Finite Group Databasebeta

← #14283258

Subgroups — #14283258

Order 1920.

652 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 652 conjugacy classes of subgroups — too many to draw. Only its 97 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
1D15×#121C211yesmaximal, characteristic
2#11750827C211yesmaximal, characteristic, complemented
3#11750765C211yesmaximal, characteristic, complemented
4C3×C5×#327C211yesmaximal, characteristic, complemented
5#11746358C211yesmaximal, characteristic, complemented
6#11746291C211yesmaximal, characteristic, complemented
7#11746272C211yesmaximal, characteristic, complemented
8#10599097—31nomaximal, Hall
9C2×D4×D15—21no—
10C2×D4×D15C411yescharacteristic, complemented
11C22×C4×D15C2211yescharacteristic
12C3×C5×#121C2211yescharacteristic
13#91828—21no—
14#91827C411yescharacteristic, complemented
15#91819C2211yescharacteristic
16C2×#6714—21no—
17C2×#6705—21no—
18#91784C411yescharacteristic, complemented
19C4⋊C4×D15C411yescharacteristic, complemented
20#91773—21no—
21C22⋊C4×D15—21no—
22C3×C5×C22⋊C8C2211yescharacteristic, complemented
23C3×C5×#95C2211yescharacteristic, complemented
24#91115—21no—
25#91115C2211yescharacteristic, complemented
26#91114C2211yescharacteristic, complemented
27#91104—21no—
28#68304—51nomaximal, Hall
29D5×#121—31no—
30#65015—31no—
31#64953—31no—
32C5×#327D311yescharacteristic, complemented
33#64757—31no—
34#64690—31no—
35#64671—31no—
36C23×D15—21no—
37C23×D15D411yescharacteristic
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4C2×C411yescharacteristic
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5C2311yescharacteristic
42C2×#1220—21no—
43C2×#1220—21no—
44C2×#1220—21no—
45C22×Dic15—21no—
46C22×Dic15D411yescharacteristic
47D4×D15—42no—
48D4×D15—42no—
49D4×D15—42no—
50C2×D60—21no—
51C2×D60C2×C411yescharacteristic
52C2×C4×D15—21no—
53C2×C4×D15—42no—
54C2×C4×D15C2×C411yescharacteristic
55C2×C4×D15C2×C411yescharacteristic
56C2×C4×D15D411yescharacteristic
57C2×C4×D15D411yescharacteristic
58C2×C3×C5×C8—21no—
59C3×C5×C4⋊C4C2×C411yescharacteristic
60C3×C5×C22⋊C4—21no—
61#6719—21no—
62#6714—21no—
63#6714—21no—
64#6714—42no—
65C4⋊Dic15C2×C411yescharacteristic
66#6712—21no—
67C2×C3⋊#168—21no—
68#6705—42no—
69D3×#121—51no—
70#4726—51no—
71#4664—51no—
72C3×#327D511yescharacteristic, complemented
73#4537—51no—
74#4470—51no—
75#4451—51no—
76C2×D4×D5—31no—
77C2×D4×D5—61no—
78C22×C4×D5—31no—
79C5×#121C2×D311yescharacteristic
80#4085—61no—
81#4084—31no—
82#4076—31no—
83C2×#685—61no—
84C2×#676—61no—
85#4041—31no—
86D5×C4⋊C4—31no—
87#4030—61no—
88D5×C22⋊C4—61no—
89C5×C22⋊C8C2×D311yescharacteristic, complemented
90C5×#95C2×D311yescharacteristic, complemented
91#3963—31no—
92#3963—61no—
93C22⋊#168—31no—
94#3952—61no—
95#1510—151noSylow
96C23×C3×C5—21no—
97C23×C3×C5C2×D411yescharacteristic
98C22×D15—21no—
99C22×D15—21no—
100C22×D15—22no—
101C22×D15—21no—
102C22×D15—41no—
103C22×D15—42no—
104C22×D15—42no—
105C22×D15—42no—
106C22×D15C22⋊C411yescharacteristic
107C22×D15C22⋊C411yescharacteristic
108C3×C5×D4—41no—
109C3×C5×D4—41no—
