Finite Group Databasebeta

← C5×#2848⋊C3 #14510940

Subgroups — C5×#2848⋊C3 #14510940

Order 1920.

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

normal subgroups only

This group has 436 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
1C4×C5×C22⋊A4C211yesmaximal, characteristic
2C5×#379⋊C3C212yesmaximal
3C5×#2848C311yesmaximal, characteristic, complemented, Hall
4C2×C5×C22⋊A4C2211yescharacteristic
5C5×Q8×A4—41nomaximal
6#2848⋊C3C511yesmaximal, characteristic, direct product factor, Hall
7C24×C4×C5C2×C311yescharacteristic
8C2×C5×C22⋊Q8—31no—
9C5×#385—32no—
10C5×#380—31no—
11C5×#379C2×C312yes—
12C5×C22⋊A4Q811yescharacteristic, complemented
13C4×C5×A4—41no—
14C4×C5×A4—42no—
15C4×C5×A4—82no—
16C4×C22⋊A4C2×C511yescharacteristic
17#379⋊C3C2×C512yes—
18C25×C5C22×C311yescharacteristic
19C22×C5×Q8A411yescharacteristic, complemented
20C23×C4×C5—31no—
21C23×C4×C5—31no—
22C23×C4×C5—62no—
23C23×C4×C5—62no—
24C5×C22⋊Q8—62no—
25C5×C22⋊Q8—62no—
26C2×C5×C4⋊C4—31no—
27C2×C5×C4⋊C4—32no—
28C2×C5×C22⋊C4—32no—
29C2×C5×C22⋊C4—32no—
30C5×#95—32no—
31#2848C3×C511yescharacteristic, complemented, Sylow
32C2×C5×A4—41no—
33C2×C5×A4—82no—
34C3×C5×Q8—161no—
35C2×C22⋊A4C22×C511yescharacteristic
36Q8×A4—41no—
37C24×C5—31no—
38C24×C5—31no—
39C24×C5—62no—
40C24×C5—62no—
41C24×C5C3×Q811yescharacteristic, complemented
42C2×C5×Q8—61no—
43C2×C5×Q8—61no—
44C22×C4×C5—22no—
45C22×C4×C5—32no—
46C22×C4×C5—32no—
47C22×C4×C5—31no—
48C22×C4×C5—32no—
49C22×C4×C5—62no—
50C22×C4×C5—62no—
51C22×C4×C5—64no—
52C22×C4×C5—62no—
53C22×C4×C5—62no—
54C22×C4×C5—64no—
55C22×C4×C5—62no—
56C22×C4×C5—62no—
57C22×C4×C5C2×A411yescharacteristic
58C22×C4×C5C2×A412yes—
59C5×C4⋊C4—61no—
60C5×C4⋊C4—61no—
61C5×C4⋊C4—64no—
62C5×C22⋊C4—64no—
63C5×C22⋊C4—64no—
64C24×C4C2×C3×C511yescharacteristic
65C2×C22⋊Q8—31no—
66#385—32no—
67#380—31no—
68#379C2×C3×C512yes—
69C5×A4—41no—
70C5×A4—82no—
71C3×C4×C5—162no—
72C3×C4×C5—161no—
73C22⋊A4C5×Q811yescharacteristic, complemented
74C4×A4—42no—
75C4×A4—41no—
76C4×A4—82no—
77C23×C5—22no—
78C23×C5—32no—
79C23×C5—32no—
80C23×C5—31no—
81C23×C5—31no—
82C23×C5—62no—
83C23×C5—62no—
84C23×C5—62no—
85C23×C5—62no—
86C23×C5—62no—
87C23×C5—64no—
88C23×C5—62no—
89C23×C5—62no—
90C23×C5—64no—
91C23×C5C22×A411yescharacteristic
92C5×Q8—41no—
93C5×Q8—121no—
94C2×C4×C5—31no—
95C2×C4×C5—31no—
96C2×C4×C5—32no—
97C2×C4×C5—62no—
98C2×C4×C5—64no—
99C2×C4×C5—62no—
100C2×C4×C5—62no—
101C2×C4×C5—64no—
102C2×C4×C5—62no—
103C2×C4×C5—62no—
104C2×C4×C5—62no—
105C2×C4×C5—62no—
106C2×C4×C5—64no—
107C25C22×C3×C511yescharacteristic
108C22×Q8C5×A411yescharacteristic, complemented
109C23×C4—31no—
110C23×C4—31no—
111C23×C4—62no—
112C23×C4—62no—
113C22⋊Q8—62no—
114C22⋊Q8—62no—
115C2×C4⋊C4—31no—
116C2×C4⋊C4—32no—
