Finite Group Databasebeta

← #14479225

Subgroups — #14479225

Order 1920.

3320 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#1009C211yesmaximal, characteristic
2#41×Dic15C211yesmaximal, characteristic, complemented
3C3×#66161C211yesmaximal, characteristic, complemented
4#11755220C212yesmaximal, complemented
5Dic5×#239C212yesmaximal, complemented
6#11754914C216yesmaximal, complemented
7D3×D4×Dic5C216yesmaximal, complemented
8#11754503C213yesmaximal, complemented
9#11754492C213yesmaximal, complemented
10#11754455C213yesmaximal, complemented
11C2×#91435C213yesmaximal, complemented
12Dic5×H(5,𝔽2)—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C5×#1009C4116yescomplemented
15C2×C5×#239C2212yes—
16C2×C5×D3×D4C2216yes—
17C2×C5×#235C2213yes—
18C22×C5×D12C2213yes—
19C22×D3×Dic5C2216yescomplemented
20Q8×Dic15C2211yescharacteristic, complemented
21Q8×Dic15C2211yescharacteristic, complemented
22D4×Dic15C2213yescomplemented
23D4×Dic15C2213yescomplemented
24#91815C2213yescomplemented
25C2×C4×Dic15C2213yescomplemented
26C3×Q8×Dic5C2212yescomplemented
27C3×D4×Dic5C2216yescomplemented
28C3×#4072C2213yescomplemented
29C2×C3×C4⋊Dic5C2213yescomplemented
30#67⋊Dic5C2216yescomplemented
31#67⋊Dic5C2216yescomplemented
32D3×C22⋊Dic5C22112yescomplemented
33Dic5×#67C22112yescomplemented
34C2×(C2×D3)⋊Dic5C2216yescomplemented
35#91435C2213yescomplemented
36#91435C2216yescomplemented
37#91435C2216yescomplemented
38#91435C2213yescomplemented
39#91435C2216yescomplemented
40D3×C4⋊Dic5C2216yescomplemented
41Dic5×D12C2216yescomplemented
42Dic5×D12C2216yescomplemented
43C4×D3×Dic5C2216yescomplemented
44#91371C2216yescomplemented
45#91344C2211yescharacteristic, complemented
46#91344C2213yescomplemented
47#91338C2216yescomplemented
48#85886—51nomaximal, Hall
49C2×C5×H(5,𝔽2)—31no—
50#66161—32no—
51#66161—33no—
52#66161D311yescharacteristic, complemented
53#41×Dic5—32no—
54#41×Dic5—33no—
55#41×Dic5—31no—
56#66132—36no—
57#66132—33no—
58C2×D4×Dic5—36no—
59C2×D4×Dic5—33no—
60C23×C5×D3C2316yes—
61C3×C5×#41C2×C418yescomplemented
62C2×C3×C5×Q8C2311yescharacteristic
63C2×C3×C5×D4C2313yes—
64C22×C3×C4×C5C2313yes—
65C22×Dic15C2313yes—
66C22×Dic15C2313yes—
67C2×C5×#67C2316yes—
68C5×#239C2×C4116yescomplemented
69C5×D3×D4C2×C4148yescomplemented
70C5×#235C2×C4124yescomplemented
71C2×C5×D12C2×C4124yescomplemented
72C2×C5×D12C2316yes—
73C2×C5×D12C2313yes—
74C2×C4×C5×D3C2316yes—
75C2×C5×Dic6C2311yescharacteristic
76C22×C3×Dic5C2316yes—
77C2×D3×Dic5—412no—
78C2×D3×Dic5C2316yes—
