Finite Group Databasebeta

← #14472171

Subgroups — #14472171

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#11752490C211yesmaximal, characteristic, complemented
2#11752486C211yesmaximal, characteristic
3#11750947C211yesmaximal, characteristic
4C5×#4849C211yesmaximal, characteristic, complemented
5C3×#65119C211yesmaximal, characteristic, complemented
6#11747985C212yesmaximal
7#11747859C212yesmaximal
8#11747855C212yesmaximal, complemented
9Dic5×Dic12C212yesmaximal, complemented
10C4×#6660C211yesmaximal, characteristic
11#11746929C211yesmaximal, characteristic, complemented
12#10612194—31nomaximal, Hall
13C4×D60C2211yescharacteristic
14#91758C2211yescharacteristic
15C2×C5×Dic12C2212yes—
16C5×#869C2211yescharacteristic
17C4×C5×Dic6C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19#91390—21no—
20#91389—21no—
21#91388C2212yes—
22#91375C2212yes—
23#91347—21no—
24#91343—22no—
25#91340—21no—
26#91337—22no—
27Dic5×Dic6C2212yes—
28Dic5×Dic6C2212yes—
29C2×#6660C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31#91105C2212yes—
32#91102C2212yes—
33C5×#816C2212yes—
34C3×#3946C2212yes—
35C3×C8×Dic5C2212yes—
36C3×C4×#168C2211yescharacteristic
37#90985C2211yescharacteristic
38#90973C2211yescharacteristic
39#90973C2212yes—
40#90973C2212yes—
41#90969C2211yescharacteristic
42#79934—51nomaximal, Hall
43#66066—31no—
44#65904—31no—
45C5×#462—31no—
46#65474—32no—
47Q16×Dic5—32no—
48#65370—31no—
49C4×#688—31no—
50#65135—31no—
51#65119D311yescharacteristic, complemented
52#65089—32no—
53#65085—32no—
54C2×D60C2311yescharacteristic
55C2×C4×D15—21no—
56C2×Dic30—21no—
57C2×C5×Dic6C2312yes—
58C2×C5×Dic6C2311yescharacteristic
59C2×C3×Dic10D411yescharacteristic
60C2×C3×C5×C8C2312yes—
61C3×C42×C5C2311yescharacteristic
62#6714—21no—
63C4⋊Dic15—21no—
64C4⋊Dic15C2312yes—
65C4⋊Dic15C2311yescharacteristic
66C5×C4⋊Dic3—21no—
67C5×C4⋊Dic3—21no—
68C5×C4⋊Dic3C2311yescharacteristic
69C5×Dic3⋊C4—21no—
70C4×C5×Dic3—21no—
71C5×Dic12—24no—
72C3×C4⋊Dic5D411yescharacteristic
73C3×#683D412yes—
74C3×C4×Dic5C2312yes—
75C2×C3×#168C2311yescharacteristic
76C2×C3×#168C2311yescharacteristic
77Dic3⋊Dic5—22no—
78Dic3⋊Dic5—22no—
79Dic3⋊Dic5—22no—
80#6669—22no—
81#6667—22no—
82#6667—22no—
83Dic3×Dic5—22no—
84Dic3×Dic5—22no—
85#6660—22no—
86#5584—51no—
87#5567—51no—
88C3×C8×Q8—51no—
89#4849D511yescharacteristic, complemented
90#4846—51no—
91#4845—52no—
92#4829—52no—
93C4×Dic12—52no—
94#4697—52no—
95C4×#204—51no—
96#4681—51no—
97C2×C5×Q16—32no—
98C5×C4⋊Q8—31no—
99C4×C5×Q8—31no—
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—61no—
113C4×Dic10C2×D311yescharacteristic
114C5×C4⋊C8C2×D311yescharacteristic
115C5×#103—32no—
116#3967—31no—
117#3967—32no—
118#3967—32no—
119#3953—32no—
120#3950—32no—
121#3946C2×D312yes—
122C8×Dic5C2×D312yes—
123#3941—31no—
124#3940—31no—
125C4×#168C2×D311yescharacteristic
126#3364—151noSylow
127C22×D15—21no—
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2411yescharacteristic
131C2×Dic15—21no—
132C2×Dic15—22no—
133D60—21no—
134D60—21no—
135C4×D15—42no—
136Dic30—42no—
137C2×C5×Dic3—21no—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—21no—
140C5×Dic6—21no—
141C5×Dic6—22no—
142C5×Dic6—22no—
143C5×Dic6#4112yes—
144C2×C3×Dic5C2×D412yes—
145C2×C3×Dic5C2×D412yes—
146C3×Dic10—22no—
147C3×C5×C8—22no—
148C3×#168—21no—
