Finite Group Databasebeta

← #14289304

Subgroups — #14289304

Order 1920.

432 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C5×#5732C211yesmaximal, characteristic, complemented
2#11751189C211yesmaximal, characteristic, complemented
3#11747078C211yesmaximal, characteristic, complemented
4#11747037C211yesmaximal, characteristic
5C3×#64767C211yesmaximal, characteristic, complemented
6#11745842C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic, complemented
8#10602724—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91763C2211yescharacteristic
11C5×#947—21no—
12C5×Q8×Dic3—21no—
13C5×#898—22no—
14C5×#897—21no—
15C5×#892—21no—
16C4×C5×D12C2211yescharacteristic
17C4×C5×Dic6C2211yescharacteristic
18C2×#6660—21no—
19C2×#6654—21no—
20#91093—22no—
21C4×C3⋊#168C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23C3×C4⋊#168C2211yescharacteristic
24#90969—21no—
25#90969—21no—
26#68433—51nomaximal, Hall
27C5×#556—31no—
28#65377—31no—
29#65316—31no—
30#65304—31no—
31#64767D311yescharacteristic, complemented
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×Q8—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×D60—21no—
38C2×C5×D12D411yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C5×Dic6D411yescharacteristic
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D412yes—
43C3×C42×C5C2311yescharacteristic
44C2×C3⋊#168—21no—
45C5×(C2×D3)⋊C4—22no—
46C5×(C2×D3)⋊C4—22no—
47C5×(C2×D3)⋊C4—21no—
48C5×C4⋊Dic3—22no—
49C5×C4⋊Dic3D411yescharacteristic
50C5×C4⋊Dic3D411yescharacteristic
51C5×Dic3⋊C4—21no—
52C4×C5×Dic3—22no—
53C4×C5×Dic3—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56#6660—42no—
57#6654—42no—
58#5732D511yescharacteristic, complemented
59#5088—51no—
60#4848—51no—
61#4843—51no—
62C3×#332—51no—
63#4484—51no—
64#4483—51no—
65C5×C4⋊Q8C2×D311yescharacteristic
66C5×#126—62no—
67C5×#124—61no—
68C5×C22⋊Q8—61no—
69C4×C5×Q8—31no—
70C4×C5×Q8—61no—
71C4×C5×D4—31no—
72C5×#117—61no—
73C2×#688—61no—
74C2×#686—61no—
75#4020—31no—
76#3941—61no—
77#3941—61no—
78#3941—62no—
79C4⋊#168C2×D311yescharacteristic
80C4⋊#168C2×D311yescharacteristic
81C4×#168—31no—
82#1628—151noSylow
83C22×D15—41no—
84C22×C5×D3—21no—
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
91D60—42no—
92D60—41no—
93D60—41no—
94D60—41no—
95D60—41no—
96C2×C5×Dic3—21no—
97C2×C5×Dic3—21no—
98C2×C5×Dic3—21no—
99C5×D12—21no—
100C5×D12—21no—
101C4×C5×D3—41no—
102C4×C5×D3—41no—
103C5×Dic6—21no—
104C5×Dic6—21no—
105C3⋊#168—41no—
106C3×#168—41no—
107C3×#168—41no—
108C3×C4⋊Q8C2×D511yescharacteristic
109#947—21no—
110Q8×Dic3—21no—
111C2×D24—101no—
112C2×#204—101no—
113#898—22no—
114#897—21no—
115#892—21no—
116#874—51no—
117C4×D12C2×D511yescharacteristic
118C4×Dic6C2×D511yescharacteristic
119C3×C4⋊C8—51no—
120C3×C4⋊C8—51no—
121#821—101no—
122#821—101no—
123#809—102no—
