Finite Group Databasebeta

← #14305911

Subgroups — #14305911

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×C5×#835C211yesmaximal, characteristic, complemented
3C2×C3×#3967C211yesmaximal, characteristic, complemented
4#11748866C211yesmaximal, characteristic, complemented
5C2×#90969C211yesmaximal, characteristic
6C2×#90968C211yesmaximal, characteristic
7C2×#90954C211yesmaximal, characteristic, complemented
8#10601020—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C22×D60C2211yescharacteristic
11#91836—22no—
12#91836C414yescomplemented
13C2×#6714—22no—
14C2×C4×Dic15C2211yescharacteristic
15C2×C5×C4⋊Dic3C2211yescharacteristic
16C22×C5×C3⋊C8C2211yescharacteristic
17C2×C3×C4⋊Dic5C2211yescharacteristic
18C22×C3×#168C2211yescharacteristic
19C2×#6669—22no—
20C5×#835—22no—
21C3×#3967—22no—
22#90969—22no—
23#90968—22no—
24#90954—22no—
25#70227—51nomaximal, Hall
26C2×#4093—31no—
27C2×C5×#103—31no—
28C2×#3967D311yescharacteristic, complemented
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×C5C2311yescharacteristic
42C22×Dic15D412yes—
43C2×D60—21no—
44C2×D60—21no—
45C2×D60—21no—
46C2×D60—21no—
47C2×D60—21no—
48C2×D60C2×C412yes—
49C22×C5×Dic3—21no—
50C22×C3×Dic5—21no—
51#6714—28no—
52C4×Dic15C2×C412yes—
53C4×Dic15D412yes—
54C5×C4⋊Dic3—21no—
55C5×C4⋊Dic3—21no—
56C2×C5×C3⋊C8—21no—
57C2×C5×C3⋊C8—21no—
58C2×C5×C3⋊C8D412yes—
59C3×C4⋊Dic5—21no—
60C3×C4⋊Dic5—21no—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C2×C3×#168D412yes—
64#6669—44no—
65C2×#947—51no—
66C2×C3×#103—51no—
67C2×#835D511yescharacteristic, complemented
68C2×#821—51no—
69C2×#815—51no—
70#4975—51no—
71C2×#809—51no—
72C22×C5×Q8C2×D311yescharacteristic
73C22×D20—31no—
74C22×C5×C8—31no—
75C2×C5×C4⋊C4—31no—
76#4093—34no—
77#4093—62no—
78C2×#685—62no—
79C2×C4⋊Dic5C2×D311yescharacteristic
80C2×#683—62no—
81C2×C4×Dic5—31no—
82C22×#168C2×D311yescharacteristic
83C5×#103—62no—
84#3967—22no—
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×C5C22×C411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×Dic15—22no—
109C2×Dic15—22no—
110C2×Dic15C22⋊C414yes—
111D60—22no—
112D60—22no—
113D60—41no—
114D60—41no—
115C2×C5×Dic3—41no—
116C2×C5×Dic3—42no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—42no—
119C3×#168—22no—
120C5×C3⋊C8—22no—
121C22×C3×Q8C2×D511yescharacteristic
122C22×D12—51no—
123C22×C3×C8—51no—
124C2×C3×C4⋊C4—51no—
125#947—54no—
126#947—102no—
127C2×(C2×D3)⋊C4—102no—
128C2×C4⋊Dic3C2×D511yescharacteristic
129C2×Dic3⋊C4—102no—
130C2×C4×Dic3—51no—
131C22×C3⋊C8C2×D511yescharacteristic
132C3×#103—102no—
133#835—22no—
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—61no—
146C22×C4×C5C22×D311yescharacteristic
147C22×Dic5—21no—
148C22×Dic5—32no—
149C2×D20—32no—
150C2×D20—61no—
151C2×D20—61no—
152C2×D20—61no—
153C2×D20—61no—
154C2×D20—61no—
155C2×C5×C8—32no—
156C2×C5×C8—61no—
157C2×C5×C8—61no—
158C5×C4⋊C4—61no—
159C5×C4⋊C4—61no—
160#685—68no—
161C4⋊Dic5—21no—
162C4⋊Dic5—21no—
163#683—124no—
164C4×Dic5—32no—
165C4×Dic5—32no—
166C2×#168—21no—
167C2×#168—21no—
168C2×#168#6712yes—
169C2×#124—151no—
170C2×#103—31no—
171C2×#103—51no—
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×C5C4×D411yescharacteristic
188C3×C4×C5C4×D411yescharacteristic
189C3×C4×C5#12111yescharacteristic
190C3×C4×C5#12111yescharacteristic
191Dic15—24no—
192C3×Dic5—81no—
193C5×Dic3—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—101no—
203C22×C3×C4C22×D511yescharacteristic
204C22×Dic3—21no—
205C22×Dic3—52no—
206C2×D12—52no—
207C2×D12—101no—
208C2×D12—101no—
209C2×D12—101no—
210C2×D12—101no—
211C2×D12—101no—
212C2×C3×C8—52no—
213C2×C3×C8—101no—
214C2×C3×C8—101no—
215C3×C4⋊C4—101no—
216C3×C4⋊C4—101no—
217(C2×D3)⋊C4—108no—
218C4⋊Dic3—21no—
219C4⋊Dic3—21no—
220Dic3⋊C4—204no—
221C4×Dic3—52no—
