Finite Group Databasebeta

← #14471835

Subgroups — #14471835

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5713C211yesmaximal, characteristic, complemented
2#11752645C211yesmaximal, characteristic, complemented
3#11751173C211yesmaximal, characteristic
4C3×#65359C211yesmaximal, characteristic, complemented
5#11749088C212yesmaximal, complemented
6#11748990C212yesmaximal, complemented
7#11748986C212yesmaximal, complemented
8#11748942C212yesmaximal, complemented
9C4×#6660C211yesmaximal, characteristic, complemented
10#11746959C211yesmaximal, characteristic, complemented
11Dic6×#168C211yesmaximal, characteristic, complemented
12#10615444—31nomaximal, Hall
13C3×C5×#127C2211yescharacteristic
14C2×#6715C2212yes—
15C4×D60C2211yescharacteristic
16C5×#936—21no—
17C5×#936C2212yes—
18C5×#935—22no—
19C5×D4×Dic3—21no—
20C5×D4×Dic3C2212yes—
21C4×C5×Dic6C2211yescharacteristic
22C4×C5×Dic6C2211yescharacteristic
23C3×#4015C2211yescharacteristic
24#91437—21no—
25#91428C2212yes—
26#91411—22no—
27#91383—21no—
28#91381C2212yes—
29C2×#6660C2211yescharacteristic
30#91116C2212yes—
31C4⋊(C3⋊#168)C2211yescharacteristic
32C3×#3964C2212yes—
33C3×#3964C2212yes—
34C3×C4×#168C2211yescharacteristic
35#90989C2212yes—
36#90985C2211yescharacteristic
37Dic3⋊#168C2212yes—
38#90973C2211yescharacteristic
39#90972C2212yes—
40#90969C2211yescharacteristic
41Dic3×#168C2212yes—
42#81585—51nomaximal, Hall
43C5×#559—31no—
44#65913—31no—
45#65361—31no—
46#65359D311yescharacteristic, complemented
47#65346—32no—
48#65345—32no—
49C4×#688—31no—
50Q8×#168—31no—
51#65310—31no—
52C4×#686—32no—
53#65298—32no—
54C2×C3×C5×D4—21no—
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4C2312yes—
57C2×D60C2311yescharacteristic
58C2×C4×D15—21no—
59C22×C5×Dic3—22no—
60C2×C5×Dic6D411yescharacteristic
61C2×C5×Dic6C2311yescharacteristic
62C2×C3×Dic10—21no—
63C2×#1200—22no—
64C3×C42×C5C2311yescharacteristic
65#6715—24no—
66#6714—21no—
67C4⋊Dic15C2311yescharacteristic
68C2×C3⋊#168C2312yes—
69C5×#217—22no—
70C5×#217—22no—
71C5×#217—22no—
72C5×C4⋊Dic3D411yescharacteristic
73C5×C4⋊Dic3C2311yescharacteristic
74C5×Dic3⋊C4—21no—
75C5×Dic3⋊C4D412yes—
76C4×C5×Dic3—21no—
77C4×C5×Dic3C2312yes—
78C3×C4⋊Dic5—21no—
79C3×C4⋊Dic5C2312yes—
80C2×C3×#168C2311yescharacteristic
81C2×C3×#168C2311yescharacteristic
82#6669—22no—
83#6668—22no—
84#6667—22no—
85#6660—22no—
86#5730—51no—
87#5713D511yescharacteristic, complemented
88C3×#486—51no—
89#5091—51no—
90#5072—51no—
91#4787—52no—
92#4768—52no—
93#4763—52no—
94#4756—52no—
95C4×#204—51no—
96C8×Dic6—51no—
97C5×#127C2×D311yescharacteristic
98C5×#124—32no—
99C5×#124—61no—
100C5×#123—62no—
101C4×C5×Q8—31no—
