Finite Group Databasebeta

← #14471511

Subgroups — #14471511

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756486C211yesmaximal, characteristic
2#11756480C211yesmaximal, characteristic, complemented
3C3×C5×#487C211yesmaximal, characteristic, complemented
4#11751195C211yesmaximal, characteristic, complemented
5#11751184C211yesmaximal, characteristic
6#11750919C212yesmaximal
7#11750893C212yesmaximal, complemented
8#11750892C212yesmaximal, complemented
9#11750889C212yesmaximal
10C4×#6706C211yesmaximal, characteristic
11C8×Dic30C211yesmaximal, characteristic, complemented
12#10613351—31nomaximal, Hall
13C2×Q8×D15—21no—
14C3×C5×C4⋊Q8C2211yescharacteristic
15C3×C5×C4⋊Q8C2211yescharacteristic
16#91835—21no—
17Q8×Dic15C2212yes—
18#91833C2212yes—
19C2×#6717C2212yes—
20C2×#6706C2211yescharacteristic
21#91785—22no—
22#91782C2212yes—
23#91779—21no—
24#91778—22no—
25#91777C2212yes—
26#91776—21no—
27C4×D60C2211yescharacteristic
28C4×Dic30C2211yescharacteristic
29C4×Dic30C2211yescharacteristic
30C3×C5×#103C2212yes—
31C3×C5×#103C2212yes—
32C3×C4×C5×C8C2211yescharacteristic
33#91119C2212yes—
34#91105C2211yescharacteristic
35#91101C2211yescharacteristic
36#91100C2211yescharacteristic
37#91098C2212yes—
38C8×Dic15C2212yes—
39#91094C2212yes—
40#91092C2212yes—
41C4⋊(C3⋊#168)C2211yescharacteristic
42#81620—51nomaximal, Hall
43#66061—31no—
44#66055—31no—
45C5×#487D311yescharacteristic, complemented
46#65383—31no—
47#65372—31no—
48#65107—32no—
49#65081—32no—
50#65080—32no—
51#65077—32no—
52C4×#677—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×Q8C2312yes—
56Q8×D15—44no—
57C2×D60C2311yescharacteristic
58C2×C4×D15—21no—
59C2×C4×D15—22no—
60C2×Dic30—22no—
61C2×Dic30D411yescharacteristic
62C2×Dic30C2311yescharacteristic
63C2×C3×C5×C8C2311yescharacteristic
64C2×C3×C5×C8C2311yescharacteristic
65C3×C5×C4⋊C4—21no—
66C3×C5×C4⋊C4—21no—
67C3×C5×C4⋊C4—21no—
68C3×C5×C4⋊C4C2312yes—
69C3×C42×C5C2311yescharacteristic
70#6717—24no—
71#6714—21no—
72#6714—22no—
73C4⋊Dic15—22no—
74C4⋊Dic15D411yescharacteristic
75C4⋊Dic15C2311yescharacteristic
76C4⋊Dic15C2311yescharacteristic
77#6712—21no—
78#6712—22no—
79#6712—22no—
80#6712—22no—
81#6712D412yes—
82C4×Dic15—21no—
83C4×Dic15—22no—
84C4×Dic15C2312yes—
85C2×C3⋊#168C2312yes—
86#6706—22no—
87#5727—51no—
88#5721—51no—
89C3×#487D511yescharacteristic, complemented
90#5094—51no—
91#5083—51no—
92#4818—52no—
93#4792—52no—
94#4791—52no—
95#4788—52no—
96C4×#204—51no—
97C8×Dic6—51no—
98C2×Q8×D5—61no—
99C5×C4⋊Q8C2×D311yescharacteristic
100C5×C4⋊Q8C2×D311yescharacteristic
101#4092—61no—
102Q8×Dic5—32no—
103#4090—32no—
104C2×#688—32no—
105C2×#677—31no—
