Finite Group Databasebeta

← #13107833

Subgroups — #13107833

Order 1600.

1744 conjugacy classes of subgroups; only the 530 normal subgroups are shown.

normal subgroups only

This group has 1744 conjugacy classes of subgroups — too many to draw. Only its 530 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
2C5×#4147C212yesmaximal, complemented
3#11717484C214yesmaximal, complemented
4Q8×D52C214yesmaximal, complemented
5#11717480C218yesmaximal, complemented
6#11717471C216yesmaximal, complemented
7#11717463C216yesmaximal, complemented
8C2×C52×Q8C2211yescharacteristic, complemented
9Q8×C5⋊D5C2214yes—
10Q8×C5⋊D5C2214yescomplemented
11C2×C4×C5⋊D5C2213yes—
12C2×#6045C2213yescomplemented
13C5×#713C2218yescomplemented
14C5×Q8×D5C2218yescomplemented
15C5×#709C22112yescomplemented
16#87886C2214yes—
17#87880C22112yescomplemented
18#87877C2216yes—
19C4×D52C22112yes—
20#87873C22112yescomplemented
21#87872C2216yes—
22#87871C22112yescomplemented
23#87870C22124yescomplemented
24D5×Dic10C22124yescomplemented
25D5×2−1+4—52nomaximal
26C22×C5⋊D5C2311yescharacteristic
27C2×D52C2314yes—
28C52×Q8C2314yes—
29C2×C4×C52C2313yes—
30C2×#1039C2313yes—
31C4×C5⋊D5C2316yes—
32C4×C5⋊D5C2316yes—
33#6045C23112yes—
34C5×C22⋊D5C2318yes—
35C5×D20C23112yes—
36C4×C5×D5C23124yes—
37C5×Dic10C23112yes—
38#6039C23112yes—
39#6038C2318yes—
40#6037C23112yes—
41#6036C2314yes—
42D5×Dic5C23124yes—
43C5×2−1+4—52no—
44#4150—58no—
45#4150—512no—
46D5×#41—58no—
47D5×#41—512no—
48#4147—58no—
49#4147D512yescomplemented
50C2×Q8×D5—52no—
51C2×Q8×D5—58no—
52C2×Q8×D5—102no—
53C22×C52C2411yescharacteristic
54C2×C5⋊D5—22no—
55C2×C5⋊D5C2411yescharacteristic
56C2×C5⋊D5C2411yescharacteristic
57C2×C5×D5C2418yes—
58D52—28no—
59C4×C52C2416yes—
60#1039C2416yes—
61C5×Dic5C2418yes—
62C5×#41—58no—
63C5×#41—512no—
64C2×C5×Q8—22no—
65C2×C5×Q8—58no—
66C2×C5×Q8C2×D512yescomplemented
67#713—512no—
68#713C2×D518yescomplemented
69Q8×D5—58no—
70Q8×D5—58no—
71Q8×D5—524no—
72Q8×D5—512no—
73Q8×D5—108no—
74Q8×D5—108no—
75Q8×D5C2×D518yescomplemented
76#711—524no—
77#711—524no—
78#711—512no—
79D4×D5—58no—
80D4×D5—512no—
81#709—524no—
82#709—524no—
83#709C2×D5112yescomplemented
84C2×C4×D5—56no—
85C2×C4×D5—524no—
86C2×C4×D5—106no—
87C2×Dic10—56no—
88C2×Dic10—524no—
89C2×Dic10—106no—
90C2×2−1+4—251noSylow
91C2×C52—21no—
92C2×C52C2511yescharacteristic
93C5⋊D5—21no—
94C5⋊D52−1+412yescomplemented
95C5×D5—28no—
96C22×D5—52no—
97C22×D5—58no—
98C22×D5—102no—
99C5×Q8—28no—
100C5×Q8—512no—
101C5×Q8C22×D518yes—
102C5×D4—58no—
103C5×D4—512no—
104C2×C4×C5—26no—
105C2×C4×C5—524no—
106C2×C4×C5C22×D516yes—
107C22⋊D5—524no—
108C22⋊D5—58no—
109C22⋊D5C22×D518yes—
110C2×Dic5—56no—
111C2×Dic5—524no—
