Finite Group Databasebeta

← #14308919

Subgroups — #14308919

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#11756278C211yesmaximal, characteristic, complemented
2C3×#65290C211yesmaximal, characteristic
3#11748785C211yesmaximal, characteristic
4#11748367C211yesmaximal, characteristic
5C5×#4532C211yesmaximal, characteristic, complemented
6#11745987C211yesmaximal, characteristic, complemented
7#11745976C211yesmaximal, characteristic, complemented
8#10599556—31nomaximal, Hall
9C22×C3×D20C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×C4⋊Dic15C2211yescharacteristic
13#91779—21no—
14#91777—21no—
15#91767—22no—
16#91759—21no—
17#91758—21no—
18C2×C4×C5×Dic3C2211yescharacteristic
19C2×C5×#208C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21C2×#6665—22no—
22C3×#3941—21no—
23C3×#3941—21no—
24#90965—21no—
25#90965—21no—
26#70313—51nomaximal, Hall
27#65853—31no—
28#65420—31no—
29#65290D311yescharacteristic
30#65228—31no—
31C5×#339—31no—
32#64774—31no—
33#64743—31no—
34C23×C3×D5—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C22×Dic15D412yes—
37C2×Dic30—22no—
38C22×C5×Dic3—21no—
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20—21no—
44C2×C3×D20Q812yescomplemented
45C3×C5×C4⋊C4D411yescharacteristic
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C5×C22⋊C4—21no—
48C3×C42×C5—21no—
49#6719—21no—
50C4⋊Dic15—22no—
51C4⋊Dic15—21no—
52C4⋊Dic15—21no—
53C4⋊Dic15D411yescharacteristic
54C4⋊Dic15D411yescharacteristic
55#6712—22no—
56#6712—22no—
57C4×Dic15—21no—
58C4×C5×Dic3—21no—
59C4×C5×Dic3—21no—
60C5×#208—21no—
61C5×#208—21no—
62C2×C5×C3⋊C8—21no—
63C3×#681—21no—
64C3×#681—21no—
65C2×C3×#168—21no—
66#6665—44no—
67#5519—51no—
68C3×#418—51no—
69#5221—51no—
70#5215—51no—
71#4555—51no—
72#4554—51no—
73#4532D511yescharacteristic, complemented
74C22×D20C2×D311yescharacteristic
75C2×C5×M16—31no—
76C5×#117C2×D311yescharacteristic
77C2×C42×C5—31no—
78C2×#685—62no—
79#4072—31no—
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—21no—
90#3941—21no—
91#2027—151noSylow
92C23×C3×C5C2×D411yescharacteristic
93C22×C3×D5—22no—
94C22×C3×D5—42no—
95C22×C3×D5—42no—
96C22×C3×D5—41no—
97C22×C3×D5—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
106C2×Dic15—21no—
107C2×Dic15—21no—
108C2×Dic15—22no—
109C2×Dic15—42no—
110Dic30—82no—
111C2×C5×Dic3—22no—
112C2×C5×Dic3—41no—
113C2×C5×Dic3—41no—
114C3×D20—22no—
115C3×D20—22no—
116C3×D20—41no—
117C3×D20—41no—
118C3×#168—41no—
119C5×C3⋊C8—41no—
120C22×C3×D4—51no—
121C2×C3×M16—51no—
122C3×#117C2×D511yescharacteristic
123C2×#217—102no—
124#926—51no—
125C2×C4⋊Dic3—51no—
126C2×C4×Dic3C2×D511yescharacteristic
127C2×#208C2×D511yescharacteristic
128#890—101no—
129#888—101no—
130#878—102no—
131#870—101no—
132#869—101no—
133C3×#102—101no—
134C3×#102—101no—
135#832—101no—
136#832—101no—
137C23×D5—21no—
138C22×C4×C5—61no—
139C22×C4×C5C22×D311yescharacteristic
140C22×Dic5—32no—
141C2×D20—21no—
142C2×D20—21no—
143C2×D20—21no—
144C2×D20—21no—
145C2×D20—21no—
146C2×D20Dic612yescomplemented
147C2×Dic10—62no—
148C5×M16—61no—
149C5×M16—61no—
150C2×C5×C8—61no—
151C5×C4⋊C4#6711yescharacteristic
152C5×C4⋊C4#6711yescharacteristic
153C5×C22⋊C4—21no—
154C42×C5—21no—
155C42×C5—61no—
156C42×C5—61no—
