6719C2211yescharacteristic
17C2×#6719C2211yescharacteristic
18#91815—24no—
19C2×C4⋊Dic15C2212yes—
20C2×C4×Dic15C2212yes—
21C2×C5×#217C2211yescharacteristic
22C2×C5×#217C2211yescharacteristic
23C2×C3×#683C418yescomplemented
24C2×C3×#683C2211yescharacteristic
25C2×C3×#683C2211yescharacteristic
26C2×C3×#683C2211yescharacteristic
27C2×C3×#683C2211yescharacteristic
28C2×#6668C2212yes—
29C2×#6668C2212yes—
30#91528—24no—
31C2×Dic3×Dic5C2212yes—
32C2×Dic3×Dic5C2212yes—
33C5×C3⋊#95C2212yes—
34C5×C3⋊#95C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#82159—51nomaximal, Hall
40C2×#4072—31no—
41C22×#683D311yescharacteristic
42C2×#4023—31no—
43C5×#381—31no—
44#65232—31no—
45#65231—31no—
46C22⋊C4×Dic5—31no—
47#64944—32no—
48#64941—32no—
49#64938—32no—
50#64936—32no—
51C24×C3×C5C2311yescharacteristic
52C22×C3×C4×C5—22no—
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5C2×C414yes—
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15C2312yes—
58C22×Dic15C2312yes—
59C22×C5×Dic3C2312yes—
60C22×C5×Dic3C2312yes—
61C22×C3×Dic5—22no—
62C22×C3×Dic5—22no—
63C22×C3×Dic5—24no—
64C22×C3×Dic5C2×C414yes—
65C22×C3×Dic5C2×C414yes—
66C22×C3×Dic5C2311yescharacteristic
67C22×C3×Dic5C2311yescharacteristic
68C22×C3×Dic5C2311yescharacteristic
69C22×C3×Dic5C2311yescharacteristic
70#6719—22no—
71#6719D414yes—
72C4⋊Dic15—24no—
73C4×Dic15—24no—
74C5×#217—22no—
75C5×#217—22no—
76C3×#683C2×C414yes—
77C3×#683C2×C414yes—
78C3×#683C2×C414yes—
79C3×#683C2×C414yes—
80#6668—24no—
81#6668—24no—
82Dic3×Dic5—24no—
83Dic3×Dic5—24no—
84C22×C3×C4⋊C4—51no—
85C2×#926—51no—
86C2×#926—51no—
87#5212—51no—
88#5211—51no—
89#5211D511yescharacteristic
90C4×#217—51no—
91#4984—52no—
92#4980—52no—
93#4980—52no—
94Dic3×C4⋊C4—52no—
95C23×C4×C5C2×D311yescharacteristic
96C23×Dic5C2×D311yescharacteristic
97C23×Dic5C2×D311yescharacteristic
98C2×C5×C22⋊C4—31no—
99C2×C5×C22⋊C4—31no—
100C2×C22⋊Dic5—31no—
101C2×C22⋊Dic5—31no—
102#4072—64no—
103C2×C4⋊Dic5—32no—
104C2×#683—32no—
105C2×#683—32no—
106C2×#683Dic318yescomplemented
107C2×#683C2×D311yescharacteristic
108C2×#683C2×D311yescharacteristic
109C2×#683C2×D311yescharacteristic
110C2×#683C2×D311yescharacteristic
111C2×C4×Dic5—32no—
112C2×C4×Dic5—32no—
113C2×C4×Dic5—32no—
114#4023—64no—
115C5×#95—32no—
116C5×#95—32no—
117#3963—32no—
118#3963—32no—
119#3963—32no—
120#3963—32no—
121#2344—151noSylow
122C23×C3×C5—22no—
123C23×C3×C5—22no—
124C23×C3×C5C22×C412yes—
125C23×C3×C5C2×D412yes—
126C23×C3×C5#4112yes—
127C23×C3×C5C2411yescharacteristic
128C2×C3×C4×C5—28no—
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5C22×C412yes—
134C2×C3×C4×C5C22×C412yes—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15C2×D414yes—
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—28no—
148C2×C3×Dic5—21no—
