Finite Group Databasebeta

← #14289436

Subgroups — #14289436

Order 1920.

512 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 90 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
1#11752536C211yesmaximal, characteristic
2#11751185C211yesmaximal, characteristic, complemented
3C5×#5085C211yesmaximal, characteristic, complemented
4C3×#65380C211yesmaximal, characteristic, complemented
5#11745853C211yesmaximal, characteristic, complemented
6#11745841C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic, complemented
8#10602064—31nomaximal, Hall
9C2×#6768—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C4×D60C2211yescharacteristic
12C2×C5×#215—22no—
13C5×#874C2211yescharacteristic
14C3×C4×Dic10C2211yescharacteristic
15#91466—21no—
16#91451—21no—
17#91416—22no—
18Dic5×D12—21no—
19#91093—21no—
20#91092—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C4×C5×C3⋊C8C2211yescharacteristic
23C3×#3942—21no—
24C3×#3939—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71160—51nomaximal, Hall
27#66052—31no—
28C5×#492—31no—
29#65380D311yescharacteristic, complemented
30#65373—31no—
31#64764—31no—
32#64679—31no—
33#64676—31no—
34C2×C3×C5×Q8—21no—
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×C5×D12—21no—
38C2×C5×D12—21no—
39C2×C5×D12D412yes—
40C2×C3×Dic10D411yescharacteristic
41C2×#1203—22no—
42C2×#1203—22no—
43C2×D3×Dic5—22no—
44#6768—42no—
45#6768—42no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C42×C5C2311yescharacteristic
49#6714—21no—
50C4⋊Dic15D411yescharacteristic
51C2×C3⋊#168—21no—
52C5×#215—44no—
53C2×C5×C3⋊C8—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C3×#683—21no—
56C3×C4×Dic5—21no—
57C2×C3×#168—21no—
58(C2×D3)⋊Dic5—22no—
59#5577—51no—
60C3×#477—51no—
61#5085D511yescharacteristic, complemented
62#5084—51no—
63#4535—51no—
64#4485—51no—
65#4483—51no—
66C2×#711—61no—
67C2×C5×SD16—62no—
68C5×C4⋊Q8C2×D311yescharacteristic
69C5×#127—31no—
70#4086—61no—
71#4085—62no—
72#4084—61no—
73D4×Dic5—61no—
74C4×D20—31no—
75C4×Dic10C2×D311yescharacteristic
76C4×C5×C8—31no—
77#3942—21no—
78#3941—61no—
79#3940—61no—
80#3939—21no—
81C4⋊#168—31no—
82C4⋊#168C2×D311yescharacteristic
83#1631—151noSylow
84C22×D15—21no—
85C22×C5×D3—22no—
86C3×C5×Q8—42no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×Dic15—21no—
92D60—21no—
93D60—21no—
94C4×D15—41no—
95C4×D15—41no—
96C5×D12—42no—
97C5×D12—41no—
98C5×D12—41no—
99C5×D12—41no—
100C5×D12—41no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—21no—
103C3×Dic10—21no—
104C3×Dic10SD1612yescomplemented
105#1203—44no—
106#1203—82no—
107D3×Dic5—44no—
108C3⋊#168—41no—
109C3×#168—41no—
110C5×C3⋊C8—22no—
111C2×#239—101no—
112C3×C4⋊Q8C2×D511yescharacteristic
113C3×C4×Q8—51no—
114C2×#215—22no—
115#895—101no—
116#895—102no—
117#874—101no—
118#874C2×D511yescharacteristic
119C4×D12—51no—
120C4×D12—101no—
121C3×#107—101no—
122C3×C4⋊C8—51no—
123C3×#103—101no—
124#809—101no—
125#808—101no—
126C4⋊(C3⋊C8)—51no—
127C4×C3⋊C8C2×D511yescharacteristic
