Finite Group Databasebeta

← C5×#70980 #14287996

Subgroups — C5×#70980 #14287996

Order 1920.

512 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5634C211yesmaximal, characteristic
2C3×C5×#451C211yesmaximal, characteristic, complemented
3C5×#5231C211yesmaximal, characteristic
4C5×#5228C211yesmaximal, characteristic, complemented
5C5×#4538C211yesmaximal, characteristic, complemented
6C5×#4468C211yesmaximal, characteristic
7C5×#4467C211yesmaximal, characteristic, complemented
8C5×#1602—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C2×C3×C5×Q16—21no—
11C3×C5×C22⋊Q8C2211yescharacteristic
12C5×#946—21no—
13C2×C5×#216—21no—
14C2×C5×(C2×D3)⋊C4—21no—
15C2×C5×(C2×D3)⋊C4C2211yescharacteristic
16C5×#924C2211yescharacteristic
17C5×#897—21no—
18C5×#896—21no—
19C5×#896—21no—
20C5×D3×C22⋊C4—21no—
21C5×#878—21no—
22C3×C5×#103—21no—
23C3×C5×C22⋊C8C2211yescharacteristic
24C5×#835—21no—
25C5×C3⋊#95—21no—
26C5×C3⋊#95C2211yescharacteristic
27C5×#830C2211yescharacteristic
28#70980C511yesmaximal, characteristic, direct product factor, Hall
29C5×#543—31no—
30C5×#451—31no—
31C5×#451D311yescharacteristic, complemented
32C5×#393—31no—
33C5×#328—31no—
34C5×#328—31no—
35C5×#323—31no—
36C23×C5×D3D411yescharacteristic
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8—42no—
40C2×C3×C5×Q8D411yescharacteristic
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5C2311yescharacteristic
43C22×C5×Dic3—21no—
44C22×C5×Dic3D411yescharacteristic
45C2×C4×C5×D3—21no—
46C2×C4×C5×D3—21no—
47C2×C5×Dic6—21no—
48C2×C5×Dic6D411yescharacteristic
49C3×C5×Q16—42no—
50C2×C3×C5×C8—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4D411yescharacteristic
53C3×C5×C22⋊C4—21no—
54C5×#217—21no—
55C5×#216—42no—
56C5×(C2×D3)⋊C4—21no—
57C5×(C2×D3)⋊C4—21no—
58C5×(C2×D3)⋊C4—21no—
59C5×(C2×D3)⋊C4—21no—
60C5×(C2×D3)⋊C4—42no—
61C5×C4⋊Dic3—21no—
62C5×C4⋊Dic3D411yescharacteristic
63C5×Dic3⋊C4—21no—
64C5×Dic3⋊C4—21no—
65C5×Dic3⋊C4—21no—
66C2×C5×C3⋊C8—21no—
67#5634C2×C511yescharacteristic
68C3×#451C2×C511yescharacteristic, complemented
69#5231C2×C511yescharacteristic
70#5228C2×C511yescharacteristic, complemented
71#4538C2×C511yescharacteristic, complemented
72#4468C2×C511yescharacteristic
73#4467C2×C511yescharacteristic, complemented
74C22×C5×Q8C2×D311yescharacteristic
75C2×C5×Q16—21no—
76C2×C5×Q16—61no—
77C5×C22⋊Q8—31no—
78C5×C22⋊Q8—61no—
79C5×C22⋊Q8—61no—
80C5×C22⋊Q8—61no—
81C5×C22⋊Q8—61no—
82C5×C22⋊Q8—61no—
83C5×C22⋊Q8C2×D311yescharacteristic
84C2×C5×C22⋊C4—31no—
85C2×C5×C22⋊C4—61no—
86C2×C5×C22⋊C4—61no—
87C5×#103—21no—
88C5×#103—61no—
89C5×C22⋊C8—31no—
90C5×C22⋊C8C2×D311yescharacteristic
91C5×#95—31no—
92C5×#95—61no—
93#1602—31noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C5×D3—21no—
