Finite Group Databasebeta

← #14316053

Subgroups — #14316053

Order 1920.

532 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 82 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×#91256C211yesmaximal, characteristic, complemented
2#11750984C211yesmaximal, characteristic, complemented
3C2×#90939C211yesmaximal, characteristic, complemented
4C2×#90938C211yesmaximal, characteristic, complemented
5C5×#4491C211yesmaximal, characteristic, complemented
6C3×#64711C211yesmaximal, characteristic, complemented
7#11745881C211yesmaximal, characteristic, complemented
8#10599984—31nomaximal, Hall
9C2×#6777—21no—
10C2×D120C2211yescharacteristic, complemented
11C2×C8×D15C2211yescharacteristic
12#91784—21no—
13C2×C5×D24C2211yescharacteristic
14C2×C3×D40C2211yescharacteristic
15C2×#6652—21no—
16#91256—22no—
17#91256—22no—
18C3×C5×#107C2211yescharacteristic, complemented
19#91093—21no—
20C2×C5×C3⋊C16C2211yescharacteristic, complemented
21C2×C3×#672C2211yescharacteristic, complemented
22#90939—22no—
23#90938—22no—
24#69191—51nomaximal, Hall
25C2×D5×D8—31no—
26C2×#3958—31no—
27C2×D80—31no—
28#65172—31no—
29C5×#357—31no—
30#64727—31no—
31#64711D311yescharacteristic, complemented
32C22×D3×D5—41no—
33C2×D60—21no—
34C2×D60—41no—
35C2×C4×D15D411yescharacteristic
36C2×C5×D12—21no—
37C2×C3×D20—21no—
38C2×#1201—41no—
39#6777—24no—
40#6777—42no—
41C2×C3×C5×C8C2311yescharacteristic
42C3×C5×C4⋊C4—21no—
43#6714—41no—
44C2×C3⋊#168D411yescharacteristic
45D120—21no—
46D120—21no—
47C8×D15—21no—
48C8×D15—21no—
49C5×D24—21no—
50C5×D24D412yescomplemented
51C3×D40—21no—
52C3×D40D412yescomplemented
53#6652—24no—
54C3×#672—21no—
55C5×C3⋊C16—21no—
56C2×D3×D8—51no—
57C2×#826—51no—
58C2×D48—51no—
59#4883—51no—
60C3×#357—51no—
61(C2×D3)⋊C16—51no—
62#4491D511yescharacteristic, complemented
63C2×D4×D5—61no—
64C2×C5×D8—31no—
65C2×#686—61no—
66D5×D8—62no—
67D5×D8—62no—
68C2×D40—31no—
69C2×D40C2×D311yescharacteristic
70C2×C8×D5—31no—
71#4041—61no—
72C2×C5×C16—31no—
73C5×#107C2×D311yescharacteristic, complemented
74#3958—62no—
75C2×#672C2×D311yescharacteristic, complemented
76#3941—61no—
77D80—62no—
78#2184—151noSylow
79C22×D15—41no—
80C22×D15D811yescharacteristic
81C22×C5×D3—41no—
82C22×C3×D5—41no—
83C2×D3×D5—44no—
84C2×D3×D5—82no—
85C2×D3×D5—82no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×Dic15D811yescharacteristic
89D60—41no—
90D60—41no—
91D60—82no—
92C4×D15—21no—
93C4×D15—21no—
94C5×D12—22no—
95C5×D12—41no—
96C3×D20—22no—
97C3×D20—41no—
98#1201—44no—
99C3×C5×C8C2×D411yescharacteristic
100C3×C5×C8C2×D411yescharacteristic
101C3⋊#168—21no—
102C2×D3×D4—101no—
103C2×C3×D8—51no—
104C2×#213—101no—
105D3×D8—102no—
106D3×D8—102no—
107C2×D24—51no—
108C2×D24C2×D511yescharacteristic
109C2×D3×C8—51no—
110#895—101no—
111C2×C3×C16—51no—
112C3×#107C2×D511yescharacteristic, complemented
113#826—102no—
114C2×C3⋊C16C2×D511yescharacteristic, complemented
115#809—101no—
116D48—102no—
117C23×D5—121no—
118C2×C5×D4—61no—
119C2×C22⋊D5—121no—
120D4×D5—64no—
