Finite Group Databasebeta

← C4×C5⋊#1020 #14514621

Subgroups — C4×C5⋊#1020 #14514621

Order 1920.

870 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 870 conjugacy classes of subgroups — too many to draw. Only its 41 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
1C2×C5⋊#1020C211yesmaximal, characteristic
2C4×C5×C22⋊A4C211yesmaximal, characteristic, complemented
3#11756927C211yesmaximal, characteristic, complemented
4C4×#4099—31nomaximal, Hall
5C2×C5×C22⋊A4C2211yescharacteristic
6C5⋊#1020C412yesdirect product factor
7C4×C5⋊S4—43nomaximal
8C4×#1020—51nomaximal, Hall
9C24×C4×C5D311yescharacteristic, complemented
10C2×#4099—31no—
11C2×C4×C22⋊D5—33no—
12#65536—31no—
13#65502—33no—
14#65499—33no—
15C4×C22⋊Dic5—33no—
16C5×C22⋊A4C2×C411yescharacteristic, complemented
17C2×C5⋊S4—43no—
18C4×C5×A4—43no—
19C4×C5×A4—81no—
20A4⋊Dic5—43no—
21C2×#1020—51no—
22C4×C22⋊A4D511yescharacteristic, complemented
23#5936—51no—
24C25×C5C2×D311yescharacteristic
25C23×C4×C5—33no—
26C23×C4×C5—33no—
27C23×C4×C5—61no—
28C23×C4×C5—61no—
29C22×C22⋊D5—33no—
30C22×C4×D5—31no—
31#4099—36no—
32#4099—32no—
33C2×C22⋊Dic5—33no—
34C2×C22⋊Dic5—33no—
35C2×C22⋊Dic5—33no—
36C4×C22⋊D5—63no—
37C4×C22⋊D5—63no—
38C4×C22⋊D5—63no—
39C4×C22⋊D5—63no—
40C2×#685—33no—
41C2×#683—33no—
42C2×C4×Dic5—33no—
43#3963—36no—
44C4×#120—151noSylow
45C2×C5×A4—43no—
46C2×C5×A4—81no—
47C5⋊S4—46no—
48C4×D15—161no—
49C2×C22⋊A4C2×D511yescharacteristic
50#1020—52no—
51C4×S4—203no—
52C24×C5—33no—
53C24×C5—33no—
54C24×C5—61no—
55C24×C5—61no—
56C24×C5C4×D311yescharacteristic, complemented
57C23×D5—31no—
58C22×C4×C5—21no—
59C22×C4×C5—31no—
60C22×C4×C5—33no—
61C22×C4×C5—33no—
62C22×C4×C5—33no—
63C22×C4×C5—33no—
64C22×C4×C5—66no—
65C22×C4×C5—63no—
66C22×C4×C5—63no—
67C22×C4×C5—61no—
68C22×C4×C5—63no—
69C22×C4×C5S413yescomplemented
70C2×C22⋊D5—36no—
71C2×C22⋊D5—36no—
72C2×C22⋊D5—63no—
73C2×C22⋊D5—63no—
74C2×C22⋊D5—63no—
75C2×C22⋊D5—63no—
76C22×Dic5—33no—
77C22×Dic5—31no—
78C22×Dic5—33no—
79C2×C4×D5—63no—
80C2×C4×D5—63no—
81C22⋊Dic5—36no—
82C22⋊Dic5—36no—
83C22⋊Dic5—63no—
84C22⋊Dic5—63no—
85C22⋊Dic5—63no—
86C22⋊Dic5—63no—
87#685—63no—
88#685—63no—
89#683—63no—
90#683—63no—
91C4×Dic5—63no—
92C4×Dic5—63no—
93C24×C4D1511yescharacteristic, complemented
94C2×#120—151no—
95C2×C4×D4—153no—
96#386—153no—
97#385—153no—
98#379—151no—
99C4×C22⋊C4—153no—
100C2×D15—161no—
101C5×A4—43no—
102C5×A4—81no—
103C3×C4×C5—161no—
104Dic15—161no—
105C22⋊A4C4×D511yescharacteristic, complemented
106C2×S4—203no—
107C4×A4—43no—
108C4×A4—81no—
109SL(2,ℤ/4)—203no—
110C23×C5—21no—
111C23×C5—31no—
112C23×C5—33no—
113C23×C5—33no—
114C23×C5—33no—
115C23×C5—33no—
116C23×C5—33no—
117C23×C5—61no—
118C23×C5—61no—
119C23×C5—63no—
120C23×C5—66no—
121C23×C5—63no—
122C23×C5—63no—
123C23×C5C2×S413yes—
124C22×D5—32no—
125C22×D5—63no—
126C22×D5—63no—
127C2×C4×C5—33no—
128C2×C4×C5—33no—
129C2×C4×C5—33no—
130C2×C4×C5—33no—
131C2×C4×C5—63no—
132C2×C4×C5—66no—
133C2×C4×C5—63no—
134C2×C4×C5—61no—
135C2×C4×C5—61no—
136C22⋊D5—66no—
137C22⋊D5—66no—
138C22⋊D5—66no—
139C22⋊D5—66no—
140C2×Dic5—36no—
141C2×Dic5—63no—
142C2×Dic5—63no—
143C2×Dic5—63no—
144C2×Dic5—63no—
145C2×Dic5—66no—
146C4×D5—123no—
147C4×D5—121no—
148C25C2×D1511yescharacteristic
149C22×D4—153no—
150C23×C4—33no—
151C23×C4—33no—
152C23×C4—61no—
153C23×C4—61no—
154C23×C4—151no—
155#120—156no—
156#120—152no—
157C4×D4—303no—
158C4×D4—303no—
159C4×D4—303no—
160C4×D4—303no—
161C2×C4⋊C4—153no—
162C2×C22⋊C4—153no—
