Finite Group Databasebeta

← #14471659

Subgroups — #14471659

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65876C211yesmaximal, characteristic, complemented
2#11752660C211yesmaximal, characteristic, complemented
3#11751109C211yesmaximal, characteristic, complemented
4C4×C5×#213C211yesmaximal, characteristic
5#11749085C212yesmaximal, complemented
6#11748978C212yesmaximal
7#11747391C212yesmaximal, complemented
8#11747218C212yesmaximal, complemented
9#11747070C211yesmaximal, characteristic, complemented
10#11746920C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic10C211yesmaximal, characteristic, complemented
12#10611299—31nomaximal, Hall
13C3×C4×C5×D4C2211yescharacteristic
14#91758C2211yescharacteristic
15C2×C5×#213C2211yescharacteristic
16C4×C5×D12C2211yescharacteristic
17C3×#4082C2212yes—
18C3×#4072—21no—
19C3×#4070—21no—
20C3×#4033C2212yes—
21C3×#4025—22no—
22C3×#4015C2211yescharacteristic
23C3×C4×Dic10C2211yescharacteristic
24#91432—22no—
25D3×C4⋊Dic5—21no—
26Dic5×D12C2212yes—
27#91388C2212yes—
28#91369—21no—
29C2×#6656C2212yes—
30#91116C2212yes—
31#91092C2212yes—
32C4⋊(C3⋊#168)C2211yescharacteristic
33C5×#832C2211yescharacteristic
34C5×#809C2211yescharacteristic
35C5×#807C2211yescharacteristic
36C4×C5×C3⋊C8C2211yescharacteristic
37#90982C2212yes—
38#90971C2212yes—
39#90971C2212yes—
40#90970C2212yes—
41Dic5×C3⋊C8C2212yes—
42#83667—51nomaximal, Hall
43#65877—31no—
44#65876D311yescharacteristic, complemented
45C4×C5×D8—31no—
46#65442—32no—
47#65308—31no—
48#65297—31no—
49#65166—32no—
50#65057—32no—
51#65047—32no—
52#64970—31no—
53C8×Dic10—31no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×Dic30—21no—
57C2×C5×D12C2311yescharacteristic
58C2×C4×C5×D3—21no—
59C2×C3×Dic10D411yescharacteristic
60C2×C3×Dic10C2312yes—
61C2×D3×Dic5—22no—
62C3×C5×C4⋊C4C2311yescharacteristic
63C3×C5×C22⋊C4—21no—
64C3×C42×C5C2311yescharacteristic
65C4⋊Dic15—21no—
66C4⋊Dic15C2312yes—
67C2×C3⋊#168C2312yes—
68C5×#213—22no—
69C5×(C2×D3)⋊C4—21no—
70C5×C4⋊Dic3C2311yescharacteristic
71C2×C5×C3⋊C8C2311yescharacteristic
72C2×C5×C3⋊C8C2311yescharacteristic
73C3×C22⋊Dic5—22no—
74C3×C22⋊Dic5—22no—
75C3×C4⋊Dic5—21no—
76C3×C4⋊Dic5—21no—
77C3×C4⋊Dic5D411yescharacteristic
78C3×#683—22no—
79C3×#683D412yes—
80C3×C4×Dic5—22no—
81C3×C4×Dic5C2312yes—
82Dic3⋊Dic5—22no—
83#6669—22no—
84(C2×D3)⋊Dic5—22no—
85#6656—24no—
86C3×#556—51no—
87#5579—51no—
88#5083—51no—
89#5079—51no—
90#5057—52no—
91#5056—52no—
92C4×#215—52no—
93Q8×C3⋊C8—51no—
94#5022—52no—
95C4×#213D511yescharacteristic
96#5008—51no—
97C2×C5×D8—31no—
98C4×C5×D4—31no—
99C4×C5×D4C2×D311yescharacteristic
100#4082C2×D312yes—
101D4×Dic5—32no—
102C2×#687—32no—
103#4072—21no—
104C2×C4⋊Dic5—61no—
105#4070—21no—
