Finite Group Databasebeta

← C5×#2852⋊C3 #14510941

Subgroups — C5×#2852⋊C3 #14510941

Order 1920.

274 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 42 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×#126⋊C3C211yesmaximal, characteristic, complemented
2C22×C5×C42⋊C3C211yesmaximal, characteristic, complemented
3C5×#383⋊C3C211yesmaximal, characteristic, complemented
4C5×#2852C311yesmaximal, characteristic, complemented, Hall
5C5×D4×A4—41nomaximal
6C5×#126⋊C3—21no—
7C2×C5×C42⋊C3—21no—
8C2×C5×C42⋊C3C2211yescharacteristic
9#2852⋊C3C511yesmaximal, characteristic, direct product factor, Hall
10C2×C5×#126C2×C311yescharacteristic, complemented
11C22×C42×C5C2×C311yescharacteristic, complemented
12C5×#388—31no—
13C5×#387—31no—
14C5×#386—31no—
15C5×#385—31no—
16C5×#383C2×C311yescharacteristic, complemented
17C22×C5×A4—41no—
18C22×C5×A4—41no—
19C4×C5×A4—41no—
20C5×C42⋊C3D411yescharacteristic, complemented
21C2×#126⋊C3C2×C511yescharacteristic, complemented
22C22×C42⋊C3C2×C511yescharacteristic, complemented
23#383⋊C3C2×C511yescharacteristic, complemented
24C22×C5×D4A411yescharacteristic
25C23×C4×C5—31no—
26C5×#126—21no—
27C5×#126—61no—
28C2×C5×C4⋊C4—31no—
29C2×C5×C4⋊C4—31no—
30C2×C5×C22⋊C4—31no—
31C2×C5×C22⋊C4—31no—
32C2×C5×C22⋊C4—31no—
33C2×C42×C5—21no—
34C2×C42×C5—31no—
35C2×C42×C5—61no—
36C2×C42×C5C22×C311yescharacteristic
37C5×#95—31no—
38C5×#95—31no—
39C5×#95—31no—
40C5×#95—31no—
41#2852C3×C511yescharacteristic, complemented, Sylow
42C2×C5×A4—41no—
43C2×C5×A4—81no—
44C2×C5×A4—81no—
45C3×C5×D4—161no—
46D4×A4—41no—
47#126⋊C3—21no—
48C2×C42⋊C3—21no—
49C2×C42⋊C3C22×C511yescharacteristic
50C24×C5C2×A411yescharacteristic
51C24×C5C2×A411yescharacteristic
52C2×C5×D4—61no—
53C2×C5×D4—61no—
54C22×C4×C5—31no—
55C22×C4×C5—31no—
56C22×C4×C5—31no—
57C22×C4×C5—31no—
58C22×C4×C5—61no—
59C22×C4×C5—61no—
60C22×C4×C5—62no—
61C22×C4×C5—61no—
62C22×C4×C5—61no—
63C22×C4×C5C2×A411yescharacteristic
64C5×C4⋊C4—61no—
65C5×C4⋊C4—61no—
66C5×C4⋊C4—62no—
67C5×C22⋊C4—61no—
68C5×C22⋊C4—61no—
69C5×C22⋊C4—62no—
70C5×C22⋊C4—61no—
71C5×C22⋊C4—61no—
72C42×C5—31no—
73C42×C5—61no—
74C42×C5—61no—
75C42×C5C3×D411yescharacteristic, complemented
76C2×#126C2×C3×C511yescharacteristic, complemented
77C22×C42C2×C3×C511yescharacteristic, complemented
78#388—31no—
79#387—31no—
80#386—31no—
81#385—31no—
82#383C2×C3×C511yescharacteristic, complemented
83C22×C3×C5—161no—
84C22×C3×C5—161no—
85C5×A4—41no—
86C3×C4×C5—161no—
87C22×A4—41no—
88C22×A4—41no—
89C4×A4—41no—
90C42⋊C3C5×D411yescharacteristic, complemented
91C23×C5—21no—
92C23×C5—21no—
93C23×C5—31no—
94C23×C5—31no—
95C23×C5—61no—
96C23×C5—61no—
97C23×C5—61no—
98C23×C5C22×A411yescharacteristic
99C5×D4—41no—
100C5×D4—121no—
101C2×C4×C5—32no—
102C2×C4×C5—31no—
103C2×C4×C5—31no—
104C2×C4×C5—61no—
105C2×C4×C5—61no—
106C2×C4×C5—61no—
107C2×C4×C5—61no—
108C2×C4×C5—62no—
109C2×C4×C5—62no—
110C2×C4×C5—62no—
111C2×C4×C5—62no—
112C2×C4×C5—61no—
113C2×C4×C5—61no—
114C2×C4×C5—61no—
115C2×C4×C5—61no—
116C2×C4×C5—61no—
117C2×C4×C5—61no—
118C2×C4×C5—61no—
119C22×D4C5×A411yescharacteristic
120C23×C4—31no—
121#126—21no—
122#126—61no—
123C2×C4⋊C4—31no—
124C2×C4⋊C4—31no—
125C2×C22⋊C4—31no—
126C2×C22⋊C4—31no—
127C2×C22⋊C4—31no—
128C2×C42—21no—
129C2×C42—31no—
