Finite Group Databasebeta

← C5×#85304 #14511042

Subgroups — C5×#85304 #14511042

Order 1920.

510 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×A4×C4⋊C4C211yesmaximal, characteristic
2C5×C4⋊SL(2,ℤ/4)C211yesmaximal, characteristic
3C5×SL(2,ℤ/4)⋊C4C211yesmaximal, characteristic
4C5×SL(2,ℤ/4)⋊C4C211yesmaximal, characteristic
5C5×SL(2,ℤ/4)⋊C4C211yesmaximal, characteristic
6C5×SL(2,ℤ/4)⋊C4C211yesmaximal, characteristic
7C4×C5×SL(2,ℤ/4)C211yesmaximal, characteristic
8C5×#2473—31nomaximal, Hall
9C2×C4×C5×A4C2211yescharacteristic
10C2×C4×C5×A4C2211yescharacteristic
11C2×C4×C5×A4C2211yescharacteristic
12C2×C5×SL(2,ℤ/4)C2211yescharacteristic
13C2×C5×SL(2,ℤ/4)C2211yescharacteristic
14C2×C5×SL(2,ℤ/4)C2211yescharacteristic
15C2×C5×SL(2,ℤ/4)C2211yescharacteristic
16C5×#889—41nomaximal
17#85304C511yesmaximal, characteristic, direct product factor, Hall
18C2×C5×#125—31no—
19C22×C5×C4⋊C4D311yescharacteristic
20C5×#400—31no—
21C5×#398—31no—
22C5×#398—31no—
23C5×#398—31no—
24C5×#389—31no—
25C5×#387—31no—
26C5×#387—31no—
27C5×#385—31no—
28C5×#385—31no—
29C5×#385—31no—
30C5×#385—31no—
31C5×#380—31no—
32C4×C5×C22⋊C4—31no—
33C22×C5×A4C2311yescharacteristic
34C4×C5×A4—21no—
35C4×C5×A4—21no—
36C4×C5×A4—21no—
37C5×SL(2,ℤ/4)—21no—
38C5×SL(2,ℤ/4)—21no—
39C5×SL(2,ℤ/4)—21no—
40C5×SL(2,ℤ/4)Q812yes—
41C3×C5×C4⋊C4—41no—
42C5×C4⋊Dic3—41no—
43C5×Dic3⋊C4—41no—
44C5×Dic3⋊C4—41no—
45C5×Dic3⋊C4—41no—
46C5×Dic3⋊C4—41no—
47C4×C5×Dic3—41no—
48A4×C4⋊C4C2×C511yescharacteristic
49C4⋊SL(2,ℤ/4)C2×C511yescharacteristic
50SL(2,ℤ/4)⋊C4C2×C511yescharacteristic
51SL(2,ℤ/4)⋊C4C2×C511yescharacteristic
52SL(2,ℤ/4)⋊C4C2×C511yescharacteristic
53SL(2,ℤ/4)⋊C4C2×C511yescharacteristic
54C4×SL(2,ℤ/4)C2×C511yescharacteristic
55C23×C4×C5C2×D311yescharacteristic
56C23×C4×C5C2×D311yescharacteristic
57C23×C4×C5C2×D311yescharacteristic
58C5×#125—61no—
59C5×#125—61no—
60C5×#125—61no—
61C5×#125—61no—
62C2×C5×C4⋊C4—31no—
63C2×C5×C4⋊C4—31no—
64C2×C5×C4⋊C4—31no—
65C2×C5×C4⋊C4—31no—
66C2×C5×C4⋊C4—31no—
67C2×C5×C4⋊C4—31no—
68C2×C5×C4⋊C4—31no—
69C2×C5×C4⋊C4—31no—
70C2×C5×C4⋊C4—31no—
71C2×C5×C4⋊C4—31no—
72C2×C5×C4⋊C4—31no—
73C2×C5×C4⋊C4—31no—
74C2×C5×C4⋊C4—31no—
75C2×C5×C4⋊C4—31no—
76C2×C5×C22⋊C4—31no—
77C2×C5×C22⋊C4—31no—
78C2×C5×C22⋊C4—31no—
79C2×C5×C22⋊C4—31no—
80C2×C42×C5—31no—
81C2×C42×C5—31no—
82C5×#95—31no—
83C5×#95—31no—
84C5×#95—31no—
85C5×#95—31no—
86C5×#95—31no—
87C5×#95—31no—
88C5×#95—31no—
89C5×#95—31no—
90C5×#95—31no—
91C5×#95—31no—
92C5×#95—31no—
93C5×#95—31no—
94#2473—31noSylow
95C2×C5×A4C2×Q811yescharacteristic
96C2×C5×A4#4111yescharacteristic
97C2×C5×A4#4111yescharacteristic