149C2×C3×Dic5—21no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5—28no—
154C2×C3×Dic5C22×C412yes—
155C2×C3×Dic5C22×C412yes—
156C2×C3×Dic5C22×C412yes—
157C2×C3×Dic5C22×C412yes—
158C2×C3×Dic5#4114yes—
159C23×C3×C4—51no—
160C23×C3×C4—51no—
161C23×C3×C4C2×D511yescharacteristic
162C2×C3×C4⋊C4—58no—
163C2×C3×C4⋊C4—51no—
164C2×C3×C4⋊C4—51no—
165C2×C3×C4⋊C4—51no—
166C2×C3×C4⋊C4—51no—
167C2×#217—51no—
168C2×#217—51no—
169C2×#217C2×D511yescharacteristic
170C2×#217C2×D511yescharacteristic
171#926—104no—
172#926—104no—
173C2×C4⋊Dic3—52no—
174C2×C4⋊Dic3—52no—
175C2×C4⋊Dic3—52no—
176C2×C4×Dic3—52no—
177C2×C4×Dic3—52no—
178C2×C4×Dic3—52no—
179C3⋊#95—52no—
180C3⋊#95—52no—
181C3⋊#95—52no—
182C3⋊#95—52no—
183C3⋊#95C2×D512yes—
184C3⋊#95C2×D512yes—
185C24×C5C22×D311yescharacteristic
186C22×C4×C5—22no—
187C22×C4×C5—22no—
188C22×C4×C5—32no—
189C22×C4×C5—32no—
190C22×C4×C5C2×Dic314yes—
191C22×C4×C5C22×D311yescharacteristic
192C22×C4×C5C22×D311yescharacteristic
193C22×Dic5—22no—
194C22×Dic5—22no—
195C22×Dic5—24no—
196C22×Dic5—32no—
197C22×Dic5—32no—
198C22×Dic5C2×Dic314yes—
199C22×Dic5C2×Dic314yes—
200C22×Dic5C22×D311yescharacteristic
201C22×Dic5C22×D311yescharacteristic
202C22×Dic5C22×D311yescharacteristic
203C22×Dic5C22×D311yescharacteristic
204C5×C22⋊C4—62no—
205C5×C22⋊C4—62no—
206C22⋊Dic5—34no—
207C22⋊Dic5—62no—
208C4⋊Dic5—64no—
209#683—64no—
210#683—64no—
211#683C2×Dic314yes—
212#683C2×Dic314yes—
213#683C2×Dic314yes—
214#683C2×Dic314yes—
215C4×Dic5—64no—
216C4×Dic5—64no—
217C4×Dic5—64no—
218C2×#117—151no—
219C2×#117—151no—
220C22×C4⋊C4—51no—
221#389—152no—
222#387—152no—
223#387—152no—
224#381—31no—
225#381—151no—
226#380—151no—
227C4×C4⋊C4—152no—
228C4×C22⋊C4—151no—
229C22×C3×C5—22no—
230C22×C3×C5—22no—
231C22×C3×C5—24no—
232C22×C3×C5—24no—
233C22×C3×C5C4×D414yes—
234C22×C3×C5C23×C411yescharacteristic
235C22×C3×C5C22×D411yescharacteristic
236C22×C3×C5C2×#4111yescharacteristic
237C22×C3×C5C2×#4112yes—
238C22×C3×C52−1+412yes—
239C3×C4×C5—22no—
240C3×C4×C5—22no—
241Dic15—24no—
242Dic15—42no—
243C3×Dic5—22no—
244C3×Dic5—22no—
245C3×Dic5—22no—
246C3×Dic5#11714yescomplemented
247C5×Dic3—42no—
248C5×Dic3—42no—
249C24×C3C22×D511yescharacteristic
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—51no—
253C22×C3×C4—54no—
254C22×C3×C4—54no—
255C22×C3×C4—51no—
256C22×C3×C4—51no—
257C22×C3×C4—51no—
258C22×C3×C4—104no—
259C22×C3×C4—102no—
260C22×C3×C4—102no—
261C22×C3×C4C4×D514yes—
262C22×C3×C4C22×D511yescharacteristic
263C22×C3×C4C22×D511yescharacteristic
264C22×Dic3—52no—
265C22×Dic3—52no—
266C22×Dic3C22×D512yes—
267C22×Dic3C22×D512yes—
268C3×C4⋊C4—54no—
269C3×C4⋊C4—54no—
270C3×C4⋊C4—54no—
271C3×C4⋊C4—54no—
272#217—22no—
273#217—22no—
274#217—54no—
275#217—102no—
276C4⋊Dic3—104no—
277C4⋊Dic3—104no—
278C4⋊Dic3—104no—
279C4×Dic3—104no—
280C4×Dic3—104no—
