Finite Group Databasebeta

← C5×C7×C3⋊#66772 #49087929

Subgroups — C5×C7×C3⋊#66772 #49087929

Order 35700.

128 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 52 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×C52×C7×D17C211yesmaximal, characteristic
2C5×C7×#66772—31nomaximal, Hall
3C3×C52×C7×C17C411yescharacteristic, complemented, Hall
4C7×C3⋊#66772C511yesmaximal, characteristic, direct product factor
5C5×C7×C3⋊#595—51nomaximal
6C52×C7×D17D311yescharacteristic
7C5×C3⋊#66772C711yesmaximal, characteristic, direct product factor, Hall
8C3×C5×C7×D17—22no—
9C3×C5×C7×D17D511yescharacteristic
10C3×C5×C7×D17C2×C511yescharacteristic
11C52×C7×C17Dic311yescharacteristic, complemented, Hall
12C3×C52×D17C2×C711yescharacteristic
13C7×#66772—31no—
14C5×C7×#595—151no—
15C5×C7×Dic15—171nomaximal, Hall
16C3×C5×C7×C17—22no—
17C3×C5×C7×C17Dic511yescharacteristic, complemented
18C3×C5×C7×C17C4×C511yescharacteristic, complemented
19C5×#66772—31noHall
20C7×C3⋊#595—51noHall
21C3×C52×C17C4×C711yescharacteristic, complemented, Hall
22C5×C7×D17—22no—
23C5×C7×D17C5×D311yescharacteristic
24C5×C7×D17D1511yescharacteristic
25C2×C3×C52×C7—171no—
26C3⋊#66772C5×C711yescharacteristic, direct product factor
27C5×C3⋊#595—51no—
28C52×D17D3×C711yescharacteristic
29C3×C7×D17C5×D511yescharacteristic
30C5×C7×Dic5—511noHall
31C5×C7×C17—22no—
32C5×C7×C17C5×Dic311yescharacteristic, complemented
33C5×C7×C17Dic1511yescharacteristic, complemented
34C3×C52×C7#59511yescharacteristic, complemented, Hall
35C3×C5×D17—22no—
36C3×C5×D17C7×D511yescharacteristic
37C3×C5×D17C2×C5×C711yescharacteristic
38C7×#595—151noHall
39C52×C17C7×Dic311yescharacteristic, complemented, Hall
40C7×Dic15—171no—
41C5×C7×Dic3—851no—
42C3×C7×C17C5×Dic511yescharacteristic, complemented, Hall
43C2×C52×C7—171no—
44#66772—31no—
45C5×#595—151no—
46C5×Dic15—171noHall
47C3×C5×C17—22no—
48C3×C5×C17C7×Dic511yescharacteristic, complemented
49C3×C5×C17C4×C5×C711yescharacteristic, complemented
50C7×D17C5×D1511yescharacteristic
51C2×C3×C5×C7—171no—
52C2×C3×C5×C7—171no—
53C2×C3×C5×C7—342no—
54C3⋊#595—51noHall
55C52×C7C3⋊#59511yescharacteristic, complemented, Hall
56C5×D17—22no—
57C5×D17C5×D3×C711yescharacteristic
58C5×D17C7×D1511yescharacteristic
59C2×C3×C52—171no—
60C4×C5×C7—2551no—
61C7×Dic5—511no—
62C7×C17C5×Dic1511yescharacteristic, complemented, Hall
63C3×C5×C7—22no—
64C3×C5×C7C5×#59511yescharacteristic, complemented
65C3×C5×C7#6677211yescharacteristic, complemented
66C3×D17C5×C7×D511yescharacteristic
67C5×Dic5—511noHall
68C5×C17—22no—
69C5×C17C5×C7×Dic311yescharacteristic, complemented
70C5×C17C7×Dic1511yescharacteristic, complemented
71C7×Dic3—851noHall
72C3×C52C7×#59511yescharacteristic, complemented, Hall
73C2×C5×C7—171no—
74C2×C5×C7—171no—
75C2×C5×C7—342no—
76#595—151noHall
77Dic15—171no—
78C5×Dic3—851no—
79C3×C17C5×C7×Dic511yescharacteristic, complemented, Hall
80C2×C52—171no—
81C2×C3×C7—171no—
82C5×C7—22no—
83C5×C7C5×C3⋊#59511yescharacteristic, complemented
84C5×C7C3⋊#6677211yescharacteristic, direct product factor
85D17C5×C7×D1511yescharacteristic
86C2×C3×C5—171no—
87C2×C3×C5—171no—
88C2×C3×C5—342no—
89C4×C7—2551noHall
90C52C7×C3⋊#59511yescharacteristic, complemented, Sylow
91C3×C7C5×#6677211yescharacteristic, complemented, Hall
92C4×C5—2551no—
93Dic5—511no—
94C17C5×C7×Dic1511yescharacteristic, complemented, Sylow
95C3×C5—22no—
96C3×C5C5×C7×#59511yescharacteristic, complemented
97C3×C5C7×#6677211yescharacteristic, complemented
98C2×C7—171no—
99Dic3—851noHall
100C2×C5—171no—
101C2×C5—171no—
102C2×C5—342no—
103C7C5×C3⋊#6677211yescharacteristic, direct product factor, Sylow
104C2×C3—171no—
105C5—22no—
106C5C5×C7×C3⋊#59511yescharacteristic, complemented
107C5C7×C3⋊#6677211yescharacteristic, direct product factor
108C4—2551noSylow
109C3C5×C7×#6677211yescharacteristic, complemented, Sylow
110C2—171no—
subgroupG/H
center, hypercenterC5×C7C3⋊#66772
commutator, hypocenterC3×C5×C17C4×C5×C7
FrattiniC1G
Fitting, socleC3×C52×C7×C17C4
prime radicalC3×C52×C7×D17C2
cosocleC3×C5×D17C2×C5×C7
LCSG ▷ C3×C5×C17
UCSC1 ◁ C5×C7

