Finite Group Databasebeta

← #14479165

Subgroups — #14479165

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×C3×D5×#41C211yesmaximal, characteristic
2#41×Dic15C211yesmaximal, characteristic, complemented
3C5×Dic3×#41C211yesmaximal, characteristic, complemented
4#11755217C212yesmaximal, complemented
5#11755140C212yesmaximal, complemented
6#11754923C216yesmaximal, complemented
7#11754910C216yesmaximal, complemented
8#11754444C213yesmaximal, complemented
9Dic3×#709C213yesmaximal, complemented
10D5×#926C213yesmaximal, complemented
11C2×#91357C213yesmaximal, complemented
12#10617735—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C3×D5×#41C4116yescomplemented
15C2×C3×#713C2211yescharacteristic
16C2×C3×Q8×D5C2211yescharacteristic
17C2×C3×#711C2213yes—
18C2×C3×D4×D5C2213yes—
19C2×C3×#709C2213yes—
20C22×C3×C4×D5C2213yes—
21Q8×Dic15C2212yescomplemented
22D4×Dic15C2216yescomplemented
23#91815C2213yescomplemented
24C2×C4×Dic15C2213yescomplemented
25C5×Q8×Dic3C2212yescomplemented
26C5×D4×Dic3C2216yescomplemented
27C5×#926C2213yescomplemented
28C2×C4×C5×Dic3C2213yescomplemented
29#91559C22112yescomplemented
30Dic3×C22⋊D5C22112yescomplemented
31D5×#217C2216yes—
32C2×#6668C2216yescomplemented
33C2×#6665C2216yes—
34#91528C2216yescomplemented
35#91434C2216yescomplemented
36Dic3×D20C2216yescomplemented
37D5×C4⋊Dic3C2216yescomplemented
38C4×D5×Dic3C2216yescomplemented
39#91358C2216yes—
40#91357C2216yes—
41#91357C2213yes—
42#91357C2211yescharacteristic
43#91357C2216yescomplemented
44#91357C2213yescomplemented
45#91357C2213yescomplemented
46#91331C2216yescomplemented
47Dic3×Dic10C2216yescomplemented
48#87260—51nomaximal, Hall
49C2×D5×#41D311yescharacteristic
50C4×C5×#41—31no—
51#41×Dic5—31no—
52#65908—32no—
53#65906—32no—
54#65880—36no—
55#65879—36no—
56#65856—33no—
57D5×#117—33no—
58C4×#709—33no—
59C2×#4018—33no—
60C23×C3×D5C2313yes—
61C3×C5×#41C2×C418yescomplemented
62C2×C3×C5×Q8C2311yescharacteristic
63C2×C3×C5×D4C2313yes—
64C22×C3×C4×C5C2313yes—
65C22×Dic15C2316yes—
66C22×C5×Dic3C2316yes—
67C2×C3×C22⋊D5C2316yes—
68C22×C3×Dic5C2313yes—
69C3×#713C2×C418yescomplemented
70C3×Q8×D5C2×C418yescomplemented
71C3×#711C2×C4124yescomplemented
72C3×D4×D5C2×C4124yescomplemented
73C3×#709C2×C4124yescomplemented
74C2×C3×D20C2313yes—
75C2×C3×C4×D5C2×C4124yescomplemented
76C2×C3×C4×D5C2313yes—
77C2×C3×C4×D5C2311yescharacteristic
78C2×C3×C4×D5C2313yes—
79C2×C3×C4×D5C2313yes—
80C2×C3×Dic10C2313yes—
81C2×D5×Dic3C23112yes—
82#6719C2316yes—
83C4⋊Dic15C2316yes—
84C4×Dic15C2316yes—
85C4×Dic15C2311yescharacteristic
86C4×Dic15C2313yes—
87C5×#217C2316yes—
88C5×C4⋊Dic3C2316yes—
89C4×C5×Dic3C2316yes—