106#4070—61no—
107#4036—32no—
108#4033C2×D312yes—
109#4025—22no—
110#4024—62no—
111#4015—31no—
112#4015C2×D311yescharacteristic
113C4×Dic10C2×D311yescharacteristic
114C5×#107—31no—
115C5×#102—31no—
116C5×#102—31no—
117C4×C5×C8—31no—
118#3964—32no—
119#3948—32no—
120#3948—32no—
121#3946—32no—
122C8×Dic5—32no—
123#3942—32no—
124#3940—32no—
125C4⋊#168—31no—
126#3360—151noSylow
127C23×C3×C5—21no—
128C22×C5×D3—21no—
129C3×C5×D4—21no—
130C3×C5×D4—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—42no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—22no—
137Dic30—81no—
138C2×C5×Dic3—21no—
139C5×D12—21no—
140C5×D12#4112yes—
141C4×C5×D3—42no—
142C2×C3×Dic5—22no—
143C2×C3×Dic5C2×D412yes—
144C2×C3×Dic5C2×D412yes—
145C3×Dic10—22no—
146C3×Dic10—22no—
147C3×Dic10—22no—
148D3×Dic5—82no—
149C3⋊#168—22no—
150C5×C3⋊C8—21no—
151C5×C3⋊C8—21no—
152C3×C4⋊Q8—51no—
153C3×#126—102no—
154C3×#124—52no—
155C3×C22⋊Q8—101no—
156C3×C4×Q8—51no—
157C3×C4×Q8—52no—
158C3×C4×D4C2×D511yescharacteristic
159C3×#117—101no—
160#946—101no—
161C2×#215—52no—
162C2×#213C2×D511yescharacteristic
163#896—102no—
164D3×C4⋊C4—101no—
165C4×D12—52no—
166C4×D12C2×D511yescharacteristic
167#870—52no—
168#869—51no—
169#835—52no—
170#835—52no—
171#835—52no—
172#832—52no—
173#832C2×D511yescharacteristic
174#809C2×D511yescharacteristic
175#808—52no—
176#807C2×D511yescharacteristic
177C4⋊(C3⋊C8)—51no—
178C4⋊(C3⋊C8)—52no—
179C4×C3⋊C8—52no—
180C4×C3⋊C8C2×D511yescharacteristic
181C2×C5×D4—31no—
182C2×C5×D4C22×D311yescharacteristic
183C22×C4×C5—21no—
184C22×C4×C5—61no—
185C22×Dic5—62no—
186C2×Dic10—61no—
187C2×Dic10#6711yescharacteristic
188C2×Dic10C22×D312yes—
189C5×D8—62no—
190C2×C5×C8—31no—
191C2×C5×C8—31no—
192C5×C4⋊C4—31no—
193C5×C4⋊C4C22×D311yescharacteristic
194C5×C22⋊C4—21no—
195C5×C22⋊C4—61no—
196C42×C5C22×D311yescharacteristic
197C22⋊Dic5—22no—
198C22⋊Dic5—22no—
199C22⋊Dic5—62no—
200#687—64no—
201C4⋊Dic5—21no—
202C4⋊Dic5—21no—
203C4⋊Dic5—32no—
204C4⋊Dic5—61no—
205C4⋊Dic5—62no—
206C4⋊Dic5#6711yescharacteristic
207#683—22no—
208#683—62no—
209#683#6712yes—
210C4×Dic5—22no—
211C4×Dic5C22×D312yes—
212C2×#168—32no—
213#556—51no—
214#554—151no—
215#488—152no—
216#487—151no—
217#479—152no—
218#476—151no—
219#463—152no—
220#461—151no—
221C8×Q8—151no—
222C4×SD16—152no—
223C4×D8—31no—
224C22×C3×C5—41no—
225C22×C3×C5—41no—
226C22×C3×C5—41no—
227C22×C3×C5C22×D411yescharacteristic
228C2×C5×D3—22no—
229C2×C5×D3—41no—
230C2×C5×D3—41no—
231C3×C4×C5—21no—
232C3×C4×C5—41no—
233C3×C4×C5#13512yes—
234C3×C4×C5C2×#4111yescharacteristic
235C3×C4×C52−1+411yescharacteristic
236Dic15—42no—
237C3×Dic5—22no—
238C3×Dic5—22no—
239C3×Dic5—42no—
240C5×Dic3—41no—
241C2×C3×Q8—51no—
242C2×C3×Q8—52no—
243C2×C3×D4C22×D511yescharacteristic
