Finite Group Databasebeta

← #14299783

Subgroups — #14299783

Order 1920.

572 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756586C211yesmaximal, characteristic
2C3×C5×#417C211yesmaximal, characteristic
3C2×#91121C211yesmaximal, characteristic
4#11751078C211yesmaximal, characteristic, complemented
5#11751065C211yesmaximal, characteristic, complemented
6#11746376C211yesmaximal, characteristic, complemented
7#11746375C211yesmaximal, characteristic, complemented
8#10601091—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12Q8×Dic15—21no—
13D4×Dic15—21no—
14D4×Dic15—22no—
15#91815—21no—
16#91815C2211yescharacteristic
17C2×C4⋊Dic15—21no—
18C2×C4⋊Dic15C2211yescharacteristic
19C2×C4×Dic15C2211yescharacteristic
20C2×#6710C2211yescharacteristic
21C3×C5×#103—21no—
22C3×C5×#102—21no—
23#91121C414yescomplemented
24#91115—22no—
25#91092—21no—
26#91091—21no—
27#70298—51nomaximal, Hall
28#66161—31no—
29C5×#417D311yescharacteristic
30C2×#3969—31no—
31#65266—31no—
32#65253—31no—
33#64775—31no—
34#64774—31no—
35C3×C5×#41—21no—
36C3×C5×#41—21no—
37C3×C5×#41C2×C412yes—
38C3×C5×#41Q812yes—
39C2×C3×C5×Q8D411yescharacteristic
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4D411yescharacteristic
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5C2311yescharacteristic
45C22×Dic15—21no—
46C22×Dic15—22no—
47C22×Dic15D412yes—
48C3×C5×M16—21no—
49C3×C5×M16—21no—
50C2×C3×C5×C8—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4—21no—
53#6719—22no—
54#6719—21no—
55C4⋊Dic15—22no—
56C4⋊Dic15—21no—
57C4⋊Dic15—21no—
58C4⋊Dic15D411yescharacteristic
59C4⋊Dic15D411yescharacteristic
60C4×Dic15—22no—
61C4×Dic15—21no—
62C4×Dic15—21no—
63C4×Dic15C2×C412yescomplemented
64#6710—21no—
65#6710C2×C412yescomplemented
66C2×C3⋊#168—21no—
67#5827—51no—
68C3×#417D511yescharacteristic
69C2×#837—51no—
70#4977—51no—
71#4964—51no—
72#4555—51no—
73#4554—51no—
74C2×C5×#41C2×D311yescharacteristic
75C2×C5×M16C2×D311yescharacteristic
76C2×C5×C4⋊C4C2×D311yescharacteristic
77Q8×Dic5—61no—
78D4×Dic5—62no—
79D4×Dic5—61no—
80#4072—31no—
81#4072—61no—
82C2×C4⋊Dic5—31no—
83C2×C4⋊Dic5—61no—
84C2×C4×Dic5—31no—
85C2×#681—31no—
86C5×#103—21no—
87C5×#102—21no—
88#3969—34no—
89#3963—62no—
90#3940—61no—
91#3939—61no—
92#1860—151noSylow
93C23×C3×C5—21no—
94C23×C3×C5C2×D411yescharacteristic
95C3×C5×Q8—21no—
96C3×C5×Q8C4⋊C412yes—
97C3×C5×D4—22no—
98C3×C5×D4—22no—
99C3×C5×D4—21no—
100C3×C5×D4C4⋊C412yes—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—22no—
103C2×C3×C4×C5—22no—
104C2×C3×C4×C5—42no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5C22×C411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5C2×Q811yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C2×C3×C4×C5#4111yescharacteristic
112C2×Dic15—22no—
113C2×Dic15—21no—
114C2×Dic15—22no—
115C2×Dic15—21no—
116C2×Dic15—41no—
117C2×Dic15—41no—
118C2×Dic15—42no—
119C2×Dic15—82no—
120C3×C5×C8—41no—
121C3⋊#168—22no—
122C2×C3×#41C2×D511yescharacteristic
123C2×C3×M16C2×D511yescharacteristic
124C2×C3×C4⋊C4C2×D511yescharacteristic
125Q8×Dic3—101no—
126D4×Dic3—102no—
127D4×Dic3—101no—
128#926—51no—
129#926—101no—
130C2×C4⋊Dic3—51no—
131C2×C4⋊Dic3—101no—
132C2×C4×Dic3—51no—
133C2×#208—51no—
134C3×#103—21no—
135C3×#102—21no—
136#837—54no—
137C3⋊#95—102no—
138#808—101no—
139#807—101no—
140C5×#41—21no—
141C5×#41—21no—
142C5×#41Dic612yes—
143C5×#41C4×D312yes—
144C2×C5×Q8#6711yescharacteristic
145C2×C5×D4—21no—
146C2×C5×D4#6711yescharacteristic
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5C22×D311yescharacteristic
