Finite Group Databasebeta

← D5×#4566 #14314101

Subgroups — D5×#4566 #14314101

Order 1920.

464 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
1C3×D5×#135C211yesmaximal, characteristic
2D5×#817C211yesmaximal, characteristic, complemented
3D5×#812C211yesmaximal, characteristic, complemented
4#11746387C211yesmaximal, characteristic, complemented
5C5×#4566C211yesmaximal, characteristic, complemented
6#11745910C211yesmaximal, characteristic, complemented
7#11745909C211yesmaximal, characteristic, complemented
8D5×#360—31nomaximal, Hall
9C3×D5×#41—21no—
10C3×C5×#135C2211yescharacteristic
11C3×#4096—21no—
12C3×#4065C411yescharacteristic, complemented
13C3×D5×Q16C411yescharacteristic, complemented
14C3×#4062—21no—
15C3×D5×SD16—21no—
16C3×#4058C411yescharacteristic, complemented
17C3×D5×D8C411yescharacteristic, complemented
18C3×#4050C2211yescharacteristic
19C2×C3×C8×D5C2211yescharacteristic
20D5×C4⋊Dic3—21no—
21#91101C2211yescharacteristic, complemented
22#91096C2211yescharacteristic, complemented
23C5×#817C2211yescharacteristic, complemented
24C5×#812C2211yescharacteristic, complemented
25#90985—21no—
26#90934—21no—
27D5×C3⋊C16—21no—
28C2×#4566—51nomaximal, Hall
29D5×#135D311yescharacteristic
30D5×M32—31no—
31D5×#106—31no—
32C5×#360—31no—
33#64786—31no—
34#64738—31no—
35#64708—31no—
36C3×C5×#41—21no—
37C3×#713—21no—
38C3×Q8×D5—21no—
39C3×#711—21no—
40C3×#711—41no—
41C3×D4×D5—21no—
42C3×D4×D5—41no—
43C3×#709—21no—
44C3×#709—41no—
45C2×C3×C4×D5—41no—
46C2×C3×C4×D5D411yescharacteristic
47C2×D5×Dic3—41no—
48C3×C5×Q16C2×C411yescharacteristic, complemented
49C3×C5×SD16—21no—
50C3×C5×D8C2×C411yescharacteristic, complemented
51C2×C3×C5×C8C2311yescharacteristic
52C4⋊Dic15—21no—
53C5×C4⋊Dic3—21no—
54C3×#689—21no—
55C3×#688—21no—
56C3×#687—21no—
57C3×#686—21no—
58C2×C3×#168D411yescharacteristic
59C3×Dic20C2×C411yescharacteristic, complemented
60C3×D40C2×C411yescharacteristic, complemented
61C3×#677—21no—
62C3×C8×D5C2×C411yescharacteristic
63C3×C8×D5C2×C411yescharacteristic
64C3×C8×D5D411yescharacteristic
65C3×C8×D5D411yescharacteristic
66#6668—41no—
67C3⋊#672—21no—
68C5×C3⋊C16—21no—
69C2×C3×#135—51no—
70C2×#817—51no—
71C2×#812—51no—
72#4566—51no—
73#4566—51no—
74#4566—51no—
75#4566D511yescharacteristic, direct product factor
76D5×#41—21no—
77C5×#135C2×D311yescharacteristic
78#4096—21no—
79#4065Dic311yescharacteristic, complemented
80D5×Q16Dic311yescharacteristic, complemented
81#4062—21no—
82D5×SD16—21no—
83#4058Dic311yescharacteristic, complemented
84D5×D8Dic311yescharacteristic, complemented
85#4050C2×D311yescharacteristic
86C2×C8×D5C2×D311yescharacteristic
87D5×C4⋊C4—61no—
88C5×M32—31no—
89C5×#106—31no—
90#3949—31no—
91#3944—31no—
92#3940—61no—
93#3930—61no—
94D5×C16—61no—
95C2×#360—151noSylow
96C22×C3×D5—41no—
97C22×C3×D5D811yescharacteristic
98C3×C5×Q8—21no—
99C3×C5×D4—21no—
