Finite Group Databasebeta

← #14289302

Subgroups — #14289302

Order 1920.

432 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 88 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#11756491C211yesmaximal, characteristic, complemented
2C5×#5088C211yesmaximal, characteristic, complemented
3#11747086C211yesmaximal, characteristic, complemented
4#11747045C211yesmaximal, characteristic
5C3×#64767C211yesmaximal, characteristic, complemented
6#11745844C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic, complemented
8#10601990—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91836—21no—
11Q8×Dic15—21no—
12#91787—22no—
13#91786—21no—
14#91781—21no—
15C4×D60C2211yescharacteristic
16C4×Dic30C2211yescharacteristic
17C5×#874C2211yescharacteristic
18C2×#6659—21no—
19C2×#6654—21no—
20C5×#809—22no—
21C4×C5×C3⋊C8C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23C3×C4⋊#168C2211yescharacteristic
24#90967—21no—
25#90967—21no—
26#68433—51nomaximal, Hall
27#66066—31no—
28C5×#486—31no—
29#65364—31no—
30#65361—31no—
31#64767D311yescharacteristic, complemented
32#64679—31no—
33#64676—31no—
34C2×C3×C5×Q8—21no—
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×Dic30D411yescharacteristic
38C2×C5×D12—21no—
39C2×C5×D12—21no—
40C2×C5×D12—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D412yes—
43C3×C42×C5C2311yescharacteristic
44#6714—22no—
45#6714—22no—
46#6714—21no—
47C4⋊Dic15—22no—
48C4⋊Dic15D411yescharacteristic
49C4⋊Dic15D411yescharacteristic
50#6712—21no—
51C4×Dic15—22no—
52C4×Dic15—21no—
53C2×C5×C3⋊C8—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56#6659—42no—
57#6654—42no—
58#5732—51no—
59#5088D511yescharacteristic, complemented
60#4848—51no—
61#4843—51no—
62C3×#332—51no—
63#4484—51no—
64#4483—51no—
65C5×C4⋊Q8C2×D311yescharacteristic
66C5×#127—31no—
67#4093—61no—
68Q8×Dic5—61no—
69C2×#687—61no—
70C2×#686—61no—
71#4044—62no—
72#4043—61no—
73#4038—61no—
74C4×D20—31no—
75C4×Dic10—31no—
76C5×#102—62no—
77C4×C5×C8—31no—
78#3964—61no—
79#3964—61no—
80C4⋊#168C2×D311yescharacteristic
81C4⋊#168C2×D311yescharacteristic
82#1628—151noSylow
83C22×D15—21no—
84C22×C5×D3—41no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C2×C3×C4×C5—22no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×Dic15—21no—
92C2×Dic15—21no—
93C2×Dic15—21no—
94D60—21no—
95D60—21no—
96C4×D15—41no—
97C4×D15—41no—
98Dic30—21no—
99Dic30—21no—
100C5×D12—42no—
101C5×D12—41no—
102C5×D12—41no—
103C5×D12—41no—
104C5×D12—41no—
105C3×#168—41no—
106C3×#168—41no—
107C5×C3⋊C8—41no—
108C3×C4⋊Q8C2×D511yescharacteristic
109#947—101no—
110Q8×Dic3—101no—
111C2×D24—101no—
112C2×#204—101no—
113#898—102no—
114#897—101no—
115#892—101no—
116#874C2×D511yescharacteristic
117C4×D12—51no—
118C4×Dic6—51no—
119C3×C4⋊C8—51no—
120C3×C4⋊C8—51no—
121#821—101no—
122#821—101no—
123#809—22no—
124C4×C3⋊C8C2×D511yescharacteristic