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C5×Dic3—41no—
102C2×C5×Dic3—41no—
103C2×C5×Dic3—41no—
104C2×C5×Dic3—41no—
105C2×C4×A4C22×C511yescharacteristic
106C2×C4×A4C22×C511yescharacteristic
107C2×C4×A4C22×C511yescharacteristic
108C2×SL(2,ℤ/4)C22×C511yescharacteristic
109C2×SL(2,ℤ/4)C22×C511yescharacteristic
110C2×SL(2,ℤ/4)C22×C511yescharacteristic
111C2×SL(2,ℤ/4)C22×C511yescharacteristic
112#889—41no—
113C24×C5C22×D311yescharacteristic
114C22×C4×C5—21no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—31no—
118C22×C4×C5—31no—
119C22×C4×C5—31no—
120C22×C4×C5—31no—
121C22×C4×C5—31no—
122C22×C4×C5—31no—
123C22×C4×C5—31no—
124C22×C4×C5—31no—
125C22×C4×C5—31no—
126C22×C4×C5—31no—
127C22×C4×C5—31no—
128C22×C4×C5—31no—
129C22×C4×C5—31no—
130C22×C4×C5—31no—
131C22×C4×C5—61no—
132C22×C4×C5—61no—
133C22×C4×C5—61no—
134C5×C4⋊C4—31no—
135C5×C4⋊C4—31no—
136C5×C4⋊C4—31no—
137C5×C4⋊C4—61no—
138C5×C4⋊C4—62no—
139C5×C4⋊C4—62no—
140C5×C4⋊C4—61no—
141C5×C4⋊C4—61no—
142C5×C4⋊C4—61no—
143C5×C4⋊C4—61no—
144C5×C4⋊C4—61no—
145C5×C4⋊C4—61no—
146C5×C4⋊C4—61no—
147C5×C4⋊C4—61no—
148C5×C4⋊C4—61no—
149C5×C4⋊C4—61no—
150C5×C4⋊C4—121no—
151C5×C4⋊C4—121no—
152C5×C4⋊C4—121no—
153C5×C4⋊C4S411yescharacteristic
154C5×C22⋊C4—32no—
155C5×C22⋊C4—32no—
156C5×C22⋊C4—61no—
157C5×C22⋊C4—61no—
158C5×C22⋊C4—61no—
159C5×C22⋊C4—61no—
160C5×C22⋊C4—61no—
161C5×C22⋊C4—61no—
162C42×C5—61no—
163C42×C5—61no—
164C42×C5—121no—
165C2×#125—31no—
166C22×C4⋊C4C5×D311yescharacteristic
167#400—31no—
168#398—31no—
169#398—31no—
170#398—31no—
171#389—31no—
172#387—31no—
173#387—31no—
174#385—31no—
175#385—31no—
176#385—31no—
177#385—31no—
178#380—31no—
179C4×C22⋊C4—31no—
180C22×C3×C5—41no—
181C5×A4#12511yescharacteristic, complemented
182C3×C4×C5—81no—
183C3×C4×C5—81no—
184C3×C4×C5—81no—
185C5×Dic3—42no—
186C5×Dic3—81no—
187C5×Dic3—81no—
188C5×Dic3—81no—
189C22×A4C23×C511yescharacteristic
190C4×A4—21no—
191C4×A4—21no—
192C4×A4—21no—
193SL(2,ℤ/4)—21no—
194SL(2,ℤ/4)—21no—
195SL(2,ℤ/4)—21no—
196SL(2,ℤ/4)C5×Q812yes—
197C3×C4⋊C4—41no—
198C4⋊Dic3—41no—
199Dic3⋊C4—41no—
200Dic3⋊C4—41no—
201Dic3⋊C4—41no—
202Dic3⋊C4—41no—
203C4×Dic3—41no—
204C23×C5—31no—
205C23×C5—31no—
206C23×C5—31no—
207C23×C5—31no—
208C23×C5#23511yescharacteristic
209C23×C5#23711yescharacteristic
210C23×C5D3×Q811yescharacteristic
211C2×C4×C5—32no—
212C2×C4×C5—32no—
213C2×C4×C5—32no—
214C2×C4×C5—31no—
215C2×C4×C5—31no—
216C2×C4×C5—31no—
217C2×C4×C5—61no—
218C2×C4×C5—61no—
219C2×C4×C5—61no—
220C2×C4×C5—61no—
221C2×C4×C5—61no—
222C2×C4×C5—61no—
223C2×C4×C5—61no—
224C2×C4×C5—61no—
225C2×C4×C5—61no—
226C2×C4×C5—61no—
227C2×C4×C5—61no—
228C2×C4×C5—61no—
