Finite Group Databasebeta

← #14289969

Subgroups — #14289969

Order 1920.

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

normal subgroups only

This group has 424 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
1C5×#5585C211yesmaximal, characteristic
2C3×#65320C211yesmaximal, characteristic, complemented
3#11746927C211yesmaximal, characteristic, complemented
4#11746901C211yesmaximal, characteristic
5#11746356C211yesmaximal, characteristic, complemented
6#11745853C211yesmaximal, characteristic
7#11745842C211yesmaximal, characteristic, complemented
8#10602738—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C5×#947—21no—
11C5×#894—22no—
12C5×#893—21no—
13C5×#875—21no—
14C5×#874C2211yescharacteristic
15C4×C5×D12—21no—
16C4×C5×Dic6C2211yescharacteristic
17C2×C3×#689—21no—
18C3×#4015C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C3×#3942—21no—
22C3×C4⋊#168C2211yescharacteristic
23#90986—21no—
24#90972—21no—
25#90966—22no—
26#71060—51nomaximal, Hall
27C5×#559—31no—
28#65359—31no—
29#65320D311yescharacteristic, complemented
30#65309—31no—
31#64764—31no—
32Q8⋊#168—31no—
33Q8⋊#168—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×D12D412yes—
38C2×C4×C5×D3—22no—
39C2×C5×Dic6D411yescharacteristic
40C2×C3×Dic10—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C42×C5—21no—
44C3×C42×C5C2311yescharacteristic
45C2×C3⋊#168—21no—
46C2×C3⋊#168—21no—
47C5×(C2×D3)⋊C4—22no—
48C5×(C2×D3)⋊C4—22no—
49C5×(C2×D3)⋊C4—22no—
50C5×C4⋊Dic3D411yescharacteristic
51C5×Dic3⋊C4—21no—
52C4×C5×Dic3—21no—
53C3×#689—42no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5—21no—
56C2×C3×#168—21no—
57#5585D511yescharacteristic
58C3×#462—51no—
59#5094—51no—
60#5088—51no—
61#4535—51no—
62#4485—51no—
63#4484—51no—
64C5×#127—31no—
65C5×#124—61no—
66C5×#124—61no—
67C5×#123—62no—
68C4×C5×Q8—31no—
69C4×C5×Q8C2×D311yescharacteristic
70C4×C5×D4—61no—
71C4×C5×D4—61no—
72C2×#689—21no—
73#4015C2×D311yescharacteristic
74#3967—61no—
75#3964—62no—
76#3942—21no—
77#3940—61no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80C4×#168—31no—
81#1640—151noSylow
82C22×C5×D3—22no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C5×Dic3—21no—
91C2×C5×Dic3—21no—
92C5×D12—42no—
93C5×D12—41no—
94C5×D12—41no—
95C5×D12—41no—
96C5×D12—41no—
97C4×C5×D3—82no—
98C5×Dic6—21no—
99C5×Dic6—21no—
100C2×C3×Dic5—41no—
101C3×Dic10—41no—
102C3×Dic10—41no—
103C3⋊#168—41no—
104C3⋊#168—41no—
105C3×#168—41no—
106C2×C3×Q16—101no—
107C3×C4⋊Q8—51no—
108C3×C4×Q8C2×D511yescharacteristic
109#947—21no—
110#894—22no—
111#893—21no—
112#875—21no—
113#874C2×D511yescharacteristic
114C4×D12—21no—
115C4×Dic6C2×D511yescharacteristic
116C3×C4⋊C8—51no—
117C3×#103—101no—
118#810—101no—
119#809—102no—
120#808—101no—
121C4⋊(C3⋊C8)—51no—
122C4×C3⋊C8—51no—
123C2×C5×Q8—31no—
124C2×C5×Q8#6711yescharacteristic
125C2×C5×D4—32no—
126C2×C5×D4—61no—
127C2×C5×D4—61no—
128C22×C4×C5—62no—
129C2×Dic10—21no—
130C5×C4⋊C4—21no—
131C5×C4⋊C4—31no—
132C5×C4⋊C4—61no—
133C5×C4⋊C4#6711yescharacteristic
134C5×C22⋊C4—62no—
135C5×C22⋊C4—62no—
136C5×C22⋊C4—62no—
137C42×C5—21no—
138C42×C5—61no—
139C42×C5C22×D311yescharacteristic
140#689—42no—
141C4⋊Dic5—21no—
142C4⋊Dic5—21no—
143C2×#168—21no—
144C2×#168—61no—
145C2×#168—61no—
146#559—31no—
147#486—151no—
148#475—151no—
149#462—51no—
150#331—151no—
151Q8⋊C8—151no—
152Q8⋊C8—151no—
153C22×C3×C5#12011yescharacteristic
154C2×C5×D3—42no—
155C2×C5×D3—42no—
156C2×C5×D3—42no—
157C3×C4×C5—21no—
158C3×C4×C5—41no—
159C3×C4×C5—41no—
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×Dic5—81no—
165C5×Dic3—41no—
166C5×Dic3—41no—
167C2×C3×Q8—101no—
168C2×C3×Q8C22⋊D511yescharacteristic
169C2×D12—21no—
170C2×D12—21no—
171C2×D12C22⋊D512yes—
172C2×C4×D3—22no—
173C2×Dic6C22⋊D511yescharacteristic
174C3×Q16—202no—
175C2×C3×C8—101no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4—101no—
179C3×C4⋊C4C22⋊D511yescharacteristic
180C3×C42—21no—
181C3×C42C22×D511yescharacteristic
182(C2×D3)⋊C4—22no—
183(C2×D3)⋊C4—22no—
184(C2×D3)⋊C4—22no—
185C4⋊Dic3C22⋊D511yescharacteristic
186Dic3⋊C4—21no—
187C4×Dic3—21no—
188C2×C3⋊C8—101no—
