Finite Group Databasebeta

← #10617785⋊C3 #14514048

Subgroups — #10617785⋊C3 #14514048

Order 1920.

554 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 79 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
2SL(2,𝔽3)×C22⋊D5C211yesmaximal, characteristic, complemented
3SL(2,𝔽3)×C22⋊D5C211yesmaximal, characteristic, complemented
4#65906⋊C3C211yesmaximal, characteristic, complemented
5SL(2,𝔽3)×D20C211yesmaximal, characteristic, complemented
6C4×D5×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
7#65903⋊C3C211yesmaximal, characteristic, complemented
8#10617785C311yesmaximal, characteristic, complemented, Hall
9C22×C5×SL(2,𝔽3)C2211yescharacteristic
10C2×D5×SL(2,𝔽3)C2211yescharacteristic
11C2×D5×SL(2,𝔽3)C2211yescharacteristic
12C3×#4030—41nomaximal
13C4×C5×SL(2,𝔽3)C2211yescharacteristic
14C4×C5×SL(2,𝔽3)C2211yescharacteristic
15Dic5×SL(2,𝔽3)C2211yescharacteristic
16Dic5×SL(2,𝔽3)C2211yescharacteristic
17#3523⋊C3—51nomaximal, Hall
18C5×#519C2×C311yescharacteristic, complemented
19Q8×C22⋊D5C2×C311yescharacteristic, complemented
20Q8×C22⋊D5C2×C311yescharacteristic, complemented
21#65917—31no—
22#65915—31no—
23#65912—31no—
24Q8×D20C2×C311yescharacteristic, complemented
25#65906C2×C311yescharacteristic, complemented
26C4×Q8×D5C2×C311yescharacteristic, complemented
27#65903C2×C311yescharacteristic, complemented
28#65901—31no—
29#65867—31no—
30#65863—31no—
31#65862—31no—
32#65852—31no—
33C2×C3×C22⋊D5—41no—
34C2×C3×C22⋊D5—41no—
35C2×C3×D20—41no—
36C2×C3×C4×D5—41no—
37C2×C5×SL(2,𝔽3)—21no—
38C2×C5×SL(2,𝔽3)C2311yescharacteristic
39D5×SL(2,𝔽3)—21no—
40D5×SL(2,𝔽3)—21no—
41C3×C5×C22⋊C4—41no—
42C3×#685—41no—
43C3×#683—41no—
44#557⋊C3—51no—
45D4×SL(2,𝔽3)—51no—
46D4×SL(2,𝔽3)—51no—
47D4×SL(2,𝔽3)—51no—
48#519⋊C3—51no—
49#519⋊C3D511yescharacteristic, complemented
50C2×C4×SL(2,𝔽3)—51no—
51C22×C5×Q8C22×C311yescharacteristic
52C2×Q8×D5C22×C311yescharacteristic
53C2×Q8×D5C22×C311yescharacteristic
54C4×C5×Q8—31no—
55C4×C5×Q8—31no—
56C4×C5×Q8C22×C311yescharacteristic
57C4×C5×Q8C22×C311yescharacteristic
58C5×#117—31no—
59C5×#117—31no—
60#4092—31no—
61#4092—31no—
62Q8×Dic5C22×C311yescharacteristic
63Q8×Dic5C22×C311yescharacteristic
64#4090—31no—
65#4090—31no—
66C4×C22⋊D5—31no—
67C4×C22⋊D5—31no—
68#4070—31no—
69#4070—31no—
70#4044—31no—
71#4043—31no—
72#4043—31no—
73#4042—31no—
74#4040—31no—
75#4038—31no—
76D5×C4⋊C4—31no—
77#4036—31no—
78#4035—32no—
79#4035—32no—
80#4035—31no—
81#4034—31no—
82#4033—31no—
83#4033—31no—
84#4031—31no—
85#4030A411yescharacteristic
86#4029—31no—
87#4025—32no—
88#4025—31no—
89#4022—32no—
90C4×D20—31no—
91#4018—32no—
92#4018—31no—
93C42×D5—31no—
94#4016—32no—
95#4016—31no—
