Finite Group Databasebeta

← #14289330

Subgroups — #14289330

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
1C3×#65918C211yesmaximal, characteristic, complemented
2#11751128C211yesmaximal, characteristic, complemented
3#11747028C211yesmaximal, characteristic
4#11746910C211yesmaximal, characteristic, complemented
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745856C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic, complemented
8#10599038—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C2×#6717—21no—
11#91763C2211yescharacteristic
12C3×#4092—21no—
13C3×#4044—22no—
14C3×#4038—21no—
15C3×#4021—21no—
16C3×C4×D20C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C3×C4×Dic10—21no—
19C2×#6653—21no—
20#91093—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C4×C5×C3⋊C8C2211yescharacteristic
24#90968—22no—
25#90968—21no—
26#71931—51nomaximal, Hall
27#65918D311yescharacteristic, complemented
28#65316—31no—
29#65132—31no—
30#64983—31no—
31C5×Q8⋊C8—31no—
32#64702—31no—
33#64679—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×D60—21no—
36C2×D60—21no—
37C2×D60—21no—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×C3×Dic10—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C42×C5—21no—
44C3×C42×C5C2311yescharacteristic
45#6717—42no—
46C2×C3⋊#168—21no—
47C2×C5×C3⋊C8—21no—
48C2×C5×C3⋊C8—21no—
49C3×#685—22no—
50C3×#685—22no—
51C3×#685—21no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5D411yescharacteristic
54C3×C4⋊Dic5D412yes—
55C3×#683—22no—
56C3×C4×Dic5—22no—
57#6653—42no—
58C3×#556—51no—
59#5088—51no—
60#5027—51no—
61#5015—51no—
62#4547—51no—
63#4535D511yescharacteristic, complemented
64D4⋊(C3⋊C8)—51no—
65C4×C5×Q8C2×D311yescharacteristic
66#4092—21no—
67C2×#688—61no—
68C2×D40—61no—
69#4044—22no—
70#4038—21no—
71#4021—21no—
72#4020—31no—
73C4×D20C2×D311yescharacteristic
74#4015C2×D311yescharacteristic
75C4×Dic10—21no—
76C5×C4⋊C8—31no—
77C4×C5×C8—31no—
78#3953—61no—
79#3953—62no—
80#3941—61no—
81C4⋊#168—31no—
82#1628—151noSylow
83C22×D15—41no—
84C22×C3×D5—21no—
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
92D60—42no—
93D60—41no—
94D60—41no—
95D60—41no—
96D60—41no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—22no—
99C3×D20—21no—
100C3×D20—21no—
101C3×C4×D5—41no—
102C3×C4×D5—41no—
103C3×Dic10—41no—
104C3×Dic10—41no—
105C3⋊#168—41no—
106C5×C3⋊C8—41no—
107C5×C3⋊C8—41no—
108C3×C4⋊Q8—51no—
109C3×#126—102no—
110C3×#124—101no—
111C3×C22⋊Q8—101no—
112C3×C4×Q8—101no—
113C3×C4×Q8C2×D511yescharacteristic
114C3×C4×D4—51no—
115C3×#117—101no—
116C2×#215—101no—
117C2×#213—101no—
118#874—51no—
119#809—101no—
120#809—102no—
121#809—101no—
122C4⋊(C3⋊C8)—51no—
123C4⋊(C3⋊C8)C2×D511yescharacteristic
124C4×C3⋊C8C2×D511yescharacteristic
125C2×C5×Q8#6711yescharacteristic
126C2×D20—61no—
127C2×D20—61no—
128C2×D20—61no—
129C2×D20#6711yescharacteristic
130C2×C4×D5—21no—
131C2×Dic10—21no—
132C2×C5×C8—61no—
133C2×C5×C8—61no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4#6711yescharacteristic
136C42×C5—21no—
137C42×C5C22×D311yescharacteristic
138#688—122no—
139#685—22no—
140#685—22no—
141#685—21no—
142C4⋊Dic5—21no—
143C4⋊Dic5#6711yescharacteristic
144C4⋊Dic5#6712yes—
145#683—22no—
146C4×Dic5—22no—
147C2×#168—61no—
148D40—122no—
149#556—51no—
150#486—151no—
151#460—151no—
152#459—151no—
153#332—151no—
154Q8⋊C8—31no—
155D4⋊C8—151no—
156C22×C3×C5#12011yescharacteristic
157C2×D15—81no—
158C2×D15—81no—
159C2×D15—81no—
160C2×C3×D5—41no—
161C2×C3×D5—41no—
162C2×C3×D5—41no—
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
170C3×Dic5—42no—
171C3×Dic5—41no—
172C2×C3×Q8—101no—
173C2×C3×Q8D2011yescharacteristic
174C2×C3×D4—51no—
175C22×C3×C4—101no—
176C2×D12—101no—
177C2×D12—101no—
178C2×D12—101no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—51no—
181C3×C4⋊C4—52no—
182C3×C4⋊C4—102no—
183C3×C4⋊C4—101no—
184C3×C4⋊C4D2011yescharacteristic
185C3×C22⋊C4—102no—
186C3×C22⋊C4—102no—
187C3×C22⋊C4—101no—
188C3×C42—21no—
189C3×C42—102no—
190C3×C42C22×D511yescharacteristic
191#215—202no—
192#213—202no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—101no—
196C22×D5—21no—
197C22×D5—121no—
198C5×Q8—21no—
199C5×Q8—21no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5C2×#6711yescharacteristic
