Finite Group Databasebeta

← #14288986

Subgroups — #14288986

Order 1920.

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

normal subgroups only

This group has 472 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#11752660C211yesmaximal, characteristic, complemented
2#11750794C211yesmaximal, characteristic, complemented
3#11747064C211yesmaximal, characteristic, complemented
4#11747037C211yesmaximal, characteristic
5C5×#4459C211yesmaximal, characteristic, complemented
6C3×#64676C211yesmaximal, characteristic, complemented
7#11745863C211yesmaximal, characteristic, complemented
8#10598991—31nomaximal, Hall
9C2×#6706—22no—
10#91763C2211yescharacteristic
11#91758C2211yescharacteristic
12C4×C5×D12C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14#91432—22no—
15D3×C4⋊Dic5—21no—
16Dic5×D12—21no—
17#91388—21no—
18#91369—21no—
19C2×#6658—21no—
20C2×#6654—21no—
21C3×C4×C5×C8C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊#168C2211yescharacteristic
24#90969—21no—
25#90968—21no—
26#68244—51nomaximal, Hall
27#65877—31no—
28#65304—31no—
29#65137—31no—
30#64982—31no—
31C5×D4⋊C8—31no—
32#64701—31no—
33#64676D311yescharacteristic, complemented
34C2×D60—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×Dic30D412yes—
38C2×C5×D12D411yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C3×Dic10D411yescharacteristic
41C2×D3×Dic5—22no—
42C2×C3×C5×C8—21no—
43C3×C42×C5C2311yescharacteristic
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46#6706—44no—
47C5×(C2×D3)⋊C4—21no—
48C5×C4⋊Dic3D411yescharacteristic
49C2×C5×C3⋊C8—21no—
50C3×C4⋊Dic5D411yescharacteristic
51C3×#683—21no—
52C3×C4×Dic5—21no—
53C2×C3×#168—21no—
54Dic3⋊Dic5—22no—
55#6669—22no—
56(C2×D3)⋊Dic5—22no—
57#6658—42no—
58#6654—42no—
59#5579—51no—
60#5027—51no—
61#4843—51no—
62#4693—51no—
63C3×Q8⋊C8—51no—
64#4481—51no—
65#4459D511yescharacteristic, complemented
66C4×C5×D4—31no—
67D4×Dic5—61no—
68C2×#686—61no—
69C2×C4⋊Dic5—61no—
70#4070—61no—
71C2×#677—62no—
72C2×#677—61no—
73#4036—61no—
74#4024—62no—
75#4020—31no—
76#4015—31no—
77C4×Dic10C2×D311yescharacteristic
78C5×C4⋊C8—31no—
79C4×C5×C8C2×D311yescharacteristic
80#3953—61no—
81#3941—61no—
82C4⋊#168C2×D311yescharacteristic
83#1622—151noSylow
84C22×D15—41no—
85C22×C5×D3—21no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—22no—
90D60—42no—
91D60—41no—
92D60—41no—
93D60—41no—
94D60—41no—
95Dic30—42no—
96C2×C5×Dic3—21no—
97C5×D12—21no—
98C5×D12SD1612yescomplemented
99C4×C5×D3—41no—
100C4×C5×D3—41no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—21no—
103C3×Dic10—21no—
104C3×Dic10—21no—
105D3×Dic5—82no—
106C3×C5×C8—22no—
107C3×#168—41no—
108C5×C3⋊C8—41no—
109C3×C4×Q8—51no—
110#946—101no—
111C2×#215—101no—
112C2×D24—101no—
113C2×#204—102no—
114#896—102no—
115D3×C4⋊C4—101no—
116#874—51no—
117C4×D12—101no—
118C4×D12C2×D511yescharacteristic
119#870—101no—
120#869—51no—
121C3×C4⋊C8—51no—
122C3×C4×C8C2×D511yescharacteristic
123#821—101no—
124#809—101no—
