Finite Group Databasebeta

← #23778460⋊C3 #44477882

Subgroups — #23778460⋊C3 #44477882

Order 30420.

148 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 36 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
1C13⋊C3×C5⋊(D13⋊C3)C211yesmaximal, characteristic
2#23778476C311yesmaximal, characteristic, complemented
3#23778472C311yesmaximal, characteristic, complemented
4#23778462C311yesmaximal, characteristic, complemented
5#23778460C311yesmaximal, characteristic, complemented
6C5×C13⋊C32C411yescharacteristic, complemented, Hall
7#14523148⋊C3—51nomaximal, Hall
8C13⋊C3×D65C2×C311yescharacteristic
9C5⋊#11759818C2×C311yescharacteristic
10C5⋊#11759817C2×C311yescharacteristic
11C13×C5⋊(D13⋊C3)C2×C311yescharacteristic
12#16810006C3211yescharacteristic, complemented, Hall
13C13⋊C3×D13⋊C3—51no—
14C5×#92789C3×C411yescharacteristic, complemented
15C5×#92788C3×C411yescharacteristic, complemented
16C5×C13×C13⋊C3C3×C411yescharacteristic, complemented
17C5×C13×C13⋊C3C3×C411yescharacteristic, complemented
18C3×#63120⋊C3—131nomaximal
19C3×#63121⋊C3—131nomaximal
20#14523157—51no—
21#14523154—51no—
22#14523149—51no—
23#14523148—51no—
24C13×D65C2×C3211yescharacteristic
25C13⋊C32AGL(1,𝔽5)11yescharacteristic, complemented, Hall
26C3×C5⋊(D13⋊C3)—131no—
27C3×D5×C13⋊C3—131no—
28D13×C13⋊C3—51no—
29#11759818—51no—
30#11759817—51no—
31C13×D13⋊C3—51no—
32C5×C132C32×C411yescharacteristic, complemented, Hall
33C3×#63120—131no—
34C3×#63121—131no—
35#63120⋊C3—131no—
36#63120⋊C3—131no—
37#63120⋊C3—391no—
38#63121⋊C3—131no—
39#63121⋊C3—131no—
40#63121⋊C3—391no—
41#10621730—51noHall
42C3×C5×C13⋊C3—131no—
43C3×C5×C13⋊C3—131no—
44#92789C3×AGL(1,𝔽5)11yescharacteristic, complemented
45#92788C3×AGL(1,𝔽5)11yescharacteristic, complemented
46C13×C13⋊C3C3×AGL(1,𝔽5)11yescharacteristic, complemented
47C13×C13⋊C3C3×AGL(1,𝔽5)11yescharacteristic, complemented
48C3×AGL(1,𝔽13)—651no—
49C3×Dic13⋊C3—651no—
50C3×D65—131no—
51C3×D5×C13—131no—
52C5⋊(D13⋊C3)—131no—
53C5⋊(D13⋊C3)—131no—
54C5⋊(D13⋊C3)D13⋊C311yescharacteristic
55D5×C13⋊C3—131no—
56D5×C13⋊C3—131no—
57D5×C13⋊C3—391no—
58C13×D13—51no—
59#63121—391no—
60#63120—391no—
61C2×C3×C13⋊C3—651no—
62C3×D13⋊C3—651no—
63C3×C5×C13—131no—
64C3×C5×C13—131no—
65C5×C13⋊C3—131no—
66C5×C13⋊C3—131no—
67C5×C13⋊C3—131no—
68C5×C13⋊C3—131no—
69C5×C13⋊C3—1561no—
70C5×C13⋊C3Dic13⋊C311yescharacteristic, complemented
71C5×C13⋊C3AGL(1,𝔽13)11yescharacteristic, complemented
72C32×AGL(1,𝔽5)—1691noHall
73C132C32×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
74C3×#261—651no—
75AGL(1,𝔽13)—651no—
76AGL(1,𝔽13)—651no—
77AGL(1,𝔽13)—1951no—
78C3×Dic13—651no—
79Dic13⋊C3—651no—
80Dic13⋊C3—651no—
81Dic13⋊C3—1951no—
82D65C3×D13⋊C311yescharacteristic
83D5×C13—391no—
84C3×C13⋊C3—131no—
85C3×C13⋊C3—131no—
86C32×D5—1691no—
87C2×C3×C13—651no—
88C3×D13—651no—
89C2×C13⋊C3—651no—
90C2×C13⋊C3—651no—
91C2×C13⋊C3—1951no—
92D13⋊C3—51no—
93D13⋊C3—651no—
94D13⋊C3—651no—
95C5×C13—121no—
96C5×C13C3×Dic13⋊C311yescharacteristic, complemented
97C5×C13C3×AGL(1,𝔽13)11yescharacteristic, complemented
98C3×AGL(1,𝔽5)—1691no—
99C3×AGL(1,𝔽5)—1691no—
100C3×AGL(1,𝔽5)—5071no—
101C3×AGL(1,𝔽5)—5071no—
102#261—1951no—
103Dic13—1951no—
104C32×C5—1691noHall
105C3×C13—131no—
106C3×C13—131no—
107C13⋊C3—131no—
108C13⋊C3—131no—
109C13⋊C3—131no—
110C13⋊C3—131no—
111C13⋊C3—1561no—
112C13⋊C3#63121⋊C311yescharacteristic, complemented
113C13⋊C3#63120⋊C311yescharacteristic, complemented
114C32×C4—8451noHall
115C3×D5—131no—
116C3×D5—1691no—
117C3×D5—1691no—
118C3×D5—1691no—
119C2×C13—1951no—
120D13—51no—
121AGL(1,𝔽5)—15211noHall
122C2×C32—8451no—
123C3×C5—131no—
124C3×C5—131no—
125C3×C5—1691no—
126C3×C5—1691no—
127C13—121no—
128C13C3×#63121⋊C311yescharacteristic, complemented
129C13C3×#63120⋊C311yescharacteristic, complemented
130C3×C4—8451no—
131C3×C4—8451no—
132C3×C4—25351no—
133C3×C4—25351no—
134D5—131no—
135C32—1691noSylow
136C2×C3—651no—
137C2×C3—8451no—
138C2×C3—8451no—
139C2×C3—25351no—
140C5#14523148⋊C311yescharacteristic, complemented, Sylow
141C4—76051noSylow
142C3—131no—
143C3—131no—
144C3—1691no—
145C3—1691no—
146C2—1951no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C132C32×C4
prime radicalC13⋊C3×C5⋊(D13⋊C3)C2
cosocleC13×D65C2×C32
LCSG ▷ C5×C132
UCSC1

