Finite Group Databasebeta

← C5×#72989 #14510713

Subgroups — C5×#72989 #14510713

Order 1920.

354 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 28 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×#5936C212yesmaximal
2C5×#379⋊C3C211yesmaximal, characteristic
3C5×#2029—31nomaximal, Hall
4C2×C5×C22⋊A4C2211yescharacteristic
5C5×A4⋊Q8—41nomaximal
6#72989C511yesmaximal, characteristic, direct product factor, Hall
7C5×#543—31no—
8C5×#379—32no—
9C5×#379D311yescharacteristic
10C5×#342—32no—
11C5×#342—31no—
12C5×C22⋊A4Q811yescharacteristic, complemented
13C4×C5×A4—41no—
14C5×SL(2,ℤ/4)—42no—
15C5×SL(2,ℤ/4)—82no—
16#5936C2×C512yes—
17#379⋊C3C2×C511yescharacteristic
18C25×C5C2×D311yescharacteristic
19C5×C22⋊Q8—62no—
20C5×C22⋊Q8—62no—
21C5×C22⋊Q8—61no—
22C5×C22⋊Q8—61no—
23C2×C5×C22⋊C4—32no—
24C2×C5×C22⋊C4—31no—
25C2×C5×C22⋊C4—31no—
26C2×C5×C22⋊C4—32no—
27C2×C5×C22⋊C4—62no—
28C2×C5×C22⋊C4—62no—
29#2029—31noSylow
30C2×C5×A4—41no—
31C2×C5×A4—82no—
32C5×Dic6—161no—
33C2×C22⋊A4C22×C511yescharacteristic
34A4⋊Q8—41no—
35C24×C5—31no—
36C24×C5—31no—
37C24×C5—62no—
38C24×C5—62no—
39C24×C5Dic611yescharacteristic, complemented
40C2×C5×Q8—61no—
41C2×C5×Q8—61no—
42C22×C4×C5—32no—
43C22×C4×C5—32no—
44C22×C4×C5—31no—
45C22×C4×C5—62no—
46C22×C4×C5S411yescharacteristic
47C5×C4⋊C4—61no—
48C5×C4⋊C4—62no—
49C5×C4⋊C4—62no—
50C5×C4⋊C4—61no—
51C5×C22⋊C4—62no—
52C5×C22⋊C4—62no—
53C5×C22⋊C4—62no—
54C5×C22⋊C4—62no—
55C5×C22⋊C4—62no—
56C5×C22⋊C4—62no—
57C5×C22⋊C4—122no—
58C5×C22⋊C4—122no—
59C5×C22⋊C4—122no—
60C5×C22⋊C4—122no—
61#543—31no—
62#379—32no—
63#379C5×D311yescharacteristic
64#342—32no—
65#342—31no—
66C5×A4—41no—
67C5×A4—82no—
68C3×C4×C5—161no—
69C5×Dic3—162no—
70C22⋊A4C5×Q811yescharacteristic, complemented
71C4×A4—41no—
72SL(2,ℤ/4)—42no—
73SL(2,ℤ/4)—82no—
74C23×C5—22no—
75C23×C5—32no—
76C23×C5—32no—
77C23×C5—31no—
78C23×C5—31no—
79C23×C5—62no—
80C23×C5—62no—
81C23×C5—62no—
82C23×C5—62no—
83C23×C5—62no—
84C23×C5—121no—
85C23×C5—121no—
86C23×C5—122no—
87C23×C5—122no—
88C23×C5C2×S411yescharacteristic
89C5×Q8—241no—
90C5×Q8—241no—
91C2×C4×C5—61no—
92C2×C4×C5—61no—
93C2×C4×C5—62no—
94C2×C4×C5—62no—
95C2×C4×C5—121no—
96C2×C4×C5—122no—
97C2×C4×C5—122no—
98C2×C4×C5—122no—
99C2×C4×C5—122no—
100C2×C4×C5—122no—
101C25C2×C5×D311yescharacteristic
102C22⋊Q8—62no—
103C22⋊Q8—62no—
104C22⋊Q8—61no—
105C22⋊Q8—61no—
106C2×C22⋊C4—32no—
107C2×C22⋊C4—31no—
108C2×C22⋊C4—31no—
109C2×C22⋊C4—32no—
110C2×C22⋊C4—62no—
