Finite Group Databasebeta

← #14308935

Subgroups — #14308935

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#11754618C211yesmaximal, characteristic, complemented
2C3×#65228C211yesmaximal, characteristic
3#11748367C211yesmaximal, characteristic
4#11748366C211yesmaximal, characteristic
5#11746344C211yesmaximal, characteristic, complemented
6C5×#4523C211yesmaximal, characteristic, complemented
7#11745985C211yesmaximal, characteristic, complemented
8#10599556—31nomaximal, Hall
9C22×C3×D20C2211yescharacteristic
10C2×C3×C42×C5C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C2×C3×#685—22no—
16C2×C3×C4⋊Dic5C2211yescharacteristic
17#91574—22no—
18#91470—21no—
19#91469—21no—
20#91384—21no—
21#91381—21no—
22#90965—21no—
23#90965—21no—
24#90964—21no—
25#90964—21no—
26#69643—51nomaximal, Hall
27#65853—31no—
28#65420—31no—
29#65290—31no—
30#65228D311yescharacteristic
31C5×#339—31no—
32#64774—31no—
33#64743—31no—
34C23×C3×D5—21no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5C2311yescharacteristic
37C22×C3×Dic5D412yes—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20Q812yescomplemented
44C2×#1204—22no—
45C3×C42×C5—21no—
46C3×C42×C5—21no—
47#6719—21no—
48C4⋊Dic15D411yescharacteristic
49C4⋊Dic15D411yescharacteristic
50C4×Dic15—21no—
51#6710—21no—
52#6710—21no—
53C2×C3⋊#168—21no—
54C5×#217—21no—
55C5×C4⋊Dic3D411yescharacteristic
56C5×C4⋊Dic3D411yescharacteristic
57C4×C5×Dic3—21no—
58C5×#208—21no—
59C5×#208—21no—
60C2×C5×C3⋊C8—21no—
61C3×#685—44no—
62C3×C4⋊Dic5—21no—
63C3×C4⋊Dic5—21no—
64Dic3⋊Dic5—22no—
65#6669—22no—
66#6668—22no—
67#5500—51no—
68C3×#390—51no—
69#5215—51no—
70#5215—51no—
71#4530—51no—
72#4523—51no—
73#4523D511yescharacteristic, complemented
74C22×D20C2×D311yescharacteristic
75C2×C5×M16—31no—
76C5×#117—31no—
77C2×C42×C5C2×D311yescharacteristic
78C2×#685—22no—
79#4072—31no—
80C2×C4⋊Dic5C2×D311yescharacteristic
81C2×#681—31no—
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×C3×D5—22no—
94C22×C3×D5—42no—
95C22×C3×D5—42no—
96C22×C3×D5—41no—
97C22×C3×D5—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—21no—
108C2×Dic15—21no—
109C2×C5×Dic3—21no—
110C2×C5×Dic3—21no—
111C2×C3×Dic5—22no—
112C2×C3×Dic5—42no—
113C3×D20—22no—
114C3×D20—22no—
115C3×D20—41no—
116C3×D20—41no—
117#1204—82no—
118C3⋊#168—41no—
119C5×C3⋊C8—41no—
120C22×C3×D4—51no—
121C2×C3×C4⋊C4—51no—
122C2×C3×C22⋊C4—102no—
123C2×C3×C42C2×D511yescharacteristic
124#926—51no—
125#926C2×D511yescharacteristic
126#924—102no—
127C2×#208—51no—
128C2×#208C2×D511yescharacteristic
129#890—101no—
130#890—101no—
131#888—101no—
132#888—101no—
133#832—101no—
134#832—101no—
135#832—101no—
136#832—101no—
137C23×D5—21no—
138C22×C4×C5—21no—
139C22×C4×C5C22×D311yescharacteristic
140C22×Dic5#6712yes—
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—31no—
152C5×C4⋊C4—31no—
153C5×C22⋊C4—61no—
154C42×C5—21no—
155C42×C5—21no—
156C42×C5—61no—
157C22⋊Dic5—61no—
158#685—44no—
159C4⋊Dic5—21no—
160C4⋊Dic5—21no—
161C4⋊Dic5—31no—
162C4⋊Dic5—31no—
163C4⋊Dic5—62no—
164#683—62no—
165#683—62no—
166C4×Dic5—61no—
167#681—61no—
168#681—61no—
169C2×#168—61no—
170#544—151no—
171#418—151no—
172#418—151no—
173#390—51no—
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—42no—
188C3×C4×C5C22⋊Q811yescharacteristic
189C3×C4×C5C22⋊Q811yescharacteristic
190C3×C4×C5#12411yescharacteristic
191C3×C4×C5#12411yescharacteristic
192Dic15—41no—
193Dic15—41no—
194C3×Dic5—42no—
195C5×Dic3—41no—
196C5×Dic3—41no—
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×C4—21no—
205C22×C3×C4—52no—
206C22×C3×C4C22×D511yescharacteristic
207C2×Dic6—102no—
208C3×C4⋊C4—101no—
209C3×C4⋊C4—101no—
210C3×C22⋊C4—204no—
211C3×C42—21no—
212C3×C42—21no—
213#217—21no—
214#217—101no—
215C4⋊Dic3—51no—
216C4⋊Dic3—51no—
217C4⋊Dic3—102no—
218C4⋊Dic3D2011yescharacteristic
219C4⋊Dic3D2011yescharacteristic
220Dic3⋊C4—102no—
221Dic3⋊C4—102no—
222C4×Dic3—21no—
223C4×Dic3—101no—
224#208—21no—
225#208—21no—
226#208—101no—
227#208—101no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8—101no—
230C23×C5C2×#6711yescharacteristic
231C22×D5—22no—
232C22×D5—42no—
233C22×D5—42no—
234C22×D5—41no—
235C22×D5—41no—
236C2×C4×C5—22no—
237C2×C4×C5—41no—
238C2×C4×C5—41no—
239C2×C4×C5—61no—
240C2×C4×C5—61no—