121D4×D5—122no—
122C2×D20—21no—
123C2×D20—61no—
124C2×D20—121no—
125C2×C4×D5—31no—
126C5×D8—32no—
127C5×D8—61no—
128C2×C5×C8C22×D311yescharacteristic
129C5×C4⋊C4—21no—
130#686—64no—
131#685—121no—
132C2×#168—31no—
133D40—21no—
134D40—61no—
135D40—61no—
136D40D1212yescomplemented
137C8×D5—61no—
138C8×D5—61no—
139C5×C16—61no—
140#672—21no—
141C22×D8—151no—
142C2×D16—151no—
143C2×D16—151no—
144#466—151no—
145#357—31no—
146#357—51no—
147C22⋊C16—151no—
148C22×C3×C5C2×D811yescharacteristic
149C2×D15—21no—
150C2×D15—21no—
151C2×D15—81no—
152C2×D15—81no—
153C2×D15—81no—
154C2×D15D1612yescomplemented
155C2×C5×D3—42no—
156C2×C5×D3—81no—
157C2×C5×D3—81no—
158C2×C3×D5—42no—
159C2×C3×D5—81no—
160C2×C3×D5—81no—
161D3×D5—88no—
162C3×C4×C5—81no—
163C3×C4×C5#12011yescharacteristic
164C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
165Dic15—21no—
166C23×D3—201no—
167C2×C3×D4—101no—
168C2×#67—201no—
169D3×D4—104no—
170D3×D4—202no—
171C2×D12—21no—
172C2×D12—101no—
173C2×D12—201no—
174C2×C4×D3—51no—
175C3×D8—52no—
176C3×D8—101no—
177C2×C3×C8C22×D511yescharacteristic
178C3×C4⋊C4—21no—
179#213—104no—
180(C2×D3)⋊C4—201no—
181C2×C3⋊C8—51no—
182D24—21no—
183D24—101no—
184D24—101no—
185D24D2012yescomplemented
186D3×C8—101no—
187D3×C8—101no—
188C3×C16—101no—
189C3⋊C16—21no—
190C23×C5—121no—
191C22×D5—31no—
192C22×D5—41no—
193C22×D5—124no—
194C22×D5—121no—
195C22×D5—242no—
196C22×D5—242no—
197C5×D4—62no—
198C5×D4—121no—
199C2×C4×C5—41no—
200C2×C4×C5D3×D411yescharacteristic
201C22⋊D5—124no—
202C2×Dic5—31no—
203D20—22no—
204D20—41no—
205D20—121no—
206D20—121no—
207D20—242no—
208C4×D5—61no—
209C4×D5—61no—
210C5×C8C2×D1211yescharacteristic
211C5×C8D3×D411yescharacteristic
212#168—61no—
213C22×D4—301no—
214C2×D8—31no—
215C2×D8—51no—
216C2×D8—151no—
217C2×D8—301no—
218C2×D8—302no—
219C2×D8—302no—
220C22×C8—151no—
221#121—301no—
222D16—302no—
223D16—302no—
224C2×C16—31no—
225C2×C16—51no—
226#107D3×D511yescharacteristic, complemented
227#102—301no—
228C2×C3×C5#44711yescharacteristic
229C2×C3×C5C2×D1611yescharacteristic
230C2×C3×C5#50911yescharacteristic
231D15—22no—
232D15—161no—
233C3×D5—82no—
234C5×D3—82no—
235C23×C3—201no—
236C22×D3—41no—
237C22×D3—51no—
238C22×D3—204no—
239C22×D3—201no—
240C22×D3—402no—
241C22×D3—402no—
242C3×D4—102no—
243C3×D4—201no—
244C2×C3×C4—41no—
245C2×C3×C4D4×D511yescharacteristic
246#67—204no—
247C2×Dic3—51no—
248D12—22no—
249D12—41no—
250D12—201no—
251D12—201no—
252D12—402no—
253C4×D3—101no—
254C4×D3—101no—
255C3×C8C2×D2011yescharacteristic
256C3×C8D4×D511yescharacteristic
257C3⋊C8—101no—
258C22×C5—122no—
259C22×C5—241no—
260C22×C5—241no—
261C22×C5D3×D811yescharacteristic
262C2×D5—32no—
263C2×D5—42no—
264C2×D5—61no—
265C2×D5—61no—
266C2×D5—81no—
267C2×D5—81no—
268C2×D5—248no—
269C2×D5—241no—
270C2×D5—241no—
271C2×D5—241no—
272C4×C5—81no—
273C4×C5#88211yescharacteristic
274C4×C5#91411yescharacteristic
275Dic5—61no—
276C24—601no—
277C2×D4—61no—
278C2×D4—101no—
279C2×D4—304no—
280C2×D4—301no—