112C2×Dic5—106no—
113D20—58no—
114D20C22×D5112yes—
115C4×D5—524no—
116C4×D5—512no—
117C4×D5—512no—
118C4×D5—58no—
119C4×D5—1012no—
120C4×D5—1012no—
121C4×D5C22×D5124yes—
122Dic10—524no—
123Dic10—524no—
124Dic10—1024no—
125Dic10C22×D5112yes—
1262−1+4—52no—
1272−1+4—258no—
1282−1+4—256no—
129C2×#41—254no—
130C2×#41—256no—
131C22×Q8—254no—
132C22×Q8—251no—
133C52C2×2−1+411yescharacteristic, complemented, Sylow
134C22×C5—22no—
135C22×C5—58no—
136C22×C5C23×D512yes—
137C2×D5—52no—
138C2×D5—52no—
139C2×D5—102no—
140C2×D5—102no—
141C2×D5—1016no—
142C2×D5—104no—
143C2×D5—108no—
144C2×D5C23×D518yes—
145C4×C5—212no—
146C4×C5—58no—
147C4×C5C23×D5112yes—
148Dic5—512no—
149Dic5—1012no—
150Dic5C23×D518yes—
151#41—58no—
152#41—512no—
153#41—2512no—
154#41—2524no—
155#41—2512no—
156#41—2512no—
157C2×Q8—58no—
158C2×Q8—2524no—
159C2×Q8—256no—
160C2×Q8—254no—
161C2×Q8—254no—
162C2×Q8—253no—
163C2×Q8D5211yescharacteristic, complemented
164C2×D4—254no—
165C2×D4—256no—
166C22×C4—2512no—
167C22×C4—253no—
168C2×C5—24no—
169C2×C5—22no—
170C2×C5—22no—
171C2×C5—108no—
172C2×C5C24×D512yes—
173D5—28no—
174D5—54no—
175D5—104no—
176D5—104no—
177D5—102no—
178C23—254no—
179C23—251no—
180Q8—512no—
181Q8—2512no—
182Q8—2512no—
183Q8C2×D5214yes—
184D4—58no—
185D4—512no—
186D4—258no—
187D4—2512no—
188C2×C4—524no—
189C2×C4—254no—
190C2×C4—2524no—
191C2×C4—253no—
192C2×C4—256no—
193C2×C4—256no—
194C2×C4C2×D5213yes—
195C5—22no—
196C5D5×2−1+412yescomplemented
197C22—58no—
198C22—251no—
199C22—251no—
200C22—502no—
201C22—508no—
202C22C22×D5211yescharacteristic
203C4—58no—
204C4—256no—
205C4C22×D5216yes—
206C2—21no—
207C2—108no—
208C2—252no—
209C2—501no—
210C2C23×D5211yescharacteristic
subgroupG/H
center, FrattiniC2C23×D52
commutator, socle, cosocleC2×C52C25
FittingC2×C52×Q8C22
hypercenterC2×Q8D52
hypocenterC52C2×2−1+4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C5⋊D5C2semidirect
2. C5×#4147C2semidirect
3. #11717484C2semidirect
4. Q8×D52C2semidirect
5. #11717480C2semidirect
6. #11717471C2semidirect
7. #11717463C2semidirect
8. C2×C52×Q8C22semidirect
10. Q8×C5⋊D5C22semidirect
12. C2×#6045C22semidirect
13. C5×#713C22semidirect
14. C5×Q8×D5C22semidirect
15. C5×#709C22semidirect
17. #87880C22semidirect
20. #87873C22semidirect
22. #87871C22semidirect
23. #87870C22semidirect
24. D5×Dic10C22semidirect
49. #4147D5semidirect
66. C2×C5×Q8C2×D5semidirect
68. #713C2×D5semidirect
75. Q8×D5C2×D5semidirect
83. #709C2×D5semidirect
94. C5⋊D52−1+4semidirect
133. C52C2×2−1+4semidirect
163. C2×Q8D52semidirect
196. C5D5×2−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C5⋊D52
C5×#41472
#117174842
Q8×D522
#117174802
#117174712
#117174632
D5×2−1+45