Finite Group Databasebeta

← #14308936

Subgroups — #14308936

Order 1920.

564 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
1#11754620C211yesmaximal, characteristic, complemented
2#11751040C211yesmaximal, characteristic
3#11748396C211yesmaximal, characteristic
4#11748392C211yesmaximal, characteristic
5C5×#4523C211yesmaximal, characteristic, complemented
6C3×#64743C211yesmaximal, characteristic, complemented
7#11745987C211yesmaximal, characteristic, complemented
8#10599556—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C2×C3×C42×C5C2211yescharacteristic
11C2×#6714—22no—
12C2×C4⋊Dic15C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C3×#4072C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17#91576—22no—
18#91469—21no—
19#91468—21no—
20#91388—21no—
21#91381—21no—
22#90969—21no—
23#90969—21no—
24#90968—21no—
25#90968—21no—
26#68763—51nomaximal, Hall
27#65853—31no—
28#65420—31no—
29#65290—31no—
30#65228—31no—
31C5×#339—31no—
32#64774—31no—
33#64743D311yescharacteristic, complemented
34C23×D15—21no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15D412yes—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60—21no—
41C2×D60—21no—
42C2×D60—21no—
43C2×D60Q812yescomplemented
44C2×#1204—22no—
45C3×C42×C5—21no—
46C3×C42×C5—21no—
47#6714—44no—
48C4⋊Dic15—21no—
49C4⋊Dic15—21no—
50C5×#217—21no—
51C5×C4⋊Dic3D411yescharacteristic
52C5×C4⋊Dic3D411yescharacteristic
53C4×C5×Dic3—21no—
54C5×#208—21no—
55C5×#208—21no—
56C2×C5×C3⋊C8—21no—
57C3×C22⋊Dic5—21no—
58C3×C4⋊Dic5D411yescharacteristic
59C3×C4⋊Dic5D411yescharacteristic
60C3×C4×Dic5—21no—
61C3×#681—21no—
62C3×#681—21no—
63C2×C3×#168—21no—
64Dic3⋊Dic5—22no—
65#6669—22no—
66#6668—22no—
67#5519—51no—
68#5131—51no—
69#5001—51no—
70#4939—51no—
71C3×#339—51no—
72#4554—51no—
73#4523D511yescharacteristic, complemented
74C22×D20—31no—
75C2×C5×M16—31no—
76C5×#117—31no—
77C2×C42×C5C2×D311yescharacteristic
78C2×#685—62no—
79#4072C2×D311yescharacteristic
80C2×C4⋊Dic5—31no—
81C2×#681C2×D311yescharacteristic
82#4036—61no—
83#4034—61no—
84#4024—62no—
85#4016—61no—
86#4015—61no—
87#3953—61no—
88#3953—61no—
89#3941—61no—
90#3941—61no—
91#2027—151noSylow
92C23×C3×C5C2×D411yescharacteristic
93C22×D15—22no—
94C22×D15—42no—
95C22×D15—42no—
96C22×D15—41no—
97C22×D15—41no—
98C2×C3×C4×C5—22no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×Q811yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107C2×Dic15—22no—
108C2×Dic15—42no—
109D60—22no—
110D60—22no—
111D60—41no—
112D60—41no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3—21no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—21no—
117#1204—82no—
118C3×#168—41no—
119C5×C3⋊C8—41no—
120C22×D12—51no—
121C2×C3×M16—51no—
122C3×#117—51no—
123C2×C3×C42C2×D511yescharacteristic
124C2×(C2×D3)⋊C4—102no—
125#926C2×D511yescharacteristic
126C2×C4⋊Dic3—51no—
127C2×#208C2×D511yescharacteristic
128#890—101no—
129#888—101no—
130#878—102no—
131#870—101no—
132#869—101no—
133#821—101no—
134#821—101no—
135#809—101no—
136#809—101no—
137C23×D5—61no—
138C22×C4×C5—21no—
139C22×C4×C5C22×D311yescharacteristic
140C22×Dic5—32no—
141C2×D20—32no—
142C2×D20—61no—
143C2×D20—61no—
144C2×D20—61no—
145C2×D20—61no—
146C2×D20—61no—
147C2×Dic10—62no—
148C5×M16—61no—
149C5×M16—61no—
150C2×C5×C8—61no—
151C5×C4⋊C4—31no—
152C5×C4⋊C4—31no—
153C5×C22⋊C4—61no—
154C42×C5—21no—
