Finite Group Databasebeta

← #10617756⋊C3 #14514039

Subgroups — #10617756⋊C3 #14514039

Order 1920.

510 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C4×C5×#41⋊C3C211yesmaximal, characteristic, complemented
2#66165⋊C3C211yesmaximal, characteristic, complemented
3#66168⋊C3C211yesmaximal, characteristic, complemented
4#65910⋊C3C211yesmaximal, characteristic, complemented
5#65906⋊C3C211yesmaximal, characteristic, complemented
6#65903⋊C3C211yesmaximal, characteristic, complemented
7#65908⋊C3C211yesmaximal, characteristic, complemented
8#10617756C311yesmaximal, characteristic, complemented, Hall
9C2×C5×#41⋊C3C2211yescharacteristic
10C2×D5×SL(2,𝔽3)C2211yescharacteristic
11C2×C5⋊(#41⋊C3)C2211yescharacteristic
12C3×#4022—41nomaximal
13C4×C5×SL(2,𝔽3)C2211yescharacteristic
14C4×C5×SL(2,𝔽3)C2211yescharacteristic
15Dic5×SL(2,𝔽3)C2211yescharacteristic
16Dic5×SL(2,𝔽3)C2211yescharacteristic
17#3524⋊C3—51nomaximal, Hall
18C4×C5×#41C2×C311yescharacteristic, complemented
19#66168C2×C311yescharacteristic, complemented
20#66165C2×C311yescharacteristic
21#65910C2×C311yescharacteristic
22#65908C2×C311yescharacteristic, complemented
23#65906C2×C311yescharacteristic
24#65903C2×C311yescharacteristic, complemented
25#65896—31no—
26#65895—31no—
27#65893—31no—
28#65892—31no—
29#65866—31no—
30#65863—31no—
31#65813—31no—
32#65813—31no—
33C5×#41⋊C3—21no—
34C2×C5×SL(2,𝔽3)C2311yescharacteristic
35D5×SL(2,𝔽3)—21no—
36C5⋊(#41⋊C3)—21no—
37C3×C42×C5—41no—
38C3×#685—41no—
39C3×#685—41no—
40C3×#685—41no—
41C3×#683—41no—
42C3×#683—41no—
43C3×#683—41no—
44#557⋊C3—51no—
45C4⋊(#41⋊C3)—51no—
46#548⋊C3—51no—
47#548⋊C3—51no—
48#520⋊C3—51no—
49#519⋊C3—51no—
50C4×#41⋊C3D511yescharacteristic, complemented
51C2×C5×#41C22×C311yescharacteristic
52C2×#713C22×C311yescharacteristic
53C2×Q8×D5C22×C311yescharacteristic
54C4×C5×Q8C22×C311yescharacteristic
55C4×C5×Q8C22×C311yescharacteristic
56C4×C5×D4—31no—
57C4×C5×D4—31no—
58C5×#117—31no—
59C2×C42×C5—31no—
60Q8×Dic5C22×C311yescharacteristic
61Q8×Dic5C22×C311yescharacteristic
62#4086—31no—
63#4084—31no—
64#4084—31no—
65#4082—31no—
66#4076—31no—
67#4076—31no—
68#4075—32no—
69#4075—31no—
70#4075—31no—
71C4×C22⋊D5—32no—
72C4×C22⋊D5—31no—
73C4×C22⋊D5—31no—
74#4070—31no—
75#4070—31no—
76#4043—31no—
77#4041—31no—
78#4039—31no—
79#4038—31no—
80D5×C4⋊C4—31no—
81#4036—31no—
82#4034—31no—
83#4033—31no—
84#4031—32no—
85#4030—32no—
86#4029—32no—
87#4025—32no—
88#4022—31no—
89#4022A411yescharacteristic
90#4021—31no—
91#4021—31no—
92C4×D20—31no—
93C4×D20—31no—
94#4018—32no—
95#4018—31no—
