Finite Group Databasebeta

← #14289294

Subgroups — #14289294

Order 1920.

432 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 91 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#11756343C211yesmaximal, characteristic, complemented
2#11751128C211yesmaximal, characteristic, complemented
3#11750944C211yesmaximal, characteristic
4#11750795C211yesmaximal, characteristic, complemented
5C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
6#11746303C211yesmaximal, characteristic, complemented
7#11746280C211yesmaximal, characteristic, complemented
8#10599038—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91835—21no—
11C2×#6717—21no—
12C2×D120—21no—
13#91787—22no—
14#91781—21no—
15#91764—21no—
16#91763C2211yescharacteristic
17C4×D60C2211yescharacteristic
18#91758C2211yescharacteristic
19C4×Dic30—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C4×C5×C8C2211yescharacteristic
22#91105—21no—
23#91105—22no—
24#91093—21no—
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68245—51nomaximal, Hall
27#65918—31no—
28#65316—31no—
29#65132—31no—
30#64983—31no—
31C5×Q8⋊C8D311yescharacteristic, complemented
32#64702—31no—
33#64679—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×D60—21no—
36C2×D60—21no—
37C2×D60—21no—
38C2×D60D411yescharacteristic
39C2×C4×D15—21no—
40C2×Dic30—21no—
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C42×C5—21no—
46C3×C42×C5C2311yescharacteristic
47#6717—42no—
48#6714—22no—
49#6714—22no—
50#6714—21no—
51C4⋊Dic15—21no—
52C4⋊Dic15D411yescharacteristic
53C4⋊Dic15D412yes—
54#6712—22no—
55C4×Dic15—22no—
56C2×C3⋊#168—21no—
57D120—42no—
58#5584—51no—
59#5027—51no—
60#4843—51no—
61#4694—51no—
62C3×Q8⋊C8D511yescharacteristic, complemented
63#4482—51no—
64#4459—51no—
65C4×C5×Q8C2×D311yescharacteristic
66#4092—61no—
67C2×#688—61no—
68C2×D40—61no—
69#4044—62no—
70#4038—61no—
71#4021—61no—
72#4020—31no—
73C4×D20—31no—
74#4015—31no—
75C4×Dic10—61no—
76C5×C4⋊C8C2×D311yescharacteristic
77C4×C5×C8C2×D311yescharacteristic
78#3953—61no—
79#3953—62no—
80#3941—61no—
81C4⋊#168—31no—
82#1628—151noSylow
83C22×D15—21no—
84C22×D15—41no—
85C3×C5×Q8—21no—
86C3×C5×Q8—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×Dic15—21no—
93C2×Dic15—22no—
94D60—21no—
95D60—21no—
96D60—42no—
97D60—41no—
98D60—41no—
99D60—41no—
100D60—41no—
101C4×D15—41no—
102C4×D15—41no—
103Dic30—41no—
104Dic30—41no—
105C3×C5×C8—41no—
106C3×C5×C8—41no—
107C3⋊#168—41no—
108C3×C4×Q8C2×D511yescharacteristic
109#946—101no—
110C2×#215—101no—
111C2×D24—101no—
112#898—102no—
113#892—101no—
114#875—101no—
115#874—51no—
116C4×D12—51no—
117#869—51no—
118C4×Dic6—101no—
119C3×C4⋊C8C2×D511yescharacteristic
120C3×C4×C8C2×D511yescharacteristic
121#821—102no—
122#821—101no—
123#809—101no—
124C4⋊(C3⋊C8)—51no—
125C2×C5×Q8D1211yescharacteristic
126C2×D20—31no—
127C2×D20—61no—
128C2×D20—61no—
129C2×D20—61no—
130C2×C4×D5—61no—