110C3×C5×D4—41no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5C22×C411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118#1220—42no—
119#1220—42no—
120#1220—41no—
121#1220—41no—
122C2×Dic15—21no—
123C2×Dic15—41no—
124C2×Dic15—41no—
125C2×Dic15—41no—
126C2×Dic15—41no—
127C2×Dic15C22⋊C411yescharacteristic
128C2×Dic15C22⋊C411yescharacteristic
129D60—41no—
130D60—42no—
131C4×D15—22no—
132C4×D15—22no—
133C4×D15—41no—
134C4×D15—41no—
135C4×D15—42no—
136C3×C5×C8—41no—
137C3⋊#168—41no—
138C2×D3×D4—51no—
139C2×D3×D4—101no—
140C22×C4×D3—51no—
141C3×#121C2×D511yescharacteristic
142#939—101no—
143#938—51no—
144#930—51no—
145C2×(C2×D3)⋊C4—101no—
146C2×ΓL(1,𝔽25)—101no—
147#895—51no—
148D3×C4⋊C4—51no—
149#884—101no—
150D3×C22⋊C4—101no—
151C3×C22⋊C8C2×D511yescharacteristic, complemented
152C3×#95C2×D511yescharacteristic, complemented
153C3⋊#95—51no—
154C3⋊#95—101no—
155#830—51no—
156(C2×D3)⋊C8—101no—
157C23×D5—31no—
158C23×D5—61no—
159C2×C5×D4—21no—
160C2×C5×D4C4×D311yescharacteristic
161C22×C4×C5—21no—
162C22×C4×C5C22×D311yescharacteristic
163C2×C22⋊D5—61no—
164C2×C22⋊D5—61no—
165C2×C22⋊D5—61no—
166C22×Dic5—31no—
167C22×Dic5—61no—
168D4×D5—122no—
169D4×D5—122no—
170D4×D5—122no—
171C2×D20—31no—
172C2×D20—61no—
173C2×C4×D5—31no—
174C2×C4×D5—31no—
175C2×C4×D5—31no—
176C2×C4×D5—31no—
177C2×C4×D5—61no—
178C2×C4×D5—122no—
179C2×C5×C8—21no—
180C5×C4⋊C4C4×D311yescharacteristic
181C5×C22⋊C4—21no—
182C22⋊Dic5—61no—
183#685—61no—
184#685—61no—
185#685—122no—
186C4⋊Dic5—31no—
187#683—61no—
188C2×#168—61no—
189#676—122no—
190C2×#121—151no—
191#407—151no—
192#381—151no—
193#327—151no—
194#327—151no—
195#327—151no—
196#327D1511yescharacteristic, complemented
197C22×C3×C5—21no—
198C22×C3×C5—21no—
199C22×C3×C5—41no—
200C22×C3×C5—41no—
201C22×C3×C5—41no—
202C22×C3×C5C2×C22⋊C411yescharacteristic
203C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
204C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
205C2×D15—21no—
206C2×D15—21no—
207C2×D15—21no—
208C2×D15—21no—
209C2×D15—21no—
210C2×D15—42no—
211C2×D15—42no—
212C2×D15—41no—
213C2×D15—41no—
214C2×D15—41no—
215C2×D15—84no—
216C2×D15#9912yes—
217C3×C4×C5—21no—
218C3×C4×C5—21no—
219C3×C4×C5—41no—
220C3×C4×C5—81no—
221Dic15—21no—
222Dic15—21no—
223Dic15—41no—
224Dic15—81no—
225C23×D3—51no—
226C23×D3—101no—
227C2×C3×D4—21no—
228C2×C3×D4C4×D511yescharacteristic
229C22×C3×C4—21no—
230C22×C3×C4C22×D511yescharacteristic
231C2×#67—101no—
232C2×#67—101no—
233C2×#67—101no—
234C22×Dic3—51no—
235C22×Dic3—101no—
236D3×D4—202no—
237D3×D4—202no—
238D3×D4—202no—
239C2×D12—51no—
240C2×D12—101no—
241C2×C4×D3—51no—
242C2×C4×D3—51no—
243C2×C4×D3—51no—
244C2×C4×D3—51no—
245C2×C4×D3—101no—
246C2×C4×D3—202no—
247C2×C3×C8—21no—
248C3×C4⋊C4C4×D511yescharacteristic
249C3×C22⋊C4—21no—
250#217—101no—
251(C2×D3)⋊C4—101no—
252(C2×D3)⋊C4—101no—
253(C2×D3)⋊C4—202no—
254C4⋊Dic3—51no—
255Dic3⋊C4—101no—
256C2×C3⋊C8—101no—
257ΓL(1,𝔽25)—202no—
258C23×C5—21no—
259C23×C5D3×D411yescharacteristic
260C22×D5—31no—
261C22×D5—31no—
262C22×D5—62no—
263C22×D5—61no—
264C22×D5—61no—
265C22×D5—61no—
266C22×D5—122no—
267C22×D5—121no—
268C22×D5—122no—
269C22×D5—122no—
270C5×D4—41no—
271C5×D4—41no—
272C5×D4—41no—
273C2×C4×C5—21no—
