Finite Group Databasebeta

← #14484797

Subgroups — #14484797

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#550C211yesmaximal, characteristic, complemented
2#11756590C212yesmaximal, complemented
3#41×Dic15C212yesmaximal, complemented
4#11756475C213yesmaximal, complemented
5#11756472C213yesmaximal, complemented
6#11756373C216yesmaximal, complemented
7#11756359C216yesmaximal, complemented
8C4×Q8×D15C211yesmaximal, characteristic, complemented
9#11756329C211yesmaximal, characteristic, complemented
10#11756301C213yesmaximal, complemented
11C4×#6819C213yesmaximal, complemented
12#10618668—31nomaximal, Hall
13C2×C3×C5×#41C2212yes—
14C2×Q8×D15C2211yescharacteristic
15C2×#6819C2213yes—
16C3×C5×#127C2213yes—
17C3×C5×#121C2216yes—
18C3×C4×C5×Q8C2211yescharacteristic
19C3×C4×C5×D4C2213yes—
20Q8×Dic15C2212yes—
21Q8×Dic15C2211yescharacteristic
22#91827C2216yes—
23#91827C2216yes—
24#91825C2216yes—
25#91825C2216yes—
26#91824C22112yes—
27D4×Dic15C2213yes—
28D4×Dic15C2216yes—
29D4×Dic15C2216yes—
30D4×Dic15C2216yes—
31C4×#1220C2216yes—
32#91815C2216yes—
33#91813C2216yes—
34C2×C4×Dic15C2216yes—
35#91781C2211yescharacteristic
36C4⋊C4×D15C2213yes—
37#91779C2216yes—
38#91776C2213yes—
39#91776C2213yes—
40#91770C2216yes—
41#91768C22112yes—
42#91766C2216yes—
43C42×D15C2213yes—
44#91758C2213yes—
45C4×Dic30C2213yes—
46C4×Dic30C2213yes—
47#86767—51nomaximal, Hall
48C5×#550D311yescharacteristic, complemented
49#66165—32no—
50#41×Dic5—32no—
51#66050—33no—
52#66047—33no—
53#65948—36no—
54#65934—36no—
55C4×Q8×D5—31no—
56#65904—31no—
57#65876—33no—
58C4×#711—33no—
59C3×C5×#41—28no—
60C2×C3×C5×Q8C2311yescharacteristic
61C2×C3×C5×D4C2316yes—
62C2×C3×C5×D4C2313yes—
63C2×C3×C5×D4C2316yes—
64C22×C3×C4×C5C2316yes—
65C2×#1220C2316yes—
66C22×Dic15C2316yes—
67C22×Dic15C2316yes—
68Q8×D15—24no—
69#6819—212no—
70C2×C4×D15C2313yes—
71C2×C4×D15C2313yes—
72C2×C4×D15C2311yescharacteristic
73C2×Dic30C2313yes—
74C2×Dic30C2313yes—
75C3×C5×C4⋊C4C2311yescharacteristic
76C3×C5×C4⋊C4C2313yes—
77C3×C5×C22⋊C4C2316yes—
78C3×C42×C5C2313yes—
79#6719C2316yes—
80#6719C23112yes—
81#6719C23112yes—
82#6714C2312yes—
83C4⋊Dic15C2311yescharacteristic
84C4⋊Dic15C2313yes—
85C4⋊Dic15C2316yes—
86C4⋊Dic15C2316yes—
87#6712C2316yes—
88#6712C2316yes—
89#6712C2316yes—
90C4×Dic15C2313yes—
91C4×Dic15C2316yes—
92C4×Dic15C2313yes—
93C4×Dic15C2313yes—
94C4×Dic15C2312yes—
95C4×Dic15C2316yes—
96C3×#550D511yescharacteristic, complemented
97#5831—52no—
98Dic3×#41—52no—
99#5716—53no—
100#5713—53no—
101#5614—56no—
102#5600—56no—
103C4×D3×Q8—51no—
104#5570—51no—
105#5542—53no—
106C4×#237—53no—
107C2×C5×#41C2×D312yes—
108C2×Q8×D5—31no—
109C2×#711—33no—
110C5×#127C2×D313yes—
111C5×#121C2×D316yes—
112C4×C5×Q8C2×D311yescharacteristic
113C4×C5×D4C2×D313yes—
114Q8×Dic5—32no—
115Q8×Dic5—31no—
116#4084—36no—
117#4084—36no—
118#4082—36no—
