Finite Group Databasebeta

← #14289329

Subgroups — #14289329

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#11756343C211yesmaximal, characteristic, complemented
2C3×#65316C211yesmaximal, characteristic, complemented
3#11747043C211yesmaximal, characteristic
4#11746890C211yesmaximal, characteristic, complemented
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745859C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic, complemented
8#10599038—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91835—21no—
11#91787—22no—
12#91781—21no—
13#91764—21no—
14C4×D60C2211yescharacteristic
15#91758C2211yescharacteristic
16C4×Dic30—21no—
17C2×C3×#688—21no—
18C3×#4020C2211yescharacteristic
19C2×#6653—21no—
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C4×C5×C3⋊C8C2211yescharacteristic
22C3×#3941—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90965—22no—
25#90965—21no—
26#71029—51nomaximal, Hall
27#65918—31no—
28#65316D311yescharacteristic, complemented
29#65132—31no—
30#64983—31no—
31C5×Q8⋊C8—31no—
32#64702—31no—
33#64679—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×Dic30—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
45#6714—22no—
46#6714—22no—
47#6714—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15D411yescharacteristic
50C4⋊Dic15D412yes—
51#6712—22no—
52C4×Dic15—22no—
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8—21no—
55C3×#688—42no—
56C2×C3×#168—21no—
57#6653—42no—
58#5584—51no—
59C3×#460—51no—
60#5072—51no—
61#5070—51no—
62#4535D511yescharacteristic, complemented
63#4486—51no—
64#4483—51no—
65C4×C5×Q8C2×D311yescharacteristic
66#4092—61no—
67C2×#688—21no—
68C2×D40—61no—
69#4044—62no—
70#4038—61no—
71#4021—61no—
72#4020C2×D311yescharacteristic
73C4×D20—31no—
74#4015—31no—
75C4×Dic10—61no—
76C5×C4⋊C8—31no—
77C4×C5×C8—31no—
78#3953—61no—
79#3953—62no—
80#3941—21no—
81C4⋊#168C2×D311yescharacteristic
82#1628—151noSylow
83C22×D15—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×Dic15—21no—
93C2×Dic15—22no—
94D60—21no—
95D60—21no—
96C4×D15—41no—
97C4×D15—41no—
98Dic30—41no—
99Dic30—41no—
100C3×D20—42no—
101C3×D20—41no—
102C3×D20—41no—
103C3×D20—41no—
104C3×D20—41no—
105C3×#168—41no—
106C5×C3⋊C8—41no—
107C5×C3⋊C8—41no—
108C2×C3×SD16—101no—
109C3×#127—51no—
110C3×C4×Q8C2×D511yescharacteristic
111#946—101no—
112C2×#213—101no—
113#898—102no—
114#892—101no—
115#875—101no—
116C4×D12—51no—
117#869—51no—
118C4×Dic6—101no—
119C3×C4⋊C8—51no—
120C3×#102—101no—
121#832—102no—
122#832—101no—
123C4⋊(C3⋊C8)C2×D511yescharacteristic
124C4×C3⋊C8C2×D511yescharacteristic
125C2×C5×Q8#6711yescharacteristic
126C2×D20—21no—
127C2×D20—21no—
128C2×D20—21no—
129C2×D20—31no—
130C2×C4×D5—61no—
131C2×Dic10—61no—
132C2×C5×C8—61no—
133C2×C5×C8—61no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4#6711yescharacteristic
136C42×C5—21no—
137C42×C5C22×D311yescharacteristic
138#688—42no—
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—21no—
148D40—122no—
149#556—151no—
150#486—151no—
151#460—51no—
152#459—151no—
153#332—151no—
154Q8⋊C8—31no—
155D4⋊C8—151no—
156C22×C3×C5#12011yescharacteristic
157C2×D15—41no—
158C2×D15—41no—
159C2×D15—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
170Dic15—42no—
171Dic15—41no—
172C2×C3×Q8D2011yescharacteristic
173C2×C3×D4—101no—
174C2×C3×D4—101no—
175C2×C3×D4—101no—
176C2×D12—51no—
177C2×C4×D3—101no—
178C2×Dic6—101no—
179C3×SD16—202no—
180C2×C3×C8—101no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4D2011yescharacteristic
183C3×C42—21no—
184C3×C42C22×D511yescharacteristic
185#213—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—21no—
195C2×C3⋊C8—21no—
196C22×D5—41no—
197C22×D5—61no—
198C5×Q8—21no—
199C5×Q8—21no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5D3×D411yescharacteristic
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5C2×#6711yescharacteristic
