Finite Group Databasebeta

← #14289060

Subgroups — #14289060

Order 1920.

480 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 91 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#11756322C211yesmaximal, characteristic, complemented
2#11751116C211yesmaximal, characteristic, complemented
3#11750944C211yesmaximal, characteristic, complemented
4#11750794C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
6#11746302C211yesmaximal, characteristic, complemented
7#11746280C211yesmaximal, characteristic, complemented
8#10598992—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10#91827—21no—
11C2×#6715—21no—
12#91819—21no—
13#91815—21no—
14C2×D120—21no—
15C2×#6706—22no—
16#91781—21no—
17#91774—22no—
18#91763C2211yescharacteristic
19C4×D60C2211yescharacteristic
20#91758C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C4×C5×C8C2211yescharacteristic
23#91105—21no—
24#91093—21no—
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68199—51nomaximal, Hall
27#65897—31no—
28#65304—31no—
29#65132—31no—
30#64982—31no—
31C5×D4⋊C8D311yescharacteristic, complemented
32#64701—31no—
33#64679—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×#1220—22no—
37C2×D60—21no—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60D411yescharacteristic
41C2×C4×D15—21no—
42C2×Dic30D412yes—
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4D411yescharacteristic
46C3×C5×C22⋊C4—21no—
47C3×C42×C5C2311yescharacteristic
48#6719—22no—
49#6715—42no—
50#6714—22no—
51#6714—21no—
52C4⋊Dic15—21no—
53C4⋊Dic15—21no—
54C4⋊Dic15D411yescharacteristic
55C4×Dic15—22no—
56C2×C3⋊#168—21no—
57D120—42no—
58#6706—44no—
59#5563—51no—
60#5015—51no—
61#4843—51no—
62#4693—51no—
63C3×D4⋊C8D511yescharacteristic, complemented
64#4481—51no—
65#4459—51no—
66C4×C5×D4C2×D311yescharacteristic
67#4084—61no—
68C2×#686—61no—
69#4076—61no—
70#4072—61no—
71C2×D40—61no—
72C2×#677—62no—
73#4038—61no—
74#4031—62no—
75#4020—31no—
76C4×D20—31no—
77#4015—31no—
78C5×C4⋊C8C2×D311yescharacteristic
79C4×C5×C8C2×D311yescharacteristic
80#3953—61no—
81#3941—61no—
82C4⋊#168—31no—
83#1624—151noSylow
84C23×C3×C5—21no—
85C22×D15—21no—
86C22×D15—41no—
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
95#1220—82no—
96C2×Dic15—21no—
97C2×Dic15—22no—
98D60—21no—
99D60—21no—
100D60—42no—
101D60—41no—
102D60—41no—
103D60—41no—
104D60—41no—
105C4×D15—41no—
106C4×D15—41no—
107Dic30—42no—
108C3×C5×C8—22no—
109C3×C5×C8—41no—
110C3⋊#168—41no—
111C3×C4×D4C2×D511yescharacteristic
112#938—101no—
113C2×#213—101no—
114#930—101no—
115#926—101no—
116C2×D24—101no—
117C2×#204—102no—
118#892—101no—
119#885—102no—
120#874—51no—
121C4×D12—51no—
122#869—51no—
123C3×C4⋊C8C2×D511yescharacteristic
124C3×C4×C8C2×D511yescharacteristic
125#821—101no—
126#809—101no—
127C4⋊(C3⋊C8)—51no—
128C2×C5×D4D1211yescharacteristic
129C22×C4×C5—21no—
130C2×C22⋊D5—62no—
131C2×D20—31no—
132C2×D20—61no—
133C2×D20—61no—
134C2×D20—61no—
135C2×C4×D5—61no—
