Finite Group Databasebeta

← #14289081

Subgroups — #14289081

Order 1920.

480 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752710C211yesmaximal, characteristic, complemented
2C5×#4843C211yesmaximal, characteristic, complemented
3#11747081C211yesmaximal, characteristic, complemented
4#11747045C211yesmaximal, characteristic, complemented
5#11746304C211yesmaximal, characteristic, complemented
6C3×#64701C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic, complemented
8#10601810—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10C2×C5×D24—21no—
11C5×#874C2211yescharacteristic
12C4×C5×D12C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14#91466—21no—
15#91460—21no—
16#91347—21no—
17#91338—21no—
18#91326—22no—
19C2×#6656—22no—
20C2×#6654—21no—
21C3×C5×C4⋊C8C2211yescharacteristic
22C4×C3⋊#168C2211yescharacteristic
23C5×#821—21no—
24C3×C4⋊#168C2211yescharacteristic
25#90967—21no—
26#68491—51nomaximal, Hall
27#65897—31no—
28C5×#459—31no—
29#65365—31no—
30#65361—31no—
31D4⋊#168—31no—
32#64703—31no—
33#64701D311yescharacteristic, complemented
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C5×D12—21no—
39C2×C5×D12D411yescharacteristic
40C2×C4×C5×D3—21no—
41C2×C3×Dic10D412yes—
42C2×#1203—22no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45#6714—21no—
46C4⋊Dic15D411yescharacteristic
47C2×C3⋊#168—21no—
48C5×(C2×D3)⋊C4—21no—
49C5×C4⋊Dic3D411yescharacteristic
50C5×D24—42no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5—21no—
53C2×C3×#168—21no—
54#6667—22no—
55(C2×D3)⋊Dic5—22no—
56Dic3×Dic5—22no—
57#6656—44no—
58#6654—42no—
59#5734—51no—
60#5085—51no—
61#4843—51no—
62#4843D511yescharacteristic, complemented
63C3×#333—51no—
64#4483—51no—
65#4483—51no—
66C2×C5×D8—61no—
67C5×#127—31no—
68C4×C5×D4—31no—
69#4084—61no—
70C2×#687—62no—
71C2×#686—61no—
72#4076—61no—
73#4072—61no—
74#4038—61no—
75#4031—62no—
76C4×D20—31no—
77#4015C2×D311yescharacteristic
78C5×C4⋊C8C2×D311yescharacteristic
79C5×#102—61no—
80#3964—61no—
81C4⋊#168C2×D311yescharacteristic
82C4×#168—31no—
83#1624—151noSylow
84C22×D15—21no—
85C22×C5×D3—21no—
86C22×C5×D3—41no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—21no—
91D60—21no—
92D60—21no—
93C4×D15—41no—
94C4×D15—41no—
95C2×C5×Dic3—21no—
96C5×D12—21no—
97C5×D12—21no—
98C5×D12—42no—
99C5×D12—41no—
100C5×D12—41no—
101C5×D12—41no—
102C5×D12—41no—
103C4×C5×D3—41no—
104C4×C5×D3—41no—
105C2×C3×Dic5—22no—
106C3×Dic10—42no—
107#1203—82no—
108C3×C5×C8—41no—
109C3⋊#168—22no—
110C3×#168—41no—
111C3×C4⋊Q8—51no—
112#947—102no—
113C2×#215—102no—
114C2×D24—21no—
115C2×D24—101no—
116#895—101no—
117#895—101no—
118#892—101no—
119#892—101no—
120#874C2×D511yescharacteristic
121C4×D12—51no—
122C4×D12C2×D511yescharacteristic
123C3×C4⋊C8—51no—
124C3×C4⋊C8C2×D511yescharacteristic
125#821—21no—
126#821—101no—
127C4×C3⋊C8—51no—
128C2×C5×D4—31no—
129C2×C5×D4—61no—
130C2×C5×D4—61no—
131C2×C5×D4—61no—
132C22×C4×C5—61no—
133C2×C22⋊D5—62no—