149C3×#168—21no—
150C3×C4×Q8—51no—
151#946—101no—
152#944—101no—
153C2×Dic12C2×D512yes—
154C2×#204—51no—
155#898—102no—
156#892—101no—
157#889—102no—
158#887—101no—
159#875—52no—
160C4×D12—51no—
161#870—52no—
162#869—51no—
163#869C2×D511yescharacteristic
164C4×Dic6—52no—
165C4×Dic6—52no—
166C4×Dic6C2×D511yescharacteristic
167C3×C4⋊C8—52no—
168C3×C4⋊C8C2×D511yescharacteristic
169C3×C4×C8—52no—
170C3×C4×C8—51no—
171#821—52no—
172#821—51no—
173#818—52no—
174#817—51no—
175#816—52no—
176#816—52no—
177#816—51no—
178#816C2×D512yes—
179C2×C5×Q8—31no—
180C2×C5×Q8—32no—
181C2×D20—31no—
182C2×C4×D5—61no—
183C2×Dic10—61no—
184C2×Dic10D1211yescharacteristic
185C5×Q16—64no—
186C2×C5×C8C22×D312yes—
187C5×C4⋊C4—31no—
188C5×C4⋊C4—61no—
189C5×C4⋊C4—61no—
190C5×C4⋊C4—61no—
191C42×C5—61no—
192C42×C5C22×D311yescharacteristic
193#688—62no—
194#685—61no—
195#685—62no—
196#685—62no—
197C4⋊Dic5—31no—
198C4⋊Dic5—32no—
199C4⋊Dic5—61no—
200C4⋊Dic5—62no—
201C4⋊Dic5—62no—
202C4⋊Dic5—62no—
203C4⋊Dic5D1211yescharacteristic
204#683—62no—
205#683D1212yes—
206C4×Dic5—62no—
207C4×Dic5—62no—
208C4×Dic5C22×D312yes—
209C2×#168C22×D311yescharacteristic
210C2×#168C22×D311yescharacteristic
211#557—151no—
212#556—151no—
213#488—152no—
214#487—151no—
215#479—152no—
216#474—151no—
217#464—152no—
218#462—31no—
219C8×Q8—51no—
220C4×Q16—152no—
221C4×SD16—151no—
222C22×C3×C5C22×D411yescharacteristic
223C2×D15—41no—
224C2×D15—41no—
225C2×D15—41no—
226C3×C4×C5—21no—
227C3×C4×C5#13512yes—
228C3×C4×C5C2×#4111yescharacteristic
229C3×C4×C52−1+411yescharacteristic
230Dic15—42no—
231Dic15—41no—
232C3×Dic5—22no—
233C3×Dic5—22no—
234C5×Dic3—22no—
235C5×Dic3—42no—
236C5×Dic3—41no—
237C2×C3×Q8—51no—
238C2×D12—51no—
239C2×C4×D3—101no—
240C2×Dic6—101no—
241C2×Dic6C22×D512yes—
242C2×Dic6C22×D511yescharacteristic
243C2×C3×C8—51no—
244C2×C3×C8—51no—
245C2×C3×C8C22×D512yes—
246C3×C4⋊C4—52no—
247C3×C4⋊C4—51no—
248C3×C42—52no—
249C3×C42C22×D511yescharacteristic
250(C2×D3)⋊C4—102no—
251(C2×D3)⋊C4—102no—
252(C2×D3)⋊C4—101no—
253C4⋊Dic3—21no—
254C4⋊Dic3—21no—
255C4⋊Dic3—52no—
256C4⋊Dic3—51no—
257C4⋊Dic3—101no—
258C4⋊Dic3C22×D511yescharacteristic
259Dic3⋊C4—21no—
260Dic3⋊C4—102no—
261Dic3⋊C4—102no—
262Dic3⋊C4—102no—
263Dic3⋊C4—102no—
264C4×Dic3—21no—
265C4×Dic3—102no—
266C4×Dic3—102no—
267Dic12—24no—
268#204—102no—
269C22×D5—61no—
270C5×Q8—32no—
271C5×Q8—61no—
272C5×Q8—62no—
273C5×Q8—62no—
274C2×C4×C5—61no—
275C2×C4×C5—62no—
276C2×C4×C5—61no—
277C2×C4×C5C2×D1211yescharacteristic
278C2×C4×C5C2×D1211yescharacteristic
279C2×C4×C5C23×D311yescharacteristic
280C2×Dic5—61no—
281C2×Dic5—62no—
282C2×Dic5C2×D1212yes—
283C2×Dic5C2×D1212yes—
284D20—61no—
285D20—61no—
286C4×D5—122no—
287Dic10—22no—
288Dic10—122no—
289C5×C8—22no—
290#168—21no—
291#168—21no—
292C2×Q16—32no—
293C2×SD16—151no—
294C4⋊Q8—31no—
295C4⋊Q8—151no—
296C4⋊Q8—301no—
297#126—302no—
298#125—152no—
299#125—302no—
300#124—152no—
301C22⋊Q8—301no—
302C4×Q8—31no—
303C4×Q8—51no—
304C4×Q8—152no—
305C4×Q8—152no—
306C4×Q8—301no—
307C4×D4—151no—
308#117—301no—
309#107—152no—
310#106—151no—
311C4⋊C8—52no—
312C4⋊C8D3×D511yescharacteristic
313#103—32no—
314#103—151no—
315#103—152no—
316#103—152no—
317#102—151no—
318#102—152no—
319C4×C8—52no—
320C4×C8—51no—
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324D15—81no—
