Finite Group Databasebeta

← #14289452

Subgroups — #14289452

Order 1920.

512 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 96 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#11756336C211yesmaximal, characteristic
2C3×#65310C211yesmaximal, characteristic, complemented
3#11747075C211yesmaximal, characteristic, complemented
4#11746942C211yesmaximal, characteristic, complemented
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745854C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic, complemented
8#10599054—31nomaximal, Hall
9C2×#6821—21no—
10C3×C4×C5×Q8C2211yescharacteristic
11#91784—22no—
12#91784—21no—
13#91763—21no—
14#91763C2211yescharacteristic
15C4×D60—21no—
16C4×D60C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C2×#6658—22no—
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C4×C5×C3⋊C8C2211yescharacteristic
21C3×#3967—21no—
22C3×#3939—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90987—21no—
25#90968—21no—
26#71160—51nomaximal, Hall
27#65911—31no—
28#65310D311yescharacteristic, complemented
29#65131—31no—
30#64982—31no—
31C5×Q8⋊C8—31no—
32#64705—31no—
33#64679—31no—
34C2×C3×C5×Q8D411yescharacteristic
35#6821—42no—
36#6821—42no—
37C2×D60—22no—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60—22no—
41C2×D60D411yescharacteristic
42C2×D60D412yes—
43C2×C4×D15—22no—
44C2×C4×D15—21no—
45C2×C3×Dic10—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C42×C5—21no—
49C3×C42×C5C2311yescharacteristic
50#6714—22no—
51#6714—21no—
52C4⋊Dic15D411yescharacteristic
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8—21no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5—21no—
57C2×C3×#168—21no—
58#6658—44no—
59#5577—51no—
60C3×#477—51no—
61#5085—51no—
62#5084—51no—
63#4535D511yescharacteristic, complemented
64#4485—51no—
65#4483—51no—
66C2×#713—61no—
67C4×C5×Q8C2×D311yescharacteristic
68C2×#677—62no—
69#4041—62no—
70#4041—61no—
71#4020—31no—
72#4020—61no—
73C4×D20—31no—
74C4×D20—61no—
75#4015C2×D311yescharacteristic
76C5×C4⋊C8—31no—
77C4×C5×C8—31no—
78#3967—21no—
79#3953—61no—
80#3949—61no—
81#3939—21no—
82C4⋊#168C2×D311yescharacteristic
83#1631—151noSylow
84C22×D15—21no—
85C22×D15—22no—
86C3×C5×Q8—21no—
87C3×C5×Q8SD1612yescomplemented
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×Dic15—21no—
94D60—21no—
95D60—21no—
96D60—44no—
97D60—42no—
98D60—41no—
99D60—41no—
100D60—41no—
101D60—41no—
102D60—82no—
103C4×D15—44no—
104C4×D15—41no—
105C4×D15—41no—
106C2×C3×Dic5—41no—
107C3×Dic10—42no—
108C3×#168—41no—
109C5×C3⋊C8—22no—
110C5×C3⋊C8—41no—
111C2×#239—101no—
112C3×C4⋊Q8—51no—
113C3×C4×Q8C2×D511yescharacteristic
114C2×#215—102no—
115#895—102no—
116#895—101no—
117#874—51no—
118#874—101no—
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)C2×D511yescharacteristic
127C4×C3⋊C8C2×D511yescharacteristic
128C2×C5×Q8#6711yescharacteristic
129#713—122no—
130#713—122no—
131C2×D20—31no—
132C2×D20—32no—
133C2×D20—62no—
134C2×D20—61no—
