Finite Group Databasebeta

← C5×#68947 #14301157

Subgroups — C5×#68947 #14301157

Order 1920.

620 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5748C211yesmaximal, characteristic
2C5×#5745C211yesmaximal, characteristic, complemented
3C5×#5139C211yesmaximal, characteristic, complemented
4C5×#5113C211yesmaximal, characteristic, complemented
5C5×#5110C211yesmaximal, characteristic, complemented
6C3×C5×#341C211yesmaximal, characteristic, complemented
7C5×#4559C211yesmaximal, characteristic, complemented
8C5×#1881—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C3×C5×M16C2211yescharacteristic
13C22×C3×C5×C8C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C2×C5×#208C2211yescharacteristic
16C5×#909—21no—
17C5×#909C412yescomplemented
18C5×#908—21no—
19C5×#908C412yescomplemented
20C5×#907—22no—
21C5×D3×M16—22no—
22C5×#904—22no—
23C5×#901—22no—
24C5×#825—22no—
25C5×#821—21no—
26C5×(C2×D3)⋊C8—22no—
27C5×#816—21no—
28#68947C511yesmaximal, characteristic, direct product factor, Hall
29C5×#575—31no—
30C5×#568—31no—
31C5×#421—31no—
32C5×#416—31no—
33C5×#408—31no—
34C5×#344—31no—
35C5×#341D311yescharacteristic, complemented
36C22×C3×C4×C5C2311yescharacteristic
37C2×C5×#67—21no—
38C2×C5×#67—21no—
39C5×#235—21no—
40C5×#235—21no—
41C5×#235—21no—
42C5×#235—21no—
43C5×#235—21no—
44C5×#235—21no—
45C5×#235C2×C412yes—
46C5×#235D412yes—
47C2×C5×D12C2×C411yescharacteristic
48C2×C5×D12D411yescharacteristic
49C2×C4×C5×D3—21no—
50C2×C4×C5×D3—21no—
51C2×C5×Dic6C2×C411yescharacteristic
52C2×C5×Dic6D411yescharacteristic
53C3×C5×M16—21no—
54C3×C5×M16—21no—
55C3×C5×M16C2×C412yes—
56C3×C5×M16D412yes—
57C2×C3×C5×C8—21no—
58C2×C3×C5×C8—21no—
59C2×C3×C5×C8—21no—
60C2×C3×C5×C8—21no—
61C2×C3×C5×C8—21no—
62C5×#217—21no—
63C5×C4⋊Dic3—21no—
64C4×C5×Dic3—21no—
65C5×#208—21no—
66C5×#208—21no—
67C2×C5×C3⋊C8D412yes—
68C5×Dic12—22no—
69C5×D24—22no—
70C5×#204—22no—
71C5×#204—22no—
72C5×ΓL(1,𝔽25)—24no—
73C5×D3×C8—24no—
74#5748C2×C511yescharacteristic
75#5745C2×C511yescharacteristic, complemented
76#5139C2×C511yescharacteristic, complemented
77#5113C2×C511yescharacteristic, complemented
78#5110C2×C511yescharacteristic, complemented
79C3×#341C2×C511yescharacteristic, complemented
80#4559C2×C511yescharacteristic, complemented
81C2×C5×#41—31no—
82C2×C5×#41—31no—
83C5×#137—32no—
84C5×#137—61no—
85C5×AGL(1,ℤ/8)—32no—
86C5×AGL(1,ℤ/8)—61no—
87C5×#135—62no—
88C5×#131—62no—
89C5×#131—62no—
90C2×C5×M16—31no—
91C2×C5×M16—62no—
92C2×C5×M16C2×D311yescharacteristic
93C2×C5×M16C2×D311yescharacteristic
94C22×C5×C8C2×D311yescharacteristic
95C5×#117—31no—
96C5×#104—62no—
97C5×#103—61no—
98C5×#102—61no—
99C5×C22⋊C8—62no—
100#1881—31noSylow
101C23×C3×C5#4111yescharacteristic
102C22×C5×D3—21no—
103C22×C5×D3—21no—
104C2×C3×C4×C5C22×C411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C5×#67—22no—
