Finite Group Databasebeta

← #14299740

Subgroups — #14299740

Order 1920.

604 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756282C211yesmaximal, characteristic
2C3×#65284C211yesmaximal, characteristic, complemented
3#11748861C211yesmaximal, characteristic, complemented
4C2×#90980C211yesmaximal, characteristic
5#11748413C211yesmaximal, characteristic
6C5×#4532C211yesmaximal, characteristic, complemented
7#11745987C211yesmaximal, characteristic, complemented
8#10599564—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12#91781—21no—
13C4⋊C4×D15—21no—
14#91770—22no—
15C4×D60—21no—
16C4×Dic30—21no—
17C2×C4×C5×Dic3C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C2×C3×C4⋊Dic5C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21C2×Dic3⋊Dic5—22no—
22C3×#3940—21no—
23C3×#3939—21no—
24#90980C414yescomplemented
25#90974—21no—
26#90968—21no—
27#70680—51nomaximal, Hall
28#65857—31no—
29#65422—31no—
30#65284D311yescharacteristic, complemented
31#65224—31no—
32C2×#3937—31no—
33C5×#339—31no—
34#64774—31no—
35C22×C3×C4×C5C2311yescharacteristic
36C2×#1220—21no—
37C22×Dic15D412yes—
38#6817—21no—
39#6817—21no—
40#6817C2×C412yes—
41#6817Q812yes—
42C2×D60D411yescharacteristic
43C2×C4×D15—21no—
44C2×C4×D15—22no—
45C2×Dic30D411yescharacteristic
46C22×C5×Dic3—21no—
47C22×C3×Dic5—21no—
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C4⋊C4D411yescharacteristic
50C3×C5×C22⋊C4—21no—
51C3×C42×C5—21no—
52#6714—22no—
53C4⋊Dic15—21no—
54C4⋊Dic15—21no—
55#6712—22no—
56C4×Dic15—22no—
57C4×C5×Dic3—21no—
58C4×C5×Dic3C2×C412yescomplemented
59C5×#208—21no—
60C5×#208—21no—
61C2×C5×C3⋊C8—21no—
62C3×C4⋊Dic5—21no—
63C3×C4⋊Dic5—21no—
64C3×#681—21no—
65C3×#681C2×C412yescomplemented
66C2×C3×#168—21no—
67Dic3⋊Dic5—44no—
68#5523—51no—
69C3×#428—51no—
70C2×#825—51no—
71#4975—51no—
72#4966—51no—
73#4554—51no—
74#4532D511yescharacteristic, complemented
75C2×#709—31no—
76C2×C5×M16—31no—
77C5×#117C2×D311yescharacteristic
78C2×C42×C5—31no—
79C2×C4⋊Dic5—31no—
80C2×C4⋊Dic5—62no—
81C2×C4⋊Dic5C2×D311yescharacteristic
82C2×#681C2×D311yescharacteristic
83#4038—61no—
84D5×C4⋊C4—61no—
85#4027—62no—
86C4×D20—61no—
87C4×Dic10—61no—
88#3953—61no—
89#3948—61no—
90#3940—21no—
91#3939—21no—
92#3937—34no—
93#1859—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×Q811yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104#1220—22no—
105#1220—22no—
106C2×Dic15—21no—
107C2×Dic15—22no—
108C2×Dic15—42no—
109D60—21no—
110D60C4⋊C412yescomplemented
111C4×D15—22no—
112C4×D15—22no—
113C4×D15—82no—
114Dic30—21no—
115Dic30C4⋊C412yescomplemented
116C2×C5×Dic3—22no—
117C2×C5×Dic3—22no—
118C2×C5×Dic3—22no—
119C2×C3×Dic5—42no—
120C2×C3×Dic5—41no—
121C3×#168—22no—
122C5×C3⋊C8—41no—
123C2×#235—51no—
124C2×C3×M16—51no—
125C3×#117C2×D511yescharacteristic
126C2×C3×C4⋊C4—51no—
127C2×C4⋊Dic3—51no—
128C2×Dic3⋊C4—102no—
129C2×C4×Dic3C2×D511yescharacteristic
130C2×#208C2×D511yescharacteristic
131#892—101no—
132D3×C4⋊C4—101no—
133#67⋊C4—102no—
134C4×D12—101no—
135C4×Dic6—101no—
136C3×#107—101no—
137C3×#106—101no—
138#825—54no—
139#810—101no—
140#809—101no—
141C22×C4×C5—61no—
142C22×C4×C5C22×D311yescharacteristic
143C2×C22⋊D5—61no—
144C22×Dic5—21no—
145C22×Dic5—32no—
146#709—32no—
147#709—32no—
148#709—61no—
149#709—61no—
150C2×D20—31no—
151C2×C4×D5—61no—
152C2×C4×D5—62no—
153C2×Dic10—31no—
154C5×M16—61no—
155C5×M16—61no—
156C2×C5×C8—61no—
157C5×C4⋊C4#6711yescharacteristic
158C5×C4⋊C4#6711yescharacteristic