135C2×D20—61no—
136C2×D20—62no—
137C2×C4×D5—62no—
138C2×C4×D5—61no—
139C2×Dic10—21no—
140C2×C5×C8—61no—
141C2×C5×C8—61no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4#6711yescharacteristic
144C42×C5—21no—
145C42×C5C22×D311yescharacteristic
146#685—62no—
147#685—61no—
148C4⋊Dic5—21no—
149C4⋊Dic5—21no—
150C4⋊Dic5—31no—
151C2×#168—21no—
152#677—124no—
153#550—151no—
154#492—151no—
155#477—51no—
156#476—151no—
157#331—151no—
158Q8⋊C8—31no—
159D4⋊C8—151no—
160C22×C3×C5#12011yescharacteristic
161C2×D15—42no—
162C2×D15—41no—
163C2×D15—41no—
164C2×D15—42no—
165C2×D15—42no—
166C2×D15—41no—
167C3×C4×C5—22no—
168C3×C4×C5—21no—
169C3×C4×C5—41no—
170C3×C4×C5C2×SD1611yescharacteristic
171C3×C4×C5#13511yescharacteristic
172C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
173C3×C4×C5#13711yescharacteristic
174Dic15—41no—
175C3×Dic5—81no—
176C2×C3×Q8—101no—
177C2×C3×Q8D2011yescharacteristic
178#239—202no—
179#239—202no—
180C2×D12—51no—
181C2×D12—52no—
182C2×D12—102no—
183C2×D12—101no—
184C2×D12—101no—
185C2×D12—102no—
186C2×C4×D3—102no—
187C2×C4×D3—101no—
188C2×C3×C8—101no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—101no—
191C3×C4⋊C4—101no—
192C3×C4⋊C4D2011yescharacteristic
193C3×C42—21no—
194C3×C42C22×D511yescharacteristic
195#215—204no—
196(C2×D3)⋊C4—102no—
197(C2×D3)⋊C4—101no—
198C4⋊Dic3—51no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—21no—
201C22×D5—61no—
202C22×D5—62no—
203C5×Q8—21no—
204C5×Q8#21512yescomplemented
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5D3×D411yescharacteristic
208C2×C4×C5D3×D411yescharacteristic
209C2×C4×C5C2×#6711yescharacteristic
210C2×Dic5—41no—
211C2×Dic5—61no—
212D20—61no—
213D20—61no—
214D20—122no—
215D20—124no—
216D20—121no—
217D20—121no—
218D20—121no—
219D20—121no—
220D20—242no—
221C4×D5—124no—
222C4×D5—121no—
223C4×D5—121no—
224Dic10—42no—
225C5×C8—62no—
226C5×C8—121no—
227#168—41no—
228C2×#41—301no—
229C2×SD16—302no—
230C4⋊Q8—51no—
231#127—151no—
232#127—301no—
233#121—302no—
234#121—301no—
235C4×Q8D3×D511yescharacteristic
236C4×D4—151no—
237C4×D4—301no—
238#107—101no—
239#106—301no—
240C4⋊C8—31no—
241C4⋊C8—51no—
242#103—101no—
243#102—301no—
244C4×C8—31no—
245C2×C3×C5#45011yescharacteristic
246C2×C3×C5#45211yescharacteristic
247C2×C3×C5#45311yescharacteristic
248D15—81no—
249D15—82no—
250C22×D3—101no—
251C22×D3—102no—
252C3×Q8—21no—
253C3×Q8—202no—
254C3×Q8#67712yescomplemented
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—201no—
258C2×C3×C4C2×D2011yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261C2×Dic3—101no—
262D12—101no—
263D12—101no—
264D12—202no—
265D12—204no—
266D12—201no—
267D12—201no—
268D12—201no—
269D12—201no—
270D12—402no—
271C4×D3—204no—
272C4×D3—201no—
273C4×D3—201no—
274C3×C8—201no—
275C3⋊C8—22no—
276C3⋊C8—41no—
277C22×C5#93711yescharacteristic
278C2×D5—121no—
279C2×D5—122no—
280C2×D5—122no—
281C2×D5—121no—
282C2×D5—122no—
283C2×D5—121no—
284C4×C5—21no—
285C4×C5—22no—
