Finite Group Databasebeta

← #14289087

Subgroups — #14289087

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#11756485C211yesmaximal, characteristic, complemented
2C3×C5×#486C211yesmaximal, characteristic, complemented
3#11751173C211yesmaximal, characteristic, complemented
4#11751173C211yesmaximal, characteristic, complemented
5#11746368C211yesmaximal, characteristic, complemented
6#11746280C211yesmaximal, characteristic, complemented
7#11746280C211yesmaximal, characteristic, complemented
8#10601989—31nomaximal, Hall
9C2×#6821—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×#127C2211yescharacteristic
12#91835—21no—
13C2×#6715—21no—
14C2×#6715—21no—
15#91784—21no—
16#91783—22no—
17C4⋊C4×D15—21no—
18C4×D60C2211yescharacteristic
19C4×D60C2211yescharacteristic
20C3×C5×#102—22no—
21C3×C4×C5×C8C2211yescharacteristic
22#91116—21no—
23#91116—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4⋊(C3⋊#168)C2211yescharacteristic
26#71196—51nomaximal, Hall
27#66060—31no—
28C5×#486D311yescharacteristic, complemented
29#65361—31no—
30#65361—31no—
31#64767—31no—
32#64679—31no—
33#64679—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38#6821—42no—
39#6821—42no—
40C2×D60—22no—
41C2×D60D411yescharacteristic
42C2×D60D411yescharacteristic
43C2×C4×D15—22no—
44C2×C4×D15—21no—
45C2×C4×D15—21no—
46C2×C3×C5×C8—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4D412yes—
49C3×C42×C5C2311yescharacteristic
50#6715—42no—
51#6715—42no—
52#6714—22no—
53#6714—21no—
54#6714—21no—
55C4⋊Dic15D411yescharacteristic
56C4⋊Dic15D411yescharacteristic
57#6712—22no—
58C2×C3⋊#168—21no—
59C2×C3⋊#168—21no—
60#5726—51no—
61C3×#486D511yescharacteristic, complemented
62#5072—51no—
63#5072—51no—
64#4547—51no—
65#4459—51no—
66#4459—51no—
67C2×#713—61no—
68C5×C4⋊Q8C2×D311yescharacteristic
69C5×#127C2×D311yescharacteristic
70#4092—61no—
71C2×#686—61no—
72C2×#686—61no—
73#4041—61no—
74#4040—62no—
75D5×C4⋊C4—61no—
76C4×D20—31no—
77C4×D20—31no—
78C5×#102—22no—
79C4×C5×C8C2×D311yescharacteristic
80#3964—61no—
81#3964—61no—
82C4⋊#168—31no—
83C4⋊#168—31no—
84#1625—151noSylow
85C23×C3×C5—41no—
86C22×D15—21no—
87C22×D15—21no—
88C3×C5×Q8—41no—
89C3×C5×Q8—41no—
90C3×C5×D4—42no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×Dic15—21no—
100C2×Dic15—21no—
101D60—21no—
102D60—21no—
103D60—21no—
104D60—44no—
105D60D812yescomplemented
106C4×D15—44no—
107C4×D15—41no—
108C4×D15—41no—
109C4×D15—41no—
110C4×D15—41no—
111C3×C5×C8—41no—
112C3⋊#168—41no—
113C3⋊#168—41no—
114C2×#239—101no—
115C3×C4⋊Q8C2×D511yescharacteristic
116C3×#127C2×D511yescharacteristic
117#946—101no—
118C2×#213—101no—
119C2×#213—101no—
120#895—101no—
121#894—102no—
122D3×C4⋊C4—101no—
123C4×D12—51no—
124C4×D12—51no—
125C3×#102—22no—
126C3×C4×C8C2×D511yescharacteristic
127#832—101no—
128#832—101no—
129C4⋊(C3⋊C8)—51no—
130C4⋊(C3⋊C8)—51no—
131C2×C5×Q8—21no—
132C2×C5×D4—21no—
133C2×C5×D4—21no—
134C2×C5×D4—21no—
135#713—122no—
136#713—122no—
137C2×D20—31no—
138C2×D20—31no—
139C2×D20—62no—
140C2×C4×D5—62no—
141C2×C4×D5—61no—
142C2×C4×D5—61no—