79C2×D3×Dic5C2316yes—
80C2×D3×Dic5C23112yes—
81#6719C2316yes—
82C4⋊Dic15C2313yes—
83C4⋊Dic15C2313yes—
84C4×Dic15C2313yes—
85C4×Dic15C2311yescharacteristic
86C4×Dic15C2313yes—
87C4×Dic15C2313yes—
88C3×C22⋊Dic5C2316yes—
89C3×C4⋊Dic5C2316yes—
90C3×C4⋊Dic5C2313yes—
91C3×C4⋊Dic5C2311yescharacteristic
92C3×C4×Dic5C2316yes—
93Dic3⋊Dic5C2316yes—
94Dic3⋊Dic5C2312yes—
95(C2×D3)⋊Dic5C2316yes—
96(C2×D3)⋊Dic5C23112yes—
97(C2×D3)⋊Dic5C2316yes—
98Dic3×Dic5C2312yes—
99Dic3×Dic5C2316yes—
100C2×#1009D511yescharacteristic
101C3×#520—51no—
102Dic3×#41—51no—
103#5574—52no—
104C4×#239—52no—
105#5545—56no—
106C4×D3×D4—56no—
107#5522—53no—
108#5521—53no—
109#5504—53no—
110C2×#893—53no—
111C5×H(5,𝔽2)—316no—
112C2×C5×#41—32no—
113C2×C5×#41—33no—
114C2×C5×#41C2×D311yescharacteristic
115C22×C5×D4—36no—
116C22×C5×D4—33no—
117C23×Dic5—36no—
118C2×C22⋊Dic5—36no—
119C2×C22⋊Dic5—312no—
120Q8×Dic5—31no—
121Q8×Dic5—31no—
122Q8×Dic5—31no—
123Q8×Dic5—33no—
124Q8×Dic5C2×D312yescomplemented
125D4×Dic5—33no—
126D4×Dic5—33no—
127D4×Dic5—312no—
128D4×Dic5—36no—
129D4×Dic5—36no—
130D4×Dic5—36no—
131D4×Dic5—33no—
132D4×Dic5—36no—
133D4×Dic5—36no—
134D4×Dic5—33no—
135D4×Dic5—36no—
136D4×Dic5—36no—
137D4×Dic5C2×D316yescomplemented
138#4072—33no—
139#4072—36no—
140#4072—36no—
141#4072C2×D313yescomplemented
142C2×C4⋊Dic5—36no—
143C2×C4⋊Dic5C2×D313yescomplemented
144C2×C4×Dic5—33no—
145C2×C4×Dic5—36no—
146C4×H(5,𝔽2)—151noSylow
147C23×C3×C5C2413yes—
148C22×C5×D3—46no—
149C22×C5×D3—46no—
150C22×C5×D3C22×C4124yescomplemented
151C22×C5×D3C2416yes—
152C3×C5×Q8C22×C414yescomplemented
153C3×C5×D4C22×C4112yescomplemented
154C2×C3×C4×C5C22×C4112yescomplemented
155C2×C3×C4×C5C2413yes—
156C2×C3×C4×C5C2411yescharacteristic
157C2×Dic15—26no—
158C2×Dic15—43no—
159C2×Dic15C2413yes—
160C2×Dic15C2411yescharacteristic
161C2×Dic15C2413yes—
162C2×Dic15C2411yescharacteristic
163C5×#67C22×C4124yescomplemented
164C2×C5×Dic3C2412yes—
165C5×D12C22×C4112yescomplemented
166C5×D12C22×C4124yescomplemented
167C4×C5×D3C22×C4124yescomplemented
168C5×Dic6C22×C414yescomplemented
169C2×C3×Dic5—46no—
170C2×C3×Dic5C2412yes—
171C2×C3×Dic5C2416yes—
172D3×Dic5—212no—
173D3×Dic5—412no—
174D3×Dic5—46no—
175C2×C3×#41C2×D511yescharacteristic
176#1009Dic5116yescomplemented
177C2×#239C2×D512yes—
178C2×D3×D4C2×D516yes—
179C2×#235C2×D513yes—
180C22×D12C2×D513yes—
181C22×C4×D3—56no—
182C3×C4×Q8—52no—
183C3×C4×D4—56no—
184C3×#117—53no—
185C2×C3×C4⋊C4—53no—
186Q8×Dic3—51no—
187Q8×Dic3—51no—
188D4×Dic3—53no—
189D4×Dic3—53no—
190C4×#67—512no—
