Finite Group Databasebeta

← #14471661

Subgroups — #14471661

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#11752654C211yesmaximal, characteristic, complemented
3C4×#6715C211yesmaximal, characteristic
4C5×#5008C211yesmaximal, characteristic, complemented
5#11749085C212yesmaximal, complemented
6#11748980C212yesmaximal
7#11747390C212yesmaximal, complemented
8#11747225C212yesmaximal, complemented
9#11747085C211yesmaximal, characteristic, complemented
10#11746924C211yesmaximal, characteristic, complemented
11#11746846C211yesmaximal, characteristic, complemented
12#10612818—31nomaximal, Hall
13C3×C4×C5×D4C2211yescharacteristic
14C2×#6715C2211yescharacteristic
15C4×D60C2211yescharacteristic
16C5×#869C2211yescharacteristic
17C3×#4082C2212yes—
18C3×#4072—21no—
19C3×#4070—21no—
20C3×#4033C2212yes—
21C3×#4025—22no—
22C3×#4015C2211yescharacteristic
23C3×C4×Dic10C2211yescharacteristic
24#91437—21no—
25#91424—22no—
26#91418C2212yes—
27#91390—21no—
28#91388C2212yes—
29C2×#6658C2212yes—
30#91116C2211yescharacteristic
31#91093C2211yescharacteristic
32#91091C2211yescharacteristic
33C4×C3⋊#168C2211yescharacteristic
34C5×#832C2212yes—
35C5×#808C2212yes—
36C5×C4⋊(C3⋊C8)C2211yescharacteristic
37#90982C2212yes—
38#90971C2212yes—
39#90970C2212yes—
40#90970C2212yes—
41Dic5×C3⋊C8C2212yes—
42#83667—51nomaximal, Hall
43#66064—31no—
44#65876D311yescharacteristic, complemented
45C5×#476—31no—
46#65382—31no—
47C4×#686—31no—
48#65146—32no—
49#65141—32no—
50#65130—31no—
51#65119—31no—
52#65076—32no—
53#65057—32no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×D60C2311yescharacteristic
57C2×C4×D15—21no—
58C2×C5×Dic6—21no—
59C2×C3×Dic10D411yescharacteristic
60C2×C3×Dic10C2312yes—
61C2×#1200—22no—
62C3×C5×C4⋊C4C2311yescharacteristic
63C3×C5×C22⋊C4—21no—
64C3×C42×C5C2311yescharacteristic
65#6715—22no—
66#6714—21no—
67C4⋊Dic15C2311yescharacteristic
68C2×C3⋊#168C2311yescharacteristic
69C2×C3⋊#168C2311yescharacteristic
70C5×C4⋊Dic3—21no—
71C5×C4⋊Dic3C2312yes—
72C2×C5×C3⋊C8C2312yes—
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#6667—22no—
85#6658—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×#213—51no—
96#5008D511yescharacteristic, complemented
97C5×C4⋊Q8—31no—
98C4×C5×D4C2×D311yescharacteristic
99#4092—62no—
100#4082C2×D312yes—
101C2×#686—31no—
102#4072—21no—
103#4070—21no—
104C2×#677—32no—
105#4043—61no—
106#4039—32no—
107D5×C4⋊C4—61no—
108#4036—32no—
109#4033C2×D312yes—
110#4025—22no—
111C4×D20—31no—
112#4015C2×D311yescharacteristic
113C4×Dic10C2×D311yescharacteristic
114C5×#106—32no—
115C5×C4⋊C8—31no—
116C5×#102—32no—
117#3964—31no—
118#3948—32no—
119#3946—32no—
120C8×Dic5—32no—
121#3942—32no—
122#3942—32no—
123#3941—31no—
124#3939—31no—
125C4×#168—31no—
126#3360—151noSylow
127C23×C3×C5—21no—
128C22×D15—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—21no—
137D60—21no—
138D60#4112yes—
139C4×D15—42no—
140C2×C5×Dic3—22no—
141C5×Dic6—81no—
142C2×C3×Dic5—22no—
143C2×C3×Dic5C2×D412yes—
144C2×C3×Dic5C2×D412yes—
145C3×Dic10—22no—
146C3×Dic10—22no—
147C3×Dic10—22no—
148#1200—82no—
149C3⋊#168—21no—
150C3⋊#168—21no—
151C5×C3⋊C8—22no—
