Finite Group Databasebeta

← #14479166

Subgroups — #14479166

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×#41×D15C211yesmaximal, characteristic
2C5×Dic3×#41C211yesmaximal, characteristic, complemented
3C3×#41×Dic5C211yesmaximal, characteristic, complemented
4#11755149C212yesmaximal, complemented
5#11755124C212yesmaximal, complemented
6#11754922C216yesmaximal, complemented
7#11754916C216yesmaximal, complemented
8#11754461C213yesmaximal, complemented
9#11754436C213yesmaximal, complemented
10#11754414C213yesmaximal, complemented
11C2×#91386C213yesmaximal, complemented
12#10617735—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14#41×D15C4116yescomplemented
15C2×#6821C2211yescharacteristic
16C2×Q8×D15C2211yescharacteristic
17C2×#6819C2213yes—
18C2×D4×D15C2213yes—
19C2×#6817C2213yes—
20C22×C4×D15C2213yes—
21C5×Q8×Dic3C2212yescomplemented
22C5×D4×Dic3C2216yescomplemented
23C5×#926C2213yescomplemented
24C2×C4×C5×Dic3C2213yescomplemented
25C3×Q8×Dic5C2212yescomplemented
26C3×D4×Dic5C2216yescomplemented
27C3×#4072C2213yescomplemented
28C2×C3×C4×Dic5C2213yescomplemented
29#91561C2216yes—
30#91556C22112yescomplemented
31#91552C22112yescomplemented
32C2×#6669C2216yescomplemented
33C2×#6667C2216yes—
34#91532C2216yescomplemented
35#91437C2216yescomplemented
36#91428C2216yescomplemented
37#91418C2216yescomplemented
38C4×#1200C2216yescomplemented
39#91386C2211yescharacteristic
40#91386C2216yes—
41#91386C2213yes—
42#91386C2216yescomplemented
43#91386C2213yescomplemented
44#91386C2213yescomplemented
45#91347C2216yes—
46#91340C2216yescomplemented
47#91333C2216yescomplemented
48#85834—51nomaximal, Hall
49C2×D5×#41—31no—
50C4×C5×#41—31no—
51#41×Dic5D311yescharacteristic, complemented
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×D15C2313yes—
61C3×C5×#41C2×C418yescomplemented
62C2×C3×C5×Q8C2311yescharacteristic
63C2×C3×C5×D4C2313yes—
64C22×C3×C4×C5C2313yes—
65C2×#1220C2316yes—
66C22×Dic15C2313yes—
67#6821C2×C418yescomplemented
68Q8×D15C2×C418yescomplemented
69#6819C2×C4124yescomplemented
70D4×D15C2×C4124yescomplemented
71#6817C2×C4124yescomplemented
72C2×D60C2313yes—
73C2×C4×D15C2×C4124yescomplemented
74C2×C4×D15C2313yes—
75C2×C4×D15C2313yes—
76C2×C4×D15C2311yescharacteristic
77C2×C4×D15C2313yes—
78C2×Dic30C2313yes—
79C22×C5×Dic3C2316yes—
80C22×C3×Dic5C2316yes—
81C2×#1200C23112yes—
82C5×#217C2316yes—
83C5×C4⋊Dic3C2316yes—
84C4×C5×Dic3C2313yes—
85C4×C5×Dic3C2316yes—
86C4×C5×Dic3C2311yescharacteristic
87C3×C22⋊Dic5C2316yes—
88C3×C4⋊Dic5C2316yes—