111C2×C22⋊C4—62no—
112C2×C3×C5—161no—
113C2×A4—41no—
114C2×A4—82no—
115Dic6—161no—
116C22×C5—22no—
117C22×C5—31no—
118C22×C5—31no—
119C22×C5—32no—
120C22×C5—32no—
121C22×C5—62no—
122C22×C5—62no—
123C22×C5—62no—
124C22×C5—62no—
125C22×C5—62no—
126C22×C5—122no—
127C22×C5—121no—
128C22×C5—121no—
129C22×C5—122no—
130C22×C5A4⋊Q811yescharacteristic
131C4×C5—41no—
132C4×C5—121no—
133C4×C5—122no—
134C4×C5—122no—
135C4×C5—242no—
136C24—31no—
137C24—31no—
138C24—62no—
139C24—62no—
140C24C5×Dic611yescharacteristic, complemented
141C2×Q8—61no—
142C2×Q8—61no—
143C22×C4—32no—
144C22×C4—32no—
145C22×C4—31no—
146C22×C4—62no—
147C22×C4C5×S411yescharacteristic
148C4⋊C4—61no—
149C4⋊C4—62no—
150C4⋊C4—62no—
151C4⋊C4—61no—
152C22⋊C4—62no—
153C22⋊C4—62no—
154C22⋊C4—62no—
155C22⋊C4—62no—
156C22⋊C4—62no—
157C22⋊C4—62no—
158C22⋊C4—122no—
159C22⋊C4—122no—
160C22⋊C4—122no—
161C22⋊C4—122no—
162C3×C5—161noHall
163A4—41no—
164A4—82no—
165C3×C4—161no—
166Dic3—162no—
167C2×C5—31no—
168C2×C5—31no—
169C2×C5—62no—
170C2×C5—62no—
171C2×C5#1020⋊C211yescharacteristic
172C23—22no—
173C23—32no—
174C23—32no—
175C23—31no—
176C23—31no—
177C23—62no—
178C23—62no—
179C23—62no—
180C23—62no—
181C23—62no—
182C23—121no—
183C23—121no—
184C23—122no—
185C23—122no—
186C23C2×C5×S411yescharacteristic
187Q8—241no—
188Q8—241no—
189C2×C4—61no—
190C2×C4—61no—
191C2×C4—62no—
192C2×C4—62no—
193C2×C4—121no—
194C2×C4—122no—
195C2×C4—122no—
196C2×C4—122no—
197C2×C4—122no—
198C2×C4—122no—
199C2×C3—161no—
200C5#7298911yescharacteristic, direct product factor, Sylow
201C22—22no—
202C22—31no—
203C22—31no—
204C22—32no—
205C22—32no—
206C22—62no—
207C22—62no—
208C22—62no—
209C22—62no—
210C22—62no—
211C22—122no—
212C22—121no—
213C22—121no—
214C22—122no—
215C22C5×A4⋊Q811yescharacteristic
216C4—41no—
217C4—121no—
218C4—122no—
219C4—122no—
220C4—242no—
221C3—161noSylow
222C2—31no—
223C2—31no—
224C2—62no—
225C2—62no—
226C2C5×#1020⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2×C5#1020⋊C2
commutator, cosocleC2×C22⋊A4C22×C5
FrattiniC23C2×C5×S4
FittingC5×#379D3
socleC23×C5C2×S4
prime radicalC2×C5×C22⋊A4C22
hypocenterC22⋊A4C5×Q8
LCSG ▷ C2×C22⋊A4 ▷ C22⋊A4
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
6. #72989C5direct (N × H)
12. C5×C22⋊A4Q8semidirect
39. C24×C5Dic6semidirect
70. C22⋊A4C5×Q8semidirect
140. C24C5×Dic6semidirect
200. C5#72989direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#59362
C5×#379⋊C32
C5×#20293
C5×A4⋊Q84
#729895