Finite Group Databasebeta

← #10617780⋊C3 #14514043

Subgroups — #10617780⋊C3 #14514043

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
1C5×#519⋊C3C211yesmaximal, characteristic, complemented
2#66151⋊C3C211yesmaximal, characteristic, complemented
3#66151⋊C3C211yesmaximal, characteristic, complemented
4C4⋊(C5⋊(#41⋊C3))C211yesmaximal, characteristic, complemented
5#65903⋊C3C211yesmaximal, characteristic, complemented
6#65908⋊C3C211yesmaximal, characteristic, complemented
7C4×C5⋊(#41⋊C3)C211yesmaximal, characteristic, complemented
8#10617780C311yesmaximal, characteristic, complemented, Hall
9C22×C5×SL(2,𝔽3)C2211yescharacteristic
10C2×C5⋊(#41⋊C3)C2211yescharacteristic
11C2×C5⋊(#41⋊C3)C2211yescharacteristic
12C3×#4025—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
18C5×#519C2×C311yescharacteristic
19#66151C2×C311yescharacteristic
20#66151C2×C311yescharacteristic
21#65919—31no—
22#65916—31no—
23#65915—31no—
24#65914—31no—
25#65911C2×C311yescharacteristic, complemented
26#65908C2×C311yescharacteristic, complemented
27C4×#713C2×C311yescharacteristic, complemented
28#65903C2×C311yescharacteristic, complemented
29#65869—31no—
30#65866—31no—
31#65864—31no—
32#65862—31no—
33C2×C5×SL(2,𝔽3)—21no—
34C2×C5×SL(2,𝔽3)C2311yescharacteristic
35C5⋊(#41⋊C3)—21no—
36C5⋊(#41⋊C3)—21no—
37C3×C5×C22⋊C4—41no—
38C3×C22⋊Dic5—41no—
39C3×C22⋊Dic5—41no—
40C3×C4⋊Dic5—41no—
41C3×#683—41no—
42C3×#683—41no—
43C3×C4×Dic5—41no—
44#557⋊C3—51no—
45C4⋊(#41⋊C3)—51no—
46#548⋊C3—51no—
47#548⋊C3—51no—
48#520⋊C3—51no—
49#519⋊C3D511yescharacteristic, complemented
50C4×#41⋊C3—51no—
51C22×C5×Q8C22×C311yescharacteristic
52C2×#713C22×C311yescharacteristic
53C2×#713C22×C311yescharacteristic
54C4×C5×Q8—31no—
55C4×C5×Q8—31no—
56C4×C5×Q8C22×C311yescharacteristic
57C4×C5×Q8C22×C311yescharacteristic
58C5×#117—31no—
59C5×#117—31no—
60#4093—31no—
61#4093—31no—
62#4092—31no—
63#4092—31no—
64Q8×Dic5C22×C311yescharacteristic
65Q8×Dic5C22×C311yescharacteristic
66#4076—31no—
67#4076—31no—
68C4×C22⋊D5—31no—
69C4×C22⋊D5—31no—
70#4044—31no—
71#4042—31no—
72#4041—31no—
73#4041—31no—
74#4040—32no—
75#4040—32no—
76#4040—31no—
77#4039—31no—
78#4039—31no—
79#4038—31no—
80D5×C4⋊C4—31no—
81#4036—31no—
82#4035—31no—
83#4034—31no—
84#4031—31no—
85#4030—32no—
86#4030—31no—
87#4029—31no—
88#4025A411yescharacteristic
89#4022—32no—
90#4021—32no—
91#4020—31no—
92C4×D20—32no—
93C4×D20—31no—
94C4×D20—31no—
95C4×D20—31no—
96#4018—32no—
97#4018—31no—
98C42×D5—31no—
99#4016—31no—
100C4×Dic10—31no—
101#3524—51noSylow
102C23×C3×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×Dic5—41no—
106C2×C3×Dic5—41no—
107C2×C3×Dic5—41no—
108C2×C3×Dic5—41no—
109C5×SL(2,𝔽3)#4111yescharacteristic
110C2×#41⋊C3—51no—
111C2×#41⋊C3—51no—
112C22×SL(2,𝔽3)C2×D511yescharacteristic
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
118C2×C5×Q8—21no—
119C2×C5×Q8—31no—
120C2×C5×Q8—61no—
121C2×C5×Q8C23×C311yescharacteristic
122C22×C4×C5—31no—
123C2×C22⋊D5—31no—
124C2×C22⋊D5—31no—
125#713—21no—
126#713—21no—
127#713—61no—
128#713—61no—
129C2×D20—31no—
130C2×D20—31no—
131C2×D20—32no—
132C2×D20—31no—
133C2×C4×D5—31no—
134C2×C4×D5—31no—
135C2×C4×D5—32no—
136C2×C4×D5—31no—
137C2×C4×D5—31no—
138C2×Dic10—31no—
139C5×C4⋊C4—31no—
