Finite Group Databasebeta

← C2×#11717395 #13107694

Subgroups — C2×#11717395 #13107694

Order 1600.

468 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 89 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×#87880C212yesmaximal, complemented
2C22×#6034C211yesmaximal, characteristic, complemented
3C2×#87839C211yesmaximal, characteristic, complemented
4C2×#87838C212yesmaximal, complemented
5#11717395C218yesmaximal, direct product factor
6C2×#87837C211yesmaximal, characteristic, complemented
7C22×#1039C2211yescharacteristic
8C2×C5×C22⋊D5—22no—
9C2×#6039C2212yes—
10C2×#6037C2212yes—
11#87880—24no—
12#87880C2218yescomplemented
13C2×D5×Dic5—22no—
14C2×#6034C2211yescharacteristic
15C2×#6034C2211yescharacteristic
16C2×#6034C2214yescomplemented
17#87839C2214yescomplemented
18#87838C2218yescomplemented
19#87837C2214yescomplemented
20C23×C52D411yescharacteristic
21C22×C5×D5—22no—
22C2×#1039D411yescharacteristic
23C2×#1039D412yes—
24C2×#1039C2311yescharacteristic
25C2×#1039C2312yes—
26C5×C22⋊D5—28no—
27C2×C5×Dic5—22no—
28#6039—22no—
29#6039C2314yes—
30#6037—22no—
31#6037C2314yes—
32D5×Dic5—28no—
33#6034C2312yes—
34#6034C2312yes—
35C2×#711—102no—
36C22×#170—101no—
37C22×C52—22no—
38C22×C52C2×D412yes—
39C22×C52C2×D411yescharacteristic
40C2×C5×D5—24no—
41C2×C5×D5—44no—
42#1039C2×D412yes—
43#1039C2×D411yescharacteristic
44#1039C2411yescharacteristic
45C5×Dic5—24no—
46C2×C5×D4—102no—
47C2×C22⋊D5—22no—
48C2×C22⋊D5—102no—
49C22×Dic5—101no—
50C22×Dic5—102no—
51C22×Dic5—102no—
52#711—108no—
53#711—108no—
54C2×C4×D5—102no—
55C2×Dic10—102no—
56C2×#170—101no—
57C2×#170—101no—
58C2×#170—104no—
59C2×#135—251nomaximal, Sylow
60C2×C52—22no—
61C2×C52#13512yescomplemented
62C2×C52C22×D411yescharacteristic
63C5×D5—44no—
64C23×C5—21no—
65C23×C5—22no—
66C23×C5—102no—
67C22×D5—22no—
68C5×D4—108no—
69C2×C4×C5—102no—
70C22⋊D5—28no—
71C22⋊D5—104no—
72C22⋊D5—104no—
73C2×Dic5—22no—
74C2×Dic5—102no—
75C2×Dic5—104no—
76C2×Dic5—102no—
77C2×Dic5—101no—
78C2×Dic5—102no—
79C2×Dic5—101no—
80C2×Dic5—102no—
81C2×Dic5—104no—
82C2×Dic5—108no—
83C4×D5—108no—
84Dic10—104no—
85Dic10—104no—
86#170—102no—
87#170—102no—
88C2×#41—252no—
89#135—258no—
90C2×Q16—251no—
91C2×SD16—252no—
92C2×D8—251no—
93C22×C8—251no—
94C52C2×#13511yescharacteristic, complemented, Sylow
95C22×C5—24no—
96C22×C5—22no—
97C22×C5—24no—
98C22×C5—22no—
99C22×C5—21no—
100C22×C5—44no—
101C22×C5—104no—
102C22×C5—204no—
103C2×D5—24no—
104C2×D5—44no—
105C4×C5—104no—
106Dic5—24no—
107Dic5—102no—
108Dic5—104no—
109Dic5—102no—
110Dic5—101no—
111Dic5—101no—
112Dic5—102no—
113#41—258no—
114#41—504no—
115C2×Q8—252no—
116C2×D4—102no—
117C2×D4—252no—
118C22×C4—251no—
119C22×C4—502no—
120Q16—254no—
121SD16—258no—
122D8—254no—
123C2×C8—251no—
124C2×C8—251no—
125C2×C8—254no—
126C2×C5—24no—
127C2×C5—24no—
128C2×C5—22no—
129C2×C5—22no—
130C2×C5—21no—
131C2×C5—44no—
132C2×C5—204no—
133D5—44no—
134C23—102no—
135C23D52⋊C211yescharacteristic
136Q8—254no—
137Q8—502no—
138D4—108no—
139D4—254no—
140D4—502no—
141C2×C4—102no—
142C2×C4—252no—
143C2×C4—252no—
144C2×C4—251no—
145C2×C4—251no—
146C2×C4—508no—
147C8—252no—
148C8—252no—
149C5—22no—
150C5—21no—
151C22—22no—
152C22—104no—
153C22—204no—
154C22C2×D52⋊C212yes—
155C22C2×D52⋊C211yescharacteristic
156C4—104no—
157C4—251no—
158C4—252no—
159C4—251no—
160C2—22no—
161C2—204no—
162C2#1171739512yesdirect product factor
163C2C22×D52⋊C211yescharacteristic
subgroupG/H
centerC22C2×D52⋊C2
commutator, cosocle#1039C24
FrattiniC2C22×D52⋊C2
FittingC23×C52D4
socleC22×C52C2×D4
hypercenterC23D52⋊C2
hypocenterC52C2×#135
LCSG ▷ #1039 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#87880C2semidirect
2. C22×#6034C2semidirect
3. C2×#87839C2semidirect
4. C2×#87838C2semidirect
5. #11717395C2direct (N × H)
6. C2×#87837C2semidirect
12. #87880C22semidirect
16. C2×#6034C22semidirect
17. #87839C22semidirect
18. #87838C22semidirect
19. #87837C22semidirect
61. C2×C52#135semidirect
94. C52C2×#135semidirect
162. C2#11717395direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#878802
C22×#60342
C2×#878392
C2×#878382
#117173952
C2×#878372
C2×#13525