229C2×C4×C5—61no—
230C2×C4×C5—61no—
231C2×C4×C5—61no—
232C2×C4×C5—61no—
233C2×C4×C5—61no—
234C2×C4×C5—61no—
235C2×C4×C5—61no—
236C2×C4×C5—61no—
237C2×C4×C5—61no—
238C2×C4×C5—61no—
239C2×C4×C5—61no—
240C2×C4×C5—61no—
241C2×C4×C5—61no—
242C2×C4×C5—61no—
243C2×C4×C5—61no—
244C2×C4×C5—61no—
245C2×C4×C5—61no—
246C2×C4×C5—61no—
247C2×C4×C5—61no—
248C2×C4×C5—61no—
249C2×C4×C5—61no—
250C2×C4×C5C2×S411yescharacteristic
251C2×C4×C5C2×S411yescharacteristic
252C2×C4×C5C2×S411yescharacteristic
253C23×C4C2×C5×D311yescharacteristic
254C23×C4C2×C5×D311yescharacteristic
255C23×C4C2×C5×D311yescharacteristic
256#125—61no—
257#125—61no—
258#125—61no—
259#125—61no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—31no—
263C2×C4⋊C4—31no—
264C2×C4⋊C4—31no—
265C2×C4⋊C4—31no—
266C2×C4⋊C4—31no—
267C2×C4⋊C4—31no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—31no—
270C2×C4⋊C4—31no—
271C2×C4⋊C4—31no—
272C2×C4⋊C4—31no—
273C2×C4⋊C4—31no—
274C2×C22⋊C4—31no—
275C2×C22⋊C4—31no—
276C2×C22⋊C4—31no—
277C2×C22⋊C4—31no—
278C2×C42—31no—
279C2×C42—31no—
280#95—31no—
281#95—31no—
282#95—31no—
283#95—31no—
284#95—31no—
285#95—31no—
286#95—31no—
287#95—31no—
288#95—31no—
289#95—31no—
290#95—31no—
291#95—31no—
292C2×C3×C5—41no—
293C2×C3×C5—41no—
294C2×C3×C5—41no—
295C2×A4C2×C5×Q811yescharacteristic
296C2×A4C5×#4111yescharacteristic
297C2×A4C5×#4111yescharacteristic
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×Dic3—41no—
302C2×Dic3—41no—
303C2×Dic3—41no—
304C2×Dic3—41no—
305C22×C5—31no—
306C22×C5—31no—
307C22×C5—31no—
308C22×C5—31no—
309C22×C5—31no—
310C22×C5—31no—
311C22×C5—31no—
312C22×C5—31no—
313C22×C5—31no—
314C22×C5—61no—
315C22×C5#88911yescharacteristic, complemented
316C22×C5C22×S411yescharacteristic
317C4×C5—21no—
318C4×C5—21no—
319C4×C5—21no—
320C4×C5—62no—
321C4×C5—61no—
322C4×C5—61no—
323C4×C5—61no—
324C4×C5—62no—
325C4×C5—121no—
326C4×C5—121no—
327C4×C5—121no—
328C4×C5—121no—
329C4×C5—121no—
330C4×C5—121no—
331C24C22×C5×D311yescharacteristic
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—31no—
336C22×C4—31no—
337C22×C4—31no—
338C22×C4—31no—
339C22×C4—31no—
340C22×C4—31no—
341C22×C4—31no—
342C22×C4—31no—
343C22×C4—31no—
344C22×C4—31no—
345C22×C4—31no—
346C22×C4—31no—
347C22×C4—31no—
348C22×C4—31no—
349C22×C4—61no—
350C22×C4—61no—
351C22×C4—61no—
352C4⋊C4—31no—
353C4⋊C4—31no—
354C4⋊C4—31no—
355C4⋊C4—61no—
356C4⋊C4—61no—
357C4⋊C4—61no—
358C4⋊C4—61no—
359C4⋊C4—61no—
360C4⋊C4—61no—
361C4⋊C4—62no—
362C4⋊C4—62no—
363C4⋊C4—61no—
364C4⋊C4—61no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C4⋊C4—121no—
369C4⋊C4—121no—
370C4⋊C4—121no—
371C4⋊C4C5×S411yescharacteristic