96C22×C5×D3—21no—
97C22×C5×D3—41no—
98C22×C5×D3—41no—
99C22×C5×D3Q1612yescomplemented
100C3×C5×Q8—22no—
101C3×C5×Q8—22no—
102C3×C5×Q8—41no—
103C3×C5×Q8—41no—
104C3×C5×Q8—41no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C5×Dic3—21no—
114C2×C5×Dic3—21no—
115C2×C5×Dic3—21no—
116C2×C5×Dic3—41no—
117C2×C5×Dic3—41no—
118C2×C5×Dic3—41no—
119C2×C5×Dic3—41no—
120C4×C5×D3—81no—
121C4×C5×D3—81no—
122C5×Dic6—41no—
123C5×Dic6—81no—
124C3×C5×C8—41no—
125C5×C3⋊C8—41no—
126C22×C3×Q8C22×C511yescharacteristic
127C2×C3×Q16—21no—
128C3×C22⋊Q8C22×C511yescharacteristic
129#946—21no—
130C2×#216—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4C22×C511yescharacteristic
133#924C22×C511yescharacteristic
134#897—21no—
135#896—21no—
136#896—21no—
137D3×C22⋊C4—21no—
138#878—21no—
139C3×#103—21no—
140C3×C22⋊C8C22×C511yescharacteristic
141#835—21no—
142C3⋊#95—21no—
143C3⋊#95C22×C511yescharacteristic
144#830C22×C511yescharacteristic
145C24×C5—31no—
146C2×C5×Q8—21no—
147C2×C5×Q8—21no—
148C2×C5×Q8—31no—
149C2×C5×Q8—42no—
150C2×C5×Q8—61no—
151C2×C5×Q8#6711yescharacteristic
152C22×C4×C5—21no—
153C22×C4×C5—31no—
154C22×C4×C5—61no—
155C22×C4×C5—61no—
156C22×C4×C5—61no—
157C22×C4×C5C22×D311yescharacteristic
158C5×Q16—42no—
159C5×Q16—122no—
160C2×C5×C8—21no—
161C2×C5×C8—61no—
162C5×C4⋊C4—21no—
163C5×C4⋊C4—31no—
164C5×C4⋊C4—61no—
165C5×C4⋊C4—61no—
166C5×C4⋊C4—61no—
167C5×C4⋊C4—61no—
168C5×C4⋊C4#6711yescharacteristic
169C5×C22⋊C4—21no—
170C5×C22⋊C4—61no—
171C5×C22⋊C4—61no—
172C5×C22⋊C4—61no—
173C5×C22⋊C4—61no—
174C5×C22⋊C4—61no—
175C5×C22⋊C4—122no—
176#543—31no—
177#451—31no—
178#451C5×D311yescharacteristic, complemented
179#393—31no—
180#328—31no—
181#328—31no—
182#323—31no—
183C22×C3×C5—21no—
184C22×C3×C5—21no—
185C22×C3×C5#12011yescharacteristic
186C22×C3×C5C2×Q1611yescharacteristic
187C22×C3×C5#13711yescharacteristic
188C2×C5×D3—22no—
189C2×C5×D3—41no—
190C2×C5×D3—41no—
191C2×C5×D3—42no—
192C2×C5×D3—81no—
193C3×C4×C5—21no—
194C3×C4×C5—21no—
195C3×C4×C5—41no—
196C3×C4×C5—41no—
197C3×C4×C5—42no—
198C5×Dic3—41no—
199C5×Dic3—41no—
200C5×Dic3—41no—
201C5×Dic3—81no—
202C23×D3C5×D411yescharacteristic
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—42no—
206C2×C3×Q8C5×D411yescharacteristic
207C22×C3×C4—21no—
208C22×C3×C4C23×C511yescharacteristic
209C22×Dic3—21no—
210C22×Dic3C5×D411yescharacteristic
211C2×C4×D3—21no—
212C2×C4×D3—21no—
213C2×Dic6—21no—
214C2×Dic6C5×D411yescharacteristic
215C3×Q16—42no—
216C2×C3×C8—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4C5×D411yescharacteristic
219C3×C22⋊C4—21no—
220#217—21no—
221#216—42no—
222(C2×D3)⋊C4—21no—
223(C2×D3)⋊C4—21no—
224(C2×D3)⋊C4—21no—
225(C2×D3)⋊C4—21no—
226(C2×D3)⋊C4—42no—