125C4⋊(C3⋊C8)C2×D511yescharacteristic
126C2×C5×D4—31no—
127C22×C4×C5—61no—
128C22×Dic5—62no—
129C2×D20—61no—
130C2×D20—61no—
131C2×D20—61no—
132C2×Dic10—32no—
133C2×Dic10D1211yescharacteristic
134C2×C5×C8—21no—
135C2×C5×C8—61no—
136C5×C4⋊C4—31no—
137C5×C22⋊C4—61no—
138C42×C5C22×D311yescharacteristic
139C22⋊Dic5—62no—
140#686—122no—
141C4⋊Dic5—62no—
142C4⋊Dic5—61no—
143C4⋊Dic5—61no—
144C4⋊Dic5D1211yescharacteristic
145#683—21no—
146#683—62no—
147C4×Dic5—21no—
148C2×#168—21no—
149#677—124no—
150#677—122no—
151#554—151no—
152#492—151no—
153#460—151no—
154#459—151no—
155#333—151no—
156Q8⋊C8—51no—
157D4⋊C8—31no—
158C22×C3×C5#12011yescharacteristic
159C2×D15—81no—
160C2×D15—81no—
161C2×D15—81no—
162C2×C5×D3—22no—
163C2×C5×D3—41no—
164C2×C5×D3—41no—
165C3×C4×C5—21no—
166C3×C4×C5C2×SD1611yescharacteristic
167C3×C4×C5#13511yescharacteristic
168C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C3×C4×C5#13711yescharacteristic
170Dic15—42no—
171C3×Dic5—41no—
172C3×Dic5—41no—
173C5×Dic3—41no—
174C2×C3×Q8—51no—
175C2×D12—101no—
176C2×D12—101no—
177C2×D12—101no—
178C2×D12D2011yescharacteristic
179C2×C4×D3—21no—
180C2×C4×D3—102no—
181C2×Dic6—52no—
182C2×C3×C8—21no—
183C2×C3×C8—101no—
184C3×C4⋊C4—51no—
185C3×C4⋊C4—101no—
186C3×C42—101no—
187C3×C42C22×D511yescharacteristic
188#215—202no—
189(C2×D3)⋊C4—21no—
190(C2×D3)⋊C4—102no—
191C4⋊Dic3—101no—
192C4⋊Dic3—101no—
193C4⋊Dic3D2011yescharacteristic
194Dic3⋊C4—102no—
195Dic3⋊C4—102no—
196C2×C3⋊C8—21no—
197D24—202no—
198#204—204no—
199C23×C5—61no—
200C22×D5—121no—
201C5×D4—32no—
202C5×D4—61no—
203C2×C4×C5—61no—
204C2×C4×C5—121no—
205C2×C4×C5—121no—
206C2×C4×C5C2×D1211yescharacteristic
207C2×C4×C5D3×D411yescharacteristic
208C2×C4×C5D3×D411yescharacteristic
209C2×Dic5—21no—
210C2×Dic5—21no—
211C2×Dic5—62no—
212C2×Dic5—242no—
213D20—122no—
214D20—121no—
215D20—121no—
216D20—121no—
217D20—121no—
218Dic10—21no—
219Dic10—21no—
220Dic10—122no—
221C5×C8—22no—
222C5×C8—121no—
223#168—41no—
224C2×SD16—302no—
225C2×SD16—301no—
226C2×D8—301no—
227C4⋊Q8—151no—
228#127—151no—
229#125—301no—
230C22⋊Q8—302no—
231C22⋊Q8—301no—
232C4×Q8—51no—
233C4×D4—31no—
234C4×D4—301no—
235C2×C4⋊C4—301no—
236C4⋊C8—31no—
237C4⋊C8—51no—
238#102—301no—
239#102—301no—
240C4×C8D3×D511yescharacteristic
241C2×C3×C5#44811yescharacteristic
242C2×C3×C5#44911yescharacteristic
243C2×C3×C5#45311yescharacteristic
244D15—161no—
245C5×D3—42no—
246C22×D3—21no—
247C22×D3—201no—
248C3×Q8—101no—
249C3×Q8—101no—
250C2×C3×C4—101no—
251C2×C3×C4—101no—
252C2×C3×C4C2×D2011yescharacteristic
253C2×C3×C4D4×D511yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255C2×Dic3—21no—
256C2×Dic3—102no—
257D12—21no—
258D12—202no—
259D12—201no—
260D12—201no—
261D12—201no—
262D12—201no—
263D12#67712yescomplemented
264C4×D3—41no—
265C4×D3—41no—
266C4×D3—402no—
267Dic6—202no—
268C3×C8—22no—
269C3×C8—201no—
270C3⋊C8—41no—
271C22×C5—62no—
272C22×C5—121no—
273C22×C5—121no—
274C22×C5#88211yescharacteristic
