Finite Group Databasebeta

← #14299786

Subgroups — #14299786

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
2C3×C5×#382C211yesmaximal, characteristic, complemented
3#11751067C211yesmaximal, characteristic
4#11751065C211yesmaximal, characteristic, complemented
5C2×#91089C211yesmaximal, characteristic
6#11746351C211yesmaximal, characteristic, complemented
7#11746344C211yesmaximal, characteristic, complemented
8#10600355—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13C4×#1220—22no—
14#91815C2211yescharacteristic
15C2×#6710C2211yescharacteristic
16C2×#6710C2211yescharacteristic
17#91782—21no—
18#91781—21no—
19C4⋊C4×D15—21no—
20#91776—21no—
21C3×C5×#95—22no—
22#91094—21no—
23#91093—21no—
24#91092—21no—
25#91091—21no—
26#91089C414yescomplemented
27#69562—51nomaximal, Hall
28#65838—31no—
29C5×#382D311yescharacteristic, complemented
30#65255—31no—
31#65253—31no—
32C2×#3937—31no—
33#64750—31no—
34#64743—31no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5D412yes—
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—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×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C42×C5—21no—
53C3×C42×C5C2×C412yescomplemented
54#6719—21no—
55#6714—22no—
56C4⋊Dic15D411yescharacteristic
57C4⋊Dic15D411yescharacteristic
58#6712—22no—
59C4×Dic15—22no—
60C4×Dic15—21no—
61#6710—21no—
62#6710—21no—
63#6710—21no—
64#6710C2×C412yescomplemented
65C2×C3⋊#168—21no—
66C2×C3⋊#168—21no—
67#5504—51no—
68C3×#382D511yescharacteristic, complemented
69#4966—51no—
70#4964—51no—
71C2×#805—51no—
72#4530—51no—
73#4523—51no—
74C2×#709—31no—
75C2×C5×C4⋊C4C2×D311yescharacteristic
76C2×C5×C4⋊C4C2×D311yescharacteristic
77C2×C42×C5C2×D311yescharacteristic
78C4×C22⋊D5—62no—
79#4072—31no—
80C2×#681—31no—
81C2×#681—31no—
82#4039—61no—
83#4038—61no—
84D5×C4⋊C4—61no—
85#4033—61no—
86C5×#95—22no—
87#3942—61no—
88#3941—61no—
89#3940—61no—
90#3939—61no—
91#3937—34no—
92#1860—151noSylow
93C23×C3×C5C2×D411yescharacteristic
94C22×D15—21no—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5—22no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—42no—
100C2×C3×C4×C5—42no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5C22×C411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×Q811yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108#1220—22no—
109#1220—22no—
110C2×Dic15—21no—
111C2×Dic15—21no—
112C2×Dic15—21no—
113D60—21no—
114D60C4⋊C412yes—
115C4×D15—22no—
116C4×D15—22no—
117C4×D15—82no—
118Dic30—21no—
119Dic30C4⋊C412yes—
120C3⋊#168—22no—
121C3⋊#168—41no—
122C2×#235—51no—
123C2×C3×C4⋊C4C2×D511yescharacteristic
124C2×C3×C4⋊C4C2×D511yescharacteristic
125C2×C3×C42C2×D511yescharacteristic
126C4×#67—102no—
127#926—51no—
128C2×#208—51no—
129C2×#208—51no—
130#893—101no—
131#892—101no—
132D3×C4⋊C4—101no—
133#887—101no—
134C3×#95—22no—
135#810—101no—
136#809—101no—
137#808—101no—
138#807—101no—
139#805—54no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5#6712yes—
143C22×C4×C5C22×D311yescharacteristic
144C2×C22⋊D5—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×C4⋊C4—21no—
154C5×C4⋊C4—21no—
155C5×C4⋊C4—21no—
156C5×C4⋊C4—21no—
157C42×C5—21no—
158C42×C5C4×D312yescomplemented
159C22⋊Dic5—61no—
160#685—62no—
161C4⋊Dic5—31no—
