Finite Group Databasebeta

← #14514382

Subgroups — #14514382

Order 1920.

634 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 78 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
2#11756726C212yesmaximal, complemented
3#11756725C212yesmaximal, complemented
4#11756722C212yesmaximal, complemented
5#10617533—31nomaximal, Hall
6C2×C5×#41⋊C3C411yescharacteristic, complemented
7#91989—41nomaximal
8D5×#41⋊C3C411yescharacteristic, complemented
9D5×#41⋊C3C411yescharacteristic, complemented
10D5×#41⋊C3C2211yescharacteristic
11D5×#41⋊C3C2211yescharacteristic
12C2×D5×SL(2,𝔽3)C2211yescharacteristic
13C2×C5⋊(#41⋊C3)C411yescharacteristic, complemented
14#91886C2214yescomplemented
15#85519—51nomaximal, Hall
16C2×D5×#41D311yescharacteristic
17C2×#4130—31no—
18C2×D5⋊M16—31no—
19#65794—32no—
20#65794—32no—
21#65793—32no—
22#65793—32no—
23#65782—32no—
24#65767—32no—
25C2×C3×C4×D5—41no—
26C5×#41⋊C3C2×C411yescharacteristic
27C5×#41⋊C3C2×C411yescharacteristic, complemented
28C2×C5×SL(2,𝔽3)C2×C411yescharacteristic, complemented
29#6763—42no—
30C4⋊ΓL(1,𝔽16)—42no—
31C4×ΓL(1,𝔽16)—42no—
32D5×SL(2,𝔽3)C2×C411yescharacteristic, complemented
33D5×SL(2,𝔽3)C2311yescharacteristic
34C5⋊(#41⋊C3)C2×C411yescharacteristic
35C5⋊(#41⋊C3)C2×C411yescharacteristic, complemented
36C22×#41⋊C3—51no—
37#5426—52no—
38#5424—52no—
39#5420—52no—
40C2×C5×#41Dic311yescharacteristic, complemented
41D5×#41—31no—
42D5×#41—31no—
43D5×#41—31no—
44D5×#41—31no—
45D5×#41Dic311yescharacteristic, complemented
46D5×#41Dic311yescharacteristic, complemented
47D5×#41C2×D311yescharacteristic
48D5×#41C2×D311yescharacteristic
49C2×#713Dic311yescharacteristic, complemented
50C2×Q8×D5C2×D311yescharacteristic
51C2×#711—31no—
52C2×D4×D5—31no—
53C2×#709—31no—
54C22×C4×D5—31no—
55C2×C22⋊AGL(1,𝔽5)—61no—
56C2×#704—61no—
57#4130—32no—
58#4130—32no—
59#4130—61no—
60#4130—61no—
61C2×C4⋊AGL(1,𝔽5)—32no—
62C2×C4×AGL(1,𝔽5)—61no—
63D5⋊M16—32no—
64D5⋊M16—32no—
65D5⋊M16—61no—
66D5⋊M16—61no—
67C2×#700—61no—
68C2×D5⋊C8—32no—
69#4009—34no—
70#4009—34no—
71#4007—34no—
72#4007—34no—
73#2896—151noSylow
74C22×C3×D5—41no—
75C2×ΓL(1,𝔽16)—44no—
76C2×C3×C4×C5—41no—
77C2×C3×Dic5—41no—
78C3×C4×D5—41no—
79C3×C4×D5—41no—
80C3×C4×D5—41no—
81C3×C4×D5—41no—
82C5×SL(2,𝔽3)C22×C411yescharacteristic
83C2×#41⋊C3—51no—
84C2×#41⋊C3—51no—
85C2×#41⋊C3—51no—
86C2×#41⋊C3—51no—
87C2×#41⋊C3—51no—
88C2×#41⋊C3AGL(1,𝔽5)11yescharacteristic, complemented
89C22×SL(2,𝔽3)—51no—
90#926—201no—
91#859—54no—
92C23×D5—31no—
93C22×AGL(1,𝔽5)—62no—
94C5×#41—31no—
95C5×#41—31no—
96C5×#41C2×Dic311yescharacteristic
97C5×#41C2×Dic311yescharacteristic
98C2×C5×Q8C2×Dic311yescharacteristic
99C2×C5×D4—31no—