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×#213—51no—
163#896—102no—
164D3×C4⋊C4—101no—
165C4×D12—51no—
166C4×D12—52no—
167#870—52no—
168#869C2×D511yescharacteristic
169#835—52no—
170#835—52no—
171#835—52no—
172#832—51no—
173#832C2×D512yes—
174#809—51no—
175#808C2×D512yes—
176#807—51no—
177C4⋊(C3⋊C8)—52no—
178C4⋊(C3⋊C8)C2×D511yescharacteristic
179C4×C3⋊C8—51no—
180C4×C3⋊C8—52no—
181C2×C5×Q8—61no—
182C2×C5×D4C22×D311yescharacteristic
183C22×C4×C5—21no—
184C2×D20—31no—
185C2×C4×D5—61no—
186C2×C4×D5—62no—
187C2×Dic10#6711yescharacteristic
188C2×Dic10C22×D312yes—
189C2×C5×C8—32no—
190C5×C4⋊C4—32no—
191C5×C4⋊C4—61no—
192C5×C4⋊C4C22×D311yescharacteristic
193C5×C22⋊C4—21no—
194C42×C5C22×D311yescharacteristic
195C22⋊Dic5—22no—
196C22⋊Dic5—22no—
197#686—62no—
198#685—61no—
199#685—62no—
200C4⋊Dic5—21no—
201C4⋊Dic5—21no—
202C4⋊Dic5—31no—
203C4⋊Dic5—62no—
204C4⋊Dic5#6711yescharacteristic
205#683—22no—
206#683—62no—
207#683#6712yes—
208C4×Dic5—22no—
209C4×Dic5C22×D312yes—
210C2×#168—31no—
211C2×#168—31no—
212#677—64no—
213#556—51no—
214#554—151no—
215#488—152no—
216#487—151no—
217#479—152no—
218#476—31no—
219#463—152no—
220#461—151no—
221C8×Q8—151no—
222C4×SD16—152no—
223C4×D8—151no—
224C22×C3×C5—41no—
225C22×C3×C5—41no—
226C22×C3×C5—41no—
227C22×C3×C5C22×D411yescharacteristic
228C2×D15—22no—
229C2×D15—41no—
230C2×D15—41no—
231C3×C4×C5—21no—
232C3×C4×C5—41no—
233C3×C4×C5#13512yes—
234C3×C4×C5C2×#4111yescharacteristic
235C3×C4×C52−1+411yescharacteristic
236Dic15—41no—
237C3×Dic5—22no—
238C3×Dic5—22no—
239C3×Dic5—42no—
240C5×Dic3—42no—
241C2×C3×Q8—51no—
242C2×C3×Q8—52no—
243C2×C3×D4C22×D511yescharacteristic
244C22×C3×C4—21no—
245C2×D12—51no—
246C2×C4×D3—101no—
247C2×C4×D3—102no—
248C2×Dic6—21no—
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—102no—
263(C2×D3)⋊C4—102no—
264(C2×D3)⋊C4—101no—
265C4⋊Dic3—21no—
266C4⋊Dic3—51no—
267C4⋊Dic3C22×D512yes—
268Dic3⋊C4—102no—
269Dic3⋊C4—102no—
270C2×C3⋊C8—51no—
271C2×C3⋊C8—51no—
272C2×C3⋊C8C22×D512yes—
273C23×C5—21no—
274C22×D5—61no—
275C5×Q8—241no—
276C5×D4—21no—
277C5×D4—21no—
278C2×C4×C5—21no—
279C2×C4×C5—42no—
280C2×C4×C5—62no—
281C2×C4×C5C2×#6711yescharacteristic
282C2×C4×C5C2×#6711yescharacteristic
283C2×C4×C5C23×D311yescharacteristic
284C2×Dic5—22no—
285C2×Dic5—61no—
286C2×Dic5C2×#6712yes—
287C2×Dic5C2×#6712yes—
288D20—32no—
289D20—61no—
290C4×D5—122no—
291C4×D5—242no—
292Dic10—22no—
293Dic10—22no—
294Dic10—22no—
295C5×C8—62no—
296#168—61no—
297#168—61no—
298C2×SD16—152no—
299C2×D8—151no—
300C4⋊Q8—31no—
301C4⋊Q8—51no—
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—152no—
311C4×D4—151no—
312C4×D4D3×D511yescharacteristic
313#117—101no—
314C2×C4⋊C4—301no—
315#107—151no—
316#106—32no—
317C4⋊C8—31no—
318C4⋊C8—152no—
319#103—152no—
320#103—152no—
321#103—152no—
322#102—32no—
323#102—151no—
324#102—151no—
325C4×C8—152no—
326C4×C8—151no—
327C2×C3×C5—81no—
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C2×#13511yescharacteristic
330C2×C3×C5#57711yescharacteristic
331D15—42no—
332C23×C3—21no—
333C22×D3—101no—
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—22no—
348C2×Dic3—101no—
