Finite Group Databasebeta

← #14283130

Subgroups — #14283130

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
1C5×D3×#121C211yesmaximal, characteristic
2#11748719C211yesmaximal, characteristic, complemented
3#11748505C211yesmaximal, characteristic, complemented
4#11746358C211yesmaximal, characteristic, complemented
5C3×#64757C211yesmaximal, characteristic, complemented
6#11745957C211yesmaximal, characteristic, complemented
7#11745956C211yesmaximal, characteristic, complemented
8#10602466—31nomaximal, Hall
9C2×C5×D3×D4—21no—
10C2×C5×D3×D4C411yescharacteristic, complemented
11C22×C4×C5×D3C2211yescharacteristic
12C3×C5×#121C2211yescharacteristic
13C5×#939—21no—
14C5×#938C411yescharacteristic, complemented
15C5×#930C2211yescharacteristic
16C5×#895C411yescharacteristic, complemented
17C5×D3×C4⋊C4C411yescharacteristic, complemented
18C5×#884—21no—
19C5×D3×C22⋊C4—21no—
20C2×(C2×D3)⋊Dic5—21no—
21C2×Dic3×Dic5—21no—
22C2×#6650—21no—
23#91115C2211yescharacteristic, complemented
24#91114C2211yescharacteristic, complemented
25C3×#3963C2211yescharacteristic, complemented
26C3×C22⋊#168C2211yescharacteristic, complemented
27(C2×D3)⋊#168—21no—
28#68303—51nomaximal, Hall
29C2×C5×#121—31no—
30C4×C22⋊Dic5—31no—
31#65496—31no—
32#64757—31no—
33#64757—31no—
34#64757—31no—
35#64757D311yescharacteristic, complemented
36C23×C5×D3—21no—
37C23×C5×D3D411yescharacteristic
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4C2×C411yescharacteristic
40C22×C3×C4×C5C2311yescharacteristic
41C22×Dic15—21no—
42C2×C5×#67—21no—
43C2×C5×#67—21no—
44C2×C5×#67—21no—
45C22×C5×Dic3D411yescharacteristic
46C5×D3×D4—42no—
47C5×D3×D4—42no—
48C5×D3×D4—42no—
49C2×C5×D12—21no—
50C2×C5×D12C2×C411yescharacteristic
51C2×C4×C5×D3—21no—
52C2×C4×C5×D3—42no—
53C2×C4×C5×D3C2×C411yescharacteristic
54C2×C4×C5×D3C2×C411yescharacteristic
55C2×C4×C5×D3D411yescharacteristic
56C2×C4×C5×D3D411yescharacteristic
57C22×C3×Dic5—21no—
58C3×C5×C4⋊C4C2×C411yescharacteristic
59C3×C5×C22⋊C4—21no—
60C2×C3⋊#168—21no—
61C5×#217—21no—
62C5×(C2×D3)⋊C4—21no—
63C5×(C2×D3)⋊C4—21no—
64C5×C4⋊Dic3C2×C411yescharacteristic
65C5×Dic3⋊C4—21no—
66C2×C3×#168—21no—
67(C2×D3)⋊Dic5—24no—
68Dic3×Dic5—42no—
69#6650—42no—
70D3×#121D511yescharacteristic
71#4726—51no—
72#4666—51no—
73C3×#327—51no—
74#4537—51no—
75#4470—51no—
76#4451—51no—
77C22×C5×D4—31no—
78C22×C5×D4—61no—
79C23×C4×C5—31no—
80C5×#121—31no—
81C5×#121—31no—
82C5×#121—31no—
83C5×#121—61no—
84C5×#121—61no—
85C5×#121C2×D311yescharacteristic
86C2×C5×C4⋊C4—31no—
87C2×C5×C22⋊C4—61no—
88C2×C22⋊Dic5—61no—
89C2×C4×Dic5—61no—
90C2×#681—61no—
91#3963—31no—
92#3963C2×D311yescharacteristic, complemented
93C22⋊#168—31no—
94C22⋊#168—61no—
95C22⋊#168C2×D311yescharacteristic, complemented
96#1507—151noSylow
97C23×C3×C5—21no—
98C23×C3×C5C2×D411yescharacteristic
99C22×C5×D3—21no—
100C22×C5×D3—21no—
101C22×C5×D3—22no—
102C22×C5×D3—21no—
103C22×C5×D3—41no—
104C22×C5×D3—42no—
105C22×C5×D3—42no—
106C22×C5×D3—42no—
107C22×C5×D3C22⋊C411yescharacteristic
108C22×C5×D3C22⋊C411yescharacteristic
109C3×C5×D4—41no—
110C3×C5×D4—41no—
111C3×C5×D4—41no—
112C2×C3×C4×C5—21no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5C22×C411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×Dic15—22no—
