Finite Group Databasebeta

← #14299798

Subgroups — #14299798

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#11756263C211yesmaximal, characteristic
2C2×#91109C211yesmaximal, characteristic
3#11751234C211yesmaximal, characteristic
4#11751222C211yesmaximal, characteristic, complemented
5#11751078C211yesmaximal, characteristic, complemented
6C3×C5×#343C211yesmaximal, characteristic, complemented
7#11746376C211yesmaximal, characteristic, complemented
8#10599796—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C4×#1220—22no—
14#91815C2211yescharacteristic
15C2×C4⋊Dic15C2211yescharacteristic
16C2×C4×Dic15C2211yescharacteristic
17#91782—21no—
18#91781—21no—
19C4⋊C4×D15—21no—
20#91776—21no—
21#91115—22no—
22#91109C414yescomplemented
23#91105—21no—
24#91102—21no—
25#91101—21no—
26#91100—21no—
27#69003—51nomaximal, Hall
28#65838—31no—
29C2×#3957—31no—
30#65422—31no—
31#65410—31no—
32#65266—31no—
33C5×#343D311yescharacteristic, complemented
34#64775—31no—
35C22×C3×C4×C5D412yes—
36C22×C3×C4×C5C2311yescharacteristic
37C2×#1220—21no—
38C22×Dic15—21no—
39C22×Dic15—21no—
40#6817—21no—
41#6817—21no—
42#6817C2×C412yes—
43#6817Q812yes—
44C2×D60D411yescharacteristic
45C2×C4×D15—21no—
46C2×C4×D15—22no—
47C2×Dic30D411yescharacteristic
48C3×C5×M16—21no—
49C3×C5×M16—21no—
50C3×C5×M16—21no—
51C3×C5×M16C2×C412yescomplemented
52C2×C3×C5×C8—21no—
53C2×C3×C5×C8—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4—21no—
56#6719—21no—
57#6714—22no—
58C4⋊Dic15—21no—
59C4⋊Dic15—21no—
60C4⋊Dic15D411yescharacteristic
61C4⋊Dic15D411yescharacteristic
62#6712—22no—
63C4×Dic15—22no—
64C4×Dic15—21no—
65C4×Dic15—21no—
66C4×Dic15C2×C412yescomplemented
67#5504—51no—
68C2×#825—51no—
69#5133—51no—
70#5121—51no—
71#4977—51no—
72C3×#343D511yescharacteristic, complemented
73#4555—51no—
74C2×#709—31no—
75C2×C5×M16C2×D311yescharacteristic
76C2×C5×M16C2×D311yescharacteristic
77C2×C5×C4⋊C4C2×D311yescharacteristic
78C4×C22⋊D5—62no—
79#4072—31no—
80C2×C4⋊Dic5—31no—
81C2×C4×Dic5—31no—
82#4039—61no—
83#4038—61no—
84D5×C4⋊C4—61no—
85#4033—61no—
86#3963—62no—
87#3957—34no—
88#3953—61no—
89#3950—61no—
90#3949—61no—
91#3948—61no—
92#1860—151noSylow
93C23×C3×C5C2×D411yescharacteristic
94C22×D15—21no—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5—42no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×Q811yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103#1220—22no—
104#1220—22no—
105C2×Dic15—21no—
106C2×Dic15—22no—
107C2×Dic15—21no—
108C2×Dic15—21no—
109C2×Dic15—41no—
110C2×Dic15—41no—
111C2×Dic15—42no—
112C2×Dic15—41no—
113D60—21no—
114D60C4⋊C412yes—
115C4×D15—22no—
116C4×D15—22no—
117C4×D15—82no—
118Dic30—21no—
119Dic30C4⋊C412yes—
120C3×C5×C8—22no—
121C3×C5×C8—41no—
122C2×#235—51no—
123C2×C3×M16C2×D511yescharacteristic
124C2×C3×M16C2×D511yescharacteristic
125C2×C3×C4⋊C4C2×D511yescharacteristic
126C4×#67—102no—
127#926—51no—
128C2×C4⋊Dic3—51no—
129C2×C4×Dic3—51no—
130#893—101no—
131#892—101no—
132D3×C4⋊C4—101no—
133#887—101no—
134C3⋊#95—102no—
135#825—54no—
136#821—101no—
137#818—101no—
138#817—101no—
139#816—101no—
140C22×C4×C5D1212yes—
141C22×C4×C5C22×D311yescharacteristic
142C2×C22⋊D5—61no—
143C22×Dic5—61no—
144C22×Dic5—61no—
145#709—32no—
146#709—32no—
147#709—61no—
148#709—61no—
149C2×D20—31no—
150C2×C4×D5—61no—
151C2×C4×D5—62no—
152C2×Dic10—31no—