100C3×C5×D4—41no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×Dic15—41no—
104C2×C5×Dic3—41no—
105C3×C22⋊D5—41no—
106C3×C22⋊D5—41no—
107C3×C22⋊D5—41no—
108C2×C3×Dic5—41no—
109C2×C3×Dic5D811yescharacteristic
110C3×D20—21no—
111C3×D20—41no—
112C3×C4×D5—41no—
113C3×C4×D5—41no—
114C3×C4×D5—41no—
115C3×C4×D5C22⋊C411yescharacteristic
116C3×C4×D5C22⋊C411yescharacteristic
117C3×C4×D5SD1611yescharacteristic
118C3×C4×D5SD1611yescharacteristic
119C3×Dic10—21no—
120C3×Dic10—41no—
121D5×Dic3—82no—
122C3×C5×C8C22×C411yescharacteristic
123C3×C5×C8C2×D411yescharacteristic
124C3×#168C22⋊C411yescharacteristic
125C3×#168C22⋊C411yescharacteristic
126C2×C3×#41—101no—
127C3×#135—51no—
128C3×#135—51no—
129C3×#135—51no—
130C3×#135—101no—
131C3×#135—101no—
132C3×#135C2×D511yescharacteristic
133C2×C3×Q16—51no—
134C2×C3×SD16—101no—
135C2×C3×D8—51no—
136C22×C3×C8—51no—
137C2×C4⋊Dic3—101no—
138#817—51no—
139#817—101no—
140#817C2×D511yescharacteristic, complemented
141#812—51no—
142#812—101no—
143#812C2×D511yescharacteristic, complemented
144C2×C3⋊C16—101no—
145C5×#41—21no—
146#713—21no—
147Q8×D5—21no—
148#711—21no—
149#711—41no—
150D4×D5—21no—
151D4×D5—41no—
152#709—21no—
153#709—41no—
154C2×C4×D5—41no—
155C2×C4×D5—121no—
156C2×C4×D5#6711yescharacteristic
157C5×Q16C2×Dic311yescharacteristic, complemented
158C5×SD16—21no—
159C5×D8C2×Dic311yescharacteristic, complemented
160C2×C5×C8C22×D311yescharacteristic
161C5×C4⋊C4—61no—
162#689—21no—
163#688—21no—
164#687—21no—
165#686—21no—
166C4⋊Dic5—61no—
167#683—121no—
168C2×#168#6711yescharacteristic
169Dic20C2×Dic311yescharacteristic, complemented
170D40C2×Dic311yescharacteristic, complemented
171#677—21no—
172C8×D5C2×Dic311yescharacteristic
173C8×D5C2×Dic311yescharacteristic
174C8×D5#6711yescharacteristic
175C8×D5#6711yescharacteristic
176C5×C16—61no—
177#672—61no—
178C2×#135—51no—
179C2×M32—151no—
180C2×#106—151no—
181#360—31no—
182#360—151no—
183#360—151no—
184#360—151no—
185C22×C3×C5—41no—
186C22×C3×C5C2×D811yescharacteristic
187C2×C3×D5—22no—
188C2×C3×D5—41no—
189C2×C3×D5—82no—
190C2×C3×D5#10211yescharacteristic
191C2×C3×D5#10211yescharacteristic
192C3×C4×C5—41no—
193C3×C4×C5C2×C22⋊C411yescharacteristic
194C3×C4×C5C2×SD1611yescharacteristic
195Dic15—81no—
196C3×Dic5—41no—
197C3×Dic5#10211yescharacteristic
198C3×Dic5#10211yescharacteristic
199C5×Dic3—81no—
200C3×#41—21no—
201C3×#41—101no—
202C3×#41—101no—
203C3×#41—101no—
204C3×#41—201no—
205C3×#41—201no—
206C2×C3×Q8—101no—
207C2×C3×D4—101no—
208C2×C3×D4—201no—
209C22×C3×C4—51no—
210C22×C3×C4—201no—
211C22×Dic3—201no—
212C3×Q16—51no—
213C3×Q16—101no—
214C3×Q16C4×D511yescharacteristic, complemented
215C3×SD16—21no—
216C3×SD16—101no—
217C3×SD16—101no—
218C3×SD16—101no—
219C3×D8—51no—
220C3×D8—101no—
221C3×D8C4×D511yescharacteristic, complemented
222C2×C3×C8—51no—
223C2×C3×C8—51no—
224C2×C3×C8—51no—
