Finite Group Databasebeta

← #14289093

Subgroups — #14289093

Order 1920.

512 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 93 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
1#11756310C211yesmaximal, characteristic, complemented
2C3×C5×#459C211yesmaximal, characteristic, complemented
3#11751173C211yesmaximal, characteristic, complemented
4#11751171C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
6#11746307C211yesmaximal, characteristic, complemented
7#11746304C211yesmaximal, characteristic, complemented
8#10601805—31nomaximal, Hall
9C2×#6817—21no—
10C2×C3×C5×D8—21no—
11C3×C5×#127C2211yescharacteristic
12C3×C4×C5×D4C2211yescharacteristic
13#91827—21no—
14C2×#6715—21no—
15#91813—21no—
16C4⋊C4×D15—21no—
17#91772—22no—
18C4×D60C2211yescharacteristic
19#91758C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×#102—21no—
22#91116—22no—
23#91116—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71012—51nomaximal, Hall
27#65885—31no—
28C5×#459D311yescharacteristic, complemented
29#65361—31no—
30#65359—31no—
31D4⋊#168—31no—
32#64706—31no—
33#64703—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4D411yescharacteristic
38C22×C3×C4×C5—21no—
39C2×#1220—22no—
40#6817—42no—
41#6817—42no—
42C2×D60D411yescharacteristic
43C2×C4×D15—22no—
44C2×C4×D15—21no—
45C2×Dic30—21no—
46C3×C5×D8—42no—
47C2×C3×C5×C8—21no—
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C22⋊C4—21no—
50C3×C42×C5C2311yescharacteristic
51#6719—22no—
52#6715—42no—
53#6714—21no—
54C4⋊Dic15—21no—
55C4⋊Dic15D412yes—
56C4⋊Dic15D411yescharacteristic
57#6712—22no—
58C2×C3⋊#168—21no—
59C2×C3⋊#168—21no—
60#5551—51no—
61C3×#459D511yescharacteristic, complemented
62#5072—51no—
63#5070—51no—
64D4⋊(C3⋊C8)—51no—
65#4486—51no—
66#4483—51no—
67C2×#709—61no—
68C2×C5×D8—21no—
69C5×#127C2×D311yescharacteristic
70C4×C5×D4C2×D311yescharacteristic
71#4084—61no—
72C2×#686—61no—
73#4070—61no—
74D5×C4⋊C4—61no—
75#4029—62no—
76C4×D20—31no—
77#4015—31no—
78C5×C4⋊C8C2×D311yescharacteristic
79C5×#102—21no—
80#3964—62no—
81#3964—61no—
82C4⋊#168—31no—
83C4×#168—31no—
84#1625—151noSylow
85C23×C3×C5—21no—
86C23×C3×C5—41no—
87C22×D15—21no—
88C3×C5×D4—21no—
89C3×C5×D4—21no—
90C3×C5×D4—42no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101#1220—44no—
102C2×Dic15—21no—
103C2×Dic15—22no—
104D60—21no—
105D60D812yescomplemented
106C4×D15—44no—
107C4×D15—41no—
108C4×D15—41no—
109Dic30—41no—
110Dic30—41no—
111C3×C5×C8—41no—
112C3⋊#168—41no—
113C3⋊#168—41no—
114C2×#235—101no—
115C2×C3×D8—21no—
116C3×#127C2×D511yescharacteristic
117C3×C4×D4C2×D511yescharacteristic
118#938—101no—
119C2×#213—101no—
120#924—101no—
121D3×C4⋊C4—101no—
122#883—102no—
123C4×D12—51no—
124#869—51no—
125C3×C4⋊C8C2×D511yescharacteristic
126C3×#102—21no—
127#832—102no—
128#832—101no—
129C4⋊(C3⋊C8)—51no—
130C4×C3⋊C8—51no—
131C2×C5×D4—21no—
132C2×C5×D4—21no—
133C2×C5×D4—21no—
134C2×C5×D4#6711yescharacteristic
135C22×C4×C5—21no—
136C2×C22⋊D5—62no—
137#709—122no—
138#709—122no—
139C2×D20—31no—
140C2×C4×D5—62no—
141C2×C4×D5—61no—
142C2×Dic10—61no—
143C5×D8—42no—
144C2×C5×C8—21no—