153C5×M16—21no—
154C5×M16—21no—
155C5×M16—21no—
156C5×M16C4×D312yescomplemented
157C2×C5×C8—21no—
158C2×C5×C8—21no—
159C5×C4⋊C4—21no—
160C5×C4⋊C4—21no—
161C22⋊Dic5—61no—
162#685—62no—
163C4⋊Dic5—31no—
164C4⋊Dic5—31no—
165C4⋊Dic5—61no—
166C4⋊Dic5—61no—
167#683—62no—
168C4×Dic5—32no—
169C4×Dic5—62no—
170C4×Dic5—61no—
171C4×Dic5—61no—
172#520—151no—
173#428—151no—
174C2×#104—151no—
175#417—151no—
176#382—151no—
177#343D1511yescharacteristic, complemented
178#339—151no—
179C22×C3×C5—21no—
180C22×C3×C5—21no—
181C22×C3×C5C4×D411yescharacteristic
182C22×C3×C5#12011yescharacteristic
183C22×C3×C5C22⋊Q811yescharacteristic
184C2×D15—22no—
185C2×D15—41no—
186C2×D15—41no—
187C3×C4×C5—42no—
188C3×C4×C5C2×C4⋊C411yescharacteristic
189C3×C4×C5C4×D411yescharacteristic
190C3×C4×C5C22⋊Q811yescharacteristic
191C3×C4×C5#12311yescharacteristic
192Dic15—22no—
193Dic15—42no—
194Dic15—41no—
195Dic15—41no—
196Dic15—81no—
197C22×C3×C4D2012yes—
198C22×C3×C4C22×D511yescharacteristic
199C2×#67—101no—
200C22×Dic3—101no—
201C22×Dic3—101no—
202#235—52no—
203#235—52no—
204#235—101no—
205#235—101no—
206C2×D12—51no—
207C2×C4×D3—101no—
208C2×C4×D3—102no—
209C2×Dic6—51no—
210C3×M16—21no—
211C3×M16—21no—
212C3×M16—21no—
213C3×M16C4×D512yescomplemented
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218#217—101no—
219(C2×D3)⋊C4—102no—
220C4⋊Dic3—51no—
221C4⋊Dic3—51no—
222C4⋊Dic3—101no—
223C4⋊Dic3—101no—
224Dic3⋊C4—102no—
225C4×Dic3—52no—
226C4×Dic3—102no—
227C4×Dic3—101no—
228C4×Dic3—101no—
229C23×C5C2×D1211yescharacteristic
230C22×D5—61no—
231C2×C4×C5—22no—
232C2×C4×C5—42no—
233C2×C4×C5C2×C4×D311yescharacteristic
234C2×C4×C5#23511yescharacteristic
235C2×C4×C5D3×D411yescharacteristic
236C2×C4×C5D3×D411yescharacteristic
237C2×C4×C5#23711yescharacteristic
238C2×C4×C5D3×Q811yescharacteristic
239C22⋊D5—62no—
240C22⋊D5—62no—
241C2×Dic5—61no—
242C2×Dic5—62no—
243C2×Dic5—61no—
244C2×Dic5—61no—
245C2×Dic5—121no—
246C2×Dic5—121no—
247C2×Dic5—122no—
248C2×Dic5—121no—
249D20—32no—
250D20—61no—
251C4×D5—62no—
252C4×D5—62no—
253C4×D5—242no—
254Dic10—32no—
255Dic10—61no—
256C5×C8—22no—
257C5×C8—41no—
258C2×#41—151no—
259C2×M16C2×D1511yescharacteristic
260C2×M16C2×D1511yescharacteristic
261C4×Q8—301no—
262C4×D4—301no—
263C4×D4—302no—
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—301no—
274#102—301no—
275#95—302no—
276C2×C3×C5—21no—
277C2×C3×C5—21no—
278C2×C3×C5#38511yescharacteristic
279C2×C3×C5#45411yescharacteristic
280C2×C3×C5#45511yescharacteristic
281D15—42no—
282C23×C3C2×D2011yescharacteristic
283C22×D3—101no—
284C2×C3×C4—22no—
285C2×C3×C4—42no—
286C2×C3×C4C2×C4×D511yescharacteristic
287C2×C3×C4#70911yescharacteristic
288C2×C3×C4D4×D511yescharacteristic
289C2×C3×C4D4×D511yescharacteristic
290C2×C3×C4#71111yescharacteristic
291C2×C3×C4Q8×D511yescharacteristic
292#67—102no—
293#67—102no—
294C2×Dic3—101no—
295C2×Dic3—102no—
296C2×Dic3—101no—
297C2×Dic3—101no—
298C2×Dic3—201no—
299C2×Dic3—201no—
300C2×Dic3—202no—
301C2×Dic3—201no—
302D12—52no—
303D12—101no—
304C4×D3—102no—
305C4×D3—102no—
306C4×D3—402no—
307Dic6—52no—
308Dic6—101no—
309C3×C8—22no—
310C3×C8—41no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5C4×D1211yescharacteristic
314C22×C5#88211yescharacteristic
315C22×C5#89711yescharacteristic
316C2×D5—62no—
317C2×D5—121no—
318C2×D5—121no—
319C4×C5—42no—
