Finite Group Databasebeta

← C4×C5×C22⋊D7 #11765086

Subgroups — C4×C5×C22⋊D7 #11765086

Order 1120.

188 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C22×C4×C5×C7C211yesmaximal, characteristic, complemented
2C2×C5×C22⋊D7C211yesmaximal, characteristic
3C2×C4×C5×D7C211yesmaximal, characteristic, complemented
4C5×C22⋊Dic7C211yesmaximal, characteristic, complemented
5C5×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
6C5×Dic7⋊C4C211yesmaximal, characteristic, complemented
7C4×C5×Dic7C211yesmaximal, characteristic, complemented
8C23×C5×C7C2211yescharacteristic
9C22×C5×D7C2211yescharacteristic
10C2×C4×C5×C7—22no—
11C2×C4×C5×C7C2211yescharacteristic
12C2×C4×C5×C7C2211yescharacteristic
13C5×C22⋊D7C414yesdirect product factor
14C2×C5×Dic7C2211yescharacteristic
15C2×C5×Dic7C2211yescharacteristic
16C2×C5×Dic7C2211yescharacteristic
17C4×C5×D7—22no—
18C4×C22⋊D7C511yesmaximal, characteristic, direct product factor, Hall
19C4×C5×D4—71nomaximal, Hall
20C22×C5×C7—21no—
21C22×C5×C7—21no—
22C22×C5×C7C2×C412yescomplemented
23C22×C5×C7C2311yescharacteristic
24C2×C5×D7—21no—
25C2×C5×D7—21no—
26C2×C5×D7C2×C412yescomplemented
27C4×C5×C7—21no—
28C4×C5×C7D412yescomplemented
29C5×Dic7—21no—
30C5×Dic7—21no—
31C5×Dic7C2×C412yescomplemented
32C22×C4×C7C2×C511yescharacteristic, complemented
33C2×C22⋊D7C2×C511yescharacteristic
34C2×C4×D7C2×C511yescharacteristic, complemented
35C22⋊Dic7C2×C511yescharacteristic, complemented
36(C2×D7)⋊C4C2×C511yescharacteristic, complemented
37Dic7⋊C4C2×C511yescharacteristic, complemented
38C4×Dic7C2×C511yescharacteristic, complemented
39C2×C5×D4—71no—
40C22×C4×C5—71no—
41C22×C4×C5D711yescharacteristic, complemented
42C5×C4⋊C4—71no—
43C5×C22⋊C4—71no—
44C5×C22⋊C4—71no—
45C42×C5—71no—
46C2×C5×C7—22no—
47C2×C5×C7C22×C411yescharacteristic
48C2×C5×C7C2×D411yescharacteristic
49C2×C5×C7#4111yescharacteristic
50C5×D7—22no—
51C23×C7C22×C511yescharacteristic
52C22×D7C22×C511yescharacteristic
53C2×C4×C7—22no—
54C2×C4×C7C22×C511yescharacteristic
55C2×C4×C7C22×C511yescharacteristic
56C22⋊D7C4×C514yesdirect product factor
57C2×Dic7C22×C511yescharacteristic
58C2×Dic7C22×C511yescharacteristic
59C2×Dic7C22×C511yescharacteristic
60C4×D7—22no—
61C23×C5—71no—
62C23×C5C2×D711yescharacteristic
63C5×D4—74no—
64C2×C4×C5—22no—
65C2×C4×C5—71no—
66C2×C4×C5—71no—
67C2×C4×C5—71no—
68C2×C4×C5—142no—
69C2×C4×C5C2×D711yescharacteristic
70C2×C4×C5C2×D711yescharacteristic
71C5×C7C4×D411yescharacteristic, complemented, Hall
72C4×D4—71noSylow
73C22×C7—21no—
74C22×C7—21no—
75C22×C7C2×C4×C512yescomplemented
76C22×C7C23×C511yescharacteristic
77C2×D7—21no—
78C2×D7—21no—
79C2×D7C2×C4×C512yescomplemented
80C4×C7—21no—
81C4×C7C5×D412yescomplemented
82Dic7—21no—
83Dic7—21no—
84Dic7C2×C4×C512yescomplemented
85C22×C5—21no—
86C22×C5—21no—
87C22×C5—72no—
88C22×C5—141no—
89C22×C5—141no—
90C22×C5C4×D712yescomplemented
91C22×C5C22×D711yescharacteristic
92C4×C5—21no—
93C4×C5—72no—
94C4×C5—141no—
95C4×C5—141no—
96C4×C5C22⋊D712yesdirect product factor
97C2×D4—71no—
98C22×C4—71no—
99C22×C4C5×D711yescharacteristic, complemented
100C4⋊C4—71no—
101C22⋊C4—71no—
102C22⋊C4—71no—
103C42—71no—
104C2×C7—22no—
105C2×C7C22×C4×C511yescharacteristic
106C2×C7C2×C5×D411yescharacteristic
107C2×C7C5×#4111yescharacteristic
108D7—22no—
109C2×C5—22no—
110C2×C5—142no—
111C2×C5C2×C4×D711yescharacteristic
112C2×C5#115711yescharacteristic
113C2×C5C2×C22⋊D711yescharacteristic
114C23—71no—
115C23C2×C5×D711yescharacteristic
116D4—74no—
117C2×C4—22no—
118C2×C4—71no—
119C2×C4—71no—
120C2×C4—71no—
121C2×C4—142no—
122C2×C4C2×C5×D711yescharacteristic
123C2×C4C2×C5×D711yescharacteristic
124C7C4×C5×D411yescharacteristic, complemented, Sylow
125C5C4×C22⋊D711yescharacteristic, direct product factor, Sylow
126C22—21no—
127C22—21no—
128C22—72no—
129C22—141no—
130C22—141no—
131C22C4×C5×D712yescomplemented
132C22C22×C5×D711yescharacteristic
133C4—21no—
134C4—72no—
135C4—141no—
136C4—141no—
137C4C5×C22⋊D712yesdirect product factor
138C2—22no—
139C2—142no—
140C2C2×C4×C5×D711yescharacteristic
141C2C5×#115711yescharacteristic
142C2C2×C5×C22⋊D711yescharacteristic
subgroupG/H
centerC2×C4×C5C2×D7
commutatorC2×C7C22×C4×C5
FrattiniC22C22×C5×D7
FittingC22×C4×C5×C7C2
socleC22×C5×C7C23
prime radicalC2×C5×C22⋊D7C2
cosocleC22×C7C23×C5
hypercenterC22×C4×C5D7
hypocenterC7C4×C5×D4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5