117C2×C22⋊C4—32no—
118C2×C22⋊C4—32no—
119#95—32no—
120C2×C3×C5—161no—
121C2×A4—41no—
122C2×A4—82no—
123C3×Q8—161no—
124C22×C5—22no—
125C22×C5—31no—
126C22×C5—31no—
127C22×C5—32no—
128C22×C5—32no—
129C22×C5—62no—
130C22×C5—64no—
131C22×C5—62no—
132C22×C5—62no—
133C22×C5—62no—
134C22×C5—62no—
135C22×C5—62no—
136C22×C5—64no—
137C22×C5—62no—
138C22×C5Q8×A411yescharacteristic
139C4×C5—31no—
140C4×C5—42no—
141C4×C5—62no—
142C4×C5—122no—
143C4×C5#120⋊C311yescharacteristic
144C24—31no—
145C24—31no—
146C24—62no—
147C24—62no—
148C24C3×C5×Q811yescharacteristic, complemented
149C2×Q8—61no—
150C2×Q8—61no—
151C22×C4—22no—
152C22×C4—32no—
153C22×C4—32no—
154C22×C4—31no—
155C22×C4—32no—
156C22×C4—62no—
157C22×C4—62no—
158C22×C4—64no—
159C22×C4—62no—
160C22×C4—62no—
161C22×C4—64no—
162C22×C4—62no—
163C22×C4—62no—
164C22×C4C2×C5×A411yescharacteristic
165C22×C4C2×C5×A412yes—
166C4⋊C4—61no—
167C4⋊C4—61no—
168C4⋊C4—64no—
169C22⋊C4—64no—
170C22⋊C4—64no—
171C3×C5—161noHall
172A4—41no—
173A4—82no—
174C3×C4—162no—
175C3×C4—161no—
176C2×C5—31no—
177C2×C5—31no—
178C2×C5—62no—
179C2×C5—62no—
180C2×C5C2×#120⋊C311yescharacteristic
181C23—22no—
182C23—32no—
183C23—32no—
184C23—31no—
185C23—31no—
186C23—62no—
187C23—62no—
188C23—62no—
189C23—62no—
190C23—62no—
191C23—64no—
192C23—62no—
193C23—62no—
194C23—64no—
195C23C22×C5×A411yescharacteristic
196Q8—41no—
197Q8—121no—
198C2×C4—31no—
199C2×C4—31no—
200C2×C4—32no—
201C2×C4—62no—
202C2×C4—64no—
203C2×C4—62no—
204C2×C4—62no—
205C2×C4—64no—
206C2×C4—62no—
207C2×C4—62no—
208C2×C4—62no—
209C2×C4—62no—
210C2×C4—64no—
211C2×C3—161no—
212C5#2848⋊C311yescharacteristic, direct product factor, Sylow
213C22—22no—
214C22—31no—
215C22—31no—
216C22—32no—
217C22—32no—
218C22—62no—
219C22—64no—
220C22—62no—
221C22—62no—
222C22—62no—
223C22—62no—
224C22—62no—
225C22—64no—
226C22—62no—
227C22C5×Q8×A411yescharacteristic
228C4—31no—
229C4—42no—
230C4—62no—
231C4—122no—
232C4C5×#120⋊C311yescharacteristic
233C3—161noSylow
234C2—31no—
235C2—31no—
236C2—62no—
237C2—62no—
238C2C2×C5×#120⋊C311yescharacteristic
subgroupG/H
centerC2×C5C2×#120⋊C3
commutator, cosocleC25C22×C3×C5
FrattiniC23C22×C5×A4
FittingC5×#2848C3
socleC23×C5C22×A4
prime radicalC2×C5×C22⋊A4C22
hypercenterC4×C5#120⋊C3
hypocenterC24C3×C5×Q8
LCSG ▷ C25 ▷ C24
UCSC1 ◁ C2×C5 ◁ C4×C5

Complements

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

NH ≅ G/Ntype
3. C5×#2848C3semidirect
6. #2848⋊C3C5direct (N × H)
12. C5×C22⋊A4Q8semidirect
19. C22×C5×Q8A4semidirect
31. #2848C3×C5semidirect
41. C24×C5C3×Q8semidirect
73. C22⋊A4C5×Q8semidirect
108. C22×Q8C5×A4semidirect
148. C24C3×C5×Q8semidirect
212. C5#2848⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C5×C22⋊A42
C5×#379⋊C32
C5×#28483
C5×Q8×A44
#2848⋊C35