372C22⋊C4—32no—
373C22⋊C4—32no—
374C22⋊C4—61no—
375C22⋊C4—61no—
376C22⋊C4—61no—
377C22⋊C4—61no—
378C22⋊C4—61no—
379C22⋊C4—61no—
380C42—61no—
381C42—61no—
382C42—121no—
383C3×C5—41noHall
384C22×C3—41no—
385A4C5×#12511yescharacteristic, complemented
386C3×C4—81no—
387C3×C4—81no—
388C3×C4—81no—
389Dic3—42no—
390Dic3—81no—
391Dic3—81no—
392Dic3—81no—
393C2×C5—31no—
394C2×C5—31no—
395C2×C5—31no—
396C2×C5—31no—
397C2×C5#591211yescharacteristic
398C2×C5#591411yescharacteristic
399C2×C5Q8×S411yescharacteristic
400C23—31no—
401C23—31no—
402C23—31no—
403C23—31no—
404C23C5×#23511yescharacteristic
405C23C5×#23711yescharacteristic
406C23C5×D3×Q811yescharacteristic
407C2×C4—32no—
408C2×C4—32no—
409C2×C4—32no—
410C2×C4—31no—
411C2×C4—31no—
412C2×C4—31no—
413C2×C4—61no—
414C2×C4—61no—
415C2×C4—61no—
416C2×C4—61no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—61no—
428C2×C4—61no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—61no—
432C2×C4—61no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—61no—
436C2×C4—61no—
437C2×C4—61no—
438C2×C4—61no—
439C2×C4—61no—
440C2×C4—61no—
441C2×C4—61no—
442C2×C4—61no—
443C2×C4—61no—
444C2×C4—61no—
445C2×C4—61no—
446C2×C4C2×C5×S411yescharacteristic
447C2×C4C2×C5×S411yescharacteristic
448C2×C4C2×C5×S411yescharacteristic
449C2×C3—41no—
450C2×C3—41no—
451C2×C3—41no—
452C5#8530411yescharacteristic, direct product factor, Sylow
453C22—31no—
454C22—31no—
455C22—31no—
456C22—31no—
457C22—31no—
458C22—31no—
459C22—31no—
460C22—31no—
461C22—31no—
462C22—61no—
463C22C5×#88911yescharacteristic, complemented
464C22C22×C5×S411yescharacteristic
465C4—21no—
466C4—21no—
467C4—21no—
468C4—62no—
469C4—61no—
470C4—61no—
471C4—61no—
472C4—62no—
473C4—121no—
474C4—121no—
475C4—121no—
476C4—121no—
477C4—121no—
478C4—121no—
479C3—41noSylow
480C2—31no—
481C2—31no—
482C2—31no—
483C2—31no—
484C2C5×#591211yescharacteristic
485C2C5×#591411yescharacteristic
486C2C5×Q8×S411yescharacteristic
subgroupG/H
centerC22×C5C22×S4
commutator, cosocleC22×A4C23×C5
FrattiniC22C22×C5×S4
FittingC22×C5×C4⋊C4D3
socleC24×C5C22×D3
prime radicalC22×C5×A4C23
hypercenterC5×C4⋊C4S4
hypocenterA4C5×#125
LCSG ▷ C22×A4 ▷ A4
UCSC1 ◁ C22×C5 ◁ C5×C4⋊C4

Complements

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

NH ≅ G/Ntype
17. #85304C5direct (N × H)
181. C5×A4#125semidirect
315. C22×C5#889semidirect
385. A4C5×#125semidirect
452. C5#85304direct (N × H)
463. C22C5×#889semidirect

Maximal subgroups

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

subgroupindex
C5×A4×C4⋊C42
C5×C4⋊SL(2,ℤ/4)2
C5×SL(2,ℤ/4)⋊C42
C4×C5×SL(2,ℤ/4)2
C5×#24733
C5×#8894
#853045