Finite Group Databasebeta

← #14471773

Subgroups — #14471773

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
1#11756489C211yesmaximal, characteristic, complemented
2#11756472C211yesmaximal, characteristic, complemented
3C3×C5×#486C211yesmaximal, characteristic, complemented
4#11751192C211yesmaximal, characteristic, complemented
5#11751173C211yesmaximal, characteristic
6#11750888C212yesmaximal, complemented
7#11750869C212yesmaximal, complemented
8#11750864C212yesmaximal, complemented
9#11750857C212yesmaximal, complemented
10C4×#6706C211yesmaximal, characteristic, complemented
11C8×Dic30C211yesmaximal, characteristic, complemented
12#10613316—31nomaximal, Hall
13C3×C5×C4⋊Q8C2211yescharacteristic
14C3×C5×#127C2211yescharacteristic
15#91835—22no—
16#91825—21no—
17#91825C2212yes—
18#91824—22no—
19D4×Dic15—21no—
20D4×Dic15C2212yes—
21C2×#6715C2212yes—
22C2×#6706C2211yescharacteristic
23#91786—21no—
24#91782C2212yes—
25C4⋊C4×D15—21no—
26#91779C2212yes—
27C4×D60C2211yescharacteristic
28C4×Dic30C2211yescharacteristic
29C4×Dic30C2211yescharacteristic
30C3×C5×#102C2212yes—
31C3×C5×#102C2212yes—
32C3×C4×C5×C8C2211yescharacteristic
33#91116C2212yes—
34#91105C2211yescharacteristic
35#91101C2211yescharacteristic
36#91100C2211yescharacteristic
37#91098C2212yes—
38C8×Dic15C2212yes—
39#91094C2212yes—
40#91091C2212yes—
41C4⋊(C3⋊#168)C2211yescharacteristic
42#81585—51nomaximal, Hall
43#66064—31no—
44#66047—31no—
45C5×#486D311yescharacteristic, complemented
46#65380—31no—
47#65361—31no—
48#65076—32no—
49#65057—32no—
50#65052—32no—
51#65045—32no—
52C4×#677—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4—21no—
57C2×C3×C5×D4C2312yes—
58C22×Dic15—22no—
59C2×D60C2311yescharacteristic
60C2×C4×D15—21no—
61C2×C4×D15—22no—
62C2×Dic30D411yescharacteristic
63C2×Dic30C2311yescharacteristic
64C2×C3×C5×C8C2311yescharacteristic
65C2×C3×C5×C8C2311yescharacteristic
66C3×C5×C4⋊C4—21no—
67C3×C5×C4⋊C4C2312yes—
68C3×C42×C5C2311yescharacteristic
69#6719—22no—
70#6719—22no—
71#6719—22no—
72#6715—24no—
73#6714—21no—
74#6714—22no—
75C4⋊Dic15—22no—
76C4⋊Dic15D411yescharacteristic
77C4⋊Dic15C2311yescharacteristic
78C4⋊Dic15C2311yescharacteristic
79#6712—21no—
80#6712—22no—
81#6712D412yes—
82C4×Dic15—21no—
83C4×Dic15C2312yes—
84C2×C3⋊#168C2312yes—
85#6706—22no—
86#5730—51no—
87#5713—51no—
88C3×#486D511yescharacteristic, complemented
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×C4⋊Q8C2×D311yescharacteristic
98C5×#127C2×D311yescharacteristic
99#4092—62no—
100#4082—32no—
101#4082—61no—
102#4081—62no—
103D4×Dic5—32no—
104D4×Dic5—61no—
105C2×#686—32no—
106C2×#677—31no—
107#4043—61no—
108#4039—32no—
109D5×C4⋊C4—61no—
110#4036—32no—
111C4×D20—31no—
112C4×Dic10—31no—
113C4×Dic10—31no—
114C5×#102C2×D312yes—
115C5×#102C2×D312yes—
116C4×C5×C8C2×D311yescharacteristic
117#3964—32no—
118#3953—31no—
119#3949—31no—
120#3948—31no—
121#3946—32no—
122C8×Dic5—32no—
123#3942—32no—
124#3939—32no—
125C4⋊#168—31no—
126#3361—151noSylow
127C23×C3×C5—22no—
128C22×D15—21no—
129C3×C5×Q8—81no—
130C3×C5×D4—22no—
131C3×C5×D4—22no—
132C3×C5×D4—42no—
133C3×C5×D4—81no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2411yescharacteristic
138C2×Dic15—21no—
139C2×Dic15—21no—
140C2×Dic15—21no—
141C2×Dic15—82no—
142C2×Dic15C2×D412yes—
143C2×Dic15C2×D412yes—
144D60—21no—
145D60#4112yes—
146C4×D15—42no—
147C4×D15—82no—
148Dic30—22no—
149Dic30—21no—
