Finite Group Databasebeta

← C5×#7499 #11930219

Subgroups — C5×#7499 #11930219

Order 1280.

272 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 70 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×#356C212yesmaximal
2C5×#1956C211yesmaximal, characteristic
3C2×C5×C4⋊Q8C2211yescharacteristic
4C2×C5×#103—22no—
5C2×C5×#101—22no—
6C2×C4×C5×C8C411yescharacteristic
7C5×#384C411yescharacteristic
8C5×#356—22no—
9C5×#356C414yescomplemented
10#7499C511yesmaximal, characteristic, direct product factor, Sylow
11C22×C5×Q8D412yes—
12C2×C5×M16—42no—
13C22×C5×C8—21no—
14C5×C4⋊Q8—41no—
15C5×C4⋊Q8C2×C412yes—
16C5×C4⋊Q8D411yescharacteristic
17C5×C4⋊Q8Q811yescharacteristic
18C2×C5×C4⋊C4—21no—
19C2×C5×C4⋊C4—41no—
20C2×C5×C4⋊C4—41no—
21C2×C42×C5C2×C411yescharacteristic
22C5×#103—44no—
23C5×#101—24no—
24C5×#101—42no—
25C4×C5×C8—41no—
26C2×#356C2×C512yes—
27#1956C2×C511yescharacteristic
28C2×C5×Q8—22no—
29C2×C5×Q8—42no—
30C2×C5×Q8—42no—
31C2×C5×Q8C22⋊C412yes—
32C2×C5×Q8C4⋊C412yes—
33C22×C4×C5—21no—
34C22×C4×C5—22no—
35C22×C4×C5—41no—
36C22×C4×C5C22⋊C411yescharacteristic
37C5×M16—44no—
38C5×M16—82no—
39C2×C5×C8—22no—
40C2×C5×C8—41no—
41C2×C5×C8—41no—
42C2×C5×C8—82no—
43C5×C4⋊C4—42no—
44C5×C4⋊C4—41no—
45C5×C4⋊C4—41no—
46C5×C4⋊C4—42no—
47C5×C4⋊C4—82no—
48C42×C5—21no—
49C42×C5C4211yescharacteristic
50C42×C5C4⋊C411yescharacteristic
51C2×C4⋊Q8C22×C511yescharacteristic
52C2×#103—22no—
53C2×#101—22no—
54C2×C4×C8C4×C511yescharacteristic
55#384C4×C511yescharacteristic
56#356—22no—
57#356C4×C514yescomplemented
58C23×C5#9911yescharacteristic
59C5×Q8—42no—
60C5×Q8—42no—
61C5×Q8—82no—
62C2×C4×C5—22no—
63C2×C4×C5—22no—
64C2×C4×C5—21no—
65C2×C4×C5—21no—
66C2×C4×C5—21no—
67C2×C4×C5—21no—
68C2×C4×C5—22no—
69C2×C4×C5—22no—
70C2×C4×C5—42no—
71C2×C4×C5—42no—
72C2×C4×C5—82no—
73C2×C4×C5—81no—
74C2×C4×C5#9511yescharacteristic
75C2×C4×C5#9911yescharacteristic
76C5×C8—42no—
77C5×C8—84no—
78C22×Q8C5×D412yes—
79C2×M16—42no—
80C22×C8—21no—
81C4⋊Q8—41no—
82C4⋊Q8C2×C4×C512yes—
83C4⋊Q8C5×D411yescharacteristic
84C4⋊Q8C5×Q811yescharacteristic
85C2×C4⋊C4—21no—
86C2×C4⋊C4—41no—
87C2×C4⋊C4—41no—
88C2×C42C2×C4×C511yescharacteristic
89#103—44no—
90#101—24no—
91#101—42no—
92C4×C8—41no—
93C22×C5—21no—
94C22×C5—21no—
95C22×C5#34211yescharacteristic
96C22×C5#35311yescharacteristic
97C22×C5#35411yescharacteristic
98C4×C5—22no—
99C4×C5—22no—
100C4×C5—21no—
101C4×C5—21no—
102C4×C5—42no—
103C4×C5—42no—
104C4×C5—161no—
105C2×Q8—22no—
106C2×Q8—42no—
107C2×Q8—42no—
108C2×Q8C5×C22⋊C412yes—
109C2×Q8C5×C4⋊C412yes—
110C22×C4—21no—
111C22×C4—22no—
112C22×C4—41no—
113C22×C4C5×C22⋊C411yescharacteristic
114M16—44no—
115M16—82no—
116C2×C8—22no—
117C2×C8—41no—
118C2×C8—41no—
119C2×C8—82no—
120C4⋊C4—42no—
121C4⋊C4—41no—
122C4⋊C4—41no—
123C4⋊C4—42no—
124C4⋊C4—82no—
125C42—21no—
126C42C42×C511yescharacteristic
127C42C5×C4⋊C411yescharacteristic
128C2×C5—21no—
129C2×C5—21no—
130C2×C5#139311yescharacteristic
131C2×C5#141011yescharacteristic
132C2×C5#141111yescharacteristic
133C23C5×#9911yescharacteristic
134Q8—42no—
135Q8—42no—
136Q8—82no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—82no—
148C2×C4—81no—
149C2×C4C5×#9511yescharacteristic
150C2×C4C5×#9911yescharacteristic
151C8—42no—
152C8—84no—
153C5#749911yescharacteristic, direct product factor, Sylow
154C22—21no—
155C22—21no—
156C22C5×#34211yescharacteristic
157C22C5×#35311yescharacteristic
158C22C5×#35411yescharacteristic
159C4—22no—
160C4—22no—
161C4—21no—
162C4—21no—
163C4—42no—
164C4—42no—
165C4—161no—
166C2—21no—
167C2—21no—
168C2C5×#139311yescharacteristic
169C2C5×#141011yescharacteristic
170C2C5×#141111yescharacteristic
subgroupG/H
center, socleC22×C5#353
commutatorC42C42×C5
Frattini, cosocleC2×C4⋊Q8C22×C5
prime radicalC23×C5#99
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C5 ◁ C22×C4×C5 ◁ C2×C5×C4⋊Q8 ◁ G

Complements

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

NH ≅ G/Ntype
9. C5×#356C4semidirect
10. #7499C5direct (N × H)
57. #356C4×C5semidirect
153. C5#7499direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3562
C5×#19562
#74995