Finite Group Databasebeta

← #14316132

Subgroups — #14316132

Order 1920.

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

normal subgroups only

This group has 460 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
1C2×C3×#4050C211yesmaximal, characteristic, complemented
2#11751216C211yesmaximal, characteristic, complemented
3C2×#90943C211yesmaximal, characteristic, complemented
4C2×#90938C211yesmaximal, characteristic, complemented
5C5×#4549C211yesmaximal, characteristic, complemented
6#11745898C211yesmaximal, characteristic, complemented
7#11745892C211yesmaximal, characteristic, complemented
8#10599902—31nomaximal, Hall
9C2×C3×#709—21no—
10C22×C3×C5×C8C2211yescharacteristic
11#91819—21no—
12C2×D120C2211yescharacteristic
13C2×C3×Dic20C2211yescharacteristic
14C3×#4050—22no—
15C3×#4050—22no—
16C2×C3×D40C2211yescharacteristic
17C2×C3×#677—21no—
18#91105—21no—
19#91102C2211yescharacteristic
20C2×C5×C3⋊C16C2211yescharacteristic
21C2×C5×C3⋊C16C2211yescharacteristic
22#90943—22no—
23#90938—22no—
24#72082—51nomaximal, Hall
25C2×#4050D311yescharacteristic, complemented
26#65404—31no—
27C2×#3932—31no—
28C2×D80—31no—
29C5×C22⋊C16—31no—
30#64729—31no—
31#64723—31no—
32C22×C3×C4×C5D411yescharacteristic
33C2×#1220—41no—
34C2×D60—21no—
35C2×C3×C22⋊D5—41no—
36C3×#709—24no—
37C3×#709—42no—
38C2×C3×D20—21no—
39C2×C3×C4×D5—41no—
40C2×C3×Dic10—21no—
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43C2×C3×C5×C8D411yescharacteristic
44C2×C3×C5×C8C2311yescharacteristic
45#6714—41no—
46C4⋊Dic15—21no—
47D120—21no—
48D120—21no—
49C3×Dic20—21no—
50C3×Dic20D412yescomplemented
51C3×D40—21no—
52C3×D40D412yescomplemented
53C3×#677—24no—
54C5×C3⋊C16—21no—
55C5×C3⋊C16—21no—
56C2×C3×#135—51no—
57C2×#828—51no—
58C2×#826—51no—
59#5115—51no—
60#4564—51no—
61#4562—51no—
62#4549D511yescharacteristic, complemented
63C2×#709—21no—
64C22×C5×C8C2×D311yescharacteristic
65#4076—61no—
66C2×Dic20C2×D311yescharacteristic
67#4050—22no—
68#4050—22no—
69C2×D40—31no—
70C2×D40C2×D311yescharacteristic
71C2×#677—21no—
72C2×C5×C16—31no—
73C2×C5×C16—31no—
74#3953—61no—
75#3950—31no—
76#3932—62no—
77D80—62no—
78#2186—151noSylow
79C23×C3×C5D811yescharacteristic
80C22×D15—41no—
81C22×C3×D5—41no—
82C2×C3×C4×C5—21no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5D811yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86#1220—82no—
87C2×Dic15—41no—
88D60—41no—
89D60—41no—
90C3×C22⋊D5—44no—
91C2×C3×Dic5—41no—
92C3×D20—22no—
93C3×D20—41no—
94C3×C4×D5—44no—
95C3×Dic10—22no—
96C3×Dic10—41no—
97C3×C5×C8—21no—
98C3×C5×C8C2×D411yescharacteristic
99C3×C5×C8C2×D411yescharacteristic
100C2×C3×#41—101no—
101C3×#135—102no—
102C3×#135—102no—
103C2×C3×Q16—51no—
104C2×C3×SD16—101no—
105C2×C3×D8—51no—
106C22×C3×C8C2×D511yescharacteristic
107#930—101no—
108C2×D24—51no—
109#828—102no—
110#826—102no—
111#821—101no—
112#818—51no—