349D12—52no—
350D12—101no—
351C4×D3—202no—
352C4×D3—402no—
353Dic6—81no—
354C3⋊C8—22no—
355C3⋊C8—101no—
356C3⋊C8—101no—
357C22×C5—41no—
358C22×C5—41no—
359C22×C5—41no—
360C22×C5C22×#6711yescharacteristic
361C2×D5—62no—
362C2×D5—121no—
363C2×D5—121no—
364C4×C5—21no—
365C4×C5—41no—
366C4×C5—122no—
367C4×C5#95012yes—
368C4×C5D3×#4111yescharacteristic
369C4×C5#101011yescharacteristic
370Dic5—22no—
371Dic5—22no—
372Dic5—42no—
373Dic5—121no—
374C2×Q8—51no—
375C2×Q8—52no—
376C2×Q8—61no—
377C2×D4—151no—
378C2×D4C2×D3×D511yescharacteristic
379C22×C4—21no—
380C22×C4—302no—
381C22×C4—301no—
382SD16—304no—
383D8—302no—
384C2×C8—32no—
385C2×C8—151no—
386C2×C8—151no—
387C4⋊C4—32no—
388C4⋊C4—51no—
389C4⋊C4—52no—
390C4⋊C4—61no—
391C4⋊C4—102no—
392C4⋊C4—101no—
393C4⋊C4—101no—
394C4⋊C4—151no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4C2×D3×D511yescharacteristic
398C22⋊C4—21no—
399C22⋊C4—102no—
400C22⋊C4—102no—
401C22⋊C4—302no—
402C22⋊C4—301no—
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—102no—
412C2×D3—201no—
413C2×D3—201no—
414C3×C4—21no—
415C3×C4—41no—
416C3×C4—102no—
417C3×C4—102no—
418C3×C4—202no—
419C3×C4#406212yes—
420C3×C4#414711yescharacteristic
421C3×C4D5×#4111yescharacteristic
422Dic3—42no—
423Dic3—201no—
424C2×C5—81no—
425C2×C5C2×#95011yescharacteristic
426C2×C5#583111yescharacteristic
427C2×C5#583711yescharacteristic
428D5—122no—
429C23—21no—
430C23—301no—
431Q8—102no—
432Q8—102no—
433Q8—102no—
434Q8—241no—
435D4—21no—
436D4—21no—
437D4—152no—
438D4—301no—
439C2×C4—21no—
440C2×C4—42no—
441C2×C4—52no—
442C2×C4—52no—
443C2×C4—62no—
444C2×C4—102no—
445C2×C4—301no—
446C2×C4—602no—
447C2×C4—1202no—
448C2×C4D5×#6711yescharacteristic
449C2×C4D5×#6711yescharacteristic
450C2×C4C22×D3×D511yescharacteristic
451C8—62no—
452C8—301no—
453C8—301no—
454C2×C3—81no—
455C2×C3#6596711yescharacteristic
456C2×C3C2×#406211yescharacteristic
457C2×C3#6610911yescharacteristic
458D3—202no—
459C5#8366711yescharacteristic, complemented, Sylow
460C22—41no—
461C22—41no—
462C22—41no—
463C22—302no—
464C22—601no—
465C22—601no—
466C22C2×D5×#6711yescharacteristic
467C4—21no—
468C4—41no—
469C4—102no—
470C4—102no—
471C4—122no—
472C4—202no—
473C4—601no—
474C4#9149212yes—
475C4#9200011yescharacteristic
476C4#9201611yescharacteristic
477C3#1061281811yescharacteristic, complemented, Sylow
478C2—81no—
479C2—602no—
480C2#1175421511yescharacteristic
481C2C2×#9149211yescharacteristic
482C2#1175531711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×#6715C22
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. #11752654C2semidirect
4. C5×#5008C2semidirect
5. #11749085C2semidirect
7. #11747390C2semidirect
8. #11747225C2semidirect
9. #11747085C2semidirect
10. #11746924C2semidirect
11. #11746846C2semidirect
44. #65876D3semidirect
96. #5008D5semidirect
406. C3×C5#3360semidirect
459. C5#83667semidirect
477. C3#10612818semidirect

Maximal subgroups

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

subgroupindex
C3×#658762
#117526542
C4×#67152
C5×#50082
#117490852
#117489802
#117473902
#117472252
#117470852
#117469242
#117468462
#106128183
#836675