Finite Group Databasebeta

← #10619176⋊C3 #14514210

Subgroups — #10619176⋊C3 #14514210

Order 1920.

766 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C22×C5×#41⋊C3C211yesmaximal, characteristic, complemented
2C2×C5⋊#994C211yesmaximal, characteristic, complemented
3#66161⋊C3C211yesmaximal, characteristic, complemented
4#66168⋊C3C212yesmaximal, complemented
5#66151⋊C3C212yesmaximal, complemented
6#10619176C311yesmaximal, characteristic, complemented, Hall
7C2×C5×#41⋊C3—22no—
8C2×C5×#41⋊C3C2211yescharacteristic
9C2×C5×#41⋊C3C2211yescharacteristic, complemented
10C22×C5×SL(2,𝔽3)C2211yescharacteristic, complemented
11C5⋊#994—22no—
12C2×C5⋊(#41⋊C3)C2212yescomplemented
13C3×#4070—41nomaximal
14Dic5×SL(2,𝔽3)C2212yescomplemented
15#3488⋊C3—51nomaximal, Hall
16C22×C5×#41C2×C311yescharacteristic
17C2×#4149C2×C311yescharacteristic, complemented
18#66168C2×C312yescomplemented
19#66167—31no—
20#66164—31no—
21#66163—32no—
22#66161C2×C311yescharacteristic, complemented
23#66151C2×C312yes—
24D4×C22⋊D5—32no—
25#66125—31no—
26C2×#4076—31no—
27C22×C3×C4×C5—41no—
28C2×C3×Dic10—41no—
29C5×#41⋊C3—21no—
30C5×#41⋊C3D412yescomplemented
31C2×C5×SL(2,𝔽3)—21no—
32C2×C5×SL(2,𝔽3)C2311yescharacteristic
33C5⋊(#41⋊C3)—22no—
34C3×C22⋊Dic5—42no—
35C3×C4⋊Dic5—41no—
36C3×#683—42no—
37C2×#994—51no—
38C22×#41⋊C3D511yescharacteristic, complemented
39C4⋊(#41⋊C3)—52no—
40#548⋊C3—52no—
41#520⋊C3—51no—
42C2×C5×#41—22no—
43C2×C5×#41—31no—
44C2×C5×#41—31no—
45C2×C5×#41—62no—
46C2×C5×#41C22×C311yescharacteristic
47C2×C5×#41C22×C311yescharacteristic
48C22×C5×Q8C22×C311yescharacteristic
49C22×C5×D4—31no—
50C23×C4×C5—31no—
51C22×C22⋊D5—32no—
52#4149—22no—
53#4149—62no—
54C2×#713C22×C312yes—
55C2×D4×D5—32no—
56C2×#709—31no—
57C22×D20—31no—
58#4099—32no—
59#4093—32no—
60#4092—32no—
61Q8×Dic5C22×C312yes—
62#4086—32no—
63#4085—34no—
64#4084—32no—
65#4083—34no—
66D4×Dic5—32no—
67#4076—32no—
68#4076—31no—
69#4076—32no—
70#4076—32no—
71#4076—31no—
72#4075—32no—
73C4×C22⋊D5—32no—
74C4×C22⋊D5—32no—
75C2×#685—32no—
76#4072—31no—
77C2×C4⋊Dic5—31no—
78#4070—31no—
79#4070A411yescharacteristic
80#3488—51noSylow
81C23×C3×C5—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—82no—
85C2×C3×Dic5—42no—
86C2×C3×Dic5—42no—
87C3×Dic10—82no—
88C5×SL(2,𝔽3)C2×D411yescharacteristic, complemented
89#994—102no—
90C2×#41⋊C3—22no—
91C2×#41⋊C3—52no—
92C2×#41⋊C3C2×D511yescharacteristic
93C2×#41⋊C3C2×D511yescharacteristic, complemented
94C22×SL(2,𝔽3)C2×D511yescharacteristic, complemented
