Finite Group Databasebeta

← #14283109

Subgroups — #14283109

Order 1920.

692 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 99 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#11750767C211yesmaximal, characteristic, complemented
4C3×C5×#327C211yesmaximal, characteristic, complemented
5#11746358C211yesmaximal, characteristic, complemented
6#11746291C211yesmaximal, characteristic, complemented
7#11746272C211yesmaximal, characteristic, complemented
8#10599096—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×C4×Dic15—21no—
18C2×#6705—21no—
19#91784C411yescharacteristic, complemented
20C4⋊C4×D15C411yescharacteristic, complemented
21#91773—21no—
22C22⋊C4×D15—21no—
23C3×C5×C22⋊C8C2211yescharacteristic, complemented
24C3×C5×#95C2211yescharacteristic, complemented
25#91115C2211yescharacteristic, complemented
26#91114C2211yescharacteristic, complemented
27#91104—21no—
28#68303—51nomaximal, Hall
29D5×#121—31no—
30#65015—31no—
31#64955—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—24no—
63#6714—21no—
64#6714—21no—
65C4⋊Dic15C2×C411yescharacteristic
66#6712—21no—
67C4×Dic15—42no—
68C2×C3⋊#168—21no—
69#6705—42no—
70D3×#121—51no—
71#4726—51no—
72#4666—51no—
73C3×#327D511yescharacteristic, complemented
74#4537—51no—
75#4470—51no—
76#4451—51no—
77C2×D4×D5—31no—
78C2×D4×D5—61no—
79C22×C4×D5—31no—
80C5×#121C2×D311yescharacteristic
81#4085—61no—
82#4084—31no—
83#4076—31no—
84C2×#685—61no—
85C2×C4×Dic5—61no—
86C2×#676—61no—
87#4041—31no—
88D5×C4⋊C4—31no—
89#4030—61no—
90D5×C22⋊C4—61no—
91C5×C22⋊C8C2×D311yescharacteristic, complemented
92C5×#95C2×D311yescharacteristic, complemented
93#3963—31no—
94C22⋊#168—31no—
95#3952—61no—
96#1507—151noSylow
97C23×C3×C5—21no—
98C23×C3×C5C2×D411yescharacteristic
99C22×D15—21no—
100C22×D15—21no—
101C22×D15—22no—
102C22×D15—21no—
103C22×D15—41no—
104C22×D15—42no—
105C22×D15—42no—
106C22×D15—42no—
107C22×D15C22⋊C411yescharacteristic
108C22×D15C22⋊C411yescharacteristic
109C3×C5×D4—41no—
110C3×C5×D4—41no—
111C3×C5×D4—41no—
112C2×C3×C4×C5—22no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5C22×C411yescharacteristic
118C2×C3×C4×C5C2×D411yescharacteristic
119#1220—42no—
120#1220—41no—
121#1220—41no—
122#1220—42no—
123C2×Dic15—22no—
124C2×Dic15—22no—
125C2×Dic15—21no—
126C2×Dic15—41no—
127C2×Dic15—41no—
128C2×Dic15C22⋊C411yescharacteristic
129C2×Dic15C22⋊C411yescharacteristic
130D60—41no—
131D60—42no—
132C4×D15—22no—
133C4×D15—22no—
134C4×D15—41no—
135C4×D15—41no—
136C4×D15—42no—
137C3×C5×C8—41no—
138C3⋊#168—41no—
139C2×D3×D4—51no—
140C2×D3×D4—101no—
141C22×C4×D3—51no—
142C3×#121C2×D511yescharacteristic
143#939—101no—
144#938—51no—
145#930—51no—
146C2×(C2×D3)⋊C4—101no—
147C2×C4×Dic3—101no—
148C2×ΓL(1,𝔽25)—101no—
149#895—51no—
150D3×C4⋊C4—51no—
151#884—101no—
152D3×C22⋊C4—101no—
153C3×C22⋊C8C2×D511yescharacteristic, complemented
