Finite Group Databasebeta

← C5×#71885 #14288185

Subgroups — C5×#71885 #14288185

Order 1920.

520 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#538C211yesmaximal, characteristic
2C5×#5050C211yesmaximal, characteristic, complemented
3C5×#5040C211yesmaximal, characteristic, complemented
4C5×#4947C211yesmaximal, characteristic, complemented
5C5×#4538C211yesmaximal, characteristic, complemented
6C5×#4537C211yesmaximal, characteristic, complemented
7C5×#4525C211yesmaximal, characteristic, complemented
8C5×#1606—31nomaximal, Hall
9C22×C5×Dic6C2211yescharacteristic
10C3×C5×#126—21no—
11C3×C5×#124—21no—
12C3×C5×#123—21no—
13C3×C5×C22⋊Q8C2211yescharacteristic
14C3×C5×#121—21no—
15C3×C5×#121C2211yescharacteristic
16C3×C5×#120—21no—
17C3×C4×C5×D4—21no—
18C2×C3×C5×C22⋊C4C2211yescharacteristic
19C2×C5×#217—21no—
20C2×C5×#216—21no—
21C2×C5×#214—21no—
22C5×C3⋊#95—21no—
23C5×C3⋊#95C2211yescharacteristic
24C5×#830C2211yescharacteristic
25C5×#830C2211yescharacteristic
26C5×#810—21no—
27C5×#810—21no—
28#71885C511yesmaximal, characteristic, direct product factor, Hall
29C5×#538D311yescharacteristic
30C5×#451—31no—
31C5×#448—31no—
32C5×#393—31no—
33C5×#328—31no—
34C5×#327—31no—
35C5×#323—31no—
36C24×C3×C5D411yescharacteristic
37C2×C3×C5×Q8D411yescharacteristic
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4D411yescharacteristic
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5D411yescharacteristic
44C22×C3×C4×C5C2311yescharacteristic
45C22×C5×Dic3—21no—
46C22×C5×Dic3—21no—
47C2×C5×Dic6—21no—
48C2×C5×Dic6—21no—
49C2×C5×Dic6—42no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4D411yescharacteristic
53C3×C5×C4⋊C4D411yescharacteristic
54C3×C5×C22⋊C4—21no—
55C3×C5×C22⋊C4—21no—
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4—21no—
58C3×C5×C22⋊C4—21no—
59C3×C5×C22⋊C4—21no—
60C3×C5×C22⋊C4—21no—
61C3×C42×C5—21no—
62C5×#217—42no—
63C5×#216—42no—
64C5×#214—42no—
65C2×C5×C3⋊C8—21no—
66C2×C5×C3⋊C8—21no—
67C3×#538C2×C511yescharacteristic
68#5050C2×C511yescharacteristic, complemented
69#5040C2×C511yescharacteristic, complemented
70#4947C2×C511yescharacteristic, complemented
71#4538C2×C511yescharacteristic, complemented
72#4537C2×C511yescharacteristic, complemented
73#4525C2×C511yescharacteristic, complemented
74C22×C5×Q8—31no—
75C2×C5×Q16—61no—
76C2×C5×SD16—61no—
77C5×#126—21no—
78C5×#124—21no—
79C5×#123—21no—
80C5×C22⋊Q8C2×D311yescharacteristic
81C5×#121—21no—
82C5×#121C2×D311yescharacteristic
83C5×#120—21no—
84C4×C5×D4—21no—
85C2×C5×C22⋊C4—61no—
86C2×C5×C22⋊C4C2×D311yescharacteristic
87C5×#103—61no—
88C5×#103—61no—
89C5×C22⋊C8—31no—
90C5×C22⋊C8—31no—
91C5×#95—31no—
92C5×#95—61no—
93#1606—31noSylow
94C23×C3×C5—21no—
95C23×C3×C5—21no—
96C23×C3×C5—21no—
97C23×C3×C5—21no—
98C23×C3×C5—41no—
99C23×C3×C5—41no—