95C3×C22⋊Q8—201no—
96C4×SL(2,𝔽3)—52no—
97C24×C5—31no—
98C23×D5—32no—
99C5×#41—21no—
100C5×#41—32no—
101C5×#41—62no—
102C5×#41—62no—
103C5×#41—62no—
104C5×#41—62no—
105C5×#41—61no—
106C5×#41C3×D412yes—
107C2×C5×Q8—21no—
108C2×C5×Q8—31no—
109C2×C5×Q8—61no—
110C2×C5×Q8C23×C311yescharacteristic
111C2×C5×D4—31no—
112C2×C5×D4—31no—
113C2×C5×D4—32no—
114C2×C5×D4—62no—
115C2×C5×D4—62no—
116C22×C4×C5—31no—
117C22×C4×C5—31no—
118C22×C4×C5—31no—
119C22×C4×C5—31no—
120C22×C4×C5—31no—
121C22×C4×C5—62no—
122C22×C4×C5—62no—
123C22×C4×C5C2×A411yescharacteristic
124C2×C22⋊D5—32no—
125C2×C22⋊D5—34no—
126C2×C22⋊D5—32no—
127C2×C22⋊D5—32no—
128C2×C22⋊D5—124no—
129C22×Dic5—32no—
130#713—22no—
131#713—62no—
132D4×D5—64no—
133D4×D5—64no—
134#709—62no—
135#709—62no—
136C2×D20—32no—
137C2×D20—31no—
138C2×D20—62no—
139C2×D20—62no—
140C2×C4×D5—32no—
141C2×Dic10C2×A411yescharacteristic
142C22⋊Dic5—32no—
143C22⋊Dic5—32no—
144C22⋊Dic5C2×A412yes—
145#685—34no—
146#685—32no—
147#685—32no—
148C4⋊Dic5—31no—
149C4⋊Dic5—32no—
150C4⋊Dic5C2×A411yescharacteristic
151#683—32no—
152#683C2×A412yes—
153C4×Dic5—32no—
154C2×H(5,𝔽2)—51no—
155C22×#41C3×D511yescharacteristic
156#550—52no—
157#548—52no—
158#546—152no—
159D42—152no—
160#537—151no—
161#535—151no—
162#525—151no—
163C2×#121—151no—
164#520—51no—
165C22×C3×C5—42no—
166C22×C3×C5—41no—
167C22×C3×C5—81no—
168C22×C3×C5—81no—
169C3×C4×C5—42no—
170C3×C4×C5—81no—
171C3×Dic5—82no—
172C3×Dic5—82no—
173C2×C3×Q8—201no—
174C22×C3×C4—41no—
175#41⋊C3—21no—
176#41⋊C3—102no—
177#41⋊C3C22⋊D512yescomplemented
178C2×SL(2,𝔽3)—21no—
179C2×SL(2,𝔽3)C22×D511yescharacteristic
180C3×C4⋊C4—202no—
181C3×C4⋊C4—201no—
182C3×C22⋊C4—202no—
183C23×C5—31no—
184C23×C5—31no—
185C23×C5—62no—
186C23×C5—62no—
187C23×C5—121no—
188C23×C5C22×A411yescharacteristic
189C22×D5—32no—
190C22×D5—64no—
191C22×D5—122no—
192C22×D5—122no—
193C5×Q8—31no—
194C5×Q8—61no—
195C5×Q8—61no—
196C5×Q8C2×C3×D411yescharacteristic
197C5×D4—32no—
198C5×D4—32no—
199C5×D4—61no—
200C5×D4—61no—
201C5×D4—64no—
202C2×C4×C5—22no—
203C2×C4×C5—31no—
204C2×C4×C5—32no—
205C2×C4×C5—32no—
206C2×C4×C5—31no—
207C2×C4×C5—61no—
208C2×C4×C5—61no—
209C2×C4×C5—62no—
210C2×C4×C5—61no—
211C2×C4×C5—61no—
212C2×C4×C5—62no—
213C2×C4×C5C22×A411yescharacteristic
214C2×C4×C5C22×A411yescharacteristic
215C22⋊D5—64no—
216C22⋊D5—64no—
217C22⋊D5—122no—
218C22⋊D5—124no—
219C2×Dic5—32no—
220C2×Dic5—122no—
221C2×Dic5C22×A412yes—
222C2×Dic5C22×A412yes—
223D20—62no—
224D20—62no—
225D20—62no—
226C4×D5—62no—