124C4×C3⋊C8—51no—
125C2×C5×Q8—21no—
126C2×C5×Q8—31no—
127C2×C5×D4—31no—
128C22×C4×C5—61no—
129C2×D20—61no—
130C2×D20—61no—
131C2×D20—61no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4—31no—
134C5×C4⋊C4—31no—
135C5×C4⋊C4—62no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4D1212yes—
138C5×C22⋊C4—62no—
139C5×C22⋊C4—62no—
140C5×C22⋊C4—61no—
141C42×C5—62no—
142C42×C5—61no—
143C42×C5C22×D311yescharacteristic
144#688—122no—
145#686—122no—
146C2×#168—21no—
147C2×#168—21no—
148C2×#168—61no—
149#556—31no—
150#486—151no—
151#460—151no—
152#459—151no—
153#332—51no—
154Q8⋊C8—151no—
155D4⋊C8—151no—
156C22×C3×C5#12011yescharacteristic
157C2×D15—81no—
158C2×D15—81no—
159C2×D15—81no—
160C2×C5×D3—41no—
161C2×C5×D3—41no—
162C2×C5×D3—41no—
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
169C5×Dic3—41no—
170C5×Dic3—41no—
171C5×Dic3—41no—
172C2×C3×Q8—21no—
173C2×D12—101no—
174C2×D12—101no—
175C2×D12—101no—
176C2×D12C22⋊D511yescharacteristic
177C2×C4×D3—21no—
178C2×Dic6C22⋊D511yescharacteristic
179C2×C3×C8—101no—
180C2×C3×C8—101no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4C22⋊D512yes—
183C3×C42C22×D511yescharacteristic
184(C2×D3)⋊C4—22no—
185(C2×D3)⋊C4—22no—
186(C2×D3)⋊C4—21no—
187C4⋊Dic3—22no—
188C4⋊Dic3C22⋊D511yescharacteristic
189C4⋊Dic3C22⋊D511yescharacteristic
190Dic3⋊C4—21no—
191C4×Dic3—22no—
192C4×Dic3—21no—
193C2×C3⋊C8—101no—
194D24—202no—
195#204—202no—
196C23×C5—61no—
197C22×D5—121no—
198C5×Q8—41no—
199C5×Q8—41no—
200C5×Q8—61no—
201C5×Q8—61no—
202C5×D4—61no—
203C5×D4—61no—
204C2×C4×C5—22no—
205C2×C4×C5—61no—
206C2×C4×C5—61no—
207C2×C4×C5—61no—
208C2×C4×C5—121no—
209C2×C4×C5—121no—
210C2×C4×C5C2×D1211yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5D3×D411yescharacteristic
213D20—122no—
214D20—121no—
215D20—121no—
216D20—121no—
217D20—121no—
218#168—41no—
219#168—41no—
220#168—121no—
221C2×SD16—301no—
222C2×D8—301no—
223C4⋊Q8D3×D511yescharacteristic
224#127—151no—
225#126—62no—
226#124—61no—
227C22⋊Q8—61no—
228C4×Q8—31no—
229C4×Q8—61no—
230C4×D4—31no—
231#117—61no—
232C4⋊C8—51no—
233C4⋊C8—51no—
234#102—301no—
235#102—301no—
236#102—302no—
237C4×C8—151no—
238C2×C3×C5#44911yescharacteristic
239C2×C3×C5#44911yescharacteristic
240C2×C3×C5#45411yescharacteristic
241D15—161no—
242C5×D3—81no—
243C22×D3—21no—
244C22×D3—201no—
245C3×Q8—41no—
246C3×Q8—41no—
247C2×C3×C4—22no—
248C2×C3×C4C2×C22⋊D511yescharacteristic
249C2×C3×C4C2×C22⋊D511yescharacteristic
250C2×C3×C4C2×C22⋊D511yescharacteristic
251C2×Dic3—21no—
252C2×Dic3—21no—
253C2×Dic3—21no—
254D12—21no—
255D12—21no—
256D12—202no—
257D12—201no—
258D12—201no—
259D12—201no—
260D12—201no—
261C4×D3—41no—
262C4×D3—41no—
263Dic6—21no—
264Dic6—21no—
265C3×C8—201no—
266C3×C8—201no—
267C3⋊C8—201no—
268C22×C5—121no—
269C22×C5—121no—
270C22×C5—121no—
271C22×C5#88211yescharacteristic