325C22×D3—101no—
326C3×Q8—102no—
327C2×C3×C4—52no—
328C2×C3×C4—52no—
329C2×C3×C4D4×D511yescharacteristic
330C2×C3×C4D4×D511yescharacteristic
331C2×C3×C4C23×D511yescharacteristic
332C2×Dic3—21no—
333C2×Dic3—21no—
334C2×Dic3—22no—
335C2×Dic3—101no—
336C2×Dic3—102no—
337D12—101no—
338D12—101no—
339C4×D3—202no—
340Dic6—21no—
341Dic6—22no—
342Dic6—22no—
343Dic6—202no—
344Dic6#71112yes—
345C3×C8—22no—
346C3×C8—101no—
347C3×C8—101no—
348C22×C5C22×D1211yescharacteristic
349C2×D5—121no—
350C2×D5—121no—
351C2×D5—121no—
352C4×C5—21no—
353C4×C5—62no—
354C4×C5—121no—
355C4×C5—122no—
356C4×C5#90412yes—
357C4×C5#100711yescharacteristic
358C4×C5D3×#4111yescharacteristic
359Dic5—22no—
360Dic5—22no—
361Dic5—122no—
362Dic5—121no—
363C2×Q8—31no—
364C2×Q8—32no—
365C2×Q8—51no—
366C2×Q8—301no—
367C2×D4—151no—
368C22×C4—301no—
369Q16—64no—
370SD16—302no—
371C2×C8—51no—
372C2×C8—51no—
373C2×C8C2×D3×D512yes—
374C4⋊C4—31no—
375C4⋊C4—51no—
376C4⋊C4—52no—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C4⋊C4—152no—
381C4⋊C4—151no—
382C4⋊C4—302no—
383C4⋊C4—302no—
384C4⋊C4—302no—
385C4⋊C4—302no—
386C4⋊C4—301no—
387C22⋊C4—302no—
388C22⋊C4—302no—
389C22⋊C4—301no—
390C42—52no—
391C42—61no—
392C42—302no—
393C42—302no—
394C42C2×D3×D511yescharacteristic
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3C2×D4×D511yescharacteristic
397C2×D3—201no—
398C2×D3—201no—
399C2×D3—201no—
400C3×C4—21no—
401C3×C4—102no—
402C3×C4—102no—
403C3×C4#406512yes—
404C3×C4C2×#71111yescharacteristic
405C3×C4#415011yescharacteristic
406Dic3—22no—
407Dic3—41no—
408Dic3—42no—
409Dic3—202no—
410Dic3—201no—
411C2×C5#557611yescharacteristic
412C2×C5C2×#90411yescharacteristic
413C2×C5#575311yescharacteristic
414D5—241no—
415C23—301no—
416Q8—32no—
417Q8—61no—
418Q8—62no—
419Q8—62no—
420Q8—102no—
421Q8—602no—
422D4—301no—
423D4—301no—
424C2×C4—52no—
425C2×C4—52no—
426C2×C4—61no—
427C2×C4—61no—
428C2×C4—62no—
429C2×C4—301no—
430C2×C4—302no—
431C2×C4—602no—
432C2×C4D5×D1211yescharacteristic
433C2×C4D5×D1211yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—22no—
436C8—101no—
437C8—101no—
438C2×C3#6593211yescharacteristic
439C2×C3C2×#406511yescharacteristic
440C2×C3#6611311yescharacteristic
441D3—401no—
442C5#7993411yescharacteristic, complemented, Sylow
443C22—601no—
444C22—601no—
445C22—601no—
446C22C2×D5×D1211yescharacteristic
447C4—21no—
448C4—62no—
449C4—102no—
450C4—102no—
451C4—121no—
452C4—122no—
453C4—601no—
454C4—602no—
455C4#9127112yes—
456C4D3×#71111yescharacteristic
457C4#9203011yescharacteristic
458C3#1061219411yescharacteristic, complemented, Sylow
459C2—1201no—
460C2#1175343711yescharacteristic
461C2C2×#9127111yescharacteristic
462C2#1175404011yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC2×D60C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #11752490C2semidirect
4. C5×#4849C2semidirect
5. C3×#65119C2semidirect
8. #11747855C2semidirect
9. Dic5×Dic12C2semidirect
11. #11746929C2semidirect
51. #65119D3semidirect
89. #4849D5semidirect
395. C3×C5#3364semidirect
442. C5#79934semidirect
458. C3#10612194semidirect

Maximal subgroups

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

subgroupindex
#117524902
#117524862
#117509472
C5×#48492
C3×#651192
#117479852
#117478592
#117478552
Dic5×Dic122
C4×#66602
#117469292
#106121943
#799345