140C5×C4⋊C4—31no—
141C5×C4⋊C4—31no—
142C5×C4⋊C4—31no—
143C5×C22⋊C4—31no—
144C5×C22⋊C4C2×A411yescharacteristic
145C42×C5—32no—
146C42×C5—31no—
147C42×C5—31no—
148C22⋊Dic5C2×A411yescharacteristic
149C22⋊Dic5C2×A411yescharacteristic
150#685—32no—
151#685—32no—
152#685—32no—
153#685—31no—
154#685—31no—
155#685—31no—
156#685—31no—
157#685—31no—
158#685—31no—
159C4⋊Dic5—31no—
160C4⋊Dic5—31no—
161C4⋊Dic5—31no—
162C4⋊Dic5C2×A411yescharacteristic
163#683—32no—
164#683—31no—
165#683—31no—
166#683—31no—
167#683—31no—
168#683C2×A411yescharacteristic
169#683C2×A411yescharacteristic
170C4×Dic5—31no—
171C4×Dic5—31no—
172C4×Dic5—31no—
173C4×Dic5C2×A411yescharacteristic
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#519C3×D511yescharacteristic
188C4×#41—51no—
189C22×C3×C5—41no—
190C22×C3×C5—81no—
191C22×C3×C5—81no—
192C22×C3×C5—81no—
193C3×C4×C5—81no—
194C3×C4×C5—81no—
195C3×Dic5—81no—
196C3×Dic5—81no—
197C3×Dic5—81no—
198C3×Dic5—81no—
199#41⋊C3—101no—
200#41⋊C3—101no—
201C2×SL(2,𝔽3)—21no—
202C2×SL(2,𝔽3)C22×D511yescharacteristic
203C3×C4⋊C4—201no—
204C3×C4⋊C4—201no—
205C3×C4⋊C4—201no—
206C3×C22⋊C4—41no—
207C3×C22⋊C4—201no—
208C3×C22⋊C4—201no—
209C3×C42—201no—
210C23×C5C22×A411yescharacteristic
211C22×D5—31no—
212C22×D5—31no—
213C5×Q8—31no—
214C5×Q8—61no—
215C5×Q8—61no—
216C5×Q8C3×#4111yescharacteristic
217C2×C4×C5—31no—
218C2×C4×C5—31no—
219C2×C4×C5—31no—
220C2×C4×C5—31no—
221C2×C4×C5—61no—
222C2×C4×C5—61no—
223C2×C4×C5C22×A411yescharacteristic
224C2×C4×C5C22×A411yescharacteristic
225C22⋊D5—121no—
226C22⋊D5—121no—
227C2×Dic5—31no—
228C2×Dic5—31no—
229C2×Dic5C22×A411yescharacteristic
230C2×Dic5C22×A411yescharacteristic
231C2×Dic5C22×A411yescharacteristic
232C2×Dic5C22×A411yescharacteristic
233D20—61no—
234D20—61no—
235D20—61no—
236D20—61no—
237D20—121no—
238D20—122no—
239C4×D5—61no—
240C4×D5—61no—
241C4×D5—61no—
242C4×D5—61no—
243C4×D5—121no—
244C4×D5—121no—
245C4×D5—122no—
246Dic10—121no—
247C2×#41—51no—
248C2×#41—51no—
249C22×Q8C2×C3×D511yescharacteristic
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—152no—
259#124—151no—
260#124—151no—
261#124—151no—
262#123—151no—
263#123—151no—
264#123—152no—
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—31no—
276C4×Q8—31no—
277C4×Q8—51no—
278C4×Q8—51no—
279C4×Q8—151no—
280C4×Q8C2×C3×D511yescharacteristic
281C4×Q8C2×C3×D511yescharacteristic
282C4×D4—151no—
283C4×D4—152no—
284C4×D4—151no—
285C4×D4—151no—
286C4×D4—151no—
287C4×D4—151no—
288C4×D4—151no—
289C4×D4—151no—
290#117—31no—
291#117—31no—
292#117—151no—
293#117—152no—
294#117—151no—
295C2×C4⋊C4—151no—
296C2×C42—151no—
297C2×C3×C5—41no—
298C2×C3×C5—41no—
299C2×C3×C5—41no—
300C2×C3×C5—161no—
301C23×C3—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—201no—
305C2×C3×C4—201no—
306C2×C3×C4—201no—
307C2×C3×C4—201no—
308SL(2,𝔽3)#70911yescharacteristic
309C22×C5—21no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5C23×A411yescharacteristic
313C2×D5—61no—
314C2×D5—61no—
315C2×D5—61no—
316C2×D5—61no—
317C2×D5—61no—
318C2×D5—61no—
319C4×C5—21no—
320C4×C5—21no—
321C4×C5—31no—
322C4×C5—31no—
323C4×C5—61no—
324C4×C5—61no—
325C4×C5—61no—
326Dic5—21no—
327Dic5—21no—
328Dic5—21no—
329Dic5—21no—
330Dic5—61no—
331Dic5—61no—
332#41—101no—
333#41—101no—
