Finite Group Databasebeta

← C7×#19129778 #50304082

Subgroups — C7×#19129778 #50304082

Order 38220.

144 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 44 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×C72×D13⋊C3C211yesmaximal, characteristic
2C7×C7⋊#63118C311yesmaximal, characteristic, complemented, Hall
3C5×C72×C13⋊C3C411yescharacteristic, complemented, Hall
4C7×#11763979—51nomaximal, Hall
5C5×C72×D13C2×C311yescharacteristic
6#19129778C711yesmaximal, characteristic, direct product factor
7C7×#63118⋊C3—71nomaximal
8C72×D13⋊C3D511yescharacteristic
9C5×C72×C13C3×C411yescharacteristic, complemented, Hall
10C3×C7×Dic35—131nomaximal, Hall
11C5×C7×D13⋊C3—23no—
12C5×C7×D13⋊C3D711yescharacteristic
13C5×C7×D13⋊C3C2×C711yescharacteristic
14C7×C7⋊#261—51noHall
15C72×C13⋊C3Dic511yescharacteristic, complemented, Hall
16C7⋊#63118C3×C711yescharacteristic, complemented
17C7×#63118—71no—
18C2×C3×C5×C72—131no—
19C5×C7×C13⋊C3—23no—
20C5×C7×C13⋊C3Dic711yescharacteristic, complemented
21C5×C7×C13⋊C3C4×C711yescharacteristic, complemented
22C72×D13C3×D511yescharacteristic
23#11763979—51no—
24C7×AGL(1,𝔽13)—351no—
25C7×Dic35—131noHall
26C5×C7×D13—23no—
27C5×C7×D13C3×D711yescharacteristic
28C5×C7×D13C2×C3×C711yescharacteristic
29#63118⋊C3—71noHall
30C3×C5×C72—131noHall
31C72×C13C3×Dic511yescharacteristic, complemented, Hall
32C3×C7×Dic7—651noHall
33C7×D13⋊C3—23no—
34C7×D13⋊C3C7×D511yescharacteristic
35C7×D13⋊C3D3511yescharacteristic
36C2×C5×C72—131no—
37C5×C7×C13—23no—
38C5×C7×C13C3×Dic711yescharacteristic, complemented
39C5×C7×C13C3×C4×C711yescharacteristic, complemented
40C3×Dic35—131no—
41C3×C7×Dic5—911no—
42C5×D13⋊C3C7×D711yescharacteristic
43C7⋊#261—51no—
44C7×#261—351no—
45C2×C3×C72—131no—
46C7×C13⋊C3—23no—
47C7×C13⋊C3C7×Dic511yescharacteristic, complemented
48C7×C13⋊C3Dic3511yescharacteristic, complemented
49#63118—71noHall
50C5×C72AGL(1,𝔽13)11yescharacteristic, complemented, Hall
51C2×C3×C5×C7—131no—
52C2×C3×C5×C7—131no—
53C2×C3×C5×C7—263no—
54C7×Dic7—651noHall
55C5×C13⋊C3C7×Dic711yescharacteristic, complemented, Hall
56C7×D13—23no—
57C7×D13C3×C7×D511yescharacteristic
58C7×D13C3×D3511yescharacteristic
59AGL(1,𝔽13)—351noHall
60C3×C72—131noHall
61Dic35—131no—
62C7×Dic5—911no—
63C5×D13C3×C7×D711yescharacteristic
64C3×C5×C7—131no—
65C3×C5×C7—131no—
66C3×C5×C7—263no—
67C2×C72—131no—
68C7×C13—23no—
69C7×C13C3×C7×Dic511yescharacteristic, complemented
70C7×C13C3×Dic3511yescharacteristic, complemented
71C3×C4×C7—4551no—
72C3×Dic7—651no—
73D13⋊C3C7×D3511yescharacteristic
74C2×C5×C7—131no—
75C2×C5×C7—131no—
76C2×C5×C7—263no—
77C5×C13C3×C7×Dic711yescharacteristic, complemented, Hall
78C3×Dic5—911noHall
79#261—351noHall
80C72#63118⋊C311yescharacteristic, complemented, Sylow
81C2×C3×C7—131no—
82C2×C3×C7—131no—
83C2×C3×C7—263no—
84C13⋊C3C7×Dic3511yescharacteristic, complemented, Hall
85C5×C7—23no—
86C5×C7C7×AGL(1,𝔽13)11yescharacteristic, complemented
87C5×C7#1176397911yescharacteristic, complemented
88C2×C3×C5—131no—
89C4×C7—4551no—
90Dic7—651no—
91D13C3×C7×D3511yescharacteristic
92C3×C7—131no—
93C3×C7—131no—
94C3×C7—263no—
95Dic5—911noHall
96C3×C5—131noHall
97C2×C7—131no—
98C2×C7—131no—
99C2×C7—263no—
100C13C3×C7×Dic3511yescharacteristic, complemented, Sylow
101C3×C4—4551noHall
102C2×C5—131no—
103C7—23no—
104C7C7×#63118⋊C311yescharacteristic, complemented
105C7#1912977811yescharacteristic, direct product factor
106C2×C3—131no—
107C5C7×#1176397911yescharacteristic, complemented, Sylow
108C4—4551noSylow
109C3—131noSylow
110C2—131no—
subgroupG/H
center, hypercenterC7#19129778
commutator, hypocenterC5×C7×C13C3×C4×C7
FrattiniC1G
Fitting, socleC5×C72×C13C3×C4
prime radicalC5×C72×D13⋊C3C2
cosocleC5×C7×D13C2×C3×C7
LCSG ▷ C5×C7×C13
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
2. C7×C7⋊#63118C3semidirect
3. C5×C72×C13⋊C3C4semidirect
6. #19129778C7direct (N × H)
9. C5×C72×C13C3×C4semidirect
15. C72×C13⋊C3Dic5semidirect
16. C7⋊#63118C3×C7semidirect
20. C5×C7×C13⋊C3Dic7semidirect
21. C5×C7×C13⋊C3C4×C7semidirect
31. C72×C13C3×Dic5semidirect
38. C5×C7×C13C3×Dic7semidirect
39. C5×C7×C13C3×C4×C7semidirect
47. C7×C13⋊C3C7×Dic5semidirect
48. C7×C13⋊C3Dic35semidirect
50. C5×C72AGL(1,𝔽13)semidirect
55. C5×C13⋊C3C7×Dic7semidirect
69. C7×C13C3×C7×Dic5semidirect
70. C7×C13C3×Dic35semidirect
77. C5×C13C3×C7×Dic7semidirect
80. C72#63118⋊C3semidirect
84. C13⋊C3C7×Dic35semidirect
86. C5×C7C7×AGL(1,𝔽13)semidirect
87. C5×C7#11763979semidirect
100. C13C3×C7×Dic35semidirect
104. C7C7×#63118⋊C3semidirect
105. C7#19129778direct (N × H)
107. C5C7×#11763979semidirect

Maximal subgroups

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

subgroupindex
C5×C72×D13⋊C32
C7×C7⋊#631183
C7×#117639795
#191297787
C7×#63118⋊C37
C3×C7×Dic3513