Finite Group Databasebeta

← #14283433

Subgroups — #14283433

Order 1920.

572 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754527C211yesmaximal, characteristic
2C3×#64956C211yesmaximal, characteristic, complemented
3#11748499C211yesmaximal, characteristic, complemented
4#11746272C211yesmaximal, characteristic, complemented
5C5×#4452C211yesmaximal, characteristic, complemented
6#11745962C211yesmaximal, characteristic, complemented
7#11745958C211yesmaximal, characteristic, complemented
8#10599130—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C2×#6773C411yescharacteristic, complemented
11#91819C2211yescharacteristic
12C5×#924C2211yescharacteristic
13C2×C3×#685—21no—
14C2×C3×#683—21no—
15#91564—21no—
16#91552—21no—
17#91450C411yescharacteristic, complemented
18#91444—21no—
19#91359C411yescharacteristic, complemented
20#91358C411yescharacteristic, complemented
21#91348—21no—
22C2×#6649—21no—
23C3×C5×#95C2211yescharacteristic
24#91114C2211yescharacteristic
25C5×#830C2211yescharacteristic
26C3×#3963C2211yescharacteristic
27#90955—21no—
28#69508—51nomaximal, Hall
29#65961—31no—
30#65015—31no—
31#64956D311yescharacteristic, complemented
32C5×#328—31no—
33#64758—31no—
34#64690—31no—
35#64671—31no—
36C23×C3×D5D411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40C2×D60C2×C411yescharacteristic
41C2×C5×Dic6C2×C411yescharacteristic
42C22×C3×Dic5—21no—
43C22×C3×Dic5D411yescharacteristic
44C2×C3×C4×D5—42no—
45C2×C3×C4×D5C2×C411yescharacteristic
46C2×C3×C4×D5C2×C411yescharacteristic
47C2×C3×C4×D5D411yescharacteristic
48C2×C3×C4×D5D411yescharacteristic
49C2×#1202—21no—
50C2×#1202—21no—
51C2×#1200—21no—
52#6773—42no—
53#6714—21no—
54C4⋊Dic15C2×C411yescharacteristic
55C2×C3⋊#168—21no—
56C5×#217—21no—
57C5×C4⋊Dic3C2×C411yescharacteristic
58C5×Dic3⋊C4—21no—
59C2×C5×C3⋊C8—21no—
60C3×#685—42no—
61C3×#683—42no—
62#6669—21no—
63#6667—21no—
64#6665—21no—
65#6665—21no—
66Dic3×Dic5—21no—
67#6649—42no—
68#5791—51no—
69C3×#380—51no—
70#5207—51no—
71#4452—51no—
72#4452D511yescharacteristic, complemented
73#4451—51no—
74#4451—51no—
75C2×#713—31no—
76C22×C4×D5C2×D311yescharacteristic
77C5×C22⋊Q8—31no—
78#4092—31no—
79#4076—31no—
80C2×#685—21no—
81C2×#683—21no—
82C2×#676—61no—
83#4041—31no—
84#4040—61no—
85#4039—61no—
86#4038—31no—
87#4028—61no—
88#4027—61no—
89C5×C22⋊C8—31no—
90C5×#95C2×D311yescharacteristic
91#3963C2×D311yescharacteristic
92C22⋊#168—31no—
93#3952—61no—
94#1513—151noSylow
95C23×C3×C5C2×D411yescharacteristic
96C22×D15—21no—
97C22×C3×D5—21no—
98C22×C3×D5—21no—
99C22×C3×D5—41no—
100C22×C3×D5—41no—
101C22×C3×D5C22⋊C411yescharacteristic
102C22×C3×D5C22⋊C411yescharacteristic
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5C22×C411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109#1220—41no—
110#1220—41no—
111C2×Dic15—21no—