134C2×D20—31no—
135C2×C4×D5—61no—
136C2×Dic10D1212yes—
137C5×D8—122no—
138C2×C5×C8—21no—
139C5×C4⋊C4—31no—
140C5×C22⋊C4—61no—
141C42×C5C22×D311yescharacteristic
142C22⋊Dic5—62no—
143#687—124no—
144#686—122no—
145#685—62no—
146#685—61no—
147C4⋊Dic5—21no—
148C4⋊Dic5—21no—
149C4⋊Dic5—31no—
150C4×Dic5—62no—
151C2×#168—21no—
152C2×#168—61no—
153#555—151no—
154#492—151no—
155#459—31no—
156#459—151no—
157#333—51no—
158D4⋊C8—151no—
159D4⋊C8—151no—
160C22×C3×C5#12011yescharacteristic
161C2×D15—41no—
162C2×D15—41no—
163C2×D15—41no—
164C2×C5×D3—41no—
165C2×C5×D3—41no—
166C2×C5×D3—41no—
167C2×C5×D3—81no—
168C2×C5×D3—81no—
169C2×C5×D3—81no—
170C3×C4×C5—21no—
171C3×C4×C5#13511yescharacteristic
172C3×C4×C5#13511yescharacteristic
173C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
174C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
175Dic15—41no—
176C3×Dic5—42no—
177C5×Dic3—41no—
178C2×C3×Q8—52no—
179C2×D12—21no—
180C2×D12—21no—
181C2×D12—21no—
182C2×D12—51no—
183C2×D12—102no—
184C2×D12C22⋊D511yescharacteristic
185C2×C4×D3—21no—
186C2×C4×D3—101no—
187C2×C3×C8—21no—
188C2×C3×C8—101no—
189C3×C4⋊C4—101no—
190C3×C4⋊C4—101no—
191C3×C42C22×D511yescharacteristic
192#215—204no—
193(C2×D3)⋊C4—21no—
194(C2×D3)⋊C4—102no—
195(C2×D3)⋊C4—102no—
196(C2×D3)⋊C4—101no—
197C4⋊Dic3—51no—
198C4⋊Dic3C22⋊D511yescharacteristic
199C4×Dic3—102no—
200C2×C3⋊C8—101no—
201D24—42no—
202D24—202no—
203C23×C5—61no—
204C23×C5—121no—
205C22×D5—61no—
206C5×D4—61no—
207C5×D4—61no—
208C5×D4—122no—
209C5×D4—121no—
210C5×D4—121no—
211C5×D4—121no—
212C5×D4—121no—
213C2×C4×C5—61no—
214C2×C4×C5—121no—
215C2×C4×C5—121no—
216C2×C4×C5C2×D1211yescharacteristic
217C2×C4×C5D3×D411yescharacteristic
218C2×C4×C5D3×D411yescharacteristic
219C22⋊D5—242no—
220C2×Dic5—22no—
221C2×Dic5—61no—
222D20—61no—
223D20—61no—
224C4×D5—121no—
225C4×D5—121no—
226Dic10—42no—
227C5×C8—41no—
228#168—41no—
229#168—62no—
230C2×SD16—302no—
231C2×D8—61no—
232C2×D8—301no—
233C4⋊Q8—51no—
234#127—31no—
235#124—302no—
236#121—301no—
237#121—301no—
238C4×D4—31no—
239C4×D4—151no—
240#117—301no—
241#117—301no—
242C4⋊C8—51no—
243C4⋊C8D3×D511yescharacteristic
244#102—61no—
245#102—301no—
246C4×C8—151no—
247C2×C3×C5#44911yescharacteristic
248C2×C3×C5#44911yescharacteristic
249C2×C3×C5#45311yescharacteristic
250D15—81no—
251C5×D3—81no—
252C5×D3—161no—
253C22×D3—21no—
254C22×D3—41no—
255C22×D3—101no—
256C3×Q8—202no—
257C2×C3×C4—102no—
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4C2×C22⋊D511yescharacteristic
261C2×Dic3—21no—
262C2×Dic3—101no—
263D12—21no—
264D12—21no—
265D12—42no—
266D12—41no—
267D12—41no—
268D12—41no—
269D12—41no—
270D12—101no—
271D12—101no—
272D12—402no—
273C4×D3—41no—
274C4×D3—41no—
275C4×D3—201no—
276C4×D3—201no—
277C3×C8—41no—
278C3×C8—201no—
279C3⋊C8—102no—
280C22×C5—121no—
281C22×C5—121no—
282C22×C5—121no—
283C22×C5—241no—
284C22×C5—241no—
285C22×C5—241no—
286C22×C5#88211yescharacteristic
287C2×D5—121no—
288C2×D5—121no—