117C2×Dic15—41no—
118C2×Dic15—41no—
119C5×#67—42no—
120C5×#67—41no—
121C5×#67—41no—
122C5×#67—42no—
123C2×C5×Dic3—22no—
124C2×C5×Dic3—21no—
125C2×C5×Dic3C22⋊C411yescharacteristic
126C2×C5×Dic3C22⋊C411yescharacteristic
127C5×D12—41no—
128C5×D12—42no—
129C4×C5×D3—22no—
130C4×C5×D3—22no—
131C4×C5×D3—41no—
132C4×C5×D3—41no—
133C4×C5×D3—42no—
134C2×C3×Dic5—22no—
135C2×C3×Dic5—41no—
136C2×C3×Dic5—41no—
137C3⋊#168—41no—
138C3×#168—41no—
139C2×D3×D4—21no—
140C2×D3×D4Dic511yescharacteristic, complemented
141C22×C4×D3C2×D511yescharacteristic
142C3×#121C2×D511yescharacteristic
143#939—21no—
144#938Dic511yescharacteristic, complemented
145#930C2×D511yescharacteristic
146C2×(C2×D3)⋊C4—101no—
147C2×C4×Dic3—101no—
148C2×ΓL(1,𝔽25)—101no—
149#895Dic511yescharacteristic, complemented
150D3×C4⋊C4Dic511yescharacteristic, complemented
151#884—21no—
152D3×C22⋊C4—21no—
153C3×C22⋊C8—51no—
154C3×#95—51no—
155C3⋊#95—51no—
156#830—51no—
157(C2×D3)⋊C8—101no—
158C24×C5—31no—
159C24×C5—61no—
160C2×C5×D4—21no—
161C2×C5×D4—31no—
162C2×C5×D4—61no—
163C2×C5×D4—61no—
164C2×C5×D4—61no—
165C2×C5×D4—61no—
166C2×C5×D4—122no—
167C2×C5×D4—122no—
168C2×C5×D4—122no—
169C2×C5×D4C4×D311yescharacteristic
170C22×C4×C5—31no—
171C22×C4×C5—31no—
172C22×C4×C5—31no—
173C22×C4×C5—31no—
174C22×C4×C5—31no—
175C22×C4×C5—61no—
176C22×C4×C5—122no—
177C22×C4×C5C22×D311yescharacteristic
178C22×Dic5—21no—
179C22×Dic5—61no—
180C5×C4⋊C4—31no—
181C5×C4⋊C4—61no—
182C5×C4⋊C4C4×D311yescharacteristic
183C5×C22⋊C4—21no—
184C5×C22⋊C4—61no—
185C5×C22⋊C4—61no—
186C5×C22⋊C4—61no—
187C22⋊Dic5—64no—
188C4×Dic5—122no—
189#681—122no—
190C2×#168—21no—
191C2×#168—61no—
192C2×#121—31no—
193#407—151no—
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×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×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—41no—
215C2×C5×D3—41no—
216C2×C5×D3—41no—
217C2×C5×D3—84no—
218C2×C5×D3#10412yes—
219C3×C4×C5—21no—
220C3×C4×C5—21no—
221C3×C4×C5—41no—
222Dic15—42no—
223C3×Dic5—42no—
224C5×Dic3—21no—
225C5×Dic3—41no—
226C5×Dic3#9912yes—
227C23×D3—21no—
228C23×D3C22⋊D511yescharacteristic
229C2×C3×D4—21no—
230C2×C3×D4C2×Dic511yescharacteristic
231C22×C3×C4—101no—
232C22×C3×C4C22×D511yescharacteristic
233C2×#67—21no—
234C2×#67—21no—
235C2×#67—21no—
236C22×Dic3—101no—
237C22×Dic3C22⋊D511yescharacteristic
238D3×D4—42no—
239D3×D4—42no—
240D3×D4—42no—
241C2×D12—21no—
242C2×D12C2×Dic511yescharacteristic
243C2×C4×D3—21no—
244C2×C4×D3—42no—
245C2×C4×D3C2×Dic511yescharacteristic
246C2×C4×D3C2×Dic511yescharacteristic
247C2×C4×D3C22⋊D511yescharacteristic
248C2×C4×D3C22⋊D511yescharacteristic
249C2×C3×C8—101no—
250C3×C4⋊C4C2×Dic511yescharacteristic
251C3×C22⋊C4—21no—
252#217—21no—
253(C2×D3)⋊C4—21no—
254(C2×D3)⋊C4—21no—
255(C2×D3)⋊C4—104no—
256C4⋊Dic3C2×Dic511yescharacteristic
257Dic3⋊C4—21no—
258C4×Dic3—202no—
259C2×C3⋊C8—101no—
260ΓL(1,𝔽25)—202no—
261C23×C5—21no—
262C23×C5—31no—
263C23×C5—31no—
264C23×C5—62no—
265C23×C5—61no—
266C23×C5—61no—
267C23×C5—61no—
268C23×C5—121no—
269C23×C5—122no—
270C23×C5—122no—
271C23×C5—122no—
272C23×C5D3×D411yescharacteristic
273C5×D4—41no—
