Finite Group Databasebeta

← C5×#73001 #14510725

Subgroups — C5×#73001 #14510725

Order 1920.

226 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 24 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×#5930C212yesmaximal
2C5×#395⋊C3C211yesmaximal, characteristic
3C5×#1605—31nomaximal, Hall
4C5×C22⋊SL(2,𝔽3)C2211yescharacteristic
5C5×A4⋊Q8—41nomaximal
6#73001C511yesmaximal, characteristic, direct product factor, Hall
7C5×#544—31no—
8C5×#451—32no—
9C5×#395D311yescharacteristic
10C5×#328—32no—
11C5×#324—31no—
12C4×C5×A4—41no—
13C5×SL(2,ℤ/4)—42no—
14C5×#226—82no—
15#5930C2×C512yes—
16#395⋊C3C2×C511yescharacteristic
17C22×C5×Q8C2×D311yescharacteristic
18C2×C5×Q16—62no—
19C5×C4⋊Q8—62no—
20C5×#125—62no—
21C5×C22⋊Q8—32no—
22C5×C22⋊Q8—61no—
23C5×#117—61no—
24C2×C5×C4⋊C4—31no—
25C5×#103—62no—
26C5×C22⋊C8—32no—
27C5×#95—31no—
28#1605—31noSylow
29C2×C5×A4—41no—
30C5×Dic6—161no—
31C5×SL(2,𝔽3)—82no—
32C22⋊SL(2,𝔽3)C22×C511yescharacteristic
33A4⋊Q8—41no—
34C2×C5×Q8—32no—
35C2×C5×Q8—62no—
36C2×C5×Q8—61no—
37C22×C4×C5—31no—
38C22×C4×C5—31no—
39C22×C4×C5S411yescharacteristic
40C5×Q16—122no—
41C5×Q16—122no—
42C2×C5×C8—62no—
43C5×C4⋊C4—32no—
44C5×C4⋊C4—62no—
45C5×C4⋊C4—62no—
46C5×C4⋊C4—61no—
47C5×C4⋊C4—61no—
48C5×C4⋊C4—61no—
49C5×C4⋊C4—62no—
50C5×C22⋊C4—62no—
51C42×C5—62no—
52#544—31no—
53#451—32no—
54#395C5×D311yescharacteristic
55#328—32no—
56#324—31no—
57C5×A4—41no—
58C3×C4×C5—161no—
59C5×Dic3—162no—
60C4×A4—41no—
61SL(2,ℤ/4)—42no—
62#226—82no—
63C23×C5C2×S411yescharacteristic
64C5×Q8—22no—
65C5×Q8—62no—
66C5×Q8—122no—
67C5×Q8—241no—
68C2×C4×C5—32no—
69C2×C4×C5—32no—
70C2×C4×C5—61no—
71C2×C4×C5—61no—
72C2×C4×C5—61no—
73C2×C4×C5—62no—
74C2×C4×C5—62no—
75C2×C4×C5—121no—
76C5×C8—122no—
77C22×Q8C2×C5×D311yescharacteristic
78C2×Q16—62no—
79C4⋊Q8—62no—
80#125—62no—
81C22⋊Q8—32no—
82C22⋊Q8—61no—
83#117—61no—
84C2×C4⋊C4—31no—
85#103—62no—
86C22⋊C8—32no—
87#95—31no—
88C2×C3×C5—161no—
89C2×A4—41no—
90Dic6—161no—
91SL(2,𝔽3)—82no—
92C22×C5—31no—
93C22×C5—31no—
94C22×C5#98411yescharacteristic
95C4×C5—41no—
96C4×C5—62no—
97C4×C5—62no—
98C4×C5—122no—
99C4×C5—122no—
100C2×Q8—32no—
101C2×Q8—62no—
102C2×Q8—61no—
103C22×C4—31no—
104C22×C4—31no—
105C22×C4C5×S411yescharacteristic
106Q16—122no—
107Q16—122no—
108C2×C8—62no—
109C4⋊C4—32no—
110C4⋊C4—62no—
111C4⋊C4—62no—
112C4⋊C4—61no—
113C4⋊C4—61no—
114C4⋊C4—61no—
115C4⋊C4—62no—
116C22⋊C4—62no—
117C42—62no—
118C3×C5—161noHall
119A4—41no—
120C3×C4—161no—
121Dic3—162no—
122C2×C5—31no—
123C2×C5—31no—
124C2×C5#1020⋊C211yescharacteristic
125C23C2×C5×S411yescharacteristic
126Q8—22no—
127Q8—62no—
128Q8—122no—
129Q8—241no—
130C2×C4—32no—
131C2×C4—32no—
132C2×C4—61no—
133C2×C4—61no—
134C2×C4—61no—
135C2×C4—62no—
136C2×C4—62no—
137C2×C4—121no—
138C8—122no—
139C2×C3—161no—
140C5#7300111yescharacteristic, direct product factor, Sylow
141C22—31no—
142C22—31no—
143C22C5×#98411yescharacteristic
144C4—41no—
145C4—62no—
146C4—62no—
147C4—122no—
148C4—122no—
149C3—161noSylow
150C2—31no—
151C2—31no—
152C2C5×#1020⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2×C5#1020⋊C2
commutator, cosocle, hypocenterC22⋊SL(2,𝔽3)C22×C5
FrattiniC23C2×C5×S4
FittingC5×#395D3
socleC23×C5C2×S4
prime radicalC5×C22⋊SL(2,𝔽3)C22
LCSG ▷ C22⋊SL(2,𝔽3)
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
6. #73001C5direct (N × H)
140. C5#73001direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#59302
C5×#395⋊C32
C5×#16053
C5×A4⋊Q84
#730015