Finite Group Databasebeta

← C5×#73004 #14510728

Subgroups — C5×#73004 #14510728

Order 1920.

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

normal subgroups only

This group has 224 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×#399⋊C3C211yesmaximal, characteristic
2C5×#4621C212yesmaximal, complemented
3C5×#1614—31nomaximal, Hall
4C2×C5×SL(2,ℤ/4)—41nomaximal
5C5×#95⋊C3C2211yescharacteristic
6#73004C511yesmaximal, characteristic, direct product factor, Hall
7C5×#543—31no—
8C5×#484—32no—
9C5×#399D311yescharacteristic
10C5×#328—32no—
11C5×#323—31no—
12C22×C5×A4—41no—
13C5×SL(2,ℤ/4)—42no—
14#399⋊C3C2×C511yescharacteristic
15#4621C2×C512yescomplemented
16C5×C22⋊Q8—32no—
17C5×C22⋊Q8—62no—
18C5×C22⋊Q8—61no—
19C5×C22⋊Q8—62no—
20C2×C5×C4⋊C4—31no—
21C2×C5×C22⋊C4—31no—
22C2×C5×C22⋊C4—61no—
23C5×#107—62no—
24C5×#103—62no—
25C5×C22⋊C8—32no—
26C5×#95C2×D311yescharacteristic
27#1614—31noSylow
28C2×C5×A4—42no—
29C2×C5×A4—41no—
30C2×C5×Dic3—161no—
31C2×SL(2,ℤ/4)—41no—
32#95⋊C3C22×C511yescharacteristic
33C24×C5S411yescharacteristic
34C2×C5×Q8—32no—
35C2×C5×Q8—61no—
36C22×C4×C5—31no—
37C22×C4×C5—31no—
38C22×C4×C5—61no—
39C22×C4×C5—61no—
40C2×C5×C8—62no—
41C5×C4⋊C4—32no—
42C5×C4⋊C4—62no—
43C5×C4⋊C4—62no—
44C5×C4⋊C4—62no—
45C5×C4⋊C4—61no—
46C5×C22⋊C4—62no—
47C5×C22⋊C4—62no—
48C5×C22⋊C4—62no—
49#543—31no—
50#484—32no—
51#399C5×D311yescharacteristic
52#328—32no—
53#323—31no—
54C22×C3×C5—161no—
55C5×A4—41no—
56C5×Dic3—162no—
57C22×A4—41no—
58SL(2,ℤ/4)—42no—
59C23×C5—61no—
60C23×C5—61no—
61C23×C5#22612yes—
62C23×C5C2×S411yescharacteristic
63C5×Q8—122no—
64C5×Q8—241no—
65C2×C4×C5—32no—
66C2×C4×C5—62no—
67C2×C4×C5—61no—
68C2×C4×C5—62no—
69C2×C4×C5—121no—
70C2×C4×C5—121no—
71C2×C4×C5—241no—
72C2×C4×C5—241no—
73C5×C8—122no—
74C22⋊Q8—32no—
75C22⋊Q8—62no—
76C22⋊Q8—61no—
77C22⋊Q8—62no—
78C2×C4⋊C4—31no—
79C2×C22⋊C4—31no—
80C2×C22⋊C4—61no—
81#107—62no—
82#103—62no—
83C22⋊C8—32no—
84#95C2×C5×D311yescharacteristic
85C2×C3×C5—162no—
86C2×C3×C5—161no—
87C2×A4—42no—
88C2×A4—41no—
89C2×Dic3—161no—
90C22×C5—31no—
91C22×C5—31no—
92C22×C5—41no—
93C22×C5—62no—
94C22×C5—121no—
95C22×C5C2×#22611yescharacteristic
96C4×C5—62no—
97C4×C5—122no—
98C4×C5—122no—
99C4×C5—121no—
100C24C5×S411yescharacteristic
101C2×Q8—32no—
102C2×Q8—61no—
103C22×C4—31no—
104C22×C4—31no—
105C22×C4—61no—
106C22×C4—61no—
107C2×C8—62no—
108C4⋊C4—32no—
109C4⋊C4—62no—
110C4⋊C4—62no—
111C4⋊C4—62no—
112C4⋊C4—61no—
113C22⋊C4—62no—
114C22⋊C4—62no—
115C22⋊C4—62no—
116C3×C5—161noHall
117C22×C3—161no—
118A4—41no—
119Dic3—162no—
120C2×C5—31no—
121C2×C5—31no—
122C2×C5—42no—
123C2×C5#857⋊C211yescharacteristic
124C23—61no—
125C23—61no—
126C23C5×#22612yes—
127C23C2×C5×S411yescharacteristic
128Q8—122no—
129Q8—241no—
130C2×C4—32no—
131C2×C4—62no—
132C2×C4—61no—
133C2×C4—62no—
134C2×C4—121no—
135C2×C4—121no—
136C2×C4—241no—
137C2×C4—241no—
138C8—122no—
139C2×C3—162no—
140C2×C3—161no—
141C5#7300411yescharacteristic, direct product factor, Sylow
142C22—31no—
143C22—31no—
144C22—41no—
145C22—62no—
146C22—121no—
147C22C2×C5×#22611yescharacteristic
148C4—62no—
149C4—122no—
150C4—121no—
151C4—122no—
152C3—161noSylow
153C2—31no—
154C2—31no—
155C2—42no—
156C2C5×#857⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2×C5#857⋊C2
commutator, cosocle, hypocenter#95⋊C3C22×C5
FrattiniC23C2×C5×S4
FittingC5×#399D3
socleC23×C5C2×S4
prime radicalC5×#399⋊C3C2
LCSG ▷ #95⋊C3
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
2. C5×#4621C2semidirect
6. #73004C5direct (N × H)
15. #4621C2×C5semidirect
141. C5#73004direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#399⋊C32
C5×#46212
C5×#16143
C2×C5×SL(2,ℤ/4)4
#730045