143C2×C5×C8—21no—
144C5×C4⋊C4—21no—
145C5×C4⋊C4#6712yes—
146C42×C5C22×D311yescharacteristic
147#686—122no—
148#686—122no—
149#685—62no—
150#685—61no—
151#685—61no—
152C4⋊Dic5—31no—
153C4⋊Dic5—31no—
154#683—62no—
155C2×#168—61no—
156C2×#168—61no—
157#547—151no—
158#486D1511yescharacteristic, complemented
159#459—151no—
160#459—151no—
161#332—151no—
162D4⋊C8—151no—
163D4⋊C8—151no—
164C22×C3×C5—81no—
165C22×C3×C5—81no—
166C22×C3×C5—81no—
167C22×C3×C5#12011yescharacteristic
168C2×D15—22no—
169C2×D15—41no—
170C2×D15—41no—
171C2×D15—41no—
172C2×D15—41no—
173C2×D15—41no—
174C3×C4×C5—21no—
175C3×C4×C5—42no—
176C3×C4×C5C2×D811yescharacteristic
177C3×C4×C5#13511yescharacteristic
178C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
179C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
180Dic15—41no—
181Dic15—41no—
182C2×C3×Q8—21no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186#239—202no—
187#239—202no—
188C2×D12—51no—
189C2×D12—51no—
190C2×D12—102no—
191C2×C4×D3—102no—
192C2×C4×D3—101no—
193C2×C4×D3—101no—
194C2×C3×C8—21no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4C22⋊D512yes—
197C3×C42C22×D511yescharacteristic
198#213—202no—
199#213—202no—
200(C2×D3)⋊C4—102no—
201(C2×D3)⋊C4—101no—
202(C2×D3)⋊C4—101no—
203C4⋊Dic3—51no—
204C4⋊Dic3—51no—
205Dic3⋊C4—102no—
206C2×C3⋊C8—101no—
207C2×C3⋊C8—101no—
208C23×C5—41no—
209C22×D5—61no—
210C22×D5—61no—
211C5×Q8—41no—
212C5×Q8—41no—
213C5×D4—42no—
214C5×D4—41no—
215C5×D4—41no—
216C5×D4—41no—
217C5×D4—41no—
218C2×C4×C5—22no—
219C2×C4×C5D3×D411yescharacteristic
220C2×C4×C5D3×D411yescharacteristic
221C2×C4×C5C2×#6711yescharacteristic
222C2×Dic5—61no—
223C2×Dic5—61no—
224D20—32no—
225D20—61no—
226D20—61no—
227D20—61no—
228D20—124no—
229C4×D5—124no—
230C4×D5—121no—
231C4×D5—121no—
232C4×D5—121no—
233C4×D5—121no—
234C5×C8—41no—
235#168—121no—
236#168—121no—
237C2×#41—301no—
238C2×D8—301no—
239C2×D8—301no—
240C4⋊Q8C2×D1511yescharacteristic
241#127C2×D1511yescharacteristic
242#123—302no—
243C22⋊Q8—301no—
244#121—301no—
245C4×D4—151no—
246C4×D4—151no—
247C2×C4⋊C4—301no—
248C4⋊C8—151no—
249C4⋊C8—151no—
250#102—22no—
251#102—301no—
252#102—301no—
253C4×C8C2×D1511yescharacteristic
254C2×C3×C5—161no—
255C2×C3×C5#44711yescharacteristic
256C2×C3×C5#44911yescharacteristic
257C2×C3×C5#45411yescharacteristic
258D15—42no—
259D15—81no—
260C23×C3—41no—
261C22×D3—101no—
262C22×D3—101no—
263C3×Q8—41no—
264C3×Q8—41no—
265C3×D4—42no—
266C3×D4—41no—
267C3×D4—41no—
268C3×D4—41no—
269C3×D4—41no—
270C2×C3×C4—22no—
271C2×C3×C4D4×D511yescharacteristic
272C2×C3×C4D4×D511yescharacteristic
273C2×C3×C4C2×C22⋊D511yescharacteristic
274C2×Dic3—101no—
275C2×Dic3—101no—
276D12—52no—
277D12—101no—
278D12—101no—
279D12—101no—
280D12—204no—
281C4×D3—204no—
282C4×D3—201no—
283C4×D3—201no—
284C4×D3—201no—
285C4×D3—201no—
286C3×C8—41no—
287C3⋊C8—201no—
288C3⋊C8—201no—
289C22×C5—81no—
290C22×C5—81no—
291C22×C5—81no—
292C22×C5#93711yescharacteristic
293C2×D5—62no—
294C2×D5—121no—
295C2×D5—121no—
296C2×D5—121no—
297C2×D5—121no—
298C2×D5—121no—
