Finite Group Databasebeta

← #14283052

Subgroups — #14283052

Order 1920.

544 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754386C211yesmaximal, characteristic
2#11750820C211yesmaximal, characteristic, complemented
3#11748653C211yesmaximal, characteristic, complemented
4C5×#4470C211yesmaximal, characteristic, complemented
5C3×#64690C211yesmaximal, characteristic, complemented
6#11745956C211yesmaximal, characteristic, complemented
7#11745954C211yesmaximal, characteristic, complemented
8#10599071—31nomaximal, Hall
9C2×#6780—21no—
10C2×C4×Dic15C2211yescharacteristic
11C5×#930C2211yescharacteristic
12C3×#4076C2211yescharacteristic
13#91571—21no—
14C2×Dic3×Dic5—21no—
15#91470C411yescharacteristic, complemented
16#91464—21no—
17#91463C411yescharacteristic, complemented
18#91442—21no—
19#91435C411yescharacteristic, complemented
20#91434C411yescharacteristic, complemented
21C3×C5×C22⋊C8C2211yescharacteristic
22#91114C2211yescharacteristic
23#91099—21no—
24#91098—21no—
25C5×C3⋊#95C2211yescharacteristic
26C3×#3963C2211yescharacteristic
27#90994—21no—
28#68278—51nomaximal, Hall
29#65930—31no—
30#65008—31no—
31#64937—31no—
32C5×#327—31no—
33#64757—31no—
34#64690D311yescharacteristic, complemented
35#64671—31no—
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15D411yescharacteristic
38C22×Dic15D411yescharacteristic
39C2×C5×#67—21no—
40C22×C5×Dic3—21no—
41C2×C5×D12C2×C411yescharacteristic
42C2×C3×C22⋊D5—21no—
43C22×C3×Dic5—21no—
44C2×C3×D20C2×C411yescharacteristic
45C2×#1204—21no—
46C2×#1201—21no—
47C2×#1201—21no—
48C2×D3×Dic5—21no—
49#6780—42no—
50#6780—42no—
51C2×D5×Dic3—21no—
52C2×C3×C5×C8—21no—
53C4×Dic15C2×C411yescharacteristic
54C4×Dic15C2×C411yescharacteristic
55C4×Dic15D411yescharacteristic
56C4×Dic15D411yescharacteristic
57C2×C3⋊#168—21no—
58C5×(C2×D3)⋊C4—21no—
59C5×C4⋊Dic3C2×C411yescharacteristic
60C3×#685—21no—
61C3×C4⋊Dic5C2×C411yescharacteristic
62#6669—21no—
63(C2×D3)⋊Dic5—21no—
64#6665—21no—
65Dic3×Dic5—24no—
66#5596—51no—
67#4719—51no—
68#4648—51no—
69C3×#327—51no—
70#4537—51no—
71#4470D511yescharacteristic, complemented
72#4451—51no—
73C2×#711—61no—
74C5×#121—31no—
75#4086—31no—
76#4085—61no—
77D4×Dic5—31no—
78#4076C2×D311yescharacteristic
79C2×C4×Dic5—31no—
80C2×C4×Dic5—61no—
81#4039—31no—
82#4034—31no—
83#4031—61no—
84#4027—61no—
85C5×C22⋊C8C2×D311yescharacteristic
86C5×#95—31no—
87#3963—61no—
88#3963C2×D311yescharacteristic
89C22⋊#168—31no—
90#3947—61no—
91#3946—61no—
92#1505—151noSylow
93C23×C3×C5C2×D411yescharacteristic
94C22×C5×D3—21no—
95C22×C3×D5—21no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×Dic15—21no—
100C2×Dic15—21no—
101C2×Dic15—22no—
102C2×Dic15C22⋊C411yescharacteristic
