Finite Group Databasebeta

← #14283002

Subgroups — #14283002

Order 1920.

668 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65961C211yesmaximal, characteristic
2D5×C3⋊#95C211yesmaximal, characteristic, complemented
3#11748499C211yesmaximal, characteristic, complemented
4#11746359C211yesmaximal, characteristic, complemented
5C5×#4538C211yesmaximal, characteristic, complemented
6#11745955C211yesmaximal, characteristic, complemented
7#11745954C211yesmaximal, characteristic, complemented
8#10599127—31nomaximal, Hall
9C2×C3×#713C411yescharacteristic, complemented
10C22×C3×C4×D5C2211yescharacteristic
11C22×D5×Dic3—21no—
12C3×C5×C22⋊Q8C2211yescharacteristic
13C3×#4092C411yescharacteristic, complemented
14C3×#4076C2211yescharacteristic
15C3×#4041C411yescharacteristic, complemented
16C3×#4040—21no—
17C3×#4039—21no—
18C3×#4038C411yescharacteristic, complemented
19C3×#4028—21no—
20C3×#4027—21no—
21C2×#6649—21no—
22#91115C2211yescharacteristic
23#91114C2211yescharacteristic
24C5×C3⋊#95C2211yescharacteristic
25C5×#830C2211yescharacteristic
26#90994—21no—
27#90955—21no—
28#71708—51nomaximal, Hall
29#65961D311yescharacteristic
30#65015—31no—
31D5×#95—31no—
32C5×#328—31no—
33#64758—31no—
34#64690—31no—
35#64671—31no—
36C23×C3×D5D411yescharacteristic
37C2×C3×C5×Q8C2×C411yescharacteristic, complemented
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C22×C5×Dic3—21no—
41C2×C3×C22⋊D5—21no—
42C22×C3×Dic5D411yescharacteristic
43C3×#713—42no—
44C2×C3×D20—21no—
45C2×C3×D20—21no—
46C2×C3×D20C2×C411yescharacteristic, complemented
47C2×C3×C4×D5—21no—
48C2×C3×C4×D5—42no—
49C2×C3×C4×D5C2×C411yescharacteristic
50C2×C3×C4×D5C2×C411yescharacteristic
51C2×C3×C4×D5D411yescharacteristic
52C2×C3×C4×D5D411yescharacteristic
53C2×D5×Dic3—24no—
54C2×D5×Dic3—42no—
55C2×D5×Dic3—42no—
56C3×C5×C4⋊C4—21no—
57C3×C5×C4⋊C4C2×C411yescharacteristic, complemented
58C3×C5×C22⋊C4—21no—
59C2×C3⋊#168—21no—
60C2×C5×C3⋊C8—21no—
61C3×#685—21no—
62C3×#685—21no—
63C3×#685—21no—
64C3×#685—21no—
65C3×C4⋊Dic5C2×C411yescharacteristic, complemented
66C3×#683—21no—
67C3×C4×Dic5—21no—
68#6649—42no—
69C3×#525—51no—
70C2×C3⋊#95—51no—
71#5207—51no—
72#4538—51no—
73#4538D511yescharacteristic, complemented
74#4537—51no—
75#4537—51no—
76C2×#713Dic311yescharacteristic, complemented
77C22×C4×D5—61no—
78C22×C4×D5C2×D311yescharacteristic
79C5×C22⋊Q8C2×D311yescharacteristic
80#4092Dic311yescharacteristic, complemented
81#4076C2×D311yescharacteristic
82C2×#676—61no—
83#4041Dic311yescharacteristic, complemented
84#4040—21no—
85#4039—21no—
86#4038Dic311yescharacteristic, complemented
87#4028—21no—
88#4027—21no—
89C5×C22⋊C8—31no—
90C5×#95—31no—
91#3963—31no—
92#3963—61no—
93C22⋊#168—31no—
94#3952—61no—
95#1504—151noSylow
96C23×C3×C5C2×D411yescharacteristic
97C22×C3×D5—21no—
98C22×C3×D5—21no—
99C22×C3×D5—22no—
100C22×C3×D5—22no—
101C22×C3×D5—21no—
102C22×C3×D5C22⋊C411yescharacteristic
103C22×C3×D5C22⋊C411yescharacteristic
104C3×C5×Q8—41no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×Dic15—22no—
111C2×Dic15—41no—
112C2×Dic15—41no—
113C2×C5×Dic3—22no—
114C2×C5×Dic3—41no—
115C2×C5×Dic3—41no—