112D60—41no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3—21no—
115C5×Dic6—41no—
116C2×C3×Dic5—22no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—41no—
119C2×C3×Dic5—41no—
120C2×C3×Dic5C22⋊C411yescharacteristic
121C2×C3×Dic5C22⋊C411yescharacteristic
122C3×C4×D5—22no—
123C3×C4×D5—22no—
124C3×C4×D5—41no—
125C3×C4×D5—41no—
126#1202—42no—
127#1202—42no—
128#1200—42no—
129C3⋊#168—41no—
130C5×C3⋊C8—41no—
131C23×C3×C4—51no—
132C2×#235—51no—
133C2×C3×C4⋊C4—101no—
134C2×C3×C22⋊C4—101no—
135#953—101no—
136#930—51no—
137#930—51no—
138#929—101no—
139C4×#67—101no—
140C4×#67—101no—
141#926—51no—
142#924—51no—
143#924C2×D511yescharacteristic
144C2×#208—101no—
145C3×#95—51no—
146C3×#95C2×D511yescharacteristic
147#830—51no—
148#830—101no—
149#830C2×D511yescharacteristic
150C23×D5#6711yescharacteristic
151C2×C5×Q8—31no—
152C22×C4×C5—21no—
153C22×C4×C5C22×D311yescharacteristic
154C2×C22⋊D5—61no—
155C22×Dic5—21no—
156C22×Dic5#6711yescharacteristic
157#713—122no—
158C2×D20—31no—
159C2×D20—61no—
160C2×D20—61no—
161C2×C4×D5—42no—
162C2×C4×D5—61no—
163C2×C4×D5C4×D311yescharacteristic
164C2×C4×D5C4×D311yescharacteristic
165C2×C4×D5D1211yescharacteristic
166C2×C4×D5D1211yescharacteristic
167C2×C5×C8—61no—
168C5×C4⋊C4—31no—
169C5×C4⋊C4—61no—
170C5×C22⋊C4—61no—
171#685—42no—
172#685—61no—
173#685—61no—
174#685—61no—
175#685—61no—
176C4⋊Dic5—31no—
177#683—42no—
178#683—61no—
179C4×Dic5—61no—
180C2×#168—61no—
181#676—122no—
182#525—151no—
183#407—151no—
184#380—51no—
185#328—31no—
186#328—151no—
187#327—151no—
188#327—151no—
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5C2×C22⋊C411yescharacteristic
192C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
193C22×C3×C5#13711yescharacteristic
194C2×D15—41no—
195C2×D15—41no—
196C2×D15—41no—
197C2×C3×D5—21no—
198C2×C3×D5—21no—
199C2×C3×D5—21no—
200C2×C3×D5—21no—
201C2×C3×D5—21no—
202C2×C3×D5—21no—
203C2×C3×D5—42no—
204C2×C3×D5—42no—
205C3×C4×C5—21no—
206C3×C4×C5—21no—
207C3×C4×C5—81no—
208Dic15—41no—
209C3×Dic5—21no—
210C3×Dic5—81no—
211C3×Dic5#9912yes—
212C5×Dic3—41no—
213C5×Dic3—41no—
214C24×C3—51no—
215C22×C3×C4—21no—
216C22×C3×C4—51no—
217C22×C3×C4—51no—
218C22×C3×C4—51no—
219C22×C3×C4—51no—
220C22×C3×C4—51no—
221C22×C3×C4—101no—
222C22×C3×C4—202no—
223C22×C3×C4C22×D511yescharacteristic
224C2×#67—101no—
225C2×#67—101no—
226C2×#67—101no—
227#235—202no—
228C2×D12—51no—
229C2×C4×D3—101no—
230C2×Dic6C4×D511yescharacteristic
231C3×C4⋊C4—202no—
232C3×C22⋊C4—202no—
233#217—21no—
234#217—101no—
235#217—101no—
236(C2×D3)⋊C4—101no—
237(C2×D3)⋊C4—101no—
238C4⋊Dic3—51no—
239C4⋊Dic3C4×D511yescharacteristic
240Dic3⋊C4—21no—
241Dic3⋊C4—101no—
242C4×Dic3—101no—
243#208—202no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—101no—
246C23×C5C2×#6711yescharacteristic
247C22×D5—21no—
248C22×D5—21no—
249C22×D5—41no—
250C22×D5—41no—
251C22×D5—61no—