145C5×C4⋊C4#6711yescharacteristic
146C5×C22⋊C4—21no—
147C42×C5C22×D311yescharacteristic
148C22⋊Dic5—62no—
149#686—122no—
150#685—61no—
151C4⋊Dic5—32no—
152C4⋊Dic5—31no—
153C4⋊Dic5—61no—
154#683—62no—
155C2×#168—61no—
156C2×#168—61no—
157#547—151no—
158#486—151no—
159#459—151no—
160#459D1511yescharacteristic, complemented
161#332—151no—
162D4⋊C8—151no—
163D4⋊C8—151no—
164C22×C3×C5—41no—
165C22×C3×C5—41no—
166C22×C3×C5—41no—
167C22×C3×C5—81no—
168C22×C3×C5—81no—
169C22×C3×C5—81no—
170C22×C3×C5#12011yescharacteristic
171C2×D15—22no—
172C2×D15—41no—
173C2×D15—41no—
174C3×C4×C5—21no—
175C3×C4×C5—41no—
176C3×C4×C5C2×D811yescharacteristic
177C3×C4×C5#13511yescharacteristic
178C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
179C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
180Dic15—42no—
181Dic15—41no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4C22⋊D511yescharacteristic
186C22×C3×C4—21no—
187C2×#67—102no—
188#235—202no—
189#235—202no—
190C2×D12—51no—
191C2×C4×D3—102no—
192C2×C4×D3—101no—
193C2×Dic6—101no—
194C3×D8—42no—
195C2×C3×C8—21no—
196C3×C4⋊C4C22⋊D511yescharacteristic
197C3×C22⋊C4—21no—
198C3×C42C22×D511yescharacteristic
199#217—102no—
200#213—202no—
201(C2×D3)⋊C4—101no—
202C4⋊Dic3—52no—
203C4⋊Dic3—51no—
204C4⋊Dic3—101no—
205Dic3⋊C4—102no—
206C2×C3⋊C8—101no—
207C2×C3⋊C8—101no—
208C23×C5—21no—
209C23×C5—41no—
210C22×D5—61no—
211C5×D4—21no—
212C5×D4—21no—
213C5×D4—42no—
214C5×D4—41no—
215C5×D4—41no—
216C5×D4—41no—
217C5×D4—41no—
218C2×C4×C5—21no—
219C2×C4×C5—41no—
220C2×C4×C5—41no—
221C2×C4×C5D3×D411yescharacteristic
222C2×C4×C5D3×D411yescharacteristic
223C2×C4×C5C2×#6711yescharacteristic
224C22⋊D5—124no—
225C2×Dic5—61no—
226C2×Dic5—62no—
227D20—32no—
228D20—61no—
229C4×D5—124no—
230C4×D5—121no—
231C4×D5—121no—
232Dic10—121no—
233Dic10—121no—
234C5×C8—41no—
235#168—121no—
236#168—121no—
237C2×#41—301no—
238C2×D8—21no—
239C2×D8—301no—
240C4⋊Q8—151no—
241#127C2×D1511yescharacteristic
242#123—302no—
243C22⋊Q8—301no—
244#121—301no—
245C4×D4—151no—
246C4×D4C2×D1511yescharacteristic
247C2×C4⋊C4—301no—
248C4⋊C8—151no—
249C4⋊C8C2×D1511yescharacteristic
250#102—21no—
251#102—301no—
252#102—302no—
253C4×C8—151no—
254C2×C3×C5—81no—
255C2×C3×C5—161no—
256C2×C3×C5#44711yescharacteristic
257C2×C3×C5#44911yescharacteristic
258C2×C3×C5#45411yescharacteristic
259D15—42no—
260C23×C3—21no—
261C23×C3—41no—
262C22×D3—101no—
263C3×D4—21no—
264C3×D4—21no—
265C3×D4—42no—
266C3×D4—41no—
267C3×D4—41no—
268C3×D4—41no—
269C3×D4—41no—
270C2×C3×C4—21no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4D4×D511yescharacteristic
274C2×C3×C4D4×D511yescharacteristic
275C2×C3×C4C2×C22⋊D511yescharacteristic
276#67—204no—
277C2×Dic3—101no—
278C2×Dic3—102no—
279D12—52no—
280D12—101no—
281C4×D3—204no—
282C4×D3—201no—
283C4×D3—201no—
284Dic6—201no—
285Dic6—201no—
286C3×C8—41no—
287C3⋊C8—201no—
288C3⋊C8—201no—
289C22×C5—41no—
290C22×C5—41no—
291C22×C5—41no—
292C22×C5—81no—
293C22×C5—81no—
294C22×C5—81no—
295C22×C5#93711yescharacteristic
296C2×D5—62no—
297C2×D5—121no—
298C2×D5—121no—
299C4×C5—21no—
300C4×C5—41no—