100C23×C3×C5C2×D411yescharacteristic
101C3×C5×Q8—41no—
102C3×C5×D4—41no—
103C3×C5×D4—41no—
104C3×C5×D4—41no—
105C3×C5×D4—81no—
106C3×C5×D4—81no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5—21no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—81no—
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C5×Dic3—22no—
117C2×C5×Dic3—41no—
118C2×C5×Dic3—41no—
119C2×C5×Dic3—41no—
120C2×C5×Dic3—41no—
121C2×C5×Dic3—41no—
122C5×Dic6—22no—
123C5×Dic6—22no—
124C5×Dic6—41no—
125C5×Dic6—41no—
126C5×C3⋊C8—41no—
127C5×C3⋊C8—41no—
128C22×Dic6C22×C511yescharacteristic
129C3×#126—21no—
130C3×#124—21no—
131C3×#123—21no—
132C3×C22⋊Q8C22×C511yescharacteristic
133C3×#121—21no—
134C3×#121C22×C511yescharacteristic
135C3×#120—21no—
136C3×C4×D4—21no—
137C2×C3×C22⋊C4C22×C511yescharacteristic
138C2×#217—21no—
139C2×#216—21no—
140C2×#214—21no—
141C3⋊#95—21no—
142C3⋊#95C22×C511yescharacteristic
143#830C22×C511yescharacteristic
144#830C22×C511yescharacteristic
145#810—21no—
146#810—21no—
147C24×C5#6711yescharacteristic
148C2×C5×Q8—61no—
149C2×C5×Q8—61no—
150C2×C5×Q8—122no—
151C2×C5×Q8#6711yescharacteristic
152C2×C5×D4—21no—
153C2×C5×D4—21no—
154C2×C5×D4—21no—
155C2×C5×D4#6711yescharacteristic
156C22×C4×C5—21no—
157C22×C4×C5—61no—
158C22×C4×C5—61no—
159C22×C4×C5#6711yescharacteristic
160C22×C4×C5C22×D311yescharacteristic
161C5×Q16—122no—
162C5×SD16—122no—
163C2×C5×C8—61no—
164C2×C5×C8—61no—
165C5×C4⋊C4—21no—
166C5×C4⋊C4—21no—
167C5×C4⋊C4#6711yescharacteristic
168C5×C4⋊C4#6711yescharacteristic
169C5×C22⋊C4—21no—
170C5×C22⋊C4—21no—
171C5×C22⋊C4—21no—
172C5×C22⋊C4—21no—
173C5×C22⋊C4—21no—
174C5×C22⋊C4—21no—
175C5×C22⋊C4—21no—
176C5×C22⋊C4—122no—
177C42×C5—21no—
178#538C5×D311yescharacteristic
179#451—31no—
180#448—31no—
181#393—31no—
182#328—31no—
183#327—31no—
184#323—31no—
185C22×C3×C5—21no—
186C22×C3×C5—21no—
187C22×C3×C5—42no—
188C22×C3×C5—41no—
189C22×C3×C5—41no—
190C22×C3×C5—41no—
191C22×C3×C5—41no—
192C22×C3×C5—41no—
193C22×C3×C5—41no—
194C22×C3×C5—81no—
195C22×C3×C5#12011yescharacteristic
196C22×C3×C5#13511yescharacteristic
197C22×C3×C5#13711yescharacteristic
198C3×C4×C5—21no—
199C3×C4×C5—21no—
200C3×C4×C5—41no—
201C3×C4×C5—41no—
202C3×C4×C5—41no—
203C3×C4×C5—41no—
204C5×Dic3—42no—
205C5×Dic3—81no—
206C24×C3C5×D411yescharacteristic
207C2×C3×Q8C5×D411yescharacteristic
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4C5×D411yescharacteristic
212C22×C3×C4—21no—
213C22×C3×C4C5×D411yescharacteristic
214C22×C3×C4C23×C511yescharacteristic
215C22×Dic3—21no—
216C22×Dic3—21no—
217C2×Dic6—21no—
218C2×Dic6—21no—
219C2×Dic6—42no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4C5×D411yescharacteristic
223C3×C4⋊C4C5×D411yescharacteristic
224C3×C22⋊C4—21no—
225C3×C22⋊C4—21no—
226C3×C22⋊C4—21no—
227C3×C22⋊C4—21no—
228C3×C22⋊C4—21no—
