Finite Group Databasebeta

← #12003472

Subgroups — #12003472

Order 1280.

402 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 83 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#10610795C211yesmaximal, characteristic
2C5×#1848C211yesmaximal, characteristic, complemented
3#10601298C212yesmaximal, complemented
4#10600528C212yesmaximal, complemented
5#10598203C211yesmaximal, characteristic, complemented
6#65811C2212yes—
7C2×C5×#108—22no—
8C5×#423C2211yescharacteristic
9C5×#423C2211yescharacteristic
10C2×C4×C5×C8C2211yescharacteristic
11#65424—22no—
12#65213C2212yes—
13#65132—22no—
14#65131—22no—
15#64705—22no—
16#64701—22no—
17#64679—24no—
18#10530—51nomaximal, Sylow
19C2×#709—22no—
20C2×C5×M16—21no—
21C2×C5×M16D412yes—
22C22×C5×C8—21no—
23C2×C42×C5C2311yescharacteristic
24#4076—22no—
25#4076—22no—
26C2×#681—22no—
27C2×D40—22no—
28#4021—22no—
29#4020D412yes—
30C4×D20—22no—
31C4×D20—22no—
32#4015D412yes—
33C5×#108—44no—
34C5×C4⋊C8—22no—
35C5×C4⋊C8—22no—
36C4×C5×C8—21no—
37C4×C5×C8D412yes—
38#3953—24no—
39#3949—22no—
40C4⋊#168—22no—
41C4⋊#168—22no—
42#3253—51no—
43#1848D511yescharacteristic, complemented
44#1560—52no—
45#1492—52no—
46#1309—51no—
47C22×C4×C5C2×D411yescharacteristic
48C22×C4×C5#4112yes—
49C2×C22⋊D5—42no—
50#709—82no—
51#709—82no—
52C2×D20—22no—
53C2×D20—22no—
54C2×D20—22no—
55C2×C4×D5—42no—
56C2×Dic10—22no—
57C5×M16—42no—
58C5×M16—42no—
59C2×C5×C8—22no—
60C2×C5×C8—22no—
61C2×C5×C8—22no—
62C2×C5×C8—22no—
63C2×C5×C8—41no—
64C42×C5C2×D411yescharacteristic
65C42×C5C2×D412yes—
66C42×C5#4111yescharacteristic
67#685—42no—
68#685—42no—
69C4⋊Dic5—22no—
70C4⋊Dic5—22no—
71#681—82no—
72C2×#168—42no—
73D40—82no—
74#532—52no—
75#476—102no—
76#469—102no—
77#459—102no—
78C2×#108—22no—
79#423—52no—
80#423C2×D511yescharacteristic
81#423C2×D511yescharacteristic
82C2×C4×C8C2×D511yescharacteristic
83#333—102no—
84#331—102no—
85D4⋊C8—104no—
86C23×C5#12411yescharacteristic
87C22×D5—42no—
88C2×C4×C5—21no—
89C2×C4×C5—21no—
90C2×C4×C5—22no—
91C2×C4×C5—22no—
92C2×C4×C5#12011yescharacteristic
93C2×C4×C5#12112yes—
94C2×C4×C5#12111yescharacteristic
95C2×C4×C5#12312yes—
96C22⋊D5—84no—
97C2×Dic5—42no—
98D20—42no—
99D20—42no—
100D20—42no—
101D20—42no—
102D20—82no—
103C4×D5—82no—
104C4×D5—82no—
105Dic10—82no—
106C5×C8—24no—
107C5×C8—42no—
108C5×C8—81no—
109#168—82no—
110C2×#41—102no—
111C2×D8—102no—
112C2×M16—21no—
113C2×M16—102no—
114C2×M16C22⋊D512yes—
115C22×C8—21no—
116C4⋊Q8—52no—
117#127—52no—
118#124—102no—
119#121—102no—
120#121—102no—
121C4×D4—102no—
122C4×D4—102no—
123C2×C42C22×D511yescharacteristic
124#108—44no—
125#106—102no—
126C4⋊C8—22no—
127C4⋊C8—22no—
128C4⋊C8—102no—
129C4⋊C8—102no—
130#102—104no—
131C4×C8—21no—
132C4×C8D2012yes—
133C22×C5—22no—
134C22×C5—21no—
135C22×C5#39411yescharacteristic
136C2×D5—82no—
137C2×D5—82no—
138C2×D5—82no—
139C4×C5—22no—
140C4×C5—21no—
141C4×C5#45311yescharacteristic
142C4×C5#45611yescharacteristic
143C4×C5#47112yes—
144C4×C5#47212yes—
145Dic5—82no—
146#41—402no—
147#41—402no—
148C2×Q8—102no—
149C2×D4—102no—
150C2×D4—102no—
151C2×D4—102no—
152C2×D4—202no—
153C22×C4—202no—
154C22×C4#71312yes—
155C22×C4C2×C22⋊D511yescharacteristic
156D8—402no—
157M16—42no—
158M16—42no—
159M16—402no—
160C2×C8—22no—
161C2×C8—22no—
162C2×C8—22no—
163C2×C8—22no—
164C2×C8—41no—
165C2×C8—202no—
166C4⋊C4—102no—
167C4⋊C4—102no—
168C22⋊C4—202no—
169C22⋊C4—202no—
170C42C2×D2011yescharacteristic
171C42#70911yescharacteristic
172C42D4×D512yes—
173C2×C5—41no—
174C2×C5#203911yescharacteristic
175C2×C5#205112yes—
176D5—162no—
177C23—202no—
178C23#409311yescharacteristic
179Q8—402no—
180D4—202no—
181D4—202no—
182D4—202no—
183D4—202no—
184D4—402no—
185D4—404no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—202no—
191C2×C4—402no—
192C2×C4—402no—
193C2×C4#404012yes—
194C2×C4#404112yes—
195C2×C4#407611yescharacteristic
196C2×C4#408311yescharacteristic
197C8—24no—
198C8—42no—
199C8—81no—
200C8—402no—
201C5#1053011yescharacteristic, complemented, Sylow
202C22—22no—
203C22—21no—
204C22—402no—
205C22—402no—
206C22—402no—
207C22#6528011yescharacteristic
208C4—22no—
209C4—21no—
210C4—402no—
211C4#6518612yes—
212C4#6518712yes—
213C4#6536611yescharacteristic
214C4#6538411yescharacteristic
215C2—41no—
216C2—802no—
217C2#1060038611yescharacteristic
218C2#1060150712yes—
subgroupG/H
centerC22#65280
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1848C2
socleC22×C5#394
prime radical#10610795C2
hypercenter#1848D5
hypocenterC5#10530
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1848

Complements

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

NH ≅ G/Ntype
2. C5×#1848C2semidirect
3. #10601298C2semidirect
4. #10600528C2semidirect
5. #10598203C2semidirect
43. #1848D5semidirect
201. C5#10530semidirect

Maximal subgroups

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

subgroupindex
#106107952
C5×#18482
#106012982
#106005282
#105982032
#105305