189C2×C3⋊C8—101no—
190C23×C5—62no—
191C5×Q8—21no—
192C5×Q8—21no—
193C5×Q8—61no—
194C5×Q8—61no—
195C5×D4—122no—
196C5×D4—121no—
197C5×D4—121no—
198C5×D4—121no—
199C5×D4—121no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5—61no—
203C2×C4×C5—61no—
204C2×C4×C5—242no—
205C2×C4×C5D3×D411yescharacteristic
206C2×C4×C5D3×D411yescharacteristic
207C2×C4×C5C2×#6711yescharacteristic
208C2×Dic5—41no—
209Dic10—41no—
210Dic10—41no—
211#168—41no—
212#168—121no—
213#168—121no—
214C2×Q16—101no—
215C4⋊Q8—51no—
216#127—31no—
217#124—61no—
218#124—61no—
219#123—62no—
220C4×Q8—31no—
221C4×Q8D3×D511yescharacteristic
222C4×D4—61no—
223C4×D4—61no—
224#106—301no—
225C4⋊C8—51no—
226C4⋊C8—151no—
227#103—101no—
228#103—301no—
229#102—302no—
230C4×C8—151no—
231C2×C3×C5#44911yescharacteristic
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45511yescharacteristic
234C5×D3—82no—
235C22×D3—22no—
236C3×Q8—21no—
237C3×Q8—21no—
238C3×Q8—201no—
239C3×Q8—201no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—201no—
243C2×C3×C4C2×C22⋊D511yescharacteristic
244C2×C3×C4C2×C22⋊D511yescharacteristic
245C2×C3×C4C2×C22⋊D511yescharacteristic
246C2×Dic3—21no—
247C2×Dic3—21no—
248D12—42no—
249D12—41no—
250D12—41no—
251D12—41no—
252D12—41no—
253C4×D3—82no—
254Dic6—21no—
255Dic6—21no—
256C3×C8—201no—
257C3⋊C8—201no—
258C3⋊C8—201no—
259C22×C5—122no—
260C22×C5—122no—
261C22×C5—122no—
262C22×C5#93711yescharacteristic
263C4×C5—21no—
264C4×C5—41no—
265C4×C5—41no—
266C4×C5—121no—
267C4×C5—121no—
268C4×C5#91811yescharacteristic
269C4×C5#91911yescharacteristic
270C4×C5#93211yescharacteristic
271C4×C5#95011yescharacteristic
272Dic5—81no—
273C2×Q8—31no—
274C2×Q8—101no—
275C2×Q8#120111yescharacteristic
276C2×D4—32no—
277C2×D4—61no—
278C2×D4—61no—
279C22×C4—62no—
280Q16—202no—
281C2×C8—101no—
282C2×C8—301no—
283C2×C8—301no—
284C4⋊C4—21no—
285C4⋊C4—31no—
286C4⋊C4—61no—
287C4⋊C4—101no—
288C4⋊C4—101no—
289C4⋊C4#120111yescharacteristic
290C22⋊C4—62no—
291C22⋊C4—62no—
292C22⋊C4—62no—
293C42—21no—
294C42—61no—
295C42C2×D3×D511yescharacteristic
296C3×C5#164011yescharacteristic, complemented, Hall
297C22×C3#409911yescharacteristic
298C2×D3—42no—
299C2×D3—42no—
300C2×D3—42no—
301C3×C4—21no—
302C3×C4—41no—
303C3×C4—41no—
304C3×C4—401no—
305C3×C4#409511yescharacteristic
306C3×C4#409611yescharacteristic
307C3×C4#409611yescharacteristic
308C3×C4#409711yescharacteristic
309Dic3—41no—
310Dic3—41no—
311C2×C5—242no—
312C2×C5#503711yescharacteristic
313C2×C5#518711yescharacteristic
314C2×C5#520211yescharacteristic
315C23—62no—
316Q8—21no—
317Q8—21no—
318Q8—61no—
319Q8—61no—
320Q8—201no—
321Q8—201no—
322D4—122no—
323D4—121no—
324D4—121no—
325D4—121no—
326D4—121no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—61no—
330C2×C4—61no—
331C2×C4—201no—
332C2×C4—242no—
333C2×C4C2×#120111yescharacteristic
334C2×C4D3×C22⋊D511yescharacteristic
335C2×C4D3×C22⋊D511yescharacteristic
336C8—201no—
337C8—601no—
338C8—601no—
339C2×C3#6552711yescharacteristic
340C2×C3#6552811yescharacteristic
341C2×C3#6553111yescharacteristic
342D3—82no—
343C5#7106011yescharacteristic, complemented, Sylow
344C22—122no—
345C22—122no—
346C22—122no—
347C22#9156811yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—121no—
352C4—121no—
353C4—401no—
354C4#9129711yescharacteristic
355C4#9129811yescharacteristic
356C4#9151011yescharacteristic
357C4#9151911yescharacteristic
358C3#1060273811yescharacteristic, complemented, Sylow
359C2—242no—
360C2#1174851711yescharacteristic
361C2#1174930511yescharacteristic
362C2#1174941611yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radicalC5×#874C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1640
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
2. C3×#65320C2semidirect
3. #11746927C2semidirect
5. #11746356C2semidirect
7. #11745842C2semidirect
29. #65320D3semidirect
296. C3×C5#1640semidirect
343. C5#71060semidirect
358. C3#10602738semidirect

Maximal subgroups

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

subgroupindex
C5×#55852
C3×#653202
#117469272
#117469012
#117463562
#117458532
#117458422
#106027383
#710605