222C4×Dic3—52no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8C22⋊D512yes—
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—122no—
240C2×C4×C5—121no—
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—42no—
249C2×Dic5—41no—
250C2×Dic5—62no—
251C2×Dic5—62no—
252D20—62no—
253D20—62no—
254D20—121no—
255D20—121no—
256C5×C8—62no—
257#168—22no—
258C22×Q8D3×D511yescharacteristic
259C22×D4—151no—
260C22×C8—31no—
261C22×C8—51no—
262#124—154no—
263#124—302no—
264C2×C4⋊C4—31no—
265C2×C4⋊C4—51no—
266C2×C4⋊C4—302no—
267C2×C22⋊C4—302no—
268C2×C42—151no—
269#103—62no—
270#103—102no—
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—202no—
294C2×C3×C4—201no—
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—42no—
302C2×Dic3—41no—
303C2×Dic3—54no—
304C2×Dic3—102no—
305C2×Dic3—102no—
306D12—102no—
307D12—102no—
308D12—201no—
309D12—201no—
310C3×C8—102no—
311C3⋊C8—22no—
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—241no—
324C4×C5#67⋊C411yescharacteristic
325C4×C5#88411yescharacteristic
326C4×C5C4×#6711yescharacteristic
327C4×C5#93911yescharacteristic
328Dic5—64no—
329Dic5—81no—
330C24—301no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8#120012yes—
337C2×D4—152no—
338C2×D4—301no—
339C2×D4—301no—
340C2×D4—301no—
341C2×D4—301no—
342C2×D4—301no—
343C22×C4—21no—
344C22×C4—61no—
345C22×C4—101no—
346C22×C4—152no—
347C22×C4C2×D3×D511yescharacteristic
348C2×C8—32no—
349C2×C8—52no—
350C2×C8—61no—
351C2×C8—61no—
352C2×C8—101no—
353C2×C8—101no—
354C4⋊C4—61no—
355C4⋊C4—61no—
356C4⋊C4—101no—
357C4⋊C4—101no—
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—401no—
375C3×C4#402711yescharacteristic
376C3×C4#403011yescharacteristic
377C3×C4C4×C22⋊D511yescharacteristic
378C3×C4#408511yescharacteristic
379Dic3—81no—
380Dic3—104no—
381C2×C5#479412yes—
382C2×C5#480312yes—
383C2×C5#495711yescharacteristic
384C2×C5#517611yescharacteristic
385C2×C5#519011yescharacteristic
386D5—242no—
387C23—302no—
388C23—602no—
389C23—602no—
390C23—601no—
391C23—601no—
392C23#679011yescharacteristic
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—122no—
405C2×C4—121no—
406C2×C4—154no—
407C2×C4—202no—
408C2×C4—201no—
409C2×C4—302no—
410C2×C4—302no—
411C2×C4#677911yescharacteristic
412C2×C4#678211yescharacteristic
413C2×C4C2×#120011yescharacteristic
414C2×C4D5×#6711yescharacteristic
415C2×C4D3×C22⋊D511yescharacteristic
416C2×C4#679011yescharacteristic
417C8—62no—
418C8—102no—
419C2×C3#6508412yes—
420C2×C3#6509212yes—
421C2×C3#6524611yescharacteristic
422C2×C3#6546511yescharacteristic
423C2×C3#6547911yescharacteristic
424D3—402no—
425C5#7022711yescharacteristic, complemented, Sylow
426C22—604no—
427C22—602no—
428C22—1201no—
429C22—1201no—
430C22—1202no—
431C22#9150612yes—
432C22#9151212yes—
433C22#9152611yescharacteristic
434C22#9156111yescharacteristic
435C22#9156711yescharacteristic
436C4—42no—
437C4—241no—
438C4—304no—
439C4—401no—
440C4#9155011yescharacteristic
441C4#9155211yescharacteristic
442C4#9155611yescharacteristic
443C4#9155811yescharacteristic
444C3#1060102011yescharacteristic, complemented, Sylow
445C2—1202no—
446C2#1174920512yes—
447C2#1174934311yescharacteristic
448C2#1174935611yescharacteristic
449C2#1174936312yes—
450C2#1174948311yescharacteristic
subgroupG/H
centerC23#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C2×D4
prime radicalC22×D60C22
cosocleC22×C3×C4×C5C23
hypercenterC22×Q8D3×D5
hypocenterC3×C5#1959
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C5×#835C2semidirect
3. C2×C3×#3967C2semidirect
4. #11748866C2semidirect
7. C2×#90954C2semidirect
12. #91836C4semidirect
28. C2×#3967D3semidirect
67. C2×#835D5semidirect
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×C5×#8352
C2×C3×#39672
#117488662
C2×#909692
C2×#909682
C2×#909542
#106010203
#702275