Finite Group Databasebeta

← #14472087

Subgroups — #14472087

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756491C211yesmaximal, characteristic
2#11756329C211yesmaximal, characteristic, complemented
3C3×C5×#462C211yesmaximal, characteristic, complemented
4#11751286C212yesmaximal
5Q16×Dic15C212yesmaximal, complemented
6#11751180C211yesmaximal, characteristic, complemented
7C4×#6717C211yesmaximal, characteristic
8#11750947C211yesmaximal, characteristic
9#11750931C211yesmaximal, characteristic, complemented
10#11750901C212yesmaximal
11#11750897C212yesmaximal, complemented
12#10612194—31nomaximal, Hall
13C2×C3×C5×Q16C2212yes—
14C3×C5×C4⋊Q8C2211yescharacteristic
15C3×C4×C5×Q8C2211yescharacteristic
16#91836C2212yes—
17Q8×Dic15C2212yes—
18Q8×Dic15C2212yes—
19C2×#6717C2211yescharacteristic
20#91787—22no—
21#91786—21no—
22#91781—21no—
23#91779—22no—
24#91779C2212yes—
25C4×D60C2211yescharacteristic
26#91758—21no—
27#91758C2211yescharacteristic
28C4×Dic30—21no—
29C4×Dic30C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31C3×C5×#103C2212yes—
32#91119C2212yes—
33#91119C2212yes—
34#91119C2211yescharacteristic
35#91105C2212yes—
36#91102C2212yes—
37#91098C2212yes—
38C8×Dic15C2212yes—
39#91093C2211yescharacteristic
40#91092C2211yescharacteristic
41C4×C3⋊#168C2211yescharacteristic
42#80463—51nomaximal, Hall
43#66066—31no—
44#65904—31no—
45C5×#462D311yescharacteristic, complemented
46#65474—32no—
47Q16×Dic5—32no—
48#65370—31no—
49C4×#688—31no—
50#65135—31no—
51#65119—31no—
52#65089—32no—
53#65085—32no—
54C2×C3×C5×Q8C2312yes—
55C2×C3×C5×Q8C2311yescharacteristic
56C2×D60C2311yescharacteristic
57C2×C4×D15—21no—
58C2×Dic30—21no—
59C2×Dic30D411yescharacteristic
60C3×C5×Q16—24no—
61C2×C3×C5×C8C2312yes—
62C3×C5×C4⋊C4—21no—
63C3×C5×C4⋊C4—21no—
64C3×C5×C4⋊C4—21no—
65C3×C5×C4⋊C4C2311yescharacteristic
66C3×C42×C5—21no—
67C3×C42×C5C2311yescharacteristic
68#6717—22no—
69#6714—21no—
70#6714—22no—
71#6714—22no—
72C4⋊Dic15—21no—
73C4⋊Dic15—22no—
74C4⋊Dic15—22no—
75C4⋊Dic15—22no—
76C4⋊Dic15D411yescharacteristic
77C4⋊Dic15C2312yes—
78C4⋊Dic15C2311yescharacteristic
79#6712—22no—
80#6712D412yes—
81C4×Dic15—22no—
82C4×Dic15—22no—
83C4×Dic15C2312yes—
84C2×C3⋊#168C2311yescharacteristic
85C2×C3⋊#168C2311yescharacteristic
86#5732—51no—
87#5570—51no—
88C3×#462D511yescharacteristic, complemented
89#5185—52no—
90Dic3×Q16—52no—
91#5079—51no—
92C4×#215—51no—
93#4846—51no—
94#4830—51no—
95#4800—52no—
96#4796—52no—
97C2×C5×Q16C2×D312yes—
98C5×C4⋊Q8C2×D311yescharacteristic
99C4×C5×Q8C2×D311yescharacteristic
100#4093—32no—
101Q8×Dic5—32no—
102Q8×Dic5—32no—
103C2×#688—31no—
104#4044—62no—
105#4043—61no—
106#4038—61no—
107#4036—32no—
108#4036—62no—
109C4×D20—31no—
110#4015—31no—
111#4015—61no—
112C4×Dic10—31no—
113C4×Dic10—61no—
114C5×C4⋊C8C2×D311yescharacteristic
115C5×#103C2×D312yes—
116#3967—31no—
117#3967—32no—
118#3967—32no—
119#3953—32no—
120#3950—32no—
121#3946—32no—
122C8×Dic5—32no—
123#3941—31no—
124#3940—31no—
125C4×#168—31no—
126#3364—151noSylow
127C22×D15—21no—
128C3×C5×Q8—21no—
129C3×C5×Q8—22no—
130C3×C5×Q8—22no—
131C3×C5×Q8#4112yes—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2411yescharacteristic
138C2×Dic15—21no—
139C2×Dic15—22no—
140C2×Dic15C2×D412yes—
141C2×Dic15C2×D412yes—
142D60—21no—
143D60—21no—
144C4×D15—42no—
145Dic30—22no—
146Dic30—42no—
147C3×C5×C8—22no—
148C3⋊#168—21no—
149C3⋊#168—21no—
