Finite Group Databasebeta

← C2×#11717484 #13107830

Subgroups — C2×#11717484 #13107830

Order 1600.

1936 conjugacy classes of subgroups; only the 544 normal subgroups are shown.

normal subgroups only

This group has 1936 conjugacy classes of subgroups — too many to draw. Only its 544 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
1C2×Q8×C5⋊D5C211yesmaximal, characteristic, complemented
2C2×C5×#713C212yesmaximal, complemented
3#11717484C2116yesmaximal, direct product factor
4C2×#87877C213yesmaximal, complemented
5C2×C4×D52C213yesmaximal, complemented
6C2×#87870C216yesmaximal, complemented
7C22×D52C2213yes—
8C2×C52×Q8C2211yescharacteristic, complemented
9Q8×C5⋊D5C2218yescomplemented
10C2×C4×C5⋊D5C2213yes—
11C2×#6045C2213yescomplemented
12C5×#713C22116yescomplemented
13C2×C5×D20C2216yescomplemented
14C2×C4×C5×D5C2216yescomplemented
15C2×#6037C2216yescomplemented
16C2×#6036C2211yescharacteristic
17C2×D5×Dic5C2216yescomplemented
18#87877C22124yescomplemented
19C4×D52C22124yescomplemented
20#87870C22148yescomplemented
21C2×D5×#41—52nomaximal
22C22×C5⋊D5C2311yescharacteristic
23C22×C5×D5C2316yes—
24C2×D52—212no—
25C2×D52C23112yes—
26C52×Q8C2314yescomplemented
27C2×C4×C52C2313yes—
28C2×#1039C2313yes—
29C4×C5⋊D5C23112yes—
30#6045C23112yescomplemented
31C2×C5×Dic5C2312yes—
32C5×D20C23124yescomplemented
33C4×C5×D5C23124yescomplemented
34#6037C23124yescomplemented
35#6036C2314yes—
36D5×Dic5C23124yescomplemented
37C2×C5×#41—52no—
38D5×#41—532no—
39C2×#713D512yescomplemented
40C2×Q8×D5—52no—
41C2×Q8×D5—102no—
42C2×#711—56no—
43C2×D4×D5—56no—
44C2×#709—56no—
45C22×C4×D5—56no—
46C22×C52C2411yescharacteristic
47C2×C5⋊D5#4114yescomplemented
48C2×C5⋊D5C2412yes—
49C2×C5×D5—212no—
50C2×C5×D5C24112yes—
51D52—224no—
52C4×C52C2416yes—
53#1039C2416yes—
54C5×Dic5C2414yes—
55C23×D5—56no—
56C5×#41—516no—
57C2×C5×Q8—22no—
58C2×C5×Q8C2×D512yescomplemented
59C2×C5×D4—56no—
60C22×C4×C5—56no—
61C2×C22⋊D5—512no—
62C22×Dic5—56no—
63#713C2×D5116yescomplemented
64Q8×D5—516no—
65Q8×D5—1016no—
66#711—548no—
67D4×D5—548no—
68#709—548no—
69C2×D20C2×D516yescomplemented
70C2×C4×D5—56no—
71C2×C4×D5—56no—
72C2×C4×D5—52no—
73C2×C4×D5—548no—
74C2×C4×D5—106no—
75C2×C4×D5C2×D516yescomplemented
76C2×Dic10—56no—
77C2×Dic10—106no—
78C22×#41—251noSylow
79C2×C52C2×#4112yescomplemented
80C2×C52C2511yescharacteristic
81C5⋊D5C2×#4114yescomplemented
82C5×D5—212no—
83C23×C5—56no—
84C22×D5—52no—
85C22×D5—524no—
86C22×D5—102no—
87C22×D5—1024no—
88C22×D5C22×D516yes—
89C5×Q8—28no—
90C5×Q8C22×D518yescomplemented
91C5×D4—524no—
92C2×C4×C5—26no—
93C2×C4×C5—52no—
94C2×C4×C5—524no—
95C2×C4×C5C22×D516yes—
96C22⋊D5—548no—
97C2×Dic5—56no—
98C2×Dic5—524no—
99C2×Dic5—106no—
100C2×Dic5C22×D512yes—
101D20C22×D5124yescomplemented
102C4×D5—524no—
103C4×D5—524no—
104C4×D5—58no—
105C4×D5—1024no—
