Finite Group Databasebeta

← #14437790

Subgroups — #14437790

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756487C211yesmaximal, characteristic, complemented
2#11756484C211yesmaximal, characteristic
3C3×C5×#487C211yesmaximal, characteristic, complemented
4#11751189C211yesmaximal, characteristic, complemented
5#11751180C211yesmaximal, characteristic, complemented
6#11750905C214yesmaximal, complemented
7#11750901C214yesmaximal, complemented
8#11750795C211yesmaximal, characteristic, complemented
9C4×C8×D15C211yesmaximal, characteristic, complemented
10#10613329—31nomaximal, Hall
11C2×#6821C2212yes—
12C3×C5×C4⋊Q8C2211yescharacteristic
13C3×C5×C4⋊Q8C2211yescharacteristic
14#91836C2212yes—
15#91835—21no—
16Q8×Dic15—21no—
17C2×C8×D15C2212yes—
18#91786—21no—
19#91784—21no—
20#91784—21no—
21#91782—21no—
22#91782—21no—
23#91781C2212yes—
24#91779C2212yes—
25#91776—21no—
26#91763C2211yescharacteristic
27C42×D15C2211yescharacteristic
28#91758C2211yescharacteristic
29C3×C5×#103C2214yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91119C2214yes—
32#91105C2214yes—
33C8×Dic15C2212yes—
34#91093C2214yes—
35C4×C3⋊#168C2211yescharacteristic
36#81598—51nomaximal, Hall
37#66062—31no—
38#66059—31no—
39C5×#487D311yescharacteristic, complemented
40#65377—31no—
41#65370—31no—
42#65093—34no—
43#65089—34no—
44#64983—31no—
45C4×C8×D5—31no—
46C2×C3×C5×Q8—21no—
47C2×C3×C5×Q8C2312yes—
48#6821—28no—
49C2×D60—22no—
50C2×D60—21no—
51C2×D60—21no—
52C2×D60C2312yes—
53C2×C4×D15—22no—
54C2×C4×D15D411yescharacteristic
55C2×C4×D15D411yescharacteristic
56C2×C4×D15C2311yescharacteristic
57C2×Dic30—21no—
58C2×C3×C5×C8C2312yes—
59C3×C5×C4⋊C4—21no—
60C3×C5×C4⋊C4—21no—
61C3×C5×C4⋊C4—21no—
62C3×C5×C4⋊C4C2312yes—
63C3×C42×C5C2311yescharacteristic
64#6714—22no—
65#6714—22no—
66#6714—22no—
67C4⋊Dic15—21no—
68C4⋊Dic15—22no—
69C4⋊Dic15C2312yes—
70#6712—22no—
71C4×Dic15—22no—
72C4×Dic15D411yescharacteristic
73C4×Dic15D411yescharacteristic
74C4×Dic15C2311yescharacteristic
75C2×C3⋊#168C2312yes—
76C8×D15—24no—
77#5728—51no—
78#5725—51no—
79C3×#487D511yescharacteristic, complemented
80#5088—51no—
81#5079—51no—
82#4804—54no—
83#4800—54no—
84#4694—51no—
85C4×D3×C8—51no—
86C2×#713—32no—
87C5×C4⋊Q8C2×D311yescharacteristic
88C5×C4⋊Q8C2×D311yescharacteristic
89#4093—32no—
90#4092—61no—
91Q8×Dic5—61no—
92C2×C8×D5—32no—
93#4043—61no—
94#4041—61no—
95#4041—61no—
96#4039—61no—
97#4039—61no—
98#4038—32no—
99#4036—32no—
100#4033—61no—
101#4020—31no—
102C42×D5—31no—
103#4015—31no—
104C5×#103C2×D314yes—
105C4×C5×C8C2×D311yescharacteristic
106#3967—34no—
107#3953—34no—
108C8×Dic5—32no—
109#3941—34no—
110C4×#168—31no—
111#3131—151noSylow
112C22×D15—22no—
113C22×D15C2×D411yescharacteristic
114C3×C5×Q8—24no—
115C3×C5×Q8—42no—
116C2×C3×C4×C5—22no—
117C2×C3×C4×C5—22no—
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5C2×D411yescharacteristic
120C2×C3×C4×C5C2411yescharacteristic
121C2×Dic15—22no—
122C2×Dic15C2×D411yescharacteristic
123C2×Dic15C2×D411yescharacteristic
124C2×Dic15C2×D411yescharacteristic
125D60—24no—
126D60—44no—
127D60—42no—
128D60—42no—
129C4×D15—22no—
130C4×D15—22no—
131C4×D15—44no—
132C4×D15#4114yes—
133Dic30—42no—
134C3×C5×C8—22no—
135C3⋊#168—22no—
136C2×#239—52no—
137C3×C4⋊Q8C2×D511yescharacteristic
138C3×C4⋊Q8C2×D511yescharacteristic
