Finite Group Databasebeta

← #14294565

Subgroups — #14294565

Order 1920.

848 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4038C211yesmaximal, characteristic
2C2×#91358C211yesmaximal, characteristic
3C22×D5×C3⋊C8C211yesmaximal, characteristic
4#11746350C211yesmaximal, characteristic, complemented
5C5×#4529C211yesmaximal, characteristic, complemented
6#11745980C211yesmaximal, characteristic, complemented
7#11745979C211yesmaximal, characteristic, complemented
8#10599659—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C5×C4⋊Dic3C2211yescharacteristic
14C22×C5×C3⋊C8C2211yescharacteristic
15C2×C3×#685—21no—
16C2×C3×C4⋊Dic5C2211yescharacteristic
17C2×C3×C4×Dic5—21no—
18C3×#4038—22no—
19C3×#4038C414yescomplemented
20C2×#6665—21no—
21C2×Dic3×Dic5—21no—
22#91358—22no—
23#91358C414yescomplemented
24C2×D5×C3⋊C8—22no—
25C2×D5×C3⋊C8—22no—
26C2×D5×C3⋊C8C414yescomplemented
27#71580—51nomaximal, Hall
28C22×C8×D5—31no—
29C2×#4038—31no—
30C2×#4038D311yescharacteristic
31C5×#340—31no—
32#64771—31no—
33#64749—31no—
34#64749—31no—
35C23×C3×D5D411yescharacteristic
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C22×C5×Dic3—21no—
40C22×C3×Dic5—21no—
41C22×C3×Dic5D411yescharacteristic
42C2×C3×C4×D5C2×C412yes—
43C2×C3×C4×D5C2×C412yes—
44C2×C3×C4×D5C2×C412yes—
45C2×C3×C4×D5D412yes—
46C2×C3×C4×D5D412yes—
47C2×C3×C4×D5Q812yes—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4C2×C412yes—
50C4⋊Dic15—21no—
51C4⋊Dic15C2×C412yes—
52C2×C3⋊#168—21no—
53C2×C3⋊#168—21no—
54C2×C3⋊#168C2×C412yes—
55C5×C4⋊Dic3—21no—
56C5×C4⋊Dic3C2×C412yes—
57C2×C5×C3⋊C8—21no—
58C2×C5×C3⋊C8—21no—
59C2×C5×C3⋊C8C2×C412yes—
60C3×#685—24no—
61C3×C4⋊Dic5—21no—
62C3×C4⋊Dic5C2×C412yes—
63C3×C4×Dic5—24no—
64#6665—24no—
65Dic3×Dic5—24no—
66D5×C3⋊C8—28no—
67C2×C3×#117—51no—
68C2×#926—51no—
69C23×C3⋊C8—51no—
70#4529—51no—
71#4529—51no—
72#4529—51no—
73#4529D511yescharacteristic, complemented
74C22×C4×D5C2×D311yescharacteristic
75C22×C5×C8—31no—
76C2×C5×C4⋊C4—31no—
77C2×C5×C4⋊C4C2×D311yescharacteristic
78C2×#685—21no—
79C2×#685—61no—
80C2×C4⋊Dic5—31no—
81C2×C4⋊Dic5C2×D311yescharacteristic
82C2×C4×Dic5—21no—
83C2×C4×Dic5—61no—
84C22×#168—31no—
85C2×C8×D5—34no—
86C2×C8×D5—62no—
87C2×C8×D5—62no—
88#4038—22no—
89#4038—34no—
90#4038—62no—
91#4038Dic314yescomplemented
92#1735—151noSylow
93C23×C3×C5C2×D411yescharacteristic
94C22×C3×D5—21no—
95C22×C3×D5—21no—
96C22×C3×D5—21no—
97C22×C3×D5—21no—
98C22×C3×D5C22⋊C412yes—
99C22×C3×D5C22⋊C412yes—
100C22×C3×D5C4⋊C412yes—
101C2×C3×C4×C5—22no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5C22×C411yescharacteristic
105C2×C3×C4×C5C22×C411yescharacteristic
106C2×C3×C4×C5C22×C411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5C2×Q811yescharacteristic
110C2×Dic15—22no—
111C2×Dic15—41no—
112C2×Dic15—41no—
113C2×C5×Dic3—22no—
114C2×C5×Dic3—41no—
115C2×C5×Dic3—41no—
116C2×C3×Dic5—22no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—41no—
119C2×C3×Dic5C22⋊C412yes—
120C2×C3×Dic5C22⋊C412yes—
121C2×C3×Dic5C4⋊C412yes—
122C3×C4×D5C4214yes—
123C3×C4×D5C22⋊C414yes—
124C3×C4×D5C4⋊C414yes—
125C3×C4×D5C4⋊C414yes—
