Finite Group Databasebeta

← #14281349

Subgroups — #14281349

Order 1920.

644 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91448C211yesmaximal, characteristic
2C3×#65015C211yesmaximal, characteristic, complemented
3D5×#830C211yesmaximal, characteristic, complemented
4#11746289C211yesmaximal, characteristic, complemented
5C5×#4468C211yesmaximal, characteristic, complemented
6#11745950C211yesmaximal, characteristic, complemented
7#11745949C211yesmaximal, characteristic, complemented
8#10598916—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C22×#1203C411yescharacteristic
11C22×#1202C411yescharacteristic
12C22×#1201C411yescharacteristic
13C2×#6714C2211yescharacteristic
14C2×C5×(C2×D3)⋊C4C2211yescharacteristic
15C2×C3×#676—21no—
16C2×#6668C411yescharacteristic
17#91448—21no—
18#91448—21no—
19#91448—21no—
20#91448—21no—
21C2×D5×C3⋊C8—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23#91114C2211yescharacteristic
24C5×#830C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26C3×#3952—21no—
27#90955—21no—
28#69970—51nomaximal, Hall
29C2×#4030—31no—
30#65015D311yescharacteristic, complemented
31D5×C22⋊C8—31no—
32C5×#323—31no—
33#64745—31no—
34#64688—31no—
35#64688—31no—
36C23×D15C2×C411yescharacteristic
37C23×C5×D3C2×C411yescharacteristic
38C23×C3×D5C2×C411yescharacteristic
39C22×C3×C4×C5C2311yescharacteristic
40C22×Dic15C2×C411yescharacteristic
41C22×C5×Dic3C2×C411yescharacteristic
42C22×C3×Dic5C2×C411yescharacteristic
43C2×C3×C4×D5—42no—
44C2×C3×C4×D5D411yescharacteristic
45C2×C3×C4×D5D411yescharacteristic
46C2×C3×C4×D5D411yescharacteristic
47C2×C3×C4×D5D411yescharacteristic
48C2×#1203—21no—
49C2×#1203—21no—
50C2×#1203—42no—
51C2×#1202—21no—
52C2×#1202—21no—
53C2×#1202—42no—
54C2×#1201—21no—
55C2×#1201—21no—
56C2×#1201—42no—
57C2×C3×C5×C8—21no—
58#6714—21no—
59#6714—21no—
60C2×C3⋊#168—21no—
61C5×(C2×D3)⋊C4—21no—
62C5×(C2×D3)⋊C4—21no—
63C2×C5×C3⋊C8—21no—
64C2×C3×#168—21no—
65C3×#676—42no—
66#6668—21no—
67#6668—21no—
68D5×C3⋊C8—42no—
69C2×#930—51no—
70C3×#407—51no—
71C2×#830—51no—
72#4468—51no—
73#4468—51no—
74#4468—51no—
75#4468D511yescharacteristic, complemented
76C22×C22⋊D5—31no—
77C22×C22⋊D5—31no—
78C22×D20—31no—
79C22×C4×D5C2×D311yescharacteristic
80C2×C5×C22⋊C4—31no—
81C2×#685—31no—
82C2×#683—31no—
83C2×#676—21no—
84C2×C8×D5—61no—
85#4030—61no—
86#4030—61no—
87#4030—61no—
88#4030—61no—
89C5×C22⋊C8—31no—
90C5×C22⋊C8C2×D311yescharacteristic
91C22⋊#168—31no—
92C22⋊#168C2×D311yescharacteristic
93#3952—21no—
94#3952—61no—
95#1471—151noSylow
96C23×C3×C5C22×C411yescharacteristic
97C22×D15—21no—
98C22×D15—21no—
99C22×D15—21no—
100C22×D15—41no—
101C22×D15—41no—
102C22×C5×D3—21no—
103C22×C5×D3—21no—
104C22×C5×D3—21no—
105C22×C5×D3—41no—
106C22×C5×D3—41no—
107C22×C3×D5—21no—
108C22×C3×D5—21no—
109C22×C3×D5—22no—
110C22×C3×D5—41no—
111C22×C3×D5C22⋊C411yescharacteristic
112C22×C3×D5C22⋊C411yescharacteristic
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×Dic15—21no—
117C2×Dic15—41no—
118C2×C5×Dic3—21no—
119C2×C5×Dic3—41no—