116C3×C22⋊D5—41no—
117C3×C22⋊D5—41no—
118C2×C3×Dic5—21no—
119C2×C3×Dic5—41no—
120C2×C3×Dic5C22⋊C411yescharacteristic
121C2×C3×Dic5C22⋊C411yescharacteristic
122C3×D20—41no—
123C3×D20—42no—
124C3×D20—42no—
125C3×C4×D5—22no—
126C3×C4×D5—22no—
127C3×C4×D5—41no—
128C3×C4×D5—41no—
129C3×C4×D5—42no—
130D5×Dic3—48no—
131C3⋊#168—41no—
132C5×C3⋊C8—41no—
133C2×C3×#41—51no—
134C23×C3×C4—51no—
135C23×Dic3—101no—
136C3×#123—101no—
137C3×C22⋊Q8—51no—
138C3×C22⋊Q8C2×D511yescharacteristic
139C3×#121—51no—
140C3×#121—51no—
141C3×#120—101no—
142C3×C4×D4—101no—
143C3×C4×D4—101no—
144C3×#117—51no—
145C2×#208—101no—
146C3⋊#95—51no—
147C3⋊#95—101no—
148C3⋊#95C2×D511yescharacteristic
149#830—51no—
150#830—101no—
151#830C2×D511yescharacteristic
152C23×D5#6711yescharacteristic
153C2×C5×Q8C2×Dic311yescharacteristic, complemented
154C22×C4×C5—61no—
155C22×C4×C5C22×D311yescharacteristic
156C2×C22⋊D5—21no—
157C22×Dic5—61no—
158C22×Dic5#6711yescharacteristic
159#713—42no—
160C2×D20—21no—
161C2×D20—21no—
162C2×D20C2×Dic311yescharacteristic, complemented
163C2×C4×D5—21no—
164C2×C4×D5—42no—
165C2×C4×D5—64no—
166C2×C4×D5—122no—
167C2×C4×D5—122no—
168C2×C4×D5C2×Dic311yescharacteristic
169C2×C4×D5C2×Dic311yescharacteristic
170C2×C4×D5#6711yescharacteristic
171C2×C4×D5#6711yescharacteristic
172C2×C5×C8—61no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4C2×Dic311yescharacteristic, complemented
175C5×C22⋊C4—21no—
176#685—21no—
177#685—21no—
178#685—21no—
179#685—21no—
180C4⋊Dic5C2×Dic311yescharacteristic, complemented
181#683—21no—
182C4×Dic5—21no—
183C2×#168—61no—
184#676—122no—
185#525—51no—
186#407—151no—
187C2×#95—151no—
188#328—31no—
189#328—151no—
190#327—151no—
191#327—151no—
192C22×C3×C5—21no—
193C22×C3×C5—21no—
194C22×C3×C5C2×C22⋊C411yescharacteristic
195C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
196C22×C3×C5#13711yescharacteristic
197C2×C3×D5—24no—
198C2×C3×D5—24no—
199C2×C3×D5—21no—
200C2×C3×D5—21no—
201C2×C3×D5—21no—
202C2×C3×D5—21no—
203C2×C3×D5—41no—
204C2×C3×D5—41no—
205C2×C3×D5—41no—
206C2×C3×D5#9912yes—
207C2×C3×D5#10412yes—
208C3×C4×C5—21no—
209C3×C4×C5—21no—
210C3×C4×C5—41no—
211C3×C4×C5—41no—
212Dic15—42no—
213C3×Dic5—21no—
214C3×Dic5—21no—
215C3×Dic5—41no—
216C5×Dic3—42no—
217C24×C3—51no—
218C3×#41—202no—
219C2×C3×Q8C4×D511yescharacteristic, complemented
220C2×C3×D4—51no—
221C2×C3×D4—101no—
222C2×C3×D4—101no—
223C2×C3×D4—101no—
224C22×C3×C4—51no—
225C22×C3×C4—51no—
226C22×C3×C4—51no—
227C22×C3×C4—51no—
228C22×C3×C4—51no—
229C22×C3×C4—101no—
230C22×C3×C4—202no—
231C22×C3×C4C22×D511yescharacteristic
232C22×Dic3—21no—
233C22×Dic3—104no—
234C22×Dic3—101no—
235C22×Dic3—202no—
236C22×Dic3—202no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—51no—
239C3×C4⋊C4—101no—
240C3×C4⋊C4C4×D511yescharacteristic, complemented
241C3×C22⋊C4—21no—
242C3×C22⋊C4—101no—
243C3×C22⋊C4—101no—
244C3×C22⋊C4—101no—
245C3×C22⋊C4—101no—
246C3×C42—101no—
247#208—202no—
248C2×C3⋊C8—21no—
249C2×C3⋊C8—101no—
250C23×C5C2×#6711yescharacteristic
251C22×D5—21no—
252C22×D5—21no—
253C22×D5—22no—
254C22×D5—22no—
255C22×D5—21no—
256C22×D5#21711yescharacteristic