334#41—301no—
335#41—301no—
336C2×Q8—21no—
337C2×Q8—31no—
338C2×Q8—61no—
339C2×Q8—151no—
340C2×Q8C22×C3×D511yescharacteristic
341C2×D4—151no—
342C2×D4—151no—
343C2×D4—152no—
344C2×D4—151no—
345C2×D4—151no—
346C2×D4—151no—
347C22×C4—31no—
348C22×C4—151no—
349C22×C4—151no—
350C22×C4—151no—
351C22×C4—152no—
352C22×C4—151no—
353C4⋊C4—31no—
354C4⋊C4—31no—
355C4⋊C4—31no—
356C4⋊C4—31no—
357C4⋊C4—51no—
358C4⋊C4—51no—
359C4⋊C4—51no—
360C4⋊C4—151no—
361C4⋊C4—151no—
362C4⋊C4—151no—
363C4⋊C4—151no—
364C4⋊C4—151no—
365C4⋊C4—151no—
366C4⋊C4—152no—
367C4⋊C4—151no—
368C22⋊C4—31no—
369C22⋊C4—51no—
370C22⋊C4—51no—
371C22⋊C4—151no—
372C22⋊C4—151no—
373C22⋊C4—151no—
374C22⋊C4—151no—
375C22⋊C4—151no—
376C22⋊C4—152no—
377C22⋊C4—152no—
378C22⋊C4—152no—
379C22⋊C4—151no—
380C22⋊C4D5×A411yescharacteristic
381C42—32no—
382C42—31no—
383C42—31no—
384C42—51no—
385C42—151no—
386C42—151no—
387C42—151no—
388C3×C5—41noHall
389C22×C3—41no—
390C22×C3—81no—
391C22×C3—81no—
392C22×C3—81no—
393C3×C4—81no—
394C3×C4—81no—
395C3×C4—401no—
396C3×C4—401no—
397C3×C4—401no—
398C3×C4—401no—
399C2×C5—41no—
400C2×C5A4×#4111yescharacteristic
401C2×C5#594511yescharacteristic
402C2×C5#594511yescharacteristic
403D5—121no—
404D5—121no—
405C23—151no—
406C23—151no—
407C23C2×D5×A411yescharacteristic
408Q8—31no—
409Q8—61no—
410Q8—61no—
411Q8—601no—
412Q8C3×#70911yescharacteristic
413D4—301no—
414D4—301no—
415D4—301no—
416D4—301no—
417D4—601no—
418D4—602no—
419D4—601no—
420D4—601no—
421C2×C4—31no—
422C2×C4—31no—
423C2×C4—31no—
424C2×C4—31no—
425C2×C4—51no—
426C2×C4—51no—
427C2×C4—51no—
428C2×C4—51no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—151no—
432C2×C4—151no—
433C2×C4—301no—
434C2×C4—301no—
435C2×C4—301no—
436C2×C4—301no—
437C2×C4—601no—
438C2×C4—601no—
439C2×C4—602no—
440C2×C4C2×D5×A411yescharacteristic
441C2×C4C2×D5×A411yescharacteristic
442C2×C3—41no—
443C2×C3—41no—
444C2×C3—41no—
445C2×C3—161no—
446C5#3524⋊C311yescharacteristic, complemented, Sylow
447C22—21no—
448C22—21no—
449C22—21no—
450C22—301no—
451C22—301no—
452C22—301no—
453C22—301no—
454C22—301no—
455C22—301no—
456C22C22×D5×A411yescharacteristic
457C4—21no—
458C4—21no—
459C4—31no—
460C4—31no—
461C4—61no—
462C4—61no—
463C4—61no—
464C4—101no—
465C4—101no—
466C4—101no—
467C4—101no—
468C4—301no—
469C4—301no—
470C3—41noSylow
471C2—41no—
472C2—601no—
473C2—601no—
474C2A4×#70911yescharacteristic
475C2#66287⋊C311yescharacteristic
476C2#66287⋊C311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, cosocleC2×C5×Q8C23×C3
FittingC5×#519C2×C3
socleC22×C5C23×A4
hypercenterC22⋊C4D5×A4
hypocenterC5×Q8C3×#41
LCSG ▷ C2×C5×Q8 ▷ C5×Q8
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C5×#519⋊C3C2semidirect
2. #66151⋊C3C2semidirect
3. #66151⋊C3C2semidirect
4. C4⋊(C5⋊(#41⋊C3))C2semidirect
5. #65903⋊C3C2semidirect
6. #65908⋊C3C2semidirect
7. C4×C5⋊(#41⋊C3)C2semidirect
8. #10617780C3semidirect
25. #65911C2×C3semidirect
26. #65908C2×C3semidirect
27. C4×#713C2×C3semidirect
28. #65903C2×C3semidirect
49. #519⋊C3D5semidirect
446. C5#3524⋊C3semidirect

Maximal subgroups

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

subgroupindex
C5×#519⋊C32
#66151⋊C32
C4⋊(C5⋊(#41⋊C3))2
#65903⋊C32
#65908⋊C32
C4×C5⋊(#41⋊C3)2
#106177803
C3×#40254
#3524⋊C35