301C4×C5D3×D811yescharacteristic
302C4×C5#91111yescharacteristic
303C4×C5#93211yescharacteristic
304C4×C5#95011yescharacteristic
305Dic5—122no—
306Dic5—121no—
307#41—602no—
308#41—602no—
309C2×Q8—301no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—151no—
314C2×D4—302no—
315C2×D4#122011yescharacteristic
316C22×C4—21no—
317C22×C4—302no—
318C22×C4—301no—
319D8—42no—
320D8—602no—
321C2×C8—21no—
322C2×C8—301no—
323C2×C8—301no—
324C4⋊C4—151no—
325C4⋊C4—152no—
326C4⋊C4—302no—
327C4⋊C4—301no—
328C4⋊C4#122011yescharacteristic
329C22⋊C4—21no—
330C22⋊C4—302no—
331C22⋊C4—301no—
332C42C22×D1511yescharacteristic
333C3×C5#162511yescharacteristic, complemented, Hall
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3—81no—
338C22×C3—81no—
339C22×C3—81no—
340C22×C3#408311yescharacteristic
341C2×D3—102no—
342C2×D3—201no—
343C2×D3—201no—
344C3×C4—21no—
345C3×C4—41no—
346C3×C4D5×D811yescharacteristic
347C3×C4#405711yescharacteristic
348C3×C4#407811yescharacteristic
349C3×C4#409611yescharacteristic
350Dic3—201no—
351Dic3—202no—
352C2×C5—81no—
353C2×C5—161no—
354C2×C5#503711yescharacteristic
355C2×C5#515611yescharacteristic
356C2×C5#520111yescharacteristic
357D5—122no—
358C23—21no—
359C23—41no—
360C23—301no—
361Q8—601no—
362Q8—601no—
363D4—21no—
364D4—21no—
365D4—42no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—41no—
370D4—152no—
371D4—301no—
372D4—604no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—301no—
377C2×C4—302no—
378C2×C4—604no—
379C2×C4—601no—
380C2×C4—601no—
381C2×C4D4×D1511yescharacteristic
382C2×C4D4×D1511yescharacteristic
383C2×C4C2×#122011yescharacteristic
384C8—41no—
385C8—601no—
386C8—601no—
387C2×C3—81no—
388C2×C3—161no—
389C2×C3#6532611yescharacteristic
390C2×C3#6544511yescharacteristic
391C2×C3#6549011yescharacteristic
392D3—202no—
393C5#7101211yescharacteristic, complemented, Sylow
394C22—41no—
395C22—41no—
396C22—41no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—302no—
401C22—601no—
402C22—601no—
403C22#9182611yescharacteristic
404C4—21no—
405C4—41no—
406C4—602no—
407C4—601no—
408C4D8×D1511yescharacteristic
409C4#9180011yescharacteristic
410C4#9182111yescharacteristic
411C4#9183911yescharacteristic
412C3#1060180511yescharacteristic, complemented, Sylow
413C2—81no—
414C2—161no—
415C2—602no—
416C2#1175113811yescharacteristic
417C2#1175125711yescharacteristic
418C2#1175130211yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#459C2
socleC22×C3×C5#120
hypercenter#459D15
hypocenterC3×C5#1625
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #11756310C2semidirect
2. C3×C5×#459C2semidirect
3. #11751173C2semidirect
4. #11751171C2semidirect
5. D4⋊(C3⋊#168)C2semidirect
6. #11746307C2semidirect
7. #11746304C2semidirect
28. C5×#459D3semidirect
61. C3×#459D5semidirect
105. D60D8semidirect
160. #459D15semidirect
333. C3×C5#1625semidirect
393. C5#71012semidirect
412. C3#10601805semidirect

Maximal subgroups

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

subgroupindex
#117563102
C3×C5×#4592
#117511732
#117511712
D4⋊(C3⋊#168)2
#117463072
#117463042
#106018053
#710125