119#4082—36no—
120#4081—312no—
121D4×Dic5—36no—
122D4×Dic5—36no—
123D4×Dic5—33no—
124D4×Dic5—36no—
125C4×C22⋊D5—36no—
126#4072—36no—
127#4070—36no—
128C2×C4×Dic5—36no—
129#4038—31no—
130D5×C4⋊C4—33no—
131#4036—36no—
132#4033—33no—
133#4033—33no—
134#4027—36no—
135#4025—312no—
136#4023—36no—
137C42×D5—33no—
138#4015—33no—
139C4×Dic10—33no—
140C4×Dic10—33no—
141#3480—151noSylow
142C23×C3×C5C2416yes—
143C22×D15C2411yescharacteristic
144C3×C5×Q8#4114yescomplemented
145C3×C5×D4—26no—
146C3×C5×D4—212no—
147C3×C5×D4—46no—
148C2×C3×C4×C5—212no—
149C2×C3×C4×C5C2412yes—
150C2×C3×C4×C5C2413yes—
151C2×C3×C4×C5C2413yes—
152C2×C3×C4×C5C2411yescharacteristic
153#1220—212no—
154C2×Dic15—212no—
155C2×Dic15—46no—
156C2×Dic15C2412yes—
157C2×Dic15C2413yes—
158C2×Dic15C2413yes—
159C2×Dic15C2416yes—
160C2×Dic15C2411yescharacteristic
161C4×D15—26no—
162C4×D15—43no—
163C4×D15#4114yescomplemented
164Dic30—26no—
165Dic30—26no—
166C2×C3×#41C2×D512yes—
167C2×D3×Q8—51no—
168C2×#237—53no—
169C3×#127C2×D513yes—
170C3×#121C2×D516yes—
171C3×C4×Q8C2×D511yescharacteristic
172C3×C4×D4C2×D513yes—
173Q8×Dic3—52no—
174Q8×Dic3—51no—
175#938—56no—
176#938—56no—
177#936—56no—
178#936—56no—
179#935—512no—
180D4×Dic3—53no—
181D4×Dic3—56no—
182D4×Dic3—56no—
183D4×Dic3—56no—
184C4×#67—56no—
185#926—56no—
186#924—56no—
187C2×C4×Dic3—56no—
188#892—51no—
189D3×C4⋊C4—53no—
190#890—56no—
191#887—53no—
192#887—53no—
193#67⋊C4—56no—
194#879—512no—
195#877—56no—
196C42×D3—53no—
197#869—53no—
198C4×Dic6—53no—
199C4×Dic6—53no—
200C5×#41—28no—
201C2×C5×Q8C22×D311yescharacteristic
202C2×C5×D4C22×D313yes—
203C2×C5×D4C22×D316yes—
204C2×C5×D4C22×D316yes—
205C22×C4×C5C22×D316yes—
206C2×C22⋊D5—36no—
207C22×Dic5—36no—
208C22×Dic5—36no—
209Q8×D5—64no—
210#711—612no—
211C2×C4×D5—31no—
212C2×C4×D5—33no—
213C2×C4×D5—33no—
214C2×Dic10—33no—
215C2×Dic10—33no—
216C5×C4⋊C4C22×D311yescharacteristic
217C5×C4⋊C4C22×D313yes—
218C5×C22⋊C4C22×D316yes—
219C42×C5C22×D313yes—
220C22⋊Dic5—36no—
221C22⋊Dic5—312no—
222C22⋊Dic5—312no—
223#685—32no—
224C4⋊Dic5—31no—
225C4⋊Dic5—33no—
226C4⋊Dic5—36no—
227C4⋊Dic5—36no—
228#683—36no—
229#683—36no—
230#683—36no—
231C4×Dic5—33no—
232C4×Dic5—36no—
233C4×Dic5—33no—
234C4×Dic5—33no—
235C4×Dic5—32no—
236C4×Dic5—36no—
237#559—153no—
238#557—151no—
239#556—153no—
240#553—156no—
241#550D1511yescharacteristic, complemented
242#548—152no—
243#532—153no—
244#529—156no—
245C4×#41—152no—
246C4×#41—153no—
247C2×C4×Q8—151no—
248C22×C3×C5—26no—
249C22×C3×C5—26no—
250C22×C3×C5—26no—
251C22×C3×C5C2511yescharacteristic
252C2×D15—21no—
253C2×D15—21no—
254C2×D15C2×#4112yes—
255C3×C4×C5—22no—
256C3×C4×C5—23no—
257C3×C4×C5C2×#4116yes—
258C3×C4×C5C2×#4112yes—
259Dic15—23no—
260Dic15—26no—
261Dic15—23no—
262Dic15—22no—
263Dic15C2×#4112yes—
264C3×#41—28no—
265C2×C3×Q8C22×D511yescharacteristic
266C2×C3×D4C22×D516yes—