227C4×D5—62no—
228Dic10—22no—
229H(5,𝔽2)—102no—
230H(5,𝔽2)—302no—
231C2×#41—22no—
232C2×#41—31no—
233C2×#41—31no—
234C2×#41—52no—
235C2×#41—62no—
236C2×#41—151no—
237C2×#41C2×C3×D511yescharacteristic
238C2×#41C2×C3×D511yescharacteristic
239C22×Q8C2×C3×D511yescharacteristic
240C22×D4—31no—
241C22×D4—151no—
242C22×D4—152no—
243C22×D4—152no—
244C23×C4—31no—
245#127—152no—
246#124—152no—
247#123—152no—
248C22⋊Q8—51no—
249C22⋊Q8—151no—
250C22⋊Q8—152no—
251#121—151no—
252#121—152no—
253#121—152no—
254#121—154no—
255#121—151no—
256#121—152no—
257#121—152no—
258#120—152no—
259#120—154no—
260C4×Q8—52no—
261C4×D4—152no—
262C4×D4—152no—
263C4×D4—152no—
264#117—151no—
265C2×C4⋊C4—151no—
266C2×C22⋊C4—152no—
267C2×C3×C5—41no—
268C2×C3×C5—41no—
269C2×C3×C5—41no—
270C2×C3×C5—82no—
271C23×C3—41no—
272C3×Q8—402no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—82no—
276C2×C3×C4—202no—
277C2×C3×C4—202no—
278SL(2,𝔽3)C2×C22⋊D511yescharacteristic, complemented
279C22×C5—21no—
280C22×C5—21no—
281C22×C5—32no—
282C22×C5—61no—
283C22×C5—61no—
284C22×C5—61no—
285C22×C5—61no—
286C22×C5—61no—
287C22×C5—124no—
288C22×C5#99412yescomplemented
289C22×C5C23×A411yescharacteristic
290C2×D5—62no—
291C2×D5—62no—
292C2×D5—62no—
293C2×D5—244no—
294C4×C5—21no—
295C4×C5—31no—
296C4×C5—31no—
297C4×C5—61no—
298C4×C5D4×A412yes—
299Dic5—22no—
300Dic5—22no—
301Dic5—62no—
302C24—31no—
303C24—152no—
304#41—21no—
305#41—32no—
306#41—62no—
307#41—62no—
308#41—62no—
309#41—62no—
310#41—61no—
311#41—102no—
312#41—302no—
313#41—302no—
314#41—302no—
315#41C3×C22⋊D512yes—
316C2×Q8—21no—
317C2×Q8—31no—
318C2×Q8—51no—
319C2×Q8—61no—
320C2×Q8C22×C3×D511yescharacteristic
321C2×D4—31no—
322C2×D4—31no—
323C2×D4—32no—
324C2×D4—62no—
325C2×D4—62no—
326C2×D4—152no—
327C2×D4—152no—
328C2×D4—152no—
329C2×D4—152no—
330C2×D4—154no—
331C2×D4—151no—
332C2×D4—302no—
333C2×D4—302no—
334C2×D4—304no—
335C2×D4—304no—
336C2×D4—604no—
337C22×C4—31no—
338C22×C4—31no—
339C22×C4—31no—
340C22×C4—31no—
341C22×C4—31no—
342C22×C4—62no—
343C22×C4—62no—
344C22×C4—152no—
345C22×C4—152no—
346C22×C4D5×A411yescharacteristic
347C4⋊C4—51no—
348C4⋊C4—52no—
349C4⋊C4—152no—
350C4⋊C4—152no—
351C4⋊C4—151no—
352C22⋊C4—52no—
353C22⋊C4—152no—
354C22⋊C4—154no—
355C22⋊C4—152no—
356C22⋊C4—152no—
357C22⋊C4—152no—
358C42—152no—
359C3×C5—41noHall
360C22×C3—42no—
361C22×C3—41no—
362C22×C3—81no—
363C22×C3—81no—
364C3×C4—42no—
365C3×C4—81no—
366C3×C4—402no—
367C3×C4—402no—
368C2×C5—22no—
369C2×C5—62no—
370C2×C5—121no—
