Finite Group Databasebeta

← #14282982

Subgroups — #14282982

Order 1920.

668 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 94 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#11754379C211yesmaximal, characteristic
2D15×#95C211yesmaximal, characteristic, complemented
3#11748509C211yesmaximal, characteristic, complemented
4C5×#4451C211yesmaximal, characteristic, complemented
5C3×#64672C211yesmaximal, characteristic, complemented
6#11745960C211yesmaximal, characteristic, complemented
7#11745957C211yesmaximal, characteristic, complemented
8#10599095—31nomaximal, Hall
9C22×C4×D15—21no—
10C22×C4×D15C2211yescharacteristic
11C2×#6768C411yescharacteristic, complemented
12C5×#930C2211yescharacteristic
13C3×#4070C2211yescharacteristic
14#91573—21no—
15#67⋊Dic5—21no—
16#91466C411yescharacteristic, complemented
17#91406—21no—
18#91390C411yescharacteristic, complemented
19#91355—21no—
20#91347C411yescharacteristic, complemented
21C2×#6651—21no—
22C3×C5×#95C2211yescharacteristic
23#91115—21no—
24#91115C2211yescharacteristic
25C5×#830C2211yescharacteristic
26C3×C22⋊#168C2211yescharacteristic
27#90957—21no—
28#68334—51nomaximal, Hall
29#65940—31no—
30#65015—31no—
31D5×#95—31no—
32C5×#327—31no—
33#64757—31no—
34#64687—31no—
35#64672D311yescharacteristic, complemented
36C23×D15D411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C22×Dic15D411yescharacteristic
41C2×C4×D15—24no—
42C2×C4×D15—42no—
43C2×C4×D15—42no—
44C2×C4×D15—42no—
45C2×C4×D15C2×C411yescharacteristic
46C2×C4×D15C2×C411yescharacteristic
47C2×C4×D15D411yescharacteristic
48C2×C4×D15D411yescharacteristic
49C2×C5×#67—21no—
50C2×C5×D12C2×C411yescharacteristic, complemented
51C2×C3×Dic10C2×C411yescharacteristic, complemented
52C2×#1203—21no—
53C2×#1203—21no—
54C2×D3×Dic5—21no—
55#6768—42no—
56C5×(C2×D3)⋊C4—21no—
57C5×C4⋊Dic3C2×C411yescharacteristic, complemented
58C2×C5×C3⋊C8—21no—
59C3×C22⋊Dic5—21no—
60C3×C4⋊Dic5C2×C411yescharacteristic, complemented
61C3×#683—21no—
62C2×C3×#168—21no—
63Dic3⋊Dic5—21no—
64#6667—21no—
65#6667—21no—
66(C2×D3)⋊Dic5—21no—
67Dic3×Dic5—21no—
68#6651—42no—
69#5627—51no—
70#4726—51no—
71D3×#95—51no—
72C3×#328—51no—
73#4538—51no—
74#4470—51no—
75#4451D511yescharacteristic, complemented
76C2×#711—31no—
77C22×C4×D5—31no—
78C22×C4×D5—61no—
79C5×#121—31no—
80#4084—31no—
81#4083—61no—
82D4×Dic5—61no—
83#4070C2×D311yescharacteristic
84C2×#676—61no—
85#4043—31no—
86#4038—31no—
87#4029—61no—
88#4027—61no—
89C5×C22⋊C8—31no—
90C5×#95C2×D311yescharacteristic
91#3963—31no—
92#3963—61no—
93C22⋊#168C2×D311yescharacteristic
94#3952—61no—
95#1504—151noSylow
96C23×C3×C5C2×D411yescharacteristic
97C22×D15—21no—
98C22×D15—21no—
99C22×D15—22no—
100C22×D15—22no—
101C22×D15C22⋊C411yescharacteristic
102C22×D15C22⋊C411yescharacteristic
103C22×C5×D3—21no—
104C2×C3×C4×C5—22no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×Dic15—22no—
111C2×Dic15—41no—
112C2×Dic15—41no—
113C2×Dic15—41no—
