Finite Group Databasebeta

← #14513945

Subgroups — #14513945

Order 1920.

612 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 61 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×#5945C211yesmaximal, characteristic, complemented
2C2×#91956C211yesmaximal, characteristic, complemented
3#11752150C212yesmaximal, complemented
4#11752148C212yesmaximal, complemented
5#11752142C211yesmaximal, characteristic, complemented
6#10615853—31nomaximal, Hall
7C5×2−1+4⋊C3—21no—
8C5×2−1+4⋊C3C2211yescharacteristic, complemented
9C5×#994C2211yescharacteristic, complemented
10C2×C5×#41⋊C3—21no—
11C2×C5×#41⋊C3C2211yescharacteristic
12#91956—21no—
13#91956C2212yescomplemented
14C2×C5⋊GL(2,𝔽3)—21no—
15#91838—41nomaximal
16#91185C2212yescomplemented
17#85543—51nomaximal, Hall
18C5×#585D311yescharacteristic, complemented
19#66164—31no—
20C2×#4095—31no—
21C2×#4095—31no—
22#65534—32no—
23#65534—32no—
24#65530—32no—
25#65530—32no—
26#65526—31no—
27#65525—31no—
28#65525—31no—
29C3×C5×#41—41no—
30C2×D60—41no—
31C5×#41⋊C3—21no—
32C5×#41⋊C3D411yescharacteristic, complemented
33C5×#41⋊C3C2311yescharacteristic
34C2×C5×SL(2,𝔽3)—21no—
35C2×C5×SL(2,𝔽3)D411yescharacteristic, complemented
36C5⋊GL(2,𝔽3)—22no—
37#6717—42no—
38#6715—42no—
39#6710—41no—
40#5945D511yescharacteristic, complemented
41C2×#986—51no—
42#5431—52no—
43#5429—52no—
44#5423—51no—
45C5×2−1+4—21no—
46C5×2−1+4—31no—
47C5×2−1+4C2×D311yescharacteristic, complemented
48C5×H(5,𝔽2)—31no—
49C5×H(5,𝔽2)—61no—
50C5×H(5,𝔽2)C2×D311yescharacteristic, complemented
51C2×C5×#41—21no—
52C2×C5×#41—31no—
53C2×C5×#41—31no—
54C2×C5×#41—61no—
55C2×C5×#41C2×D311yescharacteristic
56C22×D20—31no—
57#4095—32no—
58#4095—32no—
59#4095—32no—
60#4095—32no—
61#4095—61no—
62#4095—61no—
63#4095—61no—
64#4095—61no—
65#4093—32no—
66C2×#688—61no—
67C2×#688—61no—
68#4086—32no—
69#4083—62no—
70C2×#686—61no—
71C2×#686—61no—
72#4076—62no—
73#4072—31no—
74C2×#681—31no—
75C2×#681—31no—
76#3969—32no—
77#3969—32no—
78#3969—32no—
79#3969—32no—
80#3968—32no—
81#3965—32no—
82#3021—151noSylow
83C22×D15—81no—
84C3×C5×Q8—41no—
85C3×C5×D4—41no—
86C3×C5×D4—81no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—81no—
89D60—42no—
90D60—81no—
91C5×SL(2,𝔽3)C2×D411yescharacteristic
92C3⋊#168—42no—
932−1+4⋊C3—21no—
942−1+4⋊C3C2×D511yescharacteristic, complemented
95#994C2×D511yescharacteristic, complemented
96C2×#41⋊C3—21no—
97C2×#41⋊C3C2×D511yescharacteristic
98#986—52no—
99#986—101no—
100C2×GL(2,𝔽3)—101no—