225C2×C3×C8—51no—
226C2×C3×C8—51no—
227C2×C3×C8C22×D511yescharacteristic
228C4⋊Dic3—21no—
229C4⋊Dic3—101no—
230C4⋊Dic3—201no—
231C3⋊C16—21no—
232C3⋊C16—101no—
233C22×D5—41no—
234C22×D5#21311yescharacteristic
235C5×Q8—21no—
236C5×D4—21no—
237C5×D4—41no—
238C2×C4×C5—41no—
239C2×C4×C5—121no—
240C2×C4×C5C2×#6711yescharacteristic
241C22⋊D5—41no—
242C22⋊D5—41no—
243C22⋊D5—41no—
244C2×Dic5—41no—
245C2×Dic5—121no—
246C2×Dic5#21311yescharacteristic
247D20—21no—
248D20—41no—
249C4×D5—41no—
250C4×D5—41no—
251C4×D5—41no—
252C4×D5—242no—
253C4×D5#21411yescharacteristic
254C4×D5#21411yescharacteristic
255C4×D5#21711yescharacteristic
256C4×D5#21711yescharacteristic
257Dic10—21no—
258Dic10—41no—
259C5×C8C22×Dic311yescharacteristic
260C5×C8C2×#6711yescharacteristic
261#168#21711yescharacteristic
262#168#21711yescharacteristic
263C2×#41—101no—
264#135—51no—
265#135—51no—
266#135—51no—
267#135—101no—
268#135—101no—
269#135D3×D511yescharacteristic
270C2×Q16—51no—
271C2×SD16—101no—
272C2×D8—51no—
273C22×C8—51no—
274C2×C4⋊C4—301no—
275M32—31no—
276M32—151no—
277M32—301no—
278C2×C16—301no—
279#106—31no—
280#106—151no—
281#106—301no—
282C2×C3×C5—21no—
283C2×C3×C5—81no—
284C2×C3×C5C2×#10211yescharacteristic
285C3×D5—21no—
286C3×D5—81no—
287C3×D5#36012yescomplemented
288C23×C3—51no—
289C23×C3—201no—
290C3×Q8—21no—
291C3×Q8—101no—
292C3×Q8—201no—
293C3×D4—21no—
294C3×D4—41no—
295C3×D4—101no—
296C3×D4—201no—
297C3×D4—201no—
298C3×D4—201no—
299C3×D4—201no—
300C2×C3×C4—41no—
301C2×C3×C4—51no—
302C2×C3×C4—51no—
303C2×C3×C4—51no—
304C2×C3×C4—51no—
305C2×C3×C4—51no—
306C2×C3×C4—201no—
307C2×C3×C4—201no—
308C2×C3×C4—201no—
309C2×C3×C4—201no—
310C2×C3×C4D4×D511yescharacteristic
311C2×Dic3—41no—
312C2×Dic3—201no—
313C2×Dic3—402no—
314C3×C8—51no—
315C3×C8—51no—
316C3×C8C2×C4×D511yescharacteristic
317C3×C8D4×D511yescharacteristic
318C22×C5—41no—
319C22×C5C2×#21311yescharacteristic
320C2×D5—22no—
321C2×D5—41no—
322C2×D5—82no—
323C2×D5#83211yescharacteristic
324C2×D5#83211yescharacteristic
325C4×C5—41no—
326C4×C5—241no—
327C4×C5C2×#21411yescharacteristic
328C4×C5C2×#21711yescharacteristic
329Dic5—41no—
330Dic5—241no—
331Dic5#83211yescharacteristic
332Dic5#83211yescharacteristic
333#41—21no—
334#41—101no—
335#41—101no—
336#41—101no—
337#41—201no—
338#41—201no—
339C2×Q8—101no—
340C2×D4—101no—
341C2×D4—201no—
342C22×C4—51no—
343C22×C4—201no—
344C22×C4—601no—
345Q16—51no—
346Q16—101no—
347Q16D5×Dic311yescharacteristic, complemented
348SD16—21no—
349SD16—101no—
350SD16—101no—
351SD16—101no—
352D8—51no—
353D8—101no—
354D8D5×Dic311yescharacteristic, complemented
355C2×C8—51no—
356C2×C8—51no—
357C2×C8—51no—
358C2×C8—51no—
359C2×C8—51no—
360C2×C8C2×D3×D511yescharacteristic
361C4⋊C4—61no—
362C4⋊C4—301no—
363C4⋊C4—601no—
364C16—61no—
365C16—301no—
366C3×C5C2×#36011yescharacteristic, complemented, Hall
367C22×C3—41no—
368C22×C3—51no—
