Finite Group Databasebeta

← #14471596

Subgroups — #14471596

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
1#11756489C211yesmaximal, characteristic, complemented
2#11756301C211yesmaximal, characteristic, complemented
3C3×C5×#476C211yesmaximal, characteristic, complemented
4#11751194C211yesmaximal, characteristic, complemented
5C4×#6715C211yesmaximal, characteristic
6#11750958C212yesmaximal, complemented
7#11750953C212yesmaximal, complemented
8#11750942C211yesmaximal, characteristic, complemented
9#11750931C211yesmaximal, characteristic, complemented
10#11750888C212yesmaximal
11#11750869C212yesmaximal, complemented
12#10612818—31nomaximal, Hall
13C3×C5×C4⋊Q8C2211yescharacteristic
14C3×C4×C5×D4C2211yescharacteristic
15#91835—22no—
16#91825C2212yes—
17C2×#6715C2211yescharacteristic
18#91815—21no—
19#91813—21no—
20C2×#6706C2212yes—
21#91786—21no—
22#91782C2212yes—
23C4⋊C4×D15—21no—
24#91779C2212yes—
25#91776C2212yes—
26#91768—22no—
27C4×D60C2211yescharacteristic
28#91758C2211yescharacteristic
29C4×Dic30C2211yescharacteristic
30C3×C5×#106C2212yes—
31C3×C5×C4⋊C8C2211yescharacteristic
32C3×C5×#102C2212yes—
33#91116C2211yescharacteristic
34#91100C2212yes—
35#91098C2212yes—
36C8×Dic15C2212yes—
37#91094C2212yes—
38#91094C2212yes—
39#91093C2211yescharacteristic
40#91091C2211yescharacteristic
41C4×C3⋊#168C2211yescharacteristic
42#81087—51nomaximal, Hall
43#66064—31no—
44#65876—31no—
45C5×#476D311yescharacteristic, complemented
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×Q8—21no—
55C2×C3×C5×D4C2311yescharacteristic
56C22×C3×C4×C5—21no—
57C2×D60C2311yescharacteristic
58C2×C4×D15—21no—
59C2×C4×D15—22no—
60C2×Dic30D411yescharacteristic
61C2×Dic30C2312yes—
62C2×C3×C5×C8C2312yes—
63C3×C5×C4⋊C4—21no—
64C3×C5×C4⋊C4C2311yescharacteristic
65C3×C5×C4⋊C4C2312yes—
66C3×C5×C22⋊C4—21no—
67C3×C42×C5C2311yescharacteristic
68#6719—22no—
69#6719—22no—
70#6715—22no—
71#6714—21no—
72#6714—22no—
73C4⋊Dic15—21no—
74C4⋊Dic15—21no—
75C4⋊Dic15—22no—
76C4⋊Dic15D411yescharacteristic
77C4⋊Dic15C2311yescharacteristic
78#6712—22no—
79#6712—22no—
80#6712D412yes—
81C4×Dic15—22no—
82C4×Dic15C2312yes—
83C2×C3⋊#168C2311yescharacteristic
84C2×C3⋊#168C2311yescharacteristic
85#6706—24no—
86#5730—51no—
87#5542—51no—
88C3×#476D511yescharacteristic, complemented
89#5093—51no—
90C4×#213—51no—
91#4857—52no—
92#4852—52no—
93#4841—51no—
94#4830—51no—
95#4787—52no—
96#4768—52no—
97C5×C4⋊Q8C2×D311yescharacteristic
98C4×C5×D4C2×D311yescharacteristic
99#4092—62no—
100#4082—32no—
101C2×#686—31no—
102#4072—61no—
103#4070—61no—
104C2×#677—32no—
105#4043—61no—
106#4039—32no—
107D5×C4⋊C4—61no—
108#4036—32no—
109#4033—32no—
110#4025—62no—
111C4×D20—31no—
112#4015—31no—
113C4×Dic10—31no—
114C5×#106C2×D312yes—
115C5×C4⋊C8C2×D311yescharacteristic
116C5×#102C2×D312yes—
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×Q8—81no—
130C3×C5×D4—21no—
131C3×C5×D4—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—42no—
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2411yescharacteristic
138C2×Dic15—22no—
139C2×Dic15—21no—
140C2×Dic15C2×D412yes—
141C2×Dic15C2×D412yes—
142D60—21no—
143D60#4112yes—
144C4×D15—42no—
145C4×D15—82no—
146Dic30—22no—
147Dic30—22no—
148Dic30—22no—
149C3×C5×C8—22no—
150C3⋊#168—21no—
151C3⋊#168—21no—
152C3×C4⋊Q8C2×D511yescharacteristic