101#949—201no—
102GU(2,𝔽3)—52no—
103C23×D5—61no—
104C5×#41—21no—
105C5×#41—31no—
106C5×#41—31no—
107C5×#41—31no—
108C5×#41—31no—
109C5×#41—31no—
110C5×#41—61no—
111C5×#41—61no—
112C5×#41—61no—
113C5×#41—61no—
114C5×#41—62no—
115C5×#41—61no—
116C5×#41—61no—
117C5×#41—61no—
118C5×#41—61no—
119C5×#41#6711yescharacteristic
120C5×#41S411yescharacteristic
121C5×#41C22×D311yescharacteristic
122C2×C5×Q8—21no—
123C2×C5×Q8—31no—
124C2×C5×Q8—31no—
125C2×C5×Q8—61no—
126C2×C5×Q8#6711yescharacteristic
127C2×C5×D4—31no—
128C2×C5×D4—31no—
129C2×C5×D4—31no—
130C2×C5×D4—32no—
131C2×C5×D4—61no—
132C2×C5×D4—61no—
133C2×C5×D4—61no—
134C2×C5×D4—62no—
135C22×C4×C5—31no—
136C22×C4×C5—32no—
137C22×C4×C5—61no—
138C2×C22⋊D5—64no—
139C2×D20—32no—
140C2×D20—61no—
141C2×D20—61no—
142C2×D20—61no—
143C2×D20—61no—
144C2×D20—61no—
145C22⋊Dic5—61no—
146#688—62no—
147#688—62no—
148#688—62no—
149#688—62no—
150#686—62no—
151#686—62no—
152#686—62no—
153#686—62no—
154#685—64no—
155C4⋊Dic5—61no—
156C4×Dic5—32no—
157#681—32no—
158#681—32no—
159#681—61no—
160#681—61no—
161C2×#168—61no—
162C2×#168—61no—
163#585D1511yescharacteristic, complemented
164C2×AGL(1,ℤ/8)—151no—
165C2×AGL(1,ℤ/8)—151no—
166#535—151no—
167#454—152no—
168#454—152no—
169#453—152no—
170#453—152no—
171#421—151no—
172#421—151no—
173#413—151no—
174C22×C3×C5—41no—
175C22×C3×C5—81no—
176C2×D15—82no—
177C2×D15—162no—
178C3×C4×C5—41no—
179C3×C4×C5—41no—
180C3×C4×C5—81no—
181C3×#41—41no—
182C2×D12—201no—
183#41⋊C3—21no—
184#41⋊C3C22⋊D511yescharacteristic, complemented
185#41⋊C3C22×D511yescharacteristic
186C2×SL(2,𝔽3)—21no—
187C2×SL(2,𝔽3)C22⋊D511yescharacteristic, complemented
188GL(2,𝔽3)—102no—
189#215—202no—
190#213—202no—
191#208—201no—
192C23×C5—31no—
193C23×C5—32no—
194C23×C5—61no—
195C22×D5—62no—
196C22×D5—121no—
197C22×D5—121no—
198C22×D5—242no—
199C5×Q8—31no—
200C5×Q8—31no—
201C5×Q8—61no—
202C5×Q8—61no—
203C5×Q8C2×#6711yescharacteristic
204C5×Q8C2×S411yescharacteristic
205C5×D4—21no—
206C5×D4—31no—
207C5×D4—31no—
208C5×D4—31no—
209C5×D4—61no—
210C5×D4—61no—
211C5×D4—61no—
212C5×D4—61no—
213C5×D4—61no—
214C5×D4—62no—
215C5×D4—61no—
216C5×D4C2×S411yescharacteristic
217C2×C4×C5—21no—
218C2×C4×C5—31no—
219C2×C4×C5—31no—
220C2×C4×C5—31no—
221C2×C4×C5—31no—
222C2×C4×C5—31no—
223C2×C4×C5—32no—
224C2×C4×C5—61no—
225C2×C4×C5—61no—
226C2×C4×C5—61no—
227C2×C4×C5—62no—
228C2×C4×C5—61no—
229C2×C4×C5C2×S411yescharacteristic
230C22⋊D5—244no—
231C2×Dic5—62no—
