Finite Group Databasebeta

← #14289327

Subgroups — #14289327

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×#5584C211yesmaximal, characteristic, complemented
2C3×#65316C211yesmaximal, characteristic, complemented
3#11747033C211yesmaximal, characteristic
4#11746895C211yesmaximal, characteristic, complemented
5#11746356C211yesmaximal, characteristic, complemented
6#11745857C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic, complemented
8#10602724—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C5×#946—21no—
11C5×#898—22no—
12C5×#892—21no—
13C5×#875—21no—
14C4×C5×D12C2211yescharacteristic
15C5×#869C2211yescharacteristic
16C4×C5×Dic6—21no—
17C2×C3×#688—21no—
18C3×#4020C2211yescharacteristic
19C2×#6652—21no—
20C4⋊(C3⋊#168)C2211yescharacteristic
21C4×C3⋊#168C2211yescharacteristic
22C3×#3941—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90964—22no—
25#90964—21no—
26#71029—51nomaximal, Hall
27C5×#556—31no—
28#65377—31no—
29#65316D311yescharacteristic, complemented
30#65304—31no—
31#64767—31no—
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C5×D12D411yescharacteristic
36C2×C4×C5×D3—21no—
37C2×C5×Dic6—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C42×C5—21no—
44C3×C42×C5C2311yescharacteristic
45C2×C3⋊#168—21no—
46C2×C3⋊#168—21no—
47C5×(C2×D3)⋊C4—22no—
48C5×(C2×D3)⋊C4—22no—
49C5×(C2×D3)⋊C4—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3D411yescharacteristic
52C5×C4⋊Dic3D412yes—
53C5×Dic3⋊C4—22no—
54C4×C5×Dic3—22no—
55C3×#688—42no—
56C2×C3×#168—21no—
57#6652—42no—
58#5584D511yescharacteristic, complemented
59C3×#460—51no—
60#5072—51no—
61#5070—51no—
62#4535—51no—
63#4486—51no—
64#4483—51no—
65C5×C4⋊Q8—31no—
66C5×#126—62no—
67C5×#124—61no—
68C5×C22⋊Q8—61no—
69C4×C5×Q8—61no—
70C4×C5×Q8C2×D311yescharacteristic
71C4×C5×D4—31no—
72C5×#117—61no—
73C2×#688—21no—
74C2×#686—61no—
75#4020C2×D311yescharacteristic
76#3941—21no—
77#3941—61no—
78#3941—62no—
79C4⋊#168—31no—
80C4⋊#168C2×D311yescharacteristic
81C4×#168—31no—
82#1628—151noSylow
83C22×C5×D3—21no—
84C22×C3×D5—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×C5×Dic3—21no—
93C2×C5×Dic3—22no—
94C5×D12—21no—
95C5×D12—21no—
96C4×C5×D3—41no—
97C4×C5×D3—41no—
98C5×Dic6—41no—
99C5×Dic6—41no—
100C3×D20—42no—
101C3×D20—41no—
102C3×D20—41no—
103C3×D20—41no—
104C3×D20—41no—
105C3⋊#168—41no—
106C3⋊#168—41no—
107C3×#168—41no—
108C2×C3×SD16—101no—
109C3×#127—51no—
110C3×C4×Q8C2×D511yescharacteristic
111#946—21no—
112C2×#213—101no—
113#898—22no—
114#892—21no—
115#875—21no—
116C4×D12C2×D511yescharacteristic
117#869C2×D511yescharacteristic
118C4×Dic6—21no—
119C3×C4⋊C8—51no—
120C3×#102—101no—
121#832—102no—
122#832—101no—
123C4⋊(C3⋊C8)—51no—
124C4×C3⋊C8—51no—
125C2×C5×Q8—61no—
126C2×C5×Q8#6711yescharacteristic
127C2×C5×D4—31no—
128C22×C4×C5—61no—
