Finite Group Databasebeta

← #14479167

Subgroups — #14479167

Order 1920.

3080 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×#41C211yesmaximal, characteristic
2#41×Dic15C211yesmaximal, characteristic, complemented
3C3×#41×Dic5C211yesmaximal, characteristic, complemented
4#11755220C212yesmaximal, complemented
5#11755144C212yesmaximal, complemented
6#11754920C216yesmaximal, complemented
7#11754914C216yesmaximal, complemented
8#11754455C213yesmaximal, complemented
9D3×#4072C213yesmaximal, complemented
10Dic5×#235C213yesmaximal, complemented
11C2×#91371C213yesmaximal, complemented
12#10619161—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C5×D3×#41C4116yescomplemented
15C2×C5×#239C2211yescharacteristic
16C2×C5×D3×Q8C2211yescharacteristic
17C2×C5×#237C2213yes—
18C2×C5×D3×D4C2213yes—
19C2×C5×#235C2213yes—
20C22×C4×C5×D3C2213yes—
21Q8×Dic15C2212yescomplemented
22D4×Dic15C2216yescomplemented
23#91815C2213yescomplemented
24C2×C4×Dic15C2213yescomplemented
25C3×Q8×Dic5C2212yescomplemented
26C3×D4×Dic5C2216yescomplemented
27C3×#4072C2213yescomplemented
28C2×C3×C4×Dic5C2213yescomplemented
29#67⋊Dic5C22112yescomplemented
30D3×C22⋊Dic5C2216yes—
31Dic5×#67C22112yescomplemented
32C2×Dic3⋊Dic5C2216yescomplemented
33C2×(C2×D3)⋊Dic5C2216yes—
34#91529C2216yescomplemented
35#91435C2216yescomplemented
36D3×C4⋊Dic5C2216yescomplemented
37Dic5×D12C2216yescomplemented
38C4×D3×Dic5C2216yescomplemented
39#91371C2211yescharacteristic
40#91371C2216yes—
41#91371C2213yes—
42#91371C2213yescomplemented
43#91371C2216yescomplemented
44#91371C2213yescomplemented
45#91344C2216yescomplemented
46#91338C2216yes—
47Dic5×Dic6C2216yescomplemented
48#85834—51nomaximal, Hall
49C22×C5×#41—31no—
50#66161—32no—
51#66161—36no—
52#41×Dic5—33no—
53#41×Dic5—33no—
54#41×Dic5—31no—
55#41×Dic5D311yescharacteristic, complemented
56#66146—32no—
57#66132—36no—
58C2×#4072—33no—
59C2×#4072—33no—
60C23×C5×D3C2313yes—
61C3×C5×#41C2×C418yescomplemented
62C2×C3×C5×Q8C2311yescharacteristic
63C2×C3×C5×D4C2313yes—
64C22×C3×C4×C5C2313yes—
65C22×Dic15C2316yes—
66C2×C5×#67C2316yes—
67C22×C5×Dic3C2313yes—
68C5×#239C2×C418yescomplemented
69C5×D3×Q8C2×C418yescomplemented
70C5×#237C2×C4124yescomplemented
71C5×D3×D4C2×C4124yescomplemented
72C5×#235C2×C4124yescomplemented
73C2×C5×D12C2313yes—
74C2×C4×C5×D3C2×C4124yescomplemented
75C2×C4×C5×D3C2313yes—
76C2×C4×C5×D3C2313yes—
77C2×C4×C5×D3C2311yescharacteristic
78C2×C4×C5×D3C2313yes—
79C2×C5×Dic6C2313yes—
80C22×C3×Dic5C2316yes—
81C2×D3×Dic5C23112yes—
82#6719C2316yes—
83C4⋊Dic15C2316yes—
84C4×Dic15C2313yes—
85C4×Dic15C2316yes—
86C4×Dic15C2311yescharacteristic
87C3×C22⋊Dic5C2316yes—
88C3×C4⋊Dic5C2316yes—
89C3×C4×Dic5C2316yes—
90C3×C4×Dic5C2313yes—
91C3×C4×Dic5C2311yescharacteristic
92Dic3⋊Dic5C2316yes—