320C4×C5#67⋊C411yescharacteristic
321C4×C5#88311yescharacteristic
322C4×C5D3×C4⋊C411yescharacteristic
323C4×C5#89611yescharacteristic
324Dic5—62no—
325Dic5—122no—
326Dic5—121no—
327Dic5—121no—
328Dic5—241no—
329#41—152no—
330#41—152no—
331#41—301no—
332#41—301no—
333C2×Q8—151no—
334C2×D4—151no—
335C2×D4—301no—
336C22×C4—302no—
337C22×C4—301no—
338C22×C4—301no—
339C22×C4—301no—
340C22×C4D6012yes—
341C22×C4C22×D1511yescharacteristic
342M16—21no—
343M16—21no—
344M16—21no—
345M16C4×D1512yescomplemented
346C2×C8—21no—
347C2×C8—21no—
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×C3C4×D2011yescharacteristic
365C22×C3#402811yescharacteristic
366C22×C3#404311yescharacteristic
367C2×D3—102no—
368C2×D3—201no—
369C2×D3—201no—
370C3×C4—42no—
371C3×C4#402711yescharacteristic
372C3×C4#402911yescharacteristic
373C3×C4D5×C4⋊C411yescharacteristic
374C3×C4#404211yescharacteristic
375Dic3—102no—
376Dic3—202no—
377Dic3—201no—
378Dic3—201no—
379Dic3—401no—
380C2×C5—21no—
381C2×C5—21no—
382C2×C5#466811yescharacteristic
383C2×C5#474611yescharacteristic
384C2×C5#475311yescharacteristic
385D5—122no—
386C23—301no—
387C23C2×D6011yescharacteristic
388Q8—152no—
389Q8—301no—
390D4—152no—
391D4—302no—
392D4—302no—
393D4—301no—
394C2×C4—22no—
395C2×C4—42no—
396C2×C4—301no—
397C2×C4—302no—
398C2×C4—302no—
399C2×C4—302no—
400C2×C4—301no—
401C2×C4—301no—
402C2×C4—601no—
403C2×C4—601no—
404C2×C4—602no—
405C2×C4—601no—
406C2×C4—1202no—
407C2×C4C2×C4×D1511yescharacteristic
408C2×C4#681711yescharacteristic
409C2×C4D4×D1511yescharacteristic
410C2×C4D4×D1511yescharacteristic
411C2×C4#681911yescharacteristic
412C2×C4Q8×D1511yescharacteristic
413C8—22no—
414C8—41no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3#6495711yescharacteristic
418C2×C3#6503511yescharacteristic
419C2×C3#6504211yescharacteristic
420D3—202no—
421C5#6900311yescharacteristic, complemented, Sylow
422C22—21no—
423C22—21no—
424C22—302no—
425C22—601no—
426C22—601no—
427C22C4×D6011yescharacteristic
428C22#9177111yescharacteristic
429C22#9178611yescharacteristic
430C4—42no—
431C4—302no—
432C4—602no—
433C4—601no—
434C4—601no—
435C4—1201no—
436C4#9177011yescharacteristic
437C4#9177211yescharacteristic
438C4C4⋊C4×D1511yescharacteristic
439C4#9178511yescharacteristic
440C3#1059979611yescharacteristic, complemented, Sylow
441C2—21no—
442C2—21no—
443C2—602no—
444C2#1175076911yescharacteristic
445C2#1175084711yescharacteristic
446C2#1175085411yescharacteristic
subgroupG/H
centerC22#91771
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#343C2
socleC22×C3×C5#120
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenter#343D15
hypocenterC3×C5#1860
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
4. #11751222C2semidirect
5. #11751078C2semidirect
6. C3×C5×#343C2semidirect
7. #11746376C2semidirect
22. #91109C4semidirect
33. C5×#343D3semidirect
51. C3×C5×M16C2×C4semidirect
66. C4×Dic15C2×C4semidirect
72. C3×#343D5semidirect
156. C5×M16C4×D3semidirect
177. #343D15semidirect
213. C3×M16C4×D5semidirect
345. M16C4×D15semidirect
361. C3×C5#1860semidirect
421. C5#69003semidirect
440. C3#10599796semidirect

Maximal subgroups

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

subgroupindex
#117562632
C2×#911092
#117512342
#117512222
#117510782
C3×C5×#3432
#117463762
#105997963
#690035