150C2×C3×Q16C2×D512yes—
151C3×C4⋊Q8C2×D511yescharacteristic
152C3×C4×Q8C2×D511yescharacteristic
153#947—52no—
154Q8×Dic3—52no—
155Q8×Dic3—52no—
156C2×#215—51no—
157#898—102no—
158#897—101no—
159#892—101no—
160#890—52no—
161#890—102no—
162C4×D12—51no—
163#869—51no—
164#869—101no—
165C4×Dic6—51no—
166C4×Dic6—101no—
167C3×C4⋊C8C2×D511yescharacteristic
168C3×#103C2×D512yes—
169#835—51no—
170#835—52no—
171#835—52no—
172#821—52no—
173#818—52no—
174Dic3⋊C8—52no—
175C8×Dic3—52no—
176#809—51no—
177#808—51no—
178C4×C3⋊C8—51no—
179C2×C5×Q8C22×D312yes—
180C2×C5×Q8C22×D311yescharacteristic
181C2×D20—31no—
182C2×C4×D5—61no—
183C2×Dic10—31no—
184C2×Dic10—61no—
185C5×Q16—24no—
186C2×C5×C8C22×D312yes—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—21no—
189C5×C4⋊C4—21no—
190C5×C4⋊C4C22×D311yescharacteristic
191C42×C5—21no—
192C42×C5C22×D311yescharacteristic
193#688—62no—
194#685—62no—
195#685—62no—
196#685—61no—
197C4⋊Dic5—31no—
198C4⋊Dic5—31no—
199C4⋊Dic5—32no—
200C4⋊Dic5—62no—
201C4⋊Dic5—62no—
202C4⋊Dic5—62no—
203C4⋊Dic5—61no—
204#683—32no—
205#683—62no—
206C4×Dic5—32no—
207C4×Dic5—62no—
208C4×Dic5—62no—
209C2×#168—31no—
210C2×#168—31no—
211#557—151no—
212#556—151no—
213#488—152no—
214#487—151no—
215#479—152no—
216#474—151no—
217#464—152no—
218#462D1511yescharacteristic, complemented
219C8×Q8—151no—
220C4×Q16—152no—
221C4×SD16—151no—
222C22×C3×C5C22×D411yescharacteristic
223C2×D15—41no—
224C2×D15—41no—
225C2×D15—41no—
226C3×C4×C5—22no—
227C3×C4×C5—21no—
228C3×C4×C5—42no—
229C3×C4×C5—41no—
230C3×C4×C5#13512yes—
231C3×C4×C5C2×#4111yescharacteristic
232C3×C4×C52−1+411yescharacteristic
233Dic15—22no—
234Dic15—22no—
235Dic15—42no—
236Dic15—41no—
237C2×C3×Q8C22×D512yes—
238C2×C3×Q8C22×D511yescharacteristic
239C2×D12—51no—
240C2×C4×D3—101no—
241C2×Dic6—51no—
242C2×Dic6—101no—
243C3×Q16—24no—
244C2×C3×C8C22×D512yes—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4C22×D511yescharacteristic
249C3×C42—21no—
250C3×C42C22×D511yescharacteristic
251#215—102no—
252(C2×D3)⋊C4—102no—
253(C2×D3)⋊C4—102no—
254(C2×D3)⋊C4—101no—
255C4⋊Dic3—51no—
256C4⋊Dic3—51no—
257C4⋊Dic3—52no—
258C4⋊Dic3—102no—
259C4⋊Dic3—102no—
260C4⋊Dic3—102no—
261C4⋊Dic3—101no—
262Dic3⋊C4—52no—
263Dic3⋊C4—102no—
264C4×Dic3—52no—
265C4×Dic3—102no—
266C4×Dic3—102no—
267C2×C3⋊C8—51no—
268C2×C3⋊C8—51no—
269C22×D5—61no—
270C5×Q8—21no—
271C5×Q8—22no—
272C5×Q8—22no—
273C5×Q8#23712yes—
274C2×C4×C5—21no—
275C2×C4×C5—22no—
276C2×C4×C5—21no—
277C2×C4×C5D3×D411yescharacteristic
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5C23×D311yescharacteristic
280C2×Dic5—32no—
281C2×Dic5—32no—
282C2×Dic5—61no—
283C2×Dic5—62no—
284D20—61no—
285D20—61no—
286C4×D5—122no—
287Dic10—62no—
288Dic10—122no—
289C5×C8—22no—
290#168—61no—
291#168—61no—
292C2×Q16C2×D1512yes—
293C2×SD16—151no—
294C4⋊Q8—151no—
295C4⋊Q8—301no—
296C4⋊Q8C2×D1511yescharacteristic
297#126—302no—
298#125—152no—
299#125—302no—
300#124—152no—
301C22⋊Q8—301no—
302C4×Q8—151no—
303C4×Q8—152no—
304C4×Q8—152no—
305C4×Q8—301no—
306C4×Q8C2×D1511yescharacteristic
307C4×D4—151no—
308#117—301no—
309#107—152no—
310#106—151no—
311C4⋊C8—152no—
312C4⋊C8C2×D1511yescharacteristic
313#103—151no—
314#103—152no—
315#103—152no—
316#103C2×D1512yes—
317#102—152no—
318#102—151no—
319C4×C8—152no—
320C4×C8—151no—
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324D15—81no—
325C22×D3—101no—
326C3×Q8—21no—
327C3×Q8—22no—