126C3⋊#168—22no—
127C5×C3⋊C8—22no—
128C23×C3×C4—51no—
129C3×#117—54no—
130C3×#117—102no—
131C2×C3×C4⋊C4—51no—
132C2×C3×C4⋊C4C2×D511yescharacteristic
133C2×C3×C22⋊C4—101no—
134C2×C3×C42—101no—
135C2×#217—101no—
136#926—54no—
137#926—102no—
138C2×C4⋊Dic3—51no—
139C2×C4⋊Dic3C2×D511yescharacteristic
140C2×C4×Dic3—101no—
141C22×C3⋊C8—51no—
142C22×C3⋊C8—54no—
143C22×C3⋊C8—102no—
144C22×C3⋊C8—102no—
145C22×C3⋊C8C2×D511yescharacteristic
146C23×D5#6711yescharacteristic
147C22×C4×C5—21no—
148C22×C4×C5—61no—
149C22×C4×C5C22×D311yescharacteristic
150C22×Dic5—21no—
151C22×Dic5—61no—
152C22×Dic5#6711yescharacteristic
153C2×C4×D5Dic612yes—
154C2×C4×D5C4×D312yes—
155C2×C4×D5C4×D312yes—
156C2×C4×D5D1212yes—
157C2×C4×D5C2×Dic312yes—
158C2×C4×D5#6712yes—
159C2×C5×C8—32no—
160C2×C5×C8—61no—
161C2×C5×C8—61no—
162C5×C4⋊C4—21no—
163C5×C4⋊C4—32no—
164C5×C4⋊C4—61no—
165C5×C4⋊C4C2×Dic312yes—
166#685—24no—
167#685—64no—
168C4⋊Dic5—21no—
169C4⋊Dic5—32no—
170C4⋊Dic5—61no—
171C4⋊Dic5C2×Dic312yes—
172C4×Dic5—24no—
173C4×Dic5—64no—
174C2×#168—32no—
175C2×#168—61no—
176C2×#168—61no—
177C8×D5—68no—
178C23×C8—151no—
179C2×#117—51no—
180C2×#117—151no—
181#340—31no—
182#340—151no—
183#340—151no—
184#340—151no—
185C22×C3×C5C2×C22⋊C411yescharacteristic
186C22×C3×C5C2×C22⋊C411yescharacteristic
187C22×C3×C5C2×C4⋊C411yescharacteristic
188C22×C3×C5#13511yescharacteristic
189C22×C3×C5#13511yescharacteristic
190C22×C3×C5#13511yescharacteristic
191C22×C3×C5#13511yescharacteristic
192C2×C3×D5—22no—
193C2×C3×D5—22no—
194C2×C3×D5—22no—
195C2×C3×D5—22no—
196C2×C3×D5—22no—
197C2×C3×D5—22no—
198C2×C3×D5#9514yes—
199C3×C4×C5—42no—
200C3×C4×C5C2×C4211yescharacteristic
201C3×C4×C5C2×C22⋊C411yescharacteristic
202C3×C4×C5C2×C4⋊C411yescharacteristic
203C3×C4×C5C2×C4⋊C411yescharacteristic
204Dic15—42no—
205C3×Dic5—42no—
206C3×Dic5#9514yes—
207C5×Dic3—42no—
208C24×C3—51no—
209C22×C3×C4—21no—
210C22×C3×C4—51no—
211C22×C3×C4—52no—
212C22×C3×C4—52no—
213C22×C3×C4—52no—
214C22×C3×C4—52no—
215C22×C3×C4—52no—
216C22×C3×C4—52no—
217C22×C3×C4—101no—
218C22×C3×C4C22×D511yescharacteristic
219C22×Dic3—21no—
220C22×Dic3—101no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—52no—
223C3×C4⋊C4—101no—
224C3×C4⋊C4C4×D512yes—
225C3×C22⋊C4—104no—
226C3×C42—104no—
227#217—104no—
228C4⋊Dic3—21no—
229C4⋊Dic3—52no—
230C4⋊Dic3—101no—
231C4⋊Dic3C4×D512yes—
232C4×Dic3—104no—
233C2×C3⋊C8—21no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—52no—
236C2×C3⋊C8—108no—
237C2×C3⋊C8—101no—
238C2×C3⋊C8—101no—
239C2×C3⋊C8C4×D512yes—
240C23×C5C2×#6711yescharacteristic
241C22×D5—21no—
242C22×D5—21no—
243C22×D5—21no—
244C22×D5—21no—
245C22×D5Dic3⋊C412yes—
246C22×D5(C2×D3)⋊C412yes—
247C22×D5#21712yes—
248C2×C4×C5—22no—
249C2×C4×C5—41no—
250C2×C4×C5—41no—
251C2×C4×C5—62no—
252C2×C4×C5—121no—
253C2×C4×C5—121no—
254C2×C4×C5C2×Dic611yescharacteristic
255C2×C4×C5C2×C4×D311yescharacteristic
256C2×C4×C5C2×C4×D311yescharacteristic
257C2×C4×C5C2×D1211yescharacteristic
258C2×C4×C5C22×Dic311yescharacteristic
259C2×C4×C5C2×#6711yescharacteristic
260C2×Dic5—22no—
261C2×Dic5—41no—
