Finite Group Databasebeta

← #595×AGL(1,𝔽13) #72276471

Subgroups — #595×AGL(1,𝔽13) #72276471

Order 10608.

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 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
1#72276468C211yesmaximal, characteristic
2D17×AGL(1,𝔽13)C211yesmaximal, characteristic
3#261×#595C311yesmaximal, characteristic, complemented, Hall
4#595×D13⋊C3C211yesmaximal, characteristic
5C13⋊C3×#595C411yescharacteristic, complemented
6D17×D13⋊C3C2211yescharacteristic
7#11725133⋊C3C411yescharacteristic, complemented
8#11725132⋊C3C411yescharacteristic, complemented
9#11725131⋊C3C411yescharacteristic, complemented
10#11725130⋊C3C411yescharacteristic, complemented
11C17×AGL(1,𝔽13)C411yescharacteristic, complemented
12D13×#595C2×C311yescharacteristic
13D17×#261C2×C311yescharacteristic
14D13⋊#595C2×C311yescharacteristic
15C17⋊(D13⋊C3)C2×C411yescharacteristic
16C17×D13⋊C3C2×C411yescharacteristic
17D17×C13⋊C3C2×C411yescharacteristic
18D13×D17C22×C311yescharacteristic
19#11725133C3×C411yescharacteristic, complemented
20#11725132C3×C411yescharacteristic, complemented
21#11725131C3×C411yescharacteristic, complemented
22#11725130C3×C411yescharacteristic, complemented
23C17×#261C3×C411yescharacteristic, complemented
24C13×#595C3×C411yescharacteristic, complemented
25C3×C4×#595—131nomaximal, Hall
26C17×C13⋊C3C4211yescharacteristic, complemented, Hall
27C4×AGL(1,𝔽13)—171nomaximal, Hall
28D221C2×C3×C411yescharacteristic
29C13×D17C2×C3×C411yescharacteristic
30C17×D13C2×C3×C411yescharacteristic
31C2×C3×#595—131no—
32C2×C3×#595—131no—
33C3×C4×D17—131no—
34C2×AGL(1,𝔽13)—171no—
35C2×AGL(1,𝔽13)—171no—
36C4×D13⋊C3—171no—
37C4×#595—131noHall
38C13×C17C3×C4211yescharacteristic, complemented, Hall
39C4×#261—171noHall
40C2×C3×D17—131no—
41C3×#595—131no—
42C3×#595—131no—
43C3×#595—131no—
44C3×#595—131no—
45C3×C4×C17—131no—
46C3×Dic17—131no—
47C2×D13⋊C3—171no—
48AGL(1,𝔽13)—171no—
49AGL(1,𝔽13)—171no—
50AGL(1,𝔽13)—171no—
51AGL(1,𝔽13)#59511yescharacteristic, direct product factor
52C4×C13⋊C3—171no—
53Dic13⋊C3—171no—
54C2×#595—131no—
55C2×#595—131no—
56C4×D17—131no—
57C2×#261—171no—
58C2×#261—171no—
59C4×D13—171no—
60C2×C3×C17—131no—
61C3×D17—131no—
62C3×D17—131no—
63C2×C13⋊C3—171no—
64D13⋊C3—171no—
65D13⋊C3C2×#59511yescharacteristic
66C2×D17—131no—
67#595—131no—
68#595—131no—
69#595—131no—
70#595AGL(1,𝔽13)11yescharacteristic, direct product factor
71C4×C17—131no—
72Dic17—131no—
73C2×D13—171no—
74#261—171no—
75#261—171no—
76#261—171no—
77#261C3×#59511yescharacteristic, complemented
78C4×C13—171no—
79Dic13—171no—
80C3×C17—131noHall
81C3×C42—2211noHall
82C13⋊C3C4×#59511yescharacteristic, complemented, Hall
83C2×C17—131no—
84D17—131no—
85D17C2×AGL(1,𝔽13)11yescharacteristic
86C2×C13—171no—
87D13—171no—
88D13C2×C3×#59511yescharacteristic
89C2×C3×C4—2211no—
90C2×C3×C4—2211no—
91C2×C3×C4—2211no—
92C17C4×AGL(1,𝔽13)11yescharacteristic, complemented, Sylow
93C42—2211noSylow
94C13C3×C4×#59511yescharacteristic, complemented, Sylow
95C22×C3—2211no—
96C3×C4—131no—
97C3×C4—2211no—
98C3×C4—2211no—
99C3×C4—2211no—
100C3×C4—2211no—
101C3×C4—2211no—
102C2×C4—2211no—
103C2×C4—2211no—
104C2×C4—2211no—
105C2×C3—131no—
106C2×C3—2211no—
107C2×C3—2211no—
108C22—2211no—
109C4—131no—
110C4—171no—
111C4—2211no—
112C4—2211no—
113C4—2211no—
114C4—2211no—
115C3—131noSylow
116C2—131no—
117C2—171no—
118C2—2211no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC13×C17C3×C42
prime radicalD17×D13⋊C3C22
cosocleD13×D17C22×C3
LCSG ▷ C13×C17
UCSC1

Complements

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

NH ≅ G/Ntype
3. #261×#595C3semidirect
5. C13⋊C3×#595C4semidirect
7. #11725133⋊C3C4semidirect
8. #11725132⋊C3C4semidirect
9. #11725131⋊C3C4semidirect
10. #11725130⋊C3C4semidirect
11. C17×AGL(1,𝔽13)C4semidirect
19. #11725133C3×C4semidirect
20. #11725132C3×C4semidirect
21. #11725131C3×C4semidirect
22. #11725130C3×C4semidirect
23. C17×#261C3×C4semidirect
24. C13×#595C3×C4semidirect
26. C17×C13⋊C3C42semidirect
38. C13×C17C3×C42semidirect
51. AGL(1,𝔽13)#595direct (N × H)
70. #595AGL(1,𝔽13)direct (N × H)
77. #261C3×#595semidirect
82. C13⋊C3C4×#595semidirect
92. C17C4×AGL(1,𝔽13)semidirect
94. C13C3×C4×#595semidirect

Maximal subgroups

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

subgroupindex
#722764682
D17×AGL(1,𝔽13)2
#261×#5953
#595×D13⋊C32
C3×C4×#59513
C4×AGL(1,𝔽13)17