162C4⋊Dic5—31no—
163#683—62no—
164C4×Dic5—62no—
165C4×Dic5—61no—
166#681—32no—
167#681—61no—
168#681—61no—
169#681—61no—
170C2×#168—61no—
171C2×#168—61no—
172#520—151no—
173#428—151no—
174C2×#104—151no—
175#417—151no—
176#382D1511yescharacteristic, complemented
177#343—151no—
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×C5—42no—
189C3×C4×C5—81no—
190C3×C4×C5C2×C4⋊C411yescharacteristic
191C3×C4×C5C4×D411yescharacteristic
192C3×C4×C5C22⋊Q811yescharacteristic
193C3×C4×C5#12311yescharacteristic
194Dic15—22no—
195Dic15—41no—
196Dic15—41no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4C22⋊D512yes—
200C22×C3×C4C22×D511yescharacteristic
201C2×#67—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×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C42—21no—
215C3×C42C4×D512yescomplemented
216#217—101no—
217(C2×D3)⋊C4—102no—
218C4⋊Dic3—51no—
219C4⋊Dic3—51no—
220Dic3⋊C4—102no—
221C4×Dic3—102no—
222C4×Dic3—101no—
223#208—52no—
224#208—101no—
225#208—101no—
226#208—101no—
227C2×C3⋊C8—101no—
228C2×C3⋊C8—101no—
229C23×C5C2×#6711yescharacteristic
230C22×D5—61no—
231C2×C4×C5—22no—
232C2×C4×C5—22no—
233C2×C4×C5—41no—
234C2×C4×C5—41no—
235C2×C4×C5—42no—
236C2×C4×C5—42no—
237C2×C4×C5—41no—
238C2×C4×C5C2×C4×D311yescharacteristic
239C2×C4×C5#23511yescharacteristic
240C2×C4×C5D3×D411yescharacteristic
241C2×C4×C5D3×D411yescharacteristic
242C2×C4×C5D3×Q811yescharacteristic
243C2×C4×C5#23911yescharacteristic
244C22⋊D5—62no—
245C22⋊D5—62no—
246C2×Dic5—61no—
247C2×Dic5—61no—
248C2×Dic5—61no—
249D20—32no—
250D20—61no—
251C4×D5—62no—
252C4×D5—62no—
253C4×D5—242no—
254Dic10—32no—
255Dic10—61no—
256#168—62no—
257#168—121no—
258C2×#41—151no—
259C2×M16—151no—
260C2×M16—151no—
261C4×Q8—301no—
262C4×D4—301no—
263C4×D4—302no—
264#117—151no—
265#117—301no—
266C2×C4⋊C4—301no—
267C2×C4⋊C4C2×D1511yescharacteristic
268C2×C4⋊C4C2×D1511yescharacteristic
269C2×C42C2×D1511yescharacteristic
270#107—301no—
271#106—301no—
272#104—154no—
273#103—301no—
274#102—301no—
275#95—22no—
276C2×C3×C5—21no—
277C2×C3×C5—21no—
278C2×C3×C5#38511yescharacteristic
279C2×C3×C5#45411yescharacteristic
280C2×C3×C5#45511yescharacteristic
281D15—42no—
282C23×C3C2×C22⋊D511yescharacteristic
283C22×D3—101no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—41no—
291C2×C3×C4C2×C4×D511yescharacteristic
292C2×C3×C4#70911yescharacteristic
293C2×C3×C4D4×D511yescharacteristic
294C2×C3×C4D4×D511yescharacteristic
295C2×C3×C4Q8×D511yescharacteristic
296C2×C3×C4#71311yescharacteristic
297#67—102no—
298#67—102no—
299C2×Dic3—101no—
300C2×Dic3—101no—
301C2×Dic3—101no—
302D12—52no—
303D12—101no—
304C4×D3—102no—
305C4×D3—102no—
306C4×D3—402no—
307Dic6—52no—
308Dic6—101no—
309C3⋊C8—102no—
310C3⋊C8—201no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5C4×#6711yescharacteristic
314C22×C5#93711yescharacteristic
315C22×C5#94611yescharacteristic
316C2×D5—62no—
317C2×D5—121no—
318C2×D5—121no—
319C4×C5—42no—
320C4×C5—42no—
321C4×C5—81no—
322C4×C5D3×C4⋊C411yescharacteristic
323C4×C5#89311yescharacteristic
324C4×C5#89411yescharacteristic
325C4×C5#89611yescharacteristic
326Dic5—62no—
327Dic5—121no—
328Dic5—121no—
329#41—152no—
330#41—152no—
331#41—301no—
332#41—301no—
333C2×Q8—151no—
334C2×D4—151no—