113C2×C3⋊C16C2×D511yescharacteristic
114C2×C3⋊C16C2×D511yescharacteristic
115C22×C4×C5#6711yescharacteristic
116C2×C22⋊D5—41no—
117C2×C22⋊D5—121no—
118#709—24no—
119#709—42no—
120C2×D20—21no—
121C2×D20—61no—
122C2×C4×D5—41no—
123C2×Dic10—21no—
124C2×C5×C8—21no—
125C2×C5×C8—21no—
126C2×C5×C8#6711yescharacteristic
127C2×C5×C8C22×D311yescharacteristic
128#685—121no—
129C4⋊Dic5—61no—
130Dic20—21no—
131Dic20#6712yescomplemented
132D40—21no—
133D40—61no—
134D40—61no—
135D40#6712yescomplemented
136#677—24no—
137C5×C16—61no—
138C5×C16—61no—
139C2×#135—51no—
140C2×SD32—151no—
141C2×D16—151no—
142#466—151no—
143#358—151no—
144#357—151no—
145C22⋊C16—31no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5C2×D811yescharacteristic
150C2×D15—81no—
151C2×D15—81no—
152C2×D15—81no—
153C2×C3×D5—42no—
154C2×C3×D5—81no—
155C2×C3×D5—81no—
156C3×C4×C5—21no—
157C3×C4×C5#12011yescharacteristic
158C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
159Dic15—81no—
160C3×Dic5—42no—
161C3×#41—104no—
162C3×#41—202no—
163C2×C3×Q8—101no—
164C2×C3×D4—101no—
165C2×C3×D4—201no—
166C22×C3×C4—201no—
167C22×C3×C4D2011yescharacteristic
168C2×#67—201no—
169C2×D12—101no—
170C3×Q16—52no—
171C3×Q16—101no—
172C3×SD16—104no—
173C3×D8—52no—
174C3×D8—101no—
175C2×C3×C8—21no—
176C2×C3×C8—21no—
177C2×C3×C8D2011yescharacteristic
178C2×C3×C8C22×D511yescharacteristic
179(C2×D3)⋊C4—201no—
180C4⋊Dic3—101no—
181D24—101no—
182D24—101no—
183C3⋊C16—21no—
184C3⋊C16—21no—
185C23×C5#21311yescharacteristic
186C22×D5—41no—
187C22×D5—121no—
188C2×C4×C5—21no—
189C2×C4×C5—21no—
190C2×C4×C5#21311yescharacteristic
191C2×C4×C5C2×#6711yescharacteristic
192C22⋊D5—44no—
193C22⋊D5—242no—
194C2×Dic5—41no—
195C2×Dic5—121no—
196D20—22no—
197D20—41no—
198D20—121no—
199D20—121no—
200C4×D5—44no—
201Dic10—22no—
202Dic10—41no—
203C5×C8—21no—
204C5×C8C2×#6711yescharacteristic
205C5×C8C2×#6711yescharacteristic
206C2×#41—101no—
207#135—102no—
208#135—102no—
209C2×Q16—51no—
210C2×SD16—101no—
211C2×D8—51no—
212C2×D8—151no—
213C22×C8D3×D511yescharacteristic
214#121—301no—
215SD32—302no—
216D16—302no—
217C2×C16—31no—
218C2×C16—31no—
219#107—151no—
220#102—301no—
221C2×C3×C5—41no—
222C2×C3×C5#44711yescharacteristic
223C2×C3×C5#50811yescharacteristic
224C2×C3×C5#50911yescharacteristic
225D15—161no—
226C3×D5—82no—
227C23×C3—201no—
228C23×C3D4011yescharacteristic
229C22×D3—201no—
230C3×Q8—102no—
231C3×Q8—201no—
232C3×D4—102no—
233C3×D4—204no—
234C3×D4—201no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—204no—
238C2×C3×C4—201no—
239C2×C3×C4D4011yescharacteristic
240C2×C3×C4C2×D2011yescharacteristic
241#67—402no—
242C2×Dic3—201no—
243D12—201no—
244D12—201no—
245C3×C8—21no—
246C3×C8D4×D511yescharacteristic
247C3×C8D4×D511yescharacteristic
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5C2×#21311yescharacteristic
252C2×D5—42no—
253C2×D5—81no—
254C2×D5—81no—