125C2×C5×Q8—21no—
126C2×C5×D4—61no—
127C2×C5×D4—61no—
128C2×C5×D4—61no—
129C2×D20—31no—
130C2×C4×D5—61no—
131C2×Dic10—31no—
132C2×C5×C8—61no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4D1212yes—
135C42×C5C22×D311yescharacteristic
136#687—122no—
137#686—122no—
138#685—62no—
139#685—62no—
140#685—61no—
141C4⋊Dic5—31no—
142C4⋊Dic5—31no—
143C4⋊Dic5—62no—
144#683—61no—
145C4×Dic5—62no—
146C4×Dic5—61no—
147C2×#168—21no—
148C2×#168—21no—
149#556—151no—
150#486—31no—
151#460—151no—
152#459—151no—
153#332—51no—
154Q8⋊C8—151no—
155D4⋊C8—151no—
156C22×C3×C5#12011yescharacteristic
157C2×D15—41no—
158C2×D15—41no—
159C2×D15—41no—
160C2×C5×D3—81no—
161C2×C5×D3—81no—
162C2×C5×D3—81no—
163C3×C4×C5—21no—
164C3×C4×C5—42no—
165C3×C4×C5#13511yescharacteristic
166C3×C4×C5#13511yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
169Dic15—41no—
170Dic15—41no—
171Dic15—41no—
172C2×C3×Q8—21no—
173C2×D12—21no—
174C2×D12—21no—
175C2×D12—21no—
176C2×D12—51no—
177C2×C4×D3—101no—
178C2×Dic6—51no—
179C2×C3×C8—101no—
180C2×C3×C8—101no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4C22⋊D512yes—
183C3×C42C22×D511yescharacteristic
184(C2×D3)⋊C4—102no—
185(C2×D3)⋊C4—102no—
186(C2×D3)⋊C4—101no—
187C4⋊Dic3—51no—
188C4⋊Dic3—51no—
189C4⋊Dic3—102no—
190Dic3⋊C4—101no—
191C4×Dic3—102no—
192C4×Dic3—101no—
193C2×C3⋊C8—21no—
194D24—202no—
195#204—202no—
196C23×C5—121no—
197C22×D5—61no—
198C5×Q8—41no—
199C5×Q8—41no—
200C5×D4—122no—
201C5×D4—121no—
202C5×D4—121no—
203C5×D4—121no—
204C5×D4—121no—
205C2×C4×C5—22no—
206C2×C4×C5C2×D1211yescharacteristic
207C2×C4×C5D3×D411yescharacteristic
208C2×C4×C5D3×D411yescharacteristic
209C2×Dic5—61no—
210C2×Dic5—61no—
211C2×Dic5—61no—
212D20—61no—
213D20—61no—
214C4×D5—121no—
215C4×D5—121no—
216Dic10—61no—
217Dic10—61no—
218C5×C8—121no—
219#168—41no—
220#168—41no—
221C2×SD16—301no—
222C2×D8—301no—
223C4⋊Q8D3×D511yescharacteristic
224#127—31no—
225#126—302no—
226#124—301no—
227C22⋊Q8—301no—
228C4×Q8—151no—
229C4×Q8—301no—
230C4×D4—151no—
231#117—301no—
232C4⋊C8—51no—
233C4⋊C8—51no—
234#102—62no—
235#102—301no—
236#102—301no—
237C4×C8—31no—
238C2×C3×C5#44911yescharacteristic
239C2×C3×C5#44911yescharacteristic
240C2×C3×C5#45411yescharacteristic
241D15—81no—
242C5×D3—161no—
243C22×D3—41no—
244C22×D3—101no—
245C3×Q8—41no—
246C3×Q8—41no—
247C2×C3×C4—22no—
248C2×C3×C4D4×D511yescharacteristic
249C2×C3×C4D4×D511yescharacteristic
250C2×C3×C4C2×C22⋊D511yescharacteristic
251C2×Dic3—101no—
252C2×Dic3—101no—
253C2×Dic3—101no—
254D12—42no—
255D12—41no—
256D12—41no—
257D12—41no—
258D12—41no—
259D12—101no—
260D12—101no—
261C4×D3—201no—
262C4×D3—201no—
263Dic6—101no—
264Dic6—101no—
265C3×C8—201no—
266C3×C8—201no—
267C3⋊C8—41no—
268C22×C5—241no—
269C22×C5—241no—
270C22×C5—241no—
271C22×C5#88211yescharacteristic
272C2×D5—121no—
273C2×D5—121no—
274C2×D5—121no—
275C4×C5—21no—
276C4×C5—42no—