274C2×C4×C5—41no—
275C2×C4×C5—41no—
276C2×C4×C5—41no—
277C2×C4×C5—41no—
278C2×C4×C5C2×C4×D311yescharacteristic
279C2×C4×C5D3×D411yescharacteristic
280C22⋊D5—122no—
281C22⋊D5—122no—
282C22⋊D5—121no—
283C22⋊D5—121no—
284C2×Dic5—31no—
285C2×Dic5—31no—
286C2×Dic5—61no—
287C2×Dic5—121no—
288C2×Dic5—121no—
289C2×Dic5—121no—
290C2×Dic5—121no—
291D20—121no—
292D20—122no—
293C4×D5—62no—
294C4×D5—62no—
295C4×D5—121no—
296C4×D5—121no—
297C4×D5—122no—
298C5×C8—41no—
299#168—121no—
300C22×D4—151no—
301C22×D4—301no—
302C23×C4—151no—
303C2×M16—301no—
304#121—151no—
305#121—151no—
306#121—151no—
307#121—301no—
308#121—301no—
309#121C2×D1511yescharacteristic
310C2×C4⋊C4—151no—
311C2×C22⋊C4—301no—
312C2×C22⋊C4—301no—
313C22⋊C8—151no—
314C22⋊C8—301no—
315C22⋊C8C2×D1511yescharacteristic, complemented
316#95—151no—
317#95—301no—
318#95C2×D1511yescharacteristic, complemented
319C2×C3×C5—21no—
320C2×C3×C5—21no—
321C2×C3×C5—81no—
322C2×C3×C5C2×#9911yescharacteristic
323C2×C3×C5#41811yescharacteristic
324C2×C3×C5#42111yescharacteristic
325D15—22no—
326D15—41no—
327D15—81no—
328C23×C3—21no—
329C23×C3D4×D511yescharacteristic
330C22×D3—51no—
331C22×D3—51no—
332C22×D3—102no—
333C22×D3—101no—
334C22×D3—101no—
335C22×D3—101no—
336C22×D3—202no—
337C22×D3—201no—
338C22×D3—202no—
339C22×D3—202no—
340C3×D4—41no—
341C3×D4—41no—
342C3×D4—41no—
343C2×C3×C4—21no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4C2×C4×D511yescharacteristic
349C2×C3×C4D4×D511yescharacteristic
350#67—202no—
351#67—202no—
352#67—201no—
353#67—201no—
354C2×Dic3—51no—
355C2×Dic3—51no—
356C2×Dic3—101no—
357C2×Dic3—201no—
358C2×Dic3—201no—
359C2×Dic3—201no—
360C2×Dic3—201no—
361D12—201no—
362D12—202no—
363C4×D3—102no—
364C4×D3—102no—
365C4×D3—201no—
366C4×D3—201no—
367C4×D3—202no—
368C3×C8—41no—
369C3⋊C8—201no—
370C22×C5—21no—
371C22×C5—21no—
372C22×C5—41no—
373C22×C5—41no—
374C22×C5—41no—
375C22×C5D3×C22⋊C411yescharacteristic
376C22×C5#91111yescharacteristic
377C22×C5#91411yescharacteristic
378C2×D5—32no—
379C2×D5—61no—
380C2×D5—61no—
381C2×D5—61no—
382C2×D5—61no—
383C2×D5—61no—
384C2×D5—122no—
385C2×D5—122no—
386C2×D5—121no—
387C2×D5—121no—
388C2×D5—121no—
389C2×D5—244no—
390C4×C5—21no—
391C4×C5—21no—
392C4×C5—41no—
393C4×C5—81no—
394Dic5—61no—
395Dic5—61no—
396Dic5—121no—
397Dic5—241no—
398C24—151no—
399C24—301no—
400C2×D4—21no—
401C2×D4—151no—
402C2×D4—301no—
403C2×D4—301no—
404C2×D4—301no—
405C2×D4—301no—
406C2×D4—602no—
407C2×D4—602no—
408C2×D4—602no—
409C2×D4C4×D1511yescharacteristic
410C22×C4—21no—
411C22×C4—151no—
412C22×C4—151no—
413C22×C4—151no—
414C22×C4—151no—
415C22×C4—151no—
416C22×C4—301no—
417C22×C4—301no—
418C22×C4—602no—
419C22×C4C22×D1511yescharacteristic
420M16—602no—
421C2×C8—21no—
422C2×C8—301no—
423C4⋊C4—151no—
424C4⋊C4—301no—
425C4⋊C4C4×D1511yescharacteristic
426C22⋊C4—21no—
427C22⋊C4—301no—
428C22⋊C4—301no—
429C22⋊C4—301no—
430C22⋊C4—602no—
431C3×C5#151011yescharacteristic, complemented, Hall
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3D5×C22⋊C411yescharacteristic
438C22×C3#405711yescharacteristic
439C22×C3#406011yescharacteristic
440C2×D3—52no—
441C2×D3—101no—