232D20—62no—
233D20—62no—
234D20—121no—
235D20—121no—
236#168—62no—
237#168—62no—
2382−1+4—21no—
2392−1+4—31no—
2402−1+4C2×D1511yescharacteristic, complemented
241H(5,𝔽2)—31no—
242H(5,𝔽2)—61no—
243H(5,𝔽2)C2×D1511yescharacteristic, complemented
244C2×#41—21no—
245C2×#41—31no—
246C2×#41—31no—
247C2×#41—61no—
248C2×#41C2×D1511yescharacteristic
249C22×D4—151no—
250AGL(1,ℤ/8)—152no—
251AGL(1,ℤ/8)—152no—
252AGL(1,ℤ/8)—152no—
253AGL(1,ℤ/8)—152no—
254AGL(1,ℤ/8)—301no—
255AGL(1,ℤ/8)—301no—
256AGL(1,ℤ/8)—301no—
257AGL(1,ℤ/8)—301no—
258C2×SD16—301no—
259C2×SD16—301no—
260C2×D8—301no—
261C2×D8—301no—
262C2×M16—151no—
263C2×M16—151no—
264#127—152no—
265#124—152no—
266#121—302no—
267#120—302no—
268#117—151no—
269#104—152no—
270#104—152no—
271#104—152no—
272#104—152no—
273#101—152no—
274#100—152no—
275C2×C3×C5—41no—
276C2×C3×C5—81no—
277C2×C3×C5—161no—
278D15—162no—
279C22×D3—401no—
280C3×Q8—41no—
281C3×D4—41no—
282C3×D4—81no—
283C2×C3×C4—41no—
284C2×C3×C4—81no—
285D12—202no—
286D12—401no—
287SL(2,𝔽3)C2×C22⋊D511yescharacteristic
288C3⋊C8—202no—
289C22×C5—21no—
290C22×C5—31no—
291C22×C5—31no—
292C22×C5—61no—
293C22×C5—121no—
294C22×C5—122no—
295C22×C5—241no—
296C22×C5GL(2,ℤ/4)11yescharacteristic
297C2×D5—124no—
298C2×D5—122no—
299C2×D5—242no—
300C2×D5—242no—
301C4×C5—21no—
302C4×C5—31no—
303C4×C5—31no—
304C4×C5—61no—
305C4×C5GL(2,ℤ/4)11yescharacteristic
306C4×C5C22×S411yescharacteristic
307Dic5—122no—
308C24—301no—
309#41—21no—
310#41—31no—
311#41—31no—
312#41—31no—
313#41—31no—
314#41—31no—
315#41—61no—
316#41—61no—
317#41—61no—
318#41—61no—
319#41—62no—
320#41—61no—
321#41—61no—
322#41—61no—
323#41—61no—
324#41#122011yescharacteristic
325#41C5⋊S411yescharacteristic
326#41C22×D1511yescharacteristic
327C2×Q8—21no—
328C2×Q8—31no—
329C2×Q8—31no—
330C2×Q8—61no—
331C2×Q8#122011yescharacteristic
332C2×D4—31no—
333C2×D4—31no—
334C2×D4—31no—
335C2×D4—32no—
336C2×D4—61no—
337C2×D4—61no—
338C2×D4—61no—
339C2×D4—62no—
340C2×D4—152no—
341C2×D4—301no—
342C2×D4—301no—
343C2×D4—301no—
344C2×D4—301no—
345C2×D4—304no—
346C2×D4—301no—
347C22×C4—31no—
348C22×C4—32no—
349C22×C4—61no—
350SD16—302no—
351SD16—302no—
352SD16—302no—
353SD16—302no—
354D8—302no—
355D8—302no—
356D8—302no—
357D8—302no—
358M16—152no—
359M16—152no—
360M16—301no—
361M16—301no—
362C2×C8—301no—
363C2×C8—301no—
364C4⋊C4—301no—
365C22⋊C4—304no—
366C22⋊C4—301no—
367C42—152no—
368C3×C5—41noHall
369C22×C3—41no—
370C22×C3—81no—
371C2×D3—402no—
372C2×D3—802no—
