Finite Group Databasebeta

← C5×D3×D7×C11⋊C5 #37528443

Subgroups — C5×D3×D7×C11⋊C5 #37528443

Order 23100.

320 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 100 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×D21×C11⋊C5C211yesmaximal, characteristic, complemented
2C5×D3×C7×C11⋊C5C211yesmaximal, characteristic, complemented
3C3×C5×D7×C11⋊C5C211yesmaximal, characteristic, complemented
4C2×C5×D7×C11⋊C5—31nomaximal, Hall
5C3×C5×C7×C11⋊C5C2211yescharacteristic, complemented, Hall
6C5×D3×C11×D7C511yesmaximal, characteristic, complemented
7D3×D7×C11⋊C5C515yesmaximal, direct product factor
8C2×C5×C7×C11⋊C5—31no—
9C5×D7×C11⋊C5—31no—
10C5×D7×C11⋊C5D311yescharacteristic, direct product factor
11C2×C5×D3×C11⋊C5—71nomaximal, Hall
12D21×C11⋊C5C2×C515yescomplemented
13D3×C7×C11⋊C5C2×C515yescomplemented
14C3×D7×C11⋊C5C2×C515yescomplemented
15C5×C11×D21C2×C511yescharacteristic, complemented
16C5×D3×C7×C11C2×C511yescharacteristic, complemented
17C3×C5×C11×D7C2×C511yescharacteristic, complemented
18C52×D3×D7—111nomaximal, Hall
19C5×C7×C11⋊C5C2×D311yescharacteristic, complemented, Hall
20C2×C3×C5×C11⋊C5—71no—
21C5×D3×C11⋊C5—71no—
22C5×D3×C11⋊C5D711yescharacteristic, direct product factor
23C2×C5×C11×D7—31no—
24C2×D7×C11⋊C5—35no—
25C3×C5×C7×C11C22×C511yescharacteristic, complemented
26C3×C7×C11⋊C5C22×C515yescomplemented
27C22×C5×C11⋊C5—211noHall
28C52×D21—111no—
29C52×D3×C7—111no—
30C3×C52×D7—111no—
31D3×C11×D7C5211yescharacteristic, complemented, Hall
32C3×C5×C11⋊C5C2×D711yescharacteristic, complemented, Hall
33C2×C5×C7×C11—31no—
34C5×C11×D7—31no—
35C5×C11×D7C5×D311yescharacteristic, complemented
36C2×C7×C11⋊C5—35no—
37D7×C11⋊C5—35no—
38D7×C11⋊C5C5×D315yesdirect product factor
39C2×C52×D7—331noHall
40C2×C5×D3×C11—71no—
41C2×D3×C11⋊C5—75no—
42C2×C5×C11⋊C5—31no—
43C2×C5×C11⋊C5—71no—
44C2×C5×C11⋊C5—211no—
45C3×C52×C7—111noHall
46C11×D21C2×C5211yescharacteristic, complemented
47D3×C7×C11C2×C5211yescharacteristic, complemented
48C3×C11×D7C2×C5211yescharacteristic, complemented
49C5×D3×D7—115no—
50C5×D3×D7C11⋊C511yescharacteristic, direct product factor
51C5×C7×C11C2×C5×D311yescharacteristic, complemented
52C7×C11⋊C5C2×C5×D315yescomplemented
53C2×C52×C7—331no—
54C52×D7—111no—
55C52×D7—331no—
56C2×C3×C5×C11—71no—
57C5×D3×C11—71no—
58C5×D3×C11C5×D711yescharacteristic, complemented
59C2×C3×C11⋊C5—75no—
60D3×C11⋊C5—75no—
61D3×C11⋊C5C5×D715yesdirect product factor
62C2×C11×D7—31noHall
63C2×C52×D3—771noHall