93Dic3⋊Dic5C2312yes—
94Dic3⋊Dic5C2316yes—
95Dic3⋊Dic5C2316yes—
96(C2×D3)⋊Dic5C2316yes—
97(C2×D3)⋊Dic5C2316yes—
98(C2×D3)⋊Dic5C2312yes—
99(C2×D3)⋊Dic5C2316yes—
100Dic3×Dic5C23112yes—
101C2×D3×#41D511yescharacteristic
102C3×C4×#41—51no—
103Dic3×#41—51no—
104#5574—52no—
105#5572—52no—
106#5546—56no—
107#5545—56no—
108#5522—53no—
109D3×#117—53no—
110C4×#235—53no—
111C2×#872—53no—
112C2×C5×#41—316no—
113C2×C5×#41—31no—
114C2×C5×#41—33no—
115C2×C5×#41—33no—
116C2×C5×#41C2×D311yescharacteristic
117C22×C5×Q8—31no—
118C22×C5×D4—33no—
119C23×C4×C5—33no—
120C2×C22⋊Dic5—36no—
121C2×C22⋊Dic5—36no—
122Q8×Dic5—32no—
123Q8×Dic5—36no—
124Q8×Dic5—36no—
125Q8×Dic5C2×D312yescomplemented
126D4×Dic5—36no—
127D4×Dic5—312no—
128D4×Dic5—312no—
129D4×Dic5—36no—
130D4×Dic5—36no—
131D4×Dic5C2×D316yescomplemented
132#4072—33no—
133#4072—36no—
134#4072—36no—
135#4072—33no—
136#4072—31no—
137#4072—36no—
138#4072—33no—
139#4072—33no—
140#4072—36no—
141#4072C2×D313yescomplemented
142C2×C4⋊Dic5—36no—
143C2×C4⋊Dic5—36no—
144C2×C4×Dic5—33no—
145C2×C4×Dic5—36no—
146C2×C4×Dic5C2×D313yescomplemented
147#3428—151noSylow
148C23×C3×C5C2413yes—
149C22×C5×D3—46no—
150C22×C5×D3C22×C4112yes—
151C22×C5×D3C2411yescharacteristic
152C22×C5×D3C2413yes—
153C3×C5×Q8C22×C414yes—
154C3×C5×D4C22×C4112yes—
155C2×C3×C4×C5C22×C4112yes—
156C2×C3×C4×C5C2411yescharacteristic
157C2×C3×C4×C5C2413yes—
158C2×Dic15—46no—
159C2×Dic15C2416yes—
160C2×Dic15C2412yes—
161C5×#67C22×C4124yes—
162C2×C5×Dic3C22×C4112yes—
163C2×C5×Dic3C2413yes—
164C2×C5×Dic3C2411yescharacteristic
165C5×D12C22×C4112yes—
166C4×C5×D3C22×C414yes—
167C4×C5×D3C22×C4112yes—
168C4×C5×D3C22×C4112yes—
169C4×C5×D3C22×C4112yes—
170C5×Dic6C22×C4112yes—
171C2×C3×Dic5—46no—
172C2×C3×Dic5C2416yes—
173C2×C3×Dic5C2412yes—
174D3×Dic5—412no—
175C2×C3×#41C2×D511yescharacteristic
176D3×#41Dic5116yescomplemented
177C2×#239C2×D511yescharacteristic
178C2×D3×Q8C2×D511yescharacteristic
179C2×#237C2×D513yes—
180C2×D3×D4C2×D513yes—
181C2×#235C2×D513yes—
182C22×C4×D3C2×D513yes—
183C3×C4×Q8—52no—
184C3×C4×D4—56no—
185C3×#117—53no—
186C2×C3×C42—53no—
187Q8×Dic3—52no—
188D4×Dic3—56no—
189C4×#67—512no—
190C2×(C2×D3)⋊C4—56no—
191#926—53no—
192C2×Dic3⋊C4—56no—
193C2×C4×Dic3—53no—
194#893—56no—
195#892—56no—
196D3×C4⋊C4—56no—
197#887—56no—
198#67⋊C4—512no—
199D3×C22⋊C4—56no—
200#877—56no—
201C4×D12—56no—
202#872—51no—
203#872—53no—
204#872—53no—
205#872—53no—
206#872—56no—
207#872—56no—
208C42×D3—56no—
209C4×Dic6—56no—
210C24×C5—33no—
211C5×#41—38no—
212C5×#41—324no—
213C5×#41—324no—
214C5×#41C4×D318yescomplemented
215C2×C5×Q8—38no—
216C2×C5×Q8—33no—
217C2×C5×Q8C22×D311yescharacteristic
218C2×C5×D4—36no—
219C2×C5×D4—324no—
220C2×C5×D4—33no—
221C2×C5×D4C22×D313yes—
222C22×C4×C5—33no—
223C22×C4×C5—324no—
224C22×C4×C5—31no—
225C22×C4×C5—33no—
