Finite Group Databasebeta

← #14316085

Subgroups — #14316085

Order 1920.

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

normal subgroups only

This group has 452 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
1C2×D5×Dic12C211yesmaximal, characteristic, complemented
2C2×C5×#800C211yesmaximal, characteristic, complemented
3#11747898C211yesmaximal, characteristic
4C2×#90944C211yesmaximal, characteristic, complemented
5#11746324C211yesmaximal, characteristic, complemented
6C3×#64727C211yesmaximal, characteristic, complemented
7#11745900C211yesmaximal, characteristic, complemented
8#10602276—31nomaximal, Hall
9C2×D5×Dic6—21no—
10C2×Dic60C2211yescharacteristic
11C2×C5×Dic12C2211yescharacteristic
12C2×C5×D24C2211yescharacteristic
13C2×C3×C8×D5C2211yescharacteristic
14#91449—21no—
15C2×#6663—21no—
16D5×Dic12—22no—
17D5×Dic12—22no—
18C2×C3×C5×C16C2211yescharacteristic
19#91102C2211yescharacteristic
20C5×#800—22no—
21C2×C3×#672C2211yescharacteristic
22#90967—21no—
23#90944—22no—
24#69112—51nomaximal, Hall
25C2×D5×Q16—31no—
26C2×C5×SD32—31no—
27#65446—31no—
28C2×#3959—31no—
29#64784—31no—
30#64727D311yescharacteristic, complemented
31#64723—31no—
32C2×Dic30—21no—
33C2×C5×D12—21no—
34C2×C5×Dic6—21no—
35C2×C3×C4×D5D411yescharacteristic
36C2×#1204—41no—
37C2×#1201—41no—
38C2×D5×Dic3—41no—
39D5×Dic6—24no—
40D5×Dic6—42no—
41C2×C3×C5×C8C2311yescharacteristic
42C4⋊Dic15—21no—
43Dic60—21no—
44Dic60D412yescomplemented
45C5×Dic12—21no—
46C5×Dic12D412yescomplemented
47C5×D24—21no—
48C5×D24—21no—
49C2×C3×#168D411yescharacteristic
50C3×C8×D5—21no—
51C3×C8×D5—21no—
52(C2×D3)⋊Dic5—41no—
53#6663—24no—
54C3×C5×C16—21no—
55C3×#672—21no—
56C22×Dic12—51no—
57#5115—51no—
58C2×#800—51no—
59C2×#800D511yescharacteristic, complemented
60C3×C22⋊C16—51no—
61#4503—51no—
62#4503—51no—
63C2×Q8×D5—61no—
64C2×C5×Q16—31no—
65C2×C5×D8—31no—
66C2×#689—61no—
67#4084—61no—
68D5×Q16—62no—
69D5×Q16—62no—
70C2×Dic20—31no—
71C2×C8×D5C2×D311yescharacteristic
72C5×SD32—62no—
73C2×C5×C16C2×D311yescharacteristic
74#3964—61no—
75#3959—62no—
76#3950—31no—
77C2×#672C2×D311yescharacteristic
78#2185—151noSylow
79C22×C5×D3—41no—
80C22×C3×D5D811yescharacteristic
81C2×C3×C4×C5C2×D411yescharacteristic
82C2×Dic15—41no—
83C2×Dic15—41no—
84Dic30—22no—
85Dic30—41no—
86C2×C5×Dic3—41no—
87C5×D12—41no—
88C5×D12—41no—
89C5×Dic6—22no—
90C5×Dic6—41no—
91C2×C3×Dic5D811yescharacteristic
92C3×C4×D5—21no—
93C3×C4×D5—21no—
94#1204—44no—
95#1201—82no—
96D5×Dic3—44no—
97C3×C5×C8C2×D411yescharacteristic
98C3×C5×C8C2×D411yescharacteristic
99C3×#168—21no—
100C22×Dic6—101no—
101C22×C3×C8—51no—
102#930—101no—
103C2×Dic12—51no—
104C2×Dic12—102no—
105C2×Dic12—101no—
106C2×Dic12—102no—
107C2×Dic12C2×D511yescharacteristic
108C2×D24C2×D511yescharacteristic
109C2×C3×C16—51no—
