Finite Group Databasebeta

← #14283139

Subgroups — #14283139

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#4076C211yesmaximal, characteristic
2C5×#4726C211yesmaximal, characteristic, complemented
3#11748719C211yesmaximal, characteristic, complemented
4#11746291C211yesmaximal, characteristic, complemented
5C3×#64690C211yesmaximal, characteristic, complemented
6#11745958C211yesmaximal, characteristic, complemented
7#11745955C211yesmaximal, characteristic, complemented
8#10600770—31nomaximal, Hall
9C22×C4×C5×D3C2211yescharacteristic
10C2×D3×C22⋊D5—21no—
11C2×D3×D20C411yescharacteristic, complemented
12#91819C2211yescharacteristic
13C2×C5×ΓL(1,𝔽25)—21no—
14C3×#4076C2211yescharacteristic
15#91569—21no—
16C2×(C2×D3)⋊Dic5—21no—
17C2×Dic3×Dic5—21no—
18D3×#685—21no—
19#91460C411yescharacteristic, complemented
20#91456C411yescharacteristic, complemented
21#91454—21no—
22D3×C4⋊Dic5C411yescharacteristic, complemented
23C3×C5×C22⋊C8C2211yescharacteristic, complemented
24#91115C2211yescharacteristic, complemented
25C5×#830C2211yescharacteristic, complemented
26C5×(C2×D3)⋊C8—21no—
27C3×#3963C2211yescharacteristic, complemented
28#68303—51nomaximal, Hall
29C2×#4076—31no—
30C5×#407—31no—
31C4×C22⋊Dic5—31no—
32#64690—31no—
33#64690—31no—
34#64690—31no—
35#64690D311yescharacteristic, complemented
36C23×C5×D3D411yescharacteristic
37C22×D3×D5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40C22×Dic15—21no—
41C2×D60C2×C411yescharacteristic
42C22×C5×Dic3D411yescharacteristic
43C2×C4×C5×D3—42no—
44C2×C4×C5×D3C2×C411yescharacteristic
45C2×C4×C5×D3C2×C411yescharacteristic
46C2×C4×C5×D3D411yescharacteristic
47C2×C4×C5×D3D411yescharacteristic
48C2×C3×C22⋊D5—21no—
49C22×C3×Dic5—21no—
50C2×C3×D20C2×C411yescharacteristic
51D3×C22⋊D5—42no—
52D3×C22⋊D5—42no—
53C2×#1203—21no—
54C2×#1202—21no—
55C2×#1201—21no—
56C2×D3×Dic5—21no—
57D3×D20—42no—
58C2×C3×C5×C8—21no—
59#6714—21no—
60C4⋊Dic15C2×C411yescharacteristic
61C2×C5×C3⋊C8—21no—
62C5×ΓL(1,𝔽25)—42no—
63C3×#685—21no—
64C3×C4⋊Dic5C2×C411yescharacteristic
65Dic3⋊Dic5—21no—
66#6667—21no—
67(C2×D3)⋊Dic5—24no—
68#6665—21no—
69Dic3×Dic5—42no—
70D3×#121—51no—
71#4726D511yescharacteristic, complemented
72#4666—51no—
73C3×#327—51no—
74#4537—51no—
75#4470—51no—
76#4451—51no—
77C23×C4×C5—31no—
78C22×C22⋊D5—61no—
79C22×D20—31no—
80C2×C5×M16—61no—
81C2×C22⋊Dic5—61no—
82#4076—31no—
83#4076—31no—
84#4076—31no—
85#4076—61no—
86#4076—61no—
87#4076C2×D311yescharacteristic
88C2×#685—61no—
89C2×C4⋊Dic5—31no—
90C2×C4×Dic5—61no—
91C5×C22⋊C8—31no—
92C5×C22⋊C8—61no—