64C5×C11⋊C5D3×D711yescharacteristic, direct product factor, Hall
65C3×C7×C11C22×C5211yescharacteristic, complemented, Hall
66C22×C5×C11—211no—
67C22×C11⋊C5—215no—
68C5×D21—115no—
69C5×D21C2×C11⋊C511yescharacteristic, complemented
70C5×D3×C7—115no—
71C5×D3×C7C2×C11⋊C511yescharacteristic, complemented
72C3×C5×D7—115no—
73C3×C5×D7C2×C11⋊C511yescharacteristic, complemented
74C52×C7—111noHall
75C3×C5×C11C2×C5×D711yescharacteristic, complemented
76C3×C11⋊C5C2×C5×D715yescomplemented
77C2×C7×C11—31no—
78C11×D7—31no—
79C11×D7C52×D311yescharacteristic, complemented
80C2×C3×C52—771no—
81C52×D3—111no—
82C52×D3—771no—
83C2×C5×D7—31no—
84C2×C5×D7—335no—
85C2×D3×C11—71noHall
86C2×C5×C11—31no—
87C2×C5×C11—71no—
88C2×C5×C11—211no—
89C2×C11⋊C5—35no—
90C2×C11⋊C5—75no—
91C2×C11⋊C5—215no—
92C3×C5×C7—115no—
93C3×C5×C7C22×C11⋊C511yescharacteristic, complemented
94C22×C52—2311noHall
95D3×D7C5×C11⋊C511yescharacteristic, direct product factor, Hall
96C7×C11C2×C52×D311yescharacteristic, complemented, Hall
97C3×C52—111noHall
98C2×C5×C7—31no—
99C2×C5×C7—335no—
100C5×D7—31no—
101C5×D7—115no—
102C5×D7—335no—
103C5×D7D3×C11⋊C511yescharacteristic, direct product factor
104C2×C3×C11—71no—
105D3×C11—71no—
106D3×C11C52×D711yescharacteristic, complemented
107C2×C5×D3—71no—
108C2×C5×D3—775no—
109C5×C11C5×D3×D711yescharacteristic, complemented
110C11⋊C5C5×D3×D715yesdirect product factor
111C2×C52—331no—
112C2×C52—771no—
113C2×C52—2311no—
114C22×C11—211noHall
115D21C2×C5×C11⋊C511yescharacteristic, complemented
116C3×D7C2×C5×C11⋊C511yescharacteristic, complemented
117D3×C7C2×C5×C11⋊C511yescharacteristic, complemented
118C5×C7—115no—
119C5×C7C2×D3×C11⋊C511yescharacteristic, complemented
120C3×C11C2×C52×D711yescharacteristic, complemented, Hall
121C2×C3×C5—71no—
122C2×C3×C5—775no—
123C5×D3—71no—
124C5×D3—115no—
125C5×D3—775no—
126C5×D3D7×C11⋊C511yescharacteristic, direct product factor
127C2×D7—31noHall
128C52—111noSylow
129C2×C11—31no—
130C2×C11—71no—
131C2×C11—211no—
132C3×C7C22×C5×C11⋊C511yescharacteristic, complemented, Hall
133C22×C5—211no—
134C22×C5—2315no—
135C3×C5—115no—
136C3×C5C2×D7×C11⋊C511yescharacteristic, complemented
137C2×C7—31no—
138D7—31no—
139D7C5×D3×C11⋊C511yescharacteristic, direct product factor
140C2×D3—71noHall
141C11C52×D3×D711yescharacteristic, complemented, Sylow
142C2×C5—31no—
143C2×C5—71no—
144C2×C5—211no—
145C2×C5—335no—
146C2×C5—775no—
147C2×C5—2315no—
148C7C2×C5×D3×C11⋊C511yescharacteristic, complemented, Sylow
149C2×C3—71no—
150D3—71no—
