Finite Group Databasebeta

← #14316091

Subgroups — #14316091

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
2C3×#65172C211yesmaximal, characteristic
3C2×#90942C211yesmaximal, characteristic, complemented
4C2×#90940C211yesmaximal, characteristic, complemented
5#11746313C211yesmaximal, characteristic, complemented
6C5×#4492C211yesmaximal, characteristic, complemented
7#11745879C211yesmaximal, characteristic, complemented
8#10600016—31nomaximal, Hall
9C2×D5×Dic6—21no—
10C2×Dic60C2211yescharacteristic
11C2×C5×Dic12C2211yescharacteristic
12C2×C3×D40C2211yescharacteristic
13C2×C3×C8×D5C2211yescharacteristic
14C3×#4041—21no—
15C2×#6663—21no—
16D5×Dic12—22no—
17D5×Dic12—22no—
18C3×C5×#107C2211yescharacteristic
19C2×C3⋊#672C2211yescharacteristic
20C2×C5×C3⋊C16C2211yescharacteristic
21C3×#3941—21no—
22#90942—22no—
23#90940—22no—
24#71077—51nomaximal, Hall
25C2×D5×Q16—31no—
26C2×#3960—31no—
27C2×#3932—31no—
28#65172D311yescharacteristic
29C5×#358—31no—
30#64727—31no—
31#64712—31no—
32C2×Dic30—21no—
33C2×C5×Dic6—21no—
34C2×C3×D20—21no—
35C2×C3×D20—41no—
36C2×C3×C4×D5D411yescharacteristic
37C2×#1204—41no—
38C2×D5×Dic3—41no—
39D5×Dic6—24no—
40D5×Dic6—42no—
41C2×C3×C5×C8C2311yescharacteristic
42C3×C5×C4⋊C4—21no—
43Dic60—21no—
44Dic60D412yescomplemented
45C5×Dic12—21no—
46C5×Dic12D412yescomplemented
47C3×#685—41no—
48C2×C3×#168D411yescharacteristic
49C3×D40—21no—
50C3×D40—21no—
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×#827—51no—
60#4549—51no—
61#4492—51no—
62#4492D511yescharacteristic, complemented
63C2×Q8×D5—61no—
64C2×C5×Q16—31no—
65C2×#689—61no—
66D5×Q16—62no—
67D5×Q16—62no—
68C2×Dic20—31no—
69C2×D40C2×D311yescharacteristic
70C2×C8×D5C2×D311yescharacteristic
71#4041—21no—
72C2×C5×C16—31no—
73C5×#107C2×D311yescharacteristic
74#3960—62no—
75C2×#672—31no—
76#3941—21no—
77#3932—62no—
78#2185—151noSylow
79C22×C3×D5—41no—
80C22×C3×D5D811yescharacteristic
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×Dic15—41no—
84Dic30—22no—
85Dic30—41no—
86C2×C5×Dic3—41no—
87C5×Dic6—22no—
88C5×Dic6—41no—
89C2×C3×Dic5D811yescharacteristic
90C3×D20—41no—
91C3×D20—41no—
92C3×D20—82no—
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×D8—51no—
102C22×C3×C8—51no—
103C3×#121—101no—
104C2×Dic12—51no—
105C2×Dic12—102no—
106C2×Dic12—101no—
107C2×Dic12—102no—
108C2×Dic12C2×D511yescharacteristic
109C3×#107C2×D511yescharacteristic
110C3×#102—101no—
111#827—102no—
112#827—102no—
113C2×C3⋊C16—51no—
114C2×C3⋊C16C2×D511yescharacteristic
115C2×C5×Q8—61no—
116Q8×D5—64no—
117Q8×D5—122no—
118C2×D20—21no—
119C2×D20—41no—
120C2×C4×D5—121no—
121C2×C4×D5#6711yescharacteristic
122C2×Dic10—61no—
123C2×Dic10—121no—
124C5×Q16—32no—
125C5×Q16—61no—
126C2×C5×C8C22×D311yescharacteristic
127C5×C4⋊C4—21no—
128#689—64no—
129#685—41no—
130C2×#168#6711yescharacteristic
131Dic20—32no—
132Dic20—61no—
133D40—21no—
134D40—21no—
135C8×D5—21no—
136C8×D5—21no—
137C5×C16—61no—
138#672—61no—
139C22×Q16—151no—
140C2×SD32—151no—
141C2×SD32—151no—
142#466—51no—
143#358—31no—
144#358—151no—
145C22⋊C16—151no—
146C22×C3×C5C2×D811yescharacteristic
147C2×C3×D5—21no—
148C2×C3×D5—21no—
149C2×C3×D5—81no—
150C2×C3×D5—81no—
151C2×C3×D5—81no—
152C2×C3×D5SD3212yescomplemented
153C3×C4×C5—81no—
154C3×C4×C5#12011yescharacteristic
155C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
156Dic15—42no—
157C3×Dic5—21no—
158C5×Dic3—42no—
159C2×C3×D4—101no—
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—101no—
169C3×D8—101no—
170C2×C3×C8—51no—
171C2×C3×C8—101no—
172C2×C3×C8—101no—
173C2×C3×C8C22×D511yescharacteristic
174C3×C4⋊C4—21no—
175C3×C22⋊C4—201no—
176Dic12—21no—
177Dic12—52no—
178Dic12—104no—
179Dic12—101no—
180Dic12D2012yescomplemented
181C3⋊C16—21no—