289C2×D5—121no—
290C4×C5—21no—
291C4×C5—121no—
292C4×C5#91411yescharacteristic
293C4×C5#91411yescharacteristic
294C4×C5#91911yescharacteristic
295C4×C5#91911yescharacteristic
296Dic5—42no—
297Dic5—121no—
298C2×Q8—52no—
299C2×D4—31no—
300C2×D4—61no—
301C2×D4—61no—
302C2×D4—61no—
303C2×D4—151no—
304C2×D4—302no—
305C22×C4—61no—
306C22×C4—301no—
307SD16—604no—
308D8—122no—
309D8—602no—
310C2×C8—21no—
311C2×C8—101no—
312C2×C8—301no—
313C4⋊C4—31no—
314C4⋊C4—101no—
315C4⋊C4—101no—
316C4⋊C4—151no—
317C22⋊C4—61no—
318C22⋊C4—302no—
319C22⋊C4—302no—
320C22⋊C4—301no—
321C42—302no—
322C42C2×D3×D511yescharacteristic
323C3×C5#162411yescharacteristic, complemented, Hall
324C22×C3#408311yescharacteristic
325C2×D3—41no—
326C2×D3—41no—
327C2×D3—41no—
328C2×D3—81no—
329C2×D3—81no—
330C2×D3—81no—
331C2×D3—201no—
332C2×D3—201no—
333C2×D3—201no—
334C3×C4—21no—
335C3×C4—202no—
336C3×C4#405711yescharacteristic
337C3×C4#405811yescharacteristic
338C3×C4#407811yescharacteristic
339C3×C4#409611yescharacteristic
340Dic3—41no—
341Dic3—201no—
342C2×C5—241no—
343C2×C5—481no—
344C2×C5#474711yescharacteristic
345C2×C5#481011yescharacteristic
346C2×C5#481011yescharacteristic
347D5—241no—
348C23—61no—
349C23—121no—
350C23—301no—
351Q8—202no—
352D4—61no—
353D4—61no—
354D4—122no—
355D4—121no—
356D4—121no—
357D4—121no—
358D4—121no—
359D4—301no—
360D4—301no—
361D4—1202no—
362C2×C4—61no—
363C2×C4—102no—
364C2×C4—121no—
365C2×C4—121no—
366C2×C4—301no—
367C2×C4—601no—
368C2×C4—601no—
369C2×C4D5×D1211yescharacteristic
370C2×C4#677711yescharacteristic
371C2×C4D3×C22⋊D511yescharacteristic
372C8—41no—
373C8—201no—
374C8—302no—
375C2×C3#6532611yescharacteristic
376C2×C3#6544711yescharacteristic
377C2×C3#6548711yescharacteristic
378D3—81no—
379D3—161no—
380D3—401no—
381C5#6849111yescharacteristic, complemented, Sylow
382C22—121no—
383C22—121no—
384C22—121no—
385C22—241no—
386C22—241no—
387C22—241no—
388C22—601no—
389C22—601no—
390C22—601no—
391C22#9147511yescharacteristic
392C4—21no—
393C4—121no—
394C4—202no—
395C4—601no—
396C4#9125711yescharacteristic
397C4#9127911yescharacteristic
398C4#9149611yescharacteristic
399C4#9151911yescharacteristic
400C3#1060181011yescharacteristic, complemented, Sylow
401C2—241no—
402C2—481no—
403C2—1201no—
404C2#1174751711yescharacteristic
405C2#1174815911yescharacteristic
406C2#1174824611yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1624
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #11752710C2semidirect
2. C5×#4843C2semidirect
3. #11747081C2semidirect
4. #11747045C2semidirect
5. #11746304C2semidirect
6. C3×#64701C2semidirect
7. #11745836C2semidirect
33. #64701D3semidirect
62. #4843D5semidirect
323. C3×C5#1624semidirect
381. C5#68491semidirect
400. C3#10601810semidirect

Maximal subgroups

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

subgroupindex
#117527102
C5×#48432
#117470812
#117470452
#117463042
C3×#647012
#117458362
#106018103
#684915