Finite Group Databasebeta

← #13023230

Subgroups — #13023230

Order 1280.

306 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 82 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#10610801C211yesmaximal, characteristic
2#10604710C212yesmaximal, complemented
3#10598781C212yesmaximal
4#10598726C212yesmaximal, complemented
5#65856C411yescharacteristic
6C5×#424C411yescharacteristic
7#65418C2211yescharacteristic
8M16×Dic5C411yescharacteristic
9#65399C411yescharacteristic
10C2×C8×Dic5C2211yescharacteristic
11#65288C2211yescharacteristic
12#65129—22no—
13#65122—22no—
14C22⋊#674C2214yes—
15#64888—22no—
16#64886—22no—
17#11463—51nomaximal, Sylow
18C2×#709C2×C411yescharacteristic
19C2×C5×M16C2×C411yescharacteristic
20C22×C5×C8C2×C411yescharacteristic
21C5×#117C2×C411yescharacteristic
22C2×C4×Dic5C2×C411yescharacteristic
23C2×#681C2×C411yescharacteristic
24C22×#168C2311yescharacteristic
25#4039C812yes—
26#4033C812yes—
27#4027—22no—
28#4018—21no—
29C42×D5—21no—
30C2×#674—24no—
31C5×C4⋊C8—22no—
32#3952—22no—
33#3952—22no—
34#3947—21no—
35C8×Dic5—21no—
36C8×Dic5D412yes—
37C8×Dic5D412yes—
38C4⋊#168—22no—
39#2922—51no—
40#2163—52no—
41#1323—52no—
42#1315—52no—
43C22×C4×C5C22×C411yescharacteristic
44C2×C22⋊D5—21no—
45C22×Dic5M1612yes—
46#709—41no—
47#709—41no—
48C2×D20C2×C811yescharacteristic
49C2×C4×D5—21no—
50C2×C4×D5—22no—
51C2×Dic10C2×C811yescharacteristic
52C5×M16—41no—
53C2×C5×C8—21no—
54C2×C5×C8—41no—
55C2×C5×C8C22⋊C412yes—
56C5×C4⋊C4C2×C812yes—
57C5×C22⋊C4—21no—
58C42×C5—21no—
59#685—22no—
60#683—22no—
61C4×Dic5—22no—
62C4×Dic5C22⋊C411yescharacteristic
63C4×Dic5C22⋊C411yescharacteristic
64C4×Dic5C2×C812yes—
65#681—41no—
66C2×#168—21no—
67C2×#168—41no—
68C2×#168C2×D412yes—
69#674—44no—
70C4×#41—51no—
71#433—102no—
72#431—102no—
73#424—51no—
74#424AGL(1,𝔽5)11yescharacteristic
75#408—51no—
76#408—51no—
77C4×M16—51no—
78C2×C4×C8—51no—
79C4⋊C16—102no—
80C22⋊C16—54no—
81#346—102no—
82C23×C5C2×M1611yescharacteristic
83C22×D5—21no—
84C2×C4×C5—21no—
85C2×C4×C5—21no—
86C2×C4×C5—22no—
87C2×C4×C5C2×C22⋊C411yescharacteristic
88C2×C4×C5C22×C811yescharacteristic
89C22⋊D5—42no—
90C2×Dic5—21no—
91C2×Dic5—42no—
92C2×Dic5C22⋊C812yes—
93C2×Dic5C22⋊C812yes—
94D20—41no—
95C4×D5—44no—
96C4×D5—41no—
97C4×D5—41no—
98Dic10—41no—
99C5×C8—22no—
100C5×C8—41no—
101#168—22no—
102#168—41no—
103C2×#41—51no—
104C2×M16—51no—
105C2×M16C2×AGL(1,𝔽5)11yescharacteristic
106C22×C8—51no—
107C22×C8C2×AGL(1,𝔽5)11yescharacteristic
108C4×Q8—52no—
109C4×D4—52no—
110C4×D4—102no—
111#117—101no—
112#117C2×AGL(1,𝔽5)11yescharacteristic
113C2×C42—51no—
114C2×C42—101no—
115C2×C16—104no—
116C4⋊C8—22no—
117C4⋊C8—102no—
118C22⋊C8—102no—
119C22⋊C8—102no—
120#97—101no—
121C4×C8—52no—
122C4×C8—52no—
123C4×C8—101no—
124C22×C5—22no—
125C22×C5—21no—
126C22×C5C2×C22⋊C811yescharacteristic
127C2×D5—42no—
128C2×D5—41no—
129C4×C5—21no—
130C4×C5—42no—
131C4×C5#41011yescharacteristic
132C4×C5#41311yescharacteristic
133Dic5—22no—
134Dic5—22no—
135Dic5—41no—
136#41—201no—
137#41—201no—
138C2×Q8—51no—
139C2×D4—51no—
140C2×D4—101no—
141C22×C4—52no—
142C22×C4—102no—
143C22×C4—101no—
144C22×C4C22×AGL(1,𝔽5)11yescharacteristic
145M16—41no—
146M16—201no—
147C2×C8—21no—
148C2×C8—41no—
149C2×C8—52no—
150C2×C8—101no—
151C2×C8—201no—
152C2×C8C22⋊AGL(1,𝔽5)12yes—
153C4⋊C4—102no—
154C4⋊C4D5⋊C812yes—
155C22⋊C4—21no—
156C22⋊C4—102no—
157C42—21no—
158C42—52no—
159C42—51no—
160C42—51no—
161C42—102no—
162C16—204no—
163C2×C5—41no—
164C2×C5#145811yescharacteristic
165C2×C5#211712yes—
166D5—81no—
167C23—101no—
168C23D5⋊M1611yescharacteristic
169Q8—201no—
170D4—201no—
171D4—202no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—52no—
176C2×C4—52no—
177C2×C4—101no—
178C2×C4—204no—
179C2×C4—202no—
180C2×C4—201no—
181C2×C4—201no—
182C2×C4C2×D5⋊C811yescharacteristic
183C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
184C8—22no—
185C8—41no—
186C8—102no—
187C8—201no—
188C5#1146311yescharacteristic, complemented, Sylow
189C22—21no—
190C22—22no—
191C22—201no—
192C22—202no—
193C22D5⋊(C22⋊C8)11yescharacteristic
194C4—21no—
195C4—42no—
196C4—102no—
197C4—102no—
198C4—201no—
199C4#6577711yescharacteristic
200C4#6578511yescharacteristic
201C2—41no—
202C2—401no—
203C2#1060428911yescharacteristic
204C2#1060477612yes—
subgroupG/H
centerC2×C4C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#424C4
socleC22×C5C2×C22⋊C8
prime radicalC2×#709C2×C4
cosocleC22×#168C23
hypercenter#424AGL(1,𝔽5)
hypocenterC5#11463
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #10604710C2semidirect
4. #10598726C2semidirect
188. C5#11463semidirect

Maximal subgroups

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

subgroupindex
#106108012
#106047102
#105987812
#105987262
#114635