93C5×C22⋊C8C2×D311yescharacteristic, complemented
94#3963—31no—
95#3963C2×D311yescharacteristic, complemented
96#1507—151noSylow
97C23×C3×C5C2×D411yescharacteristic
98C22×D15—21no—
99C22×C5×D3—21no—
100C22×C5×D3—21no—
101C22×C5×D3—22no—
102C22×C5×D3—41no—
103C22×C5×D3C22⋊C411yescharacteristic
104C22×C5×D3C22⋊C411yescharacteristic
105C22×C3×D5—21no—
106C2×D3×D5—42no—
107C2×D3×D5—42no—
108C2×D3×D5—42no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5C22×C411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112#1220—41no—
113#1220—41no—
114C2×Dic15—22no—
115C2×Dic15—21no—
116C2×Dic15—41no—
117C2×Dic15—41no—
118D60—41no—
119C2×C5×Dic3—22no—
120C2×C5×Dic3C22⋊C411yescharacteristic
121C2×C5×Dic3C22⋊C411yescharacteristic
122C4×C5×D3—22no—
123C4×C5×D3—22no—
124C4×C5×D3—41no—
125C4×C5×D3—41no—
126C3×C22⋊D5—41no—
127C3×C22⋊D5—41no—
128C2×C3×Dic5—22no—
129C2×C3×Dic5—21no—
130C2×C3×Dic5—41no—
131C2×C3×Dic5—41no—
132C3×D20—41no—
133#1203—42no—
134#1202—42no—
135#1201—42no—
136D3×Dic5—42no—
137C3×C5×C8—41no—
138C5×C3⋊C8—41no—
139C2×D3×D4—51no—
140C2×D3×D4—101no—
141C22×C4×D3C2×D511yescharacteristic
142C3×#121—51no—
143#939—101no—
144#938—51no—
145#930—51no—
146C2×(C2×D3)⋊C4—101no—
147C2×C4×Dic3—101no—
148C2×ΓL(1,𝔽25)—21no—
149#895—51no—
150D3×C4⋊C4—51no—
151#884—101no—
152D3×C22⋊C4—101no—
153C3×C22⋊C8C2×D511yescharacteristic, complemented
154C3×#95—51no—
155C3⋊#95—51no—
156#830C2×D511yescharacteristic, complemented
157(C2×D3)⋊C8—21no—
158C24×C5—31no—
159C23×D5—61no—
160C22×C4×C5—31no—
161C22×C4×C5—31no—
162C22×C4×C5—31no—
163C22×C4×C5—31no—
164C22×C4×C5—31no—
165C22×C4×C5—122no—
166C22×C4×C5C22×D311yescharacteristic
167C2×C22⋊D5—21no—
168C2×C22⋊D5—61no—
169C2×C22⋊D5—61no—
170C2×C22⋊D5—61no—
171C2×C22⋊D5—122no—
172C2×C22⋊D5—122no—
173C22×Dic5—21no—
174C22×Dic5—61no—
175C22×Dic5—61no—
176C2×D20—31no—
177C2×D20—61no—
178C2×D20—122no—
179C2×D20C4×D311yescharacteristic
180C5×M16—122no—
181C2×C5×C8—21no—
182C2×C5×C8—61no—
183C22⋊Dic5—64no—
184#685—21no—
185#685—61no—
186#685—61no—
187#685—61no—
188C4⋊Dic5—31no—
189C4⋊Dic5—61no—
190C4⋊Dic5C4×D311yescharacteristic
191C4×Dic5—122no—
192C2×#121—151no—
193#407—31no—
194C4×C22⋊C4—151no—
195#327—51no—
196#327—151no—
197#327—151no—
198#327—151no—
199C22×C3×C5—21no—
200C22×C3×C5—21no—
201C22×C3×C5C2×C22⋊C411yescharacteristic
202C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
203C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
204C2×D15—41no—
205C2×D15—41no—
206C2×D15—41no—
207C2×C5×D3—21no—
208C2×C5×D3—21no—
209C2×C5×D3—21no—