102C4×C5×Q8—31no—
103C4×C5×D4—32no—
104C4×C5×D4—61no—
105#4092—61no—
106C2×#688—31no—
107C2×#686—32no—
108#4042—62no—
109D5×C4⋊C4—61no—
110C4×D20—31no—
111C4×D20—32no—
112#4016—32no—
113#4015C2×D311yescharacteristic
114#3967—32no—
115#3967—31no—
116#3964—32no—
117#3964C2×D312yes—
118#3964C2×D312yes—
119#3941—31no—
120#3940—31no—
121#3939—32no—
122C4⋊#168—31no—
123C4⋊#168—32no—
124C4×#168—32no—
125C4×#168C2×D311yescharacteristic
126#3361—151noSylow
127C23×C3×C5—22no—
128C22×D15—21no—
129C3×C5×D4—22no—
130C3×C5×D4—22no—
131C3×C5×D4—42no—
132C3×C5×D4—81no—
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—21no—
141C2×C5×Dic3—21no—
142C2×C5×Dic3—82no—
143C2×C5×Dic3C2×D412yes—
144C2×C5×Dic3C2×D412yes—
145C5×Dic6—22no—
146C5×Dic6—21no—
147C5×Dic6—21no—
148C2×C3×Dic5—22no—
149C3×Dic10—81no—
150#1200—82no—
151C3⋊#168—22no—
152C3×#168—21no—
153C3×#168—21no—
154C3×C4⋊Q8—51no—
155C3×#127C2×D511yescharacteristic
156#946—102no—
157#936—21no—
158#936C2×D512yes—
159#935—22no—
160D4×Dic3—21no—
161D4×Dic3C2×D512yes—
162C2×#213—52no—
163C2×#204—51no—
164#897—101no—
165#893—52no—
166D3×C4⋊C4—101no—
167#890—52no—
168C4×D12—51no—
169C4×Dic6C2×D511yescharacteristic
170C4×Dic6C2×D511yescharacteristic
171C3×#102—52no—
172C3×#102—52no—
173C3×C4×C8—51no—
174#832—52no—
175#821—51no—
176#817—51no—
177#816—51no—
178Dic3⋊C8—52no—
179C8×Dic3—52no—
180#810—52no—
181#807—52no—
182C4⋊(C3⋊C8)—51no—
183C2×C5×Q8—31no—
184C2×C5×Q8—31no—
185C2×C5×D4—21no—
186C2×C5×D4—21no—
187C2×C5×D4C22×D312yes—
188C22×C4×C5—62no—
189C2×D20—31no—
190C2×C4×D5—61no—
191C2×C4×D5—62no—
192C2×Dic10—21no—
193C5×C4⋊C4—31no—
194C5×C4⋊C4—32no—
195C5×C4⋊C4—31no—
196C5×C4⋊C4—61no—
197C5×C22⋊C4—62no—
198C5×C22⋊C4—62no—
199C5×C22⋊C4—62no—
200C42×C5—32no—
201C42×C5—61no—
202C42×C5C22×D311yescharacteristic
203#688—62no—
204#686—64no—
205#685—62no—
206#685—61no—
207C4⋊Dic5—21no—
208C4⋊Dic5—31no—
209C4⋊Dic5C22×D312yes—
210#683—62no—
211#683—62no—
212C2×#168—32no—
213C2×#168C22×D311yescharacteristic
214C2×#168C22×D311yescharacteristic
215#559—31no—
216#554—151no—
217#488—152no—
218#486—51no—
219#478—152no—
220#477—151no—
221#463—152no—
222#459—151no—
223C8×Q8—151no—
224C4×SD16—151no—
225C4×D8—152no—
226C22×C3×C5—42no—
227C22×C3×C5—42no—
228C22×C3×C5—42no—
229C22×C3×C5C22×D411yescharacteristic
230C2×D15—22no—
231C2×D15—41no—
232C2×D15—41no—
233C3×C4×C5—21no—
234C3×C4×C5#13512yes—
235C3×C4×C5C2×#4111yescharacteristic
236C3×C4×C52−1+411yescharacteristic
237Dic15—41no—
238C3×Dic5—42no—
239C5×Dic3—22no—
240C5×Dic3—22no—
241C5×Dic3—41no—
242C5×Dic3—41no—
243C2×C3×Q8—101no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4C22×D512yes—
247C22×Dic3—22no—