191C2×(C2×D3)⋊C4—56no—
192#926—53no—
193C2×C4×Dic3—53no—
194#893—53no—
195#893—56no—
196#893—56no—
197#893—56no—
198#893—53no—
199#892—56no—
200D3×C4⋊C4—56no—
201#887—53no—
202#887—51no—
203#67⋊C4—56no—
204#67⋊C4—56no—
205D3×C22⋊C4—512no—
206C4×D12—56no—
207C4×D12—56no—
208#872—56no—
209C42×D3—56no—
210C24×C5—36no—
211C5×#41—316no—
212C5×#41—324no—
213C5×#41C4×D318yescomplemented
214C2×C5×Q8—31no—
215C2×C5×Q8C22×D311yescharacteristic
216C2×C5×D4—36no—
217C2×C5×D4—348no—
218C2×C5×D4—324no—
219C2×C5×D4—33no—
220C2×C5×D4—36no—
221C2×C5×D4C22×D313yes—
222C22×C4×C5—36no—
223C22×C4×C5C22×D313yes—
224C22×Dic5—33no—
225C22×Dic5—33no—
226C22×Dic5—36no—
227C22×Dic5—36no—
228C22×Dic5—312no—
229C22×Dic5—1212no—
230C22×Dic5C22×D316yes—
231C22⋊Dic5—36no—
232C22⋊Dic5—36no—
233C22⋊Dic5—312no—
234C22⋊Dic5—36no—
235C22⋊Dic5C22×D316yes—
236C4⋊Dic5—33no—
237C4⋊Dic5—33no—
238C4⋊Dic5—36no—
239C4⋊Dic5—32no—
240C4⋊Dic5C22×D316yes—
241C4⋊Dic5C22×D313yes—
242C4⋊Dic5C22×D311yescharacteristic
243C4×Dic5—31no—
244C4×Dic5—33no—
245C4×Dic5—33no—
246C4×Dic5—33no—
247C4×Dic5—32no—
248C4×Dic5—36no—
249C4×Dic5C22×D316yes—
250C2×H(5,𝔽2)—31no—
251#520—51no—
252#520—153no—
253#520—152no—
254#518—153no—
255#518—156no—
256C4×#41—153no—
257C4×#41—152no—
258C4×#41—151no—
259C2×C4×D4—153no—
260C2×C4×D4—156no—
261C22×C3×C5—23no—
262C22×C3×C5—23no—
263C22×C3×C5C23×C416yes—
264C22×C3×C5C2511yescharacteristic
265C2×C5×D3—26no—
266C2×C5×D3—26no—
267C2×C5×D3—424no—
268C2×C5×D3C23×C4112yes—
269C3×C4×C5C23×C412yes—
270C3×C4×C5C23×C416yes—
271Dic15—23no—
272Dic15—23no—
273Dic15—21no—
274Dic15H(5,𝔽2)12yescomplemented
275C3×Dic5—26no—
276C3×Dic5—22no—
277C5×Dic3C23×C414yes—
278C23×D3C22×D516yes—
279C3×#41C2×Dic518yescomplemented
280C2×C3×Q8C22×D511yescharacteristic
281C2×C3×D4C22×D513yes—
282C22×C3×C4—56no—
283C22×C3×C4C22×D513yes—
284C2×#67C22×D516yes—
285C22×Dic3—53no—
286C22×Dic3—53no—
287#239C2×Dic5116yescomplemented
288D3×D4C2×Dic5148yescomplemented
289#235C2×Dic5124yescomplemented
290C2×D12C2×Dic5124yescomplemented
291C2×D12C22×D516yes—
292C2×D12C22×D513yes—
293C2×C4×D3—56no—
294C2×C4×D3—56no—
295C2×C4×D3—512no—
296C2×C4×D3—2012no—
297C2×C4×D3C22×D516yes—
298C2×Dic6C22×D511yescharacteristic
299C3×C4⋊C4—53no—
300C3×C4⋊C4—51no—
301C3×C4⋊C4—56no—
302C3×C22⋊C4—56no—
303C3×C42—56no—
304#217—56no—
305(C2×D3)⋊C4—56no—
306(C2×D3)⋊C4—56no—
307(C2×D3)⋊C4—512no—
308C4⋊Dic3—53no—
309C4⋊Dic3—53no—
310Dic3⋊C4—52no—
311Dic3⋊C4—56no—
312C4×Dic3—53no—
313C4×Dic3—53no—
314C4×Dic3—51no—
315C4×Dic3—53no—
316C4×Dic3—52no—