210C2×C5×D3—21no—
211C2×C5×D3—21no—
212C2×C5×D3—42no—
213C2×C5×D3—42no—
214C2×C5×D3#10412yes—
215C2×C3×D5—41no—
216C2×C3×D5—41no—
217C2×C3×D5—41no—
218D3×D5—84no—
219C3×C4×C5—21no—
220C3×C4×C5—21no—
221Dic15—42no—
222Dic15—41no—
223C3×Dic5—42no—
224C3×Dic5—41no—
225C5×Dic3—21no—
226C5×Dic3#9912yes—
227C23×D3—101no—
228C23×D3D2011yescharacteristic
229C2×C3×D4—51no—
230C2×C3×D4—101no—
231C22×C3×C4—101no—
232C22×C3×C4C22×D511yescharacteristic
233C2×#67—101no—
234C2×#67—101no—
235C2×#67—101no—
236C22×Dic3—101no—
237C22×Dic3D2011yescharacteristic
238D3×D4—202no—
239D3×D4—202no—
240D3×D4—202no—
241C2×D12—51no—
242C2×D12—101no—
243C2×C4×D3—42no—
244C2×C4×D3—101no—
245C2×C4×D3C4×D511yescharacteristic
246C2×C4×D3C4×D511yescharacteristic
247C2×C4×D3C22⋊D511yescharacteristic
248C2×C4×D3C22⋊D511yescharacteristic
249C2×C3×C8—21no—
250C3×C4⋊C4—51no—
251C3×C22⋊C4—101no—
252#217—101no—
253(C2×D3)⋊C4—104no—
254(C2×D3)⋊C4—101no—
255(C2×D3)⋊C4—101no—
256C4⋊Dic3—51no—
257Dic3⋊C4—101no—
258C4×Dic3—202no—
259C2×C3⋊C8—21no—
260ΓL(1,𝔽25)—42no—
261C23×C5—31no—
262C23×C5—31no—
263C23×C5—62no—
264C23×C5—61no—
265C23×C5—61no—
266C23×C5—121no—
267C23×C5D3×D411yescharacteristic
268C22×D5—21no—
269C22×D5—61no—
270C22×D5—122no—
271C22×D5—122no—
272C22×D5—122no—
273C2×C4×C5—31no—
274C2×C4×C5—31no—
275C2×C4×C5—41no—
276C2×C4×C5—62no—
277C2×C4×C5—62no—
278C2×C4×C5—62no—
279C2×C4×C5—121no—
280C2×C4×C5—121no—
281C2×C4×C5C2×C4×D311yescharacteristic
282C2×C4×C5D3×D411yescharacteristic
283C22⋊D5—41no—
284C22⋊D5—41no—
285C22⋊D5—122no—
286C22⋊D5—122no—
287C22⋊D5—121no—
288C22⋊D5—121no—
289C2×Dic5—22no—
290C2×Dic5—21no—
291C2×Dic5—41no—
292C2×Dic5—41no—
293C2×Dic5—62no—
294C2×Dic5—61no—
295C2×Dic5—122no—
296C2×Dic5—121no—
297C2×Dic5—121no—
298D20—41no—
299D20—121no—
300D20—122no—
301C5×C8—41no—
302C5×C8—121no—
303C22×D4—151no—
304C22×D4—301no—
305C23×C4—31no—
306C2×M16—61no—
307#121—51no—
308#121—151no—
309#121—151no—
310#121—151no—
311#121—301no—
312#121—301no—
313C2×C4⋊C4—151no—
314C2×C22⋊C4—301no—
315C2×C22⋊C4—301no—
316C2×C42—301no—
317C22⋊C8—31no—
318C22⋊C8—61no—
319C22⋊C8D3×D511yescharacteristic, complemented
320#95—51no—
321#95—151no—
322C2×C3×C5—21no—
323C2×C3×C5—21no—
324C2×C3×C5C2×#9911yescharacteristic
325C2×C3×C5#41811yescharacteristic
326C2×C3×C5C2×#10411yescharacteristic
327D15—81no—
328C3×D5—81no—
329C5×D3—22no—
330C5×D3—41no—
331C23×C3—101no—
332C23×C3C2×D2011yescharacteristic
333C22×D3—21no—
334C22×D3—21no—
335C22×D3—22no—
336C22×D3—41no—
337C22×D3—101no—
338C22×D3—202no—
339C22×D3—202no—