155C42×C5—21no—
156C42×C5—61no—
157C22⋊Dic5—21no—
158#685—124no—
159C4⋊Dic5—62no—
160C4⋊Dic5—61no—
161C4⋊Dic5—61no—
162C4⋊Dic5D1211yescharacteristic
163C4⋊Dic5D1211yescharacteristic
164#683—62no—
165#683—62no—
166C4×Dic5—21no—
167#681—21no—
168#681—21no—
169C2×#168—21no—
170#544—151no—
171#418—151no—
172#418—151no—
173#390—151no—
174#343—151no—
175#339—31no—
176#339—51no—
177C22×C3×C5—21no—
178C22×C3×C5—21no—
179C22×C3×C5#12011yescharacteristic
180C22×C3×C5C22⋊Q811yescharacteristic
181C22×C3×C5#12411yescharacteristic
182C2×D15—44no—
183C2×D15—42no—
184C2×D15—82no—
185C2×D15—81no—
186C2×D15—81no—
187C3×C4×C5—42no—
188C3×C4×C5C22⋊Q811yescharacteristic
189C3×C4×C5C22⋊Q811yescharacteristic
190C3×C4×C5#12411yescharacteristic
191C3×C4×C5#12411yescharacteristic
192Dic15—42no—
193C3×Dic5—41no—
194C3×Dic5—41no—
195C5×Dic3—41no—
196C5×Dic3—41no—
197C23×D3—101no—
198C22×C3×C4—21no—
199C22×C3×C4C22×D511yescharacteristic
200C22×Dic3—52no—
201C2×D12—52no—
202C2×D12—101no—
203C2×D12—101no—
204C2×D12—101no—
205C2×D12—101no—
206C2×D12—101no—
207C2×Dic6—102no—
208C3×M16—101no—
209C3×M16—101no—
210C2×C3×C8—101no—
211C3×C4⋊C4—51no—
212C3×C4⋊C4—51no—
213C3×C22⋊C4—101no—
214C3×C42—21no—
215C3×C42—21no—
216C3×C42—101no—
217#217—21no—
218(C2×D3)⋊C4—204no—
219C4⋊Dic3—102no—
220C4⋊Dic3—101no—
221C4⋊Dic3—101no—
222C4⋊Dic3D2011yescharacteristic
223C4⋊Dic3D2011yescharacteristic
224Dic3⋊C4—102no—
225Dic3⋊C4—102no—
226C4×Dic3—21no—
227#208—21no—
228#208—21no—
229C2×C3⋊C8—21no—
230C23×C5D3×D411yescharacteristic
231C22×D5—62no—
232C22×D5—122no—
233C22×D5—122no—
234C22×D5—121no—
235C22×D5—121no—
236C2×C4×C5—22no—
237C2×C4×C5—41no—
238C2×C4×C5—41no—
239C2×C4×C5—61no—
240C2×C4×C5—61no—
241C2×C4×C5C2×D1211yescharacteristic
242C2×C4×C5#23511yescharacteristic
243C2×C4×C5#23511yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5#23711yescharacteristic
246C2×C4×C5D3×Q811yescharacteristic
247C2×Dic5—21no—
248C2×Dic5—21no—
249C2×Dic5—62no—
250C2×Dic5—122no—
251D20—62no—
252D20—62no—
253D20—121no—
254D20—121no—
255Dic10—242no—
256C5×C8—121no—
257#168—41no—
258C22×D4—151no—
259C2×M16—31no—
260C2×M16—51no—
261C4⋊Q8—301no—
262C4⋊Q8—301no—
263#125—301no—
264#125—301no—
265C22⋊Q8—302no—
266#117—31no—
267#117—51no—
268C2×C4⋊C4—151no—
269C2×C22⋊C4—302no—
270C2×C42D3×D511yescharacteristic
271#102—301no—
272#102—301no—
273#102—301no—
274#102—301no—
275C2×C3×C5—21no—
276C2×C3×C5—21no—
277C2×C3×C5#39311yescharacteristic
278C2×C3×C5#45311yescharacteristic
279C2×C3×C5#45411yescharacteristic
280D15—82no—
281C23×C3D4×D511yescharacteristic
282C22×D3—102no—
283C22×D3—202no—
284C22×D3—202no—
285C22×D3—201no—
286C22×D3—201no—
287C2×C3×C4—22no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—101no—
291C2×C3×C4—101no—
292C2×C3×C4C2×D2011yescharacteristic
293C2×C3×C4#70911yescharacteristic
294C2×C3×C4#70911yescharacteristic
295C2×C3×C4D4×D511yescharacteristic
296C2×C3×C4#71111yescharacteristic
297C2×C3×C4Q8×D511yescharacteristic
298C2×Dic3—21no—
299C2×Dic3—21no—
300C2×Dic3—102no—
301C2×Dic3—202no—
302D12—102no—
303D12—102no—
304D12—201no—
305D12—201no—
306Dic6—402no—
307C3×C8—201no—
308C3⋊C8—41no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5#88211yescharacteristic
312C22×C5#88511yescharacteristic
313C22×C5#89611yescharacteristic
314C2×D5—124no—
315C2×D5—122no—
316C2×D5—242no—
317C2×D5—241no—