244C22×C3×C4—21no—
245C2×D12C22×D511yescharacteristic
246C2×C4×D3—21no—
247C2×C4×D3—102no—
248C2×Dic6—101no—
249C3×C4⋊C4—52no—
250C3×C4⋊C4—51no—
251C3×C4⋊C4—102no—
252C3×C4⋊C4—101no—
253C3×C4⋊C4—101no—
254C3×C4⋊C4C22×D511yescharacteristic
255C3×C22⋊C4—21no—
256C3×C22⋊C4—102no—
257C3×C22⋊C4—102no—
258C3×C42—52no—
259C3×C42—102no—
260C3×C42C22×D511yescharacteristic
261#215—104no—
262#213—22no—
263(C2×D3)⋊C4—21no—
264(C2×D3)⋊C4—102no—
265C4⋊Dic3—52no—
266C4⋊Dic3—101no—
267C4⋊Dic3C22×D511yescharacteristic
268Dic3⋊C4—102no—
269Dic3⋊C4—102no—
270C2×C3⋊C8—52no—
271C2×C3⋊C8C22×D511yescharacteristic
272C2×C3⋊C8C22×D511yescharacteristic
273C23×C5—21no—
274C23×C5—61no—
275C5×D4—21no—
276C5×D4—21no—
277C5×D4—32no—
278C5×D4—61no—
279C2×C4×C5—21no—
280C2×C4×C5—42no—
281C2×C4×C5—61no—
282C2×C4×C5—122no—
283C2×C4×C5C2×#6711yescharacteristic
284C2×C4×C5C2×#6711yescharacteristic
285C2×C4×C5C23×D311yescharacteristic
286C2×Dic5—22no—
287C2×Dic5—62no—
288C2×Dic5—242no—
289C2×Dic5C2×#6712yes—
290C2×Dic5C2×#6712yes—
291Dic10—22no—
292Dic10—22no—
293Dic10—22no—
294Dic10—241no—
295C5×C8—61no—
296C5×C8—61no—
297#168—62no—
298C2×SD16—152no—
299C2×D8—31no—
300C4⋊Q8—51no—
301C4⋊Q8—151no—
302#126—102no—
303#125—152no—
304#124—52no—
305C22⋊Q8—101no—
306C22⋊Q8—302no—
307C22⋊Q8—301no—
308C4×Q8—51no—
309C4×Q8—52no—
310C4×D4—31no—
311C4×D4—152no—
312C4×D4D3×D511yescharacteristic
313#117—101no—
314C2×C4⋊C4—301no—
315#107—31no—
316#106—152no—
317C4⋊C8—152no—
318C4⋊C8—151no—
319#103—152no—
320#103—152no—
321#103—152no—
322#102—31no—
323#102—31no—
324#102—152no—
325C4×C8—31no—
326C4×C8—152no—
327C2×C3×C5—81no—
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C2×#13511yescharacteristic
330C2×C3×C5#57711yescharacteristic
331C5×D3—42no—
332C23×C3—21no—
333C22×D3—21no—
334C3×Q8—102no—
335C3×Q8—102no—
336C3×Q8—102no—
337C3×D4—21no—
338C3×D4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—42no—
341C2×C3×C4—52no—
342C2×C3×C4—52no—
343C2×C3×C4—102no—
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4D4×D511yescharacteristic
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—21no—
348C2×Dic3—102no—
349D12—21no—
350D12#70912yes—
351C4×D3—42no—
352C4×D3—402no—
353Dic6—401no—
354C3⋊C8—21no—
355C3⋊C8—21no—
356C3⋊C8—102no—
357C22×C5—41no—
358C22×C5—41no—
359C22×C5—41no—
360C22×C5—62no—
361C22×C5—121no—
362C22×C5—121no—
363C22×C5C22×#6711yescharacteristic
364C4×C5—21no—
365C4×C5—41no—
366C4×C5—121no—
367C4×C5#95012yes—
368C4×C5D3×#4111yescharacteristic
369C4×C5#101011yescharacteristic
370Dic5—22no—
371Dic5—22no—
372Dic5—42no—
373Dic5—122no—
374C2×Q8—51no—
375C2×Q8—52no—
376C2×Q8—301no—
377C2×D4—31no—
378C2×D4C2×D3×D511yescharacteristic
379C22×C4—21no—
380C22×C4—61no—
