Finite Group Databasebeta

← #13099695

Subgroups — #13099695

Order 1600.

1215 conjugacy classes of subgroups; only the 511 normal subgroups are shown.

normal subgroups only

This group has 1215 conjugacy classes of subgroups — too many to draw. Only its 511 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×#41×C25C211yesmaximal, characteristic, complemented
2#11716569C214yesmaximal, complemented
3#11716568C214yesmaximal, complemented
4#41×D25C218yesmaximal, complemented
5#11716566C212yesmaximal, complemented
6#11716563C216yesmaximal, complemented
7C2×#87744C216yesmaximal, complemented
8#41×C25C2214yescomplemented
9#41×C25C2214yescomplemented
10C2×Q8×C25C2211yescharacteristic, complemented
11C2×D4×C25C2213yescomplemented
12C22×C4×C25C2213yescomplemented
13C2×C22⋊D25C22112yescomplemented
14#87748C2218yescomplemented
15Q8×D25C2218yescomplemented
16#87746C22124yescomplemented
17D4×D25C22124yescomplemented
18#87744C2214yescomplemented
19#87744C22112yescomplemented
20#87744C22112yescomplemented
21#87744C22112yescomplemented
22C2×D100C2216yescomplemented
23C2×C4×D25C22112yescomplemented
24C2×Dic50C2216yescomplemented
25#66283—51nomaximal
26C23×C25C2313yes—
27C22×D25C23112yes—
28Q8×C25C2314yes—
29D4×C25C23112yes—
30C2×C4×C25C2316yes—
31C2×C4×C25C2316yes—
32C2×C4×C25C2311yescharacteristic
33C2×C4×C25C2313yes—
34C22⋊D25C2318yes—
35C22⋊D25C23124yes—
36C2×Dic25C23112yes—
37D100C2314yes—
38D100C23112yes—
39C4×D25C2318yes—
40C4×D25C23124yes—
41Dic50C2314yes—
42Dic50C23112yes—
43C2×C5×#41D511yescharacteristic
44#4150—54no—
45#4149—54no—
46D5×#41—58no—
47#4147—52no—
48#4144—56no—
49C2×#709—56no—
50C22×C25—43no—
51C22×C25C2416yes—
52C22×C25C2411yescharacteristic
53C2×D25—412no—
54C2×D25C2418yes—
55C4×C25C2411yescharacteristic
56C4×C25C2416yes—
57C4×C25C2411yescharacteristic
58Dic25C2418yes—
59C5×#41C2×D514yes—
60C5×#41C2×D514yes—
61C2×C5×Q8C2×D511yescharacteristic
62C2×C5×D4C2×D513yes—
63C22×C4×C5C2×D513yes—
64C2×C22⋊D5—512no—
65#713—58no—
66Q8×D5—58no—
67#711—524no—
68D4×D5—524no—
69#709—54no—
70#709—512no—
71#709—512no—
72#709—512no—
73C2×D20—56no—
74C2×C4×D5—512no—
75C2×Dic10—56no—
76#585—251noSylow
77C2×C25—26no—
78C2×C25—21no—
79C2×C25C2511yescharacteristic
80D25—28no—
81C23×C5C22×D513yes—
82C22×D5—512no—
83C5×Q8C22×D514yes—
84C5×D4C22×D5112yes—
85C2×C4×C5C22×D516yes—
86C2×C4×C5C22×D516yes—
87C2×C4×C5C22×D511yescharacteristic
88C2×C4×C5C22×D513yes—
89C22⋊D5—58no—
90C22⋊D5—524no—
91C2×Dic5—512no—
92D20—54no—
93D20—512no—
94C4×D5—58no—
95C4×D5—524no—
96Dic10—54no—
97Dic10—512no—
982−1+4—254no—
992−1+4—252no—
100H(5,𝔽2)—254no—
101H(5,𝔽2)—256no—
102C2×#41—258no—
103C2×#41—256no—
104C2×#41D2511yescharacteristic, complemented
105C25#58511yescharacteristic, complemented, Sylow
106C22×C5—43no—
107C22×C5C23×D516yes—
108C22×C5C23×D511yescharacteristic
109C2×D5—58no—
110C2×D5—2012no—
111C4×C5C23×D511yescharacteristic
112C4×C5C23×D516yes—
113C4×C5C23×D511yescharacteristic
114Dic5—58no—
115#41—258no—
116#41—2524no—
117#41—2512no—
118#41—254no—
119#41—2512no—
120#41—2512no—
121#41C2×D2514yescomplemented
122#41C2×D2514yescomplemented
123C2×Q8—258no—
124C2×Q8—256no—
125C2×Q8C2×D2511yescharacteristic, complemented
126C2×D4—2512no—
127C2×D4—2524no—
128C2×D4—256no—
129C2×D4C2×D2513yescomplemented
130C22×C4—2512no—
131C22×C4C2×D2513yescomplemented
132C2×C5—26no—
133C2×C5—21no—
134C2×C5C24×D511yescharacteristic
135D5—108no—
136C23—2512no—
137C23C22×D2513yes—
138Q8—2512no—
139Q8—254no—
140Q8C22×D2514yes—
141D4—2524no—
142D4—258no—
143D4—2512no—
144D4—254no—
145D4C22×D25112yes—
146C2×C4—2512no—
147C2×C4—2524no—
148C2×C4—258no—
149C2×C4C22×D2516yes—
150C2×C4C22×D2513yes—
151C2×C4C22×D2516yes—
152C2×C4C22×D2511yescharacteristic
153C5#6628311yescharacteristic
154C22—43no—
155C22—258no—
156C22—10012no—
157C22C23×D2516yes—
158C22C23×D2511yescharacteristic
159C4—258no—
160C4C23×D2516yes—
161C4C23×D2511yescharacteristic
162C4C23×D2511yescharacteristic
163C2—21no—
164C2—26no—
165C2—508no—
166C2C24×D2511yescharacteristic
subgroupG/H
centerC4C23×D25
commutator, cosocleC2×C25C25
Frattini, socleC2×C5C24×D5
FittingC2×#41×C25C2
hypercenterC2×#41D25
hypocenterC25#585
LCSG ▷ C2×C25 ▷ C25
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×C25C2semidirect
2. #11716569C2semidirect
3. #11716568C2semidirect
4. #41×D25C2semidirect
5. #11716566C2semidirect
6. #11716563C2semidirect
7. C2×#87744C2semidirect
8. #41×C25C22semidirect
9. #41×C25C22semidirect
10. C2×Q8×C25C22semidirect
11. C2×D4×C25C22semidirect
12. C22×C4×C25C22semidirect
13. C2×C22⋊D25C22semidirect
14. #87748C22semidirect
15. Q8×D25C22semidirect
16. #87746C22semidirect
17. D4×D25C22semidirect
18. #87744C22semidirect
19. #87744C22semidirect
20. #87744C22semidirect
21. #87744C22semidirect
22. C2×D100C22semidirect
23. C2×C4×D25C22semidirect
24. C2×Dic50C22semidirect
104. C2×#41D25semidirect
105. C25#585semidirect
121. #41C2×D25semidirect
122. #41C2×D25semidirect
125. C2×Q8C2×D25semidirect
129. C2×D4C2×D25semidirect
131. C22×C4C2×D25semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C252
#117165692
#117165682
#41×D252
#117165662
#117165632
C2×#877442
#662835