157C22⋊Dic5—61no—
158#685—124no—
159C4⋊Dic5—31no—
160C4⋊Dic5—31no—
161C4⋊Dic5—62no—
162C4⋊Dic5—61no—
163C4⋊Dic5—61no—
164#683—62no—
165#683—62no—
166C4×Dic5—61no—
167#681—21no—
168#681—21no—
169C2×#168—21no—
170#544—151no—
171#418—51no—
172#418—151no—
173#390—151no—
174#343—151no—
175#339—31no—
176#339—151no—
177C22×C3×C5—21no—
178C22×C3×C5—21no—
179C22×C3×C5#12011yescharacteristic
180C22×C3×C5C22⋊Q811yescharacteristic
181C22×C3×C5#12411yescharacteristic
182C2×C3×D5—44no—
183C2×C3×D5—42no—
184C2×C3×D5—82no—
185C2×C3×D5—81no—
186C2×C3×D5—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
193Dic15—41no—
194Dic15—42no—
195Dic15—41no—
196C5×Dic3—42no—
197C24×C3—101no—
198C2×C3×D4—52no—
199C2×C3×D4—101no—
200C2×C3×D4—101no—
201C2×C3×D4—101no—
202C2×C3×D4—101no—
203C2×C3×D4—101no—
204C22×C3×C4C22×D511yescharacteristic
205C22×Dic3—21no—
206C22×Dic3—52no—
207C2×Dic6—102no—
208C3×M16—101no—
209C3×M16—101no—
210C2×C3×C8—101no—
211C3×C4⋊C4D2011yescharacteristic
212C3×C4⋊C4D2011yescharacteristic
213C3×C22⋊C4—21no—
214C3×C42—21no—
215#217—101no—
216#217—204no—
217C4⋊Dic3—51no—
218C4⋊Dic3—51no—
219C4⋊Dic3—102no—
220C4⋊Dic3—101no—
221C4⋊Dic3—101no—
222Dic3⋊C4—102no—
223Dic3⋊C4—102no—
224C4×Dic3—21no—
225C4×Dic3—21no—
226C4×Dic3—101no—
227#208—21no—
228#208—21no—
229C2×C3⋊C8—21no—
230C23×C5D3×D411yescharacteristic
231C22×D5—22no—
232C22×D5—42no—
233C22×D5—42no—
234C22×D5—41no—
235C22×D5—41no—
236C2×C4×C5—21no—
237C2×C4×C5—21no—
238C2×C4×C5—62no—
239C2×C4×C5—121no—
240C2×C4×C5—121no—
241C2×C4×C5C2×Dic611yescharacteristic
242C2×C4×C5#23511yescharacteristic
243C2×C4×C5D3×D411yescharacteristic
244C2×C4×C5#23711yescharacteristic
245C2×C4×C5#23711yescharacteristic
246C2×C4×C5C2×#6711yescharacteristic
247C2×Dic5—61no—
248C2×Dic5—61no—
249C2×Dic5—62no—
250C2×Dic5—122no—
251D20—22no—
252D20—22no—
253D20—41no—
254D20—41no—
255Dic10—242no—
256C5×C8—121no—
257#168—41no—
258C22×D4—51no—
259C2×M16—31no—
260C2×M16—51no—
261C4⋊Q8—301no—
262C4⋊Q8—301no—
263#125—301no—
264#125—301no—
265C22⋊Q8—302no—
266#117—151no—
267#117D3×D511yescharacteristic
268C2×C4⋊C4—151no—
269C2×C22⋊C4—302no—
270C2×C42—31no—
271#102—101no—
272#102—101no—
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
280C3×D5—82no—
281C23×C3—102no—
282C23×C3—202no—
283C23×C3—202no—
284C23×C3—201no—
285C23×C3—201no—
286C23×C3D4×D511yescharacteristic
287C3×D4—102no—
288C3×D4—102no—
289C3×D4—201no—
290C3×D4—201no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4C2×D2011yescharacteristic
294C2×C3×C4#70911yescharacteristic
295C2×C3×C4#70911yescharacteristic
296C2×C3×C4D4×D511yescharacteristic
297C2×C3×C4#71111yescharacteristic
298C2×C3×C4Q8×D511yescharacteristic
299C2×Dic3—22no—
300C2×Dic3—41no—
301C2×Dic3—41no—
302C2×Dic3—101no—
303C2×Dic3—101no—
304C2×Dic3—102no—
305C2×Dic3—202no—
306Dic6—402no—
307C3×C8—201no—
308C3⋊C8—41no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5#87811yescharacteristic
312C22×C5#88511yescharacteristic
313C22×C5#93711yescharacteristic
314C2×D5—44no—
315C2×D5—42no—
316C2×D5—82no—
317C2×D5—81no—
318C2×D5—81no—
319C4×C5—41no—
320C4×C5—41no—
321C4×C5—122no—
322C4×C5#87811yescharacteristic
323C4×C5#88511yescharacteristic
324C4×C5#92411yescharacteristic
325C4×C5#93611yescharacteristic