373C3×C4—41no—
374C3×C4—41no—
375C3×C4—81no—
376C2×C5—21no—
377C2×C5—41no—
378C2×C5—61no—
379C2×C5—61no—
380C2×C5—121no—
381C2×C5C2×GL(2,ℤ/4)11yescharacteristic
382D5—242no—
383C23—31no—
384C23—32no—
385C23—61no—
386C23—302no—
387C23—601no—
388C23—601no—
389C23—1202no—
390Q8—31no—
391Q8—31no—
392Q8—61no—
393Q8—61no—
394Q8C2×#122011yescharacteristic
395Q8C2×C5⋊S411yescharacteristic
396D4—21no—
397D4—31no—
398D4—31no—
399D4—31no—
400D4—61no—
401D4—61no—
402D4—61no—
403D4—61no—
404D4—61no—
405D4—62no—
406D4—61no—
407D4—302no—
408D4—302no—
409D4—601no—
410D4—601no—
411D4—1204no—
412D4C2×C5⋊S411yescharacteristic
413C2×C4—21no—
414C2×C4—31no—
415C2×C4—31no—
416C2×C4—31no—
417C2×C4—31no—
418C2×C4—31no—
419C2×C4—32no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—62no—
424C2×C4—61no—
425C2×C4—302no—
426C2×C4C2×C5⋊S411yescharacteristic
427C8—302no—
428C8—302no—
429C2×C3—41no—
430C2×C3—81no—
431C2×C3—161no—
432D3—802no—
433C5#8554311yescharacteristic, complemented, Sylow
434C22—21no—
435C22—31no—
436C22—31no—
437C22—61no—
438C22—121no—
439C22—122no—
440C22—241no—
441C22—604no—
442C22—602no—
443C22—1202no—
444C22—1202no—
445C22#9195811yescharacteristic
446C4—21no—
447C4—31no—
448C4—31no—
449C4—61no—
450C4—602no—
451C4#9195811yescharacteristic
452C4C22×C5⋊S411yescharacteristic
453C3—41noSylow
454C2—21no—
455C2—41no—
456C2—61no—
457C2—61no—
458C2—121no—
459C2—1202no—
460C2C2×#9195811yescharacteristic
subgroupG/H
centerC2C2×#91958
commutator, cosocleC5×#41⋊C3C23
FrattiniC4C22×C5⋊S4
FittingC5×#585D3
socleC2×C5C2×GL(2,ℤ/4)
hypercenter#41C5⋊S4
hypocenterC5×SL(2,𝔽3)C2×D4
LCSG ▷ C5×#41⋊C3 ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C5×#5945C2semidirect
2. C2×#91956C2semidirect
3. #11752150C2semidirect
4. #11752148C2semidirect
5. #11752142C2semidirect
8. C5×2−1+4⋊C3C22semidirect
9. C5×#994C22semidirect
13. #91956C22semidirect
16. #91185C22semidirect
18. C5×#585D3semidirect
32. C5×#41⋊C3D4semidirect
35. C2×C5×SL(2,𝔽3)D4semidirect
40. #5945D5semidirect
47. C5×2−1+4C2×D3semidirect
50. C5×H(5,𝔽2)C2×D3semidirect
94. 2−1+4⋊C3C2×D5semidirect
95. #994C2×D5semidirect
163. #585D15semidirect
184. #41⋊C3C22⋊D5semidirect
187. C2×SL(2,𝔽3)C22⋊D5semidirect
240. 2−1+4C2×D15semidirect
243. H(5,𝔽2)C2×D15semidirect
433. C5#85543semidirect

Maximal subgroups

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

subgroupindex
C5×#59452
C2×#919562
#117521502
#117521482
#117521422
#106158533
#918384
#855435