369C22×C3—51no—
370C22×C3—102no—
371C22×C3—201no—
372C22×C3—402no—
373C22×C3D5×D811yescharacteristic
374C3×C4—41no—
375C3×C4—51no—
376C3×C4—51no—
377C3×C4—201no—
378C3×C4D5×C22⋊C411yescharacteristic
379C3×C4D5×SD1611yescharacteristic
380Dic3—81no—
381Dic3—401no—
382C2×C5—21no—
383C2×C5—81no—
384C2×C5C2×#83211yescharacteristic
385D5—21no—
386D5—81no—
387D5#456612yesdirect product factor
388C23—51no—
389C23—201no—
390Q8—21no—
391Q8—101no—
392Q8—201no—
393D4—21no—
394D4—41no—
395D4—101no—
396D4—201no—
397D4—201no—
398D4—201no—
399D4—201no—
400C2×C4—41no—
401C2×C4—51no—
402C2×C4—51no—
403C2×C4—51no—
404C2×C4—51no—
405C2×C4—51no—
406C2×C4—121no—
407C2×C4—201no—
408C2×C4—201no—
409C2×C4—201no—
410C2×C4—201no—
411C2×C4—601no—
412C2×C4—1202no—
413C2×C4D5×#6711yescharacteristic
414C8—51no—
415C8—51no—
416C8C2×D5×Dic311yescharacteristic
417C8D5×#6711yescharacteristic
418C2×C3—21no—
419C2×C3—52no—
420C2×C3—81no—
421C2×C3—101no—
422C2×C3—401no—
423C2×C3D5×#10211yescharacteristic
424C5C2×#456611yescharacteristic, complemented, Sylow
425C22—41no—
426C22—51no—
427C22—51no—
428C22—102no—
429C22—201no—
430C22—402no—
431C22D5×#21311yescharacteristic
432C4—41no—
433C4—51no—
434C4—51no—
435C4—201no—
436C4—241no—
437C4—1201no—
438C4D5×#21411yescharacteristic
439C4D5×#21711yescharacteristic
440C3D5×#36011yescharacteristic, complemented, Sylow
441C2—21no—
442C2—52no—
443C2—81no—
444C2—101no—
445C2—401no—
446C2D5×#83211yescharacteristic
subgroupG/H
centerC2D5×#832
commutatorC3×C5×C8C22×C4
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#135C22
socleC2×C3×C5C2×#102
prime radicalC3×D5×#135C2
cosocleC2×C3×C5×C8C23
hypercenter#135D3×D5
hypocenterC3×C5C2×#360
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
2. D5×#817C2semidirect
3. D5×#812C2semidirect
4. #11746387C2semidirect
5. C5×#4566C2semidirect
6. #11745910C2semidirect
7. #11745909C2semidirect
12. C3×#4065C4semidirect
13. C3×D5×Q16C4semidirect
16. C3×#4058C4semidirect
17. C3×D5×D8C4semidirect
21. #91101C22semidirect
22. #91096C22semidirect
23. C5×#817C22semidirect
24. C5×#812C22semidirect
48. C3×C5×Q16C2×C4semidirect
50. C3×C5×D8C2×C4semidirect
59. C3×Dic20C2×C4semidirect
60. C3×D40C2×C4semidirect
75. #4566D5direct (N × H)
79. #4065Dic3semidirect
80. D5×Q16Dic3semidirect
83. #4058Dic3semidirect
84. D5×D8Dic3semidirect
140. #817C2×D5semidirect
143. #812C2×D5semidirect
157. C5×Q16C2×Dic3semidirect
159. C5×D8C2×Dic3semidirect
169. Dic20C2×Dic3semidirect
170. D40C2×Dic3semidirect
214. C3×Q16C4×D5semidirect
221. C3×D8C4×D5semidirect
287. C3×D5#360semidirect
347. Q16D5×Dic3semidirect
354. D8D5×Dic3semidirect
366. C3×C5C2×#360semidirect
387. D5#4566direct (N × H)
424. C5C2×#4566semidirect
440. C3D5×#360semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1352
D5×#8172
D5×#8122
#117463872
C5×#45662
#117459102
#117459092
D5×#3603
C2×#45665