159C5×C22⋊C4—21no—
160C42×C5—21no—
161C42×C5—32no—
162C42×C5—61no—
163#685—62no—
164C4⋊Dic5—21no—
165C4⋊Dic5—21no—
166C4⋊Dic5—61no—
167C4⋊Dic5—61no—
168C4⋊Dic5—124no—
169#683—62no—
170C4×Dic5—62no—
171#681—21no—
172#681C4×D312yescomplemented
173C2×#168—21no—
174#520—151no—
175#428—51no—
176C2×#104—151no—
177#417—151no—
178#384—151no—
179#343—151no—
180#339—31no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5C4×D411yescharacteristic
184C22×C3×C5#12011yescharacteristic
185C22×C3×C5C22⋊Q811yescharacteristic
186C2×D15—22no—
187C2×D15—41no—
188C2×D15—41no—
189C3×C4×C5—41no—
190C3×C4×C5—41no—
191C3×C4×C5C2×C4⋊C411yescharacteristic
192C3×C4×C5C4×D411yescharacteristic
193C3×C4×C5C22⋊Q811yescharacteristic
194C3×C4×C5#12311yescharacteristic
195Dic15—22no—
196Dic15—42no—
197C3×Dic5—81no—
198C5×Dic3—24no—
199C22×C3×C4—101no—
200C22×C3×C4C22×D511yescharacteristic
201C2×#67—101no—
202C22×Dic3—21no—
203C22×Dic3—52no—
204#235—52no—
205#235—52no—
206#235—101no—
207#235—101no—
208C2×D12—51no—
209C2×C4×D3—101no—
210C2×C4×D3—102no—
211C2×Dic6—51no—
212C3×M16—52no—
213C3×M16—101no—
214C2×C3×C8—101no—
215C3×C4⋊C4—101no—
216C3×C4⋊C4—101no—
217C3×C4⋊C4D2011yescharacteristic
218C3×C4⋊C4D2011yescharacteristic
219C3×C22⋊C4—21no—
220C3×C42—21no—
221(C2×D3)⋊C4—102no—
222C4⋊Dic3—101no—
223C4⋊Dic3—101no—
224Dic3⋊C4—102no—
225Dic3⋊C4—204no—
226C4×Dic3—21no—
227C4×Dic3—102no—
228C4×Dic3C4×D512yescomplemented
229#208—21no—
230#208—21no—
231C2×C3⋊C8—21no—
232C23×C5D3×D411yescharacteristic
233C22×D5—61no—
234C2×C4×C5—21no—
235C2×C4×C5—21no—
236C2×C4×C5—62no—
237C2×C4×C5—62no—
238C2×C4×C5—62no—
239C2×C4×C5C2×C4×D311yescharacteristic
240C2×C4×C5#23511yescharacteristic
241C2×C4×C5D3×D411yescharacteristic
242C2×C4×C5D3×Q811yescharacteristic
243C2×C4×C5#23911yescharacteristic
244C2×C4×C5C2×#6711yescharacteristic
245C22⋊D5—62no—
246C22⋊D5—62no—
247C2×Dic5—42no—
248C2×Dic5—41no—
249C2×Dic5—61no—
250C2×Dic5—62no—
251C2×Dic5—122no—
252D20—32no—
253D20—61no—
254C4×D5—62no—
255C4×D5—62no—
256C4×D5—242no—
257Dic10—32no—
258Dic10—61no—
259C5×C8—121no—
260#168—22no—
261C2×#41—151no—
262C2×M16—31no—
263C2×M16—51no—
264C4×Q8—301no—
265C4×D4—301no—
266C4×D4—302no—
267#117—301no—
268#117D3×D511yescharacteristic
269C2×C4⋊C4—51no—
270C2×C4⋊C4—151no—
271C2×C4⋊C4—301no—
272C2×C4⋊C4—302no—
273C2×C42—31no—
274#107—101no—
275#106—101no—
276#104—154no—
277#103—301no—
278#102—301no—
279C2×C3×C5—21no—
280C2×C3×C5—21no—
281C2×C3×C5#38511yescharacteristic
282C2×C3×C5#45311yescharacteristic
283C2×C3×C5#45611yescharacteristic
284D15—42no—
285C23×C3D4×D511yescharacteristic
286C22×D3—101no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—202no—
290C2×C3×C4—201no—
291C2×C3×C4C2×C4×D511yescharacteristic
292C2×C3×C4C2×D2011yescharacteristic
293C2×C3×C4#70911yescharacteristic
294C2×C3×C4D4×D511yescharacteristic
295C2×C3×C4#71111yescharacteristic
296C2×C3×C4Q8×D511yescharacteristic
297#67—102no—
298#67—102no—
299C2×Dic3—22no—
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—101no—
303C2×Dic3—102no—
304C2×Dic3—202no—
305D12—52no—
306D12—101no—
307C4×D3—102no—
308C4×D3—102no—
309C4×D3—402no—
310Dic6—52no—
311Dic6—101no—
312C3×C8—102no—
313C3⋊C8—41no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5#89311yescharacteristic
317C22×C5#89611yescharacteristic
318C22×C5#93711yescharacteristic
319C2×D5—62no—
320C2×D5—121no—
321C2×D5—121no—
322C4×C5—41no—
323C4×C5—41no—
324C4×C5—64no—
325C4×C5D3×C4⋊C411yescharacteristic