442C2×D3—101no—
443C2×D3—101no—
444C2×D3—101no—
445C2×D3—101no—
446C2×D3—202no—
447C2×D3—202no—
448C2×D3—201no—
449C2×D3—201no—
450C2×D3—201no—
451C2×D3—404no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—41no—
455C3×C4—81no—
456Dic3—101no—
457Dic3—101no—
458Dic3—201no—
459Dic3—401no—
460C2×C5—21no—
461C2×C5—21no—
462C2×C5—81no—
463C2×C5D3×#9911yescharacteristic
464C2×C5#477011yescharacteristic
465C2×C5#482111yescharacteristic
466D5—62no—
467D5—121no—
468D5—241no—
469C23—21no—
470C23—151no—
471C23—151no—
472C23—302no—
473C23—301no—
474C23—301no—
475C23—301no—
476C23—601no—
477C23—602no—
478C23—602no—
479C23—602no—
480C23D4×D1511yescharacteristic
481D4—41no—
482D4—41no—
483D4—41no—
484D4—601no—
485D4—602no—
486D4—602no—
487D4—602no—
488D4—601no—
489D4—601no—
490C2×C4—21no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—151no—
496C2×C4—151no—
497C2×C4—302no—
498C2×C4—302no—
499C2×C4—301no—
500C2×C4—601no—
501C2×C4—601no—
502C2×C4—602no—
503C2×C4—601no—
504C2×C4—601no—
505C2×C4—601no—
506C2×C4—601no—
507C2×C4C2×C4×D1511yescharacteristic
508C2×C4D4×D1511yescharacteristic
509C8—41no—
510C8—601no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—81no—
514C2×C3D5×#9911yescharacteristic
515C2×C3#6505911yescharacteristic
516C2×C3#6511011yescharacteristic
517D3—102no—
518D3—201no—
519D3—401no—
520C5#6830411yescharacteristic, complemented, Sylow
521C22—21no—
522C22—21no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—152no—
527C22—301no—
528C22—301no—
529C22—301no—
530C22—301no—
531C22—301no—
532C22—602no—
533C22—602no—
534C22—601no—
535C22—601no—
536C22—601no—
537C22—1204no—
538C22C22⋊C4×D1511yescharacteristic
539C22#9180011yescharacteristic
540C22#9180311yescharacteristic
541C4—21no—
542C4—21no—
543C4—41no—
544C4—81no—
545C4—301no—
546C4—301no—
547C4—601no—
548C4—1201no—
549C3#1059909711yescharacteristic, complemented, Sylow
550C2—21no—
551C2—21no—
552C2—81no—
553C2—302no—
554C2—601no—
555C2—1201no—
556C2D15×#9911yescharacteristic
557C2#1175087111yescharacteristic
558C2#1175092211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#327C2
socleC22×C3×C5C2×C22⋊C4
prime radicalD15×#121C2
cosocleC22×C3×C4×C5C23
hypercenter#327D15
hypocenterC3×C5#1510
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #11750827C2semidirect
3. #11750765C2semidirect
4. C3×C5×#327C2semidirect
5. #11746358C2semidirect
6. #11746291C2semidirect
7. #11746272C2semidirect
10. C2×D4×D15C4semidirect
14. #91827C4semidirect
18. #91784C4semidirect
19. C4⋊C4×D15C4semidirect
22. C3×C5×C22⋊C8C22semidirect
23. C3×C5×#95C22semidirect
25. #91115C22semidirect
26. #91114C22semidirect
32. C5×#327D3semidirect
72. C3×#327D5semidirect
89. C5×C22⋊C8C2×D3semidirect
90. C5×#95C2×D3semidirect
151. C3×C22⋊C8C2×D5semidirect
152. C3×#95C2×D5semidirect
196. #327D15semidirect
315. C22⋊C8C2×D15semidirect
318. #95C2×D15semidirect
431. C3×C5#1510semidirect
520. C5#68304semidirect
549. C3#10599097semidirect

Maximal subgroups

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

subgroupindex
D15×#1212
#117508272
#117507652
C3×C5×#3272
#117463582
#117462912
#117462722
#105990973
#683045