Finite Group Databasebeta

← D5×#568⋊C3 #14514148

Subgroups — D5×#568⋊C3 #14514148

Order 1920.

690 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#41⋊C3C211yesmaximal, characteristic
2C5×#568⋊C3C211yesmaximal, characteristic, complemented
3#66153⋊C3C211yesmaximal, characteristic, complemented
4#66084⋊C3C212yesmaximal, complemented
5D5×#131⋊C3C212yesmaximal, complemented
6D5×#568C311yesmaximal, characteristic, complemented, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8D5×#41⋊C3C411yescharacteristic
9D5×#41⋊C3C411yescharacteristic
10D5×#41⋊C3C2211yescharacteristic
11D5×#41⋊C3C2211yescharacteristic
12C2×D5×SL(2,𝔽3)C411yescharacteristic
13C2×C5⋊(#41⋊C3)C411yescharacteristic
14C3×D5×M16—41nomaximal
15C5×#131⋊C3C2212yescomplemented
16#4094⋊C3C2212yescomplemented
17C2×#568⋊C3—51nomaximal, Hall
18C2×D5×#41C2×C311yescharacteristic
19C5×#568C2×C311yescharacteristic, complemented
20#66153C2×C311yescharacteristic, complemented
21#66084—32no—
22#66084C2×C312yescomplemented
23D5×#131—32no—
24D5×#131C2×C312yescomplemented
25#66079—31no—
26#66079—31no—
27C2×D5×M16—31no—
28C2×D5×M16—31no—
29C2×C3×C4×D5—41no—
30C5×#41⋊C3C2×C411yescharacteristic
31C5×#41⋊C3C2311yescharacteristic
32C2×C5×SL(2,𝔽3)C2×C411yescharacteristic
33D5×SL(2,𝔽3)C2×C411yescharacteristic
34D5×SL(2,𝔽3)C2×C411yescharacteristic
35C5⋊(#41⋊C3)C2×C411yescharacteristic
36C5⋊(#41⋊C3)C2×C411yescharacteristic
37C3×C5×M16—41no—
38C3×#681—41no—
39C3×#676—42no—
40C3×C8×D5—42no—
41C22×#41⋊C3—51no—
42#568⋊C3—51no—
43#568⋊C3—52no—
44#568⋊C3D511yescharacteristic, direct product factor
45C2×#131⋊C3—52no—
46C2×C5×#41C22×C311yescharacteristic
47D5×#41—31no—
48D5×#41—31no—
49D5×#41—31no—
50D5×#41—31no—
51D5×#41C3×C411yescharacteristic
52D5×#41C3×C411yescharacteristic
53D5×#41C22×C311yescharacteristic
54D5×#41C22×C311yescharacteristic
55C2×#713C3×C411yescharacteristic
56C2×Q8×D5C3×C411yescharacteristic
57C2×#711—31no—
58C2×D4×D5—31no—
59C2×#709—31no—
60C22×C4×D5—31no—
61C5×#131—32no—
62C5×#131C22×C312yescomplemented
63C2×C5×M16—31no—
64C2×C5×M16—31no—
65#4094—32no—
66#4094C22×C312yescomplemented
67C2×#681—31no—
68C2×#681—31no—
69#4053—34no—
70#4053—32no—
71#4053—32no—
72D5×M16—32no—
73D5×M16—31no—
74D5×M16—31no—
75D5×M16—31no—
76D5×M16—32no—
77D5×M16—32no—
78D5×M16—32no—
79D5×M16—32no—
80D5×M16A411yescharacteristic
81#4047—34no—
82#4047—32no—
83#4047—32no—
84C2×#676—32no—
85C2×#676—32no—
86C2×C8×D5—32no—
87C2×C8×D5—32no—
88C2×#568—51noSylow
89C22×C3×D5—41no—
90C2×C3×C4×C5—41no—
91C2×C3×Dic5—41no—
92C3×C4×D5—41no—
93C3×C4×D5—41no—
94C3×C4×D5—41no—
95C3×C4×D5—41no—
96C5×SL(2,𝔽3)C22×C411yescharacteristic
97C3×C5×C8—42no—
98C3×#168—42no—
99C2×#41⋊C3—51no—
100C2×#41⋊C3—51no—
101C2×#41⋊C3—51no—
102C2×#41⋊C3—51no—
103C2×#41⋊C3—51no—
104C2×#41⋊C3C2×D511yescharacteristic
105C22×SL(2,𝔽3)—51no—