326C4×C5#89411yescharacteristic
327C4×C5C4×#6711yescharacteristic
328C4×C5#94611yescharacteristic
329Dic5—62no—
330Dic5—81no—
331Dic5—122no—
332#41—152no—
333#41—152no—
334#41—301no—
335#41—301no—
336C2×Q8—151no—
337C2×D4—151no—
338C2×D4—301no—
339C22×C4—61no—
340C22×C4—101no—
341C22×C4—152no—
342C22×C4—302no—
343C22×C4—301no—
344C22×C4C2×D3×D511yescharacteristic
345M16—52no—
346M16—61no—
347M16—61no—
348M16—101no—
349C2×C8—61no—
350C2×C8—101no—
351C4⋊C4—101no—
352C4⋊C4—101no—
353C4⋊C4—302no—
354C4⋊C4—301no—
355C4⋊C4—301no—
356C4⋊C4—604no—
357C4⋊C4#120211yescharacteristic
358C4⋊C4#120211yescharacteristic
359C22⋊C4—21no—
360C22⋊C4—302no—
361C42—21no—
362C42—32no—
363C42—61no—
364C42—302no—
365C3×C5#185911yescharacteristic, complemented, Hall
366C22×C3—21no—
367C22×C3—21no—
368C22×C3#402711yescharacteristic
369C22×C3#402811yescharacteristic
370C22×C3#404211yescharacteristic
371C2×D3—102no—
372C2×D3—201no—
373C2×D3—201no—
374C3×C4—41no—
375C3×C4—41no—
376C3×C4—401no—
377C3×C4C4×D2011yescharacteristic
378C3×C4#402911yescharacteristic
379C3×C4D5×C4⋊C411yescharacteristic
380C3×C4#404311yescharacteristic
381Dic3—24no—
382Dic3—102no—
383Dic3—202no—
384C2×C5—21no—
385C2×C5—21no—
386C2×C5#498911yescharacteristic
387C2×C5#519811yescharacteristic
388C2×C5#520511yescharacteristic
389D5—122no—
390C23—301no—
391C23#679011yescharacteristic
392Q8—152no—
393Q8—301no—
394D4—152no—
395D4—302no—
396D4—302no—
397D4—301no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—62no—
401C2×C4—62no—
402C2×C4—62no—
403C2×C4—202no—
404C2×C4—201no—
405C2×C4—301no—
406C2×C4—302no—
407C2×C4—302no—
408C2×C4—302no—
409C2×C4—602no—
410C2×C4—1202no—
411C2×C4#676811yescharacteristic
412C2×C4D15⋊Q811yescharacteristic
413C2×C4#677111yescharacteristic
414C2×C4C4×D3×D511yescharacteristic
415C2×C4C2×#120211yescharacteristic
416C2×C4#679011yescharacteristic
417C8—102no—
418C8—121no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3#6495711yescharacteristic
422C2×C3#6511111yescharacteristic
423C2×C3#6511511yescharacteristic
424D3—202no—
425C5#7068011yescharacteristic, complemented, Sylow
426C22—21no—
427C22—21no—
428C22—302no—
429C22—601no—
430C22—601no—
431C22#9137711yescharacteristic
432C22#9140611yescharacteristic
433C22#9157211yescharacteristic
434C4—41no—
435C4—41no—
436C4—64no—
437C4—302no—
438C4—401no—
439C4—602no—
440C4#9135511yescharacteristic
441C4#9139011yescharacteristic
442C4#9140411yescharacteristic
443C4C4×#120211yescharacteristic
444C3#1059956411yescharacteristic, complemented, Sylow
445C2—21no—
446C2—21no—
447C2—602no—
448C2#1174872911yescharacteristic
449C2#1174942111yescharacteristic
450C2#1174942411yescharacteristic
subgroupG/H
centerC22#91572
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5#120
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1859
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#65284C2semidirect
3. #11748861C2semidirect
6. C5×#4532C2semidirect
7. #11745987C2semidirect
24. #90980C4semidirect
30. #65284D3semidirect
58. C4×C5×Dic3C2×C4semidirect
65. C3×#681C2×C4semidirect
74. #4532D5semidirect
110. D60C4⋊C4semidirect
115. Dic30C4⋊C4semidirect
172. #681C4×D3semidirect
228. C4×Dic3C4×D5semidirect
365. C3×C5#1859semidirect
425. C5#70680semidirect
444. C3#10599564semidirect

Maximal subgroups

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

subgroupindex
#117562822
C3×#652842
#117488612
C2×#909802
#117484132
C5×#45322
#117459872
#105995643
#706805