281C4×Dic3—104no—
282C23×C5—22no—
283C23×C5—22no—
284C23×C5D3×D412yes—
285C23×C5#23712yes—
286C23×C5C22×Dic312yes—
287C23×C5C23×D311yescharacteristic
288C2×C4×C5—28no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—62no—
294C2×C4×C5—62no—
295C2×C4×C5—62no—
296C2×C4×C5—62no—
297C2×C4×C5—62no—
298C2×C4×C5—62no—
299C2×C4×C5C22×Dic312yes—
300C2×C4×C5C22×Dic312yes—
301C2×Dic5—28no—
302C2×Dic5—22no—
303C2×Dic5—21no—
304C2×Dic5—21no—
305C2×Dic5—21no—
306C2×Dic5—21no—
307C2×Dic5—28no—
308C2×Dic5—34no—
309C2×Dic5—62no—
310C2×Dic5—62no—
311C2×Dic5—62no—
312C2×Dic5—62no—
313C2×Dic5—62no—
314C2×Dic5#23514yes—
315C2×Dic5C22×Dic312yes—
316C2×Dic5C22×Dic312yes—
317C2×Dic5C22×Dic312yes—
318C2×Dic5C22×Dic312yes—
319C23×C4—51no—
320C23×C4—51no—
321C23×C4D3×D511yescharacteristic
322#117—304no—
323#117—304no—
324C2×C4⋊C4—58no—
325C2×C4⋊C4—51no—
326C2×C4⋊C4—51no—
327C2×C4⋊C4—51no—
328C2×C4⋊C4—51no—
329C2×C4⋊C4—152no—
330C2×C4⋊C4—152no—
331C2×C4⋊C4—152no—
332C2×C22⋊C4—31no—
333C2×C22⋊C4—31no—
334C2×C22⋊C4—151no—
335C2×C22⋊C4—151no—
336C2×C42—152no—
337C2×C42—152no—
338C2×C42—152no—
339#95—32no—
340#95—32no—
341#95—152no—
342#95—152no—
343#95—152no—
344#95—152no—
345C2×C3×C5—24no—
346C2×C3×C5C2×#11711yescharacteristic
347C2×C3×C5C2×C4×D411yescharacteristic
348C2×C3×C5#51911yescharacteristic
349C2×C3×C5#54712yes—
350C2×C3×C5#55212yes—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3C2×C4×D512yes—
354C23×C3D4×D512yes—
355C23×C3#71112yes—
356C23×C3C23×D511yescharacteristic
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—28no—
362C2×C3×C4—52no—
363C2×C3×C4—54no—
364C2×C3×C4—52no—
365C2×C3×C4—52no—
366C2×C3×C4—52no—
367C2×C3×C4—108no—
368C2×C3×C4—101no—
369C2×C3×C4—101no—
370C2×C3×C4—101no—
371C2×C3×C4—101no—
372C2×C3×C4—102no—
373C2×C3×C4—108no—
374C2×C3×C4C2×C4×D512yes—
375C2×C3×C4C2×C4×D512yes—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—54no—
383C2×Dic3—102no—
384C2×Dic3—102no—
385C2×Dic3—102no—
386C2×Dic3—102no—
387C2×Dic3—102no—
388C22×C5—24no—
389C22×C5—24no—
390C22×C5—22no—
391C22×C5—22no—
392C22×C5D4×Dic314yes—
393C22×C5C2×#23512yes—
394C22×C5C2×D3×D411yescharacteristic
395C22×C5C2×#23711yescharacteristic
396C22×C5#100712yes—
397C22×C5C23×Dic311yescharacteristic
398C4×C5—22no—
399C4×C5—22no—
400C4×C5—122no—
401C4×C5—122no—
402Dic5—22no—
403Dic5—22no—
404Dic5—22no—
405Dic5—64no—
406Dic5—122no—
407Dic5#92614yescomplemented
408C24C2×D3×D511yescharacteristic
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—32no—
412C22×C4—32no—
413C22×C4—51no—
414C22×C4—54no—
415C22×C4—54no—
416C22×C4—51no—
417C22×C4—51no—
418C22×C4—51no—
419C22×C4—104no—
420C22×C4—102no—
421C22×C4—102no—
422C22×C4—152no—
423C22×C4—152no—
424C22×C4D5×Dic314yes—
425C22×C4C2×D3×D511yescharacteristic
426C22×C4C2×D3×D511yescharacteristic
427C4⋊C4—54no—
