Finite Group Databasebeta

← C5×D11×#64422 #44568638

Subgroups — C5×D11×#64422 #44568638

Order 32340.

168 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 54 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×D11×#3862C211yesmaximal, characteristic, complemented
2C5×C11⋊#64422C211yesmaximal, characteristic, complemented
3C5×C11×#64422C211yesmaximal, characteristic, complemented
4C5×C7×D7×D11C311yesmaximal, characteristic, complemented, Hall
5C5×C11×#3862C2211yescharacteristic, complemented, Hall
6D11×#64422C511yesmaximal, characteristic, direct product factor, Hall
7C5×C7×D77C2×C311yescharacteristic, complemented
8C5×C7×C11×D7C2×C311yescharacteristic, complemented
9C5×C72×D11C2×C311yescharacteristic, complemented
10C2×C5×ΓL(1,𝔽8)×D11—71nomaximal
11C5×D11×AGL(1,𝔽7)—71nomaximal
12D11×#3862C2×C511yescharacteristic, complemented
13C11⋊#64422C2×C511yescharacteristic, complemented
14C11×#64422C2×C511yescharacteristic, complemented
15C2×C5×#64422—111nomaximal, Hall
16C5×C72×C11C22×C311yescharacteristic, complemented, Hall
17C5×C11⋊AGL(1,𝔽7)—71no—
18C5×C11×AGL(1,𝔽7)—71no—
19C5×ΓL(1,𝔽8)×D11—71no—
20C5×ΓL(1,𝔽8)×D11—71no—
21C5×ΓL(1,𝔽8)×D11—71no—
22C2×C5×C11×ΓL(1,𝔽8)—71no—
23C7×D7×D11C3×C511yescharacteristic, complemented, Hall
24C11×#3862C22×C511yescharacteristic, complemented, Hall
25C2×C5×C7×D11—71no—
26C5×D7×D11ΓL(1,𝔽8)11yescharacteristic, complemented
27C2×C5×#3862—111no—
28C5×#64422—111no—
29C5×#64422D1111yescharacteristic, direct product factor
30C5×C11×ΓL(1,𝔽8)—71no—
31C5×C11×ΓL(1,𝔽8)—71no—
32C7×D77C2×C3×C511yescharacteristic, complemented
33C7×C11×D7C2×C3×C511yescharacteristic, complemented
34C72×D11C2×C3×C511yescharacteristic, complemented
35C2×C5×C7×D7—111noHall
36C2×ΓL(1,𝔽8)×D11—71no—
37D11×AGL(1,𝔽7)—71no—
38C2×C5×C7×C11—71no—
39C5×D77C2×ΓL(1,𝔽8)11yescharacteristic, complemented
40C5×C11×D7C2×ΓL(1,𝔽8)11yescharacteristic, complemented
41C5×C7×D11—61no—
42C5×C7×D11—71no—
43C5×C7×D11AGL(1,𝔽7)11yescharacteristic, complemented
44C5×C7×D11C2×ΓL(1,𝔽8)11yescharacteristic, complemented
45C5×#3862C2×D1111yescharacteristic, complemented, Hall
46C2×C3×C5×D11—491noHall
47C2×#64422—111noHall
48C72×C11C22×C3×C511yescharacteristic, complemented, Hall
49C2×C5×C72—111no—
50C5×C7×D7—111no—
51C5×C7×D7C3×D1111yescharacteristic, complemented
52C2×C11×ΓL(1,𝔽8)—71no—
53C11⋊AGL(1,𝔽7)—71no—
54C11×AGL(1,𝔽7)—71no—
55ΓL(1,𝔽8)×D11—71no—
56ΓL(1,𝔽8)×D11—71no—
57ΓL(1,𝔽8)×D11—71no—
58C22×C5×ΓL(1,𝔽8)—771no—
59C2×C5×AGL(1,𝔽7)—771no—
60C5×C7×C11—61no—