114C2×Dic15C22⋊C411yescharacteristic
115C2×Dic15C22⋊C411yescharacteristic
116C4×D15—22no—
117C4×D15—22no—
118C4×D15—41no—
119C4×D15—41no—
120C4×D15—48no—
121C5×#67—41no—
122C5×#67—41no—
123C2×C5×Dic3—21no—
124C5×D12—41no—
125C2×C3×Dic5—21no—
126C2×C3×Dic5—21no—
127C3×Dic10—41no—
128#1203—42no—
129#1203—42no—
130D3×Dic5—42no—
131C3×#168—41no—
132C5×C3⋊C8—41no—
133C2×#239—51no—
134C22×C4×D3—51no—
135C22×C4×D3—101no—
136C3×C22⋊Q8—51no—
137#946—51no—
138#930C2×D511yescharacteristic
139C2×ΓL(1,𝔽25)—101no—
140#895—51no—
141#894—101no—
142#893—101no—
143#892—51no—
144#882—101no—
145#67⋊C4—101no—
146C3×C22⋊C8—51no—
147C3×#95C2×D511yescharacteristic
148C3⋊#95—51no—
149C3⋊#95—101no—
150#830C2×D511yescharacteristic
151(C2×D3)⋊C8—101no—
152C23×D5—31no—
153C2×C5×D4—31no—
154C2×C5×D4—61no—
155C22×C4×C5—21no—
156C22×C4×C5C22×D311yescharacteristic
157C2×C22⋊D5—61no—
158C2×C22⋊D5—61no—
159C22×Dic5—31no—
160C22×Dic5—61no—
161C22×Dic5—61no—
162#711—122no—
163C2×C4×D5—31no—
164C2×C4×D5—31no—
165C2×C4×D5—31no—
166C2×C4×D5—31no—
167C2×C4×D5—64no—
168C2×C4×D5—122no—
169C2×C4×D5—122no—
170C2×C4×D5—122no—
171C2×Dic10C4×D311yescharacteristic, complemented
172C2×C5×C8—61no—
173C5×C4⋊C4—31no—
174C5×C22⋊C4—61no—
175C22⋊Dic5—21no—
176C22⋊Dic5—61no—
177#685—61no—
178#685—61no—
179C4⋊Dic5—61no—
180C4⋊Dic5C4×D311yescharacteristic, complemented
181#683—21no—
182C4×Dic5—61no—
183C2×#168—21no—
184#676—122no—
185#525—151no—
186#407—151no—
187C2×#95—151no—
188#328—51no—
189#328—151no—
190#327—31no—
191#327—151no—
192C22×C3×C5—21no—
193C22×C3×C5—21no—
194C22×C3×C5C2×C22⋊C411yescharacteristic
195C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
196C22×C3×C5#13711yescharacteristic
197C2×D15—24no—
198C2×D15—24no—
199C2×D15—21no—
200C2×D15—21no—
201C2×D15—21no—
202C2×D15—21no—
203C2×D15#9912yes—
204C2×D15#10412yes—
205C2×C5×D3—41no—
206C2×C5×D3—41no—
207C2×C5×D3—41no—
208C3×C4×C5—21no—
209C3×C4×C5—21no—
210C3×C4×C5—42no—
211Dic15—21no—
212Dic15—21no—
213Dic15—42no—
214C3×Dic5—41no—
215C3×Dic5—41no—
216C5×Dic3—41no—
217C23×D3—51no—
218C2×C3×Q8—51no—
219C22×C3×C4—21no—
220C22×C3×C4C22×D511yescharacteristic
221C2×#67—21no—
222C22×Dic3—51no—
223C22×Dic3—101no—
224#239—202no—
225C2×D12—101no—
226C2×D12—101no—
227C2×D12C4×D511yescharacteristic, complemented
228C2×C4×D3—51no—
229C2×C4×D3—51no—
230C2×C4×D3—51no—
231C2×C4×D3—51no—
232C2×C4×D3—101no—
233C2×C4×D3—104no—
234C2×C4×D3—202no—
235C2×C4×D3—202no—
236C2×C4×D3—202no—
237C2×C3×C8—101no—
238C3×C4⋊C4—51no—
239C3×C4⋊C4—101no—
240C3×C22⋊C4—101no—
241(C2×D3)⋊C4—21no—
242(C2×D3)⋊C4—101no—
243(C2×D3)⋊C4—101no—
244(C2×D3)⋊C4—101no—
245C4⋊Dic3C4×D511yescharacteristic, complemented
246Dic3⋊C4—101no—
247C4×Dic3—101no—
248C2×C3⋊C8—21no—
249ΓL(1,𝔽25)—202no—
250C23×C5—61no—
251C23×C5D3×D411yescharacteristic
252C22×D5—31no—
253C22×D5—31no—
254C22×D5—62no—
255C22×D5—62no—
256C22×D5—61no—
257C22×D5—61no—
258C5×D4—121no—
259C5×D4—121no—
260C5×D4—121no—
