Finite Group Databasebeta

← #14316070

Subgroups — #14316070

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×#91111C211yesmaximal, characteristic, complemented
3C2×C5×#827C211yesmaximal, characteristic, complemented
4C3×#65446C211yesmaximal, characteristic
5#11745901C211yesmaximal, characteristic, complemented
6#11745899C211yesmaximal, characteristic, complemented
7#11745879C211yesmaximal, characteristic, complemented
8#10602276—31nomaximal, Hall
9C2×D5×Dic6—21no—
10C2×C3×C5×D8C2211yescharacteristic
11C2×Dic60C2211yescharacteristic
12C2×C5×Dic12C2211yescharacteristic
13C3×#4084—21no—
14C2×C3×C8×D5C2211yescharacteristic
15C2×#6663—21no—
16D5×Dic12—22no—
17D5×Dic12—22no—
18#91111—22no—
19C2×C3⋊#672C2211yescharacteristic
20C5×#827—22no—
21C2×C5×C3⋊C16C2211yescharacteristic
22C3×#3964—21no—
23C3×#3950C2211yescharacteristic
24#71077—51nomaximal, Hall
25C2×D5×Q16—31no—
26C2×C5×SD32—31no—
27#65446D311yescharacteristic
28C2×#3959—31no—
29#64784—31no—
30#64727—31no—
31#64723—31no—
32C2×C3×C5×D4—21no—
33C2×Dic30—21no—
34C2×C5×Dic6—21no—
35C2×C3×C22⋊D5—41no—
36C2×C3×C4×D5D411yescharacteristic
37C2×#1204—41no—
38C2×D5×Dic3—41no—
39D5×Dic6—24no—
40D5×Dic6—42no—
41C3×C5×D8—21no—
42C3×C5×D8—21no—
43C2×C3×C5×C8C2311yescharacteristic
44Dic60—21no—
45Dic60D412yescomplemented
46C5×Dic12—21no—
47C5×Dic12D412yescomplemented
48C3×C22⋊Dic5—41no—
49C3×C4⋊Dic5—21no—
50C2×C3×#168D411yescharacteristic
51C3×C8×D5—21no—
52C3×C8×D5—21no—
53#6663—24no—
54C3⋊#672—21no—
55C5×C3⋊C16—21no—
56C22×Dic12—51no—
57C3×#466—51no—
58C2×#827—51no—
59C2×#827D511yescharacteristic, complemented
60#4549—51no—
61#4492—51no—
62#4492—51no—
63C2×Q8×D5—61no—
64C2×C5×Q16—31no—
65C2×C5×D8C2×D311yescharacteristic
66C2×#689—61no—
67#4084—21no—
68D5×Q16—62no—
69D5×Q16—62no—
70C2×Dic20—31no—
71C2×C8×D5C2×D311yescharacteristic
72C5×SD32—62no—
73C2×C5×C16—31no—
74#3964—21no—
75#3959—62no—
76#3950C2×D311yescharacteristic
77C2×#672—31no—
78#2185—151noSylow
79C23×C3×C5—41no—
80C22×C3×D5D811yescharacteristic
81C3×C5×D4—41no—
82C3×C5×D4—41no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×Dic15—41no—
85Dic30—22no—
86Dic30—41no—
87C2×C5×Dic3—41no—
88C5×Dic6—22no—
89C5×Dic6—41no—
90C3×C22⋊D5—82no—
91C2×C3×Dic5—41no—
92C2×C3×Dic5D811yescharacteristic
93C3×C4×D5—21no—
94C3×C4×D5—21no—
95#1204—44no—
96D5×Dic3—44no—
97C3×C5×C8C2×D411yescharacteristic
98C3×C5×C8C2×D411yescharacteristic
99C3×#168—21no—
100C22×Dic6—101no—
101C2×C3×D8C2×D511yescharacteristic
102C22×C3×C8—51no—
103C3×#121—101no—
104C2×Dic12—51no—
105C2×Dic12—102no—
106C2×Dic12—101no—
107C2×Dic12—102no—
108C2×Dic12C2×D511yescharacteristic
109C3×#107—51no—