96#4015—31no—
97C4×Dic10—32no—
98C4×Dic10—31no—
99C4×Dic10—31no—
100C4×Dic10—31no—
101#3523—51noSylow
102C23×C3×C5—41no—
103C22×C3×D5—41no—
104C22×C3×D5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C3×C22⋊D5—82no—
108C3×C22⋊D5—82no—
109C2×C3×Dic5—41no—
110C2×C3×Dic5—41no—
111C3×D20—82no—
112C3×C4×D5—82no—
113C5×SL(2,𝔽3)#4111yescharacteristic
114C22×SL(2,𝔽3)—51no—
115C22×SL(2,𝔽3)—51no—
116C22×SL(2,𝔽3)C2×D511yescharacteristic
117C3×#121—201no—
118C4×SL(2,𝔽3)—51no—
119C4×SL(2,𝔽3)—51no—
120C4×SL(2,𝔽3)C2×D511yescharacteristic
121C4×SL(2,𝔽3)C2×D511yescharacteristic
122C2×C5×Q8—21no—
123C2×C5×Q8—31no—
124C2×C5×Q8—61no—
125C2×C5×Q8C23×C311yescharacteristic
126C22×C4×C5—31no—
127C2×C22⋊D5C2×A411yescharacteristic
128C2×C22⋊D5C2×A411yescharacteristic
129Q8×D5—21no—
130Q8×D5—21no—
131Q8×D5—61no—
132Q8×D5—61no—
133C2×D20C2×A411yescharacteristic
134C2×C4×D5—31no—
135C2×C4×D5—31no—
136C2×C4×D5—31no—
137C2×C4×D5C2×A411yescharacteristic
138C2×Dic10—31no—
139C2×Dic10—31no—
140C2×Dic10—31no—
141C5×C4⋊C4—31no—
142C5×C4⋊C4—31no—
143C5×C4⋊C4—31no—
144C5×C4⋊C4—31no—
145C5×C22⋊C4—31no—
146C5×C22⋊C4C2×A411yescharacteristic
147C42×C5—32no—
148C42×C5—31no—
149C42×C5—31no—
150C22⋊Dic5—31no—
151C22⋊Dic5—31no—
152#685—31no—
153#685—31no—
154#685—31no—
155#685—31no—
156#685—31no—
157#685C2×A411yescharacteristic
158C4⋊Dic5—32no—
159C4⋊Dic5—31no—
160C4⋊Dic5—31no—
161C4⋊Dic5—31no—
162C4⋊Dic5—31no—
163#683—32no—
164#683—32no—
165#683—32no—
166#683—32no—
167#683—31no—
168#683—31no—
169#683—31no—
170#683—31no—
171#683—31no—
172#683C2×A411yescharacteristic
173C4×Dic5—32no—
174C4×Dic5—31no—
175C4×Dic5—31no—
176C4×Dic5—31no—
177C4×Dic5—31no—
178#557—51no—
179#557—151no—
180#556—151no—
181#552—151no—
182#552—151no—
183D4×Q8—51no—
184D4×Q8—51no—
185D4×Q8—51no—
186#541—151no—
187#541—151no—
188#533—151no—
189#529—151no—
190#519—51no—
191#519C3×D511yescharacteristic, complemented
192C2×C4×Q8—51no—
193C22×C3×C5—41no—
194C22×C3×C5—81no—
195C22×C3×C5—81no—
196C22×C3×C5—81no—
197C2×C3×D5—42no—
198C2×C3×D5—81no—
199C2×C3×D5—81no—
200C2×C3×D5—81no—
201C2×C3×D5—81no—
202C2×C3×D5—81no—
203C3×C4×C5—81no—
204C3×C4×C5—81no—
205C3×Dic5—42no—
206C3×Dic5—81no—
207C2×C3×D4—201no—
208C2×C3×D4—201no—
209C2×C3×D4—201no—
210C22×C3×C4—201no—
211C2×SL(2,𝔽3)—21no—
212C2×SL(2,𝔽3)—101no—
213C2×SL(2,𝔽3)—101no—
214C2×SL(2,𝔽3)C22×D511yescharacteristic
215C3×C4⋊C4—201no—
216C3×C22⋊C4—41no—
217C3×C22⋊C4—201no—
218C23×C5C22×A411yescharacteristic
219C22×D5C22×A411yescharacteristic
220C22×D5C22×A411yescharacteristic
221C5×Q8—31no—
222C5×Q8—61no—
223C5×Q8—61no—
224C5×Q8C3×#4111yescharacteristic
225C2×C4×C5—31no—
226C2×C4×C5—31no—
227C2×C4×C5—31no—