261C2×C4×C5—22no—
262C2×C4×C5—41no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5—61no—
266C2×C4×C5C2×C4×D311yescharacteristic
267C2×C4×C5D3×D411yescharacteristic
268C22⋊D5—122no—
269C22⋊D5—122no—
270C2×Dic5—21no—
271C2×Dic5—21no—
272C2×Dic5—31no—
273C2×Dic5—31no—
274C2×Dic5—62no—
275C2×Dic5—122no—
276C2×Dic5—121no—
277C2×Dic5—121no—
278C2×Dic5—121no—
279C4×D5—62no—
280C4×D5—62no—
281C4×D5—121no—
282C4×D5—121no—
283C4×D5—128no—
284Dic10—41no—
285C5×C8—121no—
286#168—41no—
287C2×#41—151no—
288C23×C4—151no—
289C23×C4—301no—
290C2×M16—301no—
291#123—301no—
292C22⋊Q8—51no—
293C22⋊Q8—151no—
294#121—31no—
295#121—151no—
296#120—301no—
297C4×D4—301no—
298C4×D4—301no—
299#117—151no—
300C22⋊C8—31no—
301C22⋊C8—51no—
302C22⋊C8—301no—
303#95—151no—
304#95—301no—
305#95D3×D511yescharacteristic
306C2×C3×C5—21no—
307C2×C3×C5—21no—
308C2×C3×C5C2×#9911yescharacteristic
309C2×C3×C5#41711yescharacteristic
310C2×C3×C5C2×#10411yescharacteristic
311D15—22no—
312D15—22no—
313C5×D3—81no—
314C23×C3D4×D511yescharacteristic
315C22×D3—21no—
316C22×D3—51no—
317C22×D3—51no—
318C22×D3—102no—
319C22×D3—102no—
320C22×D3—101no—
321C22×D3—101no—
322C3×Q8—201no—
323C2×C3×C4—22no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—101no—
328C2×C3×C4—101no—
329C2×C3×C4C2×C4×D511yescharacteristic
330C2×C3×C4D4×D511yescharacteristic
331#67—41no—
332#67—41no—
333C2×Dic3—21no—
334C2×Dic3—51no—
335C2×Dic3—51no—
336C2×Dic3—102no—
337C2×Dic3—201no—
338C2×Dic3—201no—
339C2×Dic3—201no—
340D12—41no—
341D12—202no—
342D12—202no—
343C4×D3—102no—
344C4×D3—102no—
345C4×D3—201no—
346C4×D3—201no—
347C4×D3—202no—
348C4×D3—208no—
349C3×C8—201no—
350C3⋊C8—41no—
351C22×C5—21no—
352C22×C5—21no—
353C22×C5—121no—
354C22×C5—121no—
355C22×C5—121no—
356C22×C5D3×C22⋊C411yescharacteristic
357C22×C5#91411yescharacteristic
358C22×C5#91811yescharacteristic
359C2×D5—32no—
360C2×D5—32no—
361C2×D5—64no—
362C2×D5—64no—
363C2×D5—61no—
364C2×D5—61no—
365C2×D5—61no—
366C2×D5—61no—
367C4×C5—21no—
368C4×C5—21no—
369C4×C5—42no—
370C4×C5—121no—
371Dic5—41no—
372Dic5—41no—
373Dic5—61no—
374Dic5—61no—
375Dic5—122no—
376C24—151no—
377#41—602no—
378C2×Q8—51no—
379C2×D4—31no—
380C2×D4—61no—
381C2×D4—301no—
382C2×D4—301no—
383C22×C4—21no—
384C22×C4—151no—
385C22×C4—151no—
386C22×C4—151no—
387C22×C4—151no—
388C22×C4—151no—
389C22×C4—304no—
390C22×C4—301no—
391C22×C4—301no—
392C22×C4—602no—
393C22×C4—602no—
394C22×C4—602no—
395C22×C4C2×D3×D511yescharacteristic
396M16—602no—
397C2×C8—61no—
398C2×C8—101no—
399C4⋊C4—31no—
400C4⋊C4—51no—
401C4⋊C4—101no—
402C4⋊C4—301no—
403C22⋊C4—61no—
404C22⋊C4—101no—
405C22⋊C4—301no—
406C22⋊C4—301no—
407C22⋊C4—301no—
408C42—301no—
409C3×C5#150411yescharacteristic, complemented, Hall
410C22×C3—21no—
411C22×C3—21no—
412C22×C3D5×C22⋊C411yescharacteristic
413C22×C3#405711yescharacteristic
414C22×C3#406111yescharacteristic
415C2×D3—41no—
416C2×D3—41no—
417C2×D3—41no—
418C2×D3—52no—
419C2×D3—52no—
420C2×D3—104no—