428C4⋊C4—54no—
429C4⋊C4—54no—
430C4⋊C4—54no—
431C4⋊C4—304no—
432C4⋊C4—304no—
433C4⋊C4—304no—
434C22⋊C4—62no—
435C22⋊C4—62no—
436C22⋊C4—154no—
437C22⋊C4—302no—
438C42—304no—
439C42—304no—
440C42—304no—
441C3×C5#234411yescharacteristic, complemented, Hall
442C22×C3—22no—
443C22×C3—22no—
444C22×C3—24no—
445C22×C3—24no—
446C22×C3#402714yes—
447C22×C3C22×C4×D511yescharacteristic
448C22×C3C2×D4×D511yescharacteristic
449C22×C3C2×#71111yescharacteristic
450C22×C3D5×#4112yes—
451C22×C3#415012yes—
452C3×C4—22no—
453C3×C4—22no—
454C3×C4—54no—
455C3×C4—102no—
456C3×C4—102no—
457C3×C4—102no—
458Dic3—42no—
459Dic3—42no—
460Dic3—104no—
461Dic3—202no—
462C2×C5—24no—
463C2×C5#550712yes—
464C2×C5#551312yes—
465C2×C5C2×#92611yescharacteristic
466C2×C5C2×D4×Dic311yescharacteristic
467C2×C5#581211yescharacteristic
468C23—22no—
469C23—22no—
470C23C2×D5×Dic312yes—
471C23#678012yes—
472C23#679012yes—
473C23C22×D3×D511yescharacteristic
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—28no—
479C2×C4—54no—
480C2×C4—52no—
481C2×C4—52no—
482C2×C4—52no—
483C2×C4—52no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—108no—
491C2×C4—102no—
492C2×C4—101no—
493C2×C4—101no—
494C2×C4—101no—
495C2×C4—101no—
496C2×C4—108no—
497C2×C4—154no—
498C2×C4—302no—
499C2×C4—302no—
500C2×C4—302no—
501C2×C4—302no—
502C2×C4—302no—
503C2×C4C2×D5×Dic312yes—
504C2×C4C2×D5×Dic312yes—
505C2×C3—24no—
506C2×C3C2×#402711yescharacteristic
507C2×C3#6585011yescharacteristic
508C2×C3D5×#11711yescharacteristic
509C2×C3#6598412yes—
510C2×C3#6598912yes—
511C5#8215911yescharacteristic, complemented, Sylow
512C22—24no—
513C22—22no—
514C22—24no—
515C22—22no—
516C22#9155914yes—
517C22#9200412yes—
518C22D5×#23512yes—
519C22C22×D5×Dic311yescharacteristic
520C22C2×#678011yescharacteristic
521C22C2×#679011yescharacteristic
522C4—22no—
523C4—22no—
524C4—54no—
525C4—102no—
526C4—102no—
527C4—102no—
528C4—122no—
529C4—122no—
530C4—304no—
531C4—602no—
532C3#1060579111yescharacteristic, complemented, Sylow
533C2—24no—
534C2#1175418811yescharacteristic
535C2#1175437612yes—
536C2D5×#92611yescharacteristic
537C2#1175441212yes—
538C2C2×#9155911yescharacteristic
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#2344
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
8. #11748691C2semidirect
9. #11748680C2semidirect
10. #11748637C2semidirect
11. #11748601C2semidirect
23. C2×C3×#683C4semidirect
106. C2×#683Dic3semidirect
246. C3×Dic5#117semidirect
407. Dic5#926semidirect
441. C3×C5#2344semidirect
511. C5#82159semidirect
532. C3#10605791semidirect

Maximal subgroups

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

subgroupindex
C2×#918152
C22×C3×#6832
C2×#915282
C5×#52112
#117495062
Dic5×#2172
#117494712
#117486912
#117486802
#117486372
#117486012
#106057913
#821595