106C2×C3×M16—201no—
107#131⋊C3—52no—
108#131⋊C3C2×D512yescomplemented
109C23×D5—31no—
110C5×#41—31no—
111C5×#41—31no—
112C5×#41C2×C3×C411yescharacteristic
113C5×#41C23×C311yescharacteristic
114C2×C5×Q8C2×C3×C411yescharacteristic
115C2×C5×D4—31no—
116C22×C4×C5—31no—
117C2×C22⋊D5—32no—
118C22×Dic5—31no—
119#713—31no—
120#713—31no—
121#713C2×C3×C411yescharacteristic
122#713C2×C3×C411yescharacteristic
123Q8×D5—31no—
124Q8×D5—31no—
125Q8×D5C2×C3×C411yescharacteristic
126Q8×D5C2×C3×C411yescharacteristic
127#711—32no—
128#711—32no—
129#711—31no—
130#711—31no—
131#711—31no—
132#711—31no—
133D4×D5—31no—
134D4×D5—31no—
135D4×D5—31no—
136D4×D5—31no—
137D4×D5—32no—
138D4×D5—32no—
139#709—32no—
140#709—32no—
141#709—31no—
142#709—31no—
143#709—31no—
144#709—31no—
145C2×D20—31no—
146C2×C4×D5—31no—
147C2×C4×D5—31no—
148C2×C4×D5—31no—
149C2×C4×D5—31no—
150C2×C4×D5—31no—
151C2×C4×D5—31no—
152C2×C4×D5—31no—
153C2×C4×D5—31no—
154C2×C4×D5—31no—
155C2×C4×D5—31no—
156C2×C4×D5—31no—
157C2×C4×D5C2×A411yescharacteristic
158C2×Dic10—31no—
159C5×M16—31no—
160C5×M16—32no—
161C5×M16—32no—
162C5×M16C2×A411yescharacteristic
163C2×C5×C8—32no—
164C2×C5×C8—32no—
165#681—31no—
166#681—32no—
167#681—32no—
168#681C2×A411yescharacteristic
169C2×#168—32no—
170C2×#168—32no—
171#676—34no—
172#676—32no—
173#676—32no—
174#676—32no—
175#676C2×A412yes—
176C8×D5—34no—
177C8×D5—32no—
178C8×D5—32no—
179C8×D5—32no—
180C8×D5C2×A412yes—
181C22×#41—51no—
182#568—51no—
183#568—52no—
184#568—151no—
185#568—151no—
186#568—152no—
187#568C3×D511yescharacteristic, complemented
188C2×#131—52no—
189C2×#131—152no—
190C22×M16—151no—
191C22×M16—151no—
192C22×C3×C5—41no—
193C2×C3×D5—41no—
194C2×C3×D5—41no—
195C2×C3×D5—82no—
196C3×C4×C5—41no—
197C3×C4×C5—41no—
198C3×Dic5—41no—
199C3×Dic5—41no—
200C22×C3×C4—201no—
201#41⋊C3—51no—
202#41⋊C3—51no—
203#41⋊C3C4×D511yescharacteristic
204#41⋊C3C22×D511yescharacteristic
205C2×SL(2,𝔽3)—51no—
206C2×SL(2,𝔽3)—51no—
207C2×SL(2,𝔽3)C4×D511yescharacteristic
208C3×M16—41no—
209C3×M16—202no—
210C3×M16—201no—
211C2×C3×C8—202no—
212C23×C5—31no—
213C22×D5—31no—
214C22×D5—31no—
215C22×D5—31no—
216C22×D5—31no—
217C22×D5—31no—
218C22×D5—122no—
219C22×D5C4×A411yescharacteristic
220C5×Q8—31no—
221C5×Q8C22×C3×C411yescharacteristic
222C5×D4—31no—
223C5×D4—31no—
224C5×D4—32no—
225C2×C4×C5—31no—
226C2×C4×C5—31no—
227C2×C4×C5—31no—
228C2×C4×C5—31no—
229C2×C4×C5—31no—
230C2×C4×C5C22×A411yescharacteristic
231C22⋊D5—32no—
232C22⋊D5—32no—
233C22⋊D5—32no—
234C22⋊D5—32no—
235C2×Dic5—31no—
236C2×Dic5—31no—
237C2×Dic5—31no—
238C2×Dic5—31no—
239C2×Dic5—31no—
240C2×Dic5C4×A411yescharacteristic
241D20—31no—
242D20—31no—
243D20—32no—
244C4×D5—31no—
245C4×D5—31no—
246C4×D5—31no—
247C4×D5—31no—
248C4×D5—31no—
249C4×D5—31no—
250C4×D5—31no—
251C4×D5—31no—
252C4×D5—31no—
253C4×D5—31no—
254C4×D5—31no—
