Finite Group Databasebeta

← D4×D100 #13098875

Subgroups — D4×D100 #13098875

Order 1600.

642 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 155 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×D4×D25C212yesmaximal, complemented
2C22×D100C212yesmaximal, complemented
3C4×D4×C25C211yesmaximal, characteristic, complemented
4#11716492C212yesmaximal, complemented
5#11716457C212yesmaximal, complemented
6#11716444C214yesmaximal, complemented
7#11716436C211yesmaximal, characteristic, complemented
8C4×D100C211yesmaximal, characteristic, complemented
9C23×D25C2214yescomplemented
10C2×D4×C25C2211yescharacteristic
11C22×C4×C25C2212yescomplemented
12C2×C22⋊D25C2214yescomplemented
13D4×D25—28no—
14C2×D100—28no—
15C2×D100C2211yescharacteristic
16C2×D100C2212yescomplemented
17C2×D100C2212yescomplemented
18C2×D100C2214yescomplemented
19C2×D100C2212yescomplemented
20C2×C4×D25C2212yescomplemented
21C4⋊C4×C25C2211yescharacteristic, complemented
22C22⋊C4×C25C2212yescomplemented
23C42×C25C2211yescharacteristic, complemented
24#87720C2212yescomplemented
25#87720C2214yescomplemented
26C4⋊Dic25C2211yescharacteristic, complemented
27D4×D20—51nomaximal
28C23×C25C2312yes—
29C22×D25—28no—
30C22×D25—28no—
31C22×D25—44no—
32C22×D25C2314yes—
33C22×D25C2312yes—
34D4×C25D414yescomplemented
35C2×C4×C25—24no—
36C2×C4×C25C2311yescharacteristic
37C2×C4×C25C2312yes—
38C2×C4×C25C2311yescharacteristic
39C2×C4×C25C2311yescharacteristic
40C22⋊D25—28no—
41C2×Dic25C2312yes—
42D100—28no—
43D100—24no—
44D100—24no—
45D100—42no—
46D100D414yesdirect product factor
47C4×D25—24no—
48C2×D4×D5—52no—
49C22×D20—52no—
50C4×C5×D4D511yescharacteristic
51#4076—52no—
52#4041—52no—
53#4028—54no—
54#4020—51no—
55C4×D20—51no—
56C22×C25—22no—
57C22×C25—22no—
58C22×C25C2×D414yescomplemented
59C22×C25C2411yescharacteristic
60C2×D25—22no—
61C2×D25—22no—
62C2×D25—24no—
63C2×D25—24no—
64C2×D25—24no—
65C2×D25—416no—
66C2×D25C2×D414yescomplemented
67C4×C25—22no—
68C4×C25—21no—
69C4×C25C2×D412yescomplemented
70C4×C25C2×D412yescomplemented
71Dic25—22no—
72C23×D5—54no—
73C2×C5×D4C2×D511yescharacteristic
74C22×C4×C5C2×D512yes—
75C2×C22⋊D5—54no—
76D4×D5—108no—
77C2×D20—51no—
78C2×D20—52no—
79C2×D20—54no—
80C2×D20—52no—
81C2×D20—52no—
82C2×D20—108no—
83C2×C4×D5—52no—
84C5×C4⋊C4C2×D511yescharacteristic
85C5×C22⋊C4C2×D512yes—
86C42×C5C2×D511yescharacteristic
87#685—52no—
88#685—54no—
89C4⋊Dic5—51no—
90D42—251noSylow
91C2×C25—24no—
92C2×C25C22×D411yescharacteristic
93C2×C25C22×D411yescharacteristic
94C2×C25H(5,𝔽2)11yescharacteristic
95D25—24no—
96D25—44no—
97C23×C5C22×D512yes—
98C22×D5—52no—
99C22×D5—54no—
100C22×D5—108no—
101C22×D5—108no—
102C22×D5—204no—
103C5×D4D2014yes—
104C2×C4×C5—24no—
105C2×C4×C5C22×D511yescharacteristic
106C2×C4×C5C22×D512yes—
107C2×C4×C5C22×D511yescharacteristic
108C2×C4×C5C22×D511yescharacteristic
109C22⋊D5—108no—
110C2×Dic5—52no—
111D20—54no—
112D20—108no—
113D20—104no—
114D20—104no—
115D20—202no—
116C4×D5—104no—
117C22×D4—252no—
118C22×D4—252no—
119#127—251no—
120#121—252no—
121#121—252no—
122#120—254no—
123C4×D4—251no—
