Finite Group Databasebeta

← C5×#73051 #14510775

Subgroups — C5×#73051 #14510775

Order 1920.

310 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 64 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
3C2×C5×A4⋊C8C211yesmaximal, characteristic
4C5×#1853—31nomaximal, Hall
5C2×C4×C5×A4—21no—
6C2×C4×C5×A4C2211yescharacteristic
7C2×C5×SL(2,ℤ/4)—21no—
8C5×A4⋊C8C412yescomplemented
9C5×#808—41nomaximal
10#73051C511yesmaximal, characteristic, direct product factor, Hall
11C22×C5×C4⋊C4D311yescharacteristic
12C2×C5×#106—31no—
13C2×C5×#106—31no—
14C2×C5×C22⋊C8—31no—
15C5×#380—31no—
16C5×#340—31no—
17C5×#340—31no—
18C22×C5×A4D411yescharacteristic
19C4×C5×A4—41no—
20C4×C5×A4C2×C411yescharacteristic
21C4×C5×A4Q811yescharacteristic
22C5×SL(2,ℤ/4)—41no—
23C3×C5×C4⋊C4—41no—
24C5×C4⋊Dic3—41no—
25C2×C5×C3⋊C8—41no—
26A4×C4⋊C4C2×C511yescharacteristic
27C4⋊SL(2,ℤ/4)C2×C511yescharacteristic
28C2×A4⋊C8C2×C511yescharacteristic
29C23×C4×C5—21no—
30C23×C4×C5C2×D311yescharacteristic
31C22×C5×C8—31no—
32C22×C5×C8—31no—
33C2×C5×C4⋊C4—31no—
34C2×C5×C4⋊C4—31no—
35C2×C5×C4⋊C4—31no—
36C2×C5×C4⋊C4—31no—
37C2×C5×C4⋊C4—61no—
38C2×C5×C22⋊C4—61no—
39C5×#106—62no—
40C5×#106—61no—
41C5×#106—61no—
42C5×C22⋊C8—32no—
43C5×C22⋊C8—32no—
44C5×#95—61no—
45#1853—31noSylow
46C2×C5×A4C4⋊C411yescharacteristic
47C2×C5×A4SD1611yescharacteristic
48C2×C5×A4SD1611yescharacteristic
49C2×C3×C4×C5—41no—
50C2×C3×C4×C5—81no—
51C2×C5×Dic3—81no—
52C5×C3⋊C8—42no—
53C2×C4×A4—21no—
54C2×C4×A4C22×C511yescharacteristic
55C2×SL(2,ℤ/4)—21no—
56A4⋊C8C4×C512yescomplemented
57#808—41no—
58C24×C5#6711yescharacteristic
59C22×C4×C5—31no—
60C22×C4×C5—31no—
61C22×C4×C5—31no—
62C22×C4×C5—31no—
63C22×C4×C5—41no—
64C22×C4×C5—61no—
65C22×C4×C5—61no—
66C22×C4×C5—61no—
67C22×C4×C5—61no—
68C22×C4×C5—121no—
69C22×C4×C5Dic611yescharacteristic
70C22×C4×C5C4×D311yescharacteristic
71C2×C5×C8—32no—
72C2×C5×C8—32no—
73C2×C5×C8—61no—
74C2×C5×C8—61no—
75C2×C5×C8—61no—
76C2×C5×C8—61no—
77C5×C4⋊C4—32no—
78C5×C4⋊C4—31no—
79C5×C4⋊C4—61no—
80C5×C4⋊C4—61no—
81C5×C4⋊C4—61no—
82C5×C4⋊C4—61no—
83C5×C4⋊C4—61no—
84C5×C4⋊C4S411yescharacteristic
85C5×C22⋊C4—121no—
86C5×C22⋊C4—121no—
87C22×C4⋊C4C5×D311yescharacteristic
88C2×#106—31no—
89C2×#106—31no—
90C2×C22⋊C8—31no—
91#380—31no—
92#340—31no—
93#340—31no—
94C22×C3×C5—41no—
95C5×A4#10611yescharacteristic, complemented
96C3×C4×C5—41no—
97C3×C4×C5—41no—
98C3×C4×C5—161no—
99C5×Dic3—161no—
100C22×A4C5×D411yescharacteristic
101C4×A4—41no—
102C4×A4C2×C4×C511yescharacteristic
103C4×A4C5×Q811yescharacteristic
104SL(2,ℤ/4)—41no—
105C3×C4⋊C4—41no—
106C4⋊Dic3—41no—
107C2×C3⋊C8—41no—
108C23×C5—31no—
109C23×C5—31no—
110C23×C5—31no—
111C23×C5—31no—
112C23×C5Dic3⋊C411yescharacteristic
113C23×C5#21411yescharacteristic
114C23×C5#21511yescharacteristic
115C2×C4×C5—21no—
116C2×C4×C5—31no—
117C2×C4×C5—31no—
118C2×C4×C5—31no—
119C2×C4×C5—31no—
120C2×C4×C5—31no—
121C2×C4×C5—31no—
122C2×C4×C5—31no—
123C2×C4×C5—61no—
124C2×C4×C5—61no—
125C2×C4×C5—121no—
126C2×C4×C5—121no—
127C2×C4×C5—121no—
128C2×C4×C5—121no—
129C2×C4×C5—121no—
130C2×C4×C5—121no—
131C2×C4×C5—121no—
132C2×C4×C5—121no—
133C2×C4×C5—121no—
134C2×C4×C5—121no—
135C2×C4×C5C2×S411yescharacteristic
136C5×C8—62no—
137C5×C8—62no—
138C23×C4—21no—
139C23×C4C2×C5×D311yescharacteristic
140C22×C8—31no—
141C22×C8—31no—
142C2×C4⋊C4—31no—
143C2×C4⋊C4—31no—
144C2×C4⋊C4—31no—
145C2×C4⋊C4—31no—
146C2×C4⋊C4—61no—
147C2×C22⋊C4—61no—