120C2×C3×Dic5—22no—
121C2×C3×Dic5C22⋊C411yescharacteristic
122C2×C3×Dic5C22⋊C411yescharacteristic
123C3×C4×D5—22no—
124C3×C4×D5—22no—
125C3×C4×D5—41no—
126C3×C4×D5—41no—
127#1203—42no—
128#1203—42no—
129#1202—42no—
130#1202—42no—
131#1201—42no—
132#1201—42no—
133C3×C5×C8—41no—
134C3⋊#168—41no—
135C3×#168—41no—
136C5×C3⋊C8—41no—
137C23×C3×C4—51no—
138C22×#67—51no—
139C22×#67—51no—
140C22×D12—51no—
141C2×C3×M16—101no—
142#930—101no—
143#930—101no—
144#930—101no—
145#930—101no—
146C2×(C2×D3)⋊C4—51no—
147C2×(C2×D3)⋊C4C2×D511yescharacteristic
148C2×C4⋊Dic3—51no—
149C22×C3⋊C8—101no—
150C3×C22⋊C8—51no—
151C3×C22⋊C8—101no—
152C3×C22⋊C8C2×D511yescharacteristic
153#830—51no—
154#830—101no—
155#830C2×D511yescharacteristic
156C24×C5—31no—
157C23×D5—31no—
158C23×D5C4×D311yescharacteristic
159C22×C4×C5—31no—
160C22×C4×C5C22×D311yescharacteristic
161C2×C22⋊D5—61no—
162C2×C22⋊D5—61no—
163C2×C22⋊D5—61no—
164C2×C22⋊D5—61no—
165C2×C22⋊D5—122no—
166C2×C22⋊D5—122no—
167C22×Dic5—31no—
168C22×Dic5C4×D311yescharacteristic
169C2×D20—61no—
170C2×D20—61no—
171C2×D20—122no—
172C2×C4×D5—42no—
173C2×C4×D5D1211yescharacteristic
174C2×C4×D5D1211yescharacteristic
175C2×C4×D5#6711yescharacteristic
176C2×C4×D5#6711yescharacteristic
177C2×C5×C8—21no—
178C2×C5×C8—61no—
179C5×C22⋊C4—61no—
180C5×C22⋊C4—61no—
181#685—61no—
182#685—61no—
183#683—61no—
184#683—61no—
185C2×#168—21no—
186C2×#168—61no—
187#676—42no—
188C8×D5—122no—
189C2×#121—151no—
190#407—51no—
191C2×C22⋊C8—151no—
192#323—31no—
193#323—151no—
194#323—151no—
195#323—151no—
196C22×C3×C5—21no—
197C22×C3×C5—21no—
198C22×C3×C5C2×C22⋊C411yescharacteristic
199C22×C3×C5#13111yescharacteristic
200C22×C3×C5#13111yescharacteristic
201C2×D15—41no—
202C2×D15—41no—
203C2×D15—41no—
204C2×D15—81no—
205C2×D15—81no—
206C2×C5×D3—41no—
207C2×C5×D3—41no—
208C2×C5×D3—41no—
209C2×C5×D3—81no—
210C2×C5×D3—81no—
211C2×C3×D5—21no—
212C2×C3×D5—21no—
213C2×C3×D5—21no—
214C2×C3×D5—21no—
215C2×C3×D5—21no—
216C2×C3×D5—42no—
217C2×C3×D5—42no—
218C2×C3×D5#10012yes—
219C3×C4×C5—21no—
220C3×C4×C5—21no—
221Dic15—41no—
222C3×Dic5—21no—
223C3×Dic5#9912yes—
224C5×Dic3—41no—
225C24×C3—51no—
226C23×D3—51no—
227C23×D3C4×D511yescharacteristic
228C22×C3×C4—51no—
229C22×C3×C4—51no—
230C22×C3×C4—51no—
231C22×C3×C4—51no—
232C22×C3×C4—51no—
233C22×C3×C4—202no—
234C22×C3×C4C22×D511yescharacteristic
235C2×#67—101no—
236C2×#67—101no—
237C2×#67—101no—
238C2×#67—101no—
239C2×#67—202no—
240C2×#67—202no—
241C22×Dic3—51no—
242C22×Dic3C4×D511yescharacteristic
243C2×D12—101no—
244C2×D12—101no—
245C2×D12—202no—
246C3×M16—202no—
247C2×C3×C8—21no—
248C2×C3×C8—101no—
249(C2×D3)⋊C4—21no—
250(C2×D3)⋊C4—21no—
251(C2×D3)⋊C4—101no—
252(C2×D3)⋊C4—101no—
253C4⋊Dic3—101no—
254C4⋊Dic3—101no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8—101no—
257C2×C3⋊C8—202no—
258C23×C5—61no—
259C23×C5—61no—
260C23×C5—61no—
261C23×C5—121no—
262C23×C5—121no—
263C23×C5C2×C4×D311yescharacteristic
264C22×D5—21no—
265C22×D5—21no—
266C22×D5—22no—
267C22×D5—41no—
268C22×D5—61no—
