Finite Group Databasebeta

← #14305877

Subgroups — #14305877

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91836C211yesmaximal, characteristic
2C2×C3×C5×#103C211yesmaximal, characteristic, complemented
3C2×#91119C211yesmaximal, characteristic, complemented
4C2×#91105C211yesmaximal, characteristic
5C2×#91099C211yesmaximal, characteristic, complemented
6#11751076C211yesmaximal, characteristic, complemented
7C2×#91093C211yesmaximal, characteristic
8#10601020—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C22×D60C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13#91836—22no—
14#91836C414yescomplemented
15C2×#6714—22no—
16C2×C4⋊Dic15C2211yescharacteristic
17C2×#6712—22no—
18C2×C4×Dic15C2211yescharacteristic
19C22×C3⋊#168C2211yescharacteristic
20C3×C5×#103—22no—
21#91119—22no—
22#91105—22no—
23#91099—22no—
24#91093—22no—
25#70227—51nomaximal, Hall
26C2×#4093—31no—
27C2×C5×#103D311yescharacteristic, complemented
28C2×#3967—31no—
29C2×#3953—31no—
30C2×#3947—31no—
31#65265—31no—
32C2×#3941—31no—
33C23×D15—21no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8C2×C412yes—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5C2311yescharacteristic
43C22×Dic15—21no—
44C22×Dic15D412yes—
45C2×D60—21no—
46C2×D60—21no—
47C2×D60—21no—
48C2×D60—21no—
49C2×D60—21no—
50C2×D60C2×C412yes—
51C2×C3×C5×C8—21no—
52C2×C3×C5×C8—21no—
53C2×C3×C5×C8D412yes—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4—21no—
56#6714—28no—
57C4⋊Dic15—21no—
58C4⋊Dic15—21no—
59#6712—44no—
60C4×Dic15C2×C412yes—
61C4×Dic15D412yes—
62C2×C3⋊#168—21no—
63C2×C3⋊#168—21no—
64C2×C3⋊#168D412yes—
65C2×#947—51no—
66C2×C3×#103D511yescharacteristic, complemented
67C2×#835—51no—
68C2×#821—51no—
69C2×#815—51no—
70#4975—51no—
71C2×#809—51no—
72C22×C5×Q8C2×D311yescharacteristic
73C22×D20—31no—
74C22×C5×C8C2×D311yescharacteristic
75C2×C5×C4⋊C4C2×D311yescharacteristic
76#4093—34no—
77#4093—62no—
78C2×#685—62no—
79C2×C4⋊Dic5—31no—
80C2×#683—62no—
81C2×C4×Dic5—31no—
82C22×#168—31no—
83C5×#103—22no—
84#3967—62no—
85#3953—62no—
86#3947—62no—
87#3941—62no—
88#1959—151noSylow
89C23×C3×C5C2×D411yescharacteristic
90C22×D15—22no—
91C22×D15—41no—
92C22×D15—41no—
93C22×D15—42no—
94C22×D15—42no—
95C3×C5×Q8—22no—
96C3×C5×Q8—22no—
97C3×C5×Q8—41no—
98C3×C5×Q8—41no—
99C2×C3×C4×C5—22no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5—42no—
104C2×C3×C4×C5C22×C411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×Dic15—22no—
111C2×Dic15—22no—
112C2×Dic15—41no—
113C2×Dic15—42no—
114C2×Dic15C22⋊C414yes—
115D60—22no—
116D60—22no—
117D60—41no—
118D60—41no—
119C3×C5×C8—22no—
120C3⋊#168—22no—
121C22×C3×Q8C2×D511yescharacteristic
122C22×D12—51no—
123C22×C3×C8C2×D511yescharacteristic
124C2×C3×C4⋊C4C2×D511yescharacteristic
125#947—54no—
126#947—102no—
127C2×(C2×D3)⋊C4—102no—
128C2×C4⋊Dic3—51no—
129C2×Dic3⋊C4—102no—
130C2×C4×Dic3—51no—
131C22×C3⋊C8—51no—
132C3×#103—22no—
133#835—102no—
134#821—102no—
135#815—102no—
136#809—102no—
137C23×D5—61no—
138C2×C5×Q8—21no—
139C2×C5×Q8—21no—
140C2×C5×Q8—21no—
141C2×C5×Q8—21no—
142C2×C5×Q8—21no—
143C2×C5×Q8C4×D312yes—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5C22×D311yescharacteristic
147C22×Dic5—32no—
148C22×Dic5—61no—
149C2×D20—32no—
150C2×D20—61no—
151C2×D20—61no—
152C2×D20—61no—
153C2×D20—61no—
154C2×D20—61no—
155C2×C5×C8—21no—
156C2×C5×C8—21no—
157C2×C5×C8#6712yes—
158C5×C4⋊C4—21no—
159C5×C4⋊C4—21no—
160#685—68no—
161C4⋊Dic5—61no—
