Finite Group Databasebeta

← #12003469

Subgroups — #12003469

Order 1280.

402 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C5×#3253C211yesmaximal, characteristic
2#10602603C212yesmaximal, complemented
3#10602595C212yesmaximal, complemented
4#10601311C211yesmaximal, characteristic, complemented
5#10598203C211yesmaximal, characteristic, complemented
6C5×#532C2212yes—
7C5×#476—22no—
8C5×#469—22no—
9C5×#459—22no—
10C5×#423C2211yescharacteristic
11C2×#3954—22no—
12#65213C2212yes—
13#65213C2211yescharacteristic
14C2×C4×#168C2211yescharacteristic
15#64766—22no—
16#64764—22no—
17D4⋊#168—24no—
18#10530—51nomaximal, Sylow
19C2×C5×#41—22no—
20C2×C5×D8—22no—
21C2×C5×M16D412yes—
22C5×C4⋊Q8D412yes—
23C5×#127D412yes—
24C5×#124—22no—
25C5×#121—22no—
26C5×#121—22no—
27C4×C5×D4—22no—
28C4×C5×D4—22no—
29C2×C42×C5C2311yescharacteristic
30C2×#681—21no—
31C2×#681—22no—
32C22×#168—21no—
33C5×#106—22no—
34C5×C4⋊C8—22no—
35C5×#102—24no—
36#3954—44no—
37C4⋊#168—22no—
38C4⋊#168—22no—
39C4⋊#168—22no—
40C4×#168—21no—
41C4×#168D412yes—
42#3253D511yescharacteristic
43#1848—51no—
44#1560—52no—
45#1492—52no—
46#1309—51no—
47C5×#41—82no—
48C5×#41—82no—
49C2×C5×Q8—22no—
50C2×C5×D4—22no—
51C2×C5×D4—22no—
52C2×C5×D4—22no—
53C2×C5×D4—42no—
54C22×C4×C5—42no—
55C22×C4×C5C2×D411yescharacteristic
56C22×C4×C5#4112yes—
57C5×D8—82no—
58C5×M16—42no—
59C2×C5×C8—22no—
60C5×C4⋊C4—22no—
61C5×C4⋊C4—22no—
62C5×C22⋊C4—42no—
63C5×C22⋊C4—42no—
64C42×C5C2×D411yescharacteristic
65C42×C5C2×D412yes—
66C42×C5#4111yescharacteristic
67#681—42no—
68#681—82no—
69C2×#168—22no—
70C2×#168—22no—
71C2×#168—22no—
72C2×#168—41no—
73C2×#168—42no—
74#532C2×D512yes—
75#476—22no—
76#469—22no—
77#459—22no—
78C2×#108—102no—
79#423—51no—
80#423—52no—
81#423C2×D511yescharacteristic
82C2×C4×C8—51no—
83#333—102no—
84#331—102no—
85D4⋊C8—104no—
86C23×C5—42no—
87C23×C5#12411yescharacteristic
88C5×Q8—82no—
89C5×D4—42no—
90C5×D4—42no—
91C5×D4—42no—
92C5×D4—42no—
93C5×D4—82no—
94C5×D4—84no—
95C2×C4×C5—21no—
96C2×C4×C5—21no—
97C2×C4×C5—22no—
98C2×C4×C5—22no—
99C2×C4×C5—42no—
100C2×C4×C5—82no—
101C2×C4×C5—82no—
102C2×C4×C5#12011yescharacteristic
103C2×C4×C5#12111yescharacteristic
104C2×C4×C5#12112yes—
105C2×C4×C5#12312yes—
106C5×C8—42no—
107#168—24no—
108#168—81no—
109#168—82no—
110C2×#41—22no—
111C2×D8—22no—
112C2×M16—101no—
113C2×M16—102no—
114C2×M16C22⋊D512yes—
115C22×C8—101no—
116C4⋊Q8C22⋊D512yes—
117#127C22⋊D512yes—
118#124—22no—
119#121—22no—
120#121—22no—
121C4×D4—22no—
122C4×D4—22no—
123C2×C42C22×D511yescharacteristic
124#108—204no—
125#106—22no—
126C4⋊C8—22no—
127C4⋊C8—102no—
128C4⋊C8—102no—
129C4⋊C8—102no—
130#102—24no—
131C4×C8—52no—
132C4×C8—101no—
133C22×C5—22no—
134C22×C5—21no—
135C22×C5—82no—
136C22×C5—82no—
137C22×C5—82no—
138C22×C5#39411yescharacteristic
139C4×C5—22no—
140C4×C5—21no—
141C4×C5—82no—
142C4×C5#45311yescharacteristic
143C4×C5#45611yescharacteristic
144C4×C5#47112yes—
145C4×C5#47212yes—
146#41—82no—
147#41—82no—
148C2×Q8—22no—
149C2×D4—22no—
150C2×D4—22no—
151C2×D4—22no—
152C2×D4—42no—
153C22×C4—42no—
154C22×C4#71112yes—
155C22×C4C2×C22⋊D511yescharacteristic
156D8—82no—
157M16—42no—
158M16—202no—
159M16—402no—
160C2×C8—22no—
161C2×C8—102no—
162C2×C8—102no—
163C2×C8—102no—
164C2×C8—201no—
165C2×C8—202no—
166C4⋊C4—22no—
167C4⋊C4—22no—
168C22⋊C4—42no—
169C22⋊C4—42no—
170C42D4×D511yescharacteristic
171C42#71111yescharacteristic
172C42C2×C22⋊D512yes—
173C2×C5—41no—
174C2×C5—162no—
175C2×C5#203911yescharacteristic
176C2×C5#205112yes—
177C23—42no—
178C23#408211yescharacteristic
179Q8—82no—
180D4—42no—
181D4—42no—
182D4—42no—
183D4—42no—
184D4—82no—
185D4—84no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—42no—
191C2×C4—82no—
192C2×C4—82no—
193C2×C4#408112yes—
194C2×C4#408411yescharacteristic
195C2×C4#408512yes—
196C2×C4#409911yescharacteristic
197C8—42no—
198C8—104no—
199C8—402no—
200C8—401no—
201C5#1053011yescharacteristic, complemented, Sylow
202C22—22no—
203C22—21no—
204C22—82no—
205C22—82no—
206C22—82no—
207C22#6551111yescharacteristic
208C4—22no—
209C4—21no—
210C4—82no—
211C4#6548812yes—
212C4#6548912yes—
213C4#6553011yescharacteristic
214C4#6553511yescharacteristic
215C2—41no—
216C2—162no—
217C2#1060266911yescharacteristic
218C2#1060288612yes—
subgroupG/H
centerC22#65511
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
Fitting, prime radicalC5×#3253C2
socleC22×C5#394
hypercenter#3253D5
hypocenterC5#10530
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3253

Complements

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

NH ≅ G/Ntype
2. #10602603C2semidirect
3. #10602595C2semidirect
4. #10601311C2semidirect
5. #10598203C2semidirect
201. C5#10530semidirect

Maximal subgroups

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

subgroupindex
C5×#32532
#106026032
#106025952
#106013112
#105982032
#105305