269C22×D5—61no—
270C22×D5—61no—
271C22×D5—121no—
272C22×D5—121no—
273C22×D5(C2×D3)⋊C411yescharacteristic
274C22×D5(C2×D3)⋊C411yescharacteristic
275C2×C4×C5—41no—
276C2×C4×C5—61no—
277C2×C4×C5—121no—
278C2×C4×C5C2×D1211yescharacteristic
279C2×C4×C5C2×#6711yescharacteristic
280C22⋊D5—122no—
281C22⋊D5—122no—
282C22⋊D5—122no—
283C22⋊D5—122no—
284C2×Dic5—22no—
285C2×Dic5—61no—
286C2×Dic5—121no—
287C2×Dic5(C2×D3)⋊C411yescharacteristic
288C2×Dic5(C2×D3)⋊C411yescharacteristic
289D20—122no—
290D20—122no—
291C4×D5—22no—
292C4×D5—22no—
293C4×D5—41no—
294C4×D5—41no—
295C5×C8—41no—
296C5×C8—121no—
297#168—41no—
298#168—121no—
299C22×D4—151no—
300C22×D4—151no—
301C22×D4—151no—
302C23×C4—51no—
303C2×M16—101no—
304C22×C8—301no—
305#121—301no—
306#121—301no—
307#121—301no—
308#121—301no—
309C2×C4⋊C4—151no—
310C2×C22⋊C4—31no—
311C2×C22⋊C4—151no—
312C22⋊C8—31no—
313C22⋊C8—51no—
314C22⋊C8—101no—
315C22⋊C8—151no—
316C22⋊C8—301no—
317C22⋊C8D3×D511yescharacteristic
318C2×C3×C5—21no—
319C2×C3×C5—21no—
320C2×C3×C5#40811yescharacteristic
321C2×C3×C5C2×#9911yescharacteristic
322C2×C3×C5C2×#10011yescharacteristic
323D15—81no—
324C3×D5—22no—
325C3×D5—41no—
326C5×D3—81no—
327C23×C3—51no—
328C23×C3—51no—
329C23×C3—102no—
330C23×C3—101no—
331C23×C3—101no—
332C23×C3—201no—
333C23×C3C2×C4×D511yescharacteristic
334C22×D3—21no—
335C22×D3—21no—
336C22×D3—21no—
337C22×D3—41no—
338C22×D3—41no—
339C22×D3—101no—
340C22×D3—101no—
341C22×D3—101no—
342C22×D3—201no—
343C22×D3—201no—
344C2×C3×C4—41no—
345C2×C3×C4—51no—
346C2×C3×C4—51no—
347C2×C3×C4—102no—
348C2×C3×C4—102no—
349C2×C3×C4—102no—
350C2×C3×C4—201no—
351C2×C3×C4—201no—
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4D4×D511yescharacteristic
354#67—202no—
355#67—202no—
356#67—202no—
357#67—202no—
358C2×Dic3—21no—
359C2×Dic3—41no—
360C2×Dic3—101no—
361C2×Dic3—201no—
362D12—202no—
363D12—202no—
364C3×C8—41no—
365C3×C8—201no—
366C3⋊C8—41no—
367C3⋊C8—201no—
368C22×C5—21no—
369C22×C5—21no—
370C22×C5—121no—
371C22×C5—121no—
372C22×C5—121no—
373C22×C5—241no—
374C22×C5—241no—
375C22×C5#90711yescharacteristic
376C22×C5#90711yescharacteristic
377C22×C5C2×(C2×D3)⋊C411yescharacteristic
378C2×D5—21no—
379C2×D5—21no—
380C2×D5—21no—
381C2×D5—21no—
382C2×D5—21no—
383C2×D5—42no—
384C2×D5—42no—
385C2×D5—121no—
386C2×D5—121no—
387C2×D5—121no—
388C2×D5—241no—
389C2×D5—241no—
390C2×D5#82312yes—
391C4×C5—21no—
392C4×C5—21no—
393C4×C5—121no—
394Dic5—21no—
395Dic5—121no—
396Dic5#80612yes—
397C24—31no—
398C24—51no—
399C24—151no—
400C2×D4—301no—
401C2×D4—301no—
402C2×D4—301no—
403C2×D4—301no—
404C2×D4—301no—
405C2×D4—301no—
406C2×D4—602no—
407C2×D4—602no—
408C2×D4—602no—
409C22×C4—31no—
410C22×C4—51no—
411C22×C4—51no—
412C22×C4—51no—
413C22×C4—51no—
414C22×C4—51no—
415C22×C4—151no—
416C22×C4—202no—
417C22×C4C2×D3×D511yescharacteristic
418M16—202no—
419C2×C8—21no—
420C2×C8—61no—
421C2×C8—101no—
422C2×C8—301no—
423C2×C8—602no—
424C4⋊C4—301no—
425C4⋊C4—301no—
426C22⋊C4—61no—
427C22⋊C4—61no—
428C22⋊C4—301no—
429C22⋊C4—301no—