262C2×Dic5—41no—
263C2×Dic5—62no—
264C2×Dic5—121no—
265C2×Dic5—121no—
266C2×Dic5Dic3⋊C412yes—
267C2×Dic5(C2×D3)⋊C412yes—
268C2×Dic5#21712yes—
269C4×D5C4×Dic314yes—
270C4×D5Dic3⋊C414yes—
271C4×D5C4⋊Dic314yes—
272C4×D5(C2×D3)⋊C414yes—
273C5×C8—62no—
274#168—62no—
275C23×C4—51no—
276C22×C8—31no—
277C22×C8—154no—
278C22×C8—151no—
279C22×C8—302no—
280C22×C8—302no—
281#117—54no—
282#117—102no—
283#117—154no—
284#117—302no—
285C2×C4⋊C4—31no—
286C2×C4⋊C4—51no—
287C2×C4⋊C4—151no—
288C2×C4⋊C4D3×D511yescharacteristic
289C2×C22⋊C4—101no—
290C2×C22⋊C4—301no—
291C2×C42—101no—
292C2×C42—301no—
293C2×C3×C5C2×#9511yescharacteristic
294C2×C3×C5#41611yescharacteristic
295C2×C3×C5#41611yescharacteristic
296C2×C3×C5#41611yescharacteristic
297C2×C3×C5#41611yescharacteristic
298C2×C3×C5#42711yescharacteristic
299C2×C3×C5#42711yescharacteristic
300C3×D5—24no—
301C23×C3—52no—
302C23×C3—52no—
303C23×C3—52no—
304C23×C3—101no—
305C23×C3—101no—
306C23×C3—101no—
307C23×C3—101no—
308C23×C3D4×D511yescharacteristic
309C2×C3×C4—22no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—52no—
313C2×C3×C4—52no—
314C2×C3×C4—52no—
315C2×C3×C4—54no—
316C2×C3×C4—54no—
317C2×C3×C4—54no—
318C2×C3×C4—54no—
319C2×C3×C4—102no—
320C2×C3×C4—201no—
321C2×C3×C4—201no—
322C2×C3×C4C2×C4×D511yescharacteristic
323C2×C3×C4C2×C4×D511yescharacteristic
324C2×C3×C4C2×C4×D511yescharacteristic
325C2×C3×C4D4×D511yescharacteristic
326C2×C3×C4D4×D511yescharacteristic
327C2×C3×C4Q8×D511yescharacteristic
328C2×Dic3—22no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—102no—
332C2×Dic3—201no—
333C2×Dic3—201no—
334C3⋊C8—22no—
335C3⋊C8—102no—
336C22×C5C2×Dic3⋊C411yescharacteristic
337C22×C5C2×(C2×D3)⋊C411yescharacteristic
338C22×C5#95011yescharacteristic
339C22×C5#95011yescharacteristic
340C22×C5#95011yescharacteristic
341C22×C5#95011yescharacteristic
342C22×C5C2×#21711yescharacteristic
343C2×D5—22no—
344C2×D5—22no—
345C2×D5—22no—
346C2×D5—22no—
347C2×D5—22no—
348C2×D5—22no—
349C2×D5C3⋊#9514yes—
350C4×C5—42no—
351C4×C5—122no—
352C4×C5C2×C4×Dic311yescharacteristic
353C4×C5C2×Dic3⋊C411yescharacteristic
354C4×C5C2×C4⋊Dic311yescharacteristic
355C4×C5C2×(C2×D3)⋊C411yescharacteristic
356Dic5—42no—
357Dic5—122no—
358Dic5C3⋊#9514yes—
359C24—51no—
360C22×C4—21no—
361C22×C4—51no—
362C22×C4—52no—
363C22×C4—52no—
364C22×C4—52no—
365C22×C4—52no—
366C22×C4—52no—
367C22×C4—52no—
368C22×C4—61no—
369C22×C4—101no—
370C22×C4—301no—
371C22×C4C2×D3×D511yescharacteristic
372C2×C8—32no—
373C2×C8—61no—
374C2×C8—61no—
375C2×C8—152no—
376C2×C8—308no—
377C2×C8—301no—
378C2×C8—301no—
379C4⋊C4—21no—
380C4⋊C4—32no—
381C4⋊C4—52no—
382C4⋊C4—61no—
383C4⋊C4—101no—
384C4⋊C4—152no—
385C4⋊C4—301no—
386C4⋊C4D5×Dic312yes—
387C22⋊C4—104no—
388C22⋊C4—304no—
389C42—104no—
390C42—304no—
391C3×C5#173511yescharacteristic, complemented, Hall
392C22×C3—54no—
393C22×C3—102no—
394C22×C3—102no—
395C22×C3—102no—
396C22×C3—102no—
397C22×C3—102no—
398C22×C3—102no—
399C22×C3D5×C22⋊C411yescharacteristic
400C22×C3D5×C22⋊C411yescharacteristic
401C22×C3D5×C4⋊C411yescharacteristic
402C22×C3#405811yescharacteristic