61C5×C7×C11C2×AGL(1,𝔽7)11yescharacteristic, complemented
62C5×C7×C11C22×ΓL(1,𝔽8)11yescharacteristic, complemented
63C2×C3×C5×C11—491no—
64C3×C5×D11—491no—
65C3×C5×D11—491no—
66C2×C7×D11—71no—
67D7×D11C5×ΓL(1,𝔽8)11yescharacteristic, complemented
68C2×#3862—111no—
69#64422—111no—
70#64422C5×D1111yescharacteristic, direct product factor
71C5×C72C2×C3×D1111yescharacteristic, complemented, Hall
72C11×ΓL(1,𝔽8)—71no—
73C11×ΓL(1,𝔽8)—71no—
74C2×C5×D11—71noHall
75C2×C5×ΓL(1,𝔽8)—71no—
76C2×C5×ΓL(1,𝔽8)—771no—
77C2×C5×ΓL(1,𝔽8)—771no—
78C2×C5×ΓL(1,𝔽8)—771no—
79C5×AGL(1,𝔽7)—71no—
80C5×AGL(1,𝔽7)—771no—
81C2×C7×D7—111noHall
82C3×C5×C11—491noHall
83C2×C7×C11—71no—
84D77C2×C5×ΓL(1,𝔽8)11yescharacteristic, complemented
85C7×D11—61no—
86C7×D11—71no—
87C7×D11C5×AGL(1,𝔽7)11yescharacteristic, complemented
88C7×D11C2×C5×ΓL(1,𝔽8)11yescharacteristic, complemented
89C11×D7C2×C5×ΓL(1,𝔽8)11yescharacteristic, complemented
90#3862C2×C5×D1111yescharacteristic, complemented, Hall
91C22×C5×C7—771no—
92C2×C5×D7—111no—
93C2×C3×D11—491noHall
94C2×C5×C11—71no—
95C5×D11—71no—
96C5×D11#6442211yescharacteristic, direct product factor
97C5×ΓL(1,𝔽8)—71no—
98C5×ΓL(1,𝔽8)—71no—
99C2×C72—111no—
100C7×D7—111no—
101C7×D7C3×C5×D1111yescharacteristic, complemented
102C22×ΓL(1,𝔽8)—771no—
103C2×AGL(1,𝔽7)—771no—
104C7×C11—61no—
105C7×C11C2×C5×AGL(1,𝔽7)11yescharacteristic, complemented
106C7×C11C22×C5×ΓL(1,𝔽8)11yescharacteristic, complemented
107C2×C5×C7—71no—
108C2×C5×C7—111no—
109C2×C5×C7—111no—
110C2×C5×C7—661no—
111C2×C5×C7—771no—
112C5×D7—111no—
113C5×D7ΓL(1,𝔽8)×D1111yescharacteristic, complemented
114C2×C3×C11—491no—
115C3×D11—491no—
116C3×D11—491no—
117C22×C3×C5—5391noHall
118C5×C11C2×#6442211yescharacteristic, complemented, Hall
119C72C2×C3×C5×D1111yescharacteristic, complemented, Sylow
120C2×D11—71noHall
121C2×ΓL(1,𝔽8)—71no—
122C2×ΓL(1,𝔽8)—771no—
123C2×ΓL(1,𝔽8)—771no—
124C2×ΓL(1,𝔽8)—771no—
125AGL(1,𝔽7)—71no—
126AGL(1,𝔽7)—771no—
127C5×C7—61no—
128C5×C7D11×AGL(1,𝔽7)11yescharacteristic, complemented
129C5×C7C2×ΓL(1,𝔽8)×D1111yescharacteristic, complemented
130C3×C11—491noHall
131C2×C3×C5—5391no—
132C2×C3×C5—5391no—
133C2×C3×C5—491no—
134C22×C7—771no—
135C2×D7—111no—
136C2×C11—71no—
137D11—71no—
138D11C5×#6442211yescharacteristic, direct product factor
139ΓL(1,𝔽8)—71no—
140ΓL(1,𝔽8)—71no—
141C22×C5—771noHall
142C3×C5—491noHall
143C2×C7—71no—
144C2×C7—111no—
145C2×C7—111no—
146C2×C7—661no—
147C2×C7—771no—
148D7—111no—
149D7C5×ΓL(1,𝔽8)×D1111yescharacteristic, complemented
150C22×C3—5391noHall