154C3×#95C2×D511yescharacteristic, complemented
155C3⋊#95—51no—
156#830—51no—
157(C2×D3)⋊C8—101no—
158C23×D5—31no—
159C23×D5—61no—
160C2×C5×D4—21no—
161C2×C5×D4C4×D311yescharacteristic
162C22×C4×C5—21no—
163C22×C4×C5C22×D311yescharacteristic
164C2×C22⋊D5—61no—
165C2×C22⋊D5—61no—
166C2×C22⋊D5—61no—
167C22×Dic5—31no—
168C22×Dic5—61no—
169D4×D5—122no—
170D4×D5—122no—
171D4×D5—122no—
172C2×D20—31no—
173C2×D20—61no—
174C2×C4×D5—31no—
175C2×C4×D5—31no—
176C2×C4×D5—31no—
177C2×C4×D5—31no—
178C2×C4×D5—61no—
179C2×C4×D5—122no—
180C2×C5×C8—21no—
181C5×C4⋊C4C4×D311yescharacteristic
182C5×C22⋊C4—21no—
183C22⋊Dic5—61no—
184#685—61no—
185#685—64no—
186#685—61no—
187C4⋊Dic5—31no—
188#683—61no—
189C4×Dic5—122no—
190C2×#168—61no—
191#676—122no—
192C2×#121—151no—
193#407—151no—
194C4×C22⋊C4—151no—
195#327—151no—
196#327—151no—
197#327—151no—
198#327D1511yescharacteristic, complemented
199C22×C3×C5—21no—
200C22×C3×C5—21no—
201C22×C3×C5—41no—
202C22×C3×C5—41no—
203C22×C3×C5—41no—
204C22×C3×C5C2×C22⋊C411yescharacteristic
205C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
206C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
207C2×D15—21no—
208C2×D15—21no—
209C2×D15—21no—
210C2×D15—21no—
211C2×D15—21no—
212C2×D15—42no—
213C2×D15—42no—
214C2×D15—41no—
215C2×D15—41no—
216C2×D15—41no—
217C2×D15—84no—
218C2×D15#10412yes—
219C3×C4×C5—21no—
220C3×C4×C5—21no—
221C3×C4×C5—42no—
222C3×C4×C5—41no—
223Dic15—21no—
224Dic15—42no—
225Dic15—41no—
226Dic15#9912yes—
227C23×D3—51no—
228C23×D3—101no—
229C2×C3×D4—21no—
230C2×C3×D4C4×D511yescharacteristic
231C22×C3×C4—21no—
232C22×C3×C4C22×D511yescharacteristic
233C2×#67—101no—
234C2×#67—101no—
235C2×#67—101no—
236C22×Dic3—51no—
237C22×Dic3—101no—
238D3×D4—202no—
239D3×D4—202no—
240D3×D4—202no—
241C2×D12—51no—
242C2×D12—101no—
243C2×C4×D3—51no—
244C2×C4×D3—51no—
245C2×C4×D3—51no—
246C2×C4×D3—51no—
247C2×C4×D3—101no—
248C2×C4×D3—202no—
249C2×C3×C8—21no—
250C3×C4⋊C4C4×D511yescharacteristic
251C3×C22⋊C4—21no—
252#217—101no—
253(C2×D3)⋊C4—101no—
254(C2×D3)⋊C4—104no—
255(C2×D3)⋊C4—101no—
256C4⋊Dic3—51no—
257Dic3⋊C4—101no—
258C4×Dic3—202no—
259C2×C3⋊C8—101no—
260ΓL(1,𝔽25)—202no—
261C23×C5—21no—
262C23×C5D3×D411yescharacteristic
263C22×D5—31no—
264C22×D5—31no—
265C22×D5—62no—
266C22×D5—61no—
267C22×D5—61no—
268C22×D5—61no—
269C22×D5—122no—
270C22×D5—121no—
271C22×D5—122no—
272C22×D5—122no—
273C5×D4—41no—
274C5×D4—41no—
275C5×D4—41no—
276C2×C4×C5—22no—
277C2×C4×C5—21no—
278C2×C4×C5—41no—
279C2×C4×C5—41no—
280C2×C4×C5—41no—
281C2×C4×C5C2×C4×D311yescharacteristic
282C2×C4×C5D3×D411yescharacteristic
283C22⋊D5—122no—
284C22⋊D5—122no—
285C22⋊D5—121no—
286C22⋊D5—121no—
287C2×Dic5—31no—
288C2×Dic5—31no—
289C2×Dic5—62no—
290C2×Dic5—62no—
291C2×Dic5—61no—
292C2×Dic5—121no—
293C2×Dic5—121no—
294D20—121no—
295D20—122no—
296C4×D5—62no—
297C4×D5—62no—
298C4×D5—121no—