403C22×C3#406211yescharacteristic
404C22×C3#406211yescharacteristic
405C22×C3#406511yescharacteristic
406C3×C4—42no—
407C3×C4—54no—
408C3×C4—202no—
409C3×C4C42×D511yescharacteristic
410C3×C4D5×C22⋊C411yescharacteristic
411C3×C4D5×C4⋊C411yescharacteristic
412C3×C4D5×C4⋊C411yescharacteristic
413Dic3—42no—
414Dic3—202no—
415C2×C5#499811yescharacteristic
416C2×C5#499811yescharacteristic
417C2×C5#500211yescharacteristic
418C2×C5#500211yescharacteristic
419C2×C5C2×C3⋊#9511yescharacteristic
420C2×C5#523311yescharacteristic
421C2×C5#523311yescharacteristic
422D5—24no—
423C23—52no—
424C23—52no—
425C23—52no—
426C23—101no—
427C23—101no—
428C23—101no—
429C23—101no—
430C23D5×#6711yescharacteristic
431C2×C4—22no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—52no—
435C2×C4—52no—
436C2×C4—52no—
437C2×C4—54no—
438C2×C4—54no—
439C2×C4—54no—
440C2×C4—54no—
441C2×C4—62no—
442C2×C4—102no—
443C2×C4—121no—
444C2×C4—121no—
445C2×C4—201no—
446C2×C4—201no—
447C2×C4—302no—
448C2×C4—601no—
449C2×C4—601no—
450C2×C4D5×Dic611yescharacteristic
451C2×C4C4×D3×D511yescharacteristic
452C2×C4C4×D3×D511yescharacteristic
453C2×C4D5×D1211yescharacteristic
454C2×C4C2×D5×Dic311yescharacteristic
455C2×C4D5×#6711yescharacteristic
456C8—62no—
457C8—302no—
458C2×C3—104no—
459C2×C3D5×#9511yescharacteristic
460C2×C3#6506111yescharacteristic
461C2×C3#6506111yescharacteristic
462C2×C3#6509311yescharacteristic
463C2×C3#6509311yescharacteristic
464C2×C3#6514911yescharacteristic
465C2×C3#6516911yescharacteristic
466C5#7158011yescharacteristic, complemented, Sylow
467C22—54no—
468C22—102no—
469C22—102no—
470C22—102no—
471C22—102no—
472C22—102no—
473C22—102no—
474C22D5×Dic3⋊C411yescharacteristic
475C22D5×(C2×D3)⋊C411yescharacteristic
476C22#9149011yescharacteristic
477C22#9149211yescharacteristic
478C22#9151411yescharacteristic
479C22#9151611yescharacteristic
480C22D5×#21711yescharacteristic
481C4—42no—
482C4—54no—
483C4—122no—
484C4—202no—
485C4—602no—
486C4C4×D5×Dic311yescharacteristic
487C4D5×Dic3⋊C411yescharacteristic
488C4D5×C4⋊Dic311yescharacteristic
489C4D5×(C2×D3)⋊C411yescharacteristic
490C3#1059965911yescharacteristic, complemented, Sylow
491C2—104no—
492C2#1174743211yescharacteristic
493C2#1174743311yescharacteristic
494C2#1174749911yescharacteristic
495C2#1174750111yescharacteristic
496C2D5×C3⋊#9511yescharacteristic
497C2#1174896111yescharacteristic
498C2#1174920711yescharacteristic
subgroupG/H
centerC23D5×#67
commutatorC3×C4×C5C2×C42
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC23×C3×D5D4
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1735
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11746350C2semidirect
5. C5×#4529C2semidirect
6. #11745980C2semidirect
7. #11745979C2semidirect
19. C3×#4038C4semidirect
23. #91358C4semidirect
26. C2×D5×C3⋊C8C4semidirect
73. #4529D5semidirect
91. #4038Dic3semidirect
391. C3×C5#1735semidirect
466. C5#71580semidirect
490. C3#10599659semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40382
C2×#913582
C22×D5×C3⋊C82
#117463502
C5×#45292
#117459802
#117459792
#105996593
#715805