100C22×C4×C5—31no—
101C2×C22⋊D5—61no—
102C22×Dic5—31no—
103#713—31no—
104#713—31no—
105#713C2×Dic311yescharacteristic
106#713C2×Dic311yescharacteristic
107Q8×D5—31no—
108Q8×D5—31no—
109Q8×D5C2×Dic311yescharacteristic
110Q8×D5C22×D311yescharacteristic
111#711—31no—
112#711—31no—
113#711—31no—
114#711—31no—
115#711—61no—
116#711—61no—
117D4×D5—31no—
118D4×D5—31no—
119D4×D5—31no—
120D4×D5—31no—
121D4×D5—61no—
122D4×D5—61no—
123#709—31no—
124#709—31no—
125#709—31no—
126#709—31no—
127#709—61no—
128#709—61no—
129C2×D20—31no—
130C2×C4×D5—31no—
131C2×C4×D5—31no—
132C2×C4×D5—31no—
133C2×C4×D5—31no—
134C2×C4×D5—31no—
135C2×C4×D5—31no—
136C2×C4×D5—31no—
137C2×C4×D5—31no—
138C2×C4×D5—31no—
139C2×C4×D5—31no—
140C2×C4×D5—31no—
141C2×C4×D5S411yescharacteristic
142C2×Dic10—31no—
143C22⋊AGL(1,𝔽5)—62no—
144C22⋊AGL(1,𝔽5)—62no—
145#704—62no—
146#704—62no—
147C2×#170—62no—
148C4⋊AGL(1,𝔽5)—34no—
149C4⋊AGL(1,𝔽5)—62no—
150C4×AGL(1,𝔽5)—62no—
151C4×AGL(1,𝔽5)—62no—
152#700—62no—
153#700—62no—
154D5⋊C8—34no—
155D5⋊C8—62no—
156C22×#41—51no—
157C22×M16—151no—
158C2×#117—151no—
159#419—152no—
160#418—152no—
161#417—152no—
162#417—152no—
163#416—152no—
164#416—152no—
165C22×C3×C5—41no—
166C2×C3×D5—41no—
167C2×C3×D5—41no—
168C2×C3×D5—82no—
169ΓL(1,𝔽16)—84no—
170C3×C4×C5—41no—
171C3×C4×C5—41no—
172C3×Dic5—41no—
173C3×Dic5—41no—
174C22×C3×C4—201no—
175#41⋊C3—51no—
176#41⋊C3—51no—
177#41⋊C3C2×AGL(1,𝔽5)11yescharacteristic
178#41⋊C3C2×AGL(1,𝔽5)11yescharacteristic, complemented
179C2×SL(2,𝔽3)—51no—
180C2×SL(2,𝔽3)—51no—
181C2×SL(2,𝔽3)C2×AGL(1,𝔽5)11yescharacteristic, complemented
182#217—202no—
183C4⋊Dic3—202no—
184C4×Dic3—202no—
185C23×C5—31no—
186C22×D5—31no—
187C22×D5—31no—
188C22×D5—31no—
189C22×D5—31no—
190C22×D5—31no—
191C22×D5—122no—
192C22×D5C2×S411yescharacteristic
193C2×AGL(1,𝔽5)—64no—
194C2×AGL(1,𝔽5)—124no—
195C5×Q8—31no—
196C5×Q8C22×Dic311yescharacteristic
197C5×D4—31no—
198C5×D4—31no—
199C5×D4—61no—
200C2×C4×C5—31no—
201C2×C4×C5—31no—
202C2×C4×C5—31no—
203C2×C4×C5—31no—
204C2×C4×C5—31no—
205C2×C4×C5SL(2,ℤ/4)11yescharacteristic
206C22⋊D5—61no—
207C22⋊D5—61no—
208C22⋊D5—61no—
209C22⋊D5—61no—
210C2×Dic5—31no—
211C2×Dic5—31no—
212C2×Dic5—31no—
213C2×Dic5—31no—
214C2×Dic5—31no—
215C2×Dic5SL(2,ℤ/4)11yescharacteristic
216D20—31no—
217D20—31no—
218D20—61no—
219C4×D5—31no—
220C4×D5—31no—
221C4×D5—31no—
222C4×D5—31no—
223C4×D5—31no—
224C4×D5—31no—
225C4×D5—31no—
226C4×D5—31no—
227C4×D5—31no—
228C4×D5—31no—
229C4×D5—31no—
230C4×D5—31no—
231C4×D5SL(2,ℤ/4)11yescharacteristic
232C4×D5SL(2,ℤ/4)11yescharacteristic
233C4×D5C2×S411yescharacteristic
234C4×D5C2×S411yescharacteristic
235Dic10—31no—
236Dic10—31no—
