Finite Group Databasebeta

← #14289000

Subgroups — #14289000

Order 1920.

472 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 96 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×#65913C211yesmaximal, characteristic, complemented
2#11751128C211yesmaximal, characteristic, complemented
3#11747075C211yesmaximal, characteristic, complemented
4#11747028C211yesmaximal, characteristic
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745861C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic, complemented
8#10599037—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C2×#6717—21no—
11#91763C2211yescharacteristic
12C3×#4092—21no—
13C3×#4042—22no—
14C3×D5×C4⋊C4—21no—
15C3×C4×D20—21no—
16C3×C4×D20C2211yescharacteristic
17C3×#4016—21no—
18C3×#4015C2211yescharacteristic
19C2×#6658—22no—
20C2×#6653—21no—
21#91093—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C4×C5×C3⋊C8C2211yescharacteristic
25#90968—21no—
26#71923—51nomaximal, Hall
27#65913D311yescharacteristic, complemented
28#65316—31no—
29#65132—31no—
30#64982—31no—
31C5×Q8⋊C8—31no—
32#64701—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×C4×D5—22no—
41C2×C3×Dic10D412yes—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C42×C5—21no—
45C3×C42×C5C2311yescharacteristic
46#6717—42no—
47C2×C3⋊#168—21no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C3×#685—22no—
51C3×#685—21no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C3×#683—22no—
56C3×#683—22no—
57#6658—44no—
58#6653—42no—
59C3×#554—51no—
60#5085—51no—
61#5027—51no—
62#5015—51no—
63#4546—51no—
64#4535D511yescharacteristic, complemented
65D4⋊(C3⋊C8)—51no—
66C4×C5×Q8C2×D311yescharacteristic
67#4092—21no—
68C2×#688—61no—
69C2×D40—61no—
70C2×#677—62no—
71#4042—22no—
72D5×C4⋊C4—21no—
73#4020—31no—
74C4×D20—21no—
75C4×D20C2×D311yescharacteristic
76#4016—21no—
77#4015C2×D311yescharacteristic
78C5×C4⋊C8—31no—
79C4×C5×C8—31no—
80#3953—61no—
81#3941—61no—
82C4⋊#168—31no—
83#1622—151noSylow
84C22×D15—41no—
85C22×C3×D5—21no—
86C3×C5×Q8—21no—
87C3×C5×Q8—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93D60—42no—
94D60—41no—
95D60—41no—
96D60—41no—
97D60—41no—
98C2×C3×Dic5—21no—
99C2×C3×Dic5—22no—
100C3×D20—21no—
101C3×D20SD1612yescomplemented
102C3×C4×D5—41no—
103C3×C4×D5—41no—
104C3×C4×D5—82no—
105C3×Dic10—42no—
106C3⋊#168—41no—
107C5×C3⋊C8—22no—
108C5×C3⋊C8—41no—
109C3×C4⋊Q8—51no—
110C3×#125—101no—
111C3×C22⋊Q8—102no—
112C3×C22⋊Q8—101no—
113C3×C4×Q8C2×D511yescharacteristic
114C3×C4×D4—51no—
115C3×C4×D4—101no—
116C2×C3×C4⋊C4—101no—
117C2×#215—102no—
118C2×#215—101no—
119C2×#213—101no—
120#874—51no—
121#809—101no—
122#809—101no—
123C4⋊(C3⋊C8)—51no—
124C4⋊(C3⋊C8)C2×D511yescharacteristic
125C4×C3⋊C8C2×D511yescharacteristic
126C2×C5×Q8#6711yescharacteristic
127C2×D20—61no—
128C2×D20—61no—
129C2×D20—61no—
130C2×D20#6711yescharacteristic
131C2×C4×D5—21no—
132C2×C4×D5—22no—