326Dic5—121no—
327Dic5—122no—
328Dic5—121no—
329C24—101no—
330C2×Q8—302no—
331C2×D4—52no—
332C2×D4—101no—
333C2×D4—101no—
334C2×D4—101no—
335C2×D4—101no—
336C2×D4—101no—
337C22×C4—61no—
338C22×C4—152no—
339C22×C4C2×D3×D511yescharacteristic
340M16—61no—
341M16—61no—
342M16—101no—
343M16—101no—
344C2×C8—61no—
345C2×C8—101no—
346C4⋊C4—151no—
347C4⋊C4—151no—
348C4⋊C4—302no—
349C4⋊C4—302no—
350C4⋊C4—302no—
351C4⋊C4—301no—
352C4⋊C4—301no—
353C4⋊C4#120211yescharacteristic
354C4⋊C4#120211yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—301no—
357C22⋊C4—604no—
358C42—21no—
359C42—61no—
360C42—61no—
361C42—301no—
362C3×C5#202711yescharacteristic, complemented, Hall
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—204no—
366C22×C3—202no—
367C22×C3—402no—
368C22×C3—401no—
369C22×C3—401no—
370C22×C3#402811yescharacteristic
371C22×C3#403111yescharacteristic
372C22×C3#404211yescharacteristic
373C3×C4—41no—
374C3×C4—41no—
375C3×C4#402111yescharacteristic
376C3×C4#403111yescharacteristic
377C3×C4#404211yescharacteristic
378C3×C4#404311yescharacteristic
379Dic3—42no—
380Dic3—201no—
381Dic3—202no—
382Dic3—201no—
383C2×C5—21no—
384C2×C5—21no—
385C2×C5#494711yescharacteristic
386C2×C5#519811yescharacteristic
387C2×C5#520111yescharacteristic
388D5—82no—
389C23—102no—
390C23—202no—
391C23—202no—
392C23—201no—
393C23—201no—
394C23#679011yescharacteristic
395Q8—1202no—
396D4—102no—
397D4—102no—
398D4—201no—
399D4—201no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—62no—
403C2×C4—121no—
404C2×C4—121no—
405C2×C4—301no—
406C2×C4—301no—
407C2×C4—302no—
408C2×C4—602no—
409C2×C4D5×Dic611yescharacteristic
410C2×C4#676511yescharacteristic
411C2×C4#676511yescharacteristic
412C2×C4#677211yescharacteristic
413C2×C4C2×#120211yescharacteristic
414C2×C4#679011yescharacteristic
415C8—121no—
416C8—201no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—402no—
420C2×C3#6496211yescharacteristic
421C2×C3#6511111yescharacteristic
422C2×C3#6511611yescharacteristic
423C5#7031311yescharacteristic, complemented, Sylow
424C22—21no—
425C22—21no—
426C22—204no—
427C22—202no—
428C22—402no—
429C22—401no—
430C22—401no—
431C22#9143111yescharacteristic
432C22#9146211yescharacteristic
433C22#9157211yescharacteristic
434C4—41no—
435C4—41no—
436C4—122no—
437C4—602no—
438C4—601no—
439C4—601no—
440C4#9136011yescharacteristic
441C4#9136411yescharacteristic
442C4#9143111yescharacteristic
443C4#9146211yescharacteristic
444C3#1059955611yescharacteristic, complemented, Sylow
445C2—21no—
446C2—21no—
447C2—402no—
448C2#1174879311yescharacteristic
449C2#1174942111yescharacteristic
450C2#1174946011yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5#120
prime radicalC22×C3×D20C22
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. #11756278C2semidirect
5. C5×#4532C2semidirect
6. #11745987C2semidirect
7. #11745976C2semidirect
44. C2×C3×D20Q8semidirect
73. #4532D5semidirect
146. C2×D20Dic6semidirect
362. C3×C5#2027semidirect
423. C5#70313semidirect
444. C3#10599556semidirect

Maximal subgroups

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

subgroupindex
#117562782
C3×#652902
#117487852
#117483672
C5×#45322
#117459872
#117459762
#105995563
#703135