136C2×Dic10—32no—
137C2×C5×C8—21no—
138C2×C5×C8—21no—
139C5×C4⋊C4D1211yescharacteristic
140C5×C22⋊C4—21no—
141C42×C5C22×D311yescharacteristic
142C22⋊Dic5—62no—
143#686—122no—
144#685—62no—
145#685—61no—
146C4⋊Dic5—31no—
147C4⋊Dic5—61no—
148C4⋊Dic5—61no—
149C4×Dic5—62no—
150C2×#168—61no—
151D40—122no—
152#677—124no—
153#555—151no—
154#492—151no—
155#459—151no—
156#459—151no—
157#333—151no—
158D4⋊C8—151no—
159D4⋊C8D1511yescharacteristic, complemented
160C22×C3×C5—41no—
161C22×C3×C5—41no—
162C22×C3×C5—41no—
163C22×C3×C5#12011yescharacteristic
164C2×D15—41no—
165C2×D15—41no—
166C2×D15—41no—
167C2×D15—81no—
168C2×D15—81no—
169C2×D15—81no—
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
176Dic15—41no—
177Dic15—42no—
178C2×C3×D4D2011yescharacteristic
179C22×C3×C4—21no—
180C2×#67—102no—
181C2×D12—51no—
182C2×D12—101no—
183C2×D12—101no—
184C2×D12—101no—
185C2×C4×D3—101no—
186C2×Dic6—52no—
187C2×C3×C8—21no—
188C2×C3×C8—21no—
189C3×C4⋊C4D2011yescharacteristic
190C3×C22⋊C4—21no—
191C3×C42C22×D511yescharacteristic
192#217—102no—
193#213—202no—
194(C2×D3)⋊C4—102no—
195(C2×D3)⋊C4—101no—
196C4⋊Dic3—51no—
197C4⋊Dic3—101no—
198C4⋊Dic3—101no—
199C4×Dic3—102no—
200C2×C3⋊C8—101no—
201D24—202no—
202#204—204no—
203C23×C5—21no—
204C22×D5—61no—
205C22×D5—121no—
206C5×D4—21no—
207C5×D4—21no—
208C2×C4×C5—21no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5C2×D1211yescharacteristic
212C2×C4×C5D3×D411yescharacteristic
213C2×C4×C5D3×D411yescharacteristic
214C22⋊D5—242no—
215C2×Dic5—61no—
216C2×Dic5—62no—
217D20—61no—
218D20—61no—
219D20—122no—
220D20—121no—
221D20—121no—
222D20—121no—
223D20—121no—
224C4×D5—121no—
225C4×D5—121no—
226Dic10—122no—
227C5×C8—22no—
228C5×C8—41no—
229#168—121no—
230C2×SD16—302no—
231C2×D8—301no—
232C2×D8—301no—
233C4⋊Q8—151no—
234#127—151no—
235#124—302no—
236#121—301no—
237#121—301no—
238C4×D4—151no—
239C4×D4C2×D1511yescharacteristic
240#117—301no—
241#117—301no—
242C4⋊C8—151no—
243C4⋊C8C2×D1511yescharacteristic
244#102—301no—
245#102—301no—
246C4×C8C2×D1511yescharacteristic
247C2×C3×C5—81no—
248C2×C3×C5#44911yescharacteristic
249C2×C3×C5#44911yescharacteristic
250C2×C3×C5#45311yescharacteristic
251D15—81no—
252D15—161no—
253C23×C3—21no—
254C22×D3—101no—
255C22×D3—201no—
256C3×D4—21no—
257C3×D4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4C2×D2011yescharacteristic
262C2×C3×C4D4×D511yescharacteristic
263C2×C3×C4D4×D511yescharacteristic
264#67—402no—
265C2×Dic3—101no—
266C2×Dic3—102no—
267D12—101no—
268D12—101no—
269D12—202no—
270D12—201no—
271D12—201no—
272D12—201no—
273D12—201no—
274C4×D3—201no—
275C4×D3—201no—
276Dic6—202no—
277C3×C8—22no—
278C3×C8—41no—
279C3⋊C8—201no—
280C22×C5—41no—
281C22×C5—41no—
282C22×C5—41no—
283C22×C5#88211yescharacteristic
284C2×D5—121no—
285C2×D5—121no—
286C2×D5—121no—
287C2×D5—241no—
288C2×D5—241no—
289C2×D5—241no—
290C4×C5—21no—
291C4×C5—41no—
292C4×C5#90411yescharacteristic
293C4×C5#90811yescharacteristic
