Finite Group Databasebeta

← C5×A4×#101 #14510956

Subgroups — C5×A4×#101 #14510956

Order 1920.

372 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 72 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×Q8×A4C211yesmaximal, characteristic
2C5×A4×M16C212yesmaximal
3C22×C5×#101C311yesmaximal, characteristic, complemented, Hall
4C5×Q8×A4—22no—
5C2×C4×C5×A4C412yes—
6C2×C4×C5×A4C2211yescharacteristic
7C5×C8×A4—22no—
8C3×C5×#101—41nomaximal
9A4×#101C511yesmaximal, characteristic, direct product factor, Hall
10C23×C5×Q8C2×C311yescharacteristic
11C22×C5×M16C2×C312yes—
12C2×C5×#101—31no—
13C2×C5×#101—32no—
14C2×C5×#101—31no—
15C22×C5×A4C2×C411yescharacteristic
16C2×C3×C5×Q8—41no—
17C4×C5×A4—22no—
18C4×C5×A4D412yes—
19C3×C5×M16—42no—
20C2×Q8×A4C2×C511yescharacteristic
21A4×M16C2×C512yes—
22C22×C5×Q8—22no—
23C22×C5×Q8—31no—
24C22×C5×Q8—32no—
25C22×C5×Q8—31no—
26C22×C5×Q8—62no—
27C23×C4×C5C3×C412yes—
28C23×C4×C5C22×C311yescharacteristic
29C2×C5×M16—32no—
30C2×C5×M16—32no—
31C2×C5×M16—62no—
32C22×C5×C8—22no—
33C5×#101—32no—
34C5×#101—31no—
35C5×#101—32no—
36C5×#101A411yescharacteristic, direct product factor
37C22×#101C3×C511yescharacteristic, complemented, Sylow
38C2×C5×A4—21no—
39C2×C5×A4C22⋊C411yescharacteristic
40C3×C5×Q8—82no—
41C2×C3×C4×C5—41no—
42C2×C3×C4×C5—42no—
43C3×C5×C8—82no—
44Q8×A4—22no—
45C2×C4×A4C4×C512yes—
46C2×C4×A4C22×C511yescharacteristic
47C8×A4—22no—
48C3×#101—41no—
49C24×C5C2×C3×C411yescharacteristic
50C2×C5×Q8—32no—
51C2×C5×Q8—32no—
52C2×C5×Q8—31no—
53C2×C5×Q8—62no—
54C2×C5×Q8—62no—
55C2×C5×Q8—62no—
56C2×C5×Q8—64no—
57C2×C5×Q8—62no—
58C2×C5×Q8—64no—
59C2×C5×Q8C2×A411yescharacteristic
60C22×C4×C5—22no—
61C22×C4×C5—31no—
62C22×C4×C5—32no—
63C22×C4×C5—31no—
64C22×C4×C5—32no—
65C22×C4×C5—32no—
66C22×C4×C5—62no—
67C22×C4×C5C3×D412yes—
68C5×M16—32no—
69C5×M16—62no—
70C5×M16—62no—
71C5×M16C2×A412yes—
72C2×C5×C8—62no—
73C2×C5×C8—62no—
74C23×Q8C2×C3×C511yescharacteristic
75C22×M16C2×C3×C512yes—
76C2×#101—31no—
77C2×#101—31no—
78C2×#101—32no—
79C22×C3×C5—41no—
80C5×A4#10111yescharacteristic, direct product factor
81C3×C4×C5—42no—
82C3×C4×C5—82no—
83C22×A4C2×C4×C511yescharacteristic
84C2×C3×Q8—41no—
85C4×A4—22no—
86C4×A4C5×D412yes—
87C3×M16—42no—
88C23×C5—21no—
89C23×C5—31no—
90C23×C5—31no—
91C23×C5—61no—
92C23×C5C3×C22⋊C411yescharacteristic
93C5×Q8—22no—
94C5×Q8—64no—
95C5×Q8—64no—
96C5×Q8—62no—
97C2×C4×C5—32no—
98C2×C4×C5—31no—
99C2×C4×C5—32no—
100C2×C4×C5—32no—
101C2×C4×C5—32no—
102C2×C4×C5—32no—
103C2×C4×C5—62no—
104C2×C4×C5—62no—
105C2×C4×C5—62no—
106C2×C4×C5—62no—
107C2×C4×C5C4×A412yes—
108C2×C4×C5C22×A411yescharacteristic
109C5×C8—22no—
110C5×C8—62no—
111C22×Q8—22no—
112C22×Q8—32no—
113C22×Q8—31no—
114C22×Q8—31no—
115C22×Q8—62no—
116C23×C4C3×C4×C512yes—
117C23×C4C22×C3×C511yescharacteristic
118C2×M16—32no—
119C2×M16—32no—
120C2×M16—62no—
