Finite Group Databasebeta

← #14289075

Subgroups — #14289075

Order 1920.

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

normal subgroups only

This group has 480 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×#65897C211yesmaximal, characteristic, complemented
2#11751116C211yesmaximal, characteristic, complemented
3#11747075C211yesmaximal, characteristic, complemented
4#11747028C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#11745861C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic, complemented
8#10598992—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C2×#6715—21no—
11#91763C2211yescharacteristic
12C3×#4084—21no—
13C3×#4076—21no—
14C3×#4072—21no—
15C3×#4038—21no—
16C3×#4031—22no—
17C3×C4×D20C2211yescharacteristic
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#71927—51nomaximal, Hall
27#65897D311yescharacteristic, complemented
28#65304—31no—
29#65132—31no—
30#64982—31no—
31C5×D4⋊C8—31no—
32#64701—31no—
33#64679—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×D60—21no—
37C2×D60—21no—
38C2×D60—21no—
39C2×C3×C22⋊D5—22no—
40C2×C3×D20D411yescharacteristic
41C2×C3×C4×D5—21no—
42C2×C3×Dic10D412yes—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C5×C22⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46#6715—42no—
47C2×C3⋊#168—21no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C3×C22⋊Dic5—22no—
51C3×#685—22no—
52C3×#685—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5D411yescharacteristic
56C3×C4×Dic5—22no—
57#6658—44no—
58#6653—42no—
59C3×#555—51no—
60#5085—51no—
61#5015—51no—
62#5015—51no—
63#4546—51no—
64D4⋊(C3⋊C8)—51no—
65D4⋊(C3⋊C8)D511yescharacteristic, complemented
66C4×C5×D4C2×D311yescharacteristic
67#4084—21no—
68C2×#686—61no—
69#4076—21no—
70#4072—21no—
71C2×D40—61no—
72C2×#677—62no—
73#4038—21no—
74#4031—22no—
75#4020—31no—
76C4×D20C2×D311yescharacteristic
77#4015C2×D311yescharacteristic
78C5×C4⋊C8—31no—
79C4×C5×C8—31no—
80#3953—61no—
81#3941—61no—
82C4⋊#168—31no—
83#1624—151noSylow
84C23×C3×C5—21no—
85C22×D15—41no—
86C22×C3×D5—21no—
87C3×C5×D4—21no—
88C3×C5×D4—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95D60—42no—
96D60—41no—
97D60—41no—
98D60—41no—
99D60—41no—
100C3×C22⋊D5—82no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—22no—
103C3×D20—21no—
104C3×D20—21no—
105C3×C4×D5—41no—
106C3×C4×D5—41no—
107C3×Dic10—42no—
108C3⋊#168—41no—
109C5×C3⋊C8—22no—
110C5×C3⋊C8—41no—
111C3×C4⋊Q8—51no—
112C3×#124—102no—
113C3×#121—101no—
114C3×#121—101no—
115C3×C4×D4—51no—
116C3×C4×D4C2×D511yescharacteristic
117C3×#117—101no—
118C3×#117—101no—
119C2×#215—102no—
120C2×#213—101no—
121C2×#213—101no—
122#874—51no—
123#809—101no—
124#809—101no—
125C4⋊(C3⋊C8)—51no—
126C4⋊(C3⋊C8)C2×D511yescharacteristic
127C4×C3⋊C8C2×D511yescharacteristic
128C2×C5×D4#6711yescharacteristic
129C22×C4×C5—21no—
130C2×C22⋊D5—22no—
131C2×D20—61no—
132C2×D20—61no—
133C2×D20—61no—
134C2×D20#6711yescharacteristic
135C2×C4×D5—21no—
136C2×Dic10#6712yes—
137C2×C5×C8—61no—