227C4⋊Dic3—21no—
228C4⋊Dic3C5×D411yescharacteristic
229Dic3⋊C4—21no—
230Dic3⋊C4—21no—
231Dic3⋊C4—21no—
232C2×C3⋊C8—21no—
233C23×C5—32no—
234C23×C5—61no—
235C23×C5—61no—
236C23×C5—121no—
237C23×C5—121no—
238C23×C5D3×D411yescharacteristic
239C5×Q8—22no—
240C5×Q8—22no—
241C5×Q8—41no—
242C5×Q8—41no—
243C5×Q8—41no—
244C5×Q8—121no—
245C5×Q8—241no—
246C2×C4×C5—22no—
247C2×C4×C5—21no—
248C2×C4×C5—21no—
249C2×C4×C5—41no—
250C2×C4×C5—41no—
251C2×C4×C5—41no—
252C2×C4×C5—61no—
253C2×C4×C5—61no—
254C2×C4×C5—61no—
255C2×C4×C5—121no—
256C2×C4×C5—121no—
257C2×C4×C5—121no—
258C2×C4×C5—121no—
259C2×C4×C5—241no—
260C2×C4×C5—241no—
261C2×C4×C5D3×D411yescharacteristic
262C2×C4×C5C2×#6711yescharacteristic
263C5×C8—41no—
264C5×C8—121no—
265C22×Q8C2×C5×D311yescharacteristic
266C2×Q16—21no—
267C2×Q16—61no—
268C22⋊Q8—31no—
269C22⋊Q8—61no—
270C22⋊Q8—61no—
271C22⋊Q8—61no—
272C22⋊Q8—61no—
273C22⋊Q8—61no—
274C22⋊Q8C2×C5×D311yescharacteristic
275C2×C22⋊C4—31no—
276C2×C22⋊C4—61no—
277C2×C22⋊C4—61no—
278#103—21no—
279#103—61no—
280C22⋊C8—31no—
281C22⋊C8C2×C5×D311yescharacteristic
282#95—31no—
283#95—61no—
284C2×C3×C5—21no—
285C2×C3×C5—21no—
286C2×C3×C5#45111yescharacteristic
287C2×C3×C5#45511yescharacteristic
288C2×C3×C5B(4,𝔽2)11yescharacteristic
289C5×D3—42no—
290C23×C3C2×C5×D411yescharacteristic
291C22×D3—21no—
292C22×D3—21no—
293C22×D3—41no—
294C22×D3—41no—
295C22×D3C5×Q1612yescomplemented
296C3×Q8—22no—
297C3×Q8—22no—
298C3×Q8—41no—
299C3×Q8—41no—
300C3×Q8—41no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4C2×C5×D411yescharacteristic
308C2×C3×C4C2×C5×D411yescharacteristic
309C2×Dic3—21no—
310C2×Dic3—21no—
311C2×Dic3—21no—
312C2×Dic3—41no—
313C2×Dic3—41no—
314C2×Dic3—41no—
315C2×Dic3—41no—
316C4×D3—81no—
317C4×D3—81no—
318Dic6—41no—
319Dic6—81no—
320C3×C8—41no—
321C3⋊C8—41no—
322C22×C5—21no—
323C22×C5—21no—
324C22×C5—62no—
325C22×C5—122no—
326C22×C5—121no—
327C22×C5—121no—
328C22×C5—241no—
329C22×C5D3×Q1611yescharacteristic
330C22×C5#91811yescharacteristic
331C22×C5#93711yescharacteristic
332C4×C5—21no—
333C4×C5—21no—
334C4×C5—41no—
335C4×C5—42no—
336C4×C5—41no—
337C4×C5—121no—
338C4×C5—121no—
339C4×C5—121no—
340C4×C5—241no—
341C24—31no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—31no—
345C2×Q8—42no—
346C2×Q8—61no—
347C2×Q8C5×#6711yescharacteristic
348C22×C4—21no—
349C22×C4—31no—
350C22×C4—61no—
351C22×C4—61no—
352C22×C4—61no—
353C22×C4C22×C5×D311yescharacteristic
354Q16—42no—
355Q16—122no—
356C2×C8—21no—
357C2×C8—61no—
358C4⋊C4—21no—
359C4⋊C4—31no—
360C4⋊C4—61no—
361C4⋊C4—61no—
362C4⋊C4—61no—
363C4⋊C4—61no—
364C4⋊C4C5×#6711yescharacteristic
365C22⋊C4—21no—
366C22⋊C4—61no—
367C22⋊C4—61no—
368C22⋊C4—61no—
369C22⋊C4—61no—
370C22⋊C4—61no—