267C2×C3×D4C22×D513yes—
268C2×C3×D4C22×D516yes—
269C22×C3×C4C22×D516yes—
270C2×#67—56no—
271C22×Dic3—56no—
272C22×Dic3—56no—
273D3×Q8—104no—
274#237—1012no—
275C2×C4×D3—51no—
276C2×C4×D3—53no—
277C2×C4×D3—53no—
278C2×Dic6—53no—
279C2×Dic6—53no—
280C3×C4⋊C4C22×D511yescharacteristic
281C3×C4⋊C4C22×D513yes—
282C3×C22⋊C4C22×D516yes—
283C3×C42C22×D513yes—
284#217—56no—
285#217—512no—
286#217—512no—
287(C2×D3)⋊C4—52no—
288C4⋊Dic3—51no—
289C4⋊Dic3—53no—
290C4⋊Dic3—56no—
291C4⋊Dic3—56no—
292Dic3⋊C4—56no—
293Dic3⋊C4—56no—
294Dic3⋊C4—56no—
295C4×Dic3—53no—
296C4×Dic3—56no—
297C4×Dic3—53no—
298C4×Dic3—53no—
299C4×Dic3—52no—
300C4×Dic3—56no—
301C23×C5C23×D316yes—
302C22×D5—31no—
303C5×Q8#23714yescomplemented
304C5×D4—212no—
305C5×D4—26no—
306C5×D4—46no—
307C2×C4×C5—212no—
308C2×C4×C5C23×D312yes—
309C2×C4×C5C23×D313yes—
310C2×C4×C5C23×D313yes—
311C2×C4×C5C23×D311yescharacteristic
312C22⋊D5—612no—
313C2×Dic5—31no—
314C2×Dic5—32no—
315C2×Dic5—33no—
316C2×Dic5—33no—
317C2×Dic5—36no—
318C2×Dic5—612no—
319C2×Dic5—126no—
320C4×D5—34no—
321C4×D5—66no—
322C4×D5—123no—
323Dic10—66no—
324Dic10—66no—
325C2×#41—153no—
326C2×#41C2×D1512yes—
327C22×Q8—151no—
328C4⋊Q8—153no—
329#127C2×D1513yes—
330#126—1512no—
331#125—156no—
332#124—156no—
333#124—156no—
334#123—1512no—
335C22⋊Q8—156no—
336#121—156no—
337#121—156no—
338#121C2×D1516yes—
339C4×Q8—151no—
340C4×Q8—152no—
341C4×Q8—153no—
342C4×Q8—153no—
343C4×Q8—153no—
344C4×Q8—153no—
345C4×Q8C2×D1511yescharacteristic
346C4×D4—156no—
347C4×D4—156no—
348C4×D4—153no—
349C4×D4—156no—
350C4×D4—156no—
351C4×D4—156no—
352C4×D4C2×D1513yes—
353#117—156no—
354#117—151no—
355#117—156no—
356C2×C4⋊C4—153no—
357C2×C42—156no—
358C2×C42—153no—
359C2×C3×C5—46no—
360C2×C3×C5C22×#4111yescharacteristic
361C2×C3×C5C22×#4111yescharacteristic
362C2×C3×C5#58511yescharacteristic
363D15—22no—
364C23×C3C23×D516yes—
365C22×D3—51no—
366C3×Q8#71114yescomplemented
367C3×D4—212no—
368C3×D4—26no—
369C3×D4—46no—
370C2×C3×C4—212no—
371C2×C3×C4C23×D512yes—
372C2×C3×C4C23×D513yes—
373C2×C3×C4C23×D513yes—
374C2×C3×C4C23×D511yescharacteristic
375#67—1012no—
376C2×Dic3—51no—
377C2×Dic3—52no—
378C2×Dic3—53no—
379C2×Dic3—53no—
380C2×Dic3—56no—
381C2×Dic3—1012no—
382C2×Dic3—206no—
383C4×D3—54no—
384C4×D3—106no—
385C4×D3—203no—
386Dic6—106no—
387Dic6—106no—
388C22×C5—26no—
389C22×C5—26no—
390C22×C5—26no—
391C22×C5C24×D311yescharacteristic
392C2×D5—32no—
393C2×D5—61no—
394C2×D5—61no—
395C4×C5—22no—
396C4×C5—23no—
397C4×C5C2×#23716yes—
398C4×C5D3×#4112yes—
399Dic5—32no—
400Dic5—63no—
401Dic5—66no—
402Dic5—63no—
403Dic5—62no—
404#41—28no—
405#41—3012no—
406C2×Q8—153no—
407C2×Q8—153no—
408C2×Q8—304no—
409C2×Q8C22×D1511yescharacteristic
410C2×D4—156no—
411C2×D4C22×D1516yes—
412C2×D4C22×D1513yes—
413C2×D4C22×D1516yes—
414C22×C4—151no—
415C22×C4—156no—
416C22×C4—156no—
417C22×C4—153no—
418C22×C4—153no—