299C4×C5—21no—
300C4×C5—42no—
301C4×C5D3×D811yescharacteristic
302C4×C5#91111yescharacteristic
303C4×C5#91411yescharacteristic
304C4×C5#91611yescharacteristic
305Dic5—121no—
306Dic5—121no—
307#41—602no—
308#41—602no—
309C2×Q8—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—151no—
314C2×D4—151no—
315C2×D4—302no—
316C22×C4—302no—
317C22×C4—301no—
318C22×C4—301no—
319D8—602no—
320D8—602no—
321C2×C8—21no—
322C2×C8—301no—
323C2×C8—301no—
324C4⋊C4—21no—
325C4⋊C4—151no—
326C4⋊C4—151no—
327C4⋊C4—302no—
328C4⋊C4#122012yes—
329C22⋊C4—302no—
330C22⋊C4—301no—
331C22⋊C4—301no—
332C42C22×D1511yescharacteristic
333C3×C5#162511yescharacteristic, complemented, Hall
334C22×C3—81no—
335C22×C3—81no—
336C22×C3—81no—
337C22×C3#408311yescharacteristic
338C2×D3—102no—
339C2×D3—201no—
340C2×D3—201no—
341C2×D3—201no—
342C2×D3—201no—
343C2×D3—201no—
344C3×C4—21no—
345C3×C4—42no—
346C3×C4D5×D811yescharacteristic
347C3×C4#405711yescharacteristic
348C3×C4#406011yescharacteristic
349C3×C4#406211yescharacteristic
350Dic3—201no—
351Dic3—201no—
352C2×C5—161no—
353C2×C5#506211yescharacteristic
354C2×C5#515611yescharacteristic
355C2×C5#517211yescharacteristic
356D5—122no—
357D5—241no—
358C23—41no—
359C23—301no—
360C23—301no—
361Q8—41no—
362Q8—41no—
363D4—42no—
364D4—41no—
365D4—41no—
366D4—41no—
367D4—41no—
368D4—152no—
369D4—301no—
370D4—301no—
371D4—301no—
372D4—604no—
373C2×C4—22no—
374C2×C4—301no—
375C2×C4—301no—
376C2×C4—604no—
377C2×C4—601no—
378C2×C4—601no—
379C2×C4—601no—
380C2×C4—601no—
381C2×C4D4×D1511yescharacteristic
382C2×C4D4×D1511yescharacteristic
383C2×C4C2×#122011yescharacteristic
384C8—41no—
385C8—601no—
386C8—601no—
387C2×C3—161no—
388C2×C3#6535111yescharacteristic
389C2×C3#6544511yescharacteristic
390C2×C3#6546111yescharacteristic
391D3—202no—
392D3—401no—
393C5#7119611yescharacteristic, complemented, Sylow
394C22—81no—
395C22—81no—
396C22—81no—
397C22—302no—
398C22—601no—
399C22—601no—
400C22—601no—
401C22—601no—
402C22—601no—
403C22#9182611yescharacteristic
404C4—21no—
405C4—42no—
406C4—601no—
407C4—601no—
408C4D8×D1511yescharacteristic
409C4#9180011yescharacteristic
410C4#9180311yescharacteristic
411C4#9180511yescharacteristic
412C3#1060198911yescharacteristic, complemented, Sylow
413C2—161no—
414C2—602no—
415C2—1201no—
416C2#1175116311yescharacteristic
417C2#1175125711yescharacteristic
418C2#1175127311yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#486C2
socleC22×C3×C5#120
hypercenter#486D15
hypocenterC3×C5#1625
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #11756485C2semidirect
2. C3×C5×#486C2semidirect
3. #11751173C2semidirect
4. #11751173C2semidirect
5. #11746368C2semidirect
6. #11746280C2semidirect
7. #11746280C2semidirect
28. C5×#486D3semidirect
61. C3×#486D5semidirect
105. D60D8semidirect
158. #486D15semidirect
333. C3×C5#1625semidirect
393. C5#71196semidirect
412. C3#10601989semidirect

Maximal subgroups

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

subgroupindex
#117564852
C3×C5×#4862
#117511732
#117463682
#117462802
#106019893
#711965