299C4×D5—121no—
300C4×D5—122no—
301C5×C8—41no—
302#168—121no—
303C22×D4—151no—
304C22×D4—301no—
305C23×C4—151no—
306C2×M16—301no—
307#121—151no—
308#121—151no—
309#121—151no—
310#121—301no—
311#121—301no—
312#121C2×D1511yescharacteristic
313C2×C4⋊C4—151no—
314C2×C22⋊C4—301no—
315C2×C22⋊C4—301no—
316C2×C42—301no—
317C22⋊C8—151no—
318C22⋊C8—301no—
319C22⋊C8C2×D1511yescharacteristic, complemented
320#95—151no—
321#95C2×D1511yescharacteristic, complemented
322C2×C3×C5—21no—
323C2×C3×C5—21no—
324C2×C3×C5—81no—
325C2×C3×C5C2×#9911yescharacteristic
326C2×C3×C5#41811yescharacteristic
327C2×C3×C5C2×#10411yescharacteristic
328D15—22no—
329D15—41no—
330D15—81no—
331C23×C3—21no—
332C23×C3D4×D511yescharacteristic
333C22×D3—51no—
334C22×D3—51no—
335C22×D3—102no—
336C22×D3—101no—
337C22×D3—101no—
338C22×D3—101no—
339C22×D3—202no—
340C22×D3—201no—
341C22×D3—202no—
342C22×D3—202no—
343C3×D4—41no—
344C3×D4—41no—
345C3×D4—41no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4C2×C4×D511yescharacteristic
352C2×C3×C4D4×D511yescharacteristic
353#67—202no—
354#67—202no—
355#67—201no—
356#67—201no—
357C2×Dic3—51no—
358C2×Dic3—51no—
359C2×Dic3—102no—
360C2×Dic3—102no—
361C2×Dic3—101no—
362C2×Dic3—201no—
363C2×Dic3—201no—
364D12—201no—
365D12—202no—
366C4×D3—102no—
367C4×D3—102no—
368C4×D3—201no—
369C4×D3—201no—
370C4×D3—202no—
371C3×C8—41no—
372C3⋊C8—201no—
373C22×C5—21no—
374C22×C5—21no—
375C22×C5—41no—
376C22×C5—41no—
377C22×C5—41no—
378C22×C5D3×C22⋊C411yescharacteristic
379C22×C5#91111yescharacteristic
380C22×C5#91411yescharacteristic
381C2×D5—32no—
382C2×D5—61no—
383C2×D5—61no—
384C2×D5—61no—
385C2×D5—61no—
386C2×D5—61no—
387C2×D5—122no—
388C2×D5—122no—
389C2×D5—121no—
390C2×D5—121no—
391C2×D5—121no—
392C2×D5—244no—
393C4×C5—21no—
394C4×C5—21no—
395C4×C5—42no—
396C4×C5—41no—
397Dic5—32no—
398Dic5—61no—
399Dic5—122no—
400Dic5—121no—
401C24—151no—
402C24—301no—
403C2×D4—21no—
404C2×D4—151no—
405C2×D4—301no—
406C2×D4—301no—
407C2×D4—301no—
408C2×D4—301no—
409C2×D4—602no—
410C2×D4—602no—
411C2×D4—602no—
412C2×D4C4×D1511yescharacteristic
413C22×C4—21no—
414C22×C4—151no—
415C22×C4—151no—
416C22×C4—151no—
417C22×C4—151no—
418C22×C4—151no—
419C22×C4—301no—
420C22×C4—301no—
421C22×C4—602no—
422C22×C4C22×D1511yescharacteristic
423M16—602no—
424C2×C8—21no—
425C2×C8—301no—
426C4⋊C4—151no—
427C4⋊C4—301no—
428C4⋊C4C4×D1511yescharacteristic
429C22⋊C4—21no—
430C22⋊C4—301no—
431C22⋊C4—304no—
432C22⋊C4—301no—
433C22⋊C4—301no—
434C42—602no—
435C3×C5#150711yescharacteristic, complemented, Hall
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3D5×C22⋊C411yescharacteristic
442C22×C3#405711yescharacteristic
443C22×C3#406011yescharacteristic
444C2×D3—52no—
445C2×D3—101no—
446C2×D3—101no—
447C2×D3—101no—
448C2×D3—101no—
449C2×D3—101no—
450C2×D3—202no—
451C2×D3—202no—
452C2×D3—201no—
453C2×D3—201no—
454C2×D3—201no—