286C4×C5—41no—
287C4×C5#91811yescharacteristic
288C4×C5#91911yescharacteristic
289C4×C5C2×#21511yescharacteristic
290C4×C5#94911yescharacteristic
291Dic5—81no—
292Dic5—121no—
293#41—602no—
294#41—602no—
295C2×Q8—101no—
296C2×Q8#120211yescharacteristic
297C2×D4—151no—
298C2×D4—152no—
299C2×D4—302no—
300C2×D4—302no—
301C2×D4—301no—
302C2×D4—301no—
303C22×C4—302no—
304C22×C4—301no—
305SD16—604no—
306C2×C8—61no—
307C2×C8—61no—
308C2×C8—101no—
309C4⋊C4—21no—
310C4⋊C4—101no—
311C4⋊C4—101no—
312C4⋊C4—151no—
313C4⋊C4#120211yescharacteristic
314C22⋊C4—302no—
315C22⋊C4—301no—
316C42—21no—
317C42C2×D3×D511yescharacteristic
318C3×C5#163111yescharacteristic, complemented, Hall
319C22×C3#402811yescharacteristic
320C2×D3—201no—
321C2×D3—202no—
322C2×D3—202no—
323C2×D3—201no—
324C2×D3—202no—
325C2×D3—201no—
326C3×C4—21no—
327C3×C4—22no—
328C3×C4—41no—
329C3×C4—401no—
330C3×C4C2×#67711yescharacteristic
331C3×C4#405411yescharacteristic
332C3×C4#406211yescharacteristic
333C3×C4#406411yescharacteristic
334Dic3—201no—
335C2×C5#504611yescharacteristic
336C2×C5#518711yescharacteristic
337C2×C5#519811yescharacteristic
338D5—241no—
339D5—242no—
340C23—302no—
341C23—301no—
342Q8—21no—
343Q8—202no—
344Q8#665812yescomplemented
345D4—301no—
346D4—301no—
347D4—602no—
348D4—604no—
349D4—601no—
350D4—601no—
351D4—601no—
352D4—601no—
353D4—1202no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—201no—
357C2×C4—301no—
358C2×C4—604no—
359C2×C4—601no—
360C2×C4—601no—
361C2×C4C2×#120211yescharacteristic
362C2×C4#679011yescharacteristic
363C2×C4#679011yescharacteristic
364C8—62no—
365C8—121no—
366C8—201no—
367C2×C3#6502011yescharacteristic
368C2×C3#6509911yescharacteristic
369C2×C3#6511111yescharacteristic
370D3—401no—
371D3—402no—
372C5#7116011yescharacteristic, complemented, Sylow
373C22—602no—
374C22—601no—
375C22—601no—
376C22—602no—
377C22—602no—
378C22—601no—
379C22#9157211yescharacteristic
380C4—21no—
381C4—22no—
382C4—41no—
383C4—401no—
384C4—601no—
385C4#9130111yescharacteristic
386C4C2×#665811yescharacteristic
387C4#9151211yescharacteristic
388C4#9152311yescharacteristic
389C3#1059905411yescharacteristic, complemented, Sylow
390C2—1202no—
391C2—1201no—
392C2#1174855111yescharacteristic
393C2#1174930911yescharacteristic
394C2#1174942111yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radical#11756336C2
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. C3×#65310C2semidirect
3. #11747075C2semidirect
4. #11746942C2semidirect
5. C5×#4535C2semidirect
6. #11745854C2semidirect
7. #11745838C2semidirect
28. #65310D3semidirect
63. #4535D5semidirect
87. C3×C5×Q8SD16semidirect
204. C5×Q8#215semidirect
254. C3×Q8#677semidirect
318. C3×C5#1631semidirect
344. Q8#6658semidirect
372. C5#71160semidirect
389. C3#10599054semidirect

Maximal subgroups

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

subgroupindex
#117563362
C3×#653102
#117470752
#117469422
C5×#45352
#117458542
#117458382
#105990543
#711605