226C22×C4×C5—33no—
227C22×C4×C5—33no—
228C22×C4×C5C22×D313yes—
229C22×Dic5—36no—
230C22×Dic5—312no—
231C22×Dic5C22×D316yes—
232C22⋊Dic5—36no—
233C22⋊Dic5—36no—
234C22⋊Dic5—32no—
235C22⋊Dic5—36no—
236C22⋊Dic5—36no—
237C22⋊Dic5C22×D316yes—
238C4⋊Dic5—36no—
239C4⋊Dic5—36no—
240C4⋊Dic5—32no—
241C4⋊Dic5—36no—
242C4⋊Dic5—36no—
243C4⋊Dic5C22×D316yes—
244C4×Dic5—33no—
245C4×Dic5—31no—
246C4×Dic5—36no—
247C4×Dic5—312no—
248C4×Dic5C22×D313yes—
249C4×Dic5C22×D311yescharacteristic
250C4×Dic5C22×D316yes—
251C22×#41—31no—
252#520—156no—
253#520—152no—
254#519—152no—
255#518—156no—
256C4×#41—51no—
257C4×#41—153no—
258C4×#41—153no—
259C4×#41—151no—
260C2×#117—153no—
261C2×#117—153no—
262C22×C3×C5—26no—
263C22×C3×C5C23×C416yes—
264C22×C3×C5C2511yescharacteristic
265C2×C5×D3—26no—
266C2×C5×D3—22no—
267C2×C5×D3—412no—
268C2×C5×D3C23×C412yes—
269C2×C5×D3C23×C416yes—
270C3×C4×C5C23×C416yes—
271C3×C4×C5C23×C412yes—
272Dic15—26no—
273Dic15—22no—
274C3×Dic5—26no—
275C3×Dic5—22no—
276C5×Dic3C23×C416yes—
277C5×Dic3C23×C412yes—
278C23×D3C22×D513yes—
279C3×#41C2×Dic518yescomplemented
280C2×C3×Q8C22×D511yescharacteristic
281C2×C3×D4C22×D513yes—
282C22×C3×C4—56no—
283C22×C3×C4C22×D513yes—
284C2×#67C22×D516yes—
285C22×Dic3—56no—
286C22×Dic3C22×D513yes—
287#239C2×Dic518yescomplemented
288D3×Q8C2×Dic518yescomplemented
289#237C2×Dic5124yescomplemented
290D3×D4C2×Dic5124yescomplemented
291#235C2×Dic5124yescomplemented
292C2×D12C22×D513yes—
293C2×C4×D3—512no—
294C2×C4×D3C2×Dic5124yescomplemented
295C2×C4×D3C22×D513yes—
296C2×C4×D3C22×D511yescharacteristic
297C2×C4×D3C22×D513yes—
298C2×C4×D3C22×D513yes—
299C2×Dic6C22×D513yes—
300C3×C4⋊C4—56no—
301C3×C22⋊C4—56no—
302C3×C42—56no—
303C3×C42—53no—
304C3×C42—51no—
305#217—56no—
306(C2×D3)⋊C4—52no—
307(C2×D3)⋊C4—56no—
308(C2×D3)⋊C4—56no—
309(C2×D3)⋊C4—56no—
310C4⋊Dic3—56no—
311Dic3⋊C4—56no—
312Dic3⋊C4—52no—
313Dic3⋊C4—56no—
314Dic3⋊C4—56no—
315C4×Dic3—53no—
316C4×Dic3—51no—
317C4×Dic3—56no—
318C4×Dic3—512no—
319C23×C5—31no—
320C23×C5—33no—
321C23×C5—312no—
322C23×C5—126no—
323C23×C5C23×D313yes—
324C5×Q8—312no—
325C5×Q8C2×C4×D314yes—
326C5×D4—324no—
327C5×D4—312no—
328C5×D4C2×C4×D3112yes—
329C2×C4×C5—312no—
330C2×C4×C5—33no—
331C2×C4×C5—31no—
332C2×C4×C5—34no—
333C2×C4×C5—312no—
334C2×C4×C5—312no—
335C2×C4×C5—312no—
336C2×C4×C5C2×C4×D3112yes—
337C2×C4×C5C23×D313yes—
338C2×C4×C5C23×D311yescharacteristic
339C2×Dic5—32no—
340C2×Dic5—36no—
341C2×Dic5—46no—
342C2×Dic5—1212no—
343C2×Dic5—126no—
344C2×Dic5C23×D316yes—
345C2×Dic5C23×D312yes—
346C2×#41—316no—
347C2×#41—31no—
348C2×#41—33no—
349C2×#41—33no—
350C2×#41D3×D511yescharacteristic
351C22×Q8—31no—
352C22×D4—33no—
353C23×C4—33no—
354C4×Q8—52no—
355C4×Q8—156no—
356C4×Q8—156no—
357C4×Q8—152no—
358C4×D4—56no—
359C4×D4—156no—
360C4×D4—1512no—