90C4×C5×Dic3C2311yescharacteristic
91C4×C5×Dic3C2313yes—
92#6668C2316yes—
93#6668C2312yes—
94#6668C2316yes—
95#6668C2316yes—
96#6665C2316yes—
97#6665C2316yes—
98#6665C2312yes—
99#6665C2316yes—
100Dic3×Dic5C23112yes—
101C22×C3×#41—51no—
102#5827—52no—
103#5827—56no—
104Dic3×#41—51no—
105Dic3×#41—53no—
106Dic3×#41—53no—
107Dic3×#41D511yescharacteristic, complemented
108#5812—52no—
109#5798—56no—
110C2×#926—53no—
111C2×#926—53no—
112C2×C5×#41C2×D311yescharacteristic
113D5×#41Dic3116yescomplemented
114C2×#713C2×D311yescharacteristic
115C2×Q8×D5C2×D311yescharacteristic
116C2×#711C2×D313yes—
117C2×D4×D5C2×D313yes—
118C2×#709C2×D313yes—
119C22×C4×D5C2×D313yes—
120C4×C5×Q8—32no—
121C4×C5×D4—36no—
122C5×#117—33no—
123C2×C42×C5—33no—
124Q8×Dic5—32no—
125D4×Dic5—36no—
126C4×C22⋊D5—312no—
127C2×#685—36no—
128#4072—33no—
129C2×#683—36no—
130C2×C4×Dic5—33no—
131#4039—36no—
132#4038—36no—
133D5×C4⋊C4—36no—
134#4033—36no—
135#4027—312no—
136D5×C22⋊C4—36no—
137#4023—36no—
138C4×D20—36no—
139#4018—31no—
140#4018—33no—
141#4018—33no—
142#4018—33no—
143#4018—36no—
144#4018—36no—
145C42×D5—36no—
146C4×Dic10—36no—
147#3428—151noSylow
148C23×C3×C5C2413yes—
149C22×C3×D5—46no—
150C22×C3×D5C22×C4112yes—
151C22×C3×D5C2411yescharacteristic
152C22×C3×D5C2413yes—
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—
161C2×C5×Dic3—46no—
162C2×C5×Dic3C2416yes—
163C2×C5×Dic3C2412yes—
164C3×C22⋊D5C22×C4124yes—
165C2×C3×Dic5C22×C4112yes—
166C2×C3×Dic5C2413yes—
167C2×C3×Dic5C2411yescharacteristic
168C3×D20C22×C4112yes—
169C3×C4×D5C22×C414yes—
170C3×C4×D5C22×C4112yes—
171C3×C4×D5C22×C4112yes—
172C3×C4×D5C22×C4112yes—
173C3×Dic10C22×C4112yes—
174D5×Dic3—412no—
175C2×C3×#41—516no—
176C2×C3×#41—51no—
177C2×C3×#41—53no—
178C2×C3×#41—53no—
179C2×C3×#41C2×D511yescharacteristic
180C22×C3×Q8—51no—
181C22×C3×D4—53no—
182C23×C3×C4—53no—
183C2×#217—56no—
184C2×#217—56no—
185Q8×Dic3—52no—
186Q8×Dic3—56no—
187Q8×Dic3—56no—
188Q8×Dic3C2×D512yescomplemented
189D4×Dic3—56no—
190D4×Dic3—512no—
191D4×Dic3—512no—
192D4×Dic3—56no—
193D4×Dic3—56no—
194D4×Dic3C2×D516yescomplemented
195#926—53no—
196#926—56no—
197#926—56no—
198#926—53no—
199#926—51no—
200#926—56no—
201#926—53no—
202#926—53no—
203#926—56no—
204#926C2×D513yescomplemented
205C2×C4⋊Dic3—56no—
206C2×C4⋊Dic3—56no—
207C2×C4×Dic3—53no—
208C2×C4×Dic3—56no—
209C2×C4×Dic3C2×D513yescomplemented
210C23×D5C22×D313yes—
211C5×#41C2×Dic318yescomplemented
212C2×C5×Q8C22×D311yescharacteristic
213C2×C5×D4C22×D313yes—
214C22×C4×C5—36no—
215C22×C4×C5C22×D313yes—
216C2×C22⋊D5C22×D316yes—
217C22×Dic5—36no—
218C22×Dic5C22×D313yes—
219#713C2×Dic318yescomplemented
220Q8×D5C2×Dic318yescomplemented