153C3×C4×D4C2×D511yescharacteristic
154#946—102no—
155#936—52no—
156C2×#213—51no—
157#926—101no—
158#924—101no—
159C2×#204—52no—
160#897—101no—
161#893—52no—
162D3×C4⋊C4—101no—
163#890—52no—
164#887—52no—
165#879—102no—
166C4×D12—51no—
167#869—51no—
168C4×Dic6—51no—
169C3×#106C2×D512yes—
170C3×C4⋊C8C2×D511yescharacteristic
171C3×#102C2×D512yes—
172#832—51no—
173#816—52no—
174Dic3⋊C8—52no—
175C8×Dic3—52no—
176#810—52no—
177#810—52no—
178#809—51no—
179#807—51no—
180C4×C3⋊C8—51no—
181C2×C5×Q8—21no—
182C2×C5×D4C22×D311yescharacteristic
183C22×C4×C5—21no—
184C2×D20—31no—
185C2×C4×D5—61no—
186C2×C4×D5—62no—
187C2×Dic10—31no—
188C2×Dic10—32no—
189C2×C5×C8C22×D312yes—
190C5×C4⋊C4—21no—
191C5×C4⋊C4C22×D311yescharacteristic
192C5×C4⋊C4C22×D312yes—
193C5×C22⋊C4—21no—
194C42×C5C22×D311yescharacteristic
195C22⋊Dic5—62no—
196C22⋊Dic5—62no—
197#686—62no—
198#685—62no—
199#685—61no—
200C4⋊Dic5—31no—
201C4⋊Dic5—31no—
202C4⋊Dic5—62no—
203C4⋊Dic5—61no—
204C4⋊Dic5—61no—
205#683—32no—
206#683—62no—
207#683—62no—
208C4×Dic5—32no—
209C4×Dic5—62no—
210C2×#168—31no—
211C2×#168—31no—
212#677—64no—
213#556—151no—
214#554—151no—
215#488—152no—
216#487—151no—
217#479—152no—
218#476D1511yescharacteristic, complemented
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—42no—
234C3×C4×C5#13512yes—
235C3×C4×C5C2×#4111yescharacteristic
236C3×C4×C52−1+411yescharacteristic
237Dic15—22no—
238Dic15—22no—
239Dic15—42no—
240Dic15—41no—
241C2×C3×Q8—21no—
242C2×C3×D4C22×D511yescharacteristic
243C22×C3×C4—21no—
244C2×D12—51no—
245C2×C4×D3—101no—
246C2×C4×D3—102no—
247C2×Dic6—51no—
248C2×Dic6—52no—
249C2×C3×C8C22×D512yes—
250C3×C4⋊C4—21no—
251C3×C4⋊C4C22×D511yescharacteristic
252C3×C4⋊C4C22×D512yes—
253C3×C22⋊C4—21no—
254C3×C42C22×D511yescharacteristic
255#217—102no—
256#217—102no—
257#213—102no—
258(C2×D3)⋊C4—102no—
259(C2×D3)⋊C4—101no—
260C4⋊Dic3—51no—
261C4⋊Dic3—51no—
262C4⋊Dic3—102no—
263C4⋊Dic3—101no—
264C4⋊Dic3—101no—
265Dic3⋊C4—52no—
266Dic3⋊C4—102no—
267Dic3⋊C4—102no—
268C4×Dic3—52no—
269C4×Dic3—102no—
270C2×C3⋊C8—51no—
271C2×C3⋊C8—51no—
272#204—104no—
273C23×C5—21no—
274C22×D5—61no—
275C5×Q8—81no—
276C5×D4—21no—
277C5×D4—21no—
278C2×C4×C5—21no—
279C2×C4×C5—22no—
280C2×C4×C5—42no—
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5D3×D411yescharacteristic
283C2×C4×C5C23×D311yescharacteristic
284C2×Dic5—32no—
285C2×Dic5—32no—
286C2×Dic5—62no—
287C2×Dic5—61no—
288D20—32no—
289D20—61no—
290C4×D5—122no—
291C4×D5—242no—
292Dic10—62no—
293Dic10—62no—
294Dic10—62no—
295C5×C8—22no—
296#168—61no—
297#168—61no—
298C2×SD16—152no—
299C2×D8—151no—
300C4⋊Q8—151no—
301C4⋊Q8C2×D1511yescharacteristic
302#126—302no—
303#125—152no—
304#124—152no—
305C22⋊Q8—301no—
306C22⋊Q8—302no—
307C22⋊Q8—301no—
308C4×Q8—151no—
309C4×Q8—152no—
310C4×D4—152no—
311C4×D4—151no—
312C4×D4C2×D1511yescharacteristic
313#117—301no—
314C2×C4⋊C4—301no—
315#107—151no—
316#106C2×D1512yes—
317C4⋊C8—152no—
318C4⋊C8C2×D1511yescharacteristic
319#103—152no—
320#103—152no—
321#103—152no—
322#102—151no—
323#102—151no—
324#102C2×D1512yes—
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—81no—
335C3×D4—21no—
336C3×D4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—22no—
339C2×C3×C4—42no—
340C2×C3×C4D4×D511yescharacteristic
341C2×C3×C4D4×D511yescharacteristic
342C2×C3×C4C23×D511yescharacteristic
343C2×Dic3—52no—