229C3×C22⋊C4—21no—
230C3×C22⋊C4—21no—
231C3×C42—21no—
232#217—42no—
233#216—42no—
234#214—42no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—21no—
237C23×C5—21no—
238C23×C5—21no—
239C23×C5—21no—
240C23×C5—21no—
241C23×C5—41no—
242C23×C5—41no—
243C23×C5C2×#6711yescharacteristic
244C5×Q8—41no—
245C5×Q8—62no—
246C5×Q8—62no—
247C5×Q8—121no—
248C5×Q8—121no—
249C5×D4—41no—
250C5×D4—41no—
251C5×D4—41no—
252C5×D4—81no—
253C5×D4—81no—
254C2×C4×C5—21no—
255C2×C4×C5—21no—
256C2×C4×C5—21no—
257C2×C4×C5—21no—
258C2×C4×C5—41no—
259C2×C4×C5—41no—
260C2×C4×C5—62no—
261C2×C4×C5—81no—
262C2×C4×C5—121no—
263C2×C4×C5—121no—
264C2×C4×C5—121no—
265C2×C4×C5—121no—
266C2×C4×C5—121no—
267C2×C4×C5C2×#6711yescharacteristic
268C2×C4×C5C2×#6711yescharacteristic
269C5×C8—121no—
270C5×C8—121no—
271C22×Q8—31no—
272C2×Q16—61no—
273C2×SD16—61no—
274#126—21no—
275#124—21no—
276#123—21no—
277C22⋊Q8C2×C5×D311yescharacteristic
278#121—21no—
279#121C2×C5×D311yescharacteristic
280#120—21no—
281C4×D4—21no—
282C2×C22⋊C4—61no—
283C2×C22⋊C4C2×C5×D311yescharacteristic
284#103—61no—
285#103—61no—
286C22⋊C8—31no—
287C22⋊C8—31no—
288#95—31no—
289#95—61no—
290C2×C3×C5—21no—
291C2×C3×C5—21no—
292C2×C3×C5—81no—
293C2×C3×C5—81no—
294C2×C3×C5#45211yescharacteristic
295C2×C3×C5#45511yescharacteristic
296C2×C3×C5B(4,𝔽2)11yescharacteristic
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—41no—
302C23×C3—41no—
303C23×C3C2×C5×D411yescharacteristic
304C3×Q8—41no—
305C3×D4—41no—
306C3×D4—41no—
307C3×D4—41no—
308C3×D4—81no—
309C3×D4—81no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—81no—
317C2×C3×C4C2×C5×D411yescharacteristic
318C2×C3×C4C2×C5×D411yescharacteristic
319C2×Dic3—22no—
320C2×Dic3—41no—
321C2×Dic3—41no—
322C2×Dic3—41no—
323C2×Dic3—41no—
324C2×Dic3—41no—
325Dic6—22no—
326Dic6—22no—
327Dic6—41no—
328Dic6—41no—
329C3⋊C8—41no—
330C3⋊C8—41no—
331C22×C5—21no—
332C22×C5—21no—
333C22×C5—42no—
334C22×C5—41no—
335C22×C5—41no—
336C22×C5—41no—
337C22×C5—41no—
338C22×C5—41no—
339C22×C5—41no—
340C22×C5—81no—
341C22×C5#95011yescharacteristic
342C22×C5#95111yescharacteristic
343C22×C5#95311yescharacteristic
344C4×C5—21no—
345C4×C5—21no—
346C4×C5—41no—
347C4×C5—41no—
348C4×C5—41no—
349C4×C5—41no—
350C4×C5—122no—
351C4×C5—241no—
352C24C5×#6711yescharacteristic
353C2×Q8—61no—
354C2×Q8—61no—
355C2×Q8—122no—
356C2×Q8C5×#6711yescharacteristic
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4C5×#6711yescharacteristic
361C22×C4—21no—
362C22×C4—61no—
363C22×C4—61no—
364C22×C4C5×#6711yescharacteristic
365C22×C4C22×C5×D311yescharacteristic
366Q16—122no—
367SD16—122no—
368C2×C8—61no—
369C2×C8—61no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4C5×#6711yescharacteristic
373C4⋊C4C5×#6711yescharacteristic
374C22⋊C4—21no—
375C22⋊C4—21no—
376C22⋊C4—21no—
377C22⋊C4—21no—