151C11C2×C5×#6442211yescharacteristic, complemented, Sylow
152C2×C5—71no—
153C2×C5—111no—
154C2×C5—771no—
155C7—61no—
156C7C5×D11×AGL(1,𝔽7)11yescharacteristic, complemented
157C7C2×C5×ΓL(1,𝔽8)×D1111yescharacteristic, complemented
158C2×C3—5391no—
159C2×C3—5391no—
160C2×C3—491no—
161C5D11×#6442211yescharacteristic, direct product factor, Sylow
162C22—771noSylow
163C3—491noSylow
164C2—71no—
165C2—111no—
166C2—771no—
subgroupG/H
center, hypercenterC5D11×#64422
commutator, cosocle, hypocenterC72×C11C22×C3×C5
FrattiniC1G
Fitting, socleC5×C72×C11C22×C3
LCSG ▷ C72×C11
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×D11×#3862C2semidirect
2. C5×C11⋊#64422C2semidirect
3. C5×C11×#64422C2semidirect
4. C5×C7×D7×D11C3semidirect
5. C5×C11×#3862C22semidirect
6. D11×#64422C5direct (N × H)
7. C5×C7×D77C2×C3semidirect
8. C5×C7×C11×D7C2×C3semidirect
9. C5×C72×D11C2×C3semidirect
12. D11×#3862C2×C5semidirect
13. C11⋊#64422C2×C5semidirect
14. C11×#64422C2×C5semidirect
16. C5×C72×C11C22×C3semidirect
23. C7×D7×D11C3×C5semidirect
24. C11×#3862C22×C5semidirect
26. C5×D7×D11ΓL(1,𝔽8)semidirect
29. C5×#64422D11direct (N × H)
32. C7×D77C2×C3×C5semidirect
33. C7×C11×D7C2×C3×C5semidirect
34. C72×D11C2×C3×C5semidirect
39. C5×D77C2×ΓL(1,𝔽8)semidirect
40. C5×C11×D7C2×ΓL(1,𝔽8)semidirect
43. C5×C7×D11AGL(1,𝔽7)semidirect
44. C5×C7×D11C2×ΓL(1,𝔽8)semidirect
45. C5×#3862C2×D11semidirect
48. C72×C11C22×C3×C5semidirect
51. C5×C7×D7C3×D11semidirect
61. C5×C7×C11C2×AGL(1,𝔽7)semidirect
62. C5×C7×C11C22×ΓL(1,𝔽8)semidirect
67. D7×D11C5×ΓL(1,𝔽8)semidirect
70. #64422C5×D11direct (N × H)
71. C5×C72C2×C3×D11semidirect
84. D77C2×C5×ΓL(1,𝔽8)semidirect
87. C7×D11C5×AGL(1,𝔽7)semidirect
88. C7×D11C2×C5×ΓL(1,𝔽8)semidirect
89. C11×D7C2×C5×ΓL(1,𝔽8)semidirect
90. #3862C2×C5×D11semidirect
96. C5×D11#64422direct (N × H)
101. C7×D7C3×C5×D11semidirect
105. C7×C11C2×C5×AGL(1,𝔽7)semidirect
106. C7×C11C22×C5×ΓL(1,𝔽8)semidirect
113. C5×D7ΓL(1,𝔽8)×D11semidirect
118. C5×C11C2×#64422semidirect
119. C72C2×C3×C5×D11semidirect
128. C5×C7D11×AGL(1,𝔽7)semidirect
129. C5×C7C2×ΓL(1,𝔽8)×D11semidirect
138. D11C5×#64422direct (N × H)
149. D7C5×ΓL(1,𝔽8)×D11semidirect
151. C11C2×C5×#64422semidirect
156. C7C5×D11×AGL(1,𝔽7)semidirect
157. C7C2×C5×ΓL(1,𝔽8)×D11semidirect
161. C5D11×#64422direct (N × H)

Maximal subgroups

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

subgroupindex
C5×D11×#38622
C5×C11⋊#644222
C5×C11×#644222
C5×C7×D7×D113
D11×#644225
C2×C5×ΓL(1,𝔽8)×D117
C5×D11×AGL(1,𝔽7)7
C2×C5×#6442211