Finite Group Databasebeta

← C5×#85305 #14511043

Subgroups — C5×#85305 #14511043

Order 1920.

510 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 88 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)C212yesmaximal
3C5×C4⋊SL(2,ℤ/4)C211yesmaximal, characteristic
4C5×SL(2,ℤ/4)⋊C4C212yesmaximal
5C4×C5×SL(2,ℤ/4)C211yesmaximal, characteristic
6C5×#2442—31nomaximal, Hall
7C2×C4×C5×A4C2212yes—
8C2×C4×C5×A4C2211yescharacteristic
9C2×C5×SL(2,ℤ/4)C2211yescharacteristic
10C2×C5×SL(2,ℤ/4)C2211yescharacteristic
11C2×C5×SL(2,ℤ/4)C2212yes—
12C5×#890—41nomaximal
13#85305C511yesmaximal, characteristic, direct product factor, Hall
14C2×C5×#125—31no—
15C22×C5×C4⋊C4D311yescharacteristic
16C5×#400—32no—
17C5×#398—32no—
18C5×#389—31no—
19C5×#389—31no—
20C5×#385—32no—
21C5×#382—31no—
22C5×#380—32no—
23C5×#380—31no—
24C4×C5×C22⋊C4—31no—
25C22×C5×A4C2311yescharacteristic
26C4×C5×A4—22no—
27C4×C5×A4Q812yes—
28C5×SL(2,ℤ/4)—21no—
29C5×SL(2,ℤ/4)—21no—
30C5×SL(2,ℤ/4)—22no—
31C3×C5×C4⋊C4—41no—
32C5×C4⋊Dic3—42no—
33C5×C4⋊Dic3—41no—
34C5×Dic3⋊C4—42no—
35C4×C5×Dic3—41no—
36A4×C4⋊C4C2×C511yescharacteristic
37C4⋊SL(2,ℤ/4)C2×C512yes—
38C4⋊SL(2,ℤ/4)C2×C511yescharacteristic
39SL(2,ℤ/4)⋊C4C2×C512yes—
40C4×SL(2,ℤ/4)C2×C511yescharacteristic
41C23×C4×C5C2×D312yes—
42C23×C4×C5C2×D311yescharacteristic
43C5×#125—62no—
44C5×#125—61no—
45C5×#125—61no—
46C2×C5×C4⋊C4—31no—
47C2×C5×C4⋊C4—31no—
48C2×C5×C4⋊C4—32no—
49C2×C5×C4⋊C4—31no—
50C2×C5×C4⋊C4—31no—
51C2×C5×C4⋊C4—32no—
52C2×C5×C4⋊C4—32no—
53C2×C5×C4⋊C4—32no—
54C2×C5×C4⋊C4—32no—
55C2×C5×C22⋊C4—31no—
56C2×C5×C22⋊C4—31no—
57C2×C5×C22⋊C4—32no—
58C2×C42×C5—31no—
59C2×C42×C5—31no—
60C5×#95—31no—
61C5×#95—31no—
62C5×#95—32no—
63C5×#95—32no—
64C5×#95—32no—
65C5×#95—32no—
66C5×#95—32no—
67#2442—31noSylow
68C2×C5×A4C2×Q811yescharacteristic
69C2×C5×A4#4111yescharacteristic
70C2×C5×A4#4111yescharacteristic
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5—42no—
73C2×C5×Dic3—41no—
74C2×C5×Dic3—41no—
75C2×C5×Dic3—42no—
76C2×C4×A4C22×C512yes—
77C2×C4×A4C22×C511yescharacteristic
78C2×SL(2,ℤ/4)C22×C511yescharacteristic
79C2×SL(2,ℤ/4)C22×C511yescharacteristic
80C2×SL(2,ℤ/4)C22×C512yes—
81#890—41no—
82C24×C5C22×D311yescharacteristic
83C22×C4×C5—22no—
84C22×C4×C5—31no—
85C22×C4×C5—31no—
86C22×C4×C5—32no—
87C22×C4×C5—32no—
88C22×C4×C5—32no—
89C22×C4×C5—31no—
90C22×C4×C5—31no—
91C22×C4×C5—31no—
92C22×C4×C5—31no—
93C22×C4×C5—32no—
94C22×C4×C5—32no—
95C22×C4×C5—62no—
96C22×C4×C5Dic612yes—
97C5×C4⋊C4—32no—
98C5×C4⋊C4—31no—
99C5×C4⋊C4—61no—
100C5×C4⋊C4—62no—
101C5×C4⋊C4—61no—
102C5×C4⋊C4—62no—
103C5×C4⋊C4—62no—
104C5×C4⋊C4—62no—