110C2×C3×C16C2×D511yescharacteristic
111#821—101no—
112#818—51no—
113#800—22no—
114#800—102no—
115C2×C5×Q8—61no—
116C2×C5×D4—61no—
117C2×C22⋊D5—121no—
118Q8×D5—64no—
119Q8×D5—122no—
120C2×C4×D5—121no—
121C2×C4×D5D1211yescharacteristic
122C2×Dic10—61no—
123C2×Dic10—121no—
124C5×Q16—32no—
125C5×Q16—61no—
126C5×D8—61no—
127C5×D8—61no—
128C2×C5×C8C22×D311yescharacteristic
129C22⋊Dic5—121no—
130#689—64no—
131C4⋊Dic5—61no—
132C2×#168D1211yescharacteristic
133Dic20—32no—
134Dic20—61no—
135C8×D5—21no—
136C8×D5—21no—
137C5×C16—21no—
138#672—21no—
139C22×Q16—151no—
140C2×SD32—31no—
141C2×SD32—151no—
142#466—151no—
143#358—151no—
144#358—151no—
145C22⋊C16—51no—
146C22×C3×C5C2×D811yescharacteristic
147C2×C5×D3—81no—
148C2×C5×D3—81no—
149C2×C5×D3—81no—
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C2×C3×D5SD3212yescomplemented
153C3×C4×C5#12011yescharacteristic
154C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
155Dic15—42no—
156Dic15—81no—
157C3×Dic5—21no—
158C5×Dic3—42no—
159C22×C3×C4—51no—
160C2×#67—201no—
161C22×Dic3—201no—
162C2×D12—21no—
163C2×Dic6—21no—
164C2×Dic6—104no—
165C2×Dic6—101no—
166C2×Dic6—202no—
167C2×Dic6—201no—
168C2×C3×C8—51no—
169C2×C3×C8—101no—
170C2×C3×C8—101no—
171C2×C3×C8C22×D511yescharacteristic
172(C2×D3)⋊C4—201no—
173C4⋊Dic3—101no—
174Dic12—21no—
175Dic12—52no—
176Dic12—104no—
177Dic12—101no—
178Dic12C22⋊D512yescomplemented
179D24—21no—
180D24—21no—
181C3×C16—21no—
182C3×C16—101no—
183C23×C5—121no—
184C22×D5D2411yescharacteristic
185C5×Q8—62no—
186C5×Q8—121no—
187C5×D4—121no—
188C5×D4—121no—
189C2×C4×C5—121no—
190C2×C4×C5C2×D1211yescharacteristic
191C22⋊D5—242no—
192C2×Dic5—121no—
193C2×Dic5—121no—
194C2×Dic5D2411yescharacteristic
195C4×D5—21no—
196C4×D5—21no—
197C4×D5—124no—
198Dic10—62no—
199Dic10—124no—
200Dic10—121no—
201C5×C8D3×D411yescharacteristic
202C5×C8D3×D411yescharacteristic
203#168—21no—
204C22×Q8—301no—
205C2×Q16—31no—
206C2×Q16—151no—
207C2×Q16—301no—
208C2×Q16—302no—
209C2×Q16—302no—
210C2×D8—31no—
211C22×C8—51no—
212#121—301no—
213SD32—62no—
214SD32—302no—
215C2×C16—51no—
216C2×C16D3×D511yescharacteristic
217#107—151no—
218#102—301no—
219C2×C3×C5#44711yescharacteristic
220C2×C3×C5C2×SD3211yescharacteristic
221C2×C3×C5#51011yescharacteristic
222C3×D5—22no—
223C5×D3—161no—
224C23×C3—51no—
225C22×D3—41no—
226C2×C3×C4—51no—
227C2×C3×C4—101no—
228C2×C3×C4—101no—
229C2×C3×C4D4×D511yescharacteristic
230#67—402no—
231C2×Dic3—41no—
232C2×Dic3—204no—
233C2×Dic3—201no—
234C2×Dic3—201no—
235D12—41no—
236D12—41no—
237Dic6—22no—
238Dic6—41no—
239Dic6—102no—
240Dic6—204no—
241Dic6—201no—
242C3×C8—101no—
243C3×C8D4×D511yescharacteristic
244C3×C8C2×C22⋊D511yescharacteristic
245C22×C5—241no—
246C22×C5—241no—
247C22×C5—241no—
248C22×C5C2×D2411yescharacteristic
249C2×D5—21no—
