Finite Group Databasebeta

← #14281351

Subgroups — #14281351

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×#91454C211yesmaximal, characteristic
2C5×#4726C211yesmaximal, characteristic, complemented
3D3×C22⋊#168C211yesmaximal, characteristic, complemented
4#11746289C211yesmaximal, characteristic, complemented
5C3×#64688C211yesmaximal, characteristic, complemented
6#11745950C211yesmaximal, characteristic, complemented
7#11745948C211yesmaximal, characteristic, complemented
8#10600763—31nomaximal, Hall
9C22×C4×C5×D3C2211yescharacteristic
10C22×#1203C411yescharacteristic
11C22×#1202C411yescharacteristic
12C22×#1201C411yescharacteristic
13C2×#6714C2211yescharacteristic
14C2×C5×ΓL(1,𝔽25)—21no—
15C2×C3×#685C2211yescharacteristic
16C2×Dic3⋊Dic5C411yescharacteristic
17#91454—21no—
18#91454—21no—
19#91454—21no—
20#91454—21no—
21C2×D3×#168—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23#91114C2211yescharacteristic
24C5×#830C2211yescharacteristic
25C5×(C2×D3)⋊C8—21no—
26C3×C22⋊#168C2211yescharacteristic
27(C2×D3)⋊#168—21no—
28#68123—51nomaximal, Hall
29C2×#4076—31no—
30C5×#407—31no—
31C2×C22⋊#168—31no—
32#64688—31no—
33#64688—31no—
34#64688—31no—
35#64688D311yescharacteristic, complemented
36C23×D15C2×C411yescharacteristic
37C23×C5×D3C2×C411yescharacteristic
38C23×C3×D5C2×C411yescharacteristic
39C22×C3×C4×C5C2311yescharacteristic
40C22×Dic15C2×C411yescharacteristic
41C22×C5×Dic3C2×C411yescharacteristic
42C2×C4×C5×D3—42no—
43C2×C4×C5×D3D411yescharacteristic
44C2×C4×C5×D3D411yescharacteristic
45C2×C4×C5×D3D411yescharacteristic
46C2×C4×C5×D3D411yescharacteristic
47C22×C3×Dic5C2×C411yescharacteristic
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—
61C2×C5×C3⋊C8—21no—
62C5×ΓL(1,𝔽25)—42no—
63C3×#685—21no—
64C3×#685—21no—
65C2×C3×#168—21no—
66Dic3⋊Dic5—21no—
67Dic3⋊Dic5—21no—
68D3×#168—42no—
69C2×#884—51no—
70#4726D511yescharacteristic, complemented
71D3×C22⋊C8—51no—
72C3×#323—51no—
73#4525—51no—
74#4468—51no—
75#4468—51no—
76C23×C4×C5—31no—
77C22×C22⋊D5—31no—
78C22×C22⋊D5—31no—
79C22×D20—31no—
80C2×C5×M16—61no—
81#4076—61no—
82#4076—61no—
83#4076—61no—
84#4076—61no—
85C2×#685—31no—
86C2×#685C2×D311yescharacteristic
87C2×C4⋊Dic5—31no—
88C22×#168—61no—
89C5×C22⋊C8—31no—
90C5×C22⋊C8—61no—
91C5×C22⋊C8C2×D311yescharacteristic
92C22⋊#168—31no—
93C22⋊#168—61no—
94C22⋊#168C2×D311yescharacteristic
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—22no—
105C22×C5×D3—41no—
106C22×C5×D3C22⋊C411yescharacteristic
107C22×C5×D3C22⋊C411yescharacteristic
108C22×C3×D5—21no—
109C22×C3×D5—21no—
110C22×C3×D5—21no—
111C22×C3×D5—41no—
112C22×C3×D5—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×Dic15—21no—
117C2×Dic15—41no—
118C2×C5×Dic3—22no—