272C2×D5—241no—
273C2×D5—241no—
274C2×D5—241no—
275C4×C5—21no—
276C4×C5—42no—
277C4×C5—121no—
278C4×C5—121no—
279C4×C5—121no—
280C4×C5#91111yescharacteristic
281C4×C5#91411yescharacteristic
282C4×C5#91611yescharacteristic
283C4×C5#91911yescharacteristic
284C2×Q8—21no—
285C2×Q8—31no—
286C2×D4—31no—
287C2×D4—301no—
288C2×D4—301no—
289C2×D4—301no—
290C22×C4—61no—
291SD16—602no—
292D8—602no—
293C2×C8—101no—
294C2×C8—101no—
295C2×C8—301no—
296C4⋊C4—21no—
297C4⋊C4—31no—
298C4⋊C4—31no—
299C4⋊C4—62no—
300C4⋊C4—61no—
301C4⋊C4#120312yes—
302C22⋊C4—62no—
303C22⋊C4—62no—
304C22⋊C4—61no—
305C42—62no—
306C42—61no—
307C42C2×D3×D511yescharacteristic
308C3×C5#162811yescharacteristic, complemented, Hall
309C22×C3#409911yescharacteristic
310C2×D3—41no—
311C2×D3—41no—
312C2×D3—41no—
313C2×D3—401no—
314C2×D3—401no—
315C2×D3—401no—
316C3×C4—21no—
317C3×C4—42no—
318C3×C4#409511yescharacteristic
319C3×C4#409511yescharacteristic
320C3×C4#409611yescharacteristic
321C3×C4#409611yescharacteristic
322Dic3—41no—
323Dic3—41no—
324Dic3—41no—
325C2×C5—241no—
326C2×C5#475311yescharacteristic
327C2×C5#478111yescharacteristic
328C2×C5#481011yescharacteristic
329D5—481no—
330C23—61no—
331C23—601no—
332Q8—41no—
333Q8—41no—
334Q8—61no—
335Q8—61no—
336D4—61no—
337D4—61no—
338D4—602no—
339D4—601no—
340D4—601no—
341D4—601no—
342D4—601no—
343C2×C4—22no—
344C2×C4—61no—
345C2×C4—61no—
346C2×C4—61no—
347C2×C4—121no—
348C2×C4—121no—
349C2×C4C2×#120311yescharacteristic
350C2×C4D3×C22⋊D511yescharacteristic
351C2×C4D3×C22⋊D511yescharacteristic
352C8—201no—
353C8—201no—
354C8—601no—
355C2×C3#6552711yescharacteristic
356C2×C3#6552711yescharacteristic
357C2×C3#6553411yescharacteristic
358D3—81no—
359D3—801no—
360C5#6843311yescharacteristic, complemented, Sylow
361C22—121no—
362C22—121no—
363C22—121no—
364C22—1201no—
365C22—1201no—
366C22—1201no—
367C22#9157011yescharacteristic
368C4—21no—
369C4—42no—
370C4—121no—
371C4—121no—
372C4—121no—
373C4#9148011yescharacteristic
374C4#9149511yescharacteristic
375C4#9150411yescharacteristic
376C4#9151911yescharacteristic
377C3#1060272411yescharacteristic, complemented, Sylow
378C2—241no—
379C2—2401no—
380C2#1174903611yescharacteristic
381C2#1174928211yescharacteristic
382C2#1174938711yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radical#11747037C2
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. C5×#5732C2semidirect
2. #11751189C2semidirect
3. #11747078C2semidirect
5. C3×#64767C2semidirect
6. #11745842C2semidirect
7. #11745836C2semidirect
31. #64767D3semidirect
58. #5732D5semidirect
308. C3×C5#1628semidirect
360. C5#68433semidirect
377. C3#10602724semidirect

Maximal subgroups

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

subgroupindex
C5×#57322
#117511892
#117470782
#117470372
C3×#647672
#117458422
#117458362
#106027243
#684335