Finite Group Databasebeta

← #14313237

Subgroups — #14313237

Order 1920.

560 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C5×#5653C211yesmaximal, characteristic
2D3×#3966C211yesmaximal, characteristic, complemented
3D3×#3965C211yesmaximal, characteristic, complemented
4#11746360C211yesmaximal, characteristic, complemented
5C3×#64759C211yesmaximal, characteristic, complemented
6#11745997C211yesmaximal, characteristic, complemented
7#11745996C211yesmaximal, characteristic, complemented
8#10602640—31nomaximal, Hall
9C2×C5×D3×D4C2211yescharacteristic
10C22×C5×D12C411yescharacteristic, complemented
11C3×C5×#123C2211yescharacteristic
12C5×#937C2211yescharacteristic
13C5×#929C411yescharacteristic, complemented
14C5×#895—21no—
15C5×#894—21no—
16C5×#884—21no—
17C5×#882—21no—
18C5×#882C411yescharacteristic, complemented
19C5×D3×C22⋊C4C411yescharacteristic, complemented
20D3×C22⋊Dic5—21no—
21D3×#681—21no—
22#91118C2211yescharacteristic
23#91117C2211yescharacteristic
24C3×#3966C2211yescharacteristic
25C3×#3965C2211yescharacteristic
26#90996—21no—
27#90959—21no—
28#69143—51nomaximal, Hall
29C5×#534—31no—
30C2×#3966—31no—
31C2×#3965—31no—
32#64759—31no—
33#64759D311yescharacteristic, complemented
34#64756—31no—
35#64756—31no—
36C23×C5×D3C2×C411yescharacteristic
37C23×C5×D3C2×C411yescharacteristic, complemented
38C23×C5×D3D411yescharacteristic
39C2×C3×C5×D4C2311yescharacteristic
40C22×C3×C4×C5C2×C411yescharacteristic, complemented
41C2×C5×#67—21no—
42C2×C5×#67C2×C411yescharacteristic
43C2×C5×#67D411yescharacteristic
44C5×D3×D4—41no—
45C5×D3×D4—41no—
46C2×C5×D12—21no—
47C2×C5×D12—21no—
48C2×C5×D12—21no—
49C2×C5×D12—41no—
50C2×C5×D12—41no—
51C2×C5×D12D411yescharacteristic
52C2×C4×C5×D3—21no—
53C2×C4×C5×D3D411yescharacteristic
54C2×D3×Dic5—41no—
55C3×C5×C4⋊C4—21no—
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4C2×C411yescharacteristic, complemented
58#6719—21no—
59#6710—21no—
60C5×#217C2×C411yescharacteristic, complemented
61C5×(C2×D3)⋊C4—21no—
62C5×(C2×D3)⋊C4—21no—
63C5×(C2×D3)⋊C4—21no—
64C5×(C2×D3)⋊C4—21no—
65C5×Dic3⋊C4—21no—
66C3×C22⋊Dic5—21no—
67C3×#681—21no—
68(C2×D3)⋊Dic5—41no—
69#6650—41no—
70D3×#168—41no—
71#5653D511yescharacteristic
72D3×#100—51no—
73D3×#99—51no—
74C3×#352—51no—
75#4539—51no—
76#4475—51no—
77#4471—51no—
78C22×C5×D4—31no—
79C22×C5×D4—31no—
80C5×#123—31no—
81C5×#123—61no—
82C5×#123C2×D311yescharacteristic
83C5×#121—61no—
84C5×#121—61no—
85C5×#120—31no—
86C5×#120—31no—
87C5×#120—61no—
88C2×C5×C22⋊C4—31no—
89C2×C22⋊Dic5—61no—
90C2×#681—61no—
91#3966—31no—
92#3966—61no—
93#3966C2×D311yescharacteristic
94#3965—31no—
95#3965—61no—
96#3965C2×D311yescharacteristic
97#2121—151noSylow
98C23×C3×C5C22×C411yescharacteristic
99C23×C3×C5C2×D411yescharacteristic
100C22×C5×D3—21no—
101C22×C5×D3—21no—
102C22×C5×D3—21no—
103C22×C5×D3—21no—
104C22×C5×D3—21no—
105C22×C5×D3—41no—
106C22×C5×D3—81no—
107C22×C5×D3—81no—
108C22×C5×D3—81no—
109C22×C5×D3C22⋊C411yescharacteristic
110C22×C5×D3C22⋊C411yescharacteristic
111C22×C5×D3C22⋊C411yescharacteristic
112C3×C5×D4—41no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—21no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×Dic15—41no—