378C22⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—21no—
381C22⋊C4—122no—
382C42—21no—
383C3×C5#160611yescharacteristic, complemented, Hall
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—42no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—81no—
394C22×C3C5×#12011yescharacteristic
395C22×C3C5×#13511yescharacteristic
396C22×C3C5×#13711yescharacteristic
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—41no—
400C3×C4—41no—
401C3×C4—41no—
402C3×C4—41no—
403Dic3—42no—
404Dic3—81no—
405C2×C5—21no—
406C2×C5—21no—
407C2×C5—81no—
408C2×C5—81no—
409C2×C5#523911yescharacteristic
410C2×C5#524211yescharacteristic
411C2×C5#524411yescharacteristic
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—41no—
417C23—41no—
418C23C2×C5×#6711yescharacteristic
419Q8—41no—
420Q8—62no—
421Q8—62no—
422Q8—121no—
423Q8—121no—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—81no—
428D4—81no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—62no—
436C2×C4—81no—
437C2×C4—121no—
438C2×C4—121no—
439C2×C4—121no—
440C2×C4—121no—
441C2×C4—121no—
442C2×C4C2×C5×#6711yescharacteristic
443C2×C4C2×C5×#6711yescharacteristic
444C8—121no—
445C8—121no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—81no—
449C2×C3—81no—
450C2×C3C5×#45211yescharacteristic
451C2×C3C5×#45511yescharacteristic
452C2×C3C5×B(4,𝔽2)11yescharacteristic
453C5#7188511yescharacteristic, direct product factor, Sylow
454C22—21no—
455C22—21no—
456C22—42no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—81no—
464C22C5×#95011yescharacteristic
465C22C5×#95111yescharacteristic
466C22C5×#95311yescharacteristic
467C4—21no—
468C4—21no—
469C4—41no—
470C4—41no—
471C4—41no—
472C4—41no—
473C4—122no—
474C4—241no—
475C3C5×#160611yescharacteristic, complemented, Sylow
476C2—21no—
477C2—21no—
478C2—81no—
479C2—81no—
480C2C5×#523911yescharacteristic
481C2C5×#524211yescharacteristic
482C2C5×#524411yescharacteristic
subgroupG/H
centerC22×C5#953
commutator, cosocleC22×C3×C4C23×C5
FrattiniC22×C4C22×C5×D3
Fitting, prime radicalC3×C5×#538C2
socleC22×C3×C5#120
hypercenterC5×#538D3
hypocenterC3C5×#1606
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#538

Complements

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

NH ≅ G/Ntype
2. C5×#5050C2semidirect
3. C5×#5040C2semidirect
4. C5×#4947C2semidirect
5. C5×#4538C2semidirect
6. C5×#4537C2semidirect
7. C5×#4525C2semidirect
28. #71885C5direct (N × H)
68. #5050C2×C5semidirect
69. #5040C2×C5semidirect
70. #4947C2×C5semidirect
71. #4538C2×C5semidirect
72. #4537C2×C5semidirect
73. #4525C2×C5semidirect
383. C3×C5#1606semidirect
453. C5#71885direct (N × H)
475. C3C5×#1606semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5382
C5×#50502
C5×#50402
C5×#49472
C5×#45382
C5×#45372
C5×#45252
C5×#16063
#718855