128C2×C5×Q8—21no—
129C2×C5×D4—32no—
130C2×C5×D4—61no—
131C2×C5×D4—61no—
132C2×C22⋊D5—62no—
133C2×C22⋊D5—62no—
134C22×Dic5—62no—
135#711—122no—
136#711—122no—
137C2×D20—31no—
138C2×C4×D5—61no—
139C2×Dic10#6711yescharacteristic
140C5×SD16—124no—
141C2×C5×C8—61no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4—21no—
144C42×C5C22×D311yescharacteristic
145C22⋊Dic5—62no—
146#685—61no—
147C4⋊Dic5—31no—
148C4⋊Dic5#6711yescharacteristic
149#683—21no—
150C4×Dic5—21no—
151C2×#168—21no—
152C2×#168—61no—
153#550—151no—
154#492—31no—
155#477—51no—
156#476—151no—
157#331—151no—
158Q8⋊C8—151no—
159D4⋊C8—151no—
160C22×C3×C5#12011yescharacteristic
161C2×D15—41no—
162C2×D15—41no—
163C2×D15—41no—
164C2×C5×D3—42no—
165C2×C5×D3—42no—
166C2×C5×D3—42no—
167C3×C4×C5—21no—
168C3×C4×C5—81no—
169C3×C4×C5C2×SD1611yescharacteristic
170C3×C4×C5#13511yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172C3×C4×C5#13711yescharacteristic
173Dic15—41no—
174C3×Dic5—22no—
175C3×Dic5—41no—
176C2×C3×Q8—21no—
177C2×C3×Q8—51no—
178#239—202no—
179#239—202no—
180C2×D12—21no—
181C2×D12—21no—
182C2×D12—51no—
183C2×D12—102no—
184C2×D12—102no—
185C2×D12C22⋊D512yes—
186C2×C4×D3—102no—
187C2×C4×D3—101no—
188C2×C3×C8—101no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—51no—
192C3×C4⋊C4—101no—
193C3×C42—101no—
194C3×C42C22×D511yescharacteristic
195#215—44no—
196(C2×D3)⋊C4—102no—
197(C2×D3)⋊C4—101no—
198C4⋊Dic3—51no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—101no—
201C23×C5—62no—
202C22×D5—61no—
203C5×Q8—42no—
204C5×D4—122no—
205C5×D4—121no—
206C5×D4—121no—
207C5×D4—121no—
208C5×D4—121no—
209C2×C4×C5—41no—
210C2×C4×C5D3×D411yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5C2×#6711yescharacteristic
213C22⋊D5—124no—
214C22⋊D5—242no—
215C2×Dic5—21no—
216C2×Dic5—21no—
217C2×Dic5—61no—
218C2×Dic5—124no—
219D20—61no—
220D20—61no—
221C4×D5—121no—
222C4×D5—121no—
223Dic10—21no—
224Dic10#21512yescomplemented
225C5×C8—62no—
226#168—41no—
227#168—121no—
228C2×#41—301no—
229C2×SD16—62no—
230C4⋊Q8D3×D511yescharacteristic
231#127—31no—
232#127—301no—
233#121—301no—
234#121—302no—
235C4×Q8—51no—
236C4×D4—151no—
237C4×D4—301no—
238#107—101no—
239#106—301no—
240C4⋊C8—51no—
241C4⋊C8—151no—
242#103—101no—
243#102—301no—
244C4×C8—31no—
245C2×C3×C5#45011yescharacteristic
246C2×C3×C5#45211yescharacteristic
247C2×C3×C5#45311yescharacteristic
248D15—81no—
249C5×D3—82no—
250C22×D3—22no—
251C22×D3—101no—
252C3×Q8—42no—
253C3×Q8—52no—
254C3×Q8—101no—
255C2×C3×C4—41no—
256C2×C3×C4—101no—
257C2×C3×C4—101no—
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4C2×C22⋊D511yescharacteristic
261C2×Dic3—101no—
262D12—42no—
263D12—41no—
264D12—41no—
265D12—41no—
266D12—41no—
267D12—101no—
268D12—101no—
269D12—204no—
270D12—402no—
271C4×D3—204no—
272C4×D3—201no—
273C4×D3—201no—
274C3×C8—201no—
275C3⋊C8—22no—
276C3⋊C8—201no—
277C22×C5—122no—
278C22×C5—122no—
279C22×C5—122no—
280C22×C5#93711yescharacteristic
281C2×D5—121no—