118C5×#67—41no—
119C5×#67—41no—
120C5×#67—81no—
121C2×C5×Dic3—21no—
122C2×C5×Dic3C22⋊C411yescharacteristic
123C5×D12—41no—
124C5×D12—42no—
125C5×D12—41no—
126C5×D12—41no—
127C5×D12—81no—
128C4×C5×D3—21no—
129C4×C5×D3—21no—
130C4×C5×D3—81no—
131C2×C3×Dic5—41no—
132D3×Dic5—82no—
133C3⋊#168—41no—
134C3×#168—41no—
135C2×D3×D4C2×D511yescharacteristic
136C22×D12Dic511yescharacteristic, complemented
137C3×#123C2×D511yescharacteristic
138#937C2×D511yescharacteristic
139#929Dic511yescharacteristic, complemented
140D3×M16—101no—
141#895—21no—
142#894—21no—
143#884—21no—
144#882—21no—
145#882Dic511yescharacteristic, complemented
146D3×C22⋊C4—101no—
147D3×C22⋊C4Dic511yescharacteristic, complemented
148C3×#100—51no—
149C3×#99—51no—
150#834—51no—
151#833—51no—
152#823—101no—
153#806—101no—
154C24×C5—31no—
155C24×C5—31no—
156C24×C5—31no—
157C2×C5×D4—31no—
158C2×C5×D4—31no—
159C2×C5×D4—31no—
160C2×C5×D4—61no—
161C2×C5×D4—61no—
162C2×C5×D4—61no—
163C2×C5×D4—61no—
164C2×C5×D4—121no—
165C2×C5×D4—121no—
166C2×C5×D4—121no—
167C2×C5×D4—121no—
168C2×C5×D4C22×D311yescharacteristic
169C22×C4×C5—31no—
170C22×C4×C5—61no—
171C22×C4×C5C4×D311yescharacteristic, complemented
172C22×Dic5—121no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—61no—
175C5×C22⋊C4—21no—
176C5×C22⋊C4—31no—
177C5×C22⋊C4—61no—
178C5×C22⋊C4—61no—
179C5×C22⋊C4—61no—
180C5×C22⋊C4—61no—
181C5×C22⋊C4C4×D311yescharacteristic, complemented
182C22⋊Dic5—21no—
183C22⋊Dic5—61no—
184C22⋊Dic5—121no—
185#681—21no—
186#681—61no—
187#681—121no—
188C2×#168—121no—
189#534—31no—
190C2×#100—151no—
191C2×#99—151no—
192#352—51no—
193#352—151no—
194AΣL(1,𝔽16)—151no—
195AΣL(1,𝔽16)—151no—
196C22×C3×C5—21no—
197C22×C3×C5—21no—
198C22×C3×C5—41no—
199C22×C3×C5—41no—
200C22×C3×C5C2×C22⋊C411yescharacteristic
201C2×C5×D3—21no—
202C2×C5×D3—21no—
203C2×C5×D3—41no—
204C2×C5×D3—42no—
205C2×C5×D3—41no—
206C2×C5×D3—41no—
207C2×C5×D3—41no—
208C2×C5×D3—41no—
209C2×C5×D3—41no—
210C2×C5×D3—81no—
211C2×C5×D3—81no—
212C2×C5×D3—81no—
213C2×C5×D3—82no—
214C2×C5×D3#9911yescharacteristic
215C2×C5×D3#9911yescharacteristic
216C3×C4×C5—21no—
217C3×C4×C5—41no—
218C3×C4×C5—41no—
219Dic15—81no—
220C3×Dic5—81no—
221C5×Dic3—21no—
222C5×Dic3—41no—
223C23×D3C2×Dic511yescharacteristic
224C23×D3C2×Dic511yescharacteristic, complemented
225C23×D3C22⋊D511yescharacteristic
226C2×C3×D4C22×D511yescharacteristic
227C22×C3×C4C2×Dic511yescharacteristic, complemented
228C2×#67—21no—
229C2×#67C2×Dic511yescharacteristic
230C2×#67C22⋊D511yescharacteristic
231D3×D4—41no—
232D3×D4—41no—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—41no—
237C2×D12—41no—
238C2×D12C22⋊D511yescharacteristic
239C2×C4×D3—21no—
240C2×C4×D3—201no—
241C2×C4×D3C22⋊D511yescharacteristic
242C3×M16—101no—
243C3×C4⋊C4—21no—
244C3×C22⋊C4—21no—
245C3×C22⋊C4—101no—
246C3×C22⋊C4C2×Dic511yescharacteristic, complemented
247#217—101no—
248#217C2×Dic511yescharacteristic, complemented
249(C2×D3)⋊C4—21no—
250(C2×D3)⋊C4—21no—
251(C2×D3)⋊C4—21no—
252(C2×D3)⋊C4—21no—
253(C2×D3)⋊C4—201no—
254Dic3⋊C4—21no—
255#208—101no—
256ΓL(1,𝔽25)—201no—
257D3×C8—201no—
258C23×C5—31no—
259C23×C5—31no—