381C22×C4—302no—
382SD16—304no—
383D8—62no—
384C2×C8—31no—
385C2×C8—31no—
386C2×C8—152no—
387C4⋊C4—31no—
388C4⋊C4—51no—
389C4⋊C4—52no—
390C4⋊C4—102no—
391C4⋊C4—101no—
392C4⋊C4—101no—
393C4⋊C4—152no—
394C4⋊C4—302no—
395C4⋊C4—302no—
396C4⋊C4—301no—
397C4⋊C4C2×D3×D511yescharacteristic
398C22⋊C4—21no—
399C22⋊C4—61no—
400C22⋊C4—102no—
401C22⋊C4—102no—
402C22⋊C4—302no—
403C42—52no—
404C42—102no—
405C42C2×D3×D511yescharacteristic
406C3×C5#336011yescharacteristic, complemented, Hall
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3C2×D4×D511yescharacteristic
411C2×D3—22no—
412C2×D3—41no—
413C2×D3—41no—
414C3×C4—21no—
415C3×C4—41no—
416C3×C4—102no—
417C3×C4—102no—
418C3×C4—202no—
419C3×C4#405812yes—
420C3×C4C2×#70911yescharacteristic
421C3×C4#415011yescharacteristic
422Dic3—41no—
423Dic3—202no—
424C2×C5—81no—
425C2×C5—122no—
426C2×C5C2×#95011yescharacteristic
427C2×C5#583111yescharacteristic
428C2×C5#583711yescharacteristic
429C23—21no—
430C23—61no—
431Q8—102no—
432Q8—102no—
433Q8—102no—
434Q8—1201no—
435D4—21no—
436D4—21no—
437D4—32no—
438D4—61no—
439C2×C4—21no—
440C2×C4—42no—
441C2×C4—52no—
442C2×C4—52no—
443C2×C4—61no—
444C2×C4—102no—
445C2×C4—122no—
446C2×C4—302no—
447C2×C4—1202no—
448C2×C4D5×#6711yescharacteristic
449C2×C4D5×#6711yescharacteristic
450C2×C4C22×D3×D511yescharacteristic
451C8—61no—
452C8—61no—
453C8—302no—
454C2×C3—81no—
455C2×C3#6588611yescharacteristic
456C2×C3C2×#405811yescharacteristic
457C2×C3#6610411yescharacteristic
458D3—42no—
459C5#8366711yescharacteristic, complemented, Sylow
460C22—41no—
461C22—41no—
462C22—41no—
463C22—62no—
464C22—121no—
465C22—121no—
466C22C2×D5×#6711yescharacteristic
467C4—21no—
468C4—41no—
469C4—102no—
470C4—102no—
471C4—121no—
472C4—202no—
473C4—602no—
474C4#9149012yes—
475C4#9200111yescharacteristic
476C4D3×#70911yescharacteristic
477C3#1061129911yescharacteristic, complemented, Sylow
478C2—81no—
479C2—122no—
480C2#1175452811yescharacteristic
481C2C2×#9149011yescharacteristic
482C2#1175531911yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#213C22
hypercenterC4×D4D3×D5
hypocenterC3×C5#3360
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#65876C2semidirect
2. #11752660C2semidirect
3. #11751109C2semidirect
5. #11749085C2semidirect
7. #11747391C2semidirect
8. #11747218C2semidirect
9. #11747070C2semidirect
10. #11746920C2semidirect
11. C3⋊C8×Dic10C2semidirect
44. #65876D3semidirect
406. C3×C5#3360semidirect
459. C5#83667semidirect
477. C3#10611299semidirect

Maximal subgroups

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

subgroupindex
C3×#658762
#117526602
#117511092
C4×C5×#2132
#117490852
#117489782
#117473912
#117472182
#117470702
#117469202
C3⋊C8×Dic102
#106112993
#836675