361C4×D4—156no—
362C4×D4—1512no—
363C4×D4—156no—
364#117—53no—
365#117—151no—
366#117—153no—
367#117—153no—
368#117—153no—
369#117—156no—
370#117—156no—
371#117—156no—
372#117—156no—
373#117—153no—
374C2×C4⋊C4—156no—
375C2×C4⋊C4—156no—
376C2×C22⋊C4—156no—
377C2×C22⋊C4—156no—
378C2×C42—53no—
379C2×C42—156no—
380C2×C42—153no—
381C2×C3×C5—26no—
382C2×C3×C5C24×C411yescharacteristic
383C2×C3×C5#58512yes—
384C5×D3—22no—
385C5×D3—26no—
386C23×C3C23×D513yes—
387C22×D3—46no—
388C22×D3C22×Dic5112yes—
389C22×D3C23×D511yescharacteristic
390C22×D3C23×D513yes—
391C3×Q8C22×Dic514yes—
392C3×D4C22×Dic5112yes—
393C2×C3×C4—56no—
394C2×C3×C4—52no—
395C2×C3×C4—206no—
396C2×C3×C4C22×Dic5112yes—
397C2×C3×C4C23×D513yes—
398C2×C3×C4C23×D511yescharacteristic
399#67C22×Dic5124yes—
400C2×Dic3—52no—
401C2×Dic3—56no—
402C2×Dic3—206no—
403C2×Dic3C22×Dic5112yes—
404C2×Dic3C23×D513yes—
405C2×Dic3C23×D511yescharacteristic
406D12C22×Dic5112yes—
407C4×D3—2012no—
408C4×D3C22×Dic514yes—
409C4×D3C22×Dic5112yes—
410C4×D3C22×Dic5112yes—
411C4×D3C22×Dic5112yes—
412Dic6C22×Dic5112yes—
413C22×C5—26no—
414C22×C5—32no—
415C22×C5—36no—
416C22×C5—66no—
417C22×C5—62no—
418C22×C5—1212no—
419C22×C5C22×C4×D316yes—
420C22×C5C24×D311yescharacteristic
421C4×C5—32no—
422C4×C5—36no—
423C4×C5C22×C4×D312yes—
424C4×C5C22×C4×D316yes—
425Dic5—22no—
426Dic5—26no—
427Dic5—66no—
428Dic5—62no—
429C24—33no—
430#41—38no—
431#41—324no—
432#41—324no—
433#41D3×Dic518yescomplemented
434C2×Q8—38no—
435C2×Q8—33no—
436C2×Q8C2×D3×D511yescharacteristic
437C2×D4—36no—
438C2×D4—324no—
439C2×D4—33no—
440C2×D4C2×D3×D513yes—
441C22×C4—33no—
442C22×C4—324no—
443C22×C4—33no—
444C22×C4—33no—
445C22×C4—33no—
446C22×C4—31no—
447C22×C4—56no—
448C22×C4—1512no—
449C22×C4—156no—
450C22×C4C2×D3×D513yes—
451C4⋊C4—56no—
452C4⋊C4—152no—
453C4⋊C4—156no—
454C4⋊C4—156no—
455C4⋊C4—156no—
456C4⋊C4—156no—
457C22⋊C4—56no—
458C22⋊C4—152no—
459C22⋊C4—156no—
460C22⋊C4—156no—
461C22⋊C4—156no—
462C22⋊C4—156no—
463C42—56no—
464C42—51no—
465C42—53no—
466C42—1512no—
467C42—156no—
468C42—153no—
469C42—151no—
470C3×C5#342811yescharacteristic, complemented, Hall
471C22×C3—26no—
472C22×C3C23×Dic516yes—
473C22×C3C24×D511yescharacteristic
474C2×D3—26no—
475C2×D3—22no—
476C2×D3—412no—
477C2×D3C23×Dic512yes—
478C2×D3C23×Dic516yes—
479C3×C4—106no—
480C3×C4—102no—
481C3×C4C23×Dic516yes—
482C3×C4C23×Dic512yes—
483Dic3—106no—
484Dic3—102no—
485Dic3C23×Dic516yes—
486Dic3C23×Dic512yes—
487C2×C5—26no—
488C2×C5—62no—
489C2×C5—66no—
490C2×C5C23×C4×D311yescharacteristic
491C2×C5#596412yes—
492C23—31no—
493C23—33no—
494C23—312no—
495C23—126no—
496C23C22×D3×D513yes—
497Q8—312no—
498Q8C2×D3×Dic514yes—
499D4—324no—
500D4—312no—
501D4C2×D3×Dic5112yes—
502C2×C4—312no—
503C2×C4—33no—
504C2×C4—31no—
505C2×C4—34no—
506C2×C4—312no—