130C2×C42—61no—
131C2×C42C22×C3×C511yescharacteristic
132#95—31no—
133#95—31no—
134#95—31no—
135#95—31no—
136C2×C3×C5—161no—
137C2×C3×C5—321no—
138C2×C3×C5—321no—
139C2×A4—41no—
140C2×A4—81no—
141C2×A4—81no—
142C3×D4—161no—
143C22×C5—31no—
144C22×C5—31no—
145C22×C5—31no—
146C22×C5—41no—
147C22×C5—61no—
148C22×C5—61no—
149C22×C5—61no—
150C22×C5—61no—
151C22×C5—121no—
152C22×C5—121no—
153C22×C5#126⋊C311yescharacteristic, complemented
154C22×C5D4×A411yescharacteristic
155C4×C5—41no—
156C4×C5—62no—
157C4×C5—61no—
158C4×C5—61no—
159C4×C5—121no—
160C4×C5—121no—
161C24C2×C5×A411yescharacteristic
162C24C2×C5×A411yescharacteristic
163C2×D4—61no—
164C2×D4—61no—
165C22×C4—31no—
166C22×C4—31no—
167C22×C4—31no—
168C22×C4—31no—
169C22×C4—61no—
170C22×C4—61no—
171C22×C4—62no—
172C22×C4—61no—
173C22×C4—61no—
174C22×C4C2×C5×A411yescharacteristic
175C4⋊C4—61no—
176C4⋊C4—61no—
177C4⋊C4—62no—
178C22⋊C4—61no—
179C22⋊C4—61no—
180C22⋊C4—62no—
181C22⋊C4—61no—
182C22⋊C4—61no—
183C42—31no—
184C42—61no—
185C42—61no—
186C42C3×C5×D411yescharacteristic, complemented
187C3×C5—161noHall
188C22×C3—161no—
189C22×C3—161no—
190A4—41no—
191C3×C4—161no—
192C2×C5—21no—
193C2×C5—31no—
194C2×C5—31no—
195C2×C5—61no—
196C2×C5—81no—
197C2×C5C2×#126⋊C311yescharacteristic
198C23—21no—
199C23—21no—
200C23—31no—
201C23—31no—
202C23—61no—
203C23—61no—
204C23—61no—
205C23C22×C5×A411yescharacteristic
206D4—41no—
207D4—121no—
208C2×C4—32no—
209C2×C4—31no—
210C2×C4—31no—
211C2×C4—61no—
212C2×C4—61no—
213C2×C4—61no—
214C2×C4—61no—
215C2×C4—62no—
216C2×C4—62no—
217C2×C4—62no—
218C2×C4—62no—
219C2×C4—61no—
220C2×C4—61no—
221C2×C4—61no—
222C2×C4—61no—
223C2×C4—61no—
224C2×C4—61no—
225C2×C4—61no—
226C2×C3—161no—
227C2×C3—321no—
228C2×C3—321no—
229C5#2852⋊C311yescharacteristic, direct product factor, Sylow
230C22—31no—
231C22—31no—
232C22—31no—
233C22—41no—
234C22—61no—
235C22—61no—
236C22—61no—
237C22—61no—
238C22—121no—
239C22—121no—
240C22C5×#126⋊C311yescharacteristic, complemented
241C22C5×D4×A411yescharacteristic
242C4—41no—
243C4—62no—
244C4—61no—
245C4—61no—
246C4—121no—
247C4—121no—
248C3—161noSylow
249C2—21no—
250C2—31no—
251C2—31no—
252C2—61no—
253C2—81no—
254C2C2×C5×#126⋊C311yescharacteristic
subgroupG/H
centerC2×C5C2×#126⋊C3
commutator, cosocleC2×C42C22×C3×C5
FrattiniC23C22×C5×A4
FittingC5×#2852C3
socleC23×C5C22×A4
hypercenterC22×C5#126⋊C3
hypocenterC42C3×C5×D4
LCSG ▷ C2×C42 ▷ C42
UCSC1 ◁ C2×C5 ◁ C22×C5

Complements

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

NH ≅ G/Ntype
1. C2×C5×#126⋊C3C2semidirect
2. C22×C5×C42⋊C3C2semidirect
3. C5×#383⋊C3C2semidirect
4. C5×#2852C3semidirect
9. #2852⋊C3C5direct (N × H)
10. C2×C5×#126C2×C3semidirect
11. C22×C42×C5C2×C3semidirect
16. C5×#383C2×C3semidirect
20. C5×C42⋊C3D4semidirect
21. C2×#126⋊C3C2×C5semidirect
22. C22×C42⋊C3C2×C5semidirect
23. #383⋊C3C2×C5semidirect
41. #2852C3×C5semidirect
75. C42×C5C3×D4semidirect
76. C2×#126C2×C3×C5semidirect
77. C22×C42C2×C3×C5semidirect
82. #383C2×C3×C5semidirect
90. C42⋊C3C5×D4semidirect
153. C22×C5#126⋊C3semidirect
186. C42C3×C5×D4semidirect
229. C5#2852⋊C3direct (N × H)
240. C22C5×#126⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#126⋊C32
C22×C5×C42⋊C32
C5×#383⋊C32
C5×#28523
C5×D4×A44
#2852⋊C35