105C5×C4⋊C4—62no—
106C5×C4⋊C4—61no—
107C5×C4⋊C4—122no—
108C5×C4⋊C4—122no—
109C5×C4⋊C4S411yescharacteristic
110C5×C22⋊C4—61no—
111C5×C22⋊C4—62no—
112C5×C22⋊C4—61no—
113C5×C22⋊C4—61no—
114C5×C22⋊C4—61no—
115C5×C22⋊C4—62no—
116C42×C5—62no—
117C42×C5—61no—
118C42×C5—61no—
119C2×#125—31no—
120C22×C4⋊C4C5×D311yescharacteristic
121#400—32no—
122#398—32no—
123#389—31no—
124#389—31no—
125#385—32no—
126#382—31no—
127#380—32no—
128#380—31no—
129C4×C22⋊C4—31no—
130C22×C3×C5—41no—
131C5×A4#12511yescharacteristic, complemented
132C3×C4×C5—42no—
133C3×C4×C5—82no—
134C5×Dic3—81no—
135C5×Dic3—81no—
136C5×Dic3—82no—
137C22×A4C23×C511yescharacteristic
138C4×A4—22no—
139C4×A4C5×Q812yes—
140SL(2,ℤ/4)—21no—
141SL(2,ℤ/4)—21no—
142SL(2,ℤ/4)—22no—
143C3×C4⋊C4—41no—
144C4⋊Dic3—42no—
145C4⋊Dic3—41no—
146Dic3⋊C4—42no—
147C4×Dic3—41no—
148C23×C5—31no—
149C23×C5—31no—
150C23×C5—31no—
151C23×C5—31no—
152C23×C5C2×Dic611yescharacteristic
153C23×C5#23711yescharacteristic
154C23×C5#23911yescharacteristic
155C2×C4×C5—31no—
156C2×C4×C5—32no—
157C2×C4×C5—32no—
158C2×C4×C5—32no—
159C2×C4×C5—32no—
160C2×C4×C5—62no—
161C2×C4×C5—62no—
162C2×C4×C5—61no—
163C2×C4×C5—62no—
164C2×C4×C5—62no—
165C2×C4×C5—61no—
166C2×C4×C5—61no—
167C2×C4×C5—61no—
168C2×C4×C5—61no—
169C2×C4×C5—62no—
170C2×C4×C5—61no—
171C2×C4×C5—61no—
172C2×C4×C5—62no—
173C2×C4×C5—62no—
174C2×C4×C5—61no—
175C2×C4×C5—62no—
176C2×C4×C5—61no—
177C2×C4×C5—61no—
178C2×C4×C5—61no—
179C2×C4×C5—62no—
180C2×C4×C5—61no—
181C2×C4×C5—61no—
182C2×C4×C5—62no—
183C2×C4×C5C2×S412yes—
184C2×C4×C5C2×S411yescharacteristic
185C23×C4C2×C5×D312yes—
186C23×C4C2×C5×D311yescharacteristic
187#125—62no—
188#125—61no—
189#125—61no—
190C2×C4⋊C4—31no—
191C2×C4⋊C4—31no—
192C2×C4⋊C4—32no—
193C2×C4⋊C4—31no—
194C2×C4⋊C4—32no—
195C2×C4⋊C4—32no—
196C2×C4⋊C4—31no—
197C2×C4⋊C4—32no—
198C2×C4⋊C4—32no—
199C2×C22⋊C4—31no—
200C2×C22⋊C4—31no—
201C2×C22⋊C4—32no—
202C2×C42—31no—
203C2×C42—31no—
204#95—31no—
205#95—31no—
206#95—32no—
207#95—32no—
208#95—32no—
209#95—32no—
210#95—32no—
211C2×C3×C5—41no—
212C2×C3×C5—41no—
213C2×C3×C5—41no—
214C2×A4C2×C5×Q811yescharacteristic
215C2×A4C5×#4111yescharacteristic
216C2×A4C5×#4111yescharacteristic
217C2×C3×C4—41no—
218C2×C3×C4—42no—
219C2×Dic3—41no—
220C2×Dic3—41no—
221C2×Dic3—42no—
222C22×C5—31no—
223C22×C5—31no—
224C22×C5—31no—
225C22×C5—31no—
226C22×C5—31no—
227C22×C5—31no—
228C22×C5—31no—
229C22×C5—31no—
230C22×C5—31no—
231C22×C5—61no—
232C22×C5#89011yescharacteristic, complemented
233C22×C5C22×S411yescharacteristic
234C4×C5—22no—
235C4×C5—32no—
236C4×C5—62no—
237C4×C5—121no—
238C4×C5—122no—