96#4018—31no—
97#4016—31no—
98#4016—31no—
99C4×Dic10—31no—
100C4×Dic10—31no—
101#3524—51noSylow
102C22×C3×D5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×Dic5—41no—
107C2×C3×Dic5—41no—
108C2×C3×Dic5—41no—
109C5×SL(2,𝔽3)#4111yescharacteristic
110C2×#41⋊C3—51no—
111C2×#41⋊C3C2×D511yescharacteristic
112C22×SL(2,𝔽3)—51no—
113C3×#126—201no—
114C4×SL(2,𝔽3)—51no—
115C4×SL(2,𝔽3)—51no—
116C4×SL(2,𝔽3)C2×D511yescharacteristic
117C4×SL(2,𝔽3)C2×D511yescharacteristic
118C5×#41—21no—
119C5×#41—61no—
120C2×C5×Q8C23×C311yescharacteristic
121C2×C5×D4—31no—
122C22×C4×C5—31no—
123C22×C4×C5—31no—
124C22×C4×C5—31no—
125C2×C22⋊D5—32no—
126C2×C22⋊D5—31no—
127C2×C22⋊D5—31no—
128#713—21no—
129#713—61no—
130Q8×D5—21no—
131Q8×D5—61no—
132C2×D20—31no—
133C2×D20—31no—
134C2×C4×D5—31no—
135C2×C4×D5—31no—
136C2×C4×D5—32no—
137C2×Dic10—31no—
138C2×Dic10—31no—
139C5×C4⋊C4—31no—
140C5×C4⋊C4—31no—
141C5×C22⋊C4—32no—
142C42×C5—31no—
143C42×C5—31no—
144C42×C5—31no—
145C42×C5C2×A411yescharacteristic
146C22⋊Dic5—32no—
147C22⋊Dic5—31no—
148C22⋊Dic5—31no—
149#685—32no—
150#685—31no—
151#685—31no—
152#685—31no—
153#685—31no—
154#685—31no—
155#685C2×A411yescharacteristic
156#685C2×A411yescharacteristic
157#685C2×A411yescharacteristic
158C4⋊Dic5—31no—
159C4⋊Dic5—31no—
160C4⋊Dic5—31no—
161C4⋊Dic5—31no—
162#683—32no—
163#683—31no—
164#683—31no—
165#683—31no—
166#683—31no—
167#683—31no—
168#683C2×A411yescharacteristic
169#683C2×A411yescharacteristic
170#683C2×A411yescharacteristic
171C4×Dic5—32no—
172C4×Dic5—31no—
173C4×Dic5—31no—
174#559—151no—
175#557—51no—
176#555—151no—
177#553—151no—
178#552—151no—
179#550—51no—
180#548—51no—
181#548—51no—
182#542—151no—
183#540—151no—
184#529—151no—
185#529—151no—
186#520—51no—
187#519—51no—
188C4×#41C3×D511yescharacteristic, complemented
189C22×C3×C5—41no—
190C2×C3×D5—81no—
191C2×C3×D5—81no—
192C2×C3×D5—81no—
193C3×C4×C5—81no—
194C3×C4×C5—81no—
195C3×C4×C5—81no—
196C3×Dic5—81no—
197C3×Dic5—81no—
198C3×Dic5—81no—
199#41⋊C3—21no—
200#41⋊C3—101no—
201C2×SL(2,𝔽3)—101no—
202C2×SL(2,𝔽3)C22×D511yescharacteristic
203C3×C4⋊C4—201no—
204C3×C4⋊C4—201no—
205C3×C4⋊C4—201no—
206C3×C22⋊C4—201no—
207C3×C22⋊C4—201no—
208C3×C22⋊C4—201no—
209C3×C42—41no—
210C23×C5—31no—
211C22×D5—31no—
212C22×D5C22×A411yescharacteristic
213C5×Q8—31no—
214C5×Q8C3×#4111yescharacteristic
215C5×D4—61no—
216C5×D4—61no—
217C2×C4×C5—31no—
218C2×C4×C5—31no—
219C2×C4×C5—31no—
220C2×C4×C5—61no—
221C2×C4×C5—61no—
222C2×C4×C5—121no—
223C2×C4×C5—121no—
224C2×C4×C5C22×A411yescharacteristic
225C2×C4×C5C22×A411yescharacteristic
