Finite Group Databasebeta

← C3×C7⋊#13133347 #49087919

Subgroups — C3×C7⋊#13133347 #49087919

Order 35700.

128 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 38 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
1C3×C7×C5⋊D85C211yesmaximal, characteristic
2C7⋊#13133347C311yesmaximal, characteristic, direct product factor, Hall
3C3×C52×C7×C17C411yescharacteristic, complemented, Hall
4C3×C7⋊#66776—51nomaximal
5C3×C7⋊#66775—51nomaximal
6C7×C5⋊D85C2×C311yescharacteristic
7C3×#13133347—71nomaximal, Hall
8C3×C7×D85—51no—
9C3×C7×D85—51no—
10C3×C7×D85—102no—
11C52×C7×C17C3×C411yescharacteristic, complemented, Hall
12C3×C5⋊D85D711yescharacteristic
13C7⋊#66776—51no—
14C7⋊#66775—51no—
15C3×C7⋊#1044—171nomaximal, Hall
16C3×C5×C7×C17—22no—
17C3×C5×C7×C17AGL(1,𝔽5)11yescharacteristic, complemented
18C3×C5×C7×C17AGL(1,𝔽5)11yescharacteristic, complemented
19#13133347—71noHall
20C3×C7⋊#595—251noHall
21C3×C52×C17Dic711yescharacteristic, complemented, Hall
22C7×D85—51no—
23C7×D85—51no—
24C7×D85—102no—
25C3×C7×C5⋊D5—171no—
26C3×#66776—351no—
27C3×#66775—351no—
28C5⋊D85C3×D711yescharacteristic
29C3×C7×D17—251no—
30C7⋊#1044—171noHall
31C5×C7×C17—22no—
32C5×C7×C17C3×AGL(1,𝔽5)11yescharacteristic, complemented
33C5×C7×C17C3×AGL(1,𝔽5)11yescharacteristic, complemented
34C3×C52×C7#59511yescharacteristic, complemented, Hall
35C3×D85—51no—
36C3×D85—51no—
37C3×D85—102no—
38C7⋊#595—251noHall
39C52×C17C3×Dic711yescharacteristic, complemented, Hall
40C3×C7⋊AGL(1,𝔽5)—851no—
41C3×C7⋊AGL(1,𝔽5)—851no—
42C3×C7×C17#104411yescharacteristic, complemented, Hall
43C7×C5⋊D5—171no—
44#66776—351no—
45#66775—351no—
46C3×#1044—1191noHall
47C3×C5×C17—22no—
48C3×C5×C17C7⋊AGL(1,𝔽5)11yescharacteristic, complemented
49C3×C5×C17C7⋊AGL(1,𝔽5)11yescharacteristic, complemented
50C7×D17—251no—
51C3×C7×D5—851no—
52C3×C7×D5—851no—
53C3×C7×D5—1702no—
54C3×#595—1751noHall
55C52×C7C3×#59511yescharacteristic, complemented, Hall
56D85—51no—
57D85—51no—
58D85—102no—
59C3×C5⋊D5—171no—
60C7⋊AGL(1,𝔽5)—851no—
61C7⋊AGL(1,𝔽5)—851no—
62C7×C17C3×#104411yescharacteristic, complemented, Hall
63C3×C5×C7—22no—
64C3×C5×C7#6677511yescharacteristic, complemented
65C3×C5×C7#6677611yescharacteristic, complemented
66C3×D17—251no—
67#1044—1191noHall
68C5×C17—22no—
69C5×C17C3×C7⋊AGL(1,𝔽5)11yescharacteristic, complemented
70C5×C17C3×C7⋊AGL(1,𝔽5)11yescharacteristic, complemented
71C3×Dic7—4251noHall
72C3×C52C7⋊#59511yescharacteristic, complemented, Hall
73C7×D5—851no—
74C7×D5—851no—
75C7×D5—1702no—
76#595—1751noHall
77C3×AGL(1,𝔽5)—5951no—
78C3×AGL(1,𝔽5)—5951no—
79C3×C17C7⋊#104411yescharacteristic, complemented, Hall
80C5⋊D5—171no—
81C2×C3×C7—4251no—
82C5×C7—22no—
83C5×C7C3×#6677511yescharacteristic, complemented
84C5×C7C3×#6677611yescharacteristic, complemented
85D17—251no—
86C3×D5—851no—
87C3×D5—851no—
88C3×D5—1702no—
89Dic7—4251noHall
90C52C3×C7⋊#59511yescharacteristic, complemented, Sylow
91C3×C7#1313334711yescharacteristic, complemented, Hall
92AGL(1,𝔽5)—5951no—
93AGL(1,𝔽5)—5951no—
94C17C3×C7⋊#104411yescharacteristic, complemented, Sylow
95C3×C5—22no—
96C3×C5C7⋊#6677511yescharacteristic, complemented
97C3×C5C7⋊#6677611yescharacteristic, complemented
98C2×C7—4251no—
99C3×C4—29751noHall
100D5—851no—
101D5—851no—
102D5—1702no—
103C7C3×#1313334711yescharacteristic, complemented, Sylow
104C2×C3—4251no—
105C5—22no—
106C5C3×C7⋊#6677511yescharacteristic, complemented
107C5C3×C7⋊#6677611yescharacteristic, complemented
108C4—29751noSylow
109C3C7⋊#1313334711yescharacteristic, direct product factor, Sylow
110C2—4251no—
subgroupG/H
center, hypercenterC3C7⋊#13133347
commutator, hypocenterC52×C7×C17C3×C4
FrattiniC1G
Fitting, socleC3×C52×C7×C17C4
prime radicalC3×C7×C5⋊D85C2
cosocleC7×C5⋊D85C2×C3
LCSG ▷ C52×C7×C17
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C7⋊#13133347C3direct (N × H)
3. C3×C52×C7×C17C4semidirect
11. C52×C7×C17C3×C4semidirect
17. C3×C5×C7×C17AGL(1,𝔽5)semidirect
18. C3×C5×C7×C17AGL(1,𝔽5)semidirect
21. C3×C52×C17Dic7semidirect
32. C5×C7×C17C3×AGL(1,𝔽5)semidirect
33. C5×C7×C17C3×AGL(1,𝔽5)semidirect
34. C3×C52×C7#595semidirect
39. C52×C17C3×Dic7semidirect
42. C3×C7×C17#1044semidirect
48. C3×C5×C17C7⋊AGL(1,𝔽5)semidirect
49. C3×C5×C17C7⋊AGL(1,𝔽5)semidirect
55. C52×C7C3×#595semidirect
62. C7×C17C3×#1044semidirect
64. C3×C5×C7#66775semidirect
65. C3×C5×C7#66776semidirect
69. C5×C17C3×C7⋊AGL(1,𝔽5)semidirect
70. C5×C17C3×C7⋊AGL(1,𝔽5)semidirect
72. C3×C52C7⋊#595semidirect
79. C3×C17C7⋊#1044semidirect
83. C5×C7C3×#66775semidirect
84. C5×C7C3×#66776semidirect
90. C52C3×C7⋊#595semidirect
91. C3×C7#13133347semidirect
94. C17C3×C7⋊#1044semidirect
96. C3×C5C7⋊#66775semidirect
97. C3×C5C7⋊#66776semidirect
103. C7C3×#13133347semidirect
106. C5C3×C7⋊#66775semidirect
107. C5C3×C7⋊#66776semidirect
109. C3C7⋊#13133347direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C7×C5⋊D852
C7⋊#131333473
C3×C7⋊#667765
C3×C7⋊#667755
C3×#131333477
C3×C7⋊#104417