335C2×D4—301no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—302no—
339C22×C4—301no—
340C22×C4#122012yes—
341C22×C4C22×D1511yescharacteristic
342M16—152no—
343M16—301no—
344M16—301no—
345M16—301no—
346C2×C8—301no—
347C2×C8—301no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—151no—
353C4⋊C4—151no—
354C4⋊C4—302no—
355C22⋊C4—302no—
356C22⋊C4—301no—
357C42—21no—
358C42—302no—
359C42—301no—
360C42C4×D1512yescomplemented
361C3×C5#186011yescharacteristic, complemented, Hall
362C22×C3—21no—
363C22×C3—21no—
364C22×C3C4×C22⋊D511yescharacteristic
365C22×C3#408311yescharacteristic
366C22×C3#409211yescharacteristic
367C2×D3—102no—
368C2×D3—201no—
369C2×D3—201no—
370C3×C4—42no—
371C3×C4—42no—
372C3×C4—81no—
373C3×C4D5×C4⋊C411yescharacteristic
374C3×C4#403911yescharacteristic
375C3×C4#404011yescharacteristic
376C3×C4#404211yescharacteristic
377Dic3—102no—
378Dic3—201no—
379Dic3—201no—
380C2×C5—21no—
381C2×C5—21no—
382C2×C5#498911yescharacteristic
383C2×C5#506111yescharacteristic
384C2×C5#506211yescharacteristic
385D5—122no—
386C23—301no—
387C23C2×#122011yescharacteristic
388Q8—152no—
389Q8—301no—
390D4—152no—
391D4—302no—
392D4—302no—
393D4—301no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—301no—
402C2×C4—302no—
403C2×C4—302no—
404C2×C4—301no—
405C2×C4—301no—
406C2×C4—1202no—
407C2×C4C2×C4×D1511yescharacteristic
408C2×C4#681711yescharacteristic
409C2×C4D4×D1511yescharacteristic
410C2×C4D4×D1511yescharacteristic
411C2×C4Q8×D1511yescharacteristic
412C2×C4#682111yescharacteristic
413C8—302no—
414C8—601no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3#6527811yescharacteristic
418C2×C3#6535011yescharacteristic
419C2×C3#6535111yescharacteristic
420D3—202no—
421C5#6956211yescharacteristic, complemented, Sylow
422C22—21no—
423C22—21no—
424C22—302no—
425C22—601no—
426C22—601no—
427C22C4×#122011yescharacteristic
428C22#9182611yescharacteristic
429C22#9183511yescharacteristic
430C4—42no—
431C4—42no—
432C4—81no—
433C4—302no—
434C4—601no—
435C4—601no—
436C4C4⋊C4×D1511yescharacteristic
437C4#9178211yescharacteristic
438C4#9178311yescharacteristic
439C4#9178511yescharacteristic
440C3#1060035511yescharacteristic, complemented, Sylow
441C2—21no—
442C2—21no—
443C2—602no—
444C2#1175109011yescharacteristic
445C2#1175116211yescharacteristic
446C2#1175116311yescharacteristic
subgroupG/H
centerC22#91826
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#382C2
socleC22×C3×C5#120
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenter#382D15
hypocenterC3×C5#1860
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #382

Complements

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

NH ≅ G/Ntype
2. C3×C5×#382C2semidirect
4. #11751065C2semidirect
6. #11746351C2semidirect
7. #11746344C2semidirect
26. #91089C4semidirect
29. C5×#382D3semidirect
53. C3×C42×C5C2×C4semidirect
64. #6710C2×C4semidirect
68. C3×#382D5semidirect
158. C42×C5C4×D3semidirect
176. #382D15semidirect
215. C3×C42C4×D5semidirect
360. C42C4×D15semidirect
361. C3×C5#1860semidirect
421. C5#69562semidirect
440. C3#10600355semidirect

Maximal subgroups

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

subgroupindex
#117562632
C3×C5×#3822
#117510672
#117510652
C2×#910892
#117463512
#117463442
#106003553
#695625