106#4042—62no—
107#4039—32no—
108#4036—61no—
109#4035—62no—
110#4034—32no—
111#4033—61no—
112C4×D20—31no—
113C4×Dic10—31no—
114C4×Dic10—31no—
115C5×#103C2×D312yes—
116C5×#103C2×D312yes—
117C4×C5×C8C2×D311yescharacteristic
118#3967—32no—
119#3953—31no—
120#3949—31no—
121#3948—31no—
122#3946—32no—
123C8×Dic5—32no—
124#3942—32no—
125#3940—32no—
126C4⋊#168—31no—
127#3359—151noSylow
128C22×D15—21no—
129C3×C5×Q8—22no—
130C3×C5×Q8—22no—
131C3×C5×Q8—42no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2411yescharacteristic
137C2×Dic15—21no—
138C2×Dic15—21no—
139C2×Dic15—21no—
140C2×Dic15C2×D412yes—
141C2×Dic15C2×D412yes—
142D60—21no—
143D60#4112yes—
144C4×D15—42no—
145C4×D15—44no—
146Dic30—21no—
147Dic30—21no—
148Dic30—44no—
149Dic30SD1614yescomplemented
150C3×C5×C8—21no—
151C3×C5×C8—21no—
152C3⋊#168—22no—
153C2×D3×Q8—101no—
154C3×C4⋊Q8C2×D511yescharacteristic
155C3×C4⋊Q8C2×D511yescharacteristic
156#946—101no—
157Q8×Dic3—52no—
158#944—52no—
159C2×#215—52no—
160C2×#204—51no—
161#896—102no—
162#893—52no—
163#890—101no—
164#889—102no—
165#888—52no—
166#887—101no—
167C4×D12—51no—
168C4×Dic6—51no—
169C4×Dic6—51no—
170C3×#103C2×D512yes—
171C3×#103C2×D512yes—
172C3×C4×C8C2×D511yescharacteristic
173#835—52no—
174#821—51no—
175#817—51no—
176#816—51no—
177Dic3⋊C8—52no—
178C8×Dic3—52no—
179#810—52no—
180#808—52no—
181C4⋊(C3⋊C8)—51no—
182C2×C5×Q8—21no—
183C2×C5×Q8C22×D312yes—
184Q8×D5—124no—
185C2×D20—31no—
186C2×C4×D5—62no—
187C2×C4×D5—61no—
188C2×Dic10—31no—
189C2×Dic10—31no—
190C2×Dic10—62no—
191C2×C5×C8C22×D311yescharacteristic
192C2×C5×C8C22×D311yescharacteristic
193C5×C4⋊C4—21no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4C22×D312yes—
197C42×C5C22×D311yescharacteristic
198#688—64no—
199#685—62no—
200#685—61no—
201C4⋊Dic5—31no—
202C4⋊Dic5—31no—
203C4⋊Dic5—31no—
204C4⋊Dic5—62no—
205#683—32no—
206#683—62no—
207#683—62no—
208#683—62no—
209#683—61no—
210C4×Dic5—32no—
211C4×Dic5—62no—
212C4×Dic5—61no—
213C2×#168—32no—
214#677—62no—
215#557—151no—
216D4×Q8—151no—
217#487—152no—
218#487D1511yescharacteristic, complemented
219#475—151no—
220#475—152no—
221#461—151no—
222#461—152no—
223C8×Q8—151no—
224C4×SD16—152no—
225C4×SD16—151no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—22no—
228C2×D15—41no—
229C2×D15—41no—
230C3×C4×C5—21no—
231C3×C4×C5—42no—
232C3×C4×C5—42no—
233C3×C4×C5C2×SD1612yes—
234C3×C4×C5C2×#4111yescharacteristic
235C3×C4×C52−1+411yescharacteristic
236Dic15—22no—
237Dic15—41no—
238Dic15—41no—
239Dic15—41no—
240Dic15C2×SD1614yes—
241C2×C3×Q8—21no—
242C2×C3×Q8C22×D512yes—
243D3×Q8—204no—
244C2×D12—51no—
245C2×C4×D3—102no—