203C2×C4×C5C2×#6711yescharacteristic
204C2×C4×C5C2×#6711yescharacteristic
205C2×Dic5—21no—
206C2×Dic5—22no—
207D20—21no—
208D20—21no—
209D20—122no—
210D20—121no—
211D20—121no—
212D20—121no—
213D20—121no—
214C4×D5—41no—
215C4×D5—41no—
216Dic10—41no—
217Dic10—41no—
218C5×C8—121no—
219C5×C8—121no—
220#168—121no—
221C2×SD16—301no—
222C2×D8—301no—
223C4⋊Q8—51no—
224#127—151no—
225#126—102no—
226#124—101no—
227C22⋊Q8—101no—
228C4×Q8—101no—
229C4×Q8D3×D511yescharacteristic
230C4×D4—51no—
231#117—101no—
232C4⋊C8—31no—
233C4⋊C8—151no—
234#102—301no—
235#102—302no—
236#102—301no—
237C4×C8—31no—
238C2×C3×C5#44911yescharacteristic
239C2×C3×C5#44911yescharacteristic
240C2×C3×C5#45411yescharacteristic
241D15—161no—
242C3×D5—81no—
243C23×C3—101no—
244C22×D3—201no—
245C3×Q8—21no—
246C3×Q8—21no—
247C3×Q8—201no—
248C3×Q8—201no—
249C3×D4—101no—
250C3×D4—101no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—101no—
254C2×C3×C4—102no—
255C2×C3×C4—201no—
256C2×C3×C4—201no—
257C2×C3×C4C2×D2011yescharacteristic
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260D12—202no—
261D12—201no—
262D12—201no—
263D12—201no—
264D12—201no—
265C3⋊C8—41no—
266C3⋊C8—41no—
267C3⋊C8—201no—
268C22×C5#95311yescharacteristic
269C2×D5—41no—
270C2×D5—41no—
271C2×D5—41no—
272C2×D5—241no—
273C2×D5—241no—
274C2×D5—241no—
275C4×C5—21no—
276C4×C5—41no—
277C4×C5—41no—
278C4×C5#94911yescharacteristic
279C4×C5#94911yescharacteristic
280C4×C5#95011yescharacteristic
281C4×C5#95011yescharacteristic
282Dic5—42no—
283Dic5—41no—
284C2×Q8—101no—
285C2×Q8#120211yescharacteristic
286C2×D4—51no—
287C2×D4—301no—
288C2×D4—301no—
289C2×D4—301no—
290C22×C4—101no—
291SD16—602no—
292D8—602no—
293C2×C8—61no—
294C2×C8—61no—
295C2×C8—301no—
296C4⋊C4—21no—
297C4⋊C4—51no—
298C4⋊C4—52no—
299C4⋊C4—102no—
300C4⋊C4—101no—
301C4⋊C4#120211yescharacteristic
302C22⋊C4—102no—
303C22⋊C4—102no—
304C22⋊C4—101no—
305C42—21no—
306C42—102no—
307C42C2×D3×D511yescharacteristic
308C3×C5#162811yescharacteristic, complemented, Hall
309C22×C3—201no—
310C22×C3—201no—
311C22×C3—201no—
312C22×C3#402811yescharacteristic
313C2×D3—401no—
314C2×D3—401no—
315C2×D3—401no—
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—41no—
319C3×C4—202no—
320C3×C4—201no—
321C3×C4#405011yescharacteristic
322C3×C4#405411yescharacteristic
323C3×C4#406011yescharacteristic
324C3×C4#406511yescharacteristic
325C2×C5#523811yescharacteristic
326C2×C5#523811yescharacteristic
327C2×C5#524511yescharacteristic
328D5—81no—
329D5—481no—
330C23—101no—
331C23—601no—
332Q8—21no—
333Q8—21no—
334Q8—201no—
335Q8—201no—
336D4—101no—
337D4—101no—
338D4—602no—
339D4—601no—
340D4—601no—
341D4—601no—
342D4—601no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—101no—
346C2×C4—102no—
347C2×C4—201no—
348C2×C4—201no—
349C2×C4C2×#120211yescharacteristic
350C2×C4D5×#6711yescharacteristic
351C2×C4D5×#6711yescharacteristic
352C8—121no—
353C8—121no—
354C8—601no—
355C2×C3—401no—
356C2×C3#6502311yescharacteristic
357C2×C3#6510011yescharacteristic
358C2×C3#6511611yescharacteristic
359D3—801no—
360C5#7193111yescharacteristic, complemented, Sylow
361C22—201no—
362C22—201no—
363C22—201no—
364C22—1201no—
365C22—1201no—
366C22—1201no—
367C22#9156411yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—202no—
372C4—201no—
373C4#9130111yescharacteristic
374C4#9131111yescharacteristic
375C4#9150211yescharacteristic
376C4#9151611yescharacteristic
377C3#1059903811yescharacteristic, complemented, Sylow
378C2—401no—
379C2—2401no—
380C2#1174851311yescharacteristic
381C2#1174927211yescharacteristic
382C2#1174945711yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radical#11747028C2
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. C3×#65918C2semidirect
2. #11751128C2semidirect
4. #11746910C2semidirect
5. C5×#4535C2semidirect
6. #11745856C2semidirect
7. #11745835C2semidirect
27. #65918D3semidirect
63. #4535D5semidirect
308. C3×C5#1628semidirect
360. C5#71931semidirect
377. C3#10599038semidirect

Maximal subgroups

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

subgroupindex
C3×#659182
#117511282
#117470282
#117469102
C5×#45352
#117458562
#117458352
#105990383
#719315