237Dic10—61no—
238#170—64no—
239C2×#41—51no—
240C2×#41—51no—
241C2×#41—51no—
242C2×#41—51no—
243C2×#41—51no—
244C2×#41—151no—
245C2×#41—151no—
246C2×#41—151no—
247C2×#41—151no—
248C2×#41—151no—
249C2×#41—151no—
250C2×#41ΓL(1,𝔽16)11yescharacteristic, complemented
251C22×Q8—51no—
252C22×D4—151no—
253C23×C4—151no—
254C2×M16—152no—
255C2×M16—152no—
256C2×M16—301no—
257C2×M16—301no—
258C2×M16—301no—
259C2×M16—301no—
260C22×C8—152no—
261#117—152no—
262#117—152no—
263#117—301no—
264#117—301no—
265C2×C4⋊C4—152no—
266C2×C22⋊C4—301no—
267C2×C42—301no—
268#103—154no—
269#103—154no—
270#102—154no—
271#102—154no—
272C2×C3×C5—41no—
273C2×C3×C5—81no—
274C3×D5—42no—
275C3×D5—81no—
276C23×C3—201no—
277C2×C3×C4—41no—
278C2×C3×C4—201no—
279C2×C3×C4—201no—
280C2×C3×C4—201no—
281C2×C3×C4—201no—
282C2×C3×C4—201no—
283C2×Dic3—204no—
284SL(2,𝔽3)C22×AGL(1,𝔽5)11yescharacteristic
285C22×C5—31no—
286C22×C5—31no—
287C22×C5—121no—
288C22×C5C2×SL(2,ℤ/4)11yescharacteristic
289C2×D5—22no—
290C2×D5—31no—
291C2×D5—31no—
292C2×D5—62no—
293C2×D5—62no—
294C2×D5—121no—
295C2×D5—121no—
296C2×D5—121no—
297C2×D5C2×SL(2,ℤ/4)11yescharacteristic
298C2×D5C22×S411yescharacteristic
299AGL(1,𝔽5)—124no—
300C4×C5—31no—
301C4×C5—31no—
302C4×C5C2×SL(2,ℤ/4)11yescharacteristic
303C4×C5C2×SL(2,ℤ/4)11yescharacteristic
304Dic5—31no—
305Dic5—31no—
306Dic5C2×SL(2,ℤ/4)11yescharacteristic
307Dic5C2×SL(2,ℤ/4)11yescharacteristic
308C24—151no—
309#41—31no—
310#41—31no—
311#41—51no—
312#41—51no—
313#41—151no—
314#41—151no—
315#41—151no—
316#41—151no—
317#41—151no—
318#41—151no—
319#41—151no—
320#41—151no—
321#41—151no—
322#41—151no—
323#41—301no—
324#41—301no—
325#41—301no—
326#41—301no—
327#41C2×ΓL(1,𝔽16)11yescharacteristic
328#41C2×ΓL(1,𝔽16)11yescharacteristic
329C2×Q8—51no—
330C2×Q8—51no—
331C2×Q8—151no—
332C2×Q8—151no—
333C2×Q8—151no—
334C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
335C2×D4—31no—
336C2×D4—151no—
337C2×D4—151no—
338C2×D4—151no—
339C2×D4—151no—
340C2×D4—151no—
341C2×D4—301no—
342C2×D4—301no—
343C2×D4—301no—
344C22×C4—31no—
345C22×C4—51no—
346C22×C4—151no—
347C22×C4—151no—
348C22×C4—151no—
349C22×C4—151no—
350C22×C4—151no—
351C22×C4—151no—
352C22×C4—151no—
353C22×C4—151no—
354C22×C4—151no—
355C22×C4—151no—
356C22×C4—151no—
357C22×C4—151no—
358C22×C4—302no—
359M16—302no—
360M16—302no—
361M16—302no—
362M16—302no—
363C2×C8—154no—
364C2×C8—302no—
365C2×C8—302no—
366C4⋊C4—154no—
367C4⋊C4—302no—
368C22⋊C4—302no—
369C22⋊C4—302no—
370C42—302no—
371C42—302no—
372C3×C5—41noHall
373C22×C3—41no—
374C22×C3—201no—
375C22×C3—201no—
376C22×C3—402no—
377C3×C4—41no—
378C3×C4—41no—
379C3×C4—201no—
380C3×C4—201no—