246C2×C4×D3—101no—
247C2×Dic6—51no—
248C2×Dic6—51no—
249C2×Dic6—102no—
250C2×C3×C8C22×D511yescharacteristic
251C2×C3×C8C22×D511yescharacteristic
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4C22×D512yes—
256C3×C42C22×D511yescharacteristic
257#215—104no—
258(C2×D3)⋊C4—102no—
259(C2×D3)⋊C4—101no—
260C4⋊Dic3—51no—
261C4⋊Dic3—51no—
262C4⋊Dic3—51no—
263C4⋊Dic3—102no—
264Dic3⋊C4—52no—
265Dic3⋊C4—102no—
266Dic3⋊C4—102no—
267Dic3⋊C4—102no—
268Dic3⋊C4—101no—
269C4×Dic3—52no—
270C4×Dic3—102no—
271C4×Dic3—101no—
272C2×C3⋊C8—52no—
273#204—102no—
274C22×D5—61no—
275C5×Q8—22no—
276C5×Q8—22no—
277C5×Q8—42no—
278C2×C4×C5—22no—
279C2×C4×C5—22no—
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5C23×D311yescharacteristic
283C2×Dic5—32no—
284C2×Dic5—32no—
285C2×Dic5—61no—
286C2×Dic5—61no—
287C2×Dic5—61no—
288D20—32no—
289D20—61no—
290C4×D5—124no—
291C4×D5—122no—
292Dic10—34no—
293Dic10—61no—
294Dic10—61no—
295Dic10—124no—
296C5×C8—21no—
297C5×C8—21no—
298#168—62no—
299C22×Q8—301no—
300C2×SD16—152no—
301C2×SD16—151no—
302C4⋊Q8—152no—
303C4⋊Q8—152no—
304C4⋊Q8C2×D1511yescharacteristic
305C4⋊Q8C2×D1511yescharacteristic
306#125—302no—
307#125—301no—
308C22⋊Q8—302no—
309C22⋊Q8—301no—
310C4×Q8—151no—
311C4×Q8—152no—
312C4×Q8—151no—
313C4×Q8—301no—
314C4×D4—152no—
315C4×D4—151no—
316#106—151no—
317#106—152no—
318C4⋊C8—152no—
319C4⋊C8—151no—
320#103—152no—
321#103—151no—
322#103—152no—
323#103C2×D1512yes—
324#103C2×D1512yes—
325#102—151no—
326C4×C8—152no—
327C4×C8C2×D1511yescharacteristic
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C22×SD1611yescharacteristic
330C2×C3×C5#57811yescharacteristic
331D15—42no—
332C22×D3—101no—
333C3×Q8—22no—
334C3×Q8—22no—
335C3×Q8—42no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4D4×D511yescharacteristic
339C2×C3×C4D4×D511yescharacteristic
340C2×C3×C4C23×D511yescharacteristic
341C2×Dic3—52no—
342C2×Dic3—52no—
343C2×Dic3—101no—
344C2×Dic3—101no—
345C2×Dic3—101no—
346D12—52no—
347D12—101no—
348C4×D3—204no—
349C4×D3—202no—
350Dic6—54no—
351Dic6—101no—
352Dic6—101no—
353Dic6—204no—
354C3×C8—21no—
355C3×C8—21no—
356C3⋊C8—102no—
357C22×C5C2×D3×D411yescharacteristic
358C2×D5—62no—
359C2×D5—121no—
360C2×D5—121no—
361C4×C5—21no—
362C4×C5—42no—
363C4×C5—42no—
364C4×C5D3×SD1612yes—
365C4×C5D3×#4111yescharacteristic
366C4×C5#101011yescharacteristic
367Dic5—34no—
368Dic5—62no—
369Dic5—121no—
370Dic5—121no—
371Dic5—121no—
372C2×Q8—21no—
373C2×Q8—151no—
374C2×Q8—151no—
375C2×Q8—302no—
376C2×Q8—604no—
377C2×Q8C22×D1512yes—
378C2×D4—151no—
379C22×C4—302no—
380C22×C4—301no—
381SD16—302no—
382SD16—304no—
383C2×C8—152no—
384C2×C8C22×D1511yescharacteristic