274C5×D4—41no—
275C5×D4—41no—
276C5×D4—121no—
277C5×D4—122no—
278C5×D4—122no—
279C5×D4—122no—
280C5×D4—121no—
281C5×D4—121no—
282C2×C4×C5—21no—
283C2×C4×C5—31no—
284C2×C4×C5—31no—
285C2×C4×C5—41no—
286C2×C4×C5—62no—
287C2×C4×C5—62no—
288C2×C4×C5—62no—
289C2×C4×C5—61no—
290C2×C4×C5—121no—
291C2×C4×C5—121no—
292C2×C4×C5—122no—
293C2×C4×C5C2×C4×D311yescharacteristic
294C2×C4×C5D3×D411yescharacteristic
295C2×Dic5—22no—
296C2×Dic5—41no—
297C2×Dic5—41no—
298C2×Dic5—62no—
299C2×Dic5—121no—
300C2×Dic5—121no—
301#168—41no—
302#168—121no—
303C22×D4—31no—
304C22×D4—61no—
305C23×C4—31no—
306C2×M16—301no—
307#121—31no—
308#121—31no—
309#121—31no—
310#121—61no—
311#121—61no—
312#121D3×D511yescharacteristic
313C2×C4⋊C4—31no—
314C2×C22⋊C4—61no—
315C2×C22⋊C4—301no—
316C2×C42—301no—
317C22⋊C8—51no—
318C22⋊C8—151no—
319C22⋊C8—301no—
320#95—51no—
321#95—151no—
322C2×C3×C5—21no—
323C2×C3×C5—21no—
324C2×C3×C5—81no—
325C2×C3×C5C2×#9911yescharacteristic
326C2×C3×C5#41811yescharacteristic
327C2×C3×C5C2×#10411yescharacteristic
328C5×D3—22no—
329C5×D3—41no—
330C5×D3—81no—
331C23×C3—21no—
332C23×C3C2×C22⋊D511yescharacteristic
333C22×D3—21no—
334C22×D3—21no—
335C22×D3—22no—
336C22×D3—21no—
337C22×D3—41no—
338C22×D3—42no—
339C22×D3—42no—
340C22×D3—42no—
341C22×D3C22⋊Dic511yescharacteristic
342C22×D3C22⋊Dic511yescharacteristic
343C3×D4—41no—
344C3×D4—41no—
345C3×D4—41no—
346C2×C3×C4—21no—
347C2×C3×C4—41no—
348C2×C3×C4—102no—
349C2×C3×C4—201no—
350C2×C3×C4—201no—
351C2×C3×C4C22×Dic511yescharacteristic
352C2×C3×C4C2×C22⋊D511yescharacteristic
353#67—42no—
354#67—41no—
355#67—41no—
356#67—42no—
357C2×Dic3—22no—
358C2×Dic3—21no—
359C2×Dic3—102no—
360C2×Dic3—201no—
361C2×Dic3—201no—
362C2×Dic3C22⋊Dic511yescharacteristic
363C2×Dic3C22⋊Dic511yescharacteristic
364D12—41no—
365D12—42no—
366C4×D3—22no—
367C4×D3—22no—
368C4×D3—41no—
369C4×D3—41no—
370C4×D3—42no—
371C3×C8—201no—
372C3⋊C8—201no—
373C22×C5—21no—
374C22×C5—21no—
375C22×C5—32no—
376C22×C5—41no—
377C22×C5—41no—
378C22×C5—41no—
379C22×C5—61no—
380C22×C5—61no—
381C22×C5—61no—
382C22×C5—61no—
383C22×C5—61no—
384C22×C5—122no—
385C22×C5—122no—
386C22×C5—121no—
387C22×C5—121no—
388C22×C5—121no—
389C22×C5—244no—
390C22×C5D3×C22⋊C411yescharacteristic
391C22×C5#91111yescharacteristic
392C22×C5#91411yescharacteristic
393C4×C5—21no—
394C4×C5—21no—
395C4×C5—32no—
396C4×C5—41no—
397C4×C5—61no—
398C4×C5—121no—
399Dic5—42no—
400Dic5—122no—
401C24—31no—
402C24—61no—
403C2×D4—21no—
404C2×D4—31no—
405C2×D4—61no—
406C2×D4—61no—
407C2×D4—61no—
408C2×D4—61no—
409C2×D4—122no—
410C2×D4—122no—
411C2×D4—122no—
412C2×D4D3×Dic511yescharacteristic
413C22×C4—31no—
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—61no—
419C22×C4—101no—
420C22×C4—122no—
421C22×C4—301no—
422C22×C4C2×D3×D511yescharacteristic
423M16—602no—
424C2×C8—101no—
425C2×C8—301no—
426C4⋊C4—31no—
427C4⋊C4—61no—
428C4⋊C4D3×Dic511yescharacteristic
429C22⋊C4—21no—
430C22⋊C4—61no—
431C22⋊C4—61no—
432C22⋊C4—61no—
433C22⋊C4—304no—
434C42—602no—
435C3×C5#150711yescharacteristic, complemented, Hall
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3#407811yescharacteristic
442C22×C3#407811yescharacteristic
443C22×C3C2×C22⋊Dic511yescharacteristic