150Dic30—21no—
151C3×C5×C8—21no—
152C3×C5×C8—21no—
153C3⋊#168—22no—
154C3×C4⋊Q8C2×D511yescharacteristic
155C3×#127C2×D511yescharacteristic
156#946—102no—
157#936—52no—
158#936—101no—
159#935—102no—
160D4×Dic3—52no—
161D4×Dic3—101no—
162C2×#213—52no—
163C2×#204—51no—
164#897—101no—
165#893—52no—
166D3×C4⋊C4—101no—
167#890—52no—
168C4×D12—51no—
169C4×Dic6—51no—
170C4×Dic6—51no—
171C3×#102C2×D512yes—
172C3×#102C2×D512yes—
173C3×C4×C8C2×D511yescharacteristic
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—21no—
184C2×C5×D4—21no—
185C2×C5×D4—21no—
186C2×C5×D4C22×D312yes—
187C22×Dic5—62no—
188C2×D20—31no—
189C2×C4×D5—61no—
190C2×C4×D5—62no—
191C2×Dic10—31no—
192C2×Dic10—31no—
193C2×C5×C8C22×D311yescharacteristic
194C2×C5×C8C22×D311yescharacteristic
195C5×C4⋊C4—21no—
196C5×C4⋊C4C22×D312yes—
197C42×C5C22×D311yescharacteristic
198C22⋊Dic5—62no—
199C22⋊Dic5—62no—
200C22⋊Dic5—62no—
201#686—64no—
202#685—62no—
203#685—61no—
204C4⋊Dic5—31no—
205C4⋊Dic5—31no—
206C4⋊Dic5—31no—
207C4⋊Dic5—62no—
208#683—32no—
209#683—62no—
210#683—61no—
211C4×Dic5—32no—
212C4×Dic5—61no—
213C2×#168—32no—
214#677—62no—
215#559—151no—
216#554—151no—
217#488—152no—
218#486D1511yescharacteristic, complemented
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—42no—
235C3×C4×C5#13512yes—
236C3×C4×C5C2×#4111yescharacteristic
237C3×C4×C52−1+411yescharacteristic
238Dic15—22no—
239Dic15—22no—
240Dic15—41no—
241Dic15—41no—
242Dic15—41no—
243C2×C3×Q8—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4C22×D512yes—
247C22×Dic3—102no—
248C2×D12—51no—
249C2×C4×D3—101no—
250C2×C4×D3—102no—
251C2×Dic6—51no—
252C2×Dic6—51no—
253C2×C3×C8C22×D511yescharacteristic
254C2×C3×C8C22×D511yescharacteristic
255C3×C4⋊C4—21no—
256C3×C4⋊C4C22×D512yes—
257C3×C42C22×D511yescharacteristic
258#217—102no—
259#217—102no—
260#217—102no—
261#213—104no—
262(C2×D3)⋊C4—102no—
263(C2×D3)⋊C4—101no—
264C4⋊Dic3—51no—
265C4⋊Dic3—51no—
266C4⋊Dic3—51no—
267C4⋊Dic3—102no—
268Dic3⋊C4—52no—
269Dic3⋊C4—102no—
270Dic3⋊C4—101no—
271C4×Dic3—52no—
272C4×Dic3—101no—
273C2×C3⋊C8—52no—
274#204—102no—
275C23×C5—22no—
276C22×D5—61no—
277C5×Q8—81no—
278C5×D4—22no—
279C5×D4—22no—
280C5×D4—42no—
281C5×D4—81no—
282C2×C4×C5—22no—
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5D3×D411yescharacteristic
285C2×C4×C5C23×D311yescharacteristic
286C2×Dic5—32no—
287C2×Dic5—32no—
288C2×Dic5—61no—
289C2×Dic5—61no—
290C2×Dic5—61no—
291C2×Dic5—242no—
292D20—32no—
293D20—61no—
294C4×D5—122no—
295C4×D5—242no—
296Dic10—62no—
297Dic10—61no—
298Dic10—61no—
299C5×C8—21no—
300C5×C8—21no—
301#168—62no—
302C2×SD16—151no—
303C2×D8—152no—
304C4⋊Q8C2×D1511yescharacteristic
305#127C2×D1511yescharacteristic
306#125—152no—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—301no—
311C22⋊Q8—302no—
312C4×Q8—151no—
313C4×Q8—151no—
314C4×D4—152no—
315C4×D4—152no—
316C4×D4—151no—
317C4×D4—301no—
318C2×C4⋊C4—301no—
319#107—152no—
320#106—151no—
321C4⋊C8—152no—
322C4⋊C8—151no—
323#103—151no—
324#103—152no—
325#102—152no—
326#102—151no—
327#102C2×D1512yes—
328#102C2×D1512yes—
329C4×C8—152no—
330C4×C8C2×D1511yescharacteristic
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—81no—
339C3×D4—22no—
340C3×D4—22no—
341C3×D4—42no—
342C3×D4—81no—
343C2×C3×C4—22no—
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4D4×D511yescharacteristic
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—52no—