385C2×C8C22×D1511yescharacteristic
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—152no—
390C4⋊C4—151no—
391C4⋊C4—151no—
392C4⋊C4—151no—
393C4⋊C4—302no—
394C4⋊C4—302no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4—301no—
398C4⋊C4C22×D1512yes—
399C22⋊C4—302no—
400C22⋊C4—301no—
401C42—152no—
402C42—302no—
403C42—301no—
404C42C22×D1511yescharacteristic
405C3×C5#335911yescharacteristic, complemented, Hall
406C22×C3C2×D4×D511yescharacteristic
407C2×D3—102no—
408C2×D3—201no—
409C2×D3—201no—
410C3×C4—21no—
411C3×C4—42no—
412C3×C4—42no—
413C3×C4D5×SD1612yes—
414C3×C4D5×#4111yescharacteristic
415C3×C4#415011yescharacteristic
416Dic3—54no—
417Dic3—102no—
418Dic3—201no—
419Dic3—201no—
420Dic3—201no—
421C2×C5#567711yescharacteristic
422C2×C5C2×D3×SD1611yescharacteristic
423C2×C5#576611yescharacteristic
424D5—122no—
425C23—301no—
426Q8—22no—
427Q8—22no—
428Q8—42no—
429Q8—154no—
430Q8—301no—
431Q8—301no—
432Q8—604no—
433D4—152no—
434D4—301no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—152no—
438C2×C4—152no—
439C2×C4—301no—
440C2×C4—301no—
441C2×C4—301no—
442C2×C4—604no—
443C2×C4—602no—
444C2×C4D4×D1511yescharacteristic
445C2×C4D4×D1511yescharacteristic
446C2×C4C23×D1511yescharacteristic
447C8—21no—
448C8—21no—
449C8—302no—
450C2×C3#6601111yescharacteristic
451C2×C3C2×D5×SD1611yescharacteristic
452C2×C3#6610011yescharacteristic
453D3—202no—
454C5#8162011yescharacteristic, complemented, Sylow
455C22—302no—
456C22—601no—
457C22—601no—
458C22C2×D4×D1511yescharacteristic
459C4—21no—
460C4—42no—
461C4—42no—
462C4—154no—
463C4—302no—
464C4—601no—
465C4—601no—
466C4—601no—
467C4SD16×D1512yes—
468C4#41×D1511yescharacteristic
469C4#9210111yescharacteristic
470C3#1061335111yescharacteristic, complemented, Sylow
471C2—602no—
472C2#1175643611yescharacteristic
473C2C2×SD16×D1511yescharacteristic
474C2#1175652511yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#487C2
socleC22×C3×C5C22×D4
prime radicalC2×D60C23
hypercenter#487D15
hypocenterC3×C5#3359
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #11756480C2semidirect
3. C3×C5×#487C2semidirect
4. #11751195C2semidirect
7. #11750893C2semidirect
8. #11750892C2semidirect
11. C8×Dic30C2semidirect
45. C5×#487D3semidirect
89. C3×#487D5semidirect
149. Dic30SD16semidirect
218. #487D15semidirect
405. C3×C5#3359semidirect
454. C5#81620semidirect
470. C3#10613351semidirect

Maximal subgroups

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

subgroupindex
#117564862
#117564802
C3×C5×#4872
#117511952
#117511842
#117509192
#117508932
#117508922
#117508892
C4×#67062
C8×Dic302
#106133513
#816205