Finite Group Databasebeta

← #12019977

Subgroups — #12019977

Order 1280.

284 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 59 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#10613740C211yesmaximal, characteristic
2C5×#2219C211yesmaximal, characteristic, complemented
3#10602286C212yesmaximal, complemented
4#10598300C211yesmaximal, characteristic, complemented
5#10598071C212yesmaximal, complemented
6C2×#4050—21no—
7C2×C5×Q32C2211yescharacteristic, complemented
8C2×C5×M32C2211yescharacteristic
9C5×#467—21no—
10#65198—22no—
11#65197—22no—
12#65193—21no—
13#65193C2212yes—
14C5×#367C2211yescharacteristic, complemented
15C5×#358—21no—
16#64742—22no—
17#64741—22no—
18#64719C2212yescomplemented
19#13668—51nomaximal, Sylow
20C2×#709—41no—
21C2×C5×Q16—21no—
22C22×C5×C8D411yescharacteristic
23C5×C22⋊Q8—41no—
24C2×Dic20—21no—
25#4050—22no—
26#4050—22no—
27#4050—41no—
28#4050—41no—
29C2×D40—21no—
30C2×#677—41no—
31C5×Q32—22no—
32C5×M32—22no—
33C2×C5×C16D411yescharacteristic
34C2×C5×C16C2311yescharacteristic
35C5×#107—21no—
36C5×#103—41no—
37Dic40—21no—
38Dic40D412yes—
39#3932—22no—
40#3932—22no—
41D80—21no—
42D80D412yes—
43#3926—22no—
44#3414—51no—
45#2264—52no—
46#2219D511yescharacteristic, complemented
47#1418—52no—
48#1400—51no—
49C2×C5×Q8—41no—
50C22×C4×C5D811yescharacteristic
51C2×C22⋊D5—81no—
52#709—42no—
53#709—42no—
54#709—81no—
55#709—81no—
56C2×D20—41no—
57C2×C4×D5—81no—
58C2×Dic10—41no—
59C5×Q16—41no—
60C5×Q16—41no—
61C2×C5×C8—21no—
62C2×C5×C8—21no—
63C2×C5×C8D811yescharacteristic
64C2×C5×C8C2×D411yescharacteristic
65C5×C4⋊C4—41no—
66C5×C4⋊C4—81no—
67C5×C22⋊C4—81no—
68Dic20—22no—
69Dic20—41no—
70D40—22no—
71D40—41no—
72#677—42no—
73#677—42no—
74C5×C16—21no—
75C5×C16C2×D412yes—
76C2×#135—101no—
77#510—102no—
78#509—102no—
79#508—52no—
80#508—101no—
81C2×Q32C2×D511yescharacteristic, complemented
82C2×M32C2×D511yescharacteristic
83#467—21no—
84Q64—102no—
85SD64—102no—
86M64—52no—
87#367C2×D511yescharacteristic, complemented
88#358—21no—
89C23×C5D1611yescharacteristic
90C22×D5—81no—
91C5×Q8—81no—
92C5×Q8—81no—
93C2×C4×C5—21no—
94C2×C4×C5—21no—
95C2×C4×C5—81no—
96C2×C4×C5—81no—
97C2×C4×C5D1611yescharacteristic
98C2×C4×C5C2×D811yescharacteristic
99C22⋊D5—82no—
100C22⋊D5—82no—
101C2×Dic5—81no—
102D20—42no—
103D20—81no—
104C4×D5—82no—
105C4×D5—82no—
106Dic10—42no—
107Dic10—81no—
108C5×C8—21no—
109C5×C8#12011yescharacteristic
110C5×C8AGL(1,ℤ/8)11yescharacteristic
111C2×#41—201no—
112#135—102no—
113#135—102no—
114#135—201no—
115#135—201no—
116C2×Q16—21no—
117C2×Q16—101no—
118C2×SD16—201no—
119C2×D8—101no—
120C22×C8C22⋊D511yescharacteristic
121C22⋊Q8—41no—
122Q32—22no—
123Q32—52no—
124Q32—101no—
125SD32—102no—
126SD32—102no—
127D16—52no—
128D16—101no—
129M32—22no—
130C2×C16C22⋊D511yescharacteristic
131C2×C16C22×D511yescharacteristic
132#107—21no—
133#103—41no—
134C32—102no—
135C22×C5—21no—
136C22×C5—41no—
137C22×C5C2×D1611yescharacteristic
138C2×D5—82no—
139C2×D5—162no—
140C4×C5—21no—
141C4×C5—161no—
142C4×C5—161no—
143C4×C5#44711yescharacteristic
144C4×C5#50911yescharacteristic
145Dic5—82no—
146#41—202no—
147#41—202no—
148#41—401no—
149#41—401no—
150C2×Q8—41no—
151C2×Q8—201no—
152C2×D4—201no—
153C2×D4—401no—
154C22×C4—401no—
155C22×C4#68611yescharacteristic
156Q16—41no—
157Q16—41no—
158Q16—102no—
159Q16—201no—
160SD16—202no—
161SD16—202no—
162D8—102no—
163D8—201no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8#68611yescharacteristic
167C2×C8C2×C22⋊D511yescharacteristic
168C4⋊C4—41no—
169C4⋊C4—81no—
170C22⋊C4—81no—
171C16—21no—
172C16D4×D512yes—
173C2×C5—21no—
174C2×C5—41no—
175C2×C5#218411yescharacteristic
176D5—162no—
177C23—401no—
178C23#395811yescharacteristic
179Q8—81no—
180Q8—81no—
181Q8—202no—
182Q8—401no—
183D4—202no—
184D4—401no—
185D4—402no—
186D4—402no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—81no—
190C2×C4—81no—
191C2×C4—402no—
192C2×C4—401no—
193C2×C4—402no—
194C2×C4#395811yescharacteristic
195C2×C4C2×#68611yescharacteristic
196C8—21no—
197C8#408311yescharacteristic
198C8#409511yescharacteristic
199C5#1366811yescharacteristic, complemented, Sylow
200C22—21no—
201C22—41no—
202C22—402no—
203C22—802no—
204C22C2×#395811yescharacteristic
205C4—21no—
206C4—161no—
207C4—161no—
208C4—402no—
209C4#6532511yescharacteristic
210C4#6548211yescharacteristic
211C2—21no—
212C2—41no—
213C2—802no—
214C2#1060186811yescharacteristic
subgroupG/H
centerC2#10601868
commutator, cosocleC2×C5×C16C23
FrattiniC2×C16C22×D5
FittingC5×#2219C2
socleC2×C5#2184
prime radical#10613740C2
hypercenter#2219D5
hypocenterC5#13668
LCSG ▷ C2×C5×C16 ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C8 ◁ C2×M32 ◁ #2219

Complements

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

NH ≅ G/Ntype
2. C5×#2219C2semidirect
3. #10602286C2semidirect
4. #10598300C2semidirect
5. #10598071C2semidirect
7. C2×C5×Q32C22semidirect
14. C5×#367C22semidirect
18. #64719C22semidirect
46. #2219D5semidirect
81. C2×Q32C2×D5semidirect
87. #367C2×D5semidirect
199. C5#13668semidirect

Maximal subgroups

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

subgroupindex
#106137402
C5×#22192
#106022862
#105983002
#105980712
#136685