129C2×D20—21no—
130C2×D20—21no—
131C2×D20—21no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4—31no—
134C5×C4⋊C4—32no—
135C5×C4⋊C4—62no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4#6711yescharacteristic
138C5×C22⋊C4—62no—
139C5×C22⋊C4—62no—
140C5×C22⋊C4—61no—
141C42×C5—21no—
142C42×C5—62no—
143C42×C5C22×D311yescharacteristic
144#688—42no—
145#686—122no—
146C2×#168—21no—
147C2×#168—61no—
148C2×#168—61no—
149#556—31no—
150#486—151no—
151#460—51no—
152#459—151no—
153#332—151no—
154Q8⋊C8—151no—
155D4⋊C8—151no—
156C22×C3×C5#12011yescharacteristic
157C2×C5×D3—41no—
158C2×C5×D3—41no—
159C2×C5×D3—41no—
160C2×C3×D5—81no—
161C2×C3×D5—81no—
162C2×C3×D5—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
170C5×Dic3—42no—
171C5×Dic3—41no—
172C2×C3×Q8C22⋊D511yescharacteristic
173C2×C3×D4—101no—
174C2×C3×D4—101no—
175C2×C3×D4—101no—
176C2×D12C22⋊D511yescharacteristic
177C2×C4×D3—21no—
178C2×Dic6—21no—
179C3×SD16—202no—
180C2×C3×C8—101no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4C22⋊D511yescharacteristic
183C3×C42—21no—
184C3×C42C22×D511yescharacteristic
185#213—202no—
186(C2×D3)⋊C4—22no—
187(C2×D3)⋊C4—22no—
188(C2×D3)⋊C4—21no—
189C4⋊Dic3—21no—
190C4⋊Dic3C22⋊D511yescharacteristic
191C4⋊Dic3C22⋊D512yes—
192Dic3⋊C4—22no—
193C4×Dic3—22no—
194C2×C3⋊C8—101no—
195C2×C3⋊C8—101no—
196C23×C5—61no—
197C22×D5—41no—
198C5×Q8—21no—
199C5×Q8—21no—
200C5×Q8—121no—
201C5×Q8—121no—
202C5×D4—61no—
203C5×D4—61no—
204C2×C4×C5—21no—
205C2×C4×C5—21no—
206C2×C4×C5—61no—
207C2×C4×C5—62no—
208C2×C4×C5—121no—
209C2×C4×C5—121no—
210C2×C4×C5D3×D411yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5C2×#6711yescharacteristic
213D20—42no—
214D20—41no—
215D20—41no—
216D20—41no—
217D20—41no—
218#168—41no—
219#168—121no—
220#168—121no—
221C2×SD16—101no—
222C2×D8—301no—
223C4⋊Q8—31no—
224#127—51no—
225#126—62no—
226#124—61no—
227C22⋊Q8—61no—
228C4×Q8—61no—
229C4×Q8D3×D511yescharacteristic
230C4×D4—31no—
231#117—61no—
232C4⋊C8—51no—
233C4⋊C8—151no—
234#102—101no—
235#102—301no—
236#102—302no—
237C4×C8—151no—
238C2×C3×C5#44911yescharacteristic
239C2×C3×C5#44911yescharacteristic
240C2×C3×C5#45411yescharacteristic
241C3×D5—161no—
242C5×D3—81no—
243C23×C3—201no—
244C22×D3—21no—
245C3×Q8—21no—
246C3×Q8—21no—
247C3×D4—202no—
248C3×D4—201no—
249C3×D4—201no—
250C3×D4—201no—
251C3×D4—201no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4C2×C22⋊D511yescharacteristic
255C2×C3×C4C2×C22⋊D511yescharacteristic
256C2×C3×C4C2×C22⋊D511yescharacteristic
257C2×Dic3—21no—
258C2×Dic3—22no—
259D12—21no—
260D12—21no—
261C4×D3—41no—
262C4×D3—41no—
263Dic6—41no—
264Dic6—41no—
265C3×C8—201no—
266C3⋊C8—201no—
267C3⋊C8—201no—
268C22×C5—121no—
269C22×C5—121no—
270C22×C5—121no—
271C22×C5#93711yescharacteristic
272C2×D5—81no—
273C2×D5—81no—
274C2×D5—81no—
275C4×C5—21no—