277C4×C5#91111yescharacteristic
278C4×C5#91411yescharacteristic
279C4×C5#91611yescharacteristic
280C4×C5#91911yescharacteristic
281Dic5—121no—
282Dic5—121no—
283Dic5—121no—
284C2×Q8—21no—
285C2×Q8—151no—
286C2×D4—61no—
287C2×D4—61no—
288C2×D4—61no—
289C2×D4—151no—
290C22×C4—301no—
291SD16—602no—
292D8—602no—
293C2×C8—61no—
294C2×C8—101no—
295C2×C8—101no—
296C4⋊C4—21no—
297C4⋊C4—151no—
298C4⋊C4—151no—
299C4⋊C4—302no—
300C4⋊C4—301no—
301C4⋊C4#120312yes—
302C22⋊C4—302no—
303C22⋊C4—302no—
304C22⋊C4—301no—
305C42—302no—
306C42—301no—
307C42C2×D3×D511yescharacteristic
308C3×C5#162811yescharacteristic, complemented, Hall
309C22×C3#408311yescharacteristic
310C2×D3—81no—
311C2×D3—81no—
312C2×D3—81no—
313C2×D3—201no—
314C2×D3—201no—
315C2×D3—201no—
316C3×C4—21no—
317C3×C4—42no—
318C3×C4#405711yescharacteristic
319C3×C4#405811yescharacteristic
320C3×C4#406011yescharacteristic
321C3×C4#406211yescharacteristic
322Dic3—201no—
323Dic3—201no—
324Dic3—201no—
325C2×C5—481no—
326C2×C5#475311yescharacteristic
327C2×C5#478111yescharacteristic
328C2×C5#481011yescharacteristic
329D5—241no—
330C23—121no—
331C23—301no—
332Q8—41no—
333Q8—41no—
334Q8—301no—
335Q8—301no—
336D4—122no—
337D4—121no—
338D4—121no—
339D4—121no—
340D4—121no—
341D4—301no—
342D4—301no—
343C2×C4—22no—
344C2×C4—301no—
345C2×C4—301no—
346C2×C4—301no—
347C2×C4—601no—
348C2×C4—601no—
349C2×C4C2×#120311yescharacteristic
350C2×C4#679011yescharacteristic
351C2×C4#679011yescharacteristic
352C8—121no—
353C8—201no—
354C8—201no—
355C2×C3#6535111yescharacteristic
356C2×C3#6544711yescharacteristic
357C2×C3#6546111yescharacteristic
358D3—161no—
359D3—401no—
360C5#6843311yescharacteristic, complemented, Sylow
361C22—241no—
362C22—241no—
363C22—241no—
364C22—601no—
365C22—601no—
366C22—601no—
367C22#9157311yescharacteristic
368C4—21no—
369C4—42no—
370C4—601no—
371C4—601no—
372C4—601no—
373C4#9148211yescharacteristic
374C4#9149911yescharacteristic
375C4#9150611yescharacteristic
376C4#9152311yescharacteristic
377C3#1060199011yescharacteristic, complemented, Sylow
378C2—481no—
379C2—1201no—
380C2#1174904311yescharacteristic
381C2#1174928911yescharacteristic
382C2#1174938911yescharacteristic
subgroupG/H
centerC22#91573
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radical#11747045C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1628
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
1. #11756491C2semidirect
2. C5×#5088C2semidirect
3. #11747086C2semidirect
5. C3×#64767C2semidirect
6. #11745844C2semidirect
7. #11745838C2semidirect
31. #64767D3semidirect
59. #5088D5semidirect
308. C3×C5#1628semidirect
360. C5#68433semidirect
377. C3#10601990semidirect

Maximal subgroups

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

subgroupindex
#117564912
C5×#50882
#117470862
#117470452
C3×#647672
#117458442
#117458382
#106019903
#684335