221#711C2×Dic3124yescomplemented
222D4×D5C2×Dic3124yescomplemented
223#709C2×Dic3124yescomplemented
224C2×D20C22×D313yes—
225C2×C4×D5—312no—
226C2×C4×D5C2×Dic3124yescomplemented
227C2×C4×D5C22×D311yescharacteristic
228C2×C4×D5C22×D313yes—
229C2×C4×D5C22×D313yes—
230C2×C4×D5C22×D313yes—
231C2×Dic10C22×D313yes—
232C5×C4⋊C4—36no—
233C5×C22⋊C4—36no—
234C42×C5—31no—
235C42×C5—33no—
236C42×C5—36no—
237C22⋊Dic5—36no—
238#685—32no—
239#685—36no—
240#685—36no—
241#685—36no—
242C4⋊Dic5—36no—
243#683—36no—
244#683—32no—
245#683—36no—
246#683—36no—
247C4×Dic5—33no—
248C4×Dic5—31no—
249C4×Dic5—36no—
250C4×Dic5—312no—
251C22×#41—51no—
252#520—156no—
253#520—152no—
254#519—152no—
255#518—156no—
256C4×#41—31no—
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×C3×D5—26no—
266C2×C3×D5—22no—
267C2×C3×D5—412no—
268C2×C3×D5C23×C412yes—
269C2×C3×D5C23×C416yes—
270C3×C4×C5C23×C416yes—
271C3×C4×C5C23×C412yes—
272Dic15—26no—
273Dic15—22no—
274C3×Dic5C23×C416yes—
275C3×Dic5C23×C412yes—
276C5×Dic3—26no—
277C5×Dic3—22no—
278C24×C3—53no—
279C3×#41—58no—
280C3×#41—524no—
281C3×#41—524no—
282C3×#41C4×D518yescomplemented
283C2×C3×Q8—58no—
284C2×C3×Q8—53no—
285C2×C3×Q8C22×D511yescharacteristic
286C2×C3×D4—56no—
287C2×C3×D4—524no—
288C2×C3×D4—53no—
289C2×C3×D4C22×D513yes—
290C22×C3×C4—53no—
291C22×C3×C4—524no—
292C22×C3×C4—53no—
293C22×C3×C4—53no—
294C22×C3×C4—51no—
295C22×C3×C4—53no—
296C22×C3×C4C22×D513yes—
297C22×Dic3—56no—
298C22×Dic3—512no—
299C22×Dic3C22×D516yes—
300#217—56no—
301#217—56no—
302#217—52no—
303#217—56no—
304#217—56no—
305#217C22×D516yes—
306C4⋊Dic3—56no—
307C4⋊Dic3—56no—
308C4⋊Dic3—52no—
309C4⋊Dic3—56no—
310C4⋊Dic3—56no—
311C4⋊Dic3C22×D516yes—
312C4×Dic3—51no—
313C4×Dic3—53no—
314C4×Dic3—56no—
315C4×Dic3—512no—
316C4×Dic3C22×D513yes—
317C4×Dic3C22×D511yescharacteristic
318C4×Dic3C22×D516yes—
319C23×C5C23×D313yes—
320C22×D5—46no—
321C22×D5C22×Dic3112yes—
322C22×D5C23×D311yescharacteristic
323C22×D5C23×D313yes—
324C5×Q8C22×Dic314yes—
325C5×D4C22×Dic3112yes—
326C2×C4×C5—36no—
327C2×C4×C5—32no—
328C2×C4×C5—126no—
329C2×C4×C5C22×Dic3112yes—
330C2×C4×C5C23×D313yes—
331C2×C4×C5C23×D311yescharacteristic
332C22⋊D5C22×Dic3124yes—
333C2×Dic5—32no—
334C2×Dic5—36no—
335C2×Dic5—126no—
336C2×Dic5C22×Dic3112yes—
337C2×Dic5C23×D313yes—
338C2×Dic5C23×D311yescharacteristic
339D20C22×Dic3112yes—
340C4×D5—1212no—
341C4×D5C22×Dic314yes—
342C4×D5C22×Dic3112yes—
343C4×D5C22×Dic3112yes—
344C4×D5C22×Dic3112yes—
345Dic10C22×Dic3112yes—
346C2×#41—516no—
347C2×#41—51no—
348C2×#41—53no—
349C2×#41—53no—
350C2×#41D3×D511yescharacteristic
351C22×Q8—51no—
352C22×D4—53no—
353C23×C4—53no—
354C4×Q8—32no—