340C22×D3—202no—
341C22×D3#68511yescharacteristic
342C22×D3#68511yescharacteristic
343C3×D4—201no—
344C3×D4—201no—
345C3×D4—201no—
346C2×C3×C4—41no—
347C2×C3×C4—102no—
348C2×C3×C4—101no—
349C2×C3×C4—201no—
350C2×C3×C4—201no—
351C2×C3×C4C2×C4×D511yescharacteristic
352C2×C3×C4C2×C22⋊D511yescharacteristic
353#67—202no—
354#67—201no—
355#67—201no—
356#67—202no—
357C2×Dic3—22no—
358C2×Dic3—102no—
359C2×Dic3—101no—
360C2×Dic3—201no—
361C2×Dic3—201no—
362C2×Dic3#68511yescharacteristic
363C2×Dic3#68511yescharacteristic
364D12—201no—
365D12—202no—
366C4×D3—22no—
367C4×D3—22no—
368C4×D3—41no—
369C4×D3—41no—
370C4×D3—202no—
371C3×C8—41no—
372C3⋊C8—41no—
373C22×C5—21no—
374C22×C5—21no—
375C22×C5—32no—
376C22×C5—61no—
377C22×C5—61no—
378C22×C5—61no—
379C22×C5—61no—
380C22×C5—61no—
381C22×C5—122no—
382C22×C5—122no—
383C22×C5D3×C22⋊C411yescharacteristic
384C22×C5#91111yescharacteristic
385C22×C5#91411yescharacteristic
386C2×D5—41no—
387C2×D5—41no—
388C2×D5—41no—
389C2×D5—121no—
390C2×D5—121no—
391C2×D5—121no—
392C2×D5—244no—
393C4×C5—21no—
394C4×C5—21no—
395C4×C5—32no—
396C4×C5—61no—
397Dic5—42no—
398Dic5—41no—
399Dic5—122no—
400Dic5—121no—
401C24—31no—
402C24—301no—
403C2×D4—51no—
404C2×D4—101no—
405C2×D4—151no—
406C2×D4—301no—
407C2×D4—301no—
408C2×D4—301no—
409C2×D4—301no—
410C2×D4—602no—
411C2×D4—602no—
412C2×D4—602no—
413C22×C4—31no—
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—101no—
419C22×C4—122no—
420C22×C4—301no—
421C22×C4—301no—
422C22×C4C2×D3×D511yescharacteristic
423M16—122no—
424C2×C8—21no—
425C2×C8—61no—
426C4⋊C4—51no—
427C4⋊C4—151no—
428C4⋊C4—301no—
429C22⋊C4—101no—
430C22⋊C4—301no—
431C22⋊C4—301no—
432C22⋊C4—304no—
433C22⋊C4—301no—
434C42—602no—
435C3×C5#150711yescharacteristic, complemented, Hall
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—201no—
439C22×C3—201no—
440C22×C3—201no—
441C22×C3#405411yescharacteristic
442C22×C3#405411yescharacteristic
443C22×C3C2×#68511yescharacteristic
444C2×D3—21no—
445C2×D3—21no—
446C2×D3—21no—
447C2×D3—21no—
448C2×D3—21no—
449C2×D3—42no—
450C2×D3—42no—
451C2×D3—201no—
452C2×D3—201no—
453C2×D3—201no—
454C2×D3—404no—
455C2×D3#395712yes—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—202no—
459C3×C4—201no—
460Dic3—21no—
461Dic3—202no—
462Dic3—201no—
463Dic3#393812yes—
464C2×C5—21no—
465C2×C5—21no—
466C2×C5—62no—
467C2×C5—121no—
468C2×C5D3×#9911yescharacteristic
469C2×C5#477011yescharacteristic
470C2×C5D3×#10411yescharacteristic
471D5—81no—
472D5—241no—
473C23—31no—
474C23—31no—
475C23—62no—
476C23—61no—
477C23—61no—
