Finite Group Databasebeta

← C3×#22576424 #39908028

Subgroups — C3×#22576424 #39908028

Order 26100.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C29⋊((C5⋊D5)⋊C3)C211yesmaximal, characteristic
2C3×#15668529—31nomaximal
3#22576424C311yesmaximal, characteristic, direct product factor
4C3×C29×C52⋊C3C411yescharacteristic, complemented, Hall
5C3×C5⋊D145D311yescharacteristic
6C29⋊((C5⋊D5)⋊C3)—21no—
7C29⋊((C5⋊D5)⋊C3)C2×C311yescharacteristic
8#15668529—31noHall
9C29×C52⋊C3—21no—
10C29×C52⋊C3C3×C411yescharacteristic, complemented
11C3×C52×C29Dic311yescharacteristic, complemented
12C3×#10596814—151no—
13C3×#10596815—151no—
14C5⋊D145C3×D311yescharacteristic
15C3×C3⋊#1181—251nomaximal, Hall
16C3×#64480—291nomaximal, Hall
17C3×D145—301no—
18C3×D145—301no—
19C52×C29C3×Dic311yescharacteristic, complemented, Hall
20#10596815—151no—
21#10596814—151no—
22C32×D29—251no—
23C3×(C5⋊D5)⋊C3—291no—
24C3×C5×C29—61no—
25C3×C5×C29—61no—
26C3⋊#1181—251no—
27C3×#1181—751no—
28C3×#1044—871no—
29#64480—291no—
30D145—151no—
31D145—301no—
32C32×C29—1001noHall
33C3×C52⋊C3#118111yescharacteristic, complemented, Hall
34C3×D29—251no—
35C3×D29—251no—
36C3×D29—501no—
37C3×C5⋊D5—291no—
38(C5⋊D5)⋊C3—291no—
39(C5⋊D5)⋊C3—581no—
40C5×C29—31no—
41C5×C29—61no—
42#1181—751noHall
43#1044—871noHall
44C3×C29—1001no—
45C3×C29—1001no—
46C3×C29#6448011yescharacteristic, complemented
47C3×C52C3⋊#118111yescharacteristic, complemented
48C52⋊C3—21no—
49C52⋊C3C3×#118111yescharacteristic, complemented
50C3×AGL(1,𝔽5)—4351no—
51C3×AGL(1,𝔽5)—4351no—
52D29—251no—
53C5⋊D5—291no—
54C3×Dic3—7251noHall
55C3×D5—8701no—
56C3×D5—8701no—
57C29C3×#6448011yescharacteristic, complemented, Sylow
58C52C3×C3⋊#118111yescharacteristic, complemented, Sylow
59AGL(1,𝔽5)—4351no—
60AGL(1,𝔽5)—4351no—
61C2×C32—7251no—
62C3×C5—61no—
63C3×C5—61no—
64C3×C4—21751no—
65Dic3—7251no—
66D5—8701no—
67D5—4351no—
68C32—1001noSylow
69C2×C3—14501no—
70C2×C3—7251no—
71C2×C3—7251no—
72C5—31no—
73C5—61no—
74C4—21751noSylow
75C3—1001no—
76C3—1001no—
77C3#2257642411yescharacteristic, direct product factor
78C2—7251no—
subgroupG/H
center, hypercenterC3#22576424
commutator, hypocenterC29×C52⋊C3C3×C4
FrattiniC1G
Fitting, socleC3×C52×C29Dic3
prime radicalC3×C29⋊((C5⋊D5)⋊C3)C2
cosocleC29⋊((C5⋊D5)⋊C3)C2×C3
LCSG ▷ C29×C52⋊C3
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
3. #22576424C3direct (N × H)
4. C3×C29×C52⋊C3C4semidirect
10. C29×C52⋊C3C3×C4semidirect
11. C3×C52×C29Dic3semidirect
19. C52×C29C3×Dic3semidirect
33. C3×C52⋊C3#1181semidirect
46. C3×C29#64480semidirect
47. C3×C52C3⋊#1181semidirect
49. C52⋊C3C3×#1181semidirect
57. C29C3×#64480semidirect
58. C52C3×C3⋊#1181semidirect
77. C3#22576424direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C29⋊((C5⋊D5)⋊C3)2
C3×#156685293
#225764243
C3×C3⋊#118125
C3×#6448029