318C2×D5—241no—
319C4×C5—42no—
320C4×C5—121no—
321C4×C5—121no—
322C4×C5#87511yescharacteristic
323C4×C5#88511yescharacteristic
324C4×C5#89611yescharacteristic
325C4×C5#89711yescharacteristic
326Dic5—41no—
327Dic5—41no—
328Dic5—122no—
329C24—301no—
330C2×Q8—302no—
331C2×D4—152no—
332C2×D4—301no—
333C2×D4—301no—
334C2×D4—301no—
335C2×D4—301no—
336C2×D4—301no—
337C22×C4—21no—
338C22×C4—152no—
339C22×C4C2×D3×D511yescharacteristic
340M16—61no—
341M16—61no—
342M16—101no—
343M16—101no—
344C2×C8—61no—
345C2×C8—101no—
346C4⋊C4—31no—
347C4⋊C4—31no—
348C4⋊C4—51no—
349C4⋊C4—51no—
350C4⋊C4—302no—
351C4⋊C4—302no—
352C4⋊C4—302no—
353C4⋊C4—301no—
354C4⋊C4—301no—
355C22⋊C4—61no—
356C22⋊C4—101no—
357C22⋊C4—604no—
358C42—21no—
359C42—21no—
360C42—61no—
361C42—101no—
362C3×C5#202711yescharacteristic, complemented, Hall
363C22×C3—21no—
364C22×C3—21no—
365C22×C3#402811yescharacteristic
366C22×C3#403111yescharacteristic
367C22×C3#404211yescharacteristic
368C2×D3—204no—
369C2×D3—202no—
370C2×D3—402no—
371C2×D3—401no—
372C2×D3—401no—
373C3×C4—42no—
374C3×C4—201no—
375C3×C4—201no—
376C3×C4#402111yescharacteristic
377C3×C4#403111yescharacteristic
378C3×C4#404211yescharacteristic
379C3×C4#404311yescharacteristic
380Dic3—41no—
381Dic3—41no—
382Dic3—202no—
383C2×C5—21no—
384C2×C5—21no—
385C2×C5#467311yescharacteristic
386C2×C5#482211yescharacteristic
387C2×C5#482711yescharacteristic
388D5—242no—
389C23—302no—
390C23—602no—
391C23—602no—
392C23—601no—
393C23—601no—
394C23#679011yescharacteristic
395Q8—1202no—
396D4—302no—
397D4—302no—
398D4—601no—
399D4—601no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—101no—
406C2×C4—101no—
407C2×C4—302no—
408C2×C4—602no—
409C2×C4D15⋊Q811yescharacteristic
410C2×C4#677111yescharacteristic
411C2×C4D5×D1211yescharacteristic
412C2×C4D3×D2011yescharacteristic
413C2×C4#677911yescharacteristic
414C2×C4#678211yescharacteristic
415C8—121no—
416C8—201no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3#6496211yescharacteristic
420C2×C3#6511111yescharacteristic
421C2×C3#6511611yescharacteristic
422D3—402no—
423C5#6876311yescharacteristic, complemented, Sylow
424C22—21no—
425C22—21no—
426C22—604no—
427C22—602no—
428C22—1202no—
429C22—1201no—
430C22—1201no—
431C22#9137711yescharacteristic
432C22#9147611yescharacteristic
433C22#9152611yescharacteristic
434C4—42no—
435C4—121no—
436C4—121no—
437C4—201no—
438C4—201no—
439C4—602no—
440C4#9135011yescharacteristic
441C4#9135311yescharacteristic
442C4#9141911yescharacteristic
443C4#9142911yescharacteristic
444C3#1059955611yescharacteristic, complemented, Sylow
445C2—21no—
446C2—21no—
447C2—1202no—
448C2#1174711811yescharacteristic
449C2#1174712511yescharacteristic
450C2#1174857911yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5#120
prime radicalC22×D60C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2027
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #11754620C2semidirect
5. C5×#4523C2semidirect
6. C3×#64743C2semidirect
7. #11745987C2semidirect
33. #64743D3semidirect
43. C2×D60Q8semidirect
73. #4523D5semidirect
362. C3×C5#2027semidirect
423. C5#68763semidirect
444. C3#10599556semidirect

Maximal subgroups

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

subgroupindex
#117546202
#117510402
#117483962
#117483922
C5×#45232
C3×#647432
#117459872
#105995563
#687635