355C4×Q8—156no—
356C4×Q8—156no—
357C4×Q8—152no—
358C4×D4—36no—
359C4×D4—156no—
360C4×D4—1512no—
361C4×D4—156no—
362C4×D4—1512no—
363C4×D4—156no—
364#117—33no—
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—33no—
379C2×C42—156no—
380C2×C42—153no—
381C2×C3×C5—26no—
382C2×C3×C5C24×C411yescharacteristic
383C2×C3×C5#58512yes—
384C3×D5—22no—
385C3×D5—26no—
386C23×C3—51no—
387C23×C3—53no—
388C23×C3—512no—
389C23×C3—206no—
390C23×C3C23×D513yes—
391C3×Q8—512no—
392C3×Q8C2×C4×D514yes—
393C3×D4—524no—
394C3×D4—512no—
395C3×D4C2×C4×D5112yes—
396C2×C3×C4—512no—
397C2×C3×C4—53no—
398C2×C3×C4—51no—
399C2×C3×C4—54no—
400C2×C3×C4—512no—
401C2×C3×C4—512no—
402C2×C3×C4—512no—
403C2×C3×C4C2×C4×D5112yes—
404C2×C3×C4C23×D513yes—
405C2×C3×C4C23×D511yescharacteristic
406C2×Dic3—46no—
407C2×Dic3—56no—
408C2×Dic3—52no—
409C2×Dic3—2012no—
410C2×Dic3—206no—
411C2×Dic3C23×D516yes—
412C2×Dic3C23×D512yes—
413C22×C5—26no—
414C22×C5C23×Dic316yes—
415C22×C5C24×D311yescharacteristic
416C2×D5—26no—
417C2×D5—22no—
418C2×D5—412no—
419C2×D5C23×Dic312yes—
420C2×D5C23×Dic316yes—
421C4×C5—66no—
422C4×C5—62no—
423C4×C5C23×Dic316yes—
424C4×C5C23×Dic312yes—
425Dic5—66no—
426Dic5—62no—
427Dic5C23×Dic316yes—
428Dic5C23×Dic312yes—
429C24—53no—
430#41—58no—
431#41—524no—
432#41—524no—
433#41D5×Dic318yescomplemented
434C2×Q8—58no—
435C2×Q8—53no—
436C2×Q8C2×D3×D511yescharacteristic
437C2×D4—56no—
438C2×D4—524no—
439C2×D4—53no—
440C2×D4C2×D3×D513yes—
441C22×C4—36no—
442C22×C4—53no—
443C22×C4—524no—
444C22×C4—53no—
445C22×C4—53no—
446C22×C4—53no—
447C22×C4—51no—
448C22×C4—1512no—
449C22×C4—156no—
450C22×C4C2×D3×D513yes—
451C4⋊C4—36no—
452C4⋊C4—152no—
453C4⋊C4—156no—
454C4⋊C4—156no—
455C4⋊C4—156no—
456C4⋊C4—156no—
457C22⋊C4—36no—
458C22⋊C4—152no—
459C22⋊C4—156no—
460C22⋊C4—156no—
461C22⋊C4—156no—
462C22⋊C4—156no—
463C42—36no—
464C42—31no—
465C42—33no—
466C42—1512no—
467C42—156no—
468C42—153no—
469C42—151no—
470C3×C5#342811yescharacteristic, complemented, Hall
471C22×C3—26no—
472C22×C3—52no—
473C22×C3—56no—
474C22×C3—106no—
475C22×C3—102no—
476C22×C3—2012no—
477C22×C3C22×C4×D516yes—
478C22×C3C24×D511yescharacteristic
479C3×C4—52no—
480C3×C4—56no—
481C3×C4C22×C4×D512yes—
482C3×C4C22×C4×D516yes—
483Dic3—22no—
484Dic3—26no—
485Dic3—106no—
486Dic3—102no—
487C2×C5—26no—
488C2×C5#596412yes—
489C2×C5C24×Dic311yescharacteristic
490D5—22no—
491D5—26no—
492C23—51no—
493C23—53no—
494C23—512no—
495C23—206no—
496C23C22×D3×D513yes—
497Q8—512no—
498Q8C2×D5×Dic314yes—
499D4—524no—
500D4—512no—
501D4C2×D5×Dic3112yes—
502C2×C4—32no—
503C2×C4—36no—
504C2×C4—512no—
505C2×C4—53no—
506C2×C4—51no—
507C2×C4—54no—
508C2×C4—512no—
509C2×C4—512no—