252C22×D5(C2×D3)⋊C411yescharacteristic
253C22×D5(C2×D3)⋊C411yescharacteristic
254C5×Q8—121no—
255C2×C4×C5—41no—
256C2×C4×C5—41no—
257C2×C4×C5—41no—
258C2×C4×C5—41no—
259C2×C4×C5—61no—
260C2×C4×C5—61no—
261C2×C4×C5C2×C4×D311yescharacteristic
262C2×C4×C5C2×D1211yescharacteristic
263C22⋊D5—121no—
264C22⋊D5—121no—
265C2×Dic5—22no—
266C2×Dic5—41no—
267C2×Dic5—41no—
268C2×Dic5—41no—
269C2×Dic5—61no—
270C2×Dic5(C2×D3)⋊C411yescharacteristic
271C2×Dic5(C2×D3)⋊C411yescharacteristic
272D20—121no—
273D20—122no—
274D20—122no—
275C4×D5—22no—
276C4×D5—22no—
277C4×D5—41no—
278C4×D5—41no—
279C4×D5—122no—
280C5×C8—121no—
281#168—121no—
282C2×#41—151no—
283C23×C4—51no—
284C2×M16—301no—
285#123—301no—
286C22⋊Q8—31no—
287C22⋊Q8—151no—
288#121—151no—
289#121—151no—
290#120—301no—
291C4×D4—301no—
292C4×D4—301no—
293#117—151no—
294C2×C4⋊C4—101no—
295C2×C22⋊C4—101no—
296C22⋊C8—31no—
297C22⋊C8—151no—
298C22⋊C8—301no—
299#95—51no—
300#95D3×D511yescharacteristic
301C2×C3×C5—21no—
302C2×C3×C5—21no—
303C2×C3×C5C2×#9911yescharacteristic
304C2×C3×C5#41711yescharacteristic
305C2×C3×C5#42111yescharacteristic
306D15—81no—
307C3×D5—41no—
308C3×D5—41no—
309C23×C3—51no—
310C23×C3—51no—
311C23×C3—101no—
312C23×C3—101no—
313C23×C3—201no—
314C23×C3—201no—
315C23×C3D4×D511yescharacteristic
316C22×D3—101no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—51no—
322C2×C3×C4—51no—
323C2×C3×C4—102no—
324C2×C3×C4—102no—
325C2×C3×C4—102no—
326C2×C3×C4—201no—
327C2×C3×C4—201no—
328C2×C3×C4—201no—
329C2×C3×C4—201no—
330C2×C3×C4—201no—
331C2×C3×C4C2×C4×D511yescharacteristic
332C2×C3×C4D4×D511yescharacteristic
333#67—202no—
334#67—202no—
335#67—201no—
336#67—201no—
337C2×Dic3—21no—
338C2×Dic3—21no—
339C2×Dic3—101no—
340D12—201no—
341C4×D3—202no—
342Dic6—41no—
343C3⋊C8—41no—
344C3⋊C8—201no—
345C22×C5—21no—
346C22×C5—21no—
347C22×C5C2×(C2×D3)⋊C411yescharacteristic
348C22×C5#93211yescharacteristic
349C22×C5#94211yescharacteristic
350C2×D5—21no—
351C2×D5—21no—
352C2×D5—21no—
353C2×D5—21no—
354C2×D5—21no—
355C2×D5—21no—
356C2×D5—42no—
357C2×D5—42no—
358C2×D5—121no—
359C2×D5—121no—
360C2×D5—121no—
361C4×C5—21no—
362C4×C5—21no—
363C4×C5—81no—
364C4×C5—121no—
365C4×C5—121no—
366Dic5—21no—
367Dic5—81no—
368Dic5—121no—
369Dic5#80612yes—
370C24—51no—
371#41—602no—
372C2×Q8—31no—
373C2×D4—151no—
374C2×D4—301no—
375C2×D4—301no—
376C2×D4—301no—
377C22×C4—21no—
378C22×C4—51no—
379C22×C4—51no—
380C22×C4—51no—
381C22×C4—51no—
382C22×C4—51no—
383C22×C4—101no—
384C22×C4—202no—
385C22×C4—301no—
386C22×C4C2×D3×D511yescharacteristic
387M16—602no—
388C2×C8—61no—
389C2×C8—301no—
390C4⋊C4—31no—
391C4⋊C4—61no—
392C4⋊C4—151no—
393C4⋊C4—202no—
394C4⋊C4—301no—
395C22⋊C4—61no—
396C22⋊C4—202no—
397C22⋊C4—301no—
398C22⋊C4—301no—
399C22⋊C4—301no—
400C22⋊C4—301no—
401C42—301no—
402C3×C5#151311yescharacteristic, complemented, Hall