89C3×C4×Dic5C2316yes—
90C3×C4×Dic5C2313yes—
91C3×C4×Dic5C2311yescharacteristic
92#6669C2316yes—
93#6669C2312yes—
94#6669C2316yes—
95#6669C2316yes—
96#6667C2316yes—
97#6667C2316yes—
98#6667C2312yes—
99#6667C2316yes—
100Dic3×Dic5C23112yes—
101C2×D3×#41—51no—
102C3×C4×#41—51no—
103Dic3×#41D511yescharacteristic, complemented
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×#41C2×D311yescharacteristic
113D5×#41—316no—
114C2×#713—31no—
115C2×Q8×D5—31no—
116C2×#711—33no—
117C2×D4×D5—33no—
118C2×#709—33no—
119C22×C4×D5—33no—
120C4×C5×Q8—32no—
121C4×C5×D4—36no—
122C5×#117—33no—
123C2×C42×C5—33no—
124Q8×Dic5C2×D312yescomplemented
125D4×Dic5C2×D316yescomplemented
126C4×C22⋊D5—312no—
127C2×#685—36no—
128#4072C2×D313yescomplemented
129C2×#683—36no—
130C2×C4×Dic5C2×D313yescomplemented
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×D15—46no—
150C22×D15C22×C4112yes—
151C22×D15C2411yescharacteristic
152C22×D15C2413yes—
153C3×C5×Q8C22×C414yes—
154C3×C5×D4C22×C4112yes—
155C2×C3×C4×C5C22×C4112yes—
156C2×C3×C4×C5C2411yescharacteristic
157C2×C3×C4×C5C2413yes—
158#1220C22×C4124yes—
159C2×Dic15C22×C4112yes—
160C2×Dic15C2413yes—
161C2×Dic15C2411yescharacteristic
162D60C22×C4112yes—
163C4×D15C22×C414yes—
164C4×D15C22×C4112yes—
165C4×D15C22×C4112yes—
166C4×D15C22×C4112yes—
167Dic30C22×C4112yes—
168C2×C5×Dic3—46no—
169C2×C5×Dic3C2416yes—
170C2×C5×Dic3C2412yes—
171C2×C3×Dic5—46no—
172C2×C3×Dic5C2416yes—
173C2×C3×Dic5C2412yes—
174#1200—412no—
175C2×C3×#41C2×D511yescharacteristic
176D3×#41—516no—
177C2×#239—51no—
178C2×D3×Q8—51no—
179C2×#237—53no—
180C2×D3×D4—53no—
181C2×#235—53no—
182C22×C4×D3—53no—
183C3×C4×Q8—52no—
184C3×C4×D4—56no—
185C3×#117—53no—
186C2×C3×C42—53no—
187Q8×Dic3C2×D512yescomplemented
188D4×Dic3C2×D516yescomplemented
189C4×#67—512no—
190C2×(C2×D3)⋊C4—56no—
191#926C2×D513yescomplemented
192C2×Dic3⋊C4—56no—
193C2×C4×Dic3C2×D513yescomplemented
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—
210C23×D5—33no—
211C5×#41C4×D318yescomplemented
212C2×C5×Q8C22×D311yescharacteristic
213C2×C5×D4C22×D313yes—
214C22×C4×C5—36no—
215C22×C4×C5C22×D313yes—
216C2×C22⋊D5—36no—
217C22×Dic5—33no—
218C22×Dic5C22×D316yes—
219#713—38no—
220Q8×D5—38no—
221#711—324no—
222D4×D5—324no—
223#709—324no—
224C2×D20—33no—
225C2×C4×D5—324no—
226C2×C4×D5—31no—
227C2×C4×D5—33no—
228C2×C4×D5—33no—
229C2×C4×D5—33no—
230C2×C4×D5—312no—
231C2×Dic10—33no—
232C5×C4⋊C4—36no—
233C5×C22⋊C4—36no—
234C42×C5—31no—
235C42×C5—33no—
236C42×C5—36no—
237C22⋊Dic5C22×D316yes—
238#685—32no—
239#685—36no—
240#685—36no—