119C2×C5×Dic3C22⋊C411yescharacteristic
120C2×C5×Dic3C22⋊C411yescharacteristic
121C4×C5×D3—22no—
122C4×C5×D3—22no—
123C4×C5×D3—41no—
124C4×C5×D3—41no—
125C2×C3×Dic5—21no—
126C2×C3×Dic5—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—
137C22×#67—51no—
138C22×#67—51no—
139C22×D12—51no—
140C22×C4×D3C2×D511yescharacteristic
141C2×C3×C22⋊C4—51no—
142C2×(C2×D3)⋊C4—51no—
143C2×Dic3⋊C4—51no—
144C2×ΓL(1,𝔽25)—21no—
145C2×D3×C8—101no—
146#884—101no—
147#884—101no—
148#884—101no—
149#884—101no—
150C3×C22⋊C8—51no—
151C3×C22⋊C8C2×D511yescharacteristic
152#830—51no—
153#830C2×D511yescharacteristic
154(C2×D3)⋊C8—21no—
155(C2×D3)⋊C8—101no—
156C24×C5—31no—
157C23×D5—31no—
158C23×D5C4×D311yescharacteristic
159C22×C4×C5—31no—
160C22×C4×C5—31no—
161C22×C4×C5—31no—
162C22×C4×C5—31no—
163C22×C4×C5—31no—
164C22×C4×C5—122no—
165C22×C4×C5C22×D311yescharacteristic
166C2×C22⋊D5—61no—
167C2×C22⋊D5—61no—
168C2×C22⋊D5—61no—
169C2×C22⋊D5—61no—
170C2×C22⋊D5—122no—
171C2×C22⋊D5—122no—
172C22×Dic5—31no—
173C22×Dic5C4×D311yescharacteristic
174C2×D20—61no—
175C2×D20—61no—
176C2×D20—122no—
177C5×M16—122no—
178C2×C5×C8—21no—
179C2×C5×C8—61no—
180#685—21no—
181#685—21no—
182#685—61no—
183#685—61no—
184C4⋊Dic5—61no—
185C4⋊Dic5—61no—
186C2×#168—21no—
187C2×#168—61no—
188C2×#168—122no—
189C2×#121—151no—
190#407—31no—
191C2×C22⋊C8—151no—
192#323—51no—
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—21no—
207C2×C5×D3—21no—
208C2×C5×D3—21no—
209C2×C5×D3—21no—
210C2×C5×D3—21no—
211C2×C5×D3—42no—
212C2×C5×D3—42no—
213C2×C5×D3#10012yes—
214C2×C3×D5—41no—
215C2×C3×D5—41no—
216C2×C3×D5—41no—
217C2×C3×D5—81no—
218C2×C3×D5—81no—
219C3×C4×C5—21no—
220C3×C4×C5—21no—
221Dic15—41no—
222C3×Dic5—41no—
223C5×Dic3—21no—
224C5×Dic3#9912yes—
225C24×C3—51no—
226C23×D3—51no—
227C23×D3C4×D511yescharacteristic
228C22×C3×C4—51no—
229C22×C3×C4C22×D511yescharacteristic
230C2×#67—101no—
231C2×#67—101no—
232C2×#67—101no—
233C2×#67—101no—
234C2×#67—202no—
235C2×#67—202no—
236C22×Dic3—51no—
237C22×Dic3C4×D511yescharacteristic
238C2×D12—101no—
239C2×D12—101no—
240C2×D12—202no—
241C2×C4×D3—42no—
242C2×C4×D3D2011yescharacteristic
243C2×C4×D3D2011yescharacteristic
244C2×C4×D3C22⋊D511yescharacteristic
245C2×C4×D3C22⋊D511yescharacteristic
246C2×C3×C8—21no—
247C2×C3×C8—101no—
248C3×C22⋊C4—101no—
249C3×C22⋊C4—101no—
250(C2×D3)⋊C4—101no—
251(C2×D3)⋊C4—101no—
252Dic3⋊C4—101no—
253Dic3⋊C4—101no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—101no—
256ΓL(1,𝔽25)—42no—
257D3×C8—202no—
258C23×C5—31no—
259C23×C5—31no—
260C23×C5—62no—
261C23×C5—61no—
262C23×C5—61no—
263C23×C5—121no—
264C23×C5C2×C4×D311yescharacteristic
265C22×D5—21no—
266C22×D5—21no—
267C22×D5—21no—
268C22×D5—41no—
269C22×D5—41no—
270C22×D5—61no—