260C23×C5—31no—
261C23×C5—61no—
262C23×C5—61no—
263C23×C5—61no—
264C23×C5—61no—
265C23×C5—61no—
266C23×C5—121no—
267C23×C5—241no—
268C23×C5—241no—
269C23×C5—241no—
270C23×C5C2×C4×D311yescharacteristic
271C23×C5D3×D411yescharacteristic
272C5×D4—41no—
273C5×D4—121no—
274C5×D4—121no—
275C5×D4—121no—
276C5×D4—122no—
277C5×D4—121no—
278C5×D4—121no—
279C5×D4—241no—
280C5×D4—241no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—31no—
284C2×C4×C5—41no—
285C2×C4×C5—61no—
286C2×C4×C5—61no—
287C2×C4×C5—61no—
288C2×C4×C5—241no—
289C2×C4×C5D3×D411yescharacteristic
290C2×Dic5—41no—
291C2×Dic5—121no—
292C2×Dic5—242no—
293#168—41no—
294#168—121no—
295C22×D4—31no—
296C22×D4—31no—
297C2×M16—301no—
298#123—31no—
299#123—61no—
300#123D3×D511yescharacteristic
301#121—61no—
302#121—61no—
303#120—31no—
304#120—31no—
305#120—61no—
306C2×C22⋊C4—31no—
307C2×C22⋊C4—301no—
308#100—51no—
309#100—151no—
310#100—301no—
311#99—51no—
312#99—151no—
313#99—301no—
314C2×C3×C5—21no—
315C2×C3×C5—41no—
316C2×C3×C5—41no—
317C2×C3×C5C2×#9911yescharacteristic
318C5×D3—21no—
319C5×D3—21no—
320C5×D3—41no—
321C5×D3—41no—
322C5×D3—81no—
323C23×C3C22×Dic511yescharacteristic
324C23×C3C2×C22⋊D511yescharacteristic
325C22×D3—21no—
326C22×D3—21no—
327C22×D3—21no—
328C22×D3—21no—
329C22×D3—21no—
330C22×D3—41no—
331C22×D3—81no—
332C22×D3—81no—
333C22×D3—81no—
334C22×D3C22⋊Dic511yescharacteristic
335C22×D3C22⋊Dic511yescharacteristic
336C22×D3C22⋊Dic511yescharacteristic
337C3×D4—41no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—41no—
341C2×C3×C4—201no—
342C2×C3×C4C2×C22⋊D511yescharacteristic
343#67—41no—
344#67—41no—
345#67—81no—
346C2×Dic3—21no—
347C2×Dic3—201no—
348C2×Dic3C22⋊Dic511yescharacteristic
349D12—41no—
350D12—42no—
351D12—41no—
352D12—41no—
353D12—81no—
354C4×D3—21no—
355C4×D3—21no—
356C4×D3—81no—
357C4×D3—402no—
358C3×C8—201no—
359C3⋊C8—201no—
360C22×C5—21no—
361C22×C5—21no—
362C22×C5—31no—
363C22×C5—31no—
364C22×C5—41no—
365C22×C5—41no—
366C22×C5—61no—
367C22×C5—61no—
368C22×C5—121no—
369C22×C5—121no—
370C22×C5—121no—
371C22×C5—121no—
372C22×C5—121no—
373C22×C5—122no—
374C22×C5—121no—
375C22×C5—241no—
376C22×C5—241no—
377C22×C5—241no—
378C22×C5—242no—
379C22×C5D3×C22⋊C411yescharacteristic
380C4×C5—21no—
381C4×C5—41no—
382C4×C5—41no—
383C4×C5—61no—
384C4×C5—121no—
385Dic5—81no—
386Dic5—241no—
387C24—31no—
388C24—31no—
389C24—31no—
390C2×D4—31no—
391C2×D4—31no—
392C2×D4—31no—
393C2×D4—61no—
394C2×D4—61no—
395C2×D4—61no—
396C2×D4—61no—
397C2×D4—121no—
398C2×D4—121no—
399C2×D4—121no—
400C2×D4—121no—
401C2×D4C2×D3×D511yescharacteristic
402C22×C4—31no—
403C22×C4—61no—
404C22×C4—601no—
405C22×C4D3×Dic511yescharacteristic, complemented
406M16—101no—
407M16—301no—
408M16—601no—
409C2×C8—601no—
410C4⋊C4—21no—
411C4⋊C4—61no—
412C22⋊C4—21no—
413C22⋊C4—31no—
414C22⋊C4—61no—
415C22⋊C4—61no—
416C22⋊C4—61no—
417C22⋊C4—61no—
418C22⋊C4—101no—
419C22⋊C4—301no—
420C22⋊C4—601no—
421C22⋊C4D3×Dic511yescharacteristic, complemented
422C3×C5#212111yescharacteristic, complemented, Hall
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3C2×C22⋊Dic511yescharacteristic
428C2×D3—21no—
429C2×D3—21no—