138C2×C5×C8—61no—
139C5×C4⋊C4#6711yescharacteristic
140C5×C22⋊C4—21no—
141C42×C5C22×D311yescharacteristic
142C22⋊Dic5—22no—
143#686—122no—
144#685—22no—
145#685—21no—
146C4⋊Dic5—21no—
147C4⋊Dic5—21no—
148C4⋊Dic5#6711yescharacteristic
149C4×Dic5—22no—
150C2×#168—61no—
151D40—122no—
152#677—124no—
153#555—51no—
154#492—151no—
155#459—151no—
156#459—151no—
157#333—151no—
158D4⋊C8—31no—
159D4⋊C8—151no—
160C22×C3×C5—41no—
161C22×C3×C5—41no—
162C22×C3×C5—41no—
163C22×C3×C5#12011yescharacteristic
164C2×D15—81no—
165C2×D15—81no—
166C2×D15—81no—
167C2×C3×D5—41no—
168C2×C3×D5—41no—
169C2×C3×D5—41no—
170C3×C4×C5—21no—
171C3×C4×C5—41no—
172C3×C4×C5#13511yescharacteristic
173C3×C4×C5#13511yescharacteristic
174C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
175C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
176C3×Dic5—41no—
177C3×Dic5—42no—
178C2×C3×Q8—52no—
179C2×C3×D4—51no—
180C2×C3×D4—102no—
181C2×C3×D4D2011yescharacteristic
182C22×C3×C4—21no—
183C22×C3×C4—101no—
184C2×D12—101no—
185C2×D12—101no—
186C2×D12—101no—
187C3×C4⋊C4—51no—
188C3×C4⋊C4—101no—
189C3×C4⋊C4—101no—
190C3×C4⋊C4D2011yescharacteristic
191C3×C22⋊C4—21no—
192C3×C22⋊C4—102no—
193C3×C22⋊C4—102no—
194C3×C22⋊C4—101no—
195C3×C42—102no—
196C3×C42C22×D511yescharacteristic
197#215—204no—
198#213—202no—
199#213—202no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—101no—
203C23×C5—21no—
204C22×D5—21no—
205C22×D5—121no—
206C5×D4—21no—
207C5×D4—21no—
208C2×C4×C5—21no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5C2×#6711yescharacteristic
212C2×C4×C5C2×#6711yescharacteristic
213C2×C4×C5C2×#6711yescharacteristic
214C22⋊D5—82no—
215C2×Dic5—21no—
216C2×Dic5—22no—
217D20—21no—
218D20—21no—
219D20—122no—
220D20—121no—
221D20—121no—
222D20—121no—
223D20—121no—
224C4×D5—41no—
225C4×D5—41no—
226Dic10—42no—
227C5×C8—62no—
228C5×C8—121no—
229#168—121no—
230C2×SD16—302no—
231C2×D8—301no—
232C2×D8—301no—
233C4⋊Q8—51no—
234#127—151no—
235#124—102no—
236#121—101no—
237#121—101no—
238C4×D4—51no—
239C4×D4D3×D511yescharacteristic
240#117—101no—
241#117—101no—
242C4⋊C8—31no—
243C4⋊C8—151no—
244#102—301no—
245#102—301no—
246C4×C8—31no—
247C2×C3×C5—81no—
248C2×C3×C5#44911yescharacteristic
249C2×C3×C5#44911yescharacteristic
250C2×C3×C5#45311yescharacteristic
251D15—161no—
252C3×D5—81no—
253C23×C3—21no—
254C23×C3—101no—
255C22×D3—201no—
256C3×Q8—202no—
257C3×D4—21no—
258C3×D4—21no—
259C3×D4—101no—
260C3×D4—101no—
261C3×D4—402no—
262C2×C3×C4—21no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—101no—
266C2×C3×C4—102no—
267C2×C3×C4—201no—
268C2×C3×C4—201no—
269C2×C3×C4C2×D2011yescharacteristic
270C2×C3×C4D4×D511yescharacteristic
271C2×C3×C4D4×D511yescharacteristic
272D12—202no—
273D12—201no—
274D12—201no—
275D12—201no—
276D12—201no—
277C3⋊C8—22no—
278C3⋊C8—41no—
279C3⋊C8—201no—
280C22×C5—41no—
281C22×C5—41no—
282C22×C5—41no—
283C22×C5#95311yescharacteristic
284C2×D5—41no—
285C2×D5—41no—
286C2×D5—41no—
287C2×D5—241no—
288C2×D5—241no—
289C2×D5—241no—
290C4×C5—21no—