139#947—52no—
140#946—101no—
141Q8×Dic3—101no—
142C2×D3×C8—52no—
143#897—101no—
144#895—101no—
145#895—101no—
146#893—101no—
147#893—101no—
148#892—52no—
149#890—52no—
150#887—101no—
151#874—51no—
152C42×D3—51no—
153#869—51no—
154C3×#103C2×D514yes—
155C3×C4×C8C2×D511yescharacteristic
156#835—54no—
157#821—54no—
158C8×Dic3—52no—
159#809—54no—
160C4×C3⋊C8—51no—
161C2×C5×Q8—21no—
162C2×C5×Q8C22×D312yes—
163#713—68no—
164C2×D20—32no—
165C2×D20—62no—
166C2×D20—61no—
167C2×D20—61no—
168C2×C4×D5—31no—
169C2×C4×D5—31no—
170C2×C4×D5—31no—
171C2×C4×D5—62no—
172C2×Dic10—61no—
173C2×C5×C8C22×D312yes—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4C22×D312yes—
178C42×C5C22×D311yescharacteristic
179#685—62no—
180#685—62no—
181#685—62no—
182C4⋊Dic5—32no—
183C4⋊Dic5—62no—
184C4⋊Dic5—61no—
185#683—62no—
186C4×Dic5—31no—
187C4×Dic5—31no—
188C4×Dic5—31no—
189C4×Dic5—62no—
190C2×#168—32no—
191C8×D5—64no—
192#533—151no—
193#532—151no—
194#488—154no—
195#487—151no—
196#487D1511yescharacteristic, complemented
197#486—151no—
198#486—151no—
199#416—154no—
200C2×C4×C8—151no—
201C22×C3×C5C22×D411yescharacteristic
202C2×D15—21no—
203C2×D15—21no—
204C2×D15—42no—
205C2×D15—42no—
206C2×D15—42no—
207C2×D15#12412yes—
208C3×C4×C5—42no—
209C3×C4×C5—42no—
210C3×C4×C5#13512yes—
211C3×C4×C5#13512yes—
212C3×C4×C5C2×#4112yes—
213Dic15—21no—
214Dic15—21no—
215Dic15—42no—
216Dic15#12412yes—
217C2×C3×Q8—21no—
218C2×C3×Q8C22×D512yes—
219#239—108no—
220C2×D12—52no—
221C2×D12—102no—
222C2×D12—101no—
223C2×D12—101no—
224C2×C4×D3—51no—
225C2×C4×D3—51no—
226C2×C4×D3—51no—
227C2×C4×D3—102no—
228C2×Dic6—101no—
229C2×C3×C8C22×D512yes—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4C22×D512yes—
234C3×C42C22×D511yescharacteristic
235(C2×D3)⋊C4—102no—
236(C2×D3)⋊C4—102no—
237(C2×D3)⋊C4—102no—
238C4⋊Dic3—52no—
239C4⋊Dic3—102no—
240C4⋊Dic3—101no—
241Dic3⋊C4—102no—
242C4×Dic3—51no—
243C4×Dic3—51no—
244C4×Dic3—51no—
245C4×Dic3—102no—
246C2×C3⋊C8—52no—
247D3×C8—104no—
248C22×D5—31no—
249C22×D5—62no—
250C5×Q8—24no—
251C5×Q8—42no—
252C2×C4×C5—22no—
253C2×C4×C5—22no—
254C2×C4×C5D3×D411yescharacteristic
255C2×C4×C5D3×D411yescharacteristic
256C2×C4×C5C23×D311yescharacteristic
257C2×Dic5—31no—
258C2×Dic5—31no—
259C2×Dic5—31no—
260C2×Dic5—62no—
261D20—64no—
262D20—124no—
263D20—122no—
264D20—122no—
265C4×D5—34no—
266C4×D5—62no—
267C4×D5—62no—
268C4×D5—124no—
269Dic10—122no—
270C5×C8—22no—
271#168—62no—
272C2×#41—152no—
273C22×C8—152no—
274C4⋊Q8—151no—
275C4⋊Q8C2×D1511yescharacteristic
276C4⋊Q8C2×D1511yescharacteristic
277#127—151no—
278#125—152no—
279#124—152no—
280C22⋊Q8—301no—
281C22⋊Q8—301no—
282#121—301no—
283#121—301no—
284C4×Q8—301no—
285C4×Q8—301no—
286C4×D4—301no—
287C4×D4—301no—
288#117—152no—
289C2×C42—151no—
290#103—154no—
291#103C2×D1514yes—
292#102—154no—
293#102—154no—
294C4×C8—152no—
295C4×C8—151no—
296C4×C8C2×D1511yescharacteristic
297C2×C3×C5C2×#12411yescharacteristic
298C2×C3×C5C2×#13511yescharacteristic
299C2×C3×C5C2×#13511yescharacteristic
300D15—22no—
301D15—82no—
302C22×D3—51no—
303C22×D3—102no—
304C3×Q8—24no—
305C3×Q8—42no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4D4×D511yescharacteristic
309C2×C3×C4D4×D511yescharacteristic
310C2×C3×C4C23×D511yescharacteristic
311C2×Dic3—51no—
312C2×Dic3—51no—