317C4×Dic3—56no—
318C23×C5—36no—
319C23×C5—324no—
320C23×C5—126no—
321C23×C5—126no—
322C23×C5C23×D313yes—
323C5×Q8—34no—
324C5×Q8C2×C4×D314yescomplemented
325C5×D4—324no—
326C5×D4—324no—
327C5×D4—312no—
328C5×D4C2×C4×D3112yescomplemented
329C2×C4×C5—32no—
330C2×C4×C5—324no—
331C2×C4×C5C2×C4×D3112yescomplemented
332C2×C4×C5C23×D311yescharacteristic
333C2×C4×C5C23×D313yes—
334C2×Dic5—31no—
335C2×Dic5—31no—
336C2×Dic5—33no—
337C2×Dic5—33no—
338C2×Dic5—46no—
339C2×Dic5—612no—
340C2×Dic5—66no—
341C2×Dic5—126no—
342C2×Dic5—1212no—
343C2×Dic5—123no—
344C2×Dic5C23×D312yes—
345C2×Dic5C23×D316yes—
346H(5,𝔽2)—316no—
347C2×#41—32no—
348C2×#41—33no—
349C2×#41D3×D511yescharacteristic
350C22×D4—36no—
351C22×D4—33no—
352C23×C4—156no—
353C4×Q8—52no—
354C4×Q8—151no—
355C4×Q8—153no—
356C4×Q8—151no—
357C4×Q8—151no—
358C4×D4—56no—
359C4×D4—156no—
360C4×D4—156no—
361C4×D4—156no—
362C4×D4—156no—
363C4×D4—153no—
364C4×D4—156no—
365C4×D4—156no—
366C4×D4—156no—
367C4×D4—153no—
368C4×D4—1512no—
369C4×D4—153no—
370C4×D4—153no—
371#117—53no—
372#117—156no—
373#117—156no—
374#117—153no—
375C2×C4⋊C4—53no—
376C2×C4⋊C4—156no—
377C2×C22⋊C4—1512no—
378C2×C22⋊C4—156no—
379C2×C42—156no—
380C2×C42—153no—
381C2×C3×C5—26no—
382C2×C3×C5C24×C411yescharacteristic
383C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
384C2×C3×C5#58511yescharacteristic
385C5×D3—212no—
386C23×C3C23×D513yes—
387C22×D3—46no—
388C22×D3—46no—
389C22×D3C22×Dic5124yescomplemented
390C22×D3C23×D516yes—
391C3×Q8C22×Dic514yescomplemented
392C3×D4C22×Dic5112yescomplemented
393C2×C3×C4—52no—
394C2×C3×C4—56no—
395C2×C3×C4—206no—
396C2×C3×C4C22×Dic5112yescomplemented
397C2×C3×C4C23×D511yescharacteristic
398C2×C3×C4C23×D513yes—
399#67C22×Dic5124yescomplemented
400C2×Dic3—51no—
401C2×Dic3—51no—
402C2×Dic3—53no—
403C2×Dic3—53no—
404C2×Dic3—106no—
405C2×Dic3—203no—
406C2×Dic3C23×D512yes—
407D12C22×Dic5112yescomplemented
408D12C22×Dic5124yescomplemented
409C4×D3—1012no—
410C4×D3—206no—
411C4×D3—2012no—
412C4×D3C22×Dic5124yescomplemented
413Dic6C22×Dic514yescomplemented
414C22×C5—23no—
415C22×C5—23no—
416C22×C5—312no—
417C22×C5—66no—
418C22×C5—66no—
419C22×C5—1224no—
420C22×C5C22×C4×D316yes—
421C22×C5C24×D311yescharacteristic
422C4×C5—34no—
423C4×C5C22×C4×D316yes—
424C4×C5C22×C4×D312yes—
425Dic5—26no—
426Dic5—22no—
427Dic5—32no—
428Dic5—63no—
429Dic5—63no—
430Dic5—61no—
431C24—36no—
432#41—316no—
433#41—324no—
434#41D3×Dic518yescomplemented
435C2×Q8—31no—
436C2×Q8C2×D3×D511yescharacteristic
437C2×D4—36no—