455C2×D3—404no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—42no—
459C3×C4—41no—
460Dic3—52no—
461Dic3—101no—
462Dic3—202no—
463Dic3—201no—
464C2×C5—21no—
465C2×C5—21no—
466C2×C5—81no—
467C2×C5D3×#9911yescharacteristic
468C2×C5#477011yescharacteristic
469C2×C5D3×#10411yescharacteristic
470D5—62no—
471D5—121no—
472D5—241no—
473C23—21no—
474C23—151no—
475C23—151no—
476C23—302no—
477C23—301no—
478C23—301no—
479C23—301no—
480C23—601no—
481C23—602no—
482C23—602no—
483C23—602no—
484C23D4×D1511yescharacteristic
485D4—41no—
486D4—41no—
487D4—41no—
488D4—601no—
489D4—602no—
490D4—602no—
491D4—602no—
492D4—601no—
493D4—601no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—151no—
500C2×C4—151no—
501C2×C4—302no—
502C2×C4—302no—
503C2×C4—302no—
504C2×C4—302no—
505C2×C4—301no—
506C2×C4—601no—
507C2×C4—601no—
508C2×C4—602no—
509C2×C4—601no—
510C2×C4—601no—
511C2×C4C2×C4×D1511yescharacteristic
512C2×C4D4×D1511yescharacteristic
513C8—41no—
514C8—601no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—81no—
518C2×C3D5×#9911yescharacteristic
519C2×C3#6505911yescharacteristic
520C2×C3D5×#10411yescharacteristic
521D3—102no—
522D3—201no—
523D3—401no—
524C5#6830311yescharacteristic, complemented, Sylow
525C22—21no—
526C22—21no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—152no—
531C22—301no—
532C22—301no—
533C22—301no—
534C22—301no—
535C22—301no—
536C22—602no—
537C22—602no—
538C22—601no—
539C22—601no—
540C22—601no—
541C22—1204no—
542C22C22⋊C4×D1511yescharacteristic
543C22#9180011yescharacteristic
544C22#9180311yescharacteristic
545C4—21no—
546C4—21no—
547C4—42no—
548C4—41no—
549C4—152no—
550C4—301no—
551C4—602no—
552C4—601no—
553C3#1059909611yescharacteristic, complemented, Sylow
554C2—21no—
555C2—21no—
556C2—81no—
557C2—302no—
558C2—601no—
559C2—1201no—
560C2D15×#9911yescharacteristic
561C2#1175087111yescharacteristic
562C2D15×#10411yescharacteristic
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#1507
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. #11750767C2semidirect
4. C3×C5×#327C2semidirect
5. #11746358C2semidirect
6. #11746291C2semidirect
7. #11746272C2semidirect
10. C2×D4×D15C4semidirect
14. #91827C4semidirect
19. #91784C4semidirect
20. C4⋊C4×D15C4semidirect
23. C3×C5×C22⋊C8C22semidirect
24. C3×C5×#95C22semidirect
25. #91115C22semidirect
26. #91114C22semidirect
32. C5×#327D3semidirect
73. C3×#327D5semidirect
91. C5×C22⋊C8C2×D3semidirect
92. C5×#95C2×D3semidirect
153. C3×C22⋊C8C2×D5semidirect
154. C3×#95C2×D5semidirect
198. #327D15semidirect
319. C22⋊C8C2×D15semidirect
321. #95C2×D15semidirect
435. C3×C5#1507semidirect
524. C5#68303semidirect
553. C3#10599096semidirect

Maximal subgroups

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

subgroupindex
D15×#1212
#117508272
#117507672
C3×C5×#3272
#117463582
#117462912
#117462722
#105990963
#683035