226C2×C4×C5C22×A411yescharacteristic
227C22⋊D5—121no—
228C22⋊D5—121no—
229C22⋊D5—122no—
230C2×Dic5—31no—
231C2×Dic5—31no—
232C2×Dic5—31no—
233C2×Dic5C22×A411yescharacteristic
234C2×Dic5C22×A411yescharacteristic
235C2×Dic5C22×A411yescharacteristic
236D20—61no—
237D20—61no—
238D20—121no—
239C4×D5—61no—
240C4×D5—61no—
241C4×D5—61no—
242C4×D5—61no—
243C4×D5—122no—
244Dic10—61no—
245Dic10—61no—
246Dic10—121no—
247C2×#41—51no—
248C2×#41C2×C3×D511yescharacteristic
249C22×Q8—51no—
250C4⋊Q8—151no—
251#127—151no—
252#126—51no—
253#126—152no—
254#126—151no—
255#125—151no—
256#125—151no—
257#125—151no—
258#124—151no—
259#124—151no—
260#124—152no—
261#124—151no—
262#123—152no—
263#123—151no—
264#123—151no—
265#123—152no—
266C22⋊Q8—151no—
267C22⋊Q8—151no—
268C22⋊Q8—151no—
269#121—152no—
270#121—151no—
271#121—151no—
272#121—151no—
273#121—151no—
274#121—151no—
275C4×Q8—51no—
276C4×Q8—51no—
277C4×Q8—151no—
278C4×Q8—151no—
279C4×Q8—151no—
280C4×Q8C2×C3×D511yescharacteristic
281C4×Q8C2×C3×D511yescharacteristic
282C4×D4—31no—
283C4×D4—31no—
284C4×D4—151no—
285C4×D4—151no—
286C4×D4—151no—
287C4×D4—151no—
288C4×D4—152no—
289C4×D4—151no—
290#117—31no—
291#117—151no—
292#117—151no—
293#117—152no—
294#117—151no—
295C2×C4⋊C4—151no—
296C2×C42—31no—
297C2×C3×C5—41no—
298C2×C3×C5—41no—
299C2×C3×C5—41no—
300C3×D5—161no—
301C23×C3—201no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—201no—
306C2×C3×C4—201no—
307C2×C3×C4—201no—
308SL(2,𝔽3)#70911yescharacteristic
309C22×C5—61no—
310C22×C5—61no—
311C22×C5—61no—
312C22×C5C23×A411yescharacteristic
313C2×D5—21no—
314C2×D5—21no—
315C2×D5—21no—
316C2×D5—61no—
317C2×D5—61no—
318C2×D5—61no—
319C4×C5—21no—
320C4×C5—21no—
321C4×C5—21no—
322C4×C5—31no—
323C4×C5—31no—
324C4×C5—61no—
325C4×C5—61no—
326Dic5—21no—
327Dic5—21no—
328Dic5—21no—
329Dic5—61no—
330Dic5—61no—
331Dic5—61no—
332#41—21no—
333#41—61no—
334#41—101no—
335#41—301no—
336C2×Q8—101no—
337C2×Q8—151no—
338C2×Q8—151no—
339C2×Q8—301no—
340C2×Q8C22×C3×D511yescharacteristic
341C2×D4—31no—
342C2×D4—151no—
343C2×D4—151no—
344C2×D4—151no—
345C2×D4—151no—
346C2×D4—152no—
347C22×C4—31no—
348C22×C4—31no—
349C22×C4—31no—
350C22×C4—151no—
351C22×C4—151no—
352C22×C4—152no—
353C4⋊C4—31no—
354C4⋊C4—31no—
355C4⋊C4—51no—
356C4⋊C4—51no—
357C4⋊C4—51no—
358C4⋊C4—151no—
359C4⋊C4—151no—
360C4⋊C4—151no—
361C4⋊C4—151no—
362C4⋊C4—151no—
363C4⋊C4—151no—
364C4⋊C4—152no—
365C4⋊C4—151no—
366C4⋊C4—151no—
367C4⋊C4—151no—
368C22⋊C4—32no—
369C22⋊C4—51no—
370C22⋊C4—51no—
371C22⋊C4—51no—
372C22⋊C4—151no—
373C22⋊C4—151no—