438C2×D4—348no—
439C2×D4—324no—
440C2×D4—36no—
441C2×D4—33no—
442C2×D4C2×D3×D513yes—
443C22×C4—36no—
444C22×C4—56no—
445C22×C4—156no—
446C22×C4—156no—
447C22×C4—1512no—
448C22×C4—153no—
449C22×C4—153no—
450C22×C4—6012no—
451C22×C4C2×D3×D513yes—
452C4⋊C4—53no—
453C4⋊C4—56no—
454C4⋊C4—51no—
455C4⋊C4—156no—
456C4⋊C4—152no—
457C4⋊C4—153no—
458C4⋊C4—153no—
459C22⋊C4—56no—
460C22⋊C4—156no—
461C22⋊C4—1512no—
462C22⋊C4—156no—
463C22⋊C4—156no—
464C42—56no—
465C42—152no—
466C42—156no—
467C42—153no—
468C42—151no—
469C42—153no—
470C42—153no—
471C3×C5C4×H(5,𝔽2)11yescharacteristic, complemented, Hall
472C22×C3—23no—
473C22×C3—23no—
474C22×C3C23×Dic516yes—
475C22×C3C24×D511yescharacteristic
476C2×D3—26no—
477C2×D3—26no—
478C2×D3—424no—
479C2×D3C23×Dic5112yes—
480C3×C4—106no—
481C3×C4—102no—
482C3×C4C23×Dic512yes—
483C3×C4C23×Dic516yes—
484Dic3—52no—
485Dic3—103no—
486Dic3—103no—
487Dic3—101no—
488Dic3C23×Dic514yes—
489C2×C5—26no—
490C2×C5—612no—
491C2×C5C23×C4×D311yescharacteristic
492C2×C5D3×H(5,𝔽2)11yescharacteristic
493C2×C5#596811yescharacteristic
494C23—36no—
495C23—324no—
496C23—126no—
497C23—126no—
498C23C22×D3×D513yes—
499Q8—34no—
500Q8C2×D3×Dic514yescomplemented
501D4—324no—
502D4—324no—
503D4—312no—
504D4C2×D3×Dic5112yescomplemented
505C2×C4—32no—
506C2×C4—324no—
507C2×C4—52no—
508C2×C4—56no—
509C2×C4—151no—
510C2×C4—153no—
511C2×C4—151no—
512C2×C4—153no—
513C2×C4—206no—
514C2×C4—3012no—
515C2×C4—306no—
516C2×C4—6012no—
517C2×C4—606no—
518C2×C4—603no—
519C2×C4C2×D3×Dic5112yescomplemented
520C2×C4C22×D3×D513yes—
521C2×C4C22×D3×D511yescharacteristic
522C2×C3—26no—
523C2×C3D5×H(5,𝔽2)11yescharacteristic
524C2×C3#6628511yescharacteristic
525C2×C3C24×Dic511yescharacteristic
526D3—212no—
527C5#8588611yescharacteristic, complemented, Sylow
528C22—23no—
529C22—23no—
530C22—312no—
531C22—66no—
532C22—66no—
533C22—1224no—
534C22C22×D3×Dic516yes—
535C22C23×D3×D511yescharacteristic
536C4—34no—
537C4—102no—
538C4—106no—
539C4—152no—
540C4—303no—
541C4—301no—
542C4—303no—
543C4C22×D3×Dic516yes—
544C4C22×D3×Dic512yes—
545C3Dic5×H(5,𝔽2)11yescharacteristic, complemented, Sylow
546C2—26no—
547C2—612no—
548C2#1175705411yescharacteristic
549C2#1175706411yescharacteristic
550C2C23×D3×Dic511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutatorC2×C3×C5C24×C4
FittingC2×C3×C5×#41C22
socle, cosocleC22×C3×C5C25
prime radicalC2×C5×#1009C2
hypercenterC2×#41D3×D5
hypocenterC3×C5C4×H(5,𝔽2)
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #41×Dic15C2semidirect
3. C3×#66161C2semidirect