248C2×D12—51no—
249C2×C4×D3—101no—
250C2×C4×D3—102no—
251C2×Dic6C22⋊D511yescharacteristic
252C2×Dic6C22×D511yescharacteristic
253C2×C3×C8—51no—
254C2×C3×C8—51no—
255C3×C4⋊C4—52no—
256C3×C4⋊C4—101no—
257C3×C42C22×D511yescharacteristic
258#217—22no—
259#217—22no—
260#217—22no—
261#213—104no—
262(C2×D3)⋊C4—101no—
263(C2×D3)⋊C4—102no—
264C4⋊Dic3—51no—
265C4⋊Dic3—102no—
266C4⋊Dic3C22⋊D511yescharacteristic
267C4⋊Dic3C22×D511yescharacteristic
268Dic3⋊C4—21no—
269Dic3⋊C4—102no—
270Dic3⋊C4C22⋊D512yes—
271C4×Dic3—21no—
272C4×Dic3C22×D512yes—
273C2×C3⋊C8—52no—
274#204—102no—
275C23×C5—22no—
276C22×D5—61no—
277C5×Q8—62no—
278C5×Q8—61no—
279C5×Q8—61no—
280C5×D4—22no—
281C5×D4—22no—
282C5×D4—42no—
283C5×D4—81no—
284C2×C4×C5—32no—
285C2×C4×C5—32no—
286C2×C4×C5—61no—
287C2×C4×C5—61no—
288C2×C4×C5—242no—
289C2×C4×C5D3×D411yescharacteristic
290C2×C4×C5D3×D411yescharacteristic
291C2×C4×C5C23×D311yescharacteristic
292C2×Dic5—22no—
293C2×Dic5—61no—
294D20—32no—
295D20—61no—
296C4×D5—122no—
297C4×D5—242no—
298Dic10—81no—
299#168—21no—
300#168—21no—
301#168—62no—
302C2×SD16—151no—
303C2×D8—152no—
304C4⋊Q8—51no—
305#127D3×D511yescharacteristic
306#125—152no—
307#124—32no—
308#124—61no—
309#123—62no—
310C22⋊Q8—302no—
311C22⋊Q8—301no—
312C4×Q8—31no—
313C4×Q8—31no—
314C4×D4—32no—
315C4×D4—61no—
316C4×D4—152no—
317C4×D4—151no—
318C2×C4⋊C4—301no—
319#107—152no—
320#106—151no—
321C4⋊C8—152no—
322C4⋊C8—151no—
323#103—152no—
324#103—151no—
325#102—52no—
326#102—52no—
327#102—151no—
328#102—152no—
329C4×C8—51no—
330C4×C8—152no—
331C2×C3×C5—82no—
332C2×C3×C5#54811yescharacteristic
333C2×C3×C5C2×#13511yescharacteristic
334C2×C3×C5#57611yescharacteristic
335D15—42no—
336C23×C3—22no—
337C22×D3—101no—
338C3×Q8—401no—
339C3×D4—22no—
340C3×D4—22no—
341C3×D4—42no—
342C3×D4—81no—
343C2×C3×C4—102no—
344C2×C3×C4C2×C22⋊D511yescharacteristic
345C2×C3×C4C2×C22⋊D511yescharacteristic
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—82no—
350C2×Dic3—101no—
351C2×Dic3C2×C22⋊D512yes—
352C2×Dic3C2×C22⋊D512yes—
353D12—52no—
354D12—101no—
355C4×D3—202no—
356C4×D3—402no—
357Dic6—22no—
358Dic6—21no—
359Dic6—21no—
360C3×C8—101no—
361C3×C8—101no—
362C3⋊C8—102no—
363C22×C5—42no—
364C22×C5—42no—
365C22×C5—42no—
366C22×C5C2×D3×D411yescharacteristic
367C2×D5—62no—
368C2×D5—121no—
369C2×D5—121no—
370C4×C5—21no—
371C4×C5—62no—
372C4×C5—62no—
373C4×C5—121no—
374C4×C5—121no—
375C4×C5#91612yes—
376C4×C5D3×#4111yescharacteristic
377C4×C5#101011yescharacteristic
378Dic5—42no—
379Dic5—121no—
380C2×Q8—31no—
381C2×Q8—31no—
382C2×Q8—101no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—151no—
386C2×D4C2×D3×D512yes—
387C22×C4—62no—
388C22×C4—302no—