510C2×C4—512no—
511C2×C4—126no—
512C2×C4—156no—
513C2×C4—152no—
514C2×C4—6012no—
515C2×C4—606no—
516C2×C4C2×D5×Dic3112yes—
517C2×C4C22×D3×D513yes—
518C2×C4C22×D3×D511yescharacteristic
519C2×C3—26no—
520C2×C3—102no—
521C2×C3—106no—
522C2×C3C23×C4×D511yescharacteristic
523C2×C3#6628312yes—
524C5#8726011yescharacteristic, complemented, Sylow
525C22—26no—
526C22—52no—
527C22—56no—
528C22—106no—
529C22—102no—
530C22—2012no—
531C22C22×D5×Dic316yes—
532C22C23×D3×D511yescharacteristic
533C4—52no—
534C4—56no—
535C4—62no—
536C4—66no—
537C4—306no—
538C4—302no—
539C4C22×D5×Dic312yes—
540C4C22×D5×Dic316yes—
541C3#1061773511yescharacteristic, complemented, Sylow
542C2—26no—
543C2—102no—
544C2—106no—
545C2#1175705812yes—
546C2C23×D5×Dic311yescharacteristic
subgroupG/H
centerC2×C4C22×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC2×C3×C5×#41C22
socle, cosocleC22×C3×C5C25
prime radicalC2×C3×D5×#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. C5×Dic3×#41C2semidirect
4. #11755217C2semidirect
5. #11755140C2semidirect
6. #11754923C2semidirect
7. #11754910C2semidirect
8. #11754444C2semidirect
9. Dic3×#709C2semidirect
10. D5×#926C2semidirect
11. C2×#91357C2semidirect
14. C3×D5×#41C4semidirect
21. Q8×Dic15C22semidirect
22. D4×Dic15C22semidirect
23. #91815C22semidirect
24. C2×C4×Dic15C22semidirect
25. C5×Q8×Dic3C22semidirect
26. C5×D4×Dic3C22semidirect
27. C5×#926C22semidirect
28. C2×C4×C5×Dic3C22semidirect
29. #91559C22semidirect
30. Dic3×C22⋊D5C22semidirect
32. C2×#6668C22semidirect
34. #91528C22semidirect
35. #91434C22semidirect
36. Dic3×D20C22semidirect
37. D5×C4⋊Dic3C22semidirect
38. C4×D5×Dic3C22semidirect
43. #91357C22semidirect
44. #91357C22semidirect
45. #91357C22semidirect
46. #91331C22semidirect
47. Dic3×Dic10C22semidirect
61. C3×C5×#41C2×C4semidirect
69. C3×#713C2×C4semidirect
70. C3×Q8×D5C2×C4semidirect
71. C3×#711C2×C4semidirect
72. C3×D4×D5C2×C4semidirect
73. C3×#709C2×C4semidirect
75. C2×C3×C4×D5C2×C4semidirect
107. Dic3×#41D5semidirect
113. D5×#41Dic3semidirect
188. Q8×Dic3C2×D5semidirect
194. D4×Dic3C2×D5semidirect
204. #926C2×D5semidirect
209. C2×C4×Dic3C2×D5semidirect
211. C5×#41C2×Dic3semidirect
219. #713C2×Dic3semidirect
220. Q8×D5C2×Dic3semidirect
221. #711C2×Dic3semidirect
222. D4×D5C2×Dic3semidirect
223. #709C2×Dic3semidirect
226. C2×C4×D5C2×Dic3semidirect
282. C3×#41C4×D5semidirect
433. #41D5×Dic3semidirect
470. C3×C5#3428semidirect
524. C5#87260semidirect
541. C3#10617735semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×#412
#41×Dic152
C5×Dic3×#412
#117552172
#117551402
#117549232
#117549102
#117544442
Dic3×#7092
D5×#9262
C2×#913572
#106177353
#872605