151D3C5×D7×C11⋊C511yescharacteristic, direct product factor
152C5—115no—
153C5D3×D7×C11⋊C511yescharacteristic, direct product factor
154C22—211noSylow
155C3C2×C5×D7×C11⋊C511yescharacteristic, complemented, Sylow
156C2—31no—
157C2—71no—
158C2—211no—
subgroupG/H
center, hypercenterC5D3×D7×C11⋊C5
commutator, cosocle, hypocenterC3×C7×C11C22×C52
FrattiniC1G
Fitting, socleC3×C5×C7×C11C22×C5
LCSG ▷ C3×C7×C11
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×D21×C11⋊C5C2semidirect
2. C5×D3×C7×C11⋊C5C2semidirect
3. C3×C5×D7×C11⋊C5C2semidirect
5. C3×C5×C7×C11⋊C5C22semidirect
6. C5×D3×C11×D7C5semidirect
7. D3×D7×C11⋊C5C5direct (N × H)
10. C5×D7×C11⋊C5D3direct (N × H)
12. D21×C11⋊C5C2×C5semidirect
13. D3×C7×C11⋊C5C2×C5semidirect
14. C3×D7×C11⋊C5C2×C5semidirect
15. C5×C11×D21C2×C5semidirect
16. C5×D3×C7×C11C2×C5semidirect
17. C3×C5×C11×D7C2×C5semidirect
19. C5×C7×C11⋊C5C2×D3semidirect
22. C5×D3×C11⋊C5D7direct (N × H)
25. C3×C5×C7×C11C22×C5semidirect
26. C3×C7×C11⋊C5C22×C5semidirect
31. D3×C11×D7C52semidirect
32. C3×C5×C11⋊C5C2×D7semidirect
35. C5×C11×D7C5×D3semidirect
38. D7×C11⋊C5C5×D3direct (N × H)
46. C11×D21C2×C52semidirect
47. D3×C7×C11C2×C52semidirect
48. C3×C11×D7C2×C52semidirect
50. C5×D3×D7C11⋊C5direct (N × H)
51. C5×C7×C11C2×C5×D3semidirect
52. C7×C11⋊C5C2×C5×D3semidirect
58. C5×D3×C11C5×D7semidirect
61. D3×C11⋊C5C5×D7direct (N × H)
64. C5×C11⋊C5D3×D7direct (N × H)
65. C3×C7×C11C22×C52semidirect
69. C5×D21C2×C11⋊C5semidirect
71. C5×D3×C7C2×C11⋊C5semidirect
73. C3×C5×D7C2×C11⋊C5semidirect
75. C3×C5×C11C2×C5×D7semidirect
76. C3×C11⋊C5C2×C5×D7semidirect
79. C11×D7C52×D3semidirect
93. C3×C5×C7C22×C11⋊C5semidirect
95. D3×D7C5×C11⋊C5direct (N × H)
96. C7×C11C2×C52×D3semidirect
103. C5×D7D3×C11⋊C5direct (N × H)
106. D3×C11C52×D7semidirect
109. C5×C11C5×D3×D7semidirect
110. C11⋊C5C5×D3×D7direct (N × H)
115. D21C2×C5×C11⋊C5semidirect
116. C3×D7C2×C5×C11⋊C5semidirect
117. D3×C7C2×C5×C11⋊C5semidirect
119. C5×C7C2×D3×C11⋊C5semidirect
120. C3×C11C2×C52×D7semidirect
126. C5×D3D7×C11⋊C5direct (N × H)
132. C3×C7C22×C5×C11⋊C5semidirect
136. C3×C5C2×D7×C11⋊C5semidirect
139. D7C5×D3×C11⋊C5direct (N × H)
141. C11C52×D3×D7semidirect
148. C7C2×C5×D3×C11⋊C5semidirect
151. D3C5×D7×C11⋊C5direct (N × H)
153. C5D3×D7×C11⋊C5direct (N × H)
155. C3C2×C5×D7×C11⋊C5semidirect

Maximal subgroups

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

subgroupindex
C5×D21×C11⋊C52
C5×D3×C7×C11⋊C52
C3×C5×D7×C11⋊C52
C2×C5×D7×C11⋊C53
C5×D3×C11×D75
D3×D7×C11⋊C55
C2×C5×D3×C11⋊C57
C52×D3×D711