133C2×Dic10#6712yes—
134C2×C5×C8—61no—
135C2×C5×C8—61no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4#6711yescharacteristic
138C42×C5—21no—
139C42×C5C22×D311yescharacteristic
140#688—122no—
141#685—22no—
142#685—21no—
143C4⋊Dic5—21no—
144C4⋊Dic5—21no—
145C4⋊Dic5#6711yescharacteristic
146#683—22no—
147#683—22no—
148C2×#168—61no—
149D40—122no—
150#677—124no—
151#554—51no—
152#492—151no—
153#460—151no—
154#459—151no—
155#333—151no—
156Q8⋊C8—31no—
157D4⋊C8—151no—
158C22×C3×C5#12011yescharacteristic
159C2×D15—81no—
160C2×D15—81no—
161C2×D15—81no—
162C2×C3×D5—22no—
163C2×C3×D5—41no—
164C2×C3×D5—41no—
165C3×C4×C5—21no—
166C3×C4×C5—41no—
167C3×C4×C5—41no—
168C3×C4×C5C2×SD1611yescharacteristic
169C3×C4×C5#13511yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C3×C4×C5#13711yescharacteristic
172C3×Dic5—41no—
173C3×Dic5—42no—
174C2×C3×Q8—52no—
175C2×C3×Q8D2011yescharacteristic
176C2×C3×D4—51no—
177C22×C3×C4—102no—
178C22×C3×C4—101no—
179C2×D12—101no—
180C2×D12—101no—
181C2×D12—101no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—51no—
184C3×C4⋊C4—102no—
185C3×C4⋊C4—102no—
186C3×C4⋊C4—101no—
187C3×C4⋊C4—101no—
188C3×C4⋊C4D2011yescharacteristic
189C3×C22⋊C4—102no—
190C3×C22⋊C4—101no—
191C3×C42—21no—
192C3×C42C22×D511yescharacteristic
193#215—204no—
194#215—202no—
195#213—202no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—101no—
199C22×D5—21no—
200C22×D5—121no—
201C5×Q8—21no—
202C5×Q8—21no—
203C2×C4×C5—21no—
204C2×C4×C5—21no—
205C2×C4×C5C2×#6711yescharacteristic
206C2×C4×C5C2×#6711yescharacteristic
207C2×C4×C5C2×#6711yescharacteristic
208C2×Dic5—21no—
209C2×Dic5—22no—
210D20—21no—
211D20—122no—
212D20—121no—
213D20—121no—
214D20—121no—
215D20—121no—
216D20#21512yescomplemented
217C4×D5—41no—
218C4×D5—41no—
219C4×D5—82no—
220Dic10—42no—
221C5×C8—62no—
222C5×C8—121no—
223#168—121no—
224C2×SD16—302no—
225C2×SD16—301no—
226C2×D8—301no—
227C4⋊Q8—51no—
228#127—151no—
229#125—101no—
230C22⋊Q8—102no—
231C22⋊Q8—101no—
232C4×Q8D3×D511yescharacteristic
233C4×D4—51no—
234C4×D4—101no—
235C2×C4⋊C4—101no—
236C4⋊C8—31no—
237C4⋊C8—151no—
238#102—301no—
239#102—301no—
240C4×C8—31no—
241C2×C3×C5#44811yescharacteristic
242C2×C3×C5#44911yescharacteristic
243C2×C3×C5#45311yescharacteristic
244D15—161no—
245C3×D5—42no—
246C23×C3—101no—
247C22×D3—201no—
248C3×Q8—21no—
249C3×Q8—21no—
250C3×Q8—202no—
251C3×D4—52no—
252C3×D4—101no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—101no—
256C2×C3×C4—102no—
257C2×C3×C4—201no—
258C2×C3×C4—201no—
259C2×C3×C4—402no—
260C2×C3×C4C2×D2011yescharacteristic
261C2×C3×C4D4×D511yescharacteristic
262C2×C3×C4D4×D511yescharacteristic
263D12—202no—
264D12—201no—
265D12—201no—
266D12—201no—
267D12—201no—
268C3⋊C8—22no—
269C3⋊C8—41no—
270C3⋊C8—201no—
271C22×C5#95311yescharacteristic
272C2×D5—22no—
273C2×D5—41no—
274C2×D5—41no—
275C2×D5—241no—
276C2×D5—241no—
277C2×D5—241no—
278C4×C5—21no—