255C4×D5—31no—
256C4×D5C4×A411yescharacteristic
257C4×D5C4×A411yescharacteristic
258C4×D5C22×A411yescharacteristic
259C4×D5C22×A411yescharacteristic
260Dic10—32no—
261Dic10—31no—
262Dic10—31no—
263C5×C8—32no—
264C5×C8C22×A412yes—
265#168—32no—
266#168C22×A412yes—
267C2×#41—51no—
268C2×#41—51no—
269C2×#41—51no—
270C2×#41—51no—
271C2×#41—51no—
272C2×#41—151no—
273C2×#41—151no—
274C2×#41—151no—
275C2×#41—151no—
276C2×#41—151no—
277C2×#41—151no—
278C2×#41C2×C3×D511yescharacteristic
279C22×Q8—51no—
280C22×D4—151no—
281C23×C4—151no—
282#131—32no—
283#131—52no—
284#131—154no—
285#131—152no—
286#131—152no—
287#131—154no—
288#131—152no—
289#131—152no—
290#131—152no—
291#131C2×C3×D512yescomplemented
292C2×M16—31no—
293C2×M16—31no—
294C2×M16—51no—
295C2×M16—152no—
296C2×M16—152no—
297C2×M16—152no—
298C2×M16—151no—
299C2×M16—152no—
300C2×M16—151no—
301C2×M16—152no—
302C2×M16—152no—
303C2×M16—151no—
304C2×M16—151no—
305C2×M16—151no—
306C2×M16—152no—
307C22×C8—152no—
308C22×C8—152no—
309C2×C3×C5—41no—
310C2×C3×C5—81no—
311C3×D5—42no—
312C3×D5—81no—
313C23×C3—201no—
314C2×C3×C4—41no—
315C2×C3×C4—201no—
316C2×C3×C4—201no—
317C2×C3×C4—201no—
318C2×C3×C4—201no—
319C2×C3×C4—201no—
320SL(2,𝔽3)C2×C4×D511yescharacteristic
321C3×C8—42no—
322C3×C8—202no—
323C22×C5—31no—
324C22×C5—31no—
325C22×C5—121no—
326C22×C5C2×C4×A411yescharacteristic
327C2×D5—22no—
328C2×D5—31no—
329C2×D5—31no—
330C2×D5—62no—
331C2×D5—62no—
332C2×D5—121no—
333C2×D5—121no—
334C2×D5—121no—
335C2×D5C2×C4×A411yescharacteristic
336C2×D5C2×C4×A411yescharacteristic
337C4×C5—31no—
338C4×C5—31no—
339C4×C5C2×C4×A411yescharacteristic
340C4×C5C23×A411yescharacteristic
341Dic5—31no—
342Dic5—31no—
343Dic5C2×C4×A411yescharacteristic
344Dic5C2×C4×A411yescharacteristic
345C24—151no—
346#41—31no—
347#41—31no—
348#41—51no—
349#41—51no—
350#41—152no—
351#41—152no—
352#41—151no—
353#41—151no—
354#41—151no—
355#41—151no—
356#41—152no—
357#41—152no—
358#41—151no—
359#41—151no—
360#41—151no—
361#41—151no—
362#41—151no—
363#41—151no—
364#41C3×C4×D511yescharacteristic
365#41C22×C3×D511yescharacteristic
366C2×Q8—51no—
367C2×Q8—51no—
368C2×Q8—151no—
369C2×Q8—151no—
370C2×Q8—151no—
371C2×Q8C3×C4×D511yescharacteristic
372C2×D4—31no—
373C2×D4—151no—
374C2×D4—151no—
375C2×D4—151no—
376C2×D4—151no—
377C2×D4—151no—
378C2×D4—152no—
379C2×D4—152no—
380C2×D4—152no—
381C22×C4—31no—
382C22×C4—51no—
383C22×C4—151no—
384C22×C4—151no—
385C22×C4—151no—
386C22×C4—151no—
387C22×C4—151no—
388C22×C4—151no—
389C22×C4—151no—
390C22×C4—151no—
391C22×C4—151no—
392C22×C4—151no—
393C22×C4—151no—
394C22×C4—151no—
395M16—31no—
396M16—32no—
397M16—32no—
398M16—51no—
399M16—52no—
400M16—152no—
401M16—152no—
402M16—154no—
403M16—152no—
404M16—151no—
405M16—152no—
406M16—152no—
407M16D5×A411yescharacteristic
408C2×C8—32no—
409C2×C8—32no—
410C2×C8—52no—
