Finite Group Databasebeta

← #14308915

Subgroups — #14308915

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
1C5×#5519C211yesmaximal, characteristic, complemented
2#11751102C211yesmaximal, characteristic
3#11748768C211yesmaximal, characteristic
4#11748396C211yesmaximal, characteristic
5C3×#64752C211yesmaximal, characteristic, complemented
6#11745986C211yesmaximal, characteristic, complemented
7#11745977C211yesmaximal, characteristic, complemented
8#10602696—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C5×#926C2211yescharacteristic
13C2×C5×C4⋊Dic3C2211yescharacteristic
14C5×#890—21no—
15C5×#888—21no—
16C5×#878—22no—
17C5×#870—21no—
18C5×#869—21no—
19C2×C3×C4×Dic5C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21C2×#6667—22no—
22#91093—21no—
23#91093—21no—
24#90969—21no—
25#90969—21no—
26#68763—51nomaximal, Hall
27C5×#544—31no—
28#65290—31no—
29#65290—31no—
30#65277—31no—
31#64752—31no—
32#64752D311yescharacteristic, complemented
33#64750—31no—
34C23×D15—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C2×D60—21no—
37C2×D60—21no—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60—21no—
41C2×D60Q812yescomplemented
42C22×C5×Dic3D412yes—
43C2×C5×Dic6—22no—
44C22×C3×Dic5—21no—
45C3×C5×C4⋊C4D411yescharacteristic
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C5×C22⋊C4—21no—
48C3×C42×C5—21no—
49#6710—21no—
50#6710—21no—
51C2×C3⋊#168—21no—
52C5×#217—21no—
53C5×C4⋊Dic3—22no—
54C5×C4⋊Dic3—21no—
55C5×C4⋊Dic3—21no—
56C5×C4⋊Dic3D411yescharacteristic
57C5×C4⋊Dic3D411yescharacteristic
58C5×Dic3⋊C4—22no—
59C5×Dic3⋊C4—22no—
60C4×C5×Dic3—21no—
61C3×C4×Dic5—21no—
62C3×C4×Dic5—21no—
63C3×#681—21no—
64C3×#681—21no—
65C2×C3×#168—21no—
66#6667—44no—
67#5519D511yescharacteristic, complemented
68#5131—51no—
69#5001—51no—
70#4939—51no—
71C3×#339—51no—
72#4554—51no—
73#4523—51no—
74C22×D20—31no—
75C5×C4⋊Q8—61no—
76C5×C4⋊Q8—61no—
77C5×#125—61no—
78C5×#125—61no—
79C5×C22⋊Q8—62no—
80C5×#117—31no—
81C5×#117C2×D311yescharacteristic
82C2×C5×C4⋊C4—31no—
83C2×#685—62no—
84C2×C4×Dic5C2×D311yescharacteristic
85C2×#681—31no—
86C2×#681C2×D311yescharacteristic
87#3941—61no—
88#3941—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—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×Q811yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106D60—22no—
107D60—22no—
108D60—41no—
109D60—41no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3—21no—
112C2×C5×Dic3—22no—
113C2×C5×Dic3—42no—
114C5×Dic6—82no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—41no—
118C3⋊#168—41no—
119C3×#168—41no—
120C22×D12—51no—
121C2×C3×M16—51no—
122C3×#117C2×D511yescharacteristic
123C2×C3×C42—51no—
124C2×(C2×D3)⋊C4—102no—
125#926C2×D511yescharacteristic
126C2×C4⋊Dic3C2×D511yescharacteristic
127C2×#208—51no—
128#890—21no—
129#888—21no—
130#878—22no—
131#870—21no—
132#869—21no—
133#821—101no—
134#821—101no—
135#809—101no—
136#809—101no—
137C23×D5—61no—
138C2×C5×Q8—62no—
139C22×C4×C5—32no—
140C22×C4×C5C22×D311yescharacteristic
141C22×Dic5—21no—
142C2×D20—32no—
143C2×D20—61no—
144C2×D20—61no—
145C2×D20—61no—
146C2×D20—61no—
147C2×D20—61no—
