Finite Group Databasebeta

← #23778473⋊C3 #44477883

Subgroups — #23778473⋊C3 #44477883

Order 30420.

192 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 39 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
1D5×C13⋊C32C211yesmaximal, characteristic
2#23778479C311yesmaximal, characteristic, complemented
3#23778479C311yesmaximal, characteristic, complemented
4#23778474C311yesmaximal, characteristic, complemented
5#23778473C311yesmaximal, characteristic, complemented
6C5×C13⋊C32C411yescharacteristic, complemented, Hall
7#14523128⋊C3—51nomaximal, Hall
8D5×#92789C2×C311yescharacteristic
9D5×#92788C2×C311yescharacteristic
10D5×C13×C13⋊C3C2×C311yescharacteristic
11D5×C13×C13⋊C3C2×C311yescharacteristic
12#16810007C3211yescharacteristic, complemented, Hall
13C2×C13⋊C32—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×#63120⋊C3—131nomaximal
20#14523132—51no—
21#14523132—51no—
22#14523129—51no—
23#14523128—51no—
24D5×C132C2×C3211yescharacteristic
25C13⋊C32AGL(1,𝔽5)11yescharacteristic, complemented, Hall
26C3×D5×C13⋊C3—131no—
27C3×D5×C13⋊C3—131no—
28C2×#92789—51no—
29C2×#92788—51no—
30C2×C13×C13⋊C3—51no—
31C2×C13×C13⋊C3—51no—
32C5×C132C32×C411yescharacteristic, complemented, Hall
33C3×#63120—131no—
34C3×#63120—131no—
35#63120⋊C3—131no—
36#63120⋊C3—131no—
37#63120⋊C3—131no—
38#63120⋊C3—131no—
39#63120⋊C3—391no—
40#63120⋊C3—392no—
41#63120⋊C3—391no—
42#63120⋊C3—391no—
43#63120⋊C3—391no—
44#10621725—51noHall
45C3×C5×C13⋊C3—131no—
46C3×C5×C13⋊C3—131no—
47#92789C3×AGL(1,𝔽5)11yescharacteristic, complemented
48#92788C3×AGL(1,𝔽5)11yescharacteristic, complemented
49C13×C13⋊C3C3×AGL(1,𝔽5)11yescharacteristic, complemented
50C13×C13⋊C3C3×AGL(1,𝔽5)11yescharacteristic, complemented
51C3×Dic13⋊C3—651no—
52C3×Dic13⋊C3—651no—
53C3×D5×C13—131no—
54C3×D5×C13—131no—
55D5×C13⋊C3—131no—
56D5×C13⋊C3—131no—
57D5×C13⋊C3—131no—
58D5×C13⋊C3—131no—
59D5×C13⋊C3—391no—
60D5×C13⋊C3—392no—
61D5×C13⋊C3—391no—
62D5×C13⋊C3D13⋊C311yescharacteristic
63D5×C13⋊C3D13⋊C311yescharacteristic
64C2×C132—51no—
65#63120—391no—
66#63120—391no—
67#63120—391no—
68#63120—1172no—
69#63120—1171no—
70C2×C3×C13⋊C3—651no—
71C2×C3×C13⋊C3—651no—
72C3×C5×C13—131no—
73C3×C5×C13—131no—
74C5×C13⋊C3—131no—
75C5×C13⋊C3—131no—
76C5×C13⋊C3—131no—
77C5×C13⋊C3—131no—
78C5×C13⋊C3—391no—
79C5×C13⋊C3—392no—
80C5×C13⋊C3—391no—
81C5×C13⋊C3Dic13⋊C311yescharacteristic, complemented
82C5×C13⋊C3Dic13⋊C311yescharacteristic, complemented
83C32×AGL(1,𝔽5)—1691noHall
84C132C32×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
85C3×Dic13—651no—
86C3×Dic13—651no—
87Dic13⋊C3—651no—
88Dic13⋊C3—651no—
89Dic13⋊C3—651no—
90Dic13⋊C3—651no—
91Dic13⋊C3—651no—
92Dic13⋊C3—1951no—
93Dic13⋊C3—1952no—
94Dic13⋊C3—1951no—
95Dic13⋊C3—1951no—
96D5×C13—31no—
97D5×C13—32no—
98D5×C13—31no—