111C5×#67—22no—
112C5×#67—41no—
113C5×#67—41no—
114C2×C5×Dic3—21no—
115C2×C5×Dic3—21no—
116C2×C5×Dic3—41no—
117C5×D12—21no—
118C5×D12—21no—
119C5×D12—21no—
120C5×D12C22⋊C412yes—
121C4×C5×D3—22no—
122C4×C5×D3—22no—
123C4×C5×D3—41no—
124C4×C5×D3—41no—
125C5×Dic6—21no—
126C5×Dic6—21no—
127C5×Dic6—21no—
128C5×Dic6C22⋊C412yes—
129C3×C5×C8—22no—
130C3×C5×C8—22no—
131C3×C5×C8—41no—
132C5×C3⋊C8—22no—
133C2×#235C22×C511yescharacteristic
134C2×#235C22×C511yescharacteristic
135C2×C3×M16C22×C511yescharacteristic
136C2×C3×M16C22×C511yescharacteristic
137C22×C3×C8C22×C511yescharacteristic
138#926C22×C511yescharacteristic
139C2×#208C22×C511yescharacteristic
140#909—21no—
141#909C4×C512yescomplemented
142#908—21no—
143#908C4×C512yescomplemented
144#907—22no—
145D3×M16—22no—
146#904—22no—
147#901—22no—
148#825—22no—
149#821—21no—
150(C2×D3)⋊C8—22no—
151#816—21no—
152C5×#41—32no—
153C5×#41—32no—
154C5×#41—61no—
155C5×#41—61no—
156C5×#41—61no—
157C5×#41—61no—
158C5×#41—61no—
159C5×#41—61no—
160C2×C5×Q8—31no—
161C2×C5×Q8—31no—
162C2×C5×D4—31no—
163C2×C5×D4—31no—
164C2×C5×D4—61no—
165C2×C5×D4—61no—
166C22×C4×C5—61no—
167C22×C4×C5—61no—
168C22×C4×C5C22×D311yescharacteristic
169C5×Q16—62no—
170C5×SD16—62no—
171C5×SD16—62no—
172C5×D8—62no—
173C5×M16—21no—
174C5×M16—21no—
175C5×M16—64no—
176C5×M16—61no—
177C5×M16—61no—
178C5×M16C4×D312yes—
179C5×M16D1212yes—
180C2×C5×C8—21no—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C2×C5×C8—32no—
186C2×C5×C8—64no—
187C5×C4⋊C4—61no—
188C5×C22⋊C4—61no—
189C42×C5—61no—
190#575—31no—
191#568—31no—
192#421—31no—
193#416—31no—
194#408—31no—
195#344—31no—
196#341C5×D311yescharacteristic, complemented
197C22×C3×C5—41no—
198C22×C3×C5C4×D411yescharacteristic
199C22×C3×C5#12111yescharacteristic
200C22×C3×C5#12311yescharacteristic
201C2×C5×D3—22no—
202C2×C5×D3—42no—
203C2×C5×D3—41no—
204C2×C5×D3—81no—
205C3×C4×C5C2×C22⋊C411yescharacteristic
206C3×C4×C5C4×D411yescharacteristic
207C3×C4×C5#12011yescharacteristic
208C3×C4×C5#12111yescharacteristic
209C5×Dic3—22no—
210C5×Dic3—41no—
211C5×Dic3—81no—
212C22×C3×C4C23×C511yescharacteristic
213C2×#67—21no—
214C2×#67—21no—
215#235—21no—
216#235—21no—
217#235—21no—
218#235—21no—
219#235—21no—
220#235—21no—
221#235C2×C4×C512yes—
222#235C5×D412yes—
223C2×D12C2×C4×C511yescharacteristic
224C2×D12C5×D411yescharacteristic
225C2×C4×D3—21no—
226C2×C4×D3—21no—
227C2×Dic6C2×C4×C511yescharacteristic
228C2×Dic6C5×D411yescharacteristic
229C3×M16—21no—
230C3×M16—21no—
231C3×M16C2×C4×C512yes—
232C3×M16C5×D412yes—
233C2×C3×C8—21no—
234C2×C3×C8—21no—
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—21no—
238#217—21no—
239C4⋊Dic3—21no—
240C4×Dic3—21no—
241#208—21no—
242#208—21no—
243C2×C3⋊C8C5×D412yes—
244Dic12—22no—
245D24—22no—
246#204—22no—
247#204—22no—
248ΓL(1,𝔽25)—24no—