150C22×Dic5—32no—
151C22×Dic5—61no—
152C22×Dic5—62no—
153C5×M16—21no—
154C5×M16—21no—
155C2×C5×C8—21no—
156C5×C4⋊C4—21no—
157C5×C4⋊C4—21no—
158C22⋊Dic5—62no—
159C22⋊Dic5—61no—
160C4⋊Dic5—31no—
161C4⋊Dic5—31no—
162C4⋊Dic5—62no—
163C4⋊Dic5—61no—
164C4⋊Dic5—61no—
165C4×Dic5—32no—
166C4×Dic5—62no—
167C4×Dic5—61no—
168C4×Dic5—61no—
169#681—32no—
170#681—61no—
171C2×#168—61no—
172#520—151no—
173#428—151no—
174C2×#104—151no—
175#417D1511yescharacteristic
176#382—151no—
177#343—151no—
178#339—151no—
179C22×C3×C5—21no—
180C22×C3×C5—21no—
181C22×C3×C5—22no—
182C22×C3×C5—41no—
183C22×C3×C5—41no—
184C22×C3×C5C4×D411yescharacteristic
185C22×C3×C5#12011yescharacteristic
186C22×C3×C5C22⋊Q811yescharacteristic
187C3×C4×C5—22no—
188C3×C4×C5—81no—
189C3×C4×C5C2×C4⋊C411yescharacteristic
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5C22⋊Q811yescharacteristic
192C3×C4×C5#12311yescharacteristic
193Dic15—42no—
194Dic15—41no—
195Dic15—42no—
196Dic15—41no—
197C3×#41—21no—
198C3×#41—21no—
199C3×#41Dic1012yes—
200C3×#41C4×D512yes—
201C2×C3×Q8C22⋊D511yescharacteristic
202C2×C3×D4—21no—
203C2×C3×D4C22⋊D511yescharacteristic
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4C22×D511yescharacteristic
207C22×Dic3—52no—
208C22×Dic3—101no—
209C22×Dic3—102no—
210C3×M16—21no—
211C3×M16—21no—
212C2×C3×C8—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215#217—102no—
216#217—101no—
217C4⋊Dic3—51no—
218C4⋊Dic3—51no—
219C4⋊Dic3—102no—
220C4⋊Dic3—101no—
221C4⋊Dic3—101no—
222C4×Dic3—52no—
223C4×Dic3—102no—
224C4×Dic3—101no—
225C4×Dic3—101no—
226#208—52no—
227#208—101no—
228C2×C3⋊C8—101no—
229C23×C5—21no—
230C23×C5D3×D411yescharacteristic
231C5×Q8—21no—
232C5×Q8Dic3⋊C412yes—
233C5×D4—22no—
234C5×D4—22no—
235C5×D4—21no—
236C5×D4Dic3⋊C412yes—
237C2×C4×C5—21no—
238C2×C4×C5—22no—
239C2×C4×C5—22no—
240C2×C4×C5—42no—
241C2×C4×C5—41no—
242C2×C4×C5C2×Dic611yescharacteristic
243C2×C4×C5C2×C4×D311yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5#23711yescharacteristic
246C2×C4×C5#23711yescharacteristic
247C2×C4×C5C2×#6711yescharacteristic
248C2×Dic5—62no—
249C2×Dic5—61no—
250C2×Dic5—61no—
251C2×Dic5—62no—
252C2×Dic5—121no—
253C2×Dic5—121no—
254C2×Dic5—122no—
255C2×Dic5—242no—
256C5×C8—41no—
257#168—62no—
258C2×#41C2×D1511yescharacteristic
259C2×M16—151no—
260C2×M16C2×D1511yescharacteristic
261C4×Q8—301no—
262C4×D4—302no—
263C4×D4—301no—
264#117—151no—
265#117—301no—
266C2×C4⋊C4—151no—
267C2×C4⋊C4—301no—
268C2×C4⋊C4C2×D1511yescharacteristic
269C2×C42—151no—
270#107—301no—
271#106—301no—
272#104—154no—
273#103—21no—
274#102—21no—
275#95—302no—
276C2×C3×C5—21no—
277C2×C3×C5—21no—
278C2×C3×C5—42no—
279C2×C3×C5#38511yescharacteristic
280C2×C3×C5#45411yescharacteristic
281C2×C3×C5#45511yescharacteristic
282C23×C3—21no—
283C23×C3D4×D511yescharacteristic
284C3×Q8—21no—
285C3×Q8#68312yes—
286C3×D4—22no—
287C3×D4—22no—
288C3×D4—21no—
289C3×D4#68312yes—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—42no—
294C2×C3×C4—41no—
295C2×C3×C4C2×Dic1011yescharacteristic
296C2×C3×C4C2×C4×D511yescharacteristic
297C2×C3×C4D4×D511yescharacteristic
298C2×C3×C4#71111yescharacteristic
299C2×C3×C4#71111yescharacteristic
300C2×C3×C4C2×C22⋊D511yescharacteristic
301C2×Dic3—102no—
302C2×Dic3—101no—
303C2×Dic3—101no—
304C2×Dic3—102no—
305C2×Dic3—201no—
306C2×Dic3—201no—
307C2×Dic3—202no—
308C2×Dic3—402no—
309C3×C8—41no—
310C3⋊C8—102no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—22no—
314C22×C5—41no—
315C22×C5—41no—
316C22×C5#87811yescharacteristic