411C2×C8—152no—
412C2×C8—152no—
413C2×C8—154no—
414C2×C8—152no—
415C2×C8—152no—
416C2×C8—152no—
417C3×C5—41noHall
418C22×C3—41no—
419C22×C3—201no—
420C22×C3—201no—
421C22×C3—402no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4—201no—
425C3×C4—201no—
426C2×C5—21no—
427C2×C5—61no—
428C2×C5—61no—
429C2×C5C22×C4×A411yescharacteristic
430D5—21no—
431D5—61no—
432D5—61no—
433D5#568⋊C312yesdirect product factor
434C23—31no—
435C23—51no—
436C23—151no—
437C23—151no—
438C23—151no—
439C23—151no—
440C23—151no—
441C23—602no—
442Q8—31no—
443Q8—151no—
444Q8—151no—
445Q8—152no—
446Q8C2×C3×C4×D511yescharacteristic
447D4—31no—
448D4—31no—
449D4—32no—
450D4—151no—
451D4—151no—
452D4—152no—
453D4—152no—
454D4—152no—
455D4—152no—
456D4—152no—
457C2×C4—31no—
458C2×C4—31no—
459C2×C4—31no—
460C2×C4—31no—
461C2×C4—31no—
462C2×C4—51no—
463C2×C4—51no—
464C2×C4—51no—
465C2×C4—51no—
466C2×C4—51no—
467C2×C4—151no—
468C2×C4—151no—
469C2×C4—151no—
470C2×C4—151no—
471C2×C4—151no—
472C2×C4—151no—
473C2×C4—151no—
474C2×C4—151no—
475C2×C4—151no—
476C2×C4—151no—
477C2×C4—151no—
478C2×C4—151no—
479C2×C4—151no—
480C2×C4—151no—
481C2×C4—151no—
482C2×C4—151no—
483C2×C4—151no—
484C2×C4C2×D5×A411yescharacteristic
485C8—32no—
486C8—52no—
487C8—152no—
488C8C2×D5×A412yes—
489C2×C3—41no—
490C2×C3—81no—
491C2×C3—202no—
492C2×C3—401no—
493C5C2×#568⋊C311yescharacteristic, complemented, Sylow
494C22—31no—
495C22—31no—
496C22—51no—
497C22—51no—
498C22—102no—
499C22—121no—
500C22—151no—
501C22—151no—
502C22—302no—
503C22—302no—
504C22—601no—
505C22—601no—
506C22—601no—
507C22C4×D5×A411yescharacteristic
508C4—31no—
509C4—31no—
510C4—51no—
511C4—51no—
512C4—151no—
513C4—151no—
514C4C4×D5×A411yescharacteristic
515C4C22×D5×A411yescharacteristic
516C3—41noSylow
517C2—21no—
518C2—52no—
519C2—61no—
520C2—61no—
521C2—101no—
522C2—301no—
523C2—301no—
524C2C2×C4×D5×A411yescharacteristic
subgroupG/H
center, FrattiniC4C22×D5×A4
commutator, hypocenterC5×Q8C22×C3×C4
FittingC5×#568C2×C3
socleC2×C5C22×C4×A4
prime radicalC2×D5×#41⋊C3C2
cosocleC5×#41C23×C3
hypercenterM16D5×A4
LCSG ▷ C5×Q8
UCSC1 ◁ C4 ◁ M16

Complements

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

NH ≅ G/Ntype
2. C5×#568⋊C3C2semidirect
3. #66153⋊C3C2semidirect
4. #66084⋊C3C2semidirect
5. D5×#131⋊C3C2semidirect
6. D5×#568C3semidirect
15. C5×#131⋊C3C22semidirect
16. #4094⋊C3C22semidirect
19. C5×#568C2×C3semidirect
20. #66153C2×C3semidirect
22. #66084C2×C3semidirect
24. D5×#131C2×C3semidirect
44. #568⋊C3D5direct (N × H)
62. C5×#131C22×C3semidirect
66. #4094C22×C3semidirect
108. #131⋊C3C2×D5semidirect
187. #568C3×D5semidirect
291. #131C2×C3×D5semidirect
433. D5#568⋊C3direct (N × H)
493. C5C2×#568⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#41⋊C32
C5×#568⋊C32
#66153⋊C32
#66084⋊C32
D5×#131⋊C32
D5×#5683
C3×D5×M164
C2×#568⋊C35