249D3×C8—24no—
250C23×C5—61no—
251C23×C5—61no—
252C23×C5#23911yescharacteristic
253C5×Q8—32no—
254C5×Q8—61no—
255C5×Q8—61no—
256C5×Q8—61no—
257C5×D4—32no—
258C5×D4—62no—
259C5×D4—62no—
260C5×D4—61no—
261C5×D4—61no—
262C5×D4—61no—
263C5×D4—121no—
264C5×D4—121no—
265C2×C4×C5—61no—
266C2×C4×C5—62no—
267C2×C4×C5—62no—
268C2×C4×C5—61no—
269C2×C4×C5—121no—
270C2×C4×C5—121no—
271C2×C4×C5—121no—
272C2×C4×C5C2×C4×D311yescharacteristic
273C2×C4×C5C2×D1211yescharacteristic
274C2×C4×C5#23511yescharacteristic
275C2×C4×C5D3×D411yescharacteristic
276C2×C4×C5D3×D411yescharacteristic
277C2×C4×C5D3×D411yescharacteristic
278C5×C8—22no—
279C5×C8—22no—
280C5×C8—41no—
281C5×C8—62no—
282C2×#41—31no—
283C2×#41—31no—
284#137—32no—
285#137—61no—
286AGL(1,ℤ/8)—32no—
287AGL(1,ℤ/8)—61no—
288#135—62no—
289#131—62no—
290#131—62no—
291C2×M16—31no—
292C2×M16—62no—
293C2×M16C2×C5×D311yescharacteristic
294C2×M16C2×C5×D311yescharacteristic
295C22×C8C2×C5×D311yescharacteristic
296#117—31no—
297#104—62no—
298#103—61no—
299#102—61no—
300C22⋊C8—62no—
301C2×C3×C5—21no—
302C2×C3×C5—21no—
303C2×C3×C5—21no—
304C2×C3×C5#38611yescharacteristic
305C5×D3—42no—
306C5×D3—81no—
307C23×C3C5×#4111yescharacteristic
308C22×D3—21no—
309C22×D3—21no—
310C2×C3×C4C22×C4×C511yescharacteristic
311C2×C3×C4C2×C5×D411yescharacteristic
312C2×C3×C4C2×C5×D411yescharacteristic
313C2×C3×C4C2×C5×D411yescharacteristic
314C2×C3×C4C2×C5×D411yescharacteristic
315C2×C3×C4C5×#4111yescharacteristic
316#67—22no—
317#67—22no—
318#67—41no—
319#67—41no—
320C2×Dic3—21no—
321C2×Dic3—21no—
322C2×Dic3—41no—
323D12—21no—
324D12—21no—
325D12—21no—
326D12C5×C22⋊C412yes—
327C4×D3—22no—
328C4×D3—22no—
329C4×D3—41no—
330C4×D3—41no—
331Dic6—21no—
332Dic6—21no—
333Dic6—21no—
334Dic6C5×C22⋊C412yes—
335C3×C8—22no—
336C3×C8—22no—
337C3×C8—41no—
338C3⋊C8—22no—
339C22×C5—41no—
340C22×C5—62no—
341C22×C5—122no—
342C22×C5—121no—
343C22×C5—241no—
344C22×C5#89311yescharacteristic
345C22×C5#89411yescharacteristic
346C22×C5#89511yescharacteristic
347C4×C5—62no—
348C4×C5—121no—
349C4×C5—241no—
350C4×C5C4×D1211yescharacteristic
351C4×C5D3×C22⋊C411yescharacteristic
352C4×C5#88211yescharacteristic
353C4×C5#88411yescharacteristic
354#41—32no—
355#41—32no—
356#41—61no—
357#41—61no—
358#41—61no—
359#41—61no—
360#41—61no—
361#41—61no—
362C2×Q8—31no—
363C2×Q8—31no—
364C2×D4—31no—
365C2×D4—31no—
366C2×D4—61no—
367C2×D4—61no—
368C22×C4—61no—
369C22×C4—61no—
370C22×C4C22×C5×D311yescharacteristic
371Q16—62no—
372SD16—62no—
373SD16—62no—
374D8—62no—
375M16—21no—
376M16—21no—
377M16—64no—
378M16—61no—
379M16—61no—
380M16C4×C5×D312yes—
381M16C5×D1212yes—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—32no—
388C2×C8—64no—
389C4⋊C4—61no—
390C22⋊C4—61no—
391C42—61no—
392C3×C5#188111yescharacteristic, complemented, Hall
393C22×C3—41no—