279C4×C5—41no—
280C4×C5—41no—
281C4×C5C2×#21511yescharacteristic
282C4×C5#94211yescharacteristic
283C4×C5#94911yescharacteristic
284C4×C5#95011yescharacteristic
285Dic5—41no—
286Dic5—42no—
287C2×Q8—52no—
288C2×Q8#120211yescharacteristic
289C2×D4—51no—
290C2×D4—301no—
291C2×D4—301no—
292C2×D4—301no—
293C22×C4—102no—
294C22×C4—101no—
295SD16—604no—
296SD16—602no—
297D8—602no—
298C2×C8—61no—
299C2×C8—61no—
300C2×C8—301no—
301C4⋊C4—21no—
302C4⋊C4—51no—
303C4⋊C4—102no—
304C4⋊C4—102no—
305C4⋊C4—101no—
306C4⋊C4—101no—
307C4⋊C4#120211yescharacteristic
308C22⋊C4—102no—
309C22⋊C4—101no—
310C42—21no—
311C42C2×D3×D511yescharacteristic
312C3×C5#162211yescharacteristic, complemented, Hall
313C22×C3—102no—
314C22×C3—201no—
315C22×C3—201no—
316C22×C3#402811yescharacteristic
317C2×D3—401no—
318C2×D3—401no—
319C2×D3—401no—
320C3×C4—21no—
321C3×C4—41no—
322C3×C4—41no—
323C3×C4—202no—
324C3×C4—201no—
325C3×C4#405011yescharacteristic
326C3×C4#405411yescharacteristic
327C3×C4D5×SD1611yescharacteristic
328C3×C4#406411yescharacteristic
329C2×C5#522711yescharacteristic
330C2×C5#523811yescharacteristic
331C2×C5#524111yescharacteristic
332D5—42no—
333D5—481no—
334C23—101no—
335C23—601no—
336Q8—21no—
337Q8—21no—
338Q8—202no—
339D4—52no—
340D4—101no—
341D4—602no—
342D4—601no—
343D4—601no—
344D4—601no—
345D4—601no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—101no—
349C2×C4—102no—
350C2×C4—201no—
351C2×C4—201no—
352C2×C4—402no—
353C2×C4C2×#120211yescharacteristic
354C2×C4D5×#6711yescharacteristic
355C2×C4D5×#6711yescharacteristic
356C8—62no—
357C8—121no—
358C8—601no—
359C2×C3—202no—
360C2×C3#6502311yescharacteristic
361C2×C3#6509511yescharacteristic
362C2×C3#6511111yescharacteristic
363D3—801no—
364C5#7192311yescharacteristic, complemented, Sylow
365C22—102no—
366C22—201no—
367C22—201no—
368C22—1201no—
369C22—1201no—
370C22—1201no—
371C22#9156411yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—202no—
376C4—201no—
377C4#9130111yescharacteristic
378C4#9131111yescharacteristic
379C4D5×#21511yescharacteristic
380C4#9151511yescharacteristic
381C3#1059903711yescharacteristic, complemented, Sylow
382C2—202no—
383C2—2401no—
384C2#1174851311yescharacteristic
385C2#1174926811yescharacteristic
386C2#1174941811yescharacteristic
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#1622
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×#65913C2semidirect
2. #11751128C2semidirect
3. #11747075C2semidirect
5. C5×#4535C2semidirect
6. #11745861C2semidirect
7. #11745835C2semidirect
27. #65913D3semidirect
64. #4535D5semidirect
101. C3×D20SD16semidirect
216. D20#215semidirect
312. C3×C5#1622semidirect
364. C5#71923semidirect
381. C3#10599037semidirect

Maximal subgroups

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

subgroupindex
C3×#659132
#117511282
#117470752
#117470282
C5×#45352
#117458612
#117458352
#105990373
#719235