Complements

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

NH ≅ G/Ntype
1. C22×C4×C5×C7C2semidirect
3. C2×C4×C5×D7C2semidirect
4. C5×C22⋊Dic7C2semidirect
5. C5×(C2×D7)⋊C4C2semidirect
6. C5×Dic7⋊C4C2semidirect
7. C4×C5×Dic7C2semidirect
13. C5×C22⋊D7C4direct (N × H)
18. C4×C22⋊D7C5direct (N × H)
22. C22×C5×C7C2×C4semidirect
26. C2×C5×D7C2×C4semidirect
28. C4×C5×C7D4semidirect
31. C5×Dic7C2×C4semidirect
32. C22×C4×C7C2×C5semidirect
34. C2×C4×D7C2×C5semidirect
35. C22⋊Dic7C2×C5semidirect
36. (C2×D7)⋊C4C2×C5semidirect
37. Dic7⋊C4C2×C5semidirect
38. C4×Dic7C2×C5semidirect
41. C22×C4×C5D7semidirect
56. C22⋊D7C4×C5direct (N × H)
71. C5×C7C4×D4semidirect
75. C22×C7C2×C4×C5semidirect
79. C2×D7C2×C4×C5semidirect
81. C4×C7C5×D4semidirect
84. Dic7C2×C4×C5semidirect
90. C22×C5C4×D7semidirect
96. C4×C5C22⋊D7direct (N × H)
99. C22×C4C5×D7semidirect
124. C7C4×C5×D4semidirect
125. C5C4×C22⋊D7direct (N × H)
131. C22C4×C5×D7semidirect
137. C4C5×C22⋊D7direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C5×C72
C2×C5×C22⋊D72
C2×C4×C5×D72
C5×C22⋊Dic72
C5×(C2×D7)⋊C42
C5×Dic7⋊C42
C4×C5×Dic72
C4×C22⋊D75
C4×C5×D47