162C4⋊Dic5—61no—
163#683—124no—
164C4×Dic5—32no—
165C4×Dic5—32no—
166C2×#168—32no—
167C2×#168—61no—
168C2×#168—61no—
169C2×#124—151no—
170C2×#103—151no—
171C2×#103D1511yescharacteristic, complemented
172C2×#102—151no—
173C2×#102—151no—
174C2×#97—151no—
175#384—151no—
176C22×C3×C5C2×C22⋊C411yescharacteristic
177C22×C3×C5#12411yescharacteristic
178C22×C3×C5#12711yescharacteristic
179C22×C3×C5AGL(1,ℤ/8)12yes—
180C22×C3×C5#13712yes—
181C2×D15—42no—
182C2×D15—44no—
183C2×D15—82no—
184C2×D15—81no—
185C2×D15—81no—
186C3×C4×C5—42no—
187C3×C4×C5—81no—
188C3×C4×C5C4×D411yescharacteristic
189C3×C4×C5C4×D411yescharacteristic
190C3×C4×C5#12111yescharacteristic
191C3×C4×C5#12111yescharacteristic
192Dic15—24no—
193Dic15—81no—
194C23×D3—101no—
195C2×C3×Q8—21no—
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8C4×D512yes—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4C22×D511yescharacteristic
204C22×Dic3—52no—
205C22×Dic3—101no—
206C2×D12—52no—
207C2×D12—101no—
208C2×D12—101no—
209C2×D12—101no—
210C2×D12—101no—
211C2×D12—101no—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8C22⋊D512yes—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—21no—
217(C2×D3)⋊C4—108no—
218C4⋊Dic3—101no—
219C4⋊Dic3—101no—
220Dic3⋊C4—204no—
221C4×Dic3—52no—
222C4×Dic3—52no—
223C2×C3⋊C8—52no—
224C2×C3⋊C8—101no—
225C2×C3⋊C8—101no—
226C23×C5D3×D411yescharacteristic
227C22×D5—62no—
228C22×D5—121no—
229C22×D5—122no—
230C22×D5—122no—
231C22×D5—121no—
232C5×Q8—22no—
233C5×Q8—22no—
234C5×Q8—41no—
235C5×Q8—41no—
236C2×C4×C5—22no—
237C2×C4×C5—41no—
238C2×C4×C5—41no—
239C2×C4×C5—42no—
240C2×C4×C5—41no—
241C2×C4×C5C2×C4×D311yescharacteristic
242C2×C4×C5#23511yescharacteristic
243C2×C4×C5D3×D411yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5#23711yescharacteristic
246C2×C4×C5C2×#6711yescharacteristic
247C2×Dic5—34no—
248C2×Dic5—62no—
249C2×Dic5—62no—
250C2×Dic5—122no—
251C2×Dic5—121no—
252D20—62no—
253D20—62no—
254D20—121no—
255D20—121no—
256C5×C8—22no—
257#168—62no—
258C22×Q8C2×D1511yescharacteristic
259C22×D4—151no—
260C22×C8—151no—
261C22×C8C2×D1511yescharacteristic
262#124—154no—
263#124—302no—
264C2×C4⋊C4—151no—
265C2×C4⋊C4—302no—
266C2×C4⋊C4C2×D1511yescharacteristic
267C2×C22⋊C4—302no—
268C2×C42—151no—
269#103—22no—
270#103—302no—
271#102—302no—
272#102—302no—
273#97—302no—
274C2×C3×C5#39011yescharacteristic
275C2×C3×C5#41712yes—
276C2×C3×C5#48912yes—
277C2×C3×C5#49611yescharacteristic
278C2×C3×C5#49711yescharacteristic
279D15—82no—
280C23×C3D4×D511yescharacteristic
281C22×D3—102no—
282C22×D3—201no—
283C22×D3—202no—
284C22×D3—202no—
285C22×D3—201no—
286C3×Q8—22no—
287C3×Q8—22no—
288C3×Q8—41no—
289C3×Q8—41no—
290C2×C3×C4—22no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—42no—
294C2×C3×C4—41no—
295C2×C3×C4C2×C4×D511yescharacteristic
296C2×C3×C4#70911yescharacteristic
297C2×C3×C4D4×D511yescharacteristic
298C2×C3×C4D4×D511yescharacteristic
299C2×C3×C4#71111yescharacteristic
300C2×C3×C4C2×C22⋊D511yescharacteristic
301C2×Dic3—54no—
302C2×Dic3—102no—
303C2×Dic3—102no—
304C2×Dic3—202no—
305C2×Dic3—201no—
306D12—102no—
307D12—102no—
308D12—201no—
309D12—201no—
310C3×C8—22no—
311C3⋊C8—102no—
312C22×C5D3×C22⋊C411yescharacteristic
313C22×C5#88511yescharacteristic
314C22×C5#91412yes—
315C22×C5#91812yes—
316C22×C5#94011yescharacteristic
317C2×D5—122no—
318C2×D5—124no—
319C2×D5—241no—
320C2×D5—241no—
321C2×D5—242no—
322C4×C5—42no—
323C4×C5—81no—
324C4×C5#67⋊C411yescharacteristic