239C4×C5—121no—
240C4×C5—121no—
241C4×C5—121no—
242C4×C5—122no—
243C4×C5A4⋊Q812yes—
244C24C22×C5×D311yescharacteristic
245C22×C4—22no—
246C22×C4—31no—
247C22×C4—31no—
248C22×C4—32no—
249C22×C4—32no—
250C22×C4—32no—
251C22×C4—31no—
252C22×C4—31no—
253C22×C4—31no—
254C22×C4—32no—
255C22×C4—32no—
256C22×C4—31no—
257C22×C4—62no—
258C22×C4C5×Dic612yes—
259C4⋊C4—32no—
260C4⋊C4—31no—
261C4⋊C4—61no—
262C4⋊C4—61no—
263C4⋊C4—62no—
264C4⋊C4—62no—
265C4⋊C4—62no—
266C4⋊C4—62no—
267C4⋊C4—62no—
268C4⋊C4—61no—
269C4⋊C4—122no—
270C4⋊C4—122no—
271C4⋊C4C5×S411yescharacteristic
272C22⋊C4—61no—
273C22⋊C4—62no—
274C22⋊C4—61no—
275C22⋊C4—61no—
276C22⋊C4—61no—
277C22⋊C4—62no—
278C42—61no—
279C42—62no—
280C42—61no—
281C3×C5—41noHall
282C22×C3—41no—
283A4C5×#12511yescharacteristic, complemented
284C3×C4—42no—
285C3×C4—82no—
286Dic3—81no—
287Dic3—81no—
288Dic3—82no—
289C2×C5—31no—
290C2×C5—31no—
291C2×C5—31no—
292C2×C5—31no—
293C2×C5C2×A4⋊Q811yescharacteristic
294C2×C5#591411yescharacteristic
295C2×C5#591911yescharacteristic
296C23—31no—
297C23—31no—
298C23—31no—
299C23—31no—
300C23C2×C5×Dic611yescharacteristic
301C23C5×#23711yescharacteristic
302C23C5×#23911yescharacteristic
303C2×C4—31no—
304C2×C4—32no—
305C2×C4—32no—
306C2×C4—32no—
307C2×C4—32no—
308C2×C4—62no—
309C2×C4—62no—
310C2×C4—61no—
311C2×C4—62no—
312C2×C4—62no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4—62no—
318C2×C4—61no—
319C2×C4—61no—
320C2×C4—62no—
321C2×C4—62no—
322C2×C4—61no—
323C2×C4—62no—
324C2×C4—61no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—62no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—62no—
331C2×C4C2×C5×S412yes—
332C2×C4C2×C5×S411yescharacteristic
333C2×C3—41no—
334C2×C3—41no—
335C2×C3—41no—
336C5#8530511yescharacteristic, direct product factor, Sylow
337C22—31no—
338C22—31no—
339C22—31no—
340C22—31no—
341C22—31no—
342C22—31no—
343C22—31no—
344C22—31no—
345C22—31no—
346C22—61no—
347C22C5×#89011yescharacteristic, complemented
348C22C22×C5×S411yescharacteristic
349C4—22no—
350C4—32no—
351C4—62no—
352C4—121no—
353C4—122no—
354C4—121no—
355C4—121no—
356C4—121no—
357C4—122no—
358C4C5×A4⋊Q812yes—
359C3—41noSylow
360C2—31no—
361C2—31no—
362C2—31no—
363C2—31no—
364C2C2×C5×A4⋊Q811yescharacteristic
365C2C5×#591411yescharacteristic
366C2C5×#591911yescharacteristic
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
13. #85305C5direct (N × H)
131. C5×A4#125semidirect
232. C22×C5#890semidirect
283. A4C5×#125semidirect
336. C5#85305direct (N × H)
347. C22C5×#890semidirect

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×#24423
C5×#8904
#853055