106C4×D5C22×D5124yescomplemented
107Dic10—524no—
108Dic10—1024no—
109C2×#41—52no—
110C2×#41—256no—
111C2×#41—2516no—
112C22×Q8—251no—
113C22×D4—253no—
114C23×C4—253no—
115C52C22×#4111yescharacteristic, complemented, Sylow
116C22×C5—22no—
117C22×C5—512no—
118C22×C5—1012no—
119C22×C5C23×D512yes—
120C2×D5—212no—
121C2×D5—58no—
122C2×D5—54no—
123C2×D5—108no—
124C2×D5—104no—
125C2×D5—1048no—
126C2×D5C23×D5112yes—
127C4×C5—212no—
128C4×C5—54no—
129C4×C5C23×D5112yes—
130Dic5—512no—
131Dic5—1012no—
132Dic5C23×D514yes—
133C24—253no—
134#41—516no—
135#41—2548no—
136C2×Q8—258no—
137C2×Q8—253no—
138C2×Q8D5211yescharacteristic, complemented
139C2×D4—56no—
140C2×D4—2524no—
141C2×D4—256no—
142C22×C4—56no—
143C22×C4—251no—
144C22×C4—2524no—
145C22×C4—256no—
146C22×C4—253no—
147C2×C5—24no—
148C2×C5—22no—
149C2×C5—1012no—
150C2×C5D5×#4114yescomplemented
151C2×C5C24×D512yes—
152D5—212no—
153D5—58no—
154D5—108no—
155C23—56no—
156C23—2512no—
157C23—251no—
158C23—5012no—
159Q8—2512no—
160Q8C2×D5214yescomplemented
161D4—524no—
162D4—2524no—
163C2×C4—52no—
164C2×C4—524no—
165C2×C4—254no—
166C2×C4—2524no—
167C2×C4—253no—
168C2×C4—2512no—
169C2×C4C2×D5213yes—
170C5—22no—
171C5C2×D5×#4112yescomplemented
172C22—512no—
173C22—1012no—
174C22—254no—
175C22—252no—
176C22—5024no—
177C22C22×D5211yescharacteristic
178C4—54no—
179C4—256no—
180C4C22×D5216yes—
181C2—1012no—
182C2—254no—
183C2#1171748412yesdirect product factor
184C2C23×D5211yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C52C25
FrattiniC2C23×D52
FittingC2×C52×Q8C22
socleC22×C52C24
hypercenterC2×Q8D52
hypocenterC52C22×#41
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C5⋊D5C2semidirect
2. C2×C5×#713C2semidirect
3. #11717484C2direct (N × H)
4. C2×#87877C2semidirect
5. C2×C4×D52C2semidirect
6. C2×#87870C2semidirect
8. C2×C52×Q8C22semidirect
9. Q8×C5⋊D5C22semidirect
11. C2×#6045C22semidirect
12. C5×#713C22semidirect
13. C2×C5×D20C22semidirect
14. C2×C4×C5×D5C22semidirect
15. C2×#6037C22semidirect
17. C2×D5×Dic5C22semidirect
18. #87877C22semidirect
19. C4×D52C22semidirect
20. #87870C22semidirect
26. C52×Q8C23semidirect
30. #6045C23semidirect
32. C5×D20C23semidirect
33. C4×C5×D5C23semidirect
34. #6037C23semidirect
36. D5×Dic5C23semidirect
39. C2×#713D5semidirect
47. C2×C5⋊D5#41semidirect
58. C2×C5×Q8C2×D5semidirect
63. #713C2×D5semidirect
69. C2×D20C2×D5semidirect
75. C2×C4×D5C2×D5semidirect
79. C2×C52C2×#41semidirect
81. C5⋊D5C2×#41semidirect
90. C5×Q8C22×D5semidirect
101. D20C22×D5semidirect
106. C4×D5C22×D5semidirect
115. C52C22×#41semidirect
138. C2×Q8D52semidirect
150. C2×C5D5×#41semidirect
160. Q8C2×D52semidirect
171. C5C2×D5×#41semidirect
183. C2#11717484direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C5⋊D52
C2×C5×#7132
#117174842
C2×#878772
C2×C4×D522
C2×#878702
C2×D5×#415