281C2×D4—601no—
282C2×D4—601no—
283C2×D4—602no—
284C22×C4—151no—
285D8—32no—
286D8—52no—
287D8—61no—
288D8—101no—
289D8—304no—
290D8—301no—
291D8—301no—
292C2×C8—151no—
293C2×C8—301no—
294C2×C8—301no—
295C2×C8C2×D3×D511yescharacteristic
296C4⋊C4—21no—
297C22⋊C4—601no—
298C16—61no—
299C16—101no—
300C3×C5#218411yescharacteristic, complemented, Hall
301C22×C3—202no—
302C22×C3—401no—
303C22×C3—401no—
304C22×C3D5×D811yescharacteristic
305C2×D3—42no—
306C2×D3—52no—
307C2×D3—81no—
308C2×D3—81no—
309C2×D3—101no—
310C2×D3—101no—
311C2×D3—408no—
312C2×D3—401no—
313C2×D3—401no—
314C2×D3—401no—
315C3×C4—81no—
316C3×C4#402811yescharacteristic
317C3×C4#406011yescharacteristic
318Dic3—101no—
319C2×C5—242no—
320C2×C5#477311yescharacteristic
321C2×C5D3×D1611yescharacteristic
322C2×C5#491411yescharacteristic
323D5—62no—
324D5—82no—
325D5—481no—
326C23—121no—
327C23—151no—
328C23—201no—
329C23—604no—
330C23—601no—
331C23—1202no—
332C23—1202no—
333D4—62no—
334D4—102no—
335D4—121no—
336D4—201no—
337D4—604no—
338D4—601no—
339D4—601no—
340D4—1202no—
341C2×C4—41no—
342C2×C4—151no—
343C2×C4—301no—
344C2×C4—301no—
345C2×C4#679011yescharacteristic
346C8—301no—
347C8D5×D1211yescharacteristic
348C8D3×D2011yescharacteristic
349C2×C3—402no—
350C2×C3#6506211yescharacteristic
351C2×C3D5×D1611yescharacteristic
352C2×C3#6520311yescharacteristic
353D3—82no—
354D3—102no—
355D3—801no—
356C5#6919111yescharacteristic, complemented, Sylow
357C22—122no—
358C22—152no—
359C22—202no—
360C22—241no—
361C22—241no—
362C22—301no—
363C22—301no—
364C22—401no—
365C22—401no—
366C22—1208no—
367C22—1201no—
368C22—1201no—
369C22—1201no—
370C22#9148111yescharacteristic
371C4—81no—
372C4—301no—
373C4#9147611yescharacteristic
374C4#9150611yescharacteristic
375C3#1059998411yescharacteristic, complemented, Sylow
376C2—242no—
377C2—302no—
378C2—402no—
379C2—2401no—
380C2#1174748511yescharacteristic
381C2#1174826811yescharacteristic
382C2#1174829311yescharacteristic
subgroupG/H
centerC22#91481
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C2×D8
hypercenter#107D3×D5
hypocenterC3×C5#2184
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×#91256C2semidirect
2. #11750984C2semidirect
3. C2×#90939C2semidirect
4. C2×#90938C2semidirect
5. C5×#4491C2semidirect
6. C3×#64711C2semidirect
7. #11745881C2semidirect
10. C2×D120C22semidirect
18. C3×C5×#107C22semidirect
20. C2×C5×C3⋊C16C22semidirect
21. C2×C3×#672C22semidirect
31. #64711D3semidirect
50. C5×D24D4semidirect
52. C3×D40D4semidirect
62. #4491D5semidirect
73. C5×#107C2×D3semidirect
75. C2×#672C2×D3semidirect
112. C3×#107C2×D5semidirect
114. C2×C3⋊C16C2×D5semidirect
136. D40D12semidirect
154. C2×D15D16semidirect
185. D24D20semidirect
226. #107D3×D5semidirect
300. C3×C5#2184semidirect
356. C5#69191semidirect
375. C3#10599984semidirect

Maximal subgroups

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

subgroupindex
C2×#912562
#117509842
C2×#909392
C2×#909382
C5×#44912
C3×#647112
#117458812
#105999843
#691915