507C2×C4—312no—
508C2×C4—312no—
509C2×C4—52no—
510C2×C4—56no—
511C2×C4—156no—
512C2×C4—152no—
513C2×C4—206no—
514C2×C4—6012no—
515C2×C4—606no—
516C2×C4C2×D3×Dic5112yes—
517C2×C4C22×D3×D513yes—
518C2×C4C22×D3×D511yescharacteristic
519C2×C3—26no—
520C2×C3#6628312yes—
521C2×C3C24×Dic511yescharacteristic
522D3—22no—
523D3—26no—
524C5#8583411yescharacteristic, complemented, Sylow
525C22—26no—
526C22—32no—
527C22—36no—
528C22—66no—
529C22—62no—
530C22—1212no—
531C22C22×D3×Dic516yes—
532C22C23×D3×D511yescharacteristic
533C4—32no—
534C4—36no—
535C4—102no—
536C4—106no—
537C4—306no—
538C4—302no—
539C4C22×D3×Dic512yes—
540C4C22×D3×Dic516yes—
541C3#1061916111yescharacteristic, complemented, Sylow
542C2—26no—
543C2—62no—
544C2—66no—
545C2#1175705812yes—
546C2C23×D3×Dic511yescharacteristic
subgroupG/H
centerC2×C4C22×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC2×C3×C5×#41C22
socle, cosocleC22×C3×C5C25
prime radicalC2×C5×D3×#41C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3428
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #41×Dic15C2semidirect
3. C3×#41×Dic5C2semidirect
4. #11755220C2semidirect
5. #11755144C2semidirect
6. #11754920C2semidirect
7. #11754914C2semidirect
8. #11754455C2semidirect
9. D3×#4072C2semidirect
10. Dic5×#235C2semidirect
11. C2×#91371C2semidirect
14. C5×D3×#41C4semidirect
21. Q8×Dic15C22semidirect
22. D4×Dic15C22semidirect
23. #91815C22semidirect
24. C2×C4×Dic15C22semidirect
25. C3×Q8×Dic5C22semidirect
26. C3×D4×Dic5C22semidirect
27. C3×#4072C22semidirect
28. C2×C3×C4×Dic5C22semidirect
29. #67⋊Dic5C22semidirect
31. Dic5×#67C22semidirect
32. C2×Dic3⋊Dic5C22semidirect
34. #91529C22semidirect
35. #91435C22semidirect
36. D3×C4⋊Dic5C22semidirect
37. Dic5×D12C22semidirect
38. C4×D3×Dic5C22semidirect
42. #91371C22semidirect
43. #91371C22semidirect
44. #91371C22semidirect
45. #91344C22semidirect
47. Dic5×Dic6C22semidirect
55. #41×Dic5D3semidirect
61. C3×C5×#41C2×C4semidirect
68. C5×#239C2×C4semidirect
69. C5×D3×Q8C2×C4semidirect
70. C5×#237C2×C4semidirect
71. C5×D3×D4C2×C4semidirect
72. C5×#235C2×C4semidirect
74. C2×C4×C5×D3C2×C4semidirect
125. Q8×Dic5C2×D3semidirect
131. D4×Dic5C2×D3semidirect
141. #4072C2×D3semidirect
146. C2×C4×Dic5C2×D3semidirect
176. D3×#41Dic5semidirect
214. C5×#41C4×D3semidirect
279. C3×#41C2×Dic5semidirect
287. #239C2×Dic5semidirect
288. D3×Q8C2×Dic5semidirect
289. #237C2×Dic5semidirect
290. D3×D4C2×Dic5semidirect
291. #235C2×Dic5semidirect
294. C2×C4×D3C2×Dic5semidirect
433. #41D3×Dic5semidirect
470. C3×C5#3428semidirect
524. C5#85834semidirect
541. C3#10619161semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×#412
#41×Dic152
C3×#41×Dic52
#117552202
#117551442
#117549202
#117549142
#117544552
D3×#40722
Dic5×#2352
C2×#913712
#106191613
#858345