148#106—62no—
149#106—61no—
150#106—61no—
151C22⋊C8—32no—
152C22⋊C8—32no—
153#95—61no—
154C2×C3×C5—41no—
155C2×C3×C5—41no—
156C2×C3×C5—41no—
157C2×A4C5×C4⋊C411yescharacteristic
158C2×A4C5×SD1611yescharacteristic
159C2×A4C5×SD1611yescharacteristic
160C2×C3×C4—41no—
161C2×C3×C4—81no—
162C2×Dic3—81no—
163C3⋊C8—42no—
164C22×C5—31no—
165C22×C5—31no—
166C22×C5—31no—
167C22×C5—31no—
168C22×C5—31no—
169C22×C5—31no—
170C22×C5—31no—
171C22×C5—31no—
172C22×C5—31no—
173C22×C5—61no—
174C22×C5#80811yescharacteristic, complemented
175C22×C5GL(2,ℤ/4)11yescharacteristic
176C4×C5—31no—
177C4×C5—31no—
178C4×C5—41no—
179C4×C5—121no—
180C4×C5—241no—
181C4×C5—241no—
182C4×C5A4⋊Q811yescharacteristic
183C4×C5C4×S411yescharacteristic
184C24C5×#6711yescharacteristic
185C22×C4—31no—
186C22×C4—31no—
187C22×C4—31no—
188C22×C4—31no—
189C22×C4—41no—
190C22×C4—61no—
191C22×C4—61no—
192C22×C4—61no—
193C22×C4—61no—
194C22×C4—121no—
195C22×C4C5×Dic611yescharacteristic
196C22×C4C4×C5×D311yescharacteristic
197C2×C8—32no—
198C2×C8—32no—
199C2×C8—61no—
200C2×C8—61no—
201C2×C8—61no—
202C2×C8—61no—
203C4⋊C4—32no—
204C4⋊C4—31no—
205C4⋊C4—61no—
206C4⋊C4—61no—
207C4⋊C4—61no—
208C4⋊C4—61no—
209C4⋊C4—61no—
210C4⋊C4C5×S411yescharacteristic
211C22⋊C4—121no—
212C22⋊C4—121no—
213C3×C5—41noHall
214C22×C3—41no—
215A4C5×#10611yescharacteristic, complemented
216C3×C4—41no—
217C3×C4—41no—
218C3×C4—161no—
219Dic3—161no—
220C2×C5—31no—
221C2×C5—31no—
222C2×C5—31no—
223C2×C5—31no—
224C2×C5SL(2,ℤ/4)⋊C411yescharacteristic
225C2×C5#541411yescharacteristic
226C2×C5#541711yescharacteristic
227C23—31no—
228C23—31no—
229C23—31no—
230C23—31no—
231C23C5×Dic3⋊C411yescharacteristic
232C23C5×#21411yescharacteristic
233C23C5×#21511yescharacteristic
234C2×C4—21no—
235C2×C4—31no—
236C2×C4—31no—
237C2×C4—31no—
238C2×C4—31no—
239C2×C4—31no—
240C2×C4—31no—
241C2×C4—31no—
242C2×C4—61no—
243C2×C4—61no—
244C2×C4—121no—
245C2×C4—121no—
246C2×C4—121no—
247C2×C4—121no—
248C2×C4—121no—
249C2×C4—121no—
250C2×C4—121no—
251C2×C4—121no—
252C2×C4—121no—
253C2×C4—121no—
254C2×C4C2×C5×S411yescharacteristic
255C8—62no—
256C8—62no—
257C2×C3—41no—
258C2×C3—41no—
259C2×C3—41no—
260C5#7305111yescharacteristic, direct product factor, Sylow
261C22—31no—
262C22—31no—
263C22—31no—
264C22—31no—
265C22—31no—
266C22—31no—
267C22—31no—
268C22—31no—
269C22—31no—
270C22—61no—
271C22C5×#80811yescharacteristic, complemented
272C22C5×GL(2,ℤ/4)11yescharacteristic
273C4—31no—
274C4—31no—
275C4—41no—
276C4—121no—
277C4—241no—
278C4—241no—
279C4C5×A4⋊Q811yescharacteristic
280C4C4×C5×S411yescharacteristic
281C3—41noSylow
282C2—31no—
283C2—31no—
284C2—31no—
285C2—31no—
286C2C5×SL(2,ℤ/4)⋊C411yescharacteristic
287C2C5×#541411yescharacteristic
288C2C5×#541711yescharacteristic
subgroupG/H
centerC22×C5GL(2,ℤ/4)
commutatorC4×A4C2×C4×C5
FrattiniC2×C4C2×C5×S4
FittingC22×C5×C4⋊C4D3
socleC24×C5#67
prime radicalC22×C5×A4D4
cosocleC2×C4×A4C22×C5
hypercenterC5×C4⋊C4S4
hypocenterA4C5×#106
LCSG ▷ C4×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C5×C4⋊C4

Complements

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

NH ≅ G/Ntype
8. C5×A4⋊C8C4semidirect
10. #73051C5direct (N × H)
56. A4⋊C8C4×C5semidirect
95. C5×A4#106semidirect
174. C22×C5#808semidirect
215. A4C5×#106semidirect
260. C5#73051direct (N × H)
271. C22C5×#808semidirect

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
C2×C5×A4⋊C82
C5×#18533
C5×#8084
#730515