371C2×C5C2×D4×A411yescharacteristic
372C2×C5C2×#99411yescharacteristic
373C2×C5#594511yescharacteristic
374D5—122no—
375C23—31no—
376C23—31no—
377C23—62no—
378C23—62no—
379C23—121no—
380C23—152no—
381C23—304no—
382C23—602no—
383C23—602no—
384C23C2×D5×A411yescharacteristic
385Q8—31no—
386Q8—61no—
387Q8—61no—
388Q8—102no—
389Q8C2×C3×C22⋊D511yescharacteristic
390D4—32no—
391D4—32no—
392D4—61no—
393D4—61no—
394D4—64no—
395D4—302no—
396D4—302no—
397D4—304no—
398D4—304no—
399D4—302no—
400D4—602no—
401D4—604no—
402C2×C4—22no—
403C2×C4—31no—
404C2×C4—32no—
405C2×C4—32no—
406C2×C4—31no—
407C2×C4—52no—
408C2×C4—52no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—62no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—62no—
415C2×C4—152no—
416C2×C4—302no—
417C2×C4—302no—
418C2×C4—602no—
419C2×C4C2×D5×A411yescharacteristic
420C2×C4C2×D5×A411yescharacteristic
421C2×C3—41no—
422C2×C3—41no—
423C2×C3—41no—
424C2×C3—82no—
425C5#3488⋊C311yescharacteristic, complemented, Sylow
426C22—21no—
427C22—21no—
428C22—32no—
429C22—61no—
430C22—61no—
431C22—61no—
432C22—61no—
433C22—61no—
434C22—124no—
435C22—302no—
436C22—302no—
437C22—302no—
438C22—1204no—
439C22C5⋊#99412yescomplemented
440C22C22×D5×A411yescharacteristic
441C4—21no—
442C4—31no—
443C4—31no—
444C4—61no—
445C4—102no—
446C4—102no—
447C4—302no—
448C4A4×C22⋊D512yes—
449C3—41noSylow
450C2—22no—
451C2—62no—
452C2—121no—
453C2—602no—
454C2C2×C5⋊#99411yescharacteristic
455C2#66283⋊C311yescharacteristic
456C2C2×A4×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, cosocleC2×C5×Q8C23×C3
FittingC22×C5×#41C2×C3
socleC22×C5C23×A4
hypercenterC22×C4D5×A4
hypocenterC5×Q8C2×C3×D4
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. C22×C5×#41⋊C3C2semidirect
2. C2×C5⋊#994C2semidirect
3. #66161⋊C3C2semidirect
4. #66168⋊C3C2semidirect
5. #66151⋊C3C2semidirect
6. #10619176C3semidirect
9. C2×C5×#41⋊C3C22semidirect
10. C22×C5×SL(2,𝔽3)C22semidirect
12. C2×C5⋊(#41⋊C3)C22semidirect
14. Dic5×SL(2,𝔽3)C22semidirect
17. C2×#4149C2×C3semidirect
18. #66168C2×C3semidirect
22. #66161C2×C3semidirect
30. C5×#41⋊C3D4semidirect
38. C22×#41⋊C3D5semidirect
88. C5×SL(2,𝔽3)C2×D4semidirect
93. C2×#41⋊C3C2×D5semidirect
94. C22×SL(2,𝔽3)C2×D5semidirect
177. #41⋊C3C22⋊D5semidirect
278. SL(2,𝔽3)C2×C22⋊D5semidirect
288. C22×C5#994semidirect
425. C5#3488⋊C3semidirect
439. C22C5⋊#994semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#41⋊C32
C2×C5⋊#9942
#66161⋊C32
#66168⋊C32
#66151⋊C32
#106191763
C3×#40704
#3488⋊C35