124C4×D4D2511yescharacteristic, complemented
125C25D4211yescharacteristic, complemented, Sylow
126C22×C5—22no—
127C22×C5—22no—
128C22×C5C2×D2014yes—
129C22×C5C23×D511yescharacteristic
130C2×D5—54no—
131C2×D5—102no—
132C2×D5—102no—
133C2×D5—104no—
134C2×D5—104no—
135C2×D5—104no—
136C2×D5—2016no—
137C4×C5—22no—
138C4×C5—21no—
139C4×C5C2×D2012yes—
140C4×C5D4×D512yes—
141Dic5—102no—
142C24—254no—
143C2×D4—254no—
144C2×D4—251no—
145C2×D4—254no—
146C2×D4—252no—
147C2×D4—252no—
148C2×D4—252no—
149C2×D4—508no—
150C2×D4—508no—
151C2×D4C2×D2511yescharacteristic
152C22×C4—252no—
153C22×C4C2×D2512yescomplemented
154C4⋊C4—251no—
155C4⋊C4C2×D2511yescharacteristic, complemented
156C22⋊C4—252no—
157C22⋊C4—254no—
158C22⋊C4C2×D2512yescomplemented
159C42C2×D2511yescharacteristic, complemented
160C2×C5—24no—
161C2×C5C22×D2011yescharacteristic
162C2×C5C2×D4×D511yescharacteristic
163C2×C5#414911yescharacteristic
164D5—104no—
165D5—204no—
166C23—252no—
167C23—254no—
168C23—508no—
169C23—508no—
170C23—1004no—
171C23C22×D2512yes—
172D4—254no—
173D4—508no—
174D4—508no—
175D4—504no—
176D4—504no—
177D4—1002no—
178D4D10014yesdirect product factor
179C2×C4—24no—
180C2×C4—252no—
181C2×C4—504no—
182C2×C4C22×D2511yescharacteristic
183C2×C4C22×D2512yes—
184C2×C4C22×D2511yescharacteristic
185C2×C4C22×D2511yescharacteristic
186C5D4×D2011yescharacteristic
187C22—22no—
188C22—22no—
189C22—254no—
190C22—502no—
191C22—502no—
192C22—504no—
193C22—504no—
194C22—504no—
195C22—10016no—
196C22C2×D10014yescomplemented
197C22C23×D2511yescharacteristic
198C4—22no—
199C4—21no—
200C4—502no—
201C4C2×D10012yescomplemented
202C4D4×D2512yescomplemented
203C2—24no—
204C2—504no—
205C2—1004no—
206C2C22×D10011yescharacteristic
207C2C2×D4×D2511yescharacteristic
208C2#1171656811yescharacteristic
subgroupG/H
centerC22C23×D25
commutator, cosocleC22×C25C24
Frattini, socleC22×C5C23×D5
FittingC4×D4×C25C2
hypercenterC4×D4D25
hypocenterC25D42
LCSG ▷ C22×C25 ▷ C25
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×D25C2semidirect
2. C22×D100C2semidirect
3. C4×D4×C25C2semidirect
4. #11716492C2semidirect
5. #11716457C2semidirect
6. #11716444C2semidirect
7. #11716436C2semidirect
8. C4×D100C2semidirect
9. C23×D25C22semidirect
11. C22×C4×C25C22semidirect
12. C2×C22⋊D25C22semidirect
16. C2×D100C22semidirect
17. C2×D100C22semidirect
18. C2×D100C22semidirect
19. C2×D100C22semidirect
20. C2×C4×D25C22semidirect
21. C4⋊C4×C25C22semidirect
22. C22⋊C4×C25C22semidirect
23. C42×C25C22semidirect
24. #87720C22semidirect
25. #87720C22semidirect
26. C4⋊Dic25C22semidirect
34. D4×C25D4semidirect
46. D100D4direct (N × H)
58. C22×C25C2×D4semidirect
66. C2×D25C2×D4semidirect
69. C4×C25C2×D4semidirect
70. C4×C25C2×D4semidirect
124. C4×D4D25semidirect
125. C25D42semidirect
153. C22×C4C2×D25semidirect
155. C4⋊C4C2×D25semidirect
158. C22⋊C4C2×D25semidirect
159. C42C2×D25semidirect
178. D4D100direct (N × H)
196. C22C2×D100semidirect
201. C4C2×D100semidirect
202. C4D4×D25semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D252
C22×D1002
C4×D4×C252
#117164922
#117164572
#117164442
#117164362
C4×D1002
D4×D205