228C2×C4×C5—31no—
229C2×C4×C5—61no—
230C2×C4×C5—61no—
231C2×C4×C5C22×A411yescharacteristic
232C2×C4×C5C22×A411yescharacteristic
233C22⋊D5—22no—
234C22⋊D5—22no—
235C2×Dic5—31no—
236C2×Dic5—31no—
237C2×Dic5—31no—
238C2×Dic5—31no—
239C2×Dic5C22×A411yescharacteristic
240C2×Dic5C22×A411yescharacteristic
241D20—22no—
242C4×D5—22no—
243C4×D5—61no—
244C4×D5—61no—
245C4×D5—61no—
246C4×D5—61no—
247C4×D5—62no—
248Dic10—62no—
249Dic10—61no—
250Dic10—61no—
251Dic10—61no—
252Dic10—61no—
253C22×Q8—51no—
254C22×Q8—51no—
255C22×Q8C2×C3×D511yescharacteristic
256C4⋊Q8—151no—
257C4⋊Q8—151no—
258C4⋊Q8—151no—
259C4⋊Q8—151no—
260#126—152no—
261#126—152no—
262#126—151no—
263#126—151no—
264#125—151no—
265#125—152no—
266#125—151no—
267#125—151no—
268#125—152no—
269#125—152no—
270#124—151no—
271#123—151no—
272#123—151no—
273C22⋊Q8—151no—
274C22⋊Q8—151no—
275C22⋊Q8—151no—
276C22⋊Q8—151no—
277C22⋊Q8—151no—
278C22⋊Q8—151no—
279C22⋊Q8—151no—
280#121—51no—
281C4×Q8—31no—
282C4×Q8—31no—
283C4×Q8—51no—
284C4×Q8—51no—
285C4×Q8—151no—
286C4×Q8—152no—
287C4×Q8—151no—
288C4×Q8—151no—
289C4×Q8—151no—
290C4×Q8—151no—
291C4×Q8C2×C3×D511yescharacteristic
292C4×Q8C2×C3×D511yescharacteristic
293C4×D4—151no—
294C4×D4—151no—
295C4×D4—151no—
296#117—31no—
297#117—31no—
298#117—151no—
299#117—152no—
300#117—151no—
301C2×C4⋊C4—151no—
302C2×C42—151no—
303C2×C3×C5—41no—
304C2×C3×C5—41no—
305C2×C3×C5—41no—
306C2×C3×C5—161no—
307C3×D5—82no—
308C3×D5—161no—
309C23×C3—41no—
310C23×C3—201no—
311C23×C3—201no—
312C3×D4—402no—
313C3×D4—402no—
314C3×D4—402no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—201no—
318C2×C3×C4—201no—
319C2×C3×C4—402no—
320SL(2,𝔽3)#70911yescharacteristic
321C22×C5—21no—
322C22×C5—21no—
323C22×C5—21no—
324C22×C5C23×A411yescharacteristic
325C2×D5—21no—
326C2×D5—21no—
327C2×D5—21no—
328C2×D5—21no—
329C2×D5—21no—
330C2×D52−1+4⋊C312yes—
331C4×C5—21no—
332C4×C5—21no—
333C4×C5—31no—
334C4×C5—31no—
335C4×C5—61no—
336C4×C5—61no—
337C4×C5—61no—
338Dic5—21no—
339Dic5—61no—
340Dic5—61no—
341Dic5—61no—
342Dic5—61no—
343Dic52−1+4⋊C312yes—
344C2×Q8—21no—
345C2×Q8—31no—
346C2×Q8—61no—
347C2×Q8—101no—
348C2×Q8—101no—
349C2×Q8—151no—
350C2×Q8—151no—
351C2×Q8—151no—
352C2×Q8—301no—
353C2×Q8—301no—
354C2×Q8C22×C3×D511yescharacteristic
355C2×D4—51no—
356C2×D4—51no—
357C2×D4—51no—
358C22×C4—31no—
359C22×C4—51no—
360C22×C4—151no—
361C22×C4—151no—
362C22×C4—151no—
363C4⋊C4—31no—
364C4⋊C4—31no—
365C4⋊C4—31no—
366C4⋊C4—31no—
367C4⋊C4—51no—
368C4⋊C4—151no—
369C4⋊C4—151no—
370C4⋊C4—151no—
371C4⋊C4—151no—
372C4⋊C4—151no—
373C4⋊C4—151no—
374C4⋊C4—152no—
375C4⋊C4—152no—
376C4⋊C4—152no—
377C4⋊C4—152no—
378C4⋊C4—152no—
379C4⋊C4—151no—