255C2×D5—241no—
256C2×D5—241no—
257C2×D5—241no—
258C4×C5—21no—
259C4×C5#93211yescharacteristic
260C4×C5#95311yescharacteristic
261Dic5—42no—
262Dic5—241no—
263#41—104no—
264#41—202no—
265C2×Q8—101no—
266C2×D4—101no—
267C2×D4—201no—
268C2×D4—301no—
269C2×D4—601no—
270C22×C4—201no—
271C22×C4#120211yescharacteristic
272Q16—52no—
273Q16—101no—
274SD16—104no—
275D8—52no—
276D8—101no—
277D8—301no—
278D8—301no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8#120211yescharacteristic
282C2×C8C2×D3×D511yescharacteristic
283C4⋊C4—301no—
284C22⋊C4—601no—
285C16—61no—
286C16—61no—
287C3×C5#218611yescharacteristic, complemented, Hall
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3—202no—
292C22×C3—401no—
293C22×C3—401no—
294C22×C3C2×D4011yescharacteristic
295C2×D3—401no—
296C2×D3—401no—
297C2×D3—401no—
298C3×C4—21no—
299C3×C4—202no—
300C3×C4#402811yescharacteristic
301C3×C4#405411yescharacteristic
302Dic3—401no—
303C2×C5—41no—
304C2×C5#519311yescharacteristic
305C2×C5#519411yescharacteristic
306C2×C5#521711yescharacteristic
307D5—82no—
308D5—481no—
309C23—201no—
310C23—601no—
311C23#665311yescharacteristic
312Q8—102no—
313Q8—201no—
314D4—102no—
315D4—204no—
316D4—201no—
317D4—601no—
318D4—601no—
319D4—1202no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—204no—
323C2×C4—201no—
324C2×C4—601no—
325C2×C4#665311yescharacteristic
326C2×C4C2×#120211yescharacteristic
327C8—21no—
328C8D5×#6711yescharacteristic
329C8D5×#6711yescharacteristic
330C2×C3—41no—
331C2×C3—402no—
332C2×C3#6502111yescharacteristic
333C2×C3#6519311yescharacteristic
334C2×C3#6519711yescharacteristic
335D3—801no—
336C5#7208211yescharacteristic, complemented, Sylow
337C22—21no—
338C22—21no—
339C22—21no—
340C22—202no—
341C22—401no—
342C22—401no—
343C22—1201no—
344C22—1201no—
345C22—1201no—
346C22C2×#665311yescharacteristic
347C4—21no—
348C4—202no—
349C4—1201no—
350C4#9131211yescharacteristic
351C4#9156411yescharacteristic
352C3#1059990211yescharacteristic, complemented, Sylow
353C2—41no—
354C2—402no—
355C2—2401no—
356C2#1174754211yescharacteristic
357C2#1174754411yescharacteristic
358C2#1174851211yescharacteristic
subgroupG/H
centerC22C2×#6653
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C2×D8
hypercenterC22×C8D3×D5
hypocenterC3×C5#2186
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4050C2semidirect
2. #11751216C2semidirect
3. C2×#90943C2semidirect
4. C2×#90938C2semidirect
5. C5×#4549C2semidirect
6. #11745898C2semidirect
7. #11745892C2semidirect
25. C2×#4050D3semidirect
50. C3×Dic20D4semidirect
52. C3×D40D4semidirect
62. #4549D5semidirect
131. Dic20#67semidirect
135. D40#67semidirect
287. C3×C5#2186semidirect
336. C5#72082semidirect
352. C3#10599902semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40502
#117512162
C2×#909432
C2×#909382
C5×#45492
#117458982
#117458922
#105999023
#720825