430C2×D3—41no—
431C2×D3—42no—
432C2×D3—41no—
433C2×D3—41no—
434C2×D3—41no—
435C2×D3—41no—
436C2×D3—41no—
437C2×D3—81no—
438C2×D3—81no—
439C2×D3—81no—
440C2×D3—82no—
441C2×D3#396611yescharacteristic
442C2×D3#396611yescharacteristic
443C3×C4—21no—
444C3×C4—41no—
445C3×C4—41no—
446C3×C4—401no—
447Dic3—21no—
448Dic3—41no—
449Dic3—401no—
450C2×C5—21no—
451C2×C5—41no—
452C2×C5—41no—
453C2×C5—61no—
454C2×C5—61no—
455C2×C5—121no—
456C2×C5—121no—
457C2×C5—241no—
458C2×C5D3×#9911yescharacteristic
459C23—31no—
460C23—31no—
461C23—31no—
462C23—61no—
463C23—61no—
464C23—61no—
465C23—61no—
466C23—61no—
467C23—121no—
468C23—241no—
469C23—241no—
470C23—241no—
471C23C2×D3×Dic511yescharacteristic
472C23D3×C22⋊D511yescharacteristic
473D4—41no—
474D4—121no—
475D4—121no—
476D4—121no—
477D4—122no—
478D4—121no—
479D4—121no—
480D4—241no—
481D4—241no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—31no—
485C2×C4—41no—
486C2×C4—61no—
487C2×C4—61no—
488C2×C4—61no—
489C2×C4—201no—
490C2×C4—241no—
491C2×C4—601no—
492C2×C4—1202no—
493C2×C4D3×C22⋊D511yescharacteristic
494C8—201no—
495C8—601no—
496C2×C3—21no—
497C2×C3—41no—
498C2×C3—41no—
499C2×C3C2×#396611yescharacteristic
500D3—21no—
501D3—21no—
502D3—41no—
503D3—41no—
504D3—81no—
505C5#6914311yescharacteristic, complemented, Sylow
506C22—21no—
507C22—21no—
508C22—31no—
509C22—31no—
510C22—41no—
511C22—41no—
512C22—61no—
513C22—61no—
514C22—121no—
515C22—121no—
516C22—121no—
517C22—121no—
518C22—121no—
519C22—122no—
520C22—121no—
521C22—241no—
522C22—241no—
523C22—241no—
524C22—242no—
525C22D3×C22⋊Dic511yescharacteristic
526C4—21no—
527C4—41no—
528C4—41no—
529C4—61no—
530C4—121no—
531C4—401no—
532C4—1201no—
533C3#1060264011yescharacteristic, complemented, Sylow
534C2—21no—
535C2—41no—
536C2—41no—
537C2—61no—
538C2—61no—
539C2—121no—
540C2—121no—
541C2—241no—
542C2D3×#396611yescharacteristic
subgroupG/H
centerC2D3×#3966
commutatorC23×C3×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC3×C5×#123C22
socleC2×C3×C5C2×#99
prime radicalC5×#5653C2
cosocleC2×C3×C5×D4C23
hypercenter#123D3×D5
hypocenterC3×C5#2121
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
2. D3×#3966C2semidirect
3. D3×#3965C2semidirect
4. #11746360C2semidirect
5. C3×#64759C2semidirect
6. #11745997C2semidirect
7. #11745996C2semidirect
10. C22×C5×D12C4semidirect
13. C5×#929C4semidirect
18. C5×#882C4semidirect
19. C5×D3×C22⋊C4C4semidirect
33. #64759D3semidirect
37. C23×C5×D3C2×C4semidirect
40. C22×C3×C4×C5C2×C4semidirect
57. C3×C5×C22⋊C4C2×C4semidirect
60. C5×#217C2×C4semidirect
136. C22×D12Dic5semidirect
139. #929Dic5semidirect
145. #882Dic5semidirect
147. D3×C22⋊C4Dic5semidirect
171. C22×C4×C5C4×D3semidirect
181. C5×C22⋊C4C4×D3semidirect
224. C23×D3C2×Dic5semidirect
227. C22×C3×C4C2×Dic5semidirect
246. C3×C22⋊C4C2×Dic5semidirect
248. #217C2×Dic5semidirect
405. C22×C4D3×Dic5semidirect
421. C22⋊C4D3×Dic5semidirect
422. C3×C5#2121semidirect
505. C5#69143semidirect
533. C3#10602640semidirect

Maximal subgroups

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

subgroupindex
C5×#56532
D3×#39662
D3×#39652
#117463602
C3×#647592
#117459972
#117459962
#106026403
#691435