271C22×D5—61no—
272C22×D5—61no—
273C22×D5—121no—
274C22×D5—121no—
275C2×C4×C5—31no—
276C2×C4×C5—31no—
277C2×C4×C5—41no—
278C2×C4×C5—62no—
279C2×C4×C5—62no—
280C2×C4×C5—62no—
281C2×C4×C5—121no—
282C2×C4×C5—121no—
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5D3×D411yescharacteristic
285C22⋊D5—122no—
286C22⋊D5—122no—
287C22⋊D5—122no—
288C22⋊D5—122no—
289C2×Dic5—21no—
290C2×Dic5—41no—
291C2×Dic5—61no—
292C2×Dic5—121no—
293D20—122no—
294D20—122no—
295C5×C8—41no—
296C5×C8—121no—
297#168—41no—
298#168—121no—
299C22×D4—151no—
300C22×D4—151no—
301C22×D4—151no—
302C23×C4—31no—
303C2×M16—61no—
304C22×C8—301no—
305#121—301no—
306#121—301no—
307#121—301no—
308#121—301no—
309C2×C4⋊C4—151no—
310C2×C22⋊C4—51no—
311C2×C22⋊C4—151no—
312C22⋊C8—31no—
313C22⋊C8—51no—
314C22⋊C8—61no—
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—81no—
325C5×D3—22no—
326C5×D3—41no—
327C23×C3—101no—
328C23×C3—101no—
329C23×C3—101no—
330C23×C3—201no—
331C23×C3—201no—
332C23×C3C2×C4×D511yescharacteristic
333C22×D3—21no—
334C22×D3—21no—
335C22×D3—22no—
336C22×D3—41no—
337C22×D3—101no—
338C22×D3—101no—
339C22×D3—101no—
340C22×D3—201no—
341C22×D3—201no—
342C22×D3#68511yescharacteristic
343C22×D3#68511yescharacteristic
344C2×C3×C4—41no—
345C2×C3×C4—101no—
346C2×C3×C4—201no—
347C2×C3×C4C2×D2011yescharacteristic
348C2×C3×C4C2×C22⋊D511yescharacteristic
349#67—202no—
350#67—202no—
351#67—202no—
352#67—202no—
353C2×Dic3—22no—
354C2×Dic3—101no—
355C2×Dic3—201no—
356C2×Dic3#68511yescharacteristic
357C2×Dic3#68511yescharacteristic
358D12—202no—
359D12—202no—
360C4×D3—22no—
361C4×D3—22no—
362C4×D3—41no—
363C4×D3—41no—
364C3×C8—41no—
365C3×C8—201no—
366C3⋊C8—41no—
367C3⋊C8—201no—
368C22×C5—21no—
369C22×C5—21no—
370C22×C5—32no—
371C22×C5—61no—
372C22×C5—61no—
373C22×C5—61no—
374C22×C5—61no—
375C22×C5—61no—
376C22×C5—122no—
377C22×C5—122no—
378C22×C5D3×C22⋊C411yescharacteristic
379C22×C5#90111yescharacteristic
380C22×C5#90711yescharacteristic
381C2×D5—41no—
382C2×D5—41no—
383C2×D5—41no—
384C2×D5—81no—
385C2×D5—81no—
386C2×D5—121no—
387C2×D5—121no—
388C2×D5—121no—
389C2×D5—241no—
390C2×D5—241no—
391C4×C5—21no—
392C4×C5—21no—
393C4×C5—32no—
394C4×C5—61no—
395Dic5—41no—
396Dic5—121no—
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—31no—
411C22×C4—31no—
412C22×C4—31no—
413C22×C4—31no—
414C22×C4—51no—
415C22×C4—122no—
416C22×C4—151no—
417C22×C4C2×D3×D511yescharacteristic
418M16—122no—
419C2×C8—21no—
420C2×C8—61no—
421C2×C8—101no—
422C2×C8—301no—
423C2×C8—602no—
424C4⋊C4—301no—
425C4⋊C4—301no—
426C22⋊C4—101no—
427C22⋊C4—101no—
428C22⋊C4—301no—
429C22⋊C4—301no—
430C3×C5#147111yescharacteristic, complemented, Hall
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—201no—