99D5×C13C3×D13⋊C311yescharacteristic
100D5×C13C3×D13⋊C311yescharacteristic
101C3×C13⋊C3—131no—
102C3×C13⋊C3—131no—
103C32×D5—1691no—
104C2×C3×C13—651no—
105C2×C3×C13—651no—
106C2×C13⋊C3—51no—
107C2×C13⋊C3—51no—
108C2×C13⋊C3—651no—
109C2×C13⋊C3—651no—
110C2×C13⋊C3—651no—
111C2×C13⋊C3—651no—
112C2×C13⋊C3—1951no—
113C2×C13⋊C3—1952no—
114C2×C13⋊C3—1951no—
115C5×C13—31no—
116C5×C13—32no—
117C5×C13—31no—
118C5×C13C3×Dic13⋊C311yescharacteristic, complemented
119C5×C13C3×Dic13⋊C311yescharacteristic, complemented
120C3×AGL(1,𝔽5)—1691no—
121C3×AGL(1,𝔽5)—1691no—
122C3×AGL(1,𝔽5)—5071no—
123C3×AGL(1,𝔽5)—5071no—
124Dic13—651no—
125Dic13—5851no—
126Dic13—5852no—
127Dic13—1951no—
128Dic13—1951no—
129C32×C5—1691noHall
130C3×C13—131no—
131C3×C13—131no—
132C13⋊C3—131no—
133C13⋊C3—131no—
134C13⋊C3—131no—
135C13⋊C3—131no—
136C13⋊C3—391no—
137C13⋊C3—392no—
138C13⋊C3—391no—
139C13⋊C3#63120⋊C311yescharacteristic, complemented
140C13⋊C3#63120⋊C311yescharacteristic, complemented
141C32×C4—8451noHall
142C3×D5—131no—
143C3×D5—131no—
144C3×D5—1691no—
145C3×D5—1691no—
146C2×C13—51no—
147C2×C13—51no—
148C2×C13—151no—
149C2×C13—152no—
150C2×C13—151no—
151AGL(1,𝔽5)—15211noHall
152C2×C32—8451no—
153C3×C5—131no—
154C3×C5—131no—
155C3×C5—1691no—
156C3×C5—1691no—
157C13—31no—
158C13—32no—
159C13—31no—
160C13C3×#63120⋊C311yescharacteristic, complemented
161C13C3×#63120⋊C311yescharacteristic, complemented
162C3×C4—8451no—
163C3×C4—8451no—
164C3×C4—25351no—
165C3×C4—25351no—
166D5(C13⋊C3)⋊(D13⋊C3)11yescharacteristic
167C32—1691noSylow
168C2×C3—651no—
169C2×C3—651no—
170C2×C3—8451no—
171C2×C3—8451no—
172C5#14523128⋊C311yescharacteristic, complemented, Sylow
173C4—76051noSylow
174C3—131no—
175C3—131no—
176C3—1691no—
177C3—1691no—
178C2—51no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C132C32×C4
prime radicalD5×C13⋊C32C2
cosocleD5×C132C2×C32
LCSG ▷ C5×C132
UCSC1

Complements

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

NH ≅ G/Ntype
2. #23778479C3semidirect
3. #23778479C3semidirect
4. #23778474C3semidirect
5. #23778473C3semidirect
6. C5×C13⋊C32C4semidirect
12. #16810007C32semidirect
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
47. #92789C3×AGL(1,𝔽5)semidirect
48. #92788C3×AGL(1,𝔽5)semidirect
49. C13×C13⋊C3C3×AGL(1,𝔽5)semidirect
50. C13×C13⋊C3C3×AGL(1,𝔽5)semidirect
81. C5×C13⋊C3Dic13⋊C3semidirect
82. C5×C13⋊C3Dic13⋊C3semidirect
84. C132C32×AGL(1,𝔽5)semidirect
118. C5×C13C3×Dic13⋊C3semidirect
119. C5×C13C3×Dic13⋊C3semidirect
139. C13⋊C3#63120⋊C3semidirect
140. C13⋊C3#63120⋊C3semidirect
160. C13C3×#63120⋊C3semidirect
161. C13C3×#63120⋊C3semidirect
172. C5#14523128⋊C3semidirect

Maximal subgroups

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

subgroupindex
D5×C13⋊C322
#237784793
#237784743
#237784733
#14523128⋊C35
C3×#63120⋊C313