148C5×C4⋊C4—31no—
149C5×C4⋊C4—31no—
150C5×C4⋊C4—62no—
151C5×C4⋊C4—62no—
152C5×C4⋊C4—62no—
153C5×C4⋊C4—61no—
154C5×C4⋊C4—61no—
155C5×C4⋊C4D1211yescharacteristic
156C5×C4⋊C4D1211yescharacteristic
157C5×C22⋊C4—21no—
158C5×C22⋊C4—61no—
159C42×C5—21no—
160C42×C5—61no—
161#685—124no—
162C4×Dic5—21no—
163C4×Dic5—21no—
164#681—21no—
165#681—21no—
166#681—61no—
167#681—61no—
168C2×#168—21no—
169C2×#168—61no—
170#544—31no—
171#418—151no—
172#418—151no—
173#390—151no—
174#343—151no—
175#339—51no—
176#339—151no—
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—41no—
188C3×C4×C5—41no—
189C3×C4×C5C22⋊Q811yescharacteristic
190C3×C4×C5C22⋊Q811yescharacteristic
191C3×C4×C5#12411yescharacteristic
192C3×C4×C5#12411yescharacteristic
193C3×Dic5—42no—
194C5×Dic3—41no—
195C5×Dic3—42no—
196C5×Dic3—41no—
197C23×D3—101no—
198C22×C3×C4—101no—
199C22×C3×C4C22×D511yescharacteristic
200C22×Dic3C22⋊D512yes—
201C2×D12—52no—
202C2×D12—101no—
203C2×D12—101no—
204C2×D12—101no—
205C2×D12—101no—
206C2×D12—101no—
207C2×Dic6—22no—
208C3×M16—101no—
209C3×M16—101no—
210C2×C3×C8—101no—
211C3×C4⋊C4C22⋊D511yescharacteristic
212C3×C4⋊C4C22⋊D511yescharacteristic
213C3×C22⋊C4—21no—
214C3×C42—21no—
215C3×C42—101no—
216C3×C42—101no—
217#217—21no—
218(C2×D3)⋊C4—204no—
219C4⋊Dic3—22no—
220C4⋊Dic3—21no—
221C4⋊Dic3—21no—
222C4⋊Dic3C22⋊D511yescharacteristic
223C4⋊Dic3C22⋊D511yescharacteristic
224Dic3⋊C4—22no—
225Dic3⋊C4—22no—
226C4×Dic3—21no—
227#208—101no—
228#208—101no—
229C2×C3⋊C8—101no—
230C23×C5D3×D411yescharacteristic
231C22×D5—62no—
232C22×D5—122no—
233C22×D5—122no—
234C22×D5—121no—
235C22×D5—121no—
236C5×Q8—242no—
237C2×C4×C5—21no—
238C2×C4×C5—21no—
239C2×C4×C5—61no—
240C2×C4×C5—61no—
241C2×C4×C5—62no—
242C2×C4×C5—122no—
243C2×C4×C5C2×D1211yescharacteristic
244C2×C4×C5#23511yescharacteristic
245C2×C4×C5#23511yescharacteristic
246C2×C4×C5D3×D411yescharacteristic
247C2×C4×C5#23711yescharacteristic
248C2×C4×C5D3×Q811yescharacteristic
249C2×Dic5—22no—
250C2×Dic5—41no—
251C2×Dic5—41no—
252D20—62no—
253D20—62no—
254D20—121no—
255D20—121no—
256#168—41no—
257#168—121no—
258C22×D4—151no—
259C2×M16—51no—
260C2×M16—151no—
261C4⋊Q8—61no—
262C4⋊Q8—61no—
263#125—61no—
264#125—61no—
265C22⋊Q8—62no—
266#117—31no—
267#117D3×D511yescharacteristic
268C2×C4⋊C4—31no—
269C2×C22⋊C4—302no—
270C2×C42—51no—
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×C3C2×C22⋊D511yescharacteristic
282C22×D3—102no—
283C22×D3—202no—
284C22×D3—202no—
285C22×D3—201no—
286C22×D3—201no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—102no—
290C2×C3×C4—201no—
291C2×C3×C4—201no—
292C2×C3×C4Q8×D511yescharacteristic
293C2×C3×C4#71311yescharacteristic
294C2×C3×C4#71311yescharacteristic
295C2×C3×C4#71311yescharacteristic
296C2×C3×C4C2×C22⋊D511yescharacteristic
297C2×C3×C4C2×C22⋊D511yescharacteristic
298C2×Dic3—21no—
299C2×Dic3—21no—
300C2×Dic3—22no—
301C2×Dic3—42no—
302D12—102no—
303D12—102no—
304D12—201no—
305D12—201no—
306Dic6—82no—
307C3×C8—201no—
308C3⋊C8—201no—
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—41no—
320C4×C5—41no—
321C4×C5—122no—
322C4×C5—121no—
323C4×C5—121no—
