Finite Group Databasebeta

← C2×A5⋊C16 #14514765

Subgroups — C2×A5⋊C16 #14514765

Order 1920.

213 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 213 conjugacy classes of subgroups — too many to draw. Only its 25 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×C8×A5C211yesmaximal, characteristic
2A5⋊C16C212yesmaximal, direct product factor
3C2×C4×A5C411yescharacteristic
4C8×A5C411yescharacteristic
5C8×A5C2211yescharacteristic
6C2×A4⋊C16—51nomaximal, Hall
7C2×D5⋊C16—61nomaximal
8C22×A5C811yescharacteristic
9C4×A5C811yescharacteristic
10C4×A5C2×C411yescharacteristic
11C2×C8×A4—51no—
12C2×D3×C16—101nomaximal
13A4⋊C16—52no—
14C2×C8×D5—61no—
15C2×#674—62no—
16D5⋊C16—62no—
17D5⋊C16—62no—
18C2×C22⋊C16—151noSylow
19C2×A5C1612yescomplemented
20C2×A5C2×C811yescharacteristic
21C2×C4×A4—51no—
22C2×D3×C8—101no—
23C8×A4—51no—
24C8×A4—51no—
25C2×C3×C16—101no—
26C2×C3⋊C16—101no—
27D3×C16—102no—
28D3×C16—102no—
29C2×C4×D5—61no—
30C2×C5×C8—61no—
31C2×#168—61no—
32C8×D5—61no—
33C8×D5—61no—
34C8×D5—61no—
35C8×D5—61no—
36#674—64no—
37C23×C8—51no—
38C22×C16—151no—
39C22×C16—151no—
40C22⋊C16—152no—
41C22⋊C16—152no—
42A5C2×C1611yescharacteristic, complemented
43C22×A4—51no—
44C2×C4×D3—101no—
45C4×A4—51no—
46C4×A4—51no—
47C2×C3×C8—101no—
48C2×C3⋊C8—101no—
49D3×C8—101no—
50D3×C8—101no—
51D3×C8—101no—
52D3×C8—101no—
53C3×C16—102no—
54C3⋊C16—102no—
55C22×D5—61no—
56C2×C4×C5—61no—
57C2×Dic5—61no—
58C4×D5—61no—
59C4×D5—61no—
60C4×D5—61no—
61C4×D5—61no—
62C5×C8—61no—
63C5×C8—61no—
64#168—61no—
65#168—61no—
66C23×C4—51no—
67C22×C8—51no—
68C22×C8—51no—
69C22×C8—151no—
70C22×C8—151no—
71C22×C8—151no—
72C22×C8—151no—
73C2×C16—101no—
74C2×C16—152no—
75C2×C16—152no—
76C2×C16—301no—
77C2×C16—301no—
78C2×C16—301no—
79C22×D3—101no—
80C2×A4—52no—
81C2×A4—51no—
82C2×C3×C4—101no—
83C2×Dic3—101no—
84C4×D3—101no—
85C4×D3—101no—
86C4×D3—101no—
87C4×D3—101no—
88C3×C8—101no—
89C3×C8—101no—
90C3⋊C8—101no—
91C3⋊C8—101no—
92C22×C5—61no—
93C2×D5—61no—
94C2×D5—61no—
95C2×D5—62no—
96C2×D5—62no—
97C4×C5—61no—
98C4×C5—61no—
99Dic5—61no—
100Dic5—61no—
101C24—51no—
102C22×C4—51no—
103C22×C4—51no—
104C22×C4—151no—
105C22×C4—151no—
106C22×C4—151no—
107C22×C4—151no—
108C2×C8—151no—
109C2×C8—151no—
110C2×C8—151no—
111C2×C8—151no—
112C2×C8—151no—
113C2×C8—151no—
114C2×C8—151no—
115C2×C8—301no—
116C2×C8S511yescharacteristic
117C16—102no—
118C16—302no—
119C22×C3—101no—
120C2×D3—101no—
121C2×D3—101no—
122C2×D3—102no—
123C2×D3—102no—
124A4—51no—
125C3×C4—101no—
126C3×C4—101no—
127Dic3—101no—
128Dic3—101no—
129C2×C5—61no—
130C2×C5—62no—
131D5—61no—
132D5—62no—
133D5—61no—
134C23—51no—
135C23—52no—
136C23—151no—
137C23—151no—
138C23—152no—
139C2×C4—151no—
140C2×C4—151no—
141C2×C4—151no—
142C2×C4—151no—
143C2×C4—151no—
144C2×C4—151no—
145C2×C4—151no—
146C2×C4—301no—
147C2×C4A5⋊C411yescharacteristic
148C8—151no—
149C8—151no—
150C8A5⋊C411yescharacteristic
151C8C2×S511yescharacteristic
152C2×C3—101no—
153C2×C3—102no—
154D3—102no—
155D3—101no—
156D3—101no—
157C5—61noSylow
158C22—51no—
159C22—151no—
160C22—152no—
161C22—151no—
162C22—151no—
163C22—152no—
164C22—152no—
165C22—301no—
166C22A5⋊C811yescharacteristic
167C4—151no—
168C4—151no—
169C4A5⋊C811yescharacteristic
170C4C2×A5⋊C411yescharacteristic
171C3—101noSylow
172C2—151no—
173C2—151no—
174C2—152no—
175C2A5⋊C1612yesdirect product factor
176C2C2×A5⋊C811yescharacteristic
subgroupG/H
center, Fitting, hypercenterC2×C8S5
commutator, hypocenterA5C2×C16
FrattiniC8C2×S5
socle, prime radicalC22×A5C8
cosocleC8×A5C22
LCSG ▷ A5
UCSC1 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. A5⋊C16C2direct (N × H)
19. C2×A5C16semidirect
42. A5C2×C16semidirect
175. C2A5⋊C16direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C8×A52
A5⋊C162
C2×A4⋊C165
C2×D5⋊C166
C2×D3×C1610