103C2×Dic15C22⋊C411yescharacteristic
104C2×Dic15C22⋊C411yescharacteristic
105C2×Dic15C22⋊C411yescharacteristic
106C5×#67—41no—
107C5×#67—41no—
108C2×C5×Dic3—22no—
109C2×C5×Dic3—21no—
110C2×C5×Dic3—41no—
111C2×C5×Dic3—41no—
112C5×D12—41no—
113C3×C22⋊D5—41no—
114C3×C22⋊D5—41no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5—21no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—41no—
119C3×D20—41no—
120#1204—42no—
121#1201—42no—
122#1201—42no—
123D3×Dic5—42no—
124D5×Dic3—42no—
125C3×C5×C8—41no—
126C3⋊#168—41no—
127C2×#237—101no—
128C3×#121—51no—
129#940—51no—
130#939—101no—
131D4×Dic3—51no—
132#930C2×D511yescharacteristic
133C2×C4×Dic3—51no—
134C2×C4×Dic3—101no—
135#893—51no—
136#888—51no—
137#885—101no—
138#67⋊C4—101no—
139C3×C22⋊C8C2×D511yescharacteristic
140C3×#95—51no—
141C3⋊#95—101no—
142C3⋊#95C2×D511yescharacteristic
143#830—51no—
144#815—101no—
145Dic3⋊C8—101no—
146C2×C5×D4—31no—
147C2×C5×D4—61no—
148C22×C4×C5—61no—
149C22×C4×C5C22×D311yescharacteristic
150C2×C22⋊D5—21no—
151C2×C22⋊D5—61no—
152C2×C22⋊D5—61no—
153C22×Dic5—21no—
154C22×Dic5—31no—
155C22×Dic5—31no—
156C22×Dic5—61no—
157#711—122no—
158#711—122no—
159C2×D20C4×D311yescharacteristic
160C2×C4×D5—61no—
161C2×Dic10—61no—
162C2×C5×C8—21no—
163C5×C4⋊C4—31no—
164C5×C22⋊C4—61no—
165C22⋊Dic5—61no—
166#685—21no—
167#685—61no—
168C4⋊Dic5C4×D311yescharacteristic
169#683—61no—
170C4×Dic5—31no—
171C4×Dic5—31no—
172C4×Dic5—31no—
173C4×Dic5—31no—
174C4×Dic5—64no—
175C2×#168—61no—
176#532—151no—
177#432—151no—
178#376—151no—
179#327—31no—
180#327—51no—
181#327—151no—
182#327—151no—
183C22×C3×C5—21no—
184C22×C3×C5—21no—
185C22×C3×C5C2×C22⋊C411yescharacteristic
186C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
187C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
188C2×C5×D3—41no—
189C2×C5×D3—41no—
190C2×C5×D3—41no—
191C2×C3×D5—41no—
192C2×C3×D5—41no—
193C2×C3×D5—41no—
194C3×C4×C5—21no—
195C3×C4×C5—21no—
196Dic15—21no—
197Dic15—21no—
198Dic15—21no—
199Dic15#10412yes—
200C3×Dic5—42no—
201C3×Dic5—41no—
202C5×Dic3—42no—
203C5×Dic3—41no—
204C2×C3×D4—51no—
205C2×C3×D4—101no—
206C22×C3×C4—101no—
207C22×C3×C4C22×D511yescharacteristic
208C2×#67—21no—
209C2×#67—101no—
210C2×#67—101no—
211C22×Dic3—21no—
212C22×Dic3—51no—
213C22×Dic3—51no—
214C22×Dic3—101no—
215#237—202no—
216#237—202no—
217C2×D12C4×D511yescharacteristic
218C2×C4×D3—101no—
219C2×Dic6—101no—
220C2×C3×C8—21no—
221C3×C4⋊C4—51no—
222C3×C22⋊C4—101no—
223#217—101no—
224(C2×D3)⋊C4—21no—
225(C2×D3)⋊C4—101no—
226C4⋊Dic3C4×D511yescharacteristic
227Dic3⋊C4—101no—
228C4×Dic3—51no—
229C4×Dic3—51no—
230C4×Dic3—51no—
231C4×Dic3—51no—
232C4×Dic3—104no—
233C2×C3⋊C8—101no—