344C2×Dic3—52no—
345C2×Dic3—102no—
346C2×Dic3—101no—
347D12—52no—
348D12—101no—
349C4×D3—202no—
350C4×D3—402no—
351Dic6—102no—
352Dic6—102no—
353Dic6—102no—
354C3×C8—22no—
355C3⋊C8—101no—
356C3⋊C8—101no—
357C22×C5—41no—
358C22×C5—41no—
359C22×C5—41no—
360C22×C5C2×D3×D411yescharacteristic
361C2×D5—62no—
362C2×D5—121no—
363C2×D5—121no—
364C4×C5—21no—
365C4×C5—41no—
366C4×C5—42no—
367C4×C5#91612yes—
368C4×C5#100711yescharacteristic
369C4×C5D3×#4111yescharacteristic
370Dic5—62no—
371Dic5—62no—
372Dic5—122no—
373Dic5—121no—
374C2×Q8—21no—
375C2×Q8—151no—
376C2×Q8—152no—
377C2×D4—151no—
378C2×D4C22×D1511yescharacteristic
379C22×C4—21no—
380C22×C4—302no—
381C22×C4—301no—
382SD16—304no—
383D8—302no—
384C2×C8—151no—
385C2×C8—151no—
386C2×C8C22×D1512yes—
387C4⋊C4—21no—
388C4⋊C4—151no—
389C4⋊C4—152no—
390C4⋊C4—151no—
391C4⋊C4—302no—
392C4⋊C4—302no—
393C4⋊C4—302no—
394C4⋊C4—301no—
395C4⋊C4—301no—
396C4⋊C4C22×D1511yescharacteristic
397C4⋊C4C22×D1512yes—
398C22⋊C4—21no—
399C22⋊C4—302no—
400C22⋊C4—302no—
401C22⋊C4—302no—
402C22⋊C4—301no—
403C42—152no—
404C42—302no—
405C42C22×D1511yescharacteristic
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—42no—
417C3×C4#406212yes—
418C3×C4#414711yescharacteristic
419C3×C4D5×#4111yescharacteristic
420Dic3—102no—
421Dic3—102no—
422Dic3—201no—
423Dic3—202no—
424C2×C5—81no—
425C2×C5#563311yescharacteristic
426C2×C5C2×#91611yescharacteristic
427C2×C5#577511yescharacteristic
428D5—122no—
429C23—21no—
430C23—301no—
431Q8—81no—
432Q8—302no—
433Q8—302no—
434Q8—302no—
435D4—21no—
436D4—21no—
437D4—152no—
438D4—301no—
439C2×C4—21no—
440C2×C4—22no—
441C2×C4—42no—
442C2×C4—152no—
443C2×C4—152no—
444C2×C4—302no—
445C2×C4—301no—
446C2×C4—602no—
447C2×C4—1202no—
448C2×C4D4×D1511yescharacteristic
449C2×C4D4×D1511yescharacteristic
450C2×C4C23×D1511yescharacteristic
451C8—22no—
452C8—301no—
453C8—301no—
454C2×C3—81no—
455C2×C3#6596711yescharacteristic
456C2×C3C2×#406211yescharacteristic
457C2×C3#6610911yescharacteristic
458D3—202no—
459C5#8108711yescharacteristic, complemented, Sylow
460C22—41no—
461C22—41no—
462C22—41no—
463C22—302no—
464C22—601no—
465C22—601no—
466C22C2×D4×D1511yescharacteristic
467C4—21no—
468C4—41no—
469C4—42no—
470C4—302no—
471C4—302no—
472C4—602no—
473C4—601no—
474C4#9180512yes—
475C4#9209811yescharacteristic
476C4#41×D1511yescharacteristic
477C3#1061281811yescharacteristic, complemented, Sylow
478C2—81no—
479C2—602no—
480C2#1175639211yescharacteristic
481C2C2×#9180511yescharacteristic
482C2#1175653411yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#476C2
socleC22×C3×C5C22×D4
prime radicalC2×#6715C22
hypercenter#476D15
hypocenterC3×C5#3360
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #11756489C2semidirect
2. #11756301C2semidirect
3. C3×C5×#476C2semidirect
4. #11751194C2semidirect
6. #11750958C2semidirect
7. #11750953C2semidirect
8. #11750942C2semidirect
9. #11750931C2semidirect
11. #11750869C2semidirect
45. C5×#476D3semidirect
88. C3×#476D5semidirect
218. #476D15semidirect
406. C3×C5#3360semidirect
459. C5#81087semidirect
477. C3#10612818semidirect

Maximal subgroups

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

subgroupindex
#117564892
#117563012
C3×C5×#4762
#117511942
C4×#67152
#117509582
#117509532
#117509422
#117509312
#117508882
#117508692
#106128183
#810875