Complements

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

NH ≅ G/Ntype
3. C3×C52×C7×C17C4semidirect
4. C7×C3⋊#66772C5direct (N × H)
7. C5×C3⋊#66772C7direct (N × H)
11. C52×C7×C17Dic3semidirect
17. C3×C5×C7×C17Dic5semidirect
18. C3×C5×C7×C17C4×C5semidirect
21. C3×C52×C17C4×C7semidirect
26. C3⋊#66772C5×C7direct (N × H)
32. C5×C7×C17C5×Dic3semidirect
33. C5×C7×C17Dic15semidirect
34. C3×C52×C7#595semidirect
39. C52×C17C7×Dic3semidirect
42. C3×C7×C17C5×Dic5semidirect
48. C3×C5×C17C7×Dic5semidirect
49. C3×C5×C17C4×C5×C7semidirect
55. C52×C7C3⋊#595semidirect
62. C7×C17C5×Dic15semidirect
64. C3×C5×C7C5×#595semidirect
65. C3×C5×C7#66772semidirect
69. C5×C17C5×C7×Dic3semidirect
70. C5×C17C7×Dic15semidirect
72. C3×C52C7×#595semidirect
79. C3×C17C5×C7×Dic5semidirect
83. C5×C7C5×C3⋊#595semidirect
84. C5×C7C3⋊#66772direct (N × H)
90. C52C7×C3⋊#595semidirect
91. C3×C7C5×#66772semidirect
94. C17C5×C7×Dic15semidirect
96. C3×C5C5×C7×#595semidirect
97. C3×C5C7×#66772semidirect
103. C7C5×C3⋊#66772direct (N × H)
106. C5C5×C7×C3⋊#595semidirect
107. C5C7×C3⋊#66772direct (N × H)
109. C3C5×C7×#66772semidirect

Maximal subgroups

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

subgroupindex
C3×C52×C7×D172
C5×C7×#667723
C7×C3⋊#667725
C5×C7×C3⋊#5955
C5×C3⋊#667727
C5×C7×Dic1517