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—101no—
406C22×C3—101no—
407C22×C3—101no—
408C22×C3—101no—
409C22×C3—101no—
410C22×C3—101no—
411C22×C3—202no—
412C22×C3—202no—
413C22×C3D5×C22⋊C411yescharacteristic
414C22×C3#406011yescharacteristic
415C22×C3#406411yescharacteristic
416C2×D3—201no—
417C2×D3—201no—
418C2×D3—201no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—52no—
422C3×C4—81no—
423C3×C4—101no—
424C3×C4—401no—
425Dic3—41no—
426Dic3—41no—
427Dic3—201no—
428C2×C5—21no—
429C2×C5—21no—
430C2×C5C2×#80611yescharacteristic
431C2×C5#496611yescharacteristic
432C2×C5#500511yescharacteristic
433D5—41no—
434D5—41no—
435D5—241no—
436C23—51no—
437C23—51no—
438C23—101no—
439C23—101no—
440C23—201no—
441C23—201no—
442C23—301no—
443C23D5×#6711yescharacteristic
444Q8—121no—
445D4—601no—
446D4—602no—
447D4—602no—
448D4—601no—
449D4—601no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—51no—
455C2×C4—51no—
456C2×C4—61no—
457C2×C4—61no—
458C2×C4—102no—
459C2×C4—102no—
460C2×C4—102no—
461C2×C4—201no—
462C2×C4—201no—
463C2×C4—201no—
464C2×C4—201no—
465C2×C4—201no—
466C2×C4—301no—
467C2×C4—602no—
468C2×C4C4×D3×D511yescharacteristic
469C2×C4D5×D1211yescharacteristic
470C8—121no—
471C8—601no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—201no—
475C2×C3—201no—
476C2×C3D5×#9911yescharacteristic
477C2×C3#6509211yescharacteristic
478C2×C3#6511011yescharacteristic
479D3—401no—
480C5#6950811yescharacteristic, complemented, Sylow
481C22—21no—
482C22—21no—
483C22—101no—
484C22—101no—
485C22—101no—
486C22—101no—
487C22—101no—
488C22—101no—
489C22—202no—
490C22—202no—
491C22—601no—
492C22—601no—
493C22—601no—
494C22D5×(C2×D3)⋊C411yescharacteristic
495C22#9149111yescharacteristic
496C22#9151511yescharacteristic
497C4—21no—
498C4—21no—
499C4—52no—
500C4—81no—
501C4—101no—
502C4—121no—
503C4—121no—
504C4—401no—
505C4—601no—
506C3#1059913011yescharacteristic, complemented, Sylow
507C2—21no—
508C2—21no—
509C2—201no—
510C2—201no—
511C2—1201no—
512C2#1174710911yescharacteristic
513C2D5×#80611yescharacteristic
514C2#1174750011yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#95C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11754527C2
cosocleC22×C3×C4×C5C23
hypercenter#95D3×D5
hypocenterC3×C5#1513
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C3×#64956C2semidirect
3. #11748499C2semidirect
4. #11746272C2semidirect
5. C5×#4452C2semidirect
6. #11745962C2semidirect
7. #11745958C2semidirect
10. C2×#6773C4semidirect
17. #91450C4semidirect
19. #91359C4semidirect
20. #91358C4semidirect
31. #64956D3semidirect
72. #4452D5semidirect
402. C3×C5#1513semidirect
480. C5#69508semidirect
506. C3#10599130semidirect

Maximal subgroups

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

subgroupindex
#117545272
C3×#649562
#117484992
#117462722
C5×#44522
#117459622
#117459582
#105991303
#695085