234C23×C5—61no—
235C23×C5D3×D411yescharacteristic
236C22×D5—21no—
237C5×D4—121no—
238C5×D4—121no—
239C5×D4—121no—
240C2×C4×C5—41no—
241C2×C4×C5—62no—
242C2×C4×C5—61no—
243C2×C4×C5—121no—
244C2×C4×C5—121no—
245C2×C4×C5C2×C4×D311yescharacteristic
246C2×C4×C5D3×D411yescharacteristic
247C22⋊D5—41no—
248C22⋊D5—41no—
249C22⋊D5—122no—
250C22⋊D5—122no—
251C2×Dic5—22no—
252C2×Dic5—21no—
253C2×Dic5—31no—
254C2×Dic5—31no—
255C2×Dic5—31no—
256C2×Dic5—31no—
257C2×Dic5—41no—
258C2×Dic5—41no—
259C2×Dic5—62no—
260C2×Dic5—61no—
261C2×Dic5—61no—
262C2×Dic5—122no—
263D20—41no—
264C4×D5—122no—
265Dic10—122no—
266C5×C8—41no—
267#168—121no—
268C2×#41—301no—
269C4⋊Q8—151no—
270#127—151no—
271#124—301no—
272#121—31no—
273#121—51no—
274#121—301no—
275C4×D4—151no—
276C4×D4—151no—
277C4×D4—301no—
278C2×C42—151no—
279C2×C42—301no—
280C4⋊C8—301no—
281C22⋊C8—151no—
282C22⋊C8D3×D511yescharacteristic
283#97—301no—
284#95—31no—
285#95—51no—
286#95—301no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5#41011yescharacteristic
290C2×C3×C5#41811yescharacteristic
291C2×C3×C5C2×#10411yescharacteristic
292C3×D5—81no—
293C5×D3—81no—
294C23×C3—101no—
295C23×C3D4×D511yescharacteristic
296C22×D3—21no—
297C3×D4—201no—
298C3×D4—201no—
299C3×D4—201no—
300C2×C3×C4—41no—
301C2×C3×C4—102no—
302C2×C3×C4—101no—
303C2×C3×C4—201no—
304C2×C3×C4—201no—
305C2×C3×C4C2×C4×D511yescharacteristic
306C2×C3×C4D4×D511yescharacteristic
307#67—41no—
308#67—41no—
309#67—202no—
310#67—202no—
311C2×Dic3—22no—
312C2×Dic3—21no—
313C2×Dic3—41no—
314C2×Dic3—41no—
315C2×Dic3—51no—
316C2×Dic3—51no—
317C2×Dic3—51no—
318C2×Dic3—51no—
319C2×Dic3—102no—
320C2×Dic3—101no—
321C2×Dic3—101no—
322C2×Dic3—202no—
323D12—41no—
324C4×D3—202no—
325Dic6—202no—
326C3×C8—41no—
327C3⋊C8—201no—
328C22×C5—21no—
329C22×C5—21no—
330C22×C5—121no—
331C22×C5—121no—
332C22×C5—121no—
333C22×C5D3×C22⋊C411yescharacteristic
334C22×C5#91111yescharacteristic
335C22×C5#91411yescharacteristic
336C2×D5—41no—
337C2×D5—41no—
338C2×D5—41no—
339C4×C5—21no—
340C4×C5—21no—
341C4×C5—122no—
342C4×C5—121no—
343Dic5—32no—
344Dic5—42no—
345Dic5—41no—
346Dic5—61no—
347Dic5—61no—
348Dic5—61no—
349#41—602no—
350#41—602no—
351C2×Q8—301no—
352C2×D4—31no—
353C2×D4—51no—
354C2×D4—61no—
355C2×D4—101no—
356C2×D4—301no—
357C2×D4—301no—
358C22×C4—61no—
359C22×C4—101no—
360C22×C4—151no—
361C22×C4—151no—
362C22×C4—301no—
363C22×C4—301no—
364C22×C4C2×D3×D511yescharacteristic
365C2×C8—21no—
366C2×C8—301no—
367C4⋊C4—31no—
368C4⋊C4—51no—
369C4⋊C4—301no—
370C22⋊C4—61no—
371C22⋊C4—101no—
372C22⋊C4—301no—
373C22⋊C4—301no—
374C42—151no—
375C42—151no—
376C42—151no—
377C42—151no—
378C42—304no—
379C3×C5#150511yescharacteristic, complemented, Hall