371C22⋊C4—122no—
372C3×C5#160211yescharacteristic, complemented, Hall
373C22×C3—21no—
374C22×C3—21no—
375C22×C3C5×#12011yescharacteristic
376C22×C3C2×C5×Q1611yescharacteristic
377C22×C3C5×#13711yescharacteristic
378C2×D3—22no—
379C2×D3—41no—
380C2×D3—41no—
381C2×D3—42no—
382C2×D3—81no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—41no—
386C3×C4—41no—
387C3×C4—42no—
388Dic3—41no—
389Dic3—41no—
390Dic3—41no—
391Dic3—81no—
392C2×C5—21no—
393C2×C5—21no—
394C2×C5—122no—
395C2×C5#503211yescharacteristic
396C2×C5#518611yescharacteristic
397C2×C5#520211yescharacteristic
398C23—32no—
399C23—61no—
400C23—61no—
401C23—121no—
402C23—121no—
403C23C5×D3×D411yescharacteristic
404Q8—22no—
405Q8—22no—
406Q8—41no—
407Q8—41no—
408Q8—41no—
409Q8—121no—
410Q8—241no—
411C2×C4—22no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—121no—
421C2×C4—121no—
422C2×C4—121no—
423C2×C4—121no—
424C2×C4—241no—
425C2×C4—241no—
426C2×C4C5×D3×D411yescharacteristic
427C2×C4C2×C5×#6711yescharacteristic
428C8—41no—
429C8—121no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3C5×#45111yescharacteristic
433C2×C3C5×#45511yescharacteristic
434C2×C3C5×B(4,𝔽2)11yescharacteristic
435D3—42no—
436C5#7098011yescharacteristic, direct product factor, Sylow
437C22—21no—
438C22—21no—
439C22—62no—
440C22—122no—
441C22—121no—
442C22—121no—
443C22—241no—
444C22C5×D3×Q1611yescharacteristic
445C22C5×#91811yescharacteristic
446C22C5×#93711yescharacteristic
447C4—21no—
448C4—21no—
449C4—41no—
450C4—42no—
451C4—41no—
452C4—121no—
453C4—121no—
454C4—121no—
455C4—241no—
456C3C5×#160211yescharacteristic, complemented, Sylow
457C2—21no—
458C2—21no—
459C2—122no—
460C2C5×#503211yescharacteristic
461C2C5×#518611yescharacteristic
462C2C5×#520211yescharacteristic
subgroupG/H
centerC22×C5#937
commutator, cosocleC22×C3×C4C23×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#451C2
socleC22×C3×C5#120
prime radicalC23×C5×D3D4
hypercenterC5×#451D3
hypocenterC3C5×#1602
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#451

Complements

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

NH ≅ G/Ntype
2. C3×C5×#451C2semidirect
4. C5×#5228C2semidirect
5. C5×#4538C2semidirect
7. C5×#4467C2semidirect
28. #70980C5direct (N × H)
31. C5×#451D3semidirect
68. C3×#451C2×C5semidirect
70. #5228C2×C5semidirect
71. #4538C2×C5semidirect
73. #4467C2×C5semidirect
99. C22×C5×D3Q16semidirect
178. #451C5×D3semidirect
295. C22×D3C5×Q16semidirect
372. C3×C5#1602semidirect
436. C5#70980direct (N × H)
456. C3C5×#1602semidirect

Maximal subgroups

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

subgroupindex
C5×#56342
C3×C5×#4512
C5×#52312
C5×#52282
C5×#45382
C5×#44682
C5×#44672
C5×#16023
#709805