291C4×C5—41no—
292C4×C5#94911yescharacteristic
293C4×C5#94911yescharacteristic
294C4×C5#95011yescharacteristic
295C4×C5#95011yescharacteristic
296Dic5—41no—
297Dic5—42no—
298C2×Q8—52no—
299C2×D4—51no—
300C2×D4—102no—
301C2×D4—301no—
302C2×D4—301no—
303C2×D4—301no—
304C2×D4#120211yescharacteristic
305C22×C4—21no—
306C22×C4—101no—
307SD16—604no—
308D8—602no—
309D8—602no—
310C2×C8—61no—
311C2×C8—61no—
312C2×C8—301no—
313C4⋊C4—51no—
314C4⋊C4—101no—
315C4⋊C4—101no—
316C4⋊C4#120211yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—102no—
319C22⋊C4—102no—
320C22⋊C4—101no—
321C42—102no—
322C42C2×D3×D511yescharacteristic
323C3×C5#162411yescharacteristic, complemented, Hall
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—201no—
328C22×C3—201no—
329C22×C3—201no—
330C22×C3#402811yescharacteristic
331C2×D3—401no—
332C2×D3—401no—
333C2×D3—401no—
334C3×C4—21no—
335C3×C4—41no—
336C3×C4—202no—
337C3×C4—201no—
338C3×C4#405011yescharacteristic
339C3×C4#405411yescharacteristic
340C3×C4#405711yescharacteristic
341C3×C4#406211yescharacteristic
342C2×C5—81no—
343C2×C5#523811yescharacteristic
344C2×C5#523811yescharacteristic
345C2×C5#524111yescharacteristic
346D5—81no—
347D5—481no—
348C23—21no—
349C23—101no—
350C23—601no—
351Q8—202no—
352D4—21no—
353D4—21no—
354D4—101no—
355D4—101no—
356D4—402no—
357D4—602no—
358D4—601no—
359D4—601no—
360D4—601no—
361D4—601no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—101no—
366C2×C4—102no—
367C2×C4—201no—
368C2×C4—201no—
369C2×C4C2×#120211yescharacteristic
370C2×C4D5×#6711yescharacteristic
371C2×C4D5×#6711yescharacteristic
372C8—62no—
373C8—121no—
374C8—601no—
375C2×C3—81no—
376C2×C3—401no—
377C2×C3#6502311yescharacteristic
378C2×C3#6507011yescharacteristic
379C2×C3#6511111yescharacteristic
380D3—801no—
381C5#7192711yescharacteristic, complemented, Sylow
382C22—41no—
383C22—41no—
384C22—41no—
385C22—201no—
386C22—201no—
387C22—201no—
388C22—1201no—
389C22—1201no—
390C22—1201no—
391C22#9156411yescharacteristic
392C4—21no—
393C4—41no—
394C4—202no—
395C4—201no—
396C4#9130111yescharacteristic
397C4#9131111yescharacteristic
398C4#9147811yescharacteristic
399C4#9149211yescharacteristic
400C3#1059899211yescharacteristic, complemented, Sylow
401C2—81no—
402C2—401no—
403C2—2401no—
404C2#1174851311yescharacteristic
405C2#1174902611yescharacteristic
406C2#1174941811yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
hypercenterC4×D4D3×D5
hypocenterC3×C5#1624
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#65897C2semidirect
2. #11751116C2semidirect
3. #11747075C2semidirect
4. #11747028C2semidirect
5. C5×D4⋊(C3⋊C8)C2semidirect
6. #11745861C2semidirect
7. #11745835C2semidirect
27. #65897D3semidirect
65. D4⋊(C3⋊C8)D5semidirect
323. C3×C5#1624semidirect
381. C5#71927semidirect
400. C3#10598992semidirect

Maximal subgroups

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

subgroupindex
C3×#658972
#117511162
#117470752
#117470282
C5×D4⋊(C3⋊C8)2
#117458612
#117458352
#105989923
#719275