313C2×Dic3—51no—
314C2×Dic3—102no—
315D12—104no—
316D12—204no—
317D12—202no—
318D12—202no—
319C4×D3—54no—
320C4×D3—102no—
321C4×D3—102no—
322C4×D3—204no—
323Dic6—202no—
324C3×C8—22no—
325C3⋊C8—102no—
326C22×C5C2×D3×D411yescharacteristic
327C2×D5—32no—
328C2×D5—61no—
329C2×D5—61no—
330C2×D5—122no—
331C2×D5—122no—
332C2×D5—122no—
333C4×C5—42no—
334C4×C5—42no—
335C4×C5#91612yes—
336C4×C5#91912yes—
337C4×C5D3×#4112yes—
338Dic5—32no—
339Dic5—61no—
340Dic5—61no—
341Dic5—122no—
342#41—308no—
343C2×Q8—21no—
344C2×Q8—301no—
345C2×Q8C22×D1512yes—
346C2×D4—152no—
347C2×D4—302no—
348C2×D4—301no—
349C2×D4—301no—
350C22×C4—151no—
351C22×C4—151no—
352C22×C4—151no—
353C22×C4—302no—
354C2×C8—152no—
355C2×C8—304no—
356C2×C8C22×D1512yes—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—152no—
361C4⋊C4—302no—
362C4⋊C4—302no—
363C4⋊C4—301no—
364C4⋊C4C22×D1512yes—
365C22⋊C4—302no—
366C22⋊C4—302no—
367C22⋊C4—302no—
368C42—151no—
369C42—151no—
370C42—151no—
371C42—302no—
372C42C22×D1511yescharacteristic
373C3×C5#313111yescharacteristic, complemented, Hall
374C22×C3C2×D4×D511yescharacteristic
375C2×D3—52no—
376C2×D3—101no—
377C2×D3—101no—
378C2×D3—202no—
379C2×D3—202no—
380C2×D3—202no—
381C3×C4—42no—
382C3×C4—42no—
383C3×C4#406212yes—
384C3×C4#406512yes—
385C3×C4D5×#4112yes—
386Dic3—52no—
387Dic3—101no—
388Dic3—101no—
389Dic3—202no—
390C2×C5D3×#12411yescharacteristic
391C2×C5C2×#91611yescharacteristic
392C2×C5C2×#91911yescharacteristic
393D5—62no—
394D5—242no—
395C23—151no—
396C23—302no—
397Q8—24no—
398Q8—42no—
399Q8—602no—
400D4—304no—
401D4—604no—
402D4—602no—
403D4—602no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—151no—
407C2×C4—154no—
408C2×C4—151no—
409C2×C4—151no—
410C2×C4—302no—
411C2×C4—302no—
412C2×C4—302no—
413C2×C4—604no—
414C2×C4D4×D1511yescharacteristic
415C2×C4D4×D1511yescharacteristic
416C2×C4C23×D1511yescharacteristic
417C8—22no—
418C8—302no—
419C2×C3D5×#12411yescharacteristic
420C2×C3C2×#406211yescharacteristic
421C2×C3C2×#406511yescharacteristic
422D3—102no—
423D3—402no—
424C5#8159811yescharacteristic, complemented, Sylow
425C22—152no—
426C22—301no—
427C22—301no—
428C22—602no—
429C22—602no—
430C22—602no—
431C22C2×D4×D1511yescharacteristic
432C4—42no—
433C4—42no—
434C4—152no—
435C4—301no—
436C4—301no—
437C4—602no—
438C4#9180512yes—
439C4#9180812yes—
440C4#41×D1512yes—
441C3#1061332911yescharacteristic, complemented, Sylow
442C2—302no—
443C2—1202no—
444C2D15×#12411yescharacteristic
445C2C2×#9180511yescharacteristic
446C2C2×#9180811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#487C2
socleC22×C3×C5C22×D4
prime radical#11756484C2
hypercenter#487D15
hypocenterC3×C5#3131
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
1. #11756487C2semidirect
3. C3×C5×#487C2semidirect
4. #11751189C2semidirect
5. #11751180C2semidirect
6. #11750905C2semidirect
7. #11750901C2semidirect
8. #11750795C2semidirect
9. C4×C8×D15C2semidirect
39. C5×#487D3semidirect
79. C3×#487D5semidirect
196. #487D15semidirect
373. C3×C5#3131semidirect
424. C5#81598semidirect
441. C3#10613329semidirect

Maximal subgroups

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

subgroupindex
#117564872
#117564842
C3×C5×#4872
#117511892
#117511802
#117509052
#117509012
#117507952
C4×C8×D152
#106133293
#815985