381Dic3—404no—
382C2×C5—21no—
383C2×C5—61no—
384C2×C5—61no—
385C2×C5C22×SL(2,ℤ/4)11yescharacteristic
386D5—21no—
387D5—61no—
388D5—61no—
389D5#592312yes—
390C23—31no—
391C23—51no—
392C23—151no—
393C23—151no—
394C23—151no—
395C23—151no—
396C23—151no—
397C23—602no—
398Q8—31no—
399Q8—151no—
400Q8—151no—
401Q8—301no—
402Q8C22×ΓL(1,𝔽16)11yescharacteristic
403D4—31no—
404D4—31no—
405D4—61no—
406D4—151no—
407D4—151no—
408D4—301no—
409D4—301no—
410D4—301no—
411D4—301no—
412D4—301no—
413C2×C4—31no—
414C2×C4—31no—
415C2×C4—31no—
416C2×C4—31no—
417C2×C4—31no—
418C2×C4—51no—
419C2×C4—51no—
420C2×C4—51no—
421C2×C4—51no—
422C2×C4—51no—
423C2×C4—151no—
424C2×C4—151no—
425C2×C4—151no—
426C2×C4—151no—
427C2×C4—151no—
428C2×C4—151no—
429C2×C4—151no—
430C2×C4—151no—
431C2×C4—151no—
432C2×C4—151no—
433C2×C4—151no—
434C2×C4—151no—
435C2×C4—151no—
436C2×C4—151no—
437C2×C4—151no—
438C2×C4—151no—
439C2×C4—151no—
440C2×C4—304no—
441C2×C4—604no—
442C2×C4A4⋊AGL(1,𝔽5)11yescharacteristic
443C8—304no—
444C2×C3—41no—
445C2×C3—81no—
446C2×C3—202no—
447C2×C3—401no—
448C5#8551911yescharacteristic, complemented, Sylow
449C22—31no—
450C22—31no—
451C22—51no—
452C22—51no—
453C22—102no—
454C22—121no—
455C22—151no—
456C22—151no—
457C22—302no—
458C22—302no—
459C22—601no—
460C22—601no—
461C22—601no—
462C22C2×A4⋊AGL(1,𝔽5)11yescharacteristic
463C4—31no—
464C4—31no—
465C4—51no—
466C4—51no—
467C4—151no—
468C4—151no—
469C4—604no—
470C4C2×A4⋊AGL(1,𝔽5)11yescharacteristic
471C4C2×A4⋊AGL(1,𝔽5)11yescharacteristic
472C3—41noSylow
473C2—21no—
474C2—52no—
475C2—61no—
476C2—61no—
477C2—101no—
478C2—301no—
479C2—301no—
480C2C22×A4⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC4C2×A4⋊AGL(1,𝔽5)
commutator, hypocenterC5×SL(2,𝔽3)C22×C4
FrattiniC2C22×A4⋊AGL(1,𝔽5)
FittingC2×C5×#41Dic3
socleC2×C5C22×SL(2,ℤ/4)
prime radicalC2×D5×#41⋊C3C2
cosocleD5×SL(2,𝔽3)C23
hypercenterC2×C4A4⋊AGL(1,𝔽5)
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11756726C2semidirect
3. #11756725C2semidirect
4. #11756722C2semidirect
6. C2×C5×#41⋊C3C4semidirect
8. D5×#41⋊C3C4semidirect
9. D5×#41⋊C3C4semidirect
13. C2×C5⋊(#41⋊C3)C4semidirect
14. #91886C22semidirect
27. C5×#41⋊C3C2×C4semidirect
28. C2×C5×SL(2,𝔽3)C2×C4semidirect
32. D5×SL(2,𝔽3)C2×C4semidirect
35. C5⋊(#41⋊C3)C2×C4semidirect
40. C2×C5×#41Dic3semidirect
45. D5×#41Dic3semidirect
46. D5×#41Dic3semidirect
49. C2×#713Dic3semidirect
88. C2×#41⋊C3AGL(1,𝔽5)semidirect
178. #41⋊C3C2×AGL(1,𝔽5)semidirect
181. C2×SL(2,𝔽3)C2×AGL(1,𝔽5)semidirect
250. C2×#41ΓL(1,𝔽16)semidirect
448. C5#85519semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#41⋊C32
#117567262
#117567252
#117567222
#106175333
#919894
#855195