430C3×C5#147111yescharacteristic, complemented, Hall
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—52no—
434C22×C3—101no—
435C22×C3—101no—
436C22×C3—101no—
437C22×C3—101no—
438C22×C3—101no—
439C22×C3—202no—
440C22×C3—202no—
441C22×C3D5×C22⋊C411yescharacteristic
442C22×C3#404711yescharacteristic
443C22×C3#405311yescharacteristic
444C2×D3—41no—
445C2×D3—41no—
446C2×D3—41no—
447C2×D3—81no—
448C2×D3—81no—
449C2×D3—201no—
450C2×D3—201no—
451C2×D3—201no—
452C2×D3—401no—
453C2×D3—401no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—52no—
457C3×C4—101no—
458Dic3—41no—
459Dic3—201no—
460C2×C5—21no—
461C2×C5—21no—
462C2×C5—241no—
463C2×C5C2×#80611yescharacteristic
464C2×C5#512911yescharacteristic
465C2×C5C2×#82311yescharacteristic
466D5—22no—
467D5—41no—
468D5—241no—
469C23—51no—
470C23—51no—
471C23—61no—
472C23—61no—
473C23—61no—
474C23—102no—
475C23—101no—
476C23—101no—
477C23—121no—
478C23—121no—
479C23—201no—
480C23—301no—
481C23—301no—
482C23—301no—
483C23—601no—
484C23—601no—
485C23C4×D3×D511yescharacteristic
486D4—602no—
487D4—602no—
488D4—602no—
489D4—602no—
490D4—602no—
491D4—602no—
492C2×C4—41no—
493C2×C4—51no—
494C2×C4—51no—
495C2×C4—61no—
496C2×C4—102no—
497C2×C4—102no—
498C2×C4—102no—
499C2×C4—121no—
500C2×C4—201no—
501C2×C4—201no—
502C2×C4—301no—
503C2×C4—601no—
504C2×C4D5×D1211yescharacteristic
505C2×C4D5×#6711yescharacteristic
506C8—41no—
507C8—121no—
508C8—201no—
509C8—601no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—102no—
513C2×C3—201no—
514C2×C3#6501611yescharacteristic
515C2×C3D5×#9911yescharacteristic
516C2×C3D5×#10011yescharacteristic
517D3—81no—
518D3—401no—
519C5#6997011yescharacteristic, complemented, Sylow
520C22—21no—
521C22—21no—
522C22—52no—
523C22—101no—
524C22—101no—
525C22—101no—
526C22—101no—
527C22—101no—
528C22—121no—
529C22—121no—
530C22—121no—
531C22—202no—
532C22—202no—
533C22—241no—
534C22—241no—
535C22—601no—
536C22—601no—
537C22—601no—
538C22—1201no—
539C22—1201no—
540C22#9126711yescharacteristic
541C22#9126811yescharacteristic
542C22D5×(C2×D3)⋊C411yescharacteristic
543C4—21no—
544C4—21no—
545C4—52no—
546C4—101no—
547C4—121no—
548C4—601no—
549C3#1059891611yescharacteristic, complemented, Sylow
550C2—21no—
551C2—21no—
552C2—102no—
553C2—201no—
554C2—241no—
555C2—1201no—
556C2D5×#80611yescharacteristic
557C2#1174813611yescharacteristic
558C2D5×#82311yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#91448C2
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1471
LCSG ▷ C23×C3×C5 ▷ C2×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. C3×#65015C2semidirect
3. D5×#830C2semidirect
4. #11746289C2semidirect
5. C5×#4468C2semidirect
6. #11745950C2semidirect
7. #11745949C2semidirect
30. #65015D3semidirect
75. #4468D5semidirect
430. C3×C5#1471semidirect
519. C5#69970semidirect
549. C3#10598916semidirect

Maximal subgroups

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

subgroupindex
C2×#914482
C3×#650152
D5×#8302
#117462892
C5×#44682
#117459502
#117459492
#105989163
#699705