241#685—36no—
242C4⋊Dic5C22×D316yes—
243#683—36no—
244#683—32no—
245#683—36no—
246#683—36no—
247C4×Dic5—312no—
248C4×Dic5C22×D313yes—
249C4×Dic5C22×D311yescharacteristic
250C4×Dic5C22×D316yes—
251C22×#41—151no—
252#520—156no—
253#520—152no—
254#519—152no—
255#518—156no—
256C4×#41—31no—
257C4×#41—51no—
258C4×#41—153no—
259C4×#41—153no—
260C2×#117—153no—
261C2×#117—153no—
262C22×C3×C5—26no—
263C22×C3×C5C23×C416yes—
264C22×C3×C5C2511yescharacteristic
265C2×D15—26no—
266C2×D15—22no—
267C2×D15—412no—
268C2×D15C23×C412yes—
269C2×D15C23×C416yes—
270C3×C4×C5C23×C416yes—
271C3×C4×C5C23×C412yes—
272Dic15C23×C416yes—
273Dic15C23×C412yes—
274C3×Dic5—26no—
275C3×Dic5—22no—
276C5×Dic3—26no—
277C5×Dic3—22no—
278C23×D3—53no—
279C3×#41C4×D518yescomplemented
280C2×C3×Q8C22×D511yescharacteristic
281C2×C3×D4C22×D513yes—
282C22×C3×C4—56no—
283C22×C3×C4C22×D513yes—
284C2×#67—56no—
285C22×Dic3—53no—
286C22×Dic3C22×D516yes—
287#239—58no—
288D3×Q8—58no—
289#237—524no—
290D3×D4—524no—
291#235—524no—
292C2×D12—53no—
293C2×C4×D3—524no—
294C2×C4×D3—53no—
295C2×C4×D3—51no—
296C2×C4×D3—53no—
297C2×C4×D3—53no—
298C2×C4×D3—512no—
299C2×Dic6—53no—
300C3×C4⋊C4—56no—
301C3×C22⋊C4—56no—
302C3×C42—56no—
303C3×C42—53no—
304C3×C42—51no—
305#217C22×D516yes—
306(C2×D3)⋊C4—52no—
307(C2×D3)⋊C4—56no—
308(C2×D3)⋊C4—56no—
309(C2×D3)⋊C4—56no—
310C4⋊Dic3C22×D516yes—
311Dic3⋊C4—56no—
312Dic3⋊C4—52no—
313Dic3⋊C4—56no—
314Dic3⋊C4—56no—
315C4×Dic3—512no—
316C4×Dic3C22×D513yes—
317C4×Dic3C22×D511yescharacteristic
318C4×Dic3C22×D516yes—
319C23×C5C23×D313yes—
320C22×D5—31no—
321C22×D5—33no—
322C22×D5—312no—
323C22×D5—126no—
324C5×Q8C2×C4×D314yes—
325C5×D4C2×C4×D3112yes—
326C2×C4×C5—36no—
327C2×C4×C5—32no—
328C2×C4×C5—126no—
329C2×C4×C5C2×C4×D3112yes—
330C2×C4×C5C23×D313yes—
331C2×C4×C5C23×D311yescharacteristic
332C22⋊D5—324no—
333C2×Dic5—312no—
334C2×Dic5—33no—
335C2×Dic5—31no—
336C2×Dic5—46no—
337C2×Dic5C23×D316yes—
338C2×Dic5C23×D312yes—
339D20—312no—
340C4×D5—34no—
341C4×D5—312no—
342C4×D5—312no—
343C4×D5—312no—
344C4×D5—1212no—
345Dic10—312no—
346C2×#41—1516no—
347C2×#41—151no—
348C2×#41—153no—
349C2×#41—153no—
350C2×#41D3×D511yescharacteristic
351C22×Q8—151no—
352C22×D4—153no—
353C23×C4—153no—
354C4×Q8—32no—
355C4×Q8—52no—
356C4×Q8—156no—
357C4×Q8—156no—
358C4×D4—36no—
359C4×D4—56no—
360C4×D4—156no—
361C4×D4—156no—
362C4×D4—1512no—
363C4×D4—1512no—
364#117—33no—
365#117—53no—
366#117—151no—
367#117—153no—
368#117—153no—
369#117—153no—
370#117—156no—
371#117—156no—
372#117—156no—
373#117—156no—
374C2×C4⋊C4—156no—