4. #11755220C2semidirect
5. Dic5×#239C2semidirect
6. #11754914C2semidirect
7. D3×D4×Dic5C2semidirect
8. #11754503C2semidirect
9. #11754492C2semidirect
10. #11754455C2semidirect
11. C2×#91435C2semidirect
14. C5×#1009C4semidirect
19. C22×D3×Dic5C22semidirect
20. Q8×Dic15C22semidirect
21. Q8×Dic15C22semidirect
22. D4×Dic15C22semidirect
23. D4×Dic15C22semidirect
24. #91815C22semidirect
25. C2×C4×Dic15C22semidirect
26. C3×Q8×Dic5C22semidirect
27. C3×D4×Dic5C22semidirect
28. C3×#4072C22semidirect
29. C2×C3×C4⋊Dic5C22semidirect
30. #67⋊Dic5C22semidirect
31. #67⋊Dic5C22semidirect
32. D3×C22⋊Dic5C22semidirect
33. Dic5×#67C22semidirect
34. C2×(C2×D3)⋊Dic5C22semidirect
35. #91435C22semidirect
36. #91435C22semidirect
37. #91435C22semidirect
38. #91435C22semidirect
39. #91435C22semidirect
40. D3×C4⋊Dic5C22semidirect
41. Dic5×D12C22semidirect
42. Dic5×D12C22semidirect
43. C4×D3×Dic5C22semidirect
44. #91371C22semidirect
45. #91344C22semidirect
46. #91344C22semidirect
47. #91338C22semidirect
52. #66161D3semidirect
61. C3×C5×#41C2×C4semidirect
68. C5×#239C2×C4semidirect
69. C5×D3×D4C2×C4semidirect
70. C5×#235C2×C4semidirect
71. C2×C5×D12C2×C4semidirect
124. Q8×Dic5C2×D3semidirect
137. D4×Dic5C2×D3semidirect
141. #4072C2×D3semidirect
143. C2×C4⋊Dic5C2×D3semidirect
150. C22×C5×D3C22×C4semidirect
152. C3×C5×Q8C22×C4semidirect
153. C3×C5×D4C22×C4semidirect
154. C2×C3×C4×C5C22×C4semidirect
163. C5×#67C22×C4semidirect
165. C5×D12C22×C4semidirect
166. C5×D12C22×C4semidirect
167. C4×C5×D3C22×C4semidirect
168. C5×Dic6C22×C4semidirect
176. #1009Dic5semidirect
213. C5×#41C4×D3semidirect
274. Dic15H(5,𝔽2)semidirect
279. C3×#41C2×Dic5semidirect
287. #239C2×Dic5semidirect
288. D3×D4C2×Dic5semidirect
289. #235C2×Dic5semidirect
290. C2×D12C2×Dic5semidirect
324. C5×Q8C2×C4×D3semidirect
328. C5×D4C2×C4×D3semidirect
331. C2×C4×C5C2×C4×D3semidirect
389. C22×D3C22×Dic5semidirect
391. C3×Q8C22×Dic5semidirect
392. C3×D4C22×Dic5semidirect
396. C2×C3×C4C22×Dic5semidirect
399. #67C22×Dic5semidirect
407. D12C22×Dic5semidirect
408. D12C22×Dic5semidirect
412. C4×D3C22×Dic5semidirect
413. Dic6C22×Dic5semidirect
434. #41D3×Dic5semidirect
471. C3×C5C4×H(5,𝔽2)semidirect
500. Q8C2×D3×Dic5semidirect
504. D4C2×D3×Dic5semidirect
519. C2×C4C2×D3×Dic5semidirect
527. C5#85886semidirect
545. C3Dic5×H(5,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10092
#41×Dic152
C3×#661612
#117552202
Dic5×#2392
#117549142
D3×D4×Dic52
#117545032
#117544922
#117544552
C2×#914352
Dic5×H(5,𝔽2)3
#858865