131C2×Dic10—61no—
132C2×C5×C8—21no—
133C2×C5×C8—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4D1211yescharacteristic
136C42×C5—21no—
137C42×C5C22×D311yescharacteristic
138#688—122no—
139#685—62no—
140#685—62no—
141#685—61no—
142C4⋊Dic5—31no—
143C4⋊Dic5—32no—
144C4⋊Dic5—61no—
145#683—62no—
146C4×Dic5—62no—
147C2×#168—61no—
148D40—122no—
149#556—151no—
150#486—151no—
151#460—151no—
152#459—151no—
153#332—151no—
154Q8⋊C8D1511yescharacteristic, complemented
155D4⋊C8—151no—
156C22×C3×C5#12011yescharacteristic
157C2×D15—41no—
158C2×D15—41no—
159C2×D15—41no—
160C2×D15—81no—
161C2×D15—81no—
162C2×D15—81no—
163C3×C4×C5—21no—
164C3×C4×C5—41no—
165C3×C4×C5—41no—
166C3×C4×C5#13511yescharacteristic
167C3×C4×C5#13511yescharacteristic
168C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
170Dic15—42no—
171Dic15—41no—
172C2×C3×Q8D2011yescharacteristic
173C2×D12—51no—
174C2×D12—101no—
175C2×D12—101no—
176C2×D12—101no—
177C2×C4×D3—101no—
178C2×Dic6—101no—
179C2×C3×C8—21no—
180C2×C3×C8—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4D2011yescharacteristic
183C3×C42—21no—
184C3×C42C22×D511yescharacteristic
185#215—202no—
186(C2×D3)⋊C4—102no—
187(C2×D3)⋊C4—102no—
188(C2×D3)⋊C4—101no—
189C4⋊Dic3—51no—
190C4⋊Dic3—52no—
191C4⋊Dic3—101no—
192Dic3⋊C4—102no—
193C4×Dic3—102no—
194C2×C3⋊C8—101no—
195D24—202no—
196C22×D5—61no—
197C22×D5—121no—
198C5×Q8—21no—
199C5×Q8—21no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5C2×D1211yescharacteristic
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×Dic5—61no—
206C2×Dic5—62no—
207D20—61no—
208D20—61no—
209D20—122no—
210D20—121no—
211D20—121no—
212D20—121no—
213D20—121no—
214C4×D5—121no—
215C4×D5—121no—
216Dic10—121no—
217Dic10—121no—
218C5×C8—41no—
219C5×C8—41no—
220#168—121no—
221C2×SD16—301no—
222C2×D8—301no—
223C4⋊Q8—151no—
224#127—151no—
225#126—302no—
226#124—301no—
227C22⋊Q8—301no—
228C4×Q8—301no—
229C4×Q8C2×D1511yescharacteristic
230C4×D4—151no—
231#117—301no—
232C4⋊C8—151no—
233C4⋊C8C2×D1511yescharacteristic
234#102—301no—
235#102—302no—
236#102—301no—
237C4×C8C2×D1511yescharacteristic
238C2×C3×C5#44911yescharacteristic
239C2×C3×C5#44911yescharacteristic
240C2×C3×C5#45411yescharacteristic
241D15—81no—
242D15—161no—
243C22×D3—101no—
244C22×D3—201no—
245C3×Q8—21no—
246C3×Q8—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4C2×D2011yescharacteristic
250C2×C3×C4D4×D511yescharacteristic
251C2×C3×C4D4×D511yescharacteristic
252C2×Dic3—101no—
253C2×Dic3—102no—
254D12—101no—
255D12—101no—
256D12—202no—
257D12—201no—
258D12—201no—
259D12—201no—
260D12—201no—
261C4×D3—201no—
262C4×D3—201no—
263Dic6—201no—
264Dic6—201no—
265C3×C8—41no—
266C3×C8—41no—
267C3⋊C8—201no—
268C22×C5#88211yescharacteristic
269C2×D5—121no—
270C2×D5—121no—
271C2×D5—121no—
272C2×D5—241no—
273C2×D5—241no—
274C2×D5—241no—
275C4×C5—21no—
276C4×C5—41no—
277C4×C5—41no—
278C4×C5#90411yescharacteristic