163C2×C22⋊C4—153no—
164C2×C22⋊C4—153no—
165C2×C22⋊C4—153no—
166C2×C42—153no—
167#95—156no—
168C2×C3×C5—161no—
169D15—162no—
170C2×A4—43no—
171C2×A4—81no—
172S4—206no—
173C4×D3—801no—
174C22×C5—21no—
175C22×C5—33no—
176C22×C5—31no—
177C22×C5—33no—
178C22×C5—33no—
179C22×C5—33no—
180C22×C5—33no—
181C22×C5—63no—
182C22×C5—66no—
183C22×C5—63no—
184C22×C5—63no—
185C22×C5—61no—
186C22×C5—61no—
187C22×C5C4×S413yescomplemented
188C2×D5—66no—
189C2×D5—123no—
190C2×D5—121no—
191C4×C5—33no—
192C4×C5—61no—
193C4×C5#102011yescharacteristic, complemented
194Dic5—66no—
195Dic5—123no—
196Dic5—121no—
197C24—33no—
198C24—33no—
199C24—61no—
200C24—61no—
201C24—151no—
202C24C4×D1511yescharacteristic, complemented
203C2×D4—156no—
204C2×D4—156no—
205C2×D4—303no—
206C2×D4—303no—
207C2×D4—303no—
208C2×D4—303no—
209C22×C4—21no—
210C22×C4—31no—
211C22×C4—33no—
212C22×C4—33no—
213C22×C4—33no—
214C22×C4—33no—
215C22×C4—66no—
216C22×C4—63no—
217C22×C4—63no—
218C22×C4—61no—
219C22×C4—63no—
220C22×C4—153no—
221C22×C4—153no—
222C22×C4—151no—
223C22×C4—303no—
224C22×C4—303no—
225C22×C4C5⋊S413yescomplemented
226C4⋊C4—303no—
227C4⋊C4—303no—
228C22⋊C4—156no—
229C22⋊C4—156no—
230C22⋊C4—303no—
231C22⋊C4—303no—
232C22⋊C4—303no—
233C22⋊C4—303no—
234C22⋊C4—303no—
235C22⋊C4—303no—
236C42—303no—
237C42—303no—
238C3×C5—161noHall
239C2×D3—801no—
240A4—43no—
241A4—81no—
242C3×C4—161no—
243Dic3—801no—
244C2×C5—33no—
245C2×C5—33no—
246C2×C5—61no—
247C2×C5—61no—
248C2×C5C2×#102011yescharacteristic
249D5—122no—
250C23—21no—
251C23—31no—
252C23—33no—
253C23—33no—
254C23—33no—
255C23—33no—
256C23—33no—
257C23—61no—
258C23—61no—
259C23—63no—
260C23—66no—
261C23—63no—
262C23—63no—
263C23—152no—
264C23—303no—
265C23—303no—
266C23C2×C5⋊S413yes—
267D4—306no—
268D4—306no—
269D4—306no—
270D4—306no—
271C2×C4—33no—
272C2×C4—33no—
273C2×C4—33no—
274C2×C4—33no—
275C2×C4—63no—
276C2×C4—66no—
277C2×C4—63no—
278C2×C4—61no—
279C2×C4—61no—
280C2×C4—156no—
281C2×C4—303no—
282C2×C4—303no—
283C2×C4—303no—
284C2×C4—303no—
285C2×C4—306no—
286C2×C4—603no—
287C2×C4—601no—
288C2×C3—161no—
289D3—802no—
290C5C4×#102011yescharacteristic, complemented, Sylow
291C22—21no—
292C22—33no—
293C22—31no—
294C22—33no—
295C22—33no—
296C22—33no—
297C22—33no—
298C22—63no—
299C22—66no—
300C22—63no—
301C22—63no—
302C22—61no—
303C22—61no—
304C22—306no—
305C22—603no—
306C22—601no—
307C22C4×C5⋊S413yescomplemented
308C4—33no—
309C4—61no—
310C4—306no—
311C4—603no—
312C4—601no—
313C4C5⋊#102011yescharacteristic, direct product factor
314C3—161noSylow
315C2—33no—
316C2—33no—
317C2—61no—
318C2—61no—
319C2—602no—
320C2C2×C5⋊#102011yescharacteristic
subgroupG/H
center, hypercenterC4C5⋊#1020
commutator, hypocenterC5×C22⋊A4C2×C4
FrattiniC2C2×C5⋊#1020
FittingC24×C4×C5D3
socleC25×C5C2×D3
prime radicalC2×C5⋊#1020C2
cosocleC2×C5×C22⋊A4C22
LCSG ▷ C5×C22⋊A4
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C4×C5×C22⋊A4C2semidirect
3. #11756927C2semidirect
6. C5⋊#1020C4direct (N × H)
9. C24×C4×C5D3semidirect
16. C5×C22⋊A4C2×C4semidirect
22. C4×C22⋊A4D5semidirect
56. C24×C5C4×D3semidirect
69. C22×C4×C5S4semidirect
93. C24×C4D15semidirect
105. C22⋊A4C4×D5semidirect
187. C22×C5C4×S4semidirect
193. C4×C5#1020semidirect
202. C24C4×D15semidirect
225. C22×C4C5⋊S4semidirect
290. C5C4×#1020semidirect
307. C22C4×C5⋊S4semidirect
313. C4C5⋊#1020direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5⋊#10202
C4×C5×C22⋊A42
#117569272
C4×#40993
C4×C5⋊S44
C4×#10205