275C2×D5—241no—
276C2×D5—241no—
277C2×D5—241no—
278C4×C5—21no—
279C4×C5—121no—
280C4×C5#90411yescharacteristic
281C4×C5#90811yescharacteristic
282C4×C5D3×SD1611yescharacteristic
283C4×C5#91811yescharacteristic
284Dic5—41no—
285Dic5—41no—
286Dic5—122no—
287C2×Q8—51no—
288C2×Q8—152no—
289C2×D4—31no—
290C2×D4—301no—
291C2×D4—301no—
292C2×D4—301no—
293C22×C4—61no—
294C22×C4—302no—
295SD16—604no—
296SD16—602no—
297D8—602no—
298C2×C8—21no—
299C2×C8—61no—
300C2×C8—101no—
301C4⋊C4—31no—
302C4⋊C4—51no—
303C4⋊C4—101no—
304C4⋊C4—302no—
305C4⋊C4—302no—
306C4⋊C4—301no—
307C4⋊C4—301no—
308C22⋊C4—61no—
309C22⋊C4—302no—
310C42—101no—
311C42C2×D3×D511yescharacteristic
312C3×C5#162211yescharacteristic, complemented, Hall
313C22×C3#402811yescharacteristic
314C2×D3—22no—
315C2×D3—41no—
316C2×D3—41no—
317C2×D3—401no—
318C2×D3—401no—
319C2×D3—401no—
320C3×C4—21no—
321C3×C4—201no—
322C3×C4—201no—
323C3×C4C2×#67711yescharacteristic
324C3×C4#405511yescharacteristic
325C3×C4#405711yescharacteristic
326C3×C4#406211yescharacteristic
327Dic3—41no—
328Dic3—202no—
329C2×C5—122no—
330C2×C5#473411yescharacteristic
331C2×C5#480611yescharacteristic
332C2×C5#482211yescharacteristic
333D5—481no—
334C23—61no—
335C23—601no—
336Q8—101no—
337Q8—101no—
338Q8—602no—
339D4—32no—
340D4—61no—
341D4—602no—
342D4—601no—
343D4—601no—
344D4—601no—
345D4—601no—
346C2×C4—61no—
347C2×C4—101no—
348C2×C4—101no—
349C2×C4—121no—
350C2×C4—121no—
351C2×C4—302no—
352C2×C4—1202no—
353C2×C4D5×D1211yescharacteristic
354C2×C4D3×D2011yescharacteristic
355C2×C4#679011yescharacteristic
356C8—22no—
357C8—121no—
358C8—201no—
359C2×C3#6502711yescharacteristic
360C2×C3#6507011yescharacteristic
361C2×C3#6511111yescharacteristic
362D3—42no—
363D3—801no—
364C5#6824411yescharacteristic, complemented, Sylow
365C22—62no—
366C22—121no—
367C22—121no—
368C22—1201no—
369C22—1201no—
370C22—1201no—
371C22#9147611yescharacteristic
372C4—21no—
373C4—121no—
374C4—201no—
375C4—201no—
376C4—602no—
377C4#9125011yescharacteristic
378C4D3×#67711yescharacteristic
379C4#9126311yescharacteristic
380C4#9126911yescharacteristic
381C3#1059899111yescharacteristic, complemented, Sylow
382C2—122no—
383C2—2401no—
384C2#1174711811yescharacteristic
385C2#1174813211yescharacteristic
386C2#1174816311yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radical#11747037C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#1622
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #11752660C2semidirect
2. #11750794C2semidirect
3. #11747064C2semidirect
5. C5×#4459C2semidirect
6. C3×#64676C2semidirect
7. #11745863C2semidirect
33. #64676D3semidirect
65. #4459D5semidirect
98. C5×D12SD16semidirect
263. D12#677semidirect
312. C3×C5#1622semidirect
364. C5#68244semidirect
381. C3#10598991semidirect

Maximal subgroups

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

subgroupindex
#117526602
#117507942
#117470642
#117470372
C5×#44592
C3×#646762
#117458632
#105989913
#682445