Complements

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

NH ≅ G/Ntype
2. #23778476C3semidirect
3. #23778472C3semidirect
4. #23778462C3semidirect
5. #23778460C3semidirect
6. C5×C13⋊C32C4semidirect
12. #16810006C32semidirect
14. C5×#92789C3×C4semidirect
15. C5×#92788C3×C4semidirect
16. C5×C13×C13⋊C3C3×C4semidirect
17. C5×C13×C13⋊C3C3×C4semidirect
25. C13⋊C32AGL(1,𝔽5)semidirect
32. C5×C132C32×C4semidirect
44. #92789C3×AGL(1,𝔽5)semidirect
45. #92788C3×AGL(1,𝔽5)semidirect
46. C13×C13⋊C3C3×AGL(1,𝔽5)semidirect
47. C13×C13⋊C3C3×AGL(1,𝔽5)semidirect
70. C5×C13⋊C3Dic13⋊C3semidirect
71. C5×C13⋊C3AGL(1,𝔽13)semidirect
73. C132C32×AGL(1,𝔽5)semidirect
96. C5×C13C3×Dic13⋊C3semidirect
97. C5×C13C3×AGL(1,𝔽13)semidirect
112. C13⋊C3#63121⋊C3semidirect
113. C13⋊C3#63120⋊C3semidirect
128. C13C3×#63121⋊C3semidirect
129. C13C3×#63120⋊C3semidirect
140. C5#14523148⋊C3semidirect

Maximal subgroups

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

subgroupindex
C13⋊C3×C5⋊(D13⋊C3)2
#237784763
#237784723
#237784623
#237784603
#14523148⋊C35
C3×#63120⋊C313
C3×#63121⋊C313