110C3×#102—101no—
111#827—22no—
112#827—102no—
113C2×C3⋊C16—51no—
114C2×C3⋊C16C2×D511yescharacteristic
115C2×C5×Q8—61no—
116C2×C5×D4—21no—
117C2×C22⋊D5—41no—
118Q8×D5—64no—
119Q8×D5—122no—
120C2×C4×D5—121no—
121C2×C4×D5#6711yescharacteristic
122C2×Dic10—61no—
123C2×Dic10—121no—
124C5×Q16—32no—
125C5×Q16—61no—
126C5×D8—21no—
127C5×D8—21no—
128C2×C5×C8C22×D311yescharacteristic
129C22⋊Dic5—41no—
130#689—64no—
131C4⋊Dic5—21no—
132C2×#168#6711yescharacteristic
133Dic20—32no—
134Dic20—61no—
135C8×D5—21no—
136C8×D5—21no—
137C5×C16—61no—
138#672—61no—
139C22×Q16—151no—
140C2×SD32—31no—
141C2×SD32—151no—
142#466—51no—
143#358—151no—
144#358—151no—
145C22⋊C16—151no—
146C22×C3×C5—81no—
147C22×C3×C5—81no—
148C22×C3×C5—81no—
149C22×C3×C5C2×D811yescharacteristic
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C2×C3×D5SD3212yescomplemented
153C3×C4×C5#12011yescharacteristic
154C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
155Dic15—42no—
156C3×Dic5—21no—
157C3×Dic5—81no—
158C5×Dic3—42no—
159C2×C3×D4—21no—
160C2×C3×D4—201no—
161C22×C3×C4—51no—
162C22×Dic3—201no—
163C2×Dic6—21no—
164C2×Dic6—104no—
165C2×Dic6—101no—
166C2×Dic6—202no—
167C2×Dic6—201no—
168C3×D8—21no—
169C3×D8—21no—
170C2×C3×C8—51no—
171C2×C3×C8—101no—
172C2×C3×C8—101no—
173C2×C3×C8C22×D511yescharacteristic
174C3×C4⋊C4—101no—
175C3×C22⋊C4—201no—
176Dic12—21no—
177Dic12—52no—
178Dic12—104no—
179Dic12—101no—
180Dic12C22⋊D512yescomplemented
181C3⋊C16—21no—
182C3⋊C16—101no—
183C23×C5—41no—
184C22×D5#21311yescharacteristic
185C5×Q8—62no—
186C5×Q8—121no—
187C5×D4—41no—
188C5×D4—41no—
189C2×C4×C5—121no—
190C2×C4×C5C2×#6711yescharacteristic
191C22⋊D5—82no—
192C2×Dic5—41no—
193C2×Dic5—121no—
194C2×Dic5#21311yescharacteristic
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×D8D3×D511yescharacteristic
211C22×C8—51no—
212#121—101no—
213SD32—62no—
214SD32—302no—
215C2×C16—31no—
216C2×C16—151no—
217#107—51no—
218#102—101no—
219C2×C3×C5—161no—
220C2×C3×C5#44711yescharacteristic
221C2×C3×C5C2×SD3211yescharacteristic
222C2×C3×C5#51011yescharacteristic
223C3×D5—22no—
224C23×C3—41no—
225C23×C3—51no—
226C3×D4—41no—
227C3×D4—41no—
228C3×D4—402no—
229C2×C3×C4—51no—
230C2×C3×C4—101no—
231C2×C3×C4—101no—
232C2×C3×C4—201no—
233C2×C3×C4D4×D511yescharacteristic
234C2×Dic3—41no—
235C2×Dic3—204no—
236C2×Dic3—201no—
237Dic6—22no—
238Dic6—41no—
239Dic6—102no—
240Dic6—204no—
241Dic6—201no—
242C3×C8—101no—
243C3×C8D4×D511yescharacteristic
244C3×C8C2×C22⋊D511yescharacteristic
245C22×C5—81no—
246C22×C5—81no—
247C22×C5—81no—
248C22×C5C2×#21311yescharacteristic
249C2×D5—21no—
250C2×D5—21no—
251C2×D5#82712yescomplemented