444C2×D3—21no—
445C2×D3—21no—
446C2×D3—21no—
447C2×D3—21no—
448C2×D3—21no—
449C2×D3—42no—
450C2×D3—42no—
451C2×D3—41no—
452C2×D3—41no—
453C2×D3—41no—
454C2×D3—84no—
455C2×D3#396912yes—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—41no—
459C3×C4—202no—
460Dic3—21no—
461Dic3—41no—
462Dic3—202no—
463Dic3#396612yes—
464C2×C5—21no—
465C2×C5—21no—
466C2×C5—62no—
467C2×C5—81no—
468C2×C5—121no—
469C2×C5—241no—
470C2×C5D3×#9911yescharacteristic
471C2×C5#477011yescharacteristic
472C2×C5D3×#10411yescharacteristic
473C23—21no—
474C23—31no—
475C23—31no—
476C23—62no—
477C23—61no—
478C23—61no—
479C23—61no—
480C23—121no—
481C23—122no—
482C23—122no—
483C23—122no—
484C23D3×C22⋊D511yescharacteristic
485D4—41no—
486D4—41no—
487D4—41no—
488D4—121no—
489D4—122no—
490D4—122no—
491D4—122no—
492D4—121no—
493D4—121no—
494C2×C4—21no—
495C2×C4—31no—
496C2×C4—31no—
497C2×C4—41no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—61no—
502C2×C4—102no—
503C2×C4—121no—
504C2×C4—121no—
505C2×C4—122no—
506C2×C4—201no—
507C2×C4—201no—
508C2×C4—302no—
509C2×C4—601no—
510C2×C4—601no—
511C2×C4C2×D3×Dic511yescharacteristic
512C2×C4D3×C22⋊D511yescharacteristic
513C8—201no—
514C8—601no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—81no—
518C2×C3#6550411yescharacteristic
519C2×C3C2×#396611yescharacteristic
520C2×C3C2×#396911yescharacteristic
521D3—22no—
522D3—41no—
523D3—81no—
524C5#6830311yescharacteristic, complemented, Sylow
525C22—21no—
526C22—21no—
527C22—32no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—61no—
532C22—61no—
533C22—61no—
534C22—61no—
535C22—61no—
536C22—122no—
537C22—122no—
538C22—121no—
539C22—121no—
540C22—121no—
541C22—244no—
542C22#9149411yescharacteristic
543C22#9149611yescharacteristic
544C22D3×C22⋊Dic511yescharacteristic
545C4—21no—
546C4—21no—
547C4—32no—
548C4—41no—
549C4—61no—
550C4—121no—
551C4—202no—
552C4—602no—
553C3#1060246611yescharacteristic, complemented, Sylow
554C2—21no—
555C2—21no—
556C2—62no—
557C2—81no—
558C2—121no—
559C2—241no—
560C2#1174896711yescharacteristic
561C2D3×#396611yescharacteristic
562C2D3×#396911yescharacteristic
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#121C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×D3×#121C2
cosocleC22×C3×C4×C5C23
hypercenter#121D3×D5
hypocenterC3×C5#1507
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #11748719C2semidirect
3. #11748505C2semidirect
4. #11746358C2semidirect
5. C3×#64757C2semidirect
6. #11745957C2semidirect
7. #11745956C2semidirect
10. C2×C5×D3×D4C4semidirect
14. C5×#938C4semidirect
16. C5×#895C4semidirect
17. C5×D3×C4⋊C4C4semidirect
23. #91115C22semidirect
24. #91114C22semidirect
25. C3×#3963C22semidirect
26. C3×C22⋊#168C22semidirect
35. #64757D3semidirect
92. #3963C2×D3semidirect
95. C22⋊#168C2×D3semidirect
140. C2×D3×D4Dic5semidirect
144. #938Dic5semidirect
149. #895Dic5semidirect
150. D3×C4⋊C4Dic5semidirect
435. C3×C5#1507semidirect
524. C5#68303semidirect
553. C3#10602466semidirect

Maximal subgroups

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

subgroupindex
C5×D3×#1212
#117487192
#117485052
#117463582
C3×#647572
#117459572
#117459562
#106024663
#683035