182C3⋊C16—101no—
183C22×D5—41no—
184C22×D5#21311yescharacteristic
185C5×Q8—62no—
186C5×Q8—121no—
187C2×C4×C5—41no—
188C2×C4×C5—121no—
189C2×C4×C5C2×#6711yescharacteristic
190C2×Dic5—121no—
191C2×Dic5#21311yescharacteristic
192D20—41no—
193D20—41no—
194D20—82no—
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—51no—
211C22×C8—51no—
212#121—101no—
213SD32—302no—
214SD32—302no—
215C2×C16—31no—
216C2×C16—151no—
217#107D3×D511yescharacteristic
218#102—101no—
219C2×C3×C5#44711yescharacteristic
220C2×C3×C5C2×SD3211yescharacteristic
221C2×C3×C5#51011yescharacteristic
222C3×D5—22no—
223C3×D5—161no—
224C23×C3—51no—
225C23×C3—201no—
226C3×D4—201no—
227C3×D4—201no—
228C3×D4—402no—
229C2×C3×C4—41no—
230C2×C3×C4—51no—
231C2×C3×C4—101no—
232C2×C3×C4—101no—
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×C8C2×D2011yescharacteristic
244C3×C8D4×D511yescharacteristic
245C22×C5C2×#21311yescharacteristic
246C2×D5—21no—
247C2×D5—21no—
248C2×D5—81no—
249C2×D5—81no—
250C2×D5—81no—
251C2×D5#82712yescomplemented
252C4×C5—81no—
253C4×C5—122no—
254C4×C5#93711yescharacteristic
255C4×C5#94911yescharacteristic
256Dic5—21no—
257Dic5—122no—
258C2×Q8—61no—
259C2×Q8—304no—
260C2×Q8—301no—
261C2×Q8—601no—
262C2×Q8—602no—
263C2×D4—101no—
264C2×D4—201no—
265C22×C4—51no—
266C22×C4—601no—
267Q16—32no—
268Q16—61no—
269Q16—152no—
270Q16—304no—
271Q16—301no—
272D8—101no—
273D8—101no—
274C2×C8—51no—
275C2×C8—101no—
276C2×C8—101no—
277C2×C8C2×D3×D511yescharacteristic
278C4⋊C4—21no—
279C22⋊C4—201no—
280C16—61no—
281C16—301no—
282C3×C5#218511yescharacteristic, complemented, Hall
283C22×C3—52no—
284C22×C3—101no—
285C22×C3—101no—
286C22×C3—401no—
287C22×C3—401no—
288C22×C3—401no—
289C22×C3D5×D811yescharacteristic
290C3×C4—81no—
291C3×C4—101no—
292C3×C4#402811yescharacteristic
293C3×C4#406011yescharacteristic
294Dic3—42no—
295Dic3—202no—
296C2×C5#503611yescharacteristic
297C2×C5C2×#82711yescharacteristic
298C2×C5#519511yescharacteristic
299D5—22no—
300D5—161no—
301C23—51no—
302C23—201no—
303Q8—62no—
304Q8—121no—
305Q8—302no—
306Q8—604no—
307Q8—601no—
308D4—201no—
309D4—201no—
310D4—402no—
311C2×C4—41no—
312C2×C4—51no—
313C2×C4—101no—
314C2×C4—101no—
315C2×C4—121no—
316C2×C4—604no—
317C2×C4—601no—
318C2×C4D5×#6711yescharacteristic
319C8—101no—
320C8D3×D2011yescharacteristic
321C8#677711yescharacteristic
322C2×C3—102no—
323C2×C3—801no—
324C2×C3#6506211yescharacteristic
325C2×C3D5×SD3211yescharacteristic
326C2×C3#6520711yescharacteristic
327C5#7107711yescharacteristic, complemented, Sylow
328C22—52no—
329C22—101no—
330C22—101no—
331C22—401no—
332C22—401no—
333C22—401no—
334C22D5×#21311yescharacteristic
335C4—81no—
336C4—101no—
337C4—122no—
338C4—602no—
339C4#9147411yescharacteristic
340C4#9150211yescharacteristic
341C3#1060001611yescharacteristic, complemented, Sylow
342C2—102no—
343C2—801no—
344C2#1174748011yescharacteristic
345C2D5×#82711yescharacteristic
346C2#1174829511yescharacteristic
subgroupG/H
centerC22D5×#213
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C2×D8
prime radicalC3×#65172C2
hypercenter#107D3×D5
hypocenterC3×C5#2185
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
1. C2×D5×Dic12C2semidirect
3. C2×#90942C2semidirect
4. C2×#90940C2semidirect
5. #11746313C2semidirect
6. C5×#4492C2semidirect
7. #11745879C2semidirect
44. Dic60D4semidirect
46. C5×Dic12D4semidirect
62. #4492D5semidirect
152. C2×C3×D5SD32semidirect
180. Dic12D20semidirect
251. C2×D5#827semidirect
282. C3×C5#2185semidirect
327. C5#71077semidirect
341. C3#10600016semidirect

Maximal subgroups

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

subgroupindex
C2×D5×Dic122
C3×#651722
C2×#909422
C2×#909402
#117463132
C5×#44922
#117458792
#106000163
#710775