375C2×C4⋊C4—156no—
376C2×C22⋊C4—156no—
377C2×C22⋊C4—156no—
378C2×C42—33no—
379C2×C42—53no—
380C2×C42—156no—
381C2×C3×C5—26no—
382C2×C3×C5C24×C411yescharacteristic
383C2×C3×C5#58512yes—
384D15—22no—
385D15—26no—
386C23×C3C23×D513yes—
387C22×D3—51no—
388C22×D3—53no—
389C22×D3—512no—
390C22×D3—206no—
391C3×Q8C2×C4×D514yes—
392C3×D4C2×C4×D5112yes—
393C2×C3×C4—56no—
394C2×C3×C4—52no—
395C2×C3×C4—206no—
396C2×C3×C4C2×C4×D5112yes—
397C2×C3×C4C23×D513yes—
398C2×C3×C4C23×D511yescharacteristic
399#67—524no—
400C2×Dic3—46no—
401C2×Dic3—512no—
402C2×Dic3—53no—
403C2×Dic3—51no—
404C2×Dic3C23×D516yes—
405C2×Dic3C23×D512yes—
406D12—512no—
407C4×D3—54no—
408C4×D3—512no—
409C4×D3—512no—
410C4×D3—512no—
411C4×D3—2012no—
412Dic6—512no—
413C22×C5—26no—
414C22×C5C22×C4×D316yes—
415C22×C5C24×D311yescharacteristic
416C2×D5—32no—
417C2×D5—36no—
418C2×D5—66no—
419C2×D5—62no—
420C2×D5—1212no—
421C4×C5—66no—
422C4×C5—62no—
423C4×C5C22×C4×D316yes—
424C4×C5C22×C4×D312yes—
425Dic5—26no—
426Dic5—22no—
427Dic5—36no—
428Dic5—32no—
429C24—153no—
430#41—158no—
431#41—1524no—
432#41—1524no—
433#41#120018yescomplemented
434C2×Q8—158no—
435C2×Q8—153no—
436C2×Q8C2×D3×D511yescharacteristic
437C2×D4—156no—
438C2×D4—1524no—
439C2×D4—153no—
440C2×D4C2×D3×D513yes—
441C22×C4—36no—
442C22×C4—56no—
443C22×C4—1512no—
444C22×C4—153no—
445C22×C4—1524no—
446C22×C4—153no—
447C22×C4—153no—
448C22×C4—153no—
449C22×C4—151no—
450C22×C4C2×D3×D513yes—
451C4⋊C4—36no—
452C4⋊C4—56no—
453C4⋊C4—152no—
454C4⋊C4—156no—
455C4⋊C4—156no—
456C4⋊C4—156no—
457C22⋊C4—36no—
458C22⋊C4—56no—
459C22⋊C4—152no—
460C22⋊C4—156no—
461C22⋊C4—156no—
462C22⋊C4—156no—
463C42—36no—
464C42—31no—
465C42—33no—
466C42—56no—
467C42—51no—
468C42—53no—
469C42—1512no—
470C3×C5#342811yescharacteristic, complemented, Hall
471C22×C3—26no—
472C22×C3C22×C4×D516yes—
473C22×C3C24×D511yescharacteristic
474C2×D3—52no—
475C2×D3—56no—
476C2×D3—106no—
477C2×D3—102no—
478C2×D3—2012no—
479C3×C4—106no—
480C3×C4—102no—
481C3×C4C22×C4×D516yes—
482C3×C4C22×C4×D512yes—
483Dic3—26no—
484Dic3—22no—
485Dic3—56no—
486Dic3—52no—
487C2×C5—26no—
488C2×C5C23×C4×D311yescharacteristic
489C2×C5#596412yes—
490D5—62no—
491D5—66no—
492C23—151no—
493C23—153no—
494C23—1512no—
495C23—606no—
496C23C22×D3×D513yes—
497Q8—1512no—
498Q8C2×#120014yes—
499D4—1524no—
500D4—1512no—
501D4C2×#1200112yes—
502C2×C4—32no—
503C2×C4—36no—
504C2×C4—52no—
505C2×C4—56no—
506C2×C4—126no—
507C2×C4—1512no—
508C2×C4—153no—
509C2×C4—151no—
510C2×C4—154no—
511C2×C4—1512no—
512C2×C4—1512no—
513C2×C4—1512no—