282C2×D5—121no—
283C2×D5—121no—
284C4×C5—21no—
285C4×C5—81no—
286C4×C5#91811yescharacteristic
287C4×C5#91911yescharacteristic
288C4×C5C2×#21511yescharacteristic
289C4×C5#94911yescharacteristic
290Dic5—22no—
291Dic5—41no—
292Dic5—121no—
293#41—602no—
294#41—602no—
295C2×Q8—21no—
296C2×Q8—51no—
297C2×D4—32no—
298C2×D4—61no—
299C2×D4—61no—
300C2×D4—151no—
301C2×D4—302no—
302C2×D4—302no—
303C22×C4—302no—
304C22×C4—301no—
305SD16—124no—
306C2×C8—61no—
307C2×C8—101no—
308C2×C8—301no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—51no—
312C4⋊C4—101no—
313C4⋊C4—151no—
314C22⋊C4—302no—
315C22⋊C4—301no—
316C42—101no—
317C42C2×D3×D511yescharacteristic
318C3×C5#163111yescharacteristic, complemented, Hall
319C22×C3#408311yescharacteristic
320C2×D3—42no—
321C2×D3—42no—
322C2×D3—42no—
323C2×D3—201no—
324C2×D3—201no—
325C2×D3—201no—
326C3×C4—21no—
327C3×C4—81no—
328C3×C4—102no—
329C3×C4—201no—
330C3×C4D5×SD1611yescharacteristic
331C3×C4#406011yescharacteristic
332C3×C4#406111yescharacteristic
333C3×C4#406211yescharacteristic
334Dic3—201no—
335C2×C5—242no—
336C2×C5#504611yescharacteristic
337C2×C5#518711yescharacteristic
338C2×C5#519811yescharacteristic
339D5—241no—
340C23—62no—
341C23—301no—
342Q8—42no—
343Q8—52no—
344Q8—101no—
345D4—122no—
346D4—121no—
347D4—121no—
348D4—121no—
349D4—121no—
350D4—301no—
351D4—301no—
352D4—604no—
353D4—1202no—
354C2×C4—41no—
355C2×C4—101no—
356C2×C4—101no—
357C2×C4—301no—
358C2×C4—604no—
359C2×C4—601no—
360C2×C4—601no—
361C2×C4D5×#6711yescharacteristic
362C2×C4D3×C22⋊D511yescharacteristic
363C2×C4#679011yescharacteristic
364C8—62no—
365C8—201no—
366C8—601no—
367C2×C3#6536611yescharacteristic
368C2×C3#6545811yescharacteristic
369C2×C3#6546211yescharacteristic
370D3—82no—
371D3—401no—
372C5#7116011yescharacteristic, complemented, Sylow
373C22—122no—
374C22—122no—
375C22—122no—
376C22—601no—
377C22—601no—
378C22—601no—
379C22#9157711yescharacteristic
380C4—21no—
381C4—81no—
382C4—102no—
383C4—201no—
384C4—601no—
385C4D5×#21511yescharacteristic
386C4#9150211yescharacteristic
387C4#9152311yescharacteristic
388C4#9152411yescharacteristic
389C3#1060206411yescharacteristic, complemented, Sylow
390C2—242no—
391C2—1201no—
392C2#1174916511yescharacteristic
393C2#1174939711yescharacteristic
394C2#1174940711yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radical#11752536C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1631
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11751185C2semidirect
3. C5×#5085C2semidirect
4. C3×#65380C2semidirect
5. #11745853C2semidirect
6. #11745841C2semidirect
7. #11745838C2semidirect
29. #65380D3semidirect
61. #5085D5semidirect
104. C3×Dic10SD16semidirect
224. Dic10#215semidirect
318. C3×C5#1631semidirect
372. C5#71160semidirect
389. C3#10602064semidirect

Maximal subgroups

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

subgroupindex
#117525362
#117511852
C5×#50852
C3×#653802
#117458532
#117458412
#117458382
#106020643
#711605