394C22×C3C4×C5×D411yescharacteristic
395C22×C3C5×#12111yescharacteristic
396C22×C3C5×#12311yescharacteristic
397C2×D3—22no—
398C2×D3—42no—
399C2×D3—41no—
400C2×D3—81no—
401C3×C4C2×C5×C22⋊C411yescharacteristic
402C3×C4C4×C5×D411yescharacteristic
403C3×C4C5×#12011yescharacteristic
404C3×C4C5×#12111yescharacteristic
405Dic3—22no—
406Dic3—41no—
407Dic3—81no—
408C2×C5—21no—
409C2×C5—21no—
410C2×C5—21no—
411C2×C5—122no—
412C2×C5—241no—
413C2×C5#466511yescharacteristic
414C23—61no—
415C23—61no—
416C23C5×#23911yescharacteristic
417Q8—32no—
418Q8—61no—
419Q8—61no—
420Q8—61no—
421D4—32no—
422D4—62no—
423D4—62no—
424D4—61no—
425D4—61no—
426D4—61no—
427D4—121no—
428D4—121no—
429C2×C4—61no—
430C2×C4—62no—
431C2×C4—62no—
432C2×C4—61no—
433C2×C4—121no—
434C2×C4—121no—
435C2×C4—121no—
436C2×C4C2×C4×C5×D311yescharacteristic
437C2×C4C2×C5×D1211yescharacteristic
438C2×C4C5×#23511yescharacteristic
439C2×C4C5×D3×D411yescharacteristic
440C2×C4C5×D3×D411yescharacteristic
441C2×C4C5×D3×D411yescharacteristic
442C8—22no—
443C8—22no—
444C8—41no—
445C8—62no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3C5×#38611yescharacteristic
450D3—42no—
451D3—81no—
452C5#6894711yescharacteristic, direct product factor, Sylow
453C22—41no—
454C22—62no—
455C22—122no—
456C22—121no—
457C22—241no—
458C22C5×#89311yescharacteristic
459C22C5×#89411yescharacteristic
460C22C5×#89511yescharacteristic
461C4—62no—
462C4—121no—
463C4—241no—
464C4C4×C5×D1211yescharacteristic
465C4C5×D3×C22⋊C411yescharacteristic
466C4C5×#88211yescharacteristic
467C4C5×#88411yescharacteristic
468C3C5×#188111yescharacteristic, complemented, Sylow
469C2—21no—
470C2—21no—
471C2—21no—
472C2—122no—
473C2—241no—
474C2C5×#466511yescharacteristic
subgroupG/H
centerC4×C5#882
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#341C2
socleC2×C3×C5#386
prime radicalC5×#5748C2
cosocleC22×C3×C4C23×C5
hypercenterC5×#341D3
hypocenterC3C5×#1881
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C22×C4×C5 ◁ C5×#341

Complements

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

NH ≅ G/Ntype
2. C5×#5745C2semidirect
3. C5×#5139C2semidirect
4. C5×#5113C2semidirect
5. C5×#5110C2semidirect
6. C3×C5×#341C2semidirect
7. C5×#4559C2semidirect
17. C5×#909C4semidirect
19. C5×#908C4semidirect
28. #68947C5direct (N × H)
35. C5×#341D3semidirect
75. #5745C2×C5semidirect
76. #5139C2×C5semidirect
77. #5113C2×C5semidirect
78. #5110C2×C5semidirect
79. C3×#341C2×C5semidirect
80. #4559C2×C5semidirect
141. #909C4×C5semidirect
143. #908C4×C5semidirect
196. #341C5×D3semidirect
392. C3×C5#1881semidirect
452. C5#68947direct (N × H)
468. C3C5×#1881semidirect

Maximal subgroups

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

subgroupindex
C5×#57482
C5×#57452
C5×#51392
C5×#51132
C5×#51102
C3×C5×#3412
C5×#45592
C5×#18813
#689475