389C22×C4—301no—
390SD16—302no—
391D8—304no—
392C2×C8—51no—
393C2×C8—51no—
394C2×C8—152no—
395C4⋊C4—31no—
396C4⋊C4—32no—
397C4⋊C4—31no—
398C4⋊C4—52no—
399C4⋊C4—61no—
400C4⋊C4—101no—
401C4⋊C4—151no—
402C4⋊C4—302no—
403C4⋊C4—302no—
404C22⋊C4—62no—
405C22⋊C4—62no—
406C22⋊C4—62no—
407C22⋊C4—302no—
408C22⋊C4—301no—
409C42—32no—
410C42—61no—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3C22×C22⋊D511yescharacteristic
417C2×D3—102no—
418C2×D3—201no—
419C2×D3—201no—
420C3×C4—21no—
421C3×C4—202no—
422C3×C4#409612yes—
423C3×C4D5×#4111yescharacteristic
424C3×C4#415011yescharacteristic
425Dic3—22no—
426Dic3—22no—
427Dic3—41no—
428Dic3—41no—
429Dic3—201no—
430C2×C5—82no—
431C2×C5#567711yescharacteristic
432C2×C5#575711yescharacteristic
433C2×C5C2×#91611yescharacteristic
434D5—122no—
435C23—22no—
436C23—301no—
437Q8—62no—
438Q8—61no—
439Q8—61no—
440Q8—401no—
441D4—22no—
442D4—22no—
443D4—42no—
444D4—81no—
445D4—152no—
446D4—301no—
447C2×C4—32no—
448C2×C4—32no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—102no—
452C2×C4—242no—
453C2×C4—301no—
454C2×C4—602no—
455C2×C4—1202no—
456C2×C4D3×C22⋊D511yescharacteristic
457C2×C4D3×C22⋊D511yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—101no—
460C8—101no—
461C8—302no—
462C2×C3—82no—
463C2×C3C2×#409611yescharacteristic
464C2×C3#6616511yescharacteristic
465C2×C3#6616911yescharacteristic
466D3—202no—
467C5#8158511yescharacteristic, complemented, Sylow
468C22—42no—
469C22—42no—
470C22—42no—
471C22—302no—
472C22—601no—
473C22—601no—
474C22C2×D3×C22⋊D511yescharacteristic
475C4—21no—
476C4—62no—
477C4—62no—
478C4—121no—
479C4—121no—
480C4—202no—
481C4—601no—
482C4#9149512yes—
483C4#9202011yescharacteristic
484C4#9202411yescharacteristic
485C3#1061544411yescharacteristic, complemented, Sylow
486C2—82no—
487C2—602no—
488C2#1175469711yescharacteristic
489C2C2×#9149511yescharacteristic
490C2#1175495111yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C22×D4
prime radical#11751173C2
hypercenter#127D3×D5
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C5×#5713C2semidirect
2. #11752645C2semidirect
4. C3×#65359C2semidirect
5. #11749088C2semidirect
6. #11748990C2semidirect
7. #11748986C2semidirect
8. #11748942C2semidirect
9. C4×#6660C2semidirect
10. #11746959C2semidirect
11. Dic6×#168C2semidirect
46. #65359D3semidirect
87. #5713D5semidirect
412. C3×C5#3361semidirect
467. C5#81585semidirect
485. C3#10615444semidirect

Maximal subgroups

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

subgroupindex
C5×#57132
#117526452
#117511732
C3×#653592
#117490882
#117489902
#117489862
#117489422
C4×#66602
#117469592
Dic6×#1682
#106154443
#815855