252C4×C5—122no—
253C4×C5#93711yescharacteristic
254C4×C5#94911yescharacteristic
255Dic5—21no—
256Dic5—81no—
257Dic5—122no—
258C2×Q8—61no—
259C2×Q8—304no—
260C2×Q8—301no—
261C2×Q8—601no—
262C2×Q8—602no—
263C2×D4—21no—
264C2×D4—201no—
265C22×C4—51no—
266C22×C4—601no—
267Q16—32no—
268Q16—61no—
269Q16—152no—
270Q16—304no—
271Q16—301no—
272D8—21no—
273D8—21no—
274C2×C8—51no—
275C2×C8—101no—
276C2×C8—101no—
277C2×C8C2×D3×D511yescharacteristic
278C4⋊C4—101no—
279C22⋊C4—201no—
280C16—61no—
281C16—301no—
282C3×C5#218511yescharacteristic, complemented, Hall
283C22×C3—52no—
284C22×C3—81no—
285C22×C3—81no—
286C22×C3—81no—
287C22×C3—101no—
288C22×C3—101no—
289C22×C3D5×D811yescharacteristic
290C3×C4—101no—
291C3×C4—401no—
292C3×C4#405711yescharacteristic
293C3×C4#408311yescharacteristic
294Dic3—42no—
295Dic3—202no—
296C2×C5—161no—
297C2×C5#503611yescharacteristic
298C2×C5C2×#82711yescharacteristic
299C2×C5#519511yescharacteristic
300D5—22no—
301C23—41no—
302C23—51no—
303Q8—62no—
304Q8—121no—
305Q8—302no—
306Q8—604no—
307Q8—601no—
308D4—41no—
309D4—41no—
310D4—402no—
311C2×C4—51no—
312C2×C4—101no—
313C2×C4—101no—
314C2×C4—121no—
315C2×C4—201no—
316C2×C4—604no—
317C2×C4—601no—
318C2×C4D5×#6711yescharacteristic
319C8—101no—
320C8D3×C22⋊D511yescharacteristic
321C8#679011yescharacteristic
322C2×C3—102no—
323C2×C3—161no—
324C2×C3D5×SD3211yescharacteristic
325C2×C3#6520411yescharacteristic
326C2×C3#6544511yescharacteristic
327C5#7107711yescharacteristic, complemented, Sylow
328C22—52no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—101no—
333C22—101no—
334C22D5×#21311yescharacteristic
335C4—101no—
336C4—122no—
337C4—401no—
338C4—602no—
339C4#9147811yescharacteristic
340C4#9157711yescharacteristic
341C3#1060227611yescharacteristic, complemented, Sylow
342C2—102no—
343C2—161no—
344C2D5×#82711yescharacteristic
345C2#1174827111yescharacteristic
346C2#1174915111yescharacteristic
subgroupG/H
centerC22D5×#213
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×D8C22
socleC22×C3×C5C2×D8
prime radicalC3×#65446C2
hypercenterC2×D8D3×D5
hypocenterC3×C5#2185
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D5×Dic12C2semidirect
2. C2×#91111C2semidirect
3. C2×C5×#827C2semidirect
5. #11745901C2semidirect
6. #11745899C2semidirect
7. #11745879C2semidirect
45. Dic60D4semidirect
47. C5×Dic12D4semidirect
59. C2×#827D5semidirect
152. C2×C3×D5SD32semidirect
180. Dic12C22⋊D5semidirect
251. C2×D5#827semidirect
282. C3×C5#2185semidirect
327. C5#71077semidirect
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×#911112
C2×C5×#8272
C3×#654462
#117459012
#117458992
#117458792
#106022763
#710775