380C4⋊C4—151no—
381C4⋊C4—151no—
382C22⋊C4—31no—
383C22⋊C4—51no—
384C22⋊C4—151no—
385C22⋊C4—151no—
386C22⋊C4—151no—
387C22⋊C4—151no—
388C22⋊C4—151no—
389C22⋊C4—151no—
390C22⋊C4—151no—
391C22⋊C4D5×A411yescharacteristic
392C42—32no—
393C42—31no—
394C42—31no—
395C42—151no—
396C42—151no—
397C42—151no—
398C42—152no—
399C42—151no—
400C3×C5—41noHall
401C22×C3—41no—
402C22×C3—81no—
403C22×C3—81no—
404C22×C3—81no—
405C22×C3—202no—
406C22×C3—401no—
407C22×C3—401no—
408C22×C3—401no—
409C22×C3—401no—
410C22×C3—401no—
411C3×C4—81no—
412C3×C4—81no—
413C3×C4—202no—
414C3×C4—401no—
415C2×C5—41no—
416C2×C5A4×#4111yescharacteristic
417C2×C5C2×2−1+4⋊C311yescharacteristic
418C2×C5C2×2−1+4⋊C311yescharacteristic
419D5—22no—
420D5—41no—
421C23—51no—
422C23—51no—
423C23C2×D5×A411yescharacteristic
424Q8—31no—
425Q8—61no—
426Q8—61no—
427Q8—301no—
428Q8—301no—
429Q8—301no—
430Q8—301no—
431Q8—302no—
432Q8C3×#70911yescharacteristic
433D4—102no—
434D4—102no—
435D4—102no—
436C2×C4—31no—
437C2×C4—31no—
438C2×C4—31no—
439C2×C4—31no—
440C2×C4—51no—
441C2×C4—51no—
442C2×C4—61no—
443C2×C4—61no—
444C2×C4—102no—
445C2×C4—151no—
446C2×C4—151no—
447C2×C4—151no—
448C2×C4—151no—
449C2×C4—301no—
450C2×C4—301no—
451C2×C4—301no—
452C2×C4—301no—
453C2×C4—302no—
454C2×C4C2×D5×A411yescharacteristic
455C2×C4C2×D5×A411yescharacteristic
456C2×C3—41no—
457C2×C3—41no—
458C2×C3—41no—
459C2×C3—161no—
460C2×C3—402no—
461C2×C3—801no—
462C5#3523⋊C311yescharacteristic, complemented, Sylow
463C22—21no—
464C22—21no—
465C22—21no—
466C22—52no—
467C22—101no—
468C22—101no—
469C22—101no—
470C22—101no—
471C22—101no—
472C22C22×D5×A411yescharacteristic
473C4—21no—
474C4—21no—
475C4—31no—
476C4—31no—
477C4—52no—
478C4—61no—
479C4—61no—
480C4—61no—
481C4—101no—
482C4—301no—
483C4—301no—
484C4—301no—
485C4—301no—
486C3—41noSylow
487C2—41no—
488C2—102no—
489C2—201no—
490C2A4×#70911yescharacteristic
491C2D5×2−1+4⋊C311yescharacteristic
492C2D5×2−1+4⋊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. SL(2,𝔽3)×C22⋊D5C2semidirect
3. SL(2,𝔽3)×C22⋊D5C2semidirect
4. #65906⋊C3C2semidirect
5. SL(2,𝔽3)×D20C2semidirect
6. C4×D5×SL(2,𝔽3)C2semidirect
7. #65903⋊C3C2semidirect
8. #10617785C3semidirect
18. C5×#519C2×C3semidirect
19. Q8×C22⋊D5C2×C3semidirect
20. Q8×C22⋊D5C2×C3semidirect
24. Q8×D20C2×C3semidirect
25. #65906C2×C3semidirect
26. C4×Q8×D5C2×C3semidirect
27. #65903C2×C3semidirect
49. #519⋊C3D5semidirect
191. #519C3×D5semidirect
462. C5#3523⋊C3semidirect

Maximal subgroups

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

subgroupindex
C5×#519⋊C32
SL(2,𝔽3)×C22⋊D52
#65906⋊C32
SL(2,𝔽3)×D202
C4×D5×SL(2,𝔽3)2
#65903⋊C32
#106177853
C3×#40304
#3523⋊C35