241C2×C4×C5C2×Dic611yescharacteristic
242C2×C4×C5#23511yescharacteristic
243C2×C4×C5D3×D411yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5#23711yescharacteristic
246C2×C4×C5#23711yescharacteristic
247C2×Dic5—22no—
248C2×Dic5—42no—
249C2×Dic5—61no—
250C2×Dic5—61no—
251D20—22no—
252D20—22no—
253D20—41no—
254D20—41no—
255Dic10—242no—
256C5×C8—121no—
257#168—121no—
258C22×D4—51no—
259C2×M16—31no—
260C2×M16—151no—
261C4⋊Q8—301no—
262C4⋊Q8—301no—
263#125—301no—
264#125—301no—
265C22⋊Q8—302no—
266#117—31no—
267#117—151no—
268C2×C4⋊C4—51no—
269C2×C22⋊C4—102no—
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
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—22no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—102no—
295C2×C3×C4—202no—
296C2×C3×C4C2×D2011yescharacteristic
297C2×C3×C4#70911yescharacteristic
298C2×C3×C4#70911yescharacteristic
299C2×C3×C4D4×D511yescharacteristic
300C2×C3×C4#71111yescharacteristic
301C2×C3×C4Q8×D511yescharacteristic
302C2×Dic3—21no—
303C2×Dic3—21no—
304C2×Dic3—101no—
305C2×Dic3—101no—
306Dic6—402no—
307C3⋊C8—41no—
308C3⋊C8—201no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5#92411yescharacteristic
312C22×C5#93611yescharacteristic
313C22×C5#93711yescharacteristic
314C2×D5—44no—
315C2×D5—42no—
316C2×D5—82no—
317C2×D5—81no—
318C2×D5—81no—
319C4×C5—42no—
320C4×C5—121no—
321C4×C5—121no—
322C4×C5#87811yescharacteristic
323C4×C5#87811yescharacteristic
324C4×C5#88511yescharacteristic
325C4×C5#88511yescharacteristic
326Dic5—42no—
327Dic5—121no—
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—21no—
338C22×C4—52no—
339C22×C4C2×D3×D511yescharacteristic
340M16—61no—
341M16—61no—
342M16—301no—
343M16—301no—
344C2×C8—61no—
345C2×C8—301no—
346C4⋊C4—31no—
347C4⋊C4—31no—
348C4⋊C4—101no—
349C4⋊C4—101no—
350C4⋊C4—151no—
351C4⋊C4—151no—
352C4⋊C4—302no—
353C4⋊C4—302no—
354C4⋊C4—302no—
355C22⋊C4—61no—
356C22⋊C4—204no—
357C22⋊C4—301no—
358C42—21no—
359C42—21no—
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—42no—
374C3×C4—202no—
375C3×C4#402111yescharacteristic
376C3×C4#403111yescharacteristic
377C3×C4#404211yescharacteristic
378C3×C4#404311yescharacteristic
379Dic3—41no—
380Dic3—41no—
381Dic3—201no—
382Dic3—201no—
383C2×C5—21no—
384C2×C5—21no—
385C2×C5#494711yescharacteristic
386C2×C5#506211yescharacteristic
387C2×C5#507711yescharacteristic
388D5—82no—
389C23—102no—
390C23—202no—
391C23—202no—
392C23—201no—
393C23—201no—
394C23D5×#6711yescharacteristic
395Q8—1202no—
396D4—102no—
397D4—102no—
398D4—201no—
399D4—201no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—102no—
406C2×C4—202no—
407C2×C4—301no—
408C2×C4—301no—
409C2×C4D5×Dic611yescharacteristic
410C2×C4#677111yescharacteristic
411C2×C4D3×D2011yescharacteristic
412C2×C4#677711yescharacteristic
413C2×C4#677911yescharacteristic
414C2×C4#678011yescharacteristic
415C8—121no—
416C8—601no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—402no—
420C2×C3#6496211yescharacteristic
421C2×C3#6511111yescharacteristic
422C2×C3#6511611yescharacteristic
423C5#6964311yescharacteristic, complemented, Sylow
424C22—21no—
425C22—21no—
426C22—204no—
427C22—202no—
428C22—402no—
429C22—401no—
430C22—401no—
431C22#9134911yescharacteristic
432C22#9147411yescharacteristic
433C22#9153411yescharacteristic
434C4—42no—
435C4—121no—
436C4—121no—
437C4—202no—
438C4—601no—
439C4—601no—
440C4#9135311yescharacteristic
441C4#9142211yescharacteristic
442C4#9143011yescharacteristic
443C4#9146411yescharacteristic
444C3#1059955611yescharacteristic, complemented, Sylow
445C2—21no—
446C2—21no—
447C2—402no—
448C2#1174711411yescharacteristic
449C2#1174712111yescharacteristic
450C2#1174873611yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5#120
prime radicalC22×C3×D20C22
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. #11754618C2semidirect
5. #11746344C2semidirect
6. C5×#4523C2semidirect
7. #11745985C2semidirect
43. C2×C3×D20Q8semidirect
73. #4523D5semidirect
146. C2×D20Dic6semidirect
362. C3×C5#2027semidirect
423. C5#69643semidirect
444. C3#10599556semidirect

Maximal subgroups

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

subgroupindex
#117546182
C3×#652282
#117483672
#117483662
#117463442
C5×#45232
#117459852
#105995563
#696435