434C22×C3—201no—
435C22×C3—201no—
436C22×C3—401no—
437C22×C3—401no—
438C22×C3#405311yescharacteristic
439C22×C3#405311yescharacteristic
440C22×C3C2×#68511yescharacteristic
441C2×D3—21no—
442C2×D3—21no—
443C2×D3—21no—
444C2×D3—21no—
445C2×D3—21no—
446C2×D3—42no—
447C2×D3—42no—
448C2×D3—201no—
449C2×D3—201no—
450C2×D3—201no—
451C2×D3—401no—
452C2×D3—401no—
453C2×D3#395512yes—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—201no—
457Dic3—21no—
458Dic3—201no—
459Dic3#393812yes—
460C2×C5—21no—
461C2×C5—21no—
462C2×C5—62no—
463C2×C5—121no—
464C2×C5#472711yescharacteristic
465C2×C5D3×#9911yescharacteristic
466C2×C5D3×#10011yescharacteristic
467D5—81no—
468D5—241no—
469C23—31no—
470C23—31no—
471C23—62no—
472C23—61no—
473C23—61no—
474C23—101no—
475C23—101no—
476C23—101no—
477C23—121no—
478C23—201no—
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—31no—
493C2×C4—31no—
494C2×C4—41no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—101no—
499C2×C4—121no—
500C2×C4—121no—
501C2×C4—201no—
502C2×C4—301no—
503C2×C4—601no—
504C2×C4D3×D2011yescharacteristic
505C2×C4D3×C22⋊D511yescharacteristic
506C8—41no—
507C8—121no—
508C8—201no—
509C8—601no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—401no—
513C2×C3C2×#393811yescharacteristic
514C2×C3#6541811yescharacteristic
515C2×C3C2×#395511yescharacteristic
516D3—22no—
517D3—41no—
518D3—401no—
519C5#6812311yescharacteristic, complemented, Sylow
520C22—21no—
521C22—21no—
522C22—32no—
523C22—61no—
524C22—61no—
525C22—61no—
526C22—61no—
527C22—61no—
528C22—122no—
529C22—122no—
530C22—201no—
531C22—201no—
532C22—201no—
533C22—401no—
534C22—401no—
535C22—601no—
536C22—601no—
537C22—601no—
538C22—1201no—
539C22—1201no—
540C22#9126611yescharacteristic
541C22#9126811yescharacteristic
542C22D3×#68511yescharacteristic
543C4—21no—
544C4—21no—
545C4—32no—
546C4—61no—
547C4—201no—
548C4—601no—
549C3#1060076311yescharacteristic, complemented, Sylow
550C2—21no—
551C2—21no—
552C2—62no—
553C2—121no—
554C2—401no—
555C2—1201no—
556C2D3×#393811yescharacteristic
557C2#1174814011yescharacteristic
558C2D3×#395511yescharacteristic
subgroupG/H
centerC22D3×#685
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#91454C2
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. C5×#4726C2semidirect
3. D3×C22⋊#168C2semidirect
4. #11746289C2semidirect
5. C3×#64688C2semidirect
6. #11745950C2semidirect
7. #11745948C2semidirect
35. #64688D3semidirect
70. #4726D5semidirect
430. C3×C5#1471semidirect
519. C5#68123semidirect
549. C3#10600763semidirect

Maximal subgroups

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

subgroupindex
C2×#914542
C5×#47262
D3×C22⋊#1682
#117462892
C3×#646882
#117459502
#117459482
#106007633
#681235