348C2×Dic3—52no—
349C2×Dic3—101no—
350C2×Dic3—101no—
351C2×Dic3—101no—
352C2×Dic3—402no—
353D12—52no—
354D12—101no—
355C4×D3—202no—
356C4×D3—402no—
357Dic6—102no—
358Dic6—101no—
359Dic6—101no—
360C3×C8—21no—
361C3×C8—21no—
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—42no—
372C4×C5#91612yes—
373C4×C5D3×#4111yescharacteristic
374C4×C5#101011yescharacteristic
375Dic5—62no—
376Dic5—62no—
377Dic5—121no—
378Dic5—121no—
379Dic5—121no—
380C2×Q8—21no—
381C2×Q8—151no—
382C2×Q8—151no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—151no—
386C2×D4C22×D1512yes—
387C22×C4—302no—
388C22×C4—302no—
389C22×C4—301no—
390SD16—302no—
391D8—304no—
392C2×C8—152no—
393C2×C8C22×D1511yescharacteristic
394C2×C8C22×D1511yescharacteristic
395C4⋊C4—21no—
396C4⋊C4—151no—
397C4⋊C4—152no—
398C4⋊C4—151no—
399C4⋊C4—151no—
400C4⋊C4—302no—
401C4⋊C4—302no—
402C4⋊C4—301no—
403C4⋊C4C22×D1512yes—
404C22⋊C4—302no—
405C22⋊C4—302no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—301no—
409C42—152no—
410C42—301no—
411C42C22×D1511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3C2×D4×D511yescharacteristic
417C2×D3—102no—
418C2×D3—201no—
419C2×D3—201no—
420C3×C4—21no—
421C3×C4—42no—
422C3×C4#406212yes—
423C3×C4D5×#4111yescharacteristic
424C3×C4#415011yescharacteristic
425Dic3—102no—
426Dic3—102no—
427Dic3—201no—
428Dic3—201no—
429Dic3—201no—
430C2×C5—82no—
431C2×C5#567711yescharacteristic
432C2×C5#575711yescharacteristic
433C2×C5C2×#91611yescharacteristic
434D5—122no—
435C23—22no—
436C23—301no—
437Q8—81no—
438Q8—302no—
439Q8—301no—
440Q8—301no—
441D4—22no—
442D4—22no—
443D4—42no—
444D4—81no—
445D4—152no—
446D4—301no—
447C2×C4—22no—
448C2×C4—152no—
449C2×C4—152no—
450C2×C4—301no—
451C2×C4—301no—
452C2×C4—301no—
453C2×C4—602no—
454C2×C4—1202no—
455C2×C4—1202no—
456C2×C4D4×D1511yescharacteristic
457C2×C4D4×D1511yescharacteristic
458C2×C4C23×D1511yescharacteristic
459C8—21no—
460C8—21no—
461C8—302no—
462C2×C3—82no—
463C2×C3#6601111yescharacteristic
464C2×C3#6609111yescharacteristic
465C2×C3C2×#406211yescharacteristic
466D3—202no—
467C5#8158511yescharacteristic, complemented, Sylow
468C22—42no—
469C22—42no—
470C22—42no—
471C22—302no—
472C22—601no—
473C22—601no—
474C22C2×D4×D1511yescharacteristic
475C4—21no—
476C4—42no—
477C4—302no—
478C4—302no—
479C4—601no—
480C4—601no—
481C4—601no—
482C4#9180512yes—
483C4#41×D1511yescharacteristic
484C4#9210111yescharacteristic
485C3#1061331611yescharacteristic, complemented, Sylow
486C2—82no—
487C2—602no—
488C2#1175643611yescharacteristic
489C2#1175651611yescharacteristic
490C2C2×#9180511yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#486C2
socleC22×C3×C5C22×D4
prime radical#11751173C2
hypercenter#486D15
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #11756489C2semidirect
2. #11756472C2semidirect
3. C3×C5×#486C2semidirect
4. #11751192C2semidirect
6. #11750888C2semidirect
7. #11750869C2semidirect
8. #11750864C2semidirect
9. #11750857C2semidirect
10. C4×#6706C2semidirect
11. C8×Dic30C2semidirect
45. C5×#486D3semidirect
88. C3×#486D5semidirect
218. #486D15semidirect
412. C3×C5#3361semidirect
467. C5#81585semidirect
485. C3#10613316semidirect

Maximal subgroups

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

subgroupindex
#117564892
#117564722
C3×C5×#4862
#117511922
#117511732
#117508882
#117508692
#117508642
#117508572
C4×#67062
C8×Dic302
#106133163
#815855