276C4×C5—41no—
277C4×C5—41no—
278C4×C5—122no—
279C4×C5—121no—
280C4×C5#91411yescharacteristic
281C4×C5#91611yescharacteristic
282C4×C5#93211yescharacteristic
283C4×C5#95011yescharacteristic
284C2×Q8—61no—
285C2×Q8#120111yescharacteristic
286C2×D4—31no—
287C2×D4—101no—
288C2×D4—101no—
289C2×D4—101no—
290C22×C4—61no—
291SD16—202no—
292D8—602no—
293C2×C8—101no—
294C2×C8—301no—
295C2×C8—301no—
296C4⋊C4—21no—
297C4⋊C4—31no—
298C4⋊C4—32no—
299C4⋊C4—62no—
300C4⋊C4—61no—
301C4⋊C4#120111yescharacteristic
302C22⋊C4—62no—
303C22⋊C4—62no—
304C22⋊C4—61no—
305C42—21no—
306C42—62no—
307C42C2×D3×D511yescharacteristic
308C3×C5#162811yescharacteristic, complemented, Hall
309C22×C3—401no—
310C22×C3—401no—
311C22×C3—401no—
312C22×C3#409911yescharacteristic
313C2×D3—41no—
314C2×D3—41no—
315C2×D3—41no—
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—41no—
319C3×C4#409511yescharacteristic
320C3×C4#409511yescharacteristic
321C3×C4#409611yescharacteristic
322C3×C4#409611yescharacteristic
323Dic3—42no—
324Dic3—41no—
325C2×C5—241no—
326C2×C5#503711yescharacteristic
327C2×C5#517211yescharacteristic
328C2×C5#520111yescharacteristic
329D5—161no—
330C23—61no—
331C23—201no—
332Q8—21no—
333Q8—21no—
334Q8—121no—
335Q8—121no—
336D4—61no—
337D4—61no—
338D4—202no—
339D4—201no—
340D4—201no—
341D4—201no—
342D4—201no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—61no—
346C2×C4—62no—
347C2×C4—121no—
348C2×C4—121no—
349C2×C4C2×#120111yescharacteristic
350C2×C4D3×C22⋊D511yescharacteristic
351C2×C4D3×C22⋊D511yescharacteristic
352C8—201no—
353C8—601no—
354C8—601no—
355C2×C3—801no—
356C2×C3#6552711yescharacteristic
357C2×C3#6552711yescharacteristic
358C2×C3#6553411yescharacteristic
359D3—81no—
360C5#7102911yescharacteristic, complemented, Sylow
361C22—121no—
362C22—121no—
363C22—121no—
364C22—401no—
365C22—401no—
366C22—401no—
367C22#9156811yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—122no—
372C4—121no—
373C4#9129711yescharacteristic
374C4#9129811yescharacteristic
375C4#9150411yescharacteristic
376C4#9151711yescharacteristic
377C3#1060272411yescharacteristic, complemented, Sylow
378C2—241no—
379C2—801no—
380C2#1174851711yescharacteristic
381C2#1174928111yescharacteristic
382C2#1174945811yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radical#11747033C2
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×#5584C2semidirect
2. C3×#65316C2semidirect
4. #11746895C2semidirect
5. #11746356C2semidirect
6. #11745857C2semidirect
7. #11745836C2semidirect
29. #65316D3semidirect
58. #5584D5semidirect
308. C3×C5#1628semidirect
360. C5#71029semidirect
377. C3#10602724semidirect

Maximal subgroups

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

subgroupindex
C5×#55842
C3×#653162
#117470332
#117468952
#117463562
#117458572
#117458362
#106027243
#710295