478C23—101no—
479C23—121no—
480C23—301no—
481C23—602no—
482C23—602no—
483C23—602no—
484C23D3×D2011yescharacteristic
485D4—201no—
486D4—201no—
487D4—201no—
488D4—601no—
489D4—602no—
490D4—602no—
491D4—602no—
492D4—601no—
493D4—601no—
494C2×C4—31no—
495C2×C4—31no—
496C2×C4—41no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—102no—
501C2×C4—101no—
502C2×C4—121no—
503C2×C4—121no—
504C2×C4—201no—
505C2×C4—201no—
506C2×C4—302no—
507C2×C4—301no—
508C2×C4—602no—
509C2×C4—601no—
510C2×C4—601no—
511C2×C4C4×D3×D511yescharacteristic
512C2×C4D3×C22⋊D511yescharacteristic
513C8—41no—
514C8—121no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—401no—
518C2×C3C2×#393811yescharacteristic
519C2×C3#6542011yescharacteristic
520C2×C3C2×#395711yescharacteristic
521D3—22no—
522D3—41no—
523D3—401no—
524C5#6830311yescharacteristic, complemented, Sylow
525C22—21no—
526C22—21no—
527C22—32no—
528C22—61no—
529C22—61no—
530C22—61no—
531C22—61no—
532C22—61no—
533C22—122no—
534C22—122no—
535C22—201no—
536C22—201no—
537C22—201no—
538C22—601no—
539C22—601no—
540C22—601no—
541C22—1204no—
542C22#9125311yescharacteristic
543C22#9125411yescharacteristic
544C22D3×#68511yescharacteristic
545C4—21no—
546C4—21no—
547C4—32no—
548C4—61no—
549C4—202no—
550C4—201no—
551C4—602no—
552C4—601no—
553C3#1060077011yescharacteristic, complemented, Sylow
554C2—21no—
555C2—21no—
556C2—62no—
557C2—121no—
558C2—401no—
559C2—1201no—
560C2D3×#393811yescharacteristic
561C2#1174810711yescharacteristic
562C2D3×#395711yescharacteristic
subgroupG/H
centerC22D3×#685
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalD3×#4076C2
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1507
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. C5×#4726C2semidirect
3. #11748719C2semidirect
4. #11746291C2semidirect
5. C3×#64690C2semidirect
6. #11745958C2semidirect
7. #11745955C2semidirect
11. C2×D3×D20C4semidirect
19. #91460C4semidirect
20. #91456C4semidirect
22. D3×C4⋊Dic5C4semidirect
23. C3×C5×C22⋊C8C22semidirect
24. #91115C22semidirect
25. C5×#830C22semidirect
27. C3×#3963C22semidirect
35. #64690D3semidirect
71. #4726D5semidirect
93. C5×C22⋊C8C2×D3semidirect
95. #3963C2×D3semidirect
153. C3×C22⋊C8C2×D5semidirect
156. #830C2×D5semidirect
319. C22⋊C8D3×D5semidirect
435. C3×C5#1507semidirect
524. C5#68303semidirect
553. C3#10600770semidirect

Maximal subgroups

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

subgroupindex
D3×#40762
C5×#47262
#117487192
#117462912
C3×#646902
#117459582
#117459552
#106007703
#683035