279C4×C5#90811yescharacteristic
280C4×C5#91411yescharacteristic
281C4×C5#91911yescharacteristic
282Dic5—121no—
283Dic5—122no—
284C2×Q8—301no—
285C2×Q8D6011yescharacteristic
286C2×D4—151no—
287C2×D4—301no—
288C2×D4—301no—
289C2×D4—301no—
290C22×C4—301no—
291SD16—602no—
292D8—602no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—301no—
296C4⋊C4—21no—
297C4⋊C4—151no—
298C4⋊C4—152no—
299C4⋊C4—302no—
300C4⋊C4—301no—
301C4⋊C4D6011yescharacteristic
302C22⋊C4—302no—
303C22⋊C4—302no—
304C22⋊C4—301no—
305C42—21no—
306C42—302no—
307C42C22×D1511yescharacteristic
308C3×C5#162811yescharacteristic, complemented, Hall
309C22×C3#402811yescharacteristic
310C2×D3—201no—
311C2×D3—201no—
312C2×D3—201no—
313C2×D3—401no—
314C2×D3—401no—
315C2×D3—401no—
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—41no—
319C3×C4#405011yescharacteristic
320C3×C4#405411yescharacteristic
321C3×C4#406011yescharacteristic
322C3×C4#406511yescharacteristic
323Dic3—202no—
324Dic3—201no—
325C2×C5#473411yescharacteristic
326C2×C5#481011yescharacteristic
327C2×C5#482711yescharacteristic
328D5—241no—
329D5—481no—
330C23—301no—
331C23—601no—
332Q8—21no—
333Q8—21no—
334Q8—601no—
335Q8—601no—
336D4—301no—
337D4—301no—
338D4—602no—
339D4—601no—
340D4—601no—
341D4—601no—
342D4—601no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—301no—
346C2×C4—302no—
347C2×C4—601no—
348C2×C4—601no—
349C2×C4C2×D6011yescharacteristic
350C2×C4D4×D1511yescharacteristic
351C2×C4D4×D1511yescharacteristic
352C8—41no—
353C8—41no—
354C8—601no—
355C2×C3#6502311yescharacteristic
356C2×C3#6510011yescharacteristic
357C2×C3#6511611yescharacteristic
358D3—401no—
359D3—801no—
360C5#6824511yescharacteristic, complemented, Sylow
361C22—601no—
362C22—601no—
363C22—601no—
364C22—1201no—
365C22—1201no—
366C22—1201no—
367C22#9177111yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—601no—
372C4—602no—
373C4#9179311yescharacteristic
374C4#9179711yescharacteristic
375C4#9180311yescharacteristic
376C4#9180811yescharacteristic
377C3#1059903811yescharacteristic, complemented, Sylow
378C2—1201no—
379C2—2401no—
380C2#1175083511yescharacteristic
381C2#1175091111yescharacteristic
382C2#1175092811yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×Q8⋊C8C2
socleC22×C3×C5#120
prime radical#11750944C2
hypercenterQ8⋊C8D15
hypocenterC3×C5#1628
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #11756343C2semidirect
2. #11751128C2semidirect
4. #11750795C2semidirect
5. C3×C5×Q8⋊C8C2semidirect
6. #11746303C2semidirect
7. #11746280C2semidirect
31. C5×Q8⋊C8D3semidirect
62. C3×Q8⋊C8D5semidirect
154. Q8⋊C8D15semidirect
308. C3×C5#1628semidirect
360. C5#68245semidirect
377. C3#10599038semidirect

Maximal subgroups

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

subgroupindex
#117563432
#117511282
#117509442
#117507952
C3×C5×Q8⋊C82
#117463032
#117462802
#105990383
#682455