294C4×C5#91111yescharacteristic
295C4×C5#91611yescharacteristic
296Dic5—121no—
297Dic5—122no—
298C2×Q8—152no—
299C2×D4—151no—
300C2×D4—302no—
301C2×D4—301no—
302C2×D4—301no—
303C2×D4—301no—
304C2×D4D6011yescharacteristic
305C22×C4—21no—
306C22×C4—301no—
307SD16—604no—
308D8—602no—
309D8—602no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—301no—
313C4⋊C4—151no—
314C4⋊C4—301no—
315C4⋊C4—301no—
316C4⋊C4D6011yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—302no—
319C22⋊C4—302no—
320C22⋊C4—301no—
321C42—302no—
322C42C22×D1511yescharacteristic
323C3×C5#162411yescharacteristic, complemented, Hall
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3#402811yescharacteristic
328C2×D3—201no—
329C2×D3—201no—
330C2×D3—201no—
331C2×D3—401no—
332C2×D3—401no—
333C2×D3—401no—
334C3×C4—21no—
335C3×C4—41no—
336C3×C4#405011yescharacteristic
337C3×C4#405411yescharacteristic
338C3×C4#405711yescharacteristic
339C3×C4#406211yescharacteristic
340Dic3—202no—
341Dic3—201no—
342C2×C5—81no—
343C2×C5#473411yescharacteristic
344C2×C5#478111yescharacteristic
345C2×C5#482211yescharacteristic
346D5—241no—
347D5—481no—
348C23—21no—
349C23—301no—
350C23—601no—
351Q8—602no—
352D4—21no—
353D4—21no—
354D4—301no—
355D4—301no—
356D4—602no—
357D4—601no—
358D4—601no—
359D4—601no—
360D4—601no—
361D4—1202no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—301no—
366C2×C4—302no—
367C2×C4—601no—
368C2×C4—601no—
369C2×C4C2×D6011yescharacteristic
370C2×C4D4×D1511yescharacteristic
371C2×C4D4×D1511yescharacteristic
372C8—22no—
373C8—41no—
374C8—601no—
375C2×C3—81no—
376C2×C3#6502311yescharacteristic
377C2×C3#6507011yescharacteristic
378C2×C3#6511111yescharacteristic
379D3—401no—
380D3—801no—
381C5#6819911yescharacteristic, complemented, Sylow
382C22—41no—
383C22—41no—
384C22—41no—
385C22—601no—
386C22—601no—
387C22—601no—
388C22—1201no—
389C22—1201no—
390C22—1201no—
391C22#9177111yescharacteristic
392C4—21no—
393C4—41no—
394C4—602no—
395C4—601no—
396C4#9179311yescharacteristic
397C4#9179711yescharacteristic
398C4#9180011yescharacteristic
399C4#9180511yescharacteristic
400C3#1059899211yescharacteristic, complemented, Sylow
401C2—81no—
402C2—1201no—
403C2—2401no—
404C2#1175083511yescharacteristic
405C2#1175088211yescharacteristic
406C2#1175092311yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5#120
hypercenterD4⋊C8D15
hypocenterC3×C5#1624
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #11756322C2semidirect
2. #11751116C2semidirect
3. #11750944C2semidirect
4. #11750794C2semidirect
5. C3×C5×D4⋊C8C2semidirect
6. #11746302C2semidirect
7. #11746280C2semidirect
31. C5×D4⋊C8D3semidirect
63. C3×D4⋊C8D5semidirect
159. D4⋊C8D15semidirect
323. C3×C5#1624semidirect
381. C5#68199semidirect
400. C3#10598992semidirect

Maximal subgroups

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

subgroupindex
#117563222
#117511162
#117509442
#117507942
C3×C5×D4⋊C82
#117463022
#117462802
#105989923
#681995