205C2×Dic5—61no—
206C2×Dic5—62no—
207D20—42no—
208D20—41no—
209D20—41no—
210D20—41no—
211D20—41no—
212D20—61no—
213D20—61no—
214C4×D5—121no—
215C4×D5—121no—
216Dic10—121no—
217Dic10—121no—
218C5×C8—121no—
219C5×C8—121no—
220#168—41no—
221C2×SD16—101no—
222C2×D8—301no—
223C4⋊Q8—151no—
224#127—51no—
225#126—302no—
226#124—301no—
227C22⋊Q8—301no—
228C4×Q8—301no—
229C4×Q8D3×D511yescharacteristic
230C4×D4—151no—
231#117—301no—
232C4⋊C8—31no—
233C4⋊C8—51no—
234#102—101no—
235#102—301no—
236#102—302no—
237C4×C8—31no—
238C2×C3×C5#44911yescharacteristic
239C2×C3×C5#44911yescharacteristic
240C2×C3×C5#45411yescharacteristic
241D15—81no—
242C3×D5—161no—
243C23×C3—201no—
244C22×D3—101no—
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×D2011yescharacteristic
255C2×C3×C4D4×D511yescharacteristic
256C2×C3×C4D4×D511yescharacteristic
257C2×Dic3—101no—
258C2×Dic3—102no—
259D12—101no—
260D12—101no—
261C4×D3—201no—
262C4×D3—201no—
263Dic6—201no—
264Dic6—201no—
265C3×C8—201no—
266C3⋊C8—41no—
267C3⋊C8—41no—
268C22×C5#93711yescharacteristic
269C2×D5—81no—
270C2×D5—81no—
271C2×D5—81no—
272C2×D5—121no—
273C2×D5—121no—
274C2×D5—121no—
275C4×C5—21no—
276C4×C5—41no—
277C4×C5—41no—
278C4×C5#91411yescharacteristic
279C4×C5#91611yescharacteristic
280C4×C5#93211yescharacteristic
281C4×C5#95011yescharacteristic
282Dic5—122no—
283Dic5—121no—
284C2×Q8—301no—
285C2×Q8#120211yescharacteristic
286C2×D4—101no—
287C2×D4—101no—
288C2×D4—101no—
289C2×D4—151no—
290C22×C4—301no—
291SD16—202no—
292D8—602no—
293C2×C8—61no—
294C2×C8—61no—
295C2×C8—101no—
296C4⋊C4—21no—
297C4⋊C4—151no—
298C4⋊C4—152no—
299C4⋊C4—302no—
300C4⋊C4—301no—
301C4⋊C4#120211yescharacteristic
302C22⋊C4—302no—
303C22⋊C4—302no—
304C22⋊C4—301no—
305C42—21no—
306C42—302no—
307C42C2×D3×D511yescharacteristic
308C3×C5#162811yescharacteristic, complemented, Hall
309C22×C3—401no—
310C22×C3—401no—
311C22×C3—401no—
312C22×C3#402811yescharacteristic
313C2×D3—201no—
314C2×D3—201no—
315C2×D3—201no—
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#503711yescharacteristic
326C2×C5#517211yescharacteristic
327C2×C5#520111yescharacteristic
328D5—161no—
329D5—241no—
330C23—201no—
331C23—301no—
332Q8—21no—
333Q8—21no—
334Q8—601no—
335Q8—601no—
336D4—202no—
337D4—201no—
338D4—201no—
339D4—201no—
340D4—201no—
341D4—301no—
342D4—301no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—301no—
346C2×C4—302no—
347C2×C4—601no—
348C2×C4—601no—
349C2×C4C2×#120211yescharacteristic
350C2×C4#679011yescharacteristic
351C2×C4#679011yescharacteristic
352C8—121no—
353C8—121no—
354C8—201no—
355C2×C3—801no—
356C2×C3#6502311yescharacteristic
357C2×C3#6510011yescharacteristic
358C2×C3#6511611yescharacteristic
359D3—401no—
360C5#7102911yescharacteristic, complemented, Sylow
361C22—401no—
362C22—401no—
363C22—401no—
364C22—601no—
365C22—601no—
366C22—601no—
367C22#9157211yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—602no—
372C4—601no—
373C4#9131111yescharacteristic
374C4#9131211yescharacteristic
375C4#9150611yescharacteristic
376C4#9152111yescharacteristic
377C3#1059903811yescharacteristic, complemented, Sylow
378C2—801no—
379C2—1201no—
380C2#1174855011yescharacteristic
381C2#1174928811yescharacteristic
382C2#1174946011yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radical#11747043C2
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. #11756343C2semidirect
2. C3×#65316C2semidirect
4. #11746890C2semidirect
5. C5×#4535C2semidirect
6. #11745859C2semidirect
7. #11745838C2semidirect
28. #65316D3semidirect
62. #4535D5semidirect
308. C3×C5#1628semidirect
360. C5#71029semidirect
377. C3#10599038semidirect

Maximal subgroups

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

subgroupindex
#117563432
C3×#653162
#117470432
#117468902
C5×#45352
#117458592
#117458382
#105990383
#710295