Finite Group Databasebeta

← #13098097

Subgroups — #13098097

Order 1600.

252 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 51 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
1#11716568C211yesmaximal, characteristic, complemented
2#11716512C211yesmaximal, characteristic, complemented
3#11716470C211yesmaximal, characteristic, complemented
4#11716436C211yesmaximal, characteristic, complemented
5C25×#104C211yesmaximal, characteristic, complemented
6#11716372C211yesmaximal, characteristic, complemented
7#11716353C211yesmaximal, characteristic, complemented
8#41×C25C2211yescharacteristic
9#87748—21no—
10D4×D25—22no—
11D4×D25—21no—
12#87744—21no—
13#87744C2211yescharacteristic
14C2×D100—21no—
15C2×D100—22no—
16C2×D100C2211yescharacteristic
17C2×D100C2211yescharacteristic, complemented
18M16×C25C2211yescharacteristic, complemented
19C42×C25C2211yescharacteristic, complemented
20#87724—21no—
21#87722—21no—
22#87716C2211yescharacteristic, complemented
23D200—21no—
24#87713—21no—
25#65111—51nomaximal
26C22×D25—22no—
27C22×D25—21no—
28C22×D25D412yes—
29Q8×C25D411yescharacteristic, complemented
30D4×C25—21no—
31D4×C25D411yescharacteristic, complemented
32C2×C4×C25—21no—
33C2×C4×C25—21no—
34C2×C4×C25C2311yescharacteristic
35C22⋊D25—22no—
36C22⋊D25—21no—
37D100—22no—
38D100—21no—
39D100—21no—
40D100—21no—
41D100—21no—
42D100—44no—
43D100D411yescharacteristic, complemented
44C4×D25—22no—
45C4×D25—21no—
46Dic50D411yescharacteristic, complemented
47C8×C25—21no—
48#6014—21no—
49#4149—51no—
50#4095—51no—
51#4054—51no—
52#4020—51no—
53C5×#104D511yescharacteristic
54#3955—51no—
55#3937—51no—
56C22×C25—21no—
57C22×C25C2×D411yescharacteristic
58C2×D25—22no—
59C2×D25—21no—
60C2×D25—42no—
61C2×D25—42no—
62C2×D25—41no—
63C2×D25—82no—
64C4×C25—22no—
65C4×C25—21no—
66C4×C25C2×D411yescharacteristic
67C4×C25C2×D411yescharacteristic
68Dic25—21no—
69C5×#41C2×D511yescharacteristic
70#713—101no—
71D4×D5—102no—
72D4×D5—101no—
73#709—51no—
74#709—101no—
75C2×D20—51no—
76C2×D20—51no—
77C2×D20—101no—
78C2×D20—102no—
79C5×M16C2×D511yescharacteristic
80C42×C5C2×D511yescharacteristic
81#688—101no—
82#686—101no—
83#681—51no—
84D40—101no—
85#677—101no—
86#453—251noSylow
87C2×C25—21no—
88C2×C25—41no—
89C2×C25#12011yescharacteristic
90D25—42no—
91D25—41no—
92D25—81no—
93C22×D5—52no—
94C22×D5—102no—
95C22×D5—101no—
96C5×Q8D2011yescharacteristic
97C5×D4—21no—
98C5×D4D2011yescharacteristic
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5C22×D511yescharacteristic
102C22⋊D5—102no—
103C22⋊D5—101no—
104D20—51no—
105D20—102no—
106D20—101no—
107D20—101no—
108D20—101no—
109D20—101no—
110D20—204no—
111C4×D5—102no—
112C4×D5—101no—
113Dic10—51no—
114C5×C8—21no—
115#168—101no—
116H(5,𝔽2)—251no—
117AGL(1,ℤ/8)—251no—
118AGL(1,ℤ/8)—251no—
119#127—251no—
120#104—251no—
121#104D2511yescharacteristic, complemented
122#100—251no—
123C25#45311yescharacteristic, complemented, Sylow
124C22×C5—21no—
125C22×C5D4×D511yescharacteristic
126C2×D5—101no—
127C2×D5—102no—
128C2×D5—202no—
129C2×D5—202no—
130C2×D5—201no—
131C2×D5—402no—
132C4×C5—22no—
133C4×C5—21no—
134C4×C5C2×D2011yescharacteristic
135C4×C5D4×D511yescharacteristic
136Dic5—101no—
137#41—251no—
138#41—501no—
139#41—501no—
140#41C2×D2511yescharacteristic
141C2×D4—251no—
142C2×D4—251no—
143C2×D4—501no—
144C2×D4—502no—
145C2×D4—502no—
146C2×D4—501no—
147SD16—501no—
148SD16—501no—
149D8—501no—
150D8—501no—
151M16—251no—
152M16C2×D2511yescharacteristic, complemented
153C42C2×D2511yescharacteristic, complemented
154C2×C5—21no—
155C2×C5—41no—
156C2×C5#402811yescharacteristic
157D5—202no—
158D5—201no—
159D5—401no—
160C23—252no—
161C23—502no—
162C23—501no—
163Q8—251no—
164Q8D10011yescharacteristic, complemented
165D4—21no—
166D4—251no—
167D4—502no—
168D4—502no—
169D4—501no—
170D4—501no—
171D4—501no—
172D4—501no—
173D4—501no—
174D4—1004no—
175D4D10011yescharacteristic, complemented
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—502no—
179C2×C4—501no—
180C2×C4C22×D2511yescharacteristic
181C8—21no—
182C8—501no—
183C5#6511111yescharacteristic
184C22—21no—
185C22—501no—
186C22—502no—
187C22—1002no—
188C22—1002no—
189C22—1001no—
190C22—2002no—
191C22D4×D2511yescharacteristic
192C4—22no—
193C4—21no—
194C4—501no—
195C4C2×D10011yescharacteristic
196C4D4×D2511yescharacteristic
197C2—21no—
198C2—41no—
199C2—1002no—
200C2—1001no—
201C2—2001no—
202C2#1171644411yescharacteristic
subgroupG/H
centerC2#11716444
commutator, cosocleC2×C4×C25C23
FrattiniC2×C4×C5C22×D5
FittingC25×#104C2
socleC2×C5#4028
hypercenter#104D25
hypocenterC25#453
LCSG ▷ C2×C4×C25 ▷ C2×C25 ▷ C25
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
1. #11716568C2semidirect
2. #11716512C2semidirect
3. #11716470C2semidirect
4. #11716436C2semidirect
5. C25×#104C2semidirect
6. #11716372C2semidirect
7. #11716353C2semidirect
17. C2×D100C22semidirect
18. M16×C25C22semidirect
19. C42×C25C22semidirect
22. #87716C22semidirect
29. Q8×C25D4semidirect
31. D4×C25D4semidirect
43. D100D4semidirect
46. Dic50D4semidirect
121. #104D25semidirect
123. C25#453semidirect
152. M16C2×D25semidirect
153. C42C2×D25semidirect
164. Q8D100semidirect
175. D4D100semidirect

Maximal subgroups

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

subgroupindex
#117165682
#117165122
#117164702
#117164362
C25×#1042
#117163722
#117163532
#651115