328C3×Q8—22no—
329C3×Q8#71112yes—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4D4×D511yescharacteristic
334C2×C3×C4D4×D511yescharacteristic
335C2×C3×C4C23×D511yescharacteristic
336C2×Dic3—52no—
337C2×Dic3—52no—
338C2×Dic3—101no—
339C2×Dic3—102no—
340D12—101no—
341D12—101no—
342C4×D3—202no—
343Dic6—102no—
344Dic6—202no—
345C3×C8—22no—
346C3⋊C8—101no—
347C3⋊C8—101no—
348C22×C5C2×D3×D411yescharacteristic
349C2×D5—121no—
350C2×D5—121no—
351C2×D5—121no—
352C4×C5—21no—
353C4×C5—22no—
354C4×C5—41no—
355C4×C5—42no—
356C4×C5#91912yes—
357C4×C5C2×#23711yescharacteristic
358C4×C5#101011yescharacteristic
359Dic5—62no—
360Dic5—62no—
361Dic5—122no—
362Dic5—121no—
363C2×Q8—151no—
364C2×Q8—301no—
365C2×Q8C22×D1512yes—
366C2×Q8C22×D1511yescharacteristic
367C2×D4—151no—
368C22×C4—301no—
369Q16—24no—
370SD16—302no—
371C2×C8—151no—
372C2×C8—151no—
373C2×C8C22×D1512yes—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—151no—
378C4⋊C4—152no—
379C4⋊C4—152no—
380C4⋊C4—151no—
381C4⋊C4—302no—
382C4⋊C4—302no—
383C4⋊C4—302no—
384C4⋊C4—302no—
385C4⋊C4—301no—
386C4⋊C4C22×D1511yescharacteristic
387C22⋊C4—302no—
388C22⋊C4—302no—
389C22⋊C4—301no—
390C42—21no—
391C42—152no—
392C42—302no—
393C42—302no—
394C42C22×D1511yescharacteristic
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3C2×D4×D511yescharacteristic
397C2×D3—201no—
398C2×D3—201no—
399C2×D3—201no—
400C3×C4—21no—
401C3×C4—22no—
402C3×C4—41no—
403C3×C4—42no—
404C3×C4#406512yes—
405C3×C4C2×#71111yescharacteristic
406C3×C4#415011yescharacteristic
407Dic3—102no—
408Dic3—102no—
409Dic3—202no—
410Dic3—201no—
411C2×C5#559811yescharacteristic
412C2×C5C2×#91911yescharacteristic
413C2×C5#577911yescharacteristic
414D5—241no—
415C23—301no—
416Q8—21no—
417Q8—22no—
418Q8—22no—
419Q8—302no—
420Q8—602no—
421Q8#681912yes—
422D4—301no—
423D4—301no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—152no—
428C2×C4—152no—
429C2×C4—301no—
430C2×C4—302no—
431C2×C4—602no—
432C2×C4D4×D1511yescharacteristic
433C2×C4D4×D1511yescharacteristic
434C2×C4C23×D1511yescharacteristic
435C8—22no—
436C8—301no—
437C8—301no—
438C2×C3#6593211yescharacteristic
439C2×C3C2×#406511yescharacteristic
440C2×C3#6611311yescharacteristic
441D3—401no—
442C5#8046311yescharacteristic, complemented, Sylow
443C22—601no—
444C22—601no—
445C22—601no—
446C22C2×D4×D1511yescharacteristic
447C4—22no—
448C4—21no—
449C4—42no—
450C4—41no—
451C4—302no—
452C4—302no—
453C4—601no—
454C4—602no—
455C4#9180812yes—
456C4C2×#681911yescharacteristic
457C4#9210111yescharacteristic
458C3#1061219411yescharacteristic, complemented, Sylow
459C2—1201no—
460C2#1175635711yescharacteristic
461C2C2×#9180811yescharacteristic
462C2#1175653811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#462C2
socleC22×C3×C5C22×D4
prime radicalC2×D60C23
hypercenter#462D15
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #11756329C2semidirect
3. C3×C5×#462C2semidirect
5. Q16×Dic15C2semidirect
6. #11751180C2semidirect
9. #11750931C2semidirect
11. #11750897C2semidirect
45. C5×#462D3semidirect
88. C3×#462D5semidirect
218. #462D15semidirect
395. C3×C5#3364semidirect
442. C5#80463semidirect
458. C3#10612194semidirect

Maximal subgroups

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

subgroupindex
#117564912
#117563292
C3×C5×#4622
#117512862
Q16×Dic152
#117511802
C4×#67172
#117509472
#117509312
#117509012
#117508972
#106121943
#804635