325C4×C5#88411yescharacteristic
326C4×C5C4×#6711yescharacteristic
327C4×C5#93911yescharacteristic
328Dic5—64no—
329Dic5—241no—
330C24—301no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8C4×D1512yes—
337C2×D4—152no—
338C2×D4—301no—
339C2×D4—301no—
340C2×D4—301no—
341C2×D4—301no—
342C2×D4—301no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—152no—
346C22×C4—301no—
347C22×C4C22×D1511yescharacteristic
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—152no—
351C2×C8—301no—
352C2×C8—301no—
353C2×C8#122012yes—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—301no—
357C4⋊C4—301no—
358C4⋊C4—604no—
359C22⋊C4—308no—
360C42—152no—
361C42—152no—
362C3×C5#195911yescharacteristic, complemented, Hall
363C22×C3D5×C22⋊C411yescharacteristic
364C22×C3#403111yescharacteristic
365C22×C3#406012yes—
366C22×C3#406412yes—
367C22×C3#408611yescharacteristic
368C2×D3—204no—
369C2×D3—202no—
370C2×D3—402no—
371C2×D3—401no—
372C2×D3—401no—
373C3×C4—42no—
374C3×C4—81no—
375C3×C4#402711yescharacteristic
376C3×C4#403011yescharacteristic
377C3×C4C4×C22⋊D511yescharacteristic
378C3×C4#408511yescharacteristic
379Dic3—104no—
380Dic3—401no—
381C2×C5#479412yes—
382C2×C5#480312yes—
383C2×C5#495711yescharacteristic
384C2×C5#517611yescharacteristic
385C2×C5#519011yescharacteristic
386D5—242no—
387C23—302no—
388C23—601no—
389C23—602no—
390C23—602no—
391C23—601no—
392C23D4×D1511yescharacteristic
393Q8—22no—
394Q8—22no—
395Q8—41no—
396Q8—41no—
397D4—302no—
398D4—302no—
399D4—601no—
400D4—601no—
401C2×C4—22no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—154no—
407C2×C4—302no—
408C2×C4—302no—
409C2×C4—602no—
410C2×C4—601no—
411C2×C4C2×C4×D1511yescharacteristic
412C2×C4#681711yescharacteristic
413C2×C4D4×D1511yescharacteristic
414C2×C4D4×D1511yescharacteristic
415C2×C4#681911yescharacteristic
416C2×C4C2×#122011yescharacteristic
417C8—22no—
418C8—302no—
419C2×C3#6508412yes—
420C2×C3#6509212yes—
421C2×C3#6524611yescharacteristic
422C2×C3#6546511yescharacteristic
423C2×C3#6547911yescharacteristic
424D3—402no—
425C5#7022711yescharacteristic, complemented, Sylow
426C22—602no—
427C22—604no—
428C22—1201no—
429C22—1201no—
430C22—1202no—
431C22C22⋊C4×D1511yescharacteristic
432C22#9177411yescharacteristic
433C22#9180312yes—
434C22#9180712yes—
435C22#9182911yescharacteristic
436C4—42no—
437C4—81no—
438C4—304no—
439C4—1201no—
440C4#9177011yescharacteristic
441C4#9177311yescharacteristic
442C4C4×#122011yescharacteristic
443C4#9182811yescharacteristic
444C3#1060102011yescharacteristic, complemented, Sylow
445C2—1202no—
446C2#1175089512yes—
447C2#1175090412yes—
448C2#1175105811yescharacteristic
449C2#1175127711yescharacteristic
450C2#1175129111yescharacteristic
subgroupG/H
centerC23D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#103C2
socleC23×C3×C5C2×D4
prime radicalC22×D60C22
cosocleC22×C3×C4×C5C23
hypercenterC2×#103D15
hypocenterC3×C5#1959
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#103C2semidirect
3. C2×#91119C2semidirect
5. C2×#91099C2semidirect
6. #11751076C2semidirect
14. #91836C4semidirect
27. C2×C5×#103D3semidirect
66. C2×C3×#103D5semidirect
171. C2×#103D15semidirect
362. C3×C5#1959semidirect
425. C5#70227semidirect
444. C3#10601020semidirect

Maximal subgroups

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

subgroupindex
C2×#918362
C2×C3×C5×#1032
C2×#911192
C2×#911052
C2×#910992
#117510762
C2×#910932
#106010203
#702275