421C2×D3—104no—
422C2×D3—101no—
423C2×D3—101no—
424C2×D3—101no—
425C2×D3—101no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—42no—
429C3×C4—201no—
430C3×C4—201no—
431Dic3—41no—
432Dic3—101no—
433Dic3—101no—
434Dic3—202no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5—241no—
438C2×C5D3×#9911yescharacteristic
439C2×C5#480311yescharacteristic
440C2×C5D3×#10411yescharacteristic
441D5—62no—
442D5—62no—
443C23—61no—
444C23—151no—
445C23—151no—
446C23—302no—
447C23—302no—
448C23—301no—
449C23—301no—
450C23#679011yescharacteristic
451Q8—201no—
452D4—121no—
453D4—121no—
454D4—121no—
455D4—602no—
456D4—602no—
457C2×C4—22no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—61no—
462C2×C4—101no—
463C2×C4—101no—
464C2×C4—151no—
465C2×C4—151no—
466C2×C4—302no—
467C2×C4—302no—
468C2×C4—302no—
469C2×C4—601no—
470C2×C4—601no—
471C2×C4—608no—
472C2×C4—602no—
473C2×C4—601no—
474C2×C4—601no—
475C2×C4—601no—
476C2×C4C4×D3×D511yescharacteristic
477C2×C4#677711yescharacteristic
478C8—121no—
479C8—201no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3D5×#9911yescharacteristic
483C2×C3#6506011yescharacteristic
484C2×C3D5×#10411yescharacteristic
485D3—81no—
486D3—102no—
487D3—102no—
488C5#6833411yescharacteristic, complemented, Sylow
489C22—21no—
490C22—21no—
491C22—121no—
492C22—121no—
493C22—121no—
494C22—152no—
495C22—152no—
496C22—304no—
497C22—304no—
498C22—301no—
499C22—301no—
500C22—301no—
501C22—301no—
502C22#9147311yescharacteristic
503C22#9150011yescharacteristic
504C22#9152411yescharacteristic
505C4—21no—
506C4—21no—
507C4—42no—
508C4—121no—
509C4—201no—
510C4—201no—
511C4—301no—
512C4—301no—
513C4—602no—
514C3#1059909511yescharacteristic, complemented, Sylow
515C2—21no—
516C2—21no—
517C2—241no—
518C2—302no—
519C2—302no—
520C2#1174711211yescharacteristic
521C2#1174712811yescharacteristic
522C2#1174750911yescharacteristic
subgroupG/H
centerC22#91473
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#95C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11754379C2
cosocleC22×C3×C4×C5C23
hypercenter#95D3×D5
hypocenterC3×C5#1504
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. D15×#95C2semidirect
3. #11748509C2semidirect
4. C5×#4451C2semidirect
5. C3×#64672C2semidirect
6. #11745960C2semidirect
7. #11745957C2semidirect
11. C2×#6768C4semidirect
16. #91466C4semidirect
18. #91390C4semidirect
20. #91347C4semidirect
35. #64672D3semidirect
50. C2×C5×D12C2×C4semidirect
51. C2×C3×Dic10C2×C4semidirect
57. C5×C4⋊Dic3C2×C4semidirect
60. C3×C4⋊Dic5C2×C4semidirect
75. #4451D5semidirect
171. C2×Dic10C4×D3semidirect
180. C4⋊Dic5C4×D3semidirect
227. C2×D12C4×D5semidirect
245. C4⋊Dic3C4×D5semidirect
409. C3×C5#1504semidirect
488. C5#68334semidirect
514. C3#10599095semidirect

Maximal subgroups

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

subgroupindex
#117543792
D15×#952
#117485092
C5×#44512
C3×#646722
#117459602
#117459572
#105990953
#683345