257C22×D5#21711yescharacteristic
258C5×Q8—41no—
259C2×C4×C5—21no—
260C2×C4×C5—21no—
261C2×C4×C5—41no—
262C2×C4×C5—62no—
263C2×C4×C5—121no—
264C2×C4×C5—121no—
265C2×C4×C5C22×Dic311yescharacteristic
266C2×C4×C5C2×#6711yescharacteristic
267C22⋊D5—41no—
268C22⋊D5—41no—
269C2×Dic5—21no—
270C2×Dic5—41no—
271C2×Dic5—62no—
272C2×Dic5—121no—
273C2×Dic5—121no—
274C2×Dic5#21711yescharacteristic
275C2×Dic5#21711yescharacteristic
276D20—41no—
277D20—42no—
278D20—42no—
279C4×D5—22no—
280C4×D5—22no—
281C4×D5—41no—
282C4×D5—41no—
283C4×D5—42no—
284C4×D5—128no—
285C5×C8—121no—
286#168—121no—
287C2×#41—51no—
288C23×C4—51no—
289C23×C4—301no—
290C2×M16—301no—
291#123—101no—
292C22⋊Q8—51no—
293C22⋊Q8D3×D511yescharacteristic
294#121—51no—
295#121—51no—
296#120—101no—
297C4×D4—101no—
298C4×D4—101no—
299#117—51no—
300C22⋊C8—31no—
301C22⋊C8—151no—
302C22⋊C8—301no—
303#95—31no—
304#95—151no—
305#95—301no—
306C2×C3×C5—21no—
307C2×C3×C5—21no—
308C2×C3×C5C2×#9911yescharacteristic
309C2×C3×C5#41711yescharacteristic
310C2×C3×C5C2×#10411yescharacteristic
311C3×D5—22no—
312C3×D5—22no—
313C3×D5—81no—
314C23×C3—51no—
315C23×C3—51no—
316C23×C3—102no—
317C23×C3—102no—
318C23×C3—101no—
319C23×C3—101no—
320C23×C3—101no—
321C23×C3D4×D511yescharacteristic
322C3×Q8—41no—
323C3×D4—201no—
324C3×D4—202no—
325C3×D4—202no—
326C3×D4—201no—
327C3×D4—201no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—41no—
331C2×C3×C4—51no—
332C2×C3×C4—51no—
333C2×C3×C4—102no—
334C2×C3×C4—102no—
335C2×C3×C4—101no—
336C2×C3×C4—201no—
337C2×C3×C4—201no—
338C2×C3×C4—202no—
339C2×C3×C4—201no—
340C2×C3×C4C2×C4×D511yescharacteristic
341C2×C3×C4D4×D511yescharacteristic
342C2×Dic3—22no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—102no—
346C2×Dic3—208no—
347C2×Dic3—201no—
348C2×Dic3—201no—
349C3⋊C8—41no—
350C3⋊C8—201no—
351C22×C5—21no—
352C22×C5—21no—
353C22×C5#94911yescharacteristic
354C22×C5#95111yescharacteristic
355C22×C5C2×#21711yescharacteristic
356C2×D5—24no—
357C2×D5—24no—
358C2×D5—21no—
359C2×D5—21no—
360C2×D5—21no—
361C2×D5—21no—
362C2×D5—41no—
363C2×D5—41no—
364C2×D5—41no—
365C2×D5#83412yes—
366C2×D5#83712yes—
367C4×C5—21no—
368C4×C5—21no—
369C4×C5—41no—
370C4×C5—41no—
371C4×C5—122no—
372Dic5—21no—
373Dic5—21no—
374Dic5—41no—
375Dic5—122no—
376C24—51no—
377#41—202no—
378C2×Q8D5×Dic311yescharacteristic, complemented
379C2×D4—51no—
380C2×D4—101no—
381C2×D4—101no—
382C2×D4—101no—
383C22×C4—51no—
384C22×C4—51no—
385C22×C4—51no—
386C22×C4—51no—
387C22×C4—51no—
388C22×C4—61no—
389C22×C4—101no—
390C22×C4—202no—
391C22×C4—304no—
392C22×C4—301no—
393C22×C4—602no—
394C22×C4—602no—
395C22×C4C2×D3×D511yescharacteristic
396M16—602no—
397C2×C8—61no—
398C2×C8—301no—
399C4⋊C4—21no—
400C4⋊C4—51no—
401C4⋊C4—101no—
402C4⋊C4D5×Dic311yescharacteristic, complemented
403C22⋊C4—21no—
404C22⋊C4—101no—
405C22⋊C4—101no—
406C22⋊C4—101no—
407C22⋊C4—101no—
408C42—101no—
409C3×C5#150411yescharacteristic, complemented, Hall
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—52no—
413C22×C3—52no—
414C22×C3—104no—
415C22×C3—104no—
416C22×C3—101no—
417C22×C3—101no—
418C22×C3—101no—
419C22×C3—101no—
420C22×C3—201no—
421C22×C3—201no—