374C22⋊C4—152no—
375C22⋊C4—151no—
376C22⋊C4—151no—
377C22⋊C4—152no—
378C22⋊C4—151no—
379C22⋊C4—151no—
380C22⋊C4—151no—
381C42—31no—
382C42—31no—
383C42—31no—
384C42—151no—
385C42—151no—
386C42—152no—
387C42D5×A411yescharacteristic
388C3×C5—41noHall
389C22×C3—41no—
390C22×C3—401no—
391C22×C3—401no—
392C22×C3—401no—
393C3×C4—81no—
394C3×C4—81no—
395C3×C4—81no—
396C3×C4—401no—
397C3×C4—401no—
398C3×C4—401no—
399C2×C5—121no—
400C2×C5A4×#4111yescharacteristic
401C2×C5#594511yescharacteristic
402C2×C5#594511yescharacteristic
403D5—41no—
404D5—121no—
405C23—31no—
406C23—51no—
407C23—151no—
408Q8—31no—
409Q8—301no—
410Q8—301no—
411Q8—601no—
412Q8C3×#70911yescharacteristic
413D4—61no—
414D4—61no—
415D4—301no—
416D4—301no—
417D4—601no—
418D4—601no—
419D4—601no—
420D4—602no—
421C2×C4—31no—
422C2×C4—31no—
423C2×C4—31no—
424C2×C4—51no—
425C2×C4—51no—
426C2×C4—51no—
427C2×C4—61no—
428C2×C4—61no—
429C2×C4—121no—
430C2×C4—121no—
431C2×C4—151no—
432C2×C4—151no—
433C2×C4—151no—
434C2×C4—301no—
435C2×C4—301no—
436C2×C4—301no—
437C2×C4—301no—
438C2×C4—602no—
439C2×C4C2×D5×A411yescharacteristic
440C2×C4C2×D5×A411yescharacteristic
441C2×C4C2×D5×A411yescharacteristic
442C2×C3—41no—
443C2×C3—41no—
444C2×C3—41no—
445C2×C3—801no—
446C5#3524⋊C311yescharacteristic, complemented, Sylow
447C22—61no—
448C22—61no—
449C22—61no—
450C22—101no—
451C22—101no—
452C22—101no—
453C22—301no—
454C22—301no—
455C22—301no—
456C22C22×D5×A411yescharacteristic
457C4—21no—
458C4—21no—
459C4—21no—
460C4—31no—
461C4—31no—
462C4—61no—
463C4—61no—
464C4—101no—
465C4—101no—
466C4—101no—
467C4—301no—
468C4—301no—
469C4—301no—
470C3—41noSylow
471C2—121no—
472C2—201no—
473C2—601no—
474C2A4×#70911yescharacteristic
475C2#66283⋊C311yescharacteristic
476C2#66283⋊C311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, cosocleC2×C5×Q8C23×C3
FittingC4×C5×#41C2×C3
socleC22×C5C23×A4
hypercenterC42D5×A4
hypocenterC5×Q8C3×#41
LCSG ▷ C2×C5×Q8 ▷ C5×Q8
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C4×C5×#41⋊C3C2semidirect
2. #66165⋊C3C2semidirect
3. #66168⋊C3C2semidirect
4. #65910⋊C3C2semidirect
5. #65906⋊C3C2semidirect
6. #65903⋊C3C2semidirect
7. #65908⋊C3C2semidirect
8. #10617756C3semidirect
18. C4×C5×#41C2×C3semidirect
19. #66168C2×C3semidirect
22. #65908C2×C3semidirect
24. #65903C2×C3semidirect
50. C4×#41⋊C3D5semidirect
188. C4×#41C3×D5semidirect
446. C5#3524⋊C3semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#41⋊C32
#66165⋊C32
#66168⋊C32
#65910⋊C32
#65906⋊C32
#65903⋊C32
#65908⋊C32
#106177563
C3×#40224
#3524⋊C35