324C4×C5#87511yescharacteristic
325C4×C5#88511yescharacteristic
326C4×C5#89611yescharacteristic
327C4×C5#89711yescharacteristic
328Dic5—42no—
329C24—301no—
330C2×Q8—62no—
331C2×D4—152no—
332C2×D4—301no—
333C2×D4—301no—
334C2×D4—301no—
335C2×D4—301no—
336C2×D4—301no—
337C22×C4—32no—
338C22×C4—101no—
339C22×C4C2×D3×D511yescharacteristic
340M16—101no—
341M16—101no—
342M16—301no—
343M16—301no—
344C2×C8—101no—
345C2×C8—301no—
346C4⋊C4—31no—
347C4⋊C4—31no—
348C4⋊C4—62no—
349C4⋊C4—62no—
350C4⋊C4—62no—
351C4⋊C4—61no—
352C4⋊C4—61no—
353C4⋊C4#120311yescharacteristic
354C4⋊C4#120311yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—61no—
357C22⋊C4—604no—
358C42—21no—
359C42—61no—
360C42—101no—
361C42—101no—
362C3×C5#202711yescharacteristic, complemented, Hall
363C22×C3—21no—
364C22×C3—21no—
365C22×C3#409211yescharacteristic
366C22×C3#409311yescharacteristic
367C22×C3#409911yescharacteristic
368C2×D3—204no—
369C2×D3—202no—
370C2×D3—402no—
371C2×D3—401no—
372C2×D3—401no—
373C3×C4—41no—
374C3×C4—41no—
375C3×C4—202no—
376C3×C4#409211yescharacteristic
377C3×C4#409211yescharacteristic
378C3×C4#409311yescharacteristic
379C3×C4#409311yescharacteristic
380Dic3—41no—
381Dic3—42no—
382Dic3—41no—
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—
394C23D3×C22⋊D511yescharacteristic
395Q8—242no—
396D4—302no—
397D4—302no—
398D4—601no—
399D4—601no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—62no—
405C2×C4—102no—
406C2×C4—122no—
407C2×C4—201no—
408C2×C4—201no—
409C2×C4#676611yescharacteristic
410C2×C4D15⋊Q811yescharacteristic
411C2×C4#677311yescharacteristic
412C2×C4#677311yescharacteristic
413C2×C4C2×#120311yescharacteristic
414C2×C4D3×C22⋊D511yescharacteristic
415C8—201no—
416C8—601no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3#6552011yescharacteristic
420C2×C3#6553011yescharacteristic
421C2×C3#6553411yescharacteristic
422D3—402no—
423C5#6876311yescharacteristic, complemented, Sylow
424C22—21no—
425C22—21no—
426C22—604no—
427C22—602no—
428C22—1202no—
429C22—1201no—
430C22—1201no—
431C22#9142411yescharacteristic
432C22#9145511yescharacteristic
433C22#9157011yescharacteristic
434C4—41no—
435C4—41no—
436C4—122no—
437C4—121no—
438C4—121no—
439C4—202no—
440C4#9137511yescharacteristic
441C4#9138311yescharacteristic
442C4#9142411yescharacteristic
443C4#9145511yescharacteristic
444C3#1060269611yescharacteristic, complemented, Sylow
445C2—21no—
446C2—21no—
447C2—1202no—
448C2#1174878411yescharacteristic
449C2#1174942011yescharacteristic
450C2#1174945911yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5#120
prime radicalC22×D60C22
hypercenter#117D3×D5
hypocenterC3×C5#2027
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C5×#5519C2semidirect
5. C3×#64752C2semidirect
6. #11745986C2semidirect
7. #11745977C2semidirect
32. #64752D3semidirect
41. C2×D60Q8semidirect
67. #5519D5semidirect
362. C3×C5#2027semidirect
423. C5#68763semidirect
444. C3#10602696semidirect

Maximal subgroups

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

subgroupindex
C5×#55192
#117511022
#117487682
#117483962
C3×#647522
#117459862
#117459772
#106026963
#687635