422C22×C3—201no—
423C22×C3D5×C22⋊C411yescharacteristic
424C22×C3#406011yescharacteristic
425C22×C3#406411yescharacteristic
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—41no—
429C3×C4—41no—
430C3×C4—101no—
431C3×C4—101no—
432C3×C4—201no—
433Dic3—42no—
434Dic3—202no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5C2×#83411yescharacteristic
438C2×C5#523211yescharacteristic
439C2×C5C2×#83711yescharacteristic
440D5—22no—
441D5—22no—
442D5—81no—
443C23—51no—
444C23—51no—
445C23—102no—
446C23—102no—
447C23—101no—
448C23—101no—
449C23—101no—
450C23D5×#6711yescharacteristic
451Q8—41no—
452D4—201no—
453D4—202no—
454D4—202no—
455D4—201no—
456D4—201no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—41no—
460C2×C4—51no—
461C2×C4—51no—
462C2×C4—62no—
463C2×C4—102no—
464C2×C4—102no—
465C2×C4—101no—
466C2×C4—121no—
467C2×C4—121no—
468C2×C4—201no—
469C2×C4—201no—
470C2×C4—202no—
471C2×C4—201no—
472C2×C4—302no—
473C2×C4—608no—
474C2×C4—601no—
475C2×C4—601no—
476C2×C4C2×D5×Dic311yescharacteristic
477C2×C4D5×#6711yescharacteristic
478C8—121no—
479C8—601no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—102no—
483C2×C3—102no—
484C2×C3—401no—
485C2×C3D5×#9911yescharacteristic
486C2×C3#6509211yescharacteristic
487C2×C3D5×#10411yescharacteristic
488C5#7170811yescharacteristic, complemented, Sylow
489C22—21no—
490C22—21no—
491C22—52no—
492C22—52no—
493C22—104no—
494C22—104no—
495C22—101no—
496C22—101no—
497C22—101no—
498C22—101no—
499C22—201no—
500C22—201no—
501C22—201no—
502C22#9150211yescharacteristic
503C22#9150811yescharacteristic
504C22D5×#21711yescharacteristic
505C4—21no—
506C4—21no—
507C4—41no—
508C4—41no—
509C4—101no—
510C4—101no—
511C4—122no—
512C4—201no—
513C4—602no—
514C3#1059912711yescharacteristic, complemented, Sylow
515C2—21no—
516C2—21no—
517C2—102no—
518C2—102no—
519C2—401no—
520C2D5×#83411yescharacteristic
521C2#1174919811yescharacteristic
522C2D5×#83711yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#65961C2
cosocleC22×C3×C4×C5C23
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#1504
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. D5×C3⋊#95C2semidirect
3. #11748499C2semidirect
4. #11746359C2semidirect
5. C5×#4538C2semidirect
6. #11745955C2semidirect
7. #11745954C2semidirect
9. C2×C3×#713C4semidirect
13. C3×#4092C4semidirect
15. C3×#4041C4semidirect
18. C3×#4038C4semidirect
37. C2×C3×C5×Q8C2×C4semidirect
46. C2×C3×D20C2×C4semidirect
57. C3×C5×C4⋊C4C2×C4semidirect
65. C3×C4⋊Dic5C2×C4semidirect
73. #4538D5semidirect
76. C2×#713Dic3semidirect
80. #4092Dic3semidirect
83. #4041Dic3semidirect
86. #4038Dic3semidirect
153. C2×C5×Q8C2×Dic3semidirect
162. C2×D20C2×Dic3semidirect
174. C5×C4⋊C4C2×Dic3semidirect
180. C4⋊Dic5C2×Dic3semidirect
219. C2×C3×Q8C4×D5semidirect
240. C3×C4⋊C4C4×D5semidirect
378. C2×Q8D5×Dic3semidirect
402. C4⋊C4D5×Dic3semidirect
409. C3×C5#1504semidirect
488. C5#71708semidirect
514. C3#10599127semidirect

Maximal subgroups

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

subgroupindex
C3×#659612
D5×C3⋊#952
#117484992
#117463592
C5×#45382
#117459552
#117459542
#105991273
#717085