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—201no—
383C22×C3—201no—
384C22×C3—201no—
385C22×C3D5×C22⋊C411yescharacteristic
386C22×C3#405711yescharacteristic
387C22×C3#406011yescharacteristic
388C2×D3—41no—
389C2×D3—41no—
390C2×D3—41no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—202no—
394C3×C4—201no—
395Dic3—42no—
396Dic3—41no—
397Dic3—52no—
398Dic3—101no—
399Dic3—101no—
400Dic3—101no—
401C2×C5—21no—
402C2×C5—21no—
403C2×C5—241no—
404C2×C5#474011yescharacteristic
405C2×C5#477011yescharacteristic
406C2×C5D3×#10411yescharacteristic
407D5—81no—
408C23—61no—
409C23—101no—
410C23#677711yescharacteristic
411Q8—602no—
412D4—121no—
413D4—121no—
414D4—121no—
415D4—201no—
416D4—201no—
417D4—201no—
418D4—602no—
419D4—602no—
420C2×C4—41no—
421C2×C4—62no—
422C2×C4—61no—
423C2×C4—102no—
424C2×C4—101no—
425C2×C4—121no—
426C2×C4—121no—
427C2×C4—151no—
428C2×C4—151no—
429C2×C4—151no—
430C2×C4—151no—
431C2×C4—201no—
432C2×C4—201no—
433C2×C4—302no—
434C2×C4—301no—
435C2×C4—301no—
436C2×C4—602no—
437C2×C4—602no—
438C2×C4C4×D3×D511yescharacteristic
439C2×C4#679011yescharacteristic
440C8—41no—
441C8—601no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—401no—
445C2×C3#6502911yescharacteristic
446C2×C3#6505911yescharacteristic
447C2×C3D5×#10411yescharacteristic
448D3—81no—
449C5#6827811yescharacteristic, complemented, Sylow
450C22—21no—
451C22—21no—
452C22—121no—
453C22—121no—
454C22—121no—
455C22—201no—
456C22—201no—
457C22—201no—
458C22#9125711yescharacteristic
459C22#9125811yescharacteristic
460C22#9147311yescharacteristic
461C4—21no—
462C4—21no—
463C4—122no—
464C4—121no—
465C4—152no—
466C4—202no—
467C4—201no—
468C4—301no—
469C4—301no—
470C4—301no—
471C3#1059907111yescharacteristic, complemented, Sylow
472C2—21no—
473C2—21no—
474C2—241no—
475C2—401no—
476C2#1174713111yescharacteristic
477C2#1174810911yescharacteristic
478C2#1174823611yescharacteristic
subgroupG/H
centerC22#91473
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11754386C2
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1505
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #11750820C2semidirect
3. #11748653C2semidirect
4. C5×#4470C2semidirect
5. C3×#64690C2semidirect
6. #11745956C2semidirect
7. #11745954C2semidirect
15. #91470C4semidirect
17. #91463C4semidirect
19. #91435C4semidirect
20. #91434C4semidirect
34. #64690D3semidirect
71. #4470D5semidirect
379. C3×C5#1505semidirect
449. C5#68278semidirect
471. C3#10599071semidirect

Maximal subgroups

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

subgroupindex
#117543862
#117508202
#117486532
C5×#44702
C3×#646902
#117459562
#117459542
#105990713
#682785