514C2×C4—206no—
515C2×C4—6012no—
516C2×C4C2×#1200112yes—
517C2×C4C22×D3×D513yes—
518C2×C4C22×D3×D511yescharacteristic
519C2×C3—26no—
520C2×C3C23×C4×D511yescharacteristic
521C2×C3#6628312yes—
522D3—102no—
523D3—106no—
524C5#8583411yescharacteristic, complemented, Sylow
525C22—26no—
526C22—152no—
527C22—156no—
528C22—306no—
529C22—302no—
530C22—6012no—
531C22C22×#120016yes—
532C22C23×D3×D511yescharacteristic
533C4—62no—
534C4—66no—
535C4—102no—
536C4—106no—
537C4—152no—
538C4—156no—
539C4C22×#120012yes—
540C4C22×#120016yes—
541C3#1061773511yescharacteristic, complemented, Sylow
542C2—26no—
543C2—302no—
544C2—306no—
545C2#1175705812yes—
546C2C23×#120011yescharacteristic
subgroupG/H
centerC2×C4C22×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC2×C3×C5×#41C22
socle, cosocleC22×C3×C5C25
prime radicalC2×#41×D15C2
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. C5×Dic3×#41C2semidirect
3. C3×#41×Dic5C2semidirect
4. #11755149C2semidirect
5. #11755124C2semidirect
6. #11754922C2semidirect
7. #11754916C2semidirect
8. #11754461C2semidirect
9. #11754436C2semidirect
10. #11754414C2semidirect
11. C2×#91386C2semidirect
14. #41×D15C4semidirect
21. C5×Q8×Dic3C22semidirect
22. C5×D4×Dic3C22semidirect
23. C5×#926C22semidirect
24. C2×C4×C5×Dic3C22semidirect
25. C3×Q8×Dic5C22semidirect
26. C3×D4×Dic5C22semidirect
27. C3×#4072C22semidirect
28. C2×C3×C4×Dic5C22semidirect
30. #91556C22semidirect
31. #91552C22semidirect
32. C2×#6669C22semidirect
34. #91532C22semidirect
35. #91437C22semidirect
36. #91428C22semidirect
37. #91418C22semidirect
38. C4×#1200C22semidirect
42. #91386C22semidirect
43. #91386C22semidirect
44. #91386C22semidirect
46. #91340C22semidirect
47. #91333C22semidirect
51. #41×Dic5D3semidirect
61. C3×C5×#41C2×C4semidirect
67. #6821C2×C4semidirect
68. Q8×D15C2×C4semidirect
69. #6819C2×C4semidirect
70. D4×D15C2×C4semidirect
71. #6817C2×C4semidirect
73. C2×C4×D15C2×C4semidirect
103. Dic3×#41D5semidirect
124. Q8×Dic5C2×D3semidirect
125. D4×Dic5C2×D3semidirect
128. #4072C2×D3semidirect
130. C2×C4×Dic5C2×D3semidirect
187. Q8×Dic3C2×D5semidirect
188. D4×Dic3C2×D5semidirect
191. #926C2×D5semidirect
193. C2×C4×Dic3C2×D5semidirect
211. C5×#41C4×D3semidirect
279. C3×#41C4×D5semidirect
433. #41#1200semidirect
470. C3×C5#3428semidirect
524. C5#85834semidirect
541. C3#10617735semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D152
C5×Dic3×#412
C3×#41×Dic52
#117551492
#117551242
#117549222
#117549162
#117544612
#117544362
#117544142
C2×#913862
#106177353
#858345