250C2×D5—21no—
251C2×D5#80012yescomplemented
252C4×C5—122no—
253C4×C5#88211yescharacteristic
254C4×C5#90811yescharacteristic
255Dic5—21no—
256Dic5—122no—
257Dic5—241no—
258C2×Q8—61no—
259C2×Q8—304no—
260C2×Q8—301no—
261C2×Q8—601no—
262C2×Q8—602no—
263C2×D4—61no—
264C2×D4—601no—
265C22×C4—51no—
266C22×C4—601no—
267Q16—32no—
268Q16—61no—
269Q16—152no—
270Q16—304no—
271Q16—301no—
272D8—61no—
273D8—61no—
274C2×C8—51no—
275C2×C8—101no—
276C2×C8—101no—
277C2×C8C2×D3×D511yescharacteristic
278C4⋊C4—301no—
279C22⋊C4—601no—
280C16—21no—
281C16—101no—
282C3×C5#218511yescharacteristic, complemented, Hall
283C22×C3—52no—
284C22×C3—101no—
285C22×C3—101no—
286C22×C3D5×D811yescharacteristic
287C2×D3—81no—
288C2×D3—81no—
289C2×D3—81no—
290C3×C4—101no—
291C3×C4#405711yescharacteristic
292C3×C4#408311yescharacteristic
293Dic3—42no—
294Dic3—202no—
295Dic3—401no—
296C2×C5—481no—
297C2×C5#473211yescharacteristic
298C2×C5C2×#80011yescharacteristic
299C2×C5#490911yescharacteristic
300D5—22no—
301C23—51no—
302C23—121no—
303Q8—62no—
304Q8—121no—
305Q8—302no—
306Q8—604no—
307Q8—601no—
308D4—121no—
309D4—121no—
310D4—1202no—
311C2×C4—51no—
312C2×C4—101no—
313C2×C4—101no—
314C2×C4—121no—
315C2×C4—604no—
316C2×C4—601no—
317C2×C4—601no—
318C2×C4D5×D1211yescharacteristic
319C8—101no—
320C8#677711yescharacteristic
321C8D3×C22⋊D511yescharacteristic
322C2×C3—102no—
323C2×C3D5×SD3211yescharacteristic
324C2×C3#6520411yescharacteristic
325C2×C3#6544511yescharacteristic
326D3—161no—
327C5#6911211yescharacteristic, complemented, Sylow
328C22—52no—
329C22—101no—
330C22—101no—
331C22—241no—
332C22—241no—
333C22—241no—
334C22D5×D2411yescharacteristic
335C4—101no—
336C4—122no—
337C4—602no—
338C4—1201no—
339C4#9125011yescharacteristic
340C4#9147511yescharacteristic
341C3#1060227611yescharacteristic, complemented, Sylow
342C2—102no—
343C2—481no—
344C2D5×#80011yescharacteristic
345C2#1174682811yescharacteristic
346C2#1174811611yescharacteristic
subgroupG/H
centerC22D5×D24
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×C16C22
socleC22×C3×C5C2×D8
prime radical#11747898C2
hypercenterC2×C16D3×D5
hypocenterC3×C5#2185
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. C2×D5×Dic12C2semidirect
2. C2×C5×#800C2semidirect
4. C2×#90944C2semidirect
5. #11746324C2semidirect
6. C3×#64727C2semidirect
7. #11745900C2semidirect
30. #64727D3semidirect
44. Dic60D4semidirect
46. C5×Dic12D4semidirect
59. C2×#800D5semidirect
152. C2×C3×D5SD32semidirect
178. Dic12C22⋊D5semidirect
251. C2×D5#800semidirect
282. C3×C5#2185semidirect
327. C5#69112semidirect
341. C3#10602276semidirect

Maximal subgroups

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

subgroupindex
C2×D5×Dic122
C2×C5×#8002
#117478982
C2×#909442
#117463242
C3×#647272
#117459002
#106022763
#691125