317C22×C5#67⋊C411yescharacteristic
318C22×C5#93711yescharacteristic
319C4×C5—22no—
320C4×C5—81no—
321C4×C5#87811yescharacteristic
322C4×C5#67⋊C411yescharacteristic
323C4×C5C2×Dic3⋊C411yescharacteristic
324C4×C5#93511yescharacteristic
325Dic5—122no—
326Dic5—121no—
327Dic5—122no—
328Dic5—121no—
329#41—21no—
330#41—21no—
331#41Dic3012yes—
332#41C4×D1512yes—
333C2×Q8#122011yescharacteristic
334C2×D4—21no—
335C2×D4#122011yescharacteristic
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—152no—
339C22×C4—301no—
340C22×C4—302no—
341C22×C4C22×D1511yescharacteristic
342M16—21no—
343M16—21no—
344M16—152no—
345M16—301no—
346C2×C8—21no—
347C2×C8—301no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—151no—
351C4⋊C4—151no—
352C4⋊C4—302no—
353C4⋊C4—301no—
354C4⋊C4—301no—
355C22⋊C4—302no—
356C22⋊C4—301no—
357C42—152no—
358C42—302no—
359C42—301no—
360C42—301no—
361C3×C5#186011yescharacteristic, complemented, Hall
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—22no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3#402411yescharacteristic
368C22×C3#402711yescharacteristic
369C22×C3#408311yescharacteristic
370C3×C4—22no—
371C3×C4—81no—
372C3×C4#402411yescharacteristic
373C3×C4#402711yescharacteristic
374C3×C4C2×#68311yescharacteristic
375C3×C4#408111yescharacteristic
376Dic3—202no—
377Dic3—201no—
378Dic3—202no—
379Dic3—201no—
380C2×C5—21no—
381C2×C5—21no—
382C2×C5—42no—
383C2×C5#494611yescharacteristic
384C2×C5#520111yescharacteristic
385C2×C5#520211yescharacteristic
386C23—21no—
387C23D4×D1511yescharacteristic
388Q8—21no—
389Q8#671212yes—
390D4—22no—
391D4—22no—
392D4—21no—
393D4#671212yes—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—302no—
400C2×C4—301no—
401C2×C4—301no—
402C2×C4—302no—
403C2×C4—601no—
404C2×C4—601no—
405C2×C4—602no—
406C2×C4—1202no—
407C2×C4C2×Dic3011yescharacteristic
408C2×C4C2×C4×D1511yescharacteristic
409C2×C4D4×D1511yescharacteristic
410C2×C4#681911yescharacteristic
411C2×C4#681911yescharacteristic
412C2×C4C2×#122011yescharacteristic
413C8—41no—
414C8—302no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—42no—
418C2×C3#6523511yescharacteristic
419C2×C3#6549011yescharacteristic
420C2×C3#6549111yescharacteristic
421C5#7029811yescharacteristic, complemented, Sylow
422C22—21no—
423C22—21no—
424C22—22no—
425C22—41no—
426C22—41no—
427C22#9176711yescharacteristic
428C22#9177011yescharacteristic
429C22#9182611yescharacteristic
430C4—22no—
431C4—81no—
432C4—602no—
433C4—601no—
434C4—602no—
435C4—601no—
436C4#9176711yescharacteristic
437C4#9177011yescharacteristic
438C4C2×#671211yescharacteristic
439C4#9182411yescharacteristic
440C3#1060109111yescharacteristic, complemented, Sylow
441C2—21no—
442C2—21no—
443C2—42no—
444C2#1175104711yescharacteristic
445C2#1175130211yescharacteristic
446C2#1175130311yescharacteristic
subgroupG/H
centerC22#91826
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#417C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×#41C22
cosocleC22×C3×C4×C5C23
hypercenter#417D15
hypocenterC3×C5#1860
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
4. #11751078C2semidirect
5. #11751065C2semidirect
6. #11746376C2semidirect
7. #11746375C2semidirect
23. #91121C4semidirect
63. C4×Dic15C2×C4semidirect
65. #6710C2×C4semidirect
361. C3×C5#1860semidirect
421. C5#70298semidirect
440. C3#10601091semidirect

Maximal subgroups

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

subgroupindex
#117565862
C3×C5×#4172
C2×#911212
#117510782
#117510652
#117463762
#117463752
#106010913
#702985