419C22×C4C22×D1516yes—
420C4⋊C4—153no—
421C4⋊C4—156no—
422C4⋊C4—151no—
423C4⋊C4—156no—
424C4⋊C4—156no—
425C4⋊C4—156no—
426C4⋊C4—156no—
427C4⋊C4C22×D1513yes—
428C4⋊C4C22×D1511yescharacteristic
429C22⋊C4—1512no—
430C22⋊C4—156no—
431C22⋊C4—1512no—
432C22⋊C4—152no—
433C22⋊C4C22×D1516yes—
434C42—152no—
435C42—153no—
436C42—153no—
437C42—156no—
438C42—156no—
439C42—153no—
440C42C22×D1513yes—
441C3×C5#348011yescharacteristic, complemented, Hall
442C22×C3—26no—
443C22×C3—26no—
444C22×C3—26no—
445C22×C3C24×D511yescharacteristic
446C2×D3—52no—
447C2×D3—101no—
448C2×D3—101no—
449C3×C4—22no—
450C3×C4—23no—
451C3×C4C2×#71116yes—
452C3×C4D5×#4112yes—
453Dic3—52no—
454Dic3—103no—
455Dic3—106no—
456Dic3—103no—
457Dic3—102no—
458C2×C5—46no—
459C2×C5C22×#23711yescharacteristic
460C2×C5C2×D3×#4111yescharacteristic
461C2×C5#596611yescharacteristic
462D5—62no—
463C23—151no—
464C23C23×D1516yes—
465Q8—306no—
466Q8—306no—
467Q8#681914yescomplemented
468D4—212no—
469D4—26no—
470D4—46no—
471D4—3012no—
472C2×C4—212no—
473C2×C4—151no—
474C2×C4—154no—
475C2×C4—152no—
476C2×C4—153no—
477C2×C4—153no—
478C2×C4—156no—
479C2×C4—3012no—
480C2×C4—306no—
481C2×C4—603no—
482C2×C4—606no—
483C2×C4C23×D1512yes—
484C2×C4C23×D1513yes—
485C2×C4C23×D1513yes—
486C2×C4C23×D1511yescharacteristic
487C2×C3—46no—
488C2×C3C22×#71111yescharacteristic
489C2×C3C2×D5×#4111yescharacteristic
490C2×C3#6628511yescharacteristic
491D3—102no—
492C5#8676711yescharacteristic, complemented, Sylow
493C22—26no—
494C22—26no—
495C22—26no—
496C22—152no—
497C22—301no—
498C22—301no—
499C22C24×D1511yescharacteristic
500C4—22no—
501C4—23no—
502C4—152no—
503C4—303no—
504C4—306no—
505C4—303no—
506C4—302no—
507C4C2×#681916yes—
508C4#41×D1512yes—
509C3#1061866811yescharacteristic, complemented, Sylow
510C2—46no—
511C2—302no—
512C2C22×#681911yescharacteristic
513C2C2×#41×D1511yescharacteristic
514C2#1175714811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D15
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C5×#550C2
hypercenter#550D15
hypocenterC3×C5#3480
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C3×C5×#550C2semidirect
2. #11756590C2semidirect
3. #41×Dic15C2semidirect
4. #11756475C2semidirect
5. #11756472C2semidirect
6. #11756373C2semidirect
7. #11756359C2semidirect
8. C4×Q8×D15C2semidirect
9. #11756329C2semidirect
10. #11756301C2semidirect
11. C4×#6819C2semidirect
48. C5×#550D3semidirect
96. C3×#550D5semidirect
144. C3×C5×Q8#41semidirect
163. C4×D15#41semidirect
241. #550D15semidirect
303. C5×Q8#237semidirect
366. C3×Q8#711semidirect
441. C3×C5#3480semidirect
467. Q8#6819semidirect
492. C5#86767semidirect
509. C3#10618668semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5502
#117565902
#41×Dic152
#117564752
#117564722
#117563732
#117563592
C4×Q8×D152
#117563292
#117563012
C4×#68192
#106186683
#867675