121C22×C8—22no—
122#101—32no—
123#101—31no—
124#101—32no—
125#101C5×A411yescharacteristic, direct product factor
126C2×C3×C5—41no—
127C2×C3×C5—81no—
128C2×A4—21no—
129C2×A4C5×C22⋊C411yescharacteristic
130C3×Q8—82no—
131C2×C3×C4—42no—
132C2×C3×C4—41no—
133C3×C8—82no—
134C22×C5—31no—
135C22×C5—31no—
136C22×C5—31no—
137C22×C5—61no—
138C22×C5—61no—
139C22×C5—61no—
140C22×C5—61no—
141C22×C5C3×#10111yescharacteristic, complemented
142C22×C5C2×C4×A411yescharacteristic
143C4×C5—22no—
144C4×C5—32no—
145C4×C5—62no—
146C4×C5D4×A412yes—
147C24C2×C3×C4×C511yescharacteristic
148C2×Q8—32no—
149C2×Q8—32no—
150C2×Q8—31no—
151C2×Q8—62no—
152C2×Q8—62no—
153C2×Q8—62no—
154C2×Q8—64no—
155C2×Q8—62no—
156C2×Q8—64no—
157C2×Q8C2×C5×A411yescharacteristic
158C22×C4—22no—
159C22×C4—31no—
160C22×C4—32no—
161C22×C4—31no—
162C22×C4—32no—
163C22×C4—32no—
164C22×C4—62no—
165C22×C4C3×C5×D412yes—
166M16—32no—
167M16—62no—
168M16—62no—
169M16C2×C5×A412yes—
170C2×C8—62no—
171C2×C8—62no—
172C3×C5—41noHall
173C22×C3—41no—
174A4C5×#10111yescharacteristic, direct product factor
175C3×C4—42no—
176C3×C4—82no—
177C2×C5—21no—
178C2×C5—31no—
179C2×C5—31no—
180C2×C5—61no—
181C2×C5A4×C22⋊C411yescharacteristic
182C23—21no—
183C23—31no—
184C23—31no—
185C23—61no—
186C23C3×C5×C22⋊C411yescharacteristic
187Q8—22no—
188Q8—64no—
189Q8—64no—
190Q8—62no—
191C2×C4—32no—
192C2×C4—31no—
193C2×C4—32no—
194C2×C4—32no—
195C2×C4—32no—
196C2×C4—32no—
197C2×C4—62no—
198C2×C4—62no—
199C2×C4—62no—
200C2×C4—62no—
201C2×C4C4×C5×A412yes—
202C2×C4C22×C5×A411yescharacteristic
203C8—22no—
204C8—62no—
205C2×C3—41no—
206C2×C3—81no—
207C5A4×#10111yescharacteristic, direct product factor, Sylow
208C22—31no—
209C22—31no—
210C22—31no—
211C22—61no—
212C22—61no—
213C22—61no—
214C22—61no—
215C22C3×C5×#10111yescharacteristic, complemented
216C22C2×C4×C5×A411yescharacteristic
217C4—22no—
218C4—32no—
219C4—62no—
220C4C5×D4×A412yes—
221C3—41noSylow
222C2—21no—
223C2—31no—
224C2—31no—
225C2—61no—
226C2C5×A4×C22⋊C411yescharacteristic
subgroupG/H
centerC2×C5A4×C22⋊C4
commutatorC24C2×C3×C4×C5
FrattiniC2×C4C22×C5×A4
FittingC22×C5×#101C3
socleC23×C5C3×C22⋊C4
prime radicalC22×C5×A4C2×C4
cosocleC23×C4C22×C3×C5
hypercenterC5×#101A4
hypocenterC22C3×C5×#101
LCSG ▷ C24 ▷ C23 ▷ C22
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×#101

Complements

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

NH ≅ G/Ntype
3. C22×C5×#101C3semidirect
9. A4×#101C5direct (N × H)
36. C5×#101A4direct (N × H)
37. C22×#101C3×C5semidirect
80. C5×A4#101direct (N × H)
125. #101C5×A4direct (N × H)
141. C22×C5C3×#101semidirect
174. A4C5×#101direct (N × H)
207. C5A4×#101direct (N × H)
215. C22C3×C5×#101semidirect

Maximal subgroups

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

subgroupindex
C2×C5×Q8×A42
C5×A4×M162
C22×C5×#1013
C3×C5×#1014
A4×#1015