Finite Group Databasebeta

← #13018861

Subgroups — #13018861

Order 1280.

386 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 98 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#10617095C211yesmaximal, characteristic
2#10604739C212yesmaximal
3#10604330C211yesmaximal, characteristic
4#10599766C211yesmaximal, characteristic
5#10598787C212yesmaximal
6C2×#4033C2211yescharacteristic
7#65759—22no—
8#65748C2212yes—
9C2×C4⋊#170C2211yescharacteristic
10C2×C4×#170C2211yescharacteristic
11#65709—22no—
12#65709—22no—
13C2×#3956C412yes—
14M16×Dic5C2212yes—
15#64918—22no—
16#64884—22no—
17#64883—22no—
18C5×#343C411yescharacteristic
19#64750C411yescharacteristic
20#8838—51nomaximal, Sylow
21C22×Dic10C2×C411yescharacteristic
22C22×#170—21no—
23C22×#170—21no—
24C2×C5×M16C2×C412yes—
25C2×C5×C4⋊C4C2×C411yescharacteristic
26C2×#683Q812yes—
27C2×C4×Dic5D412yes—
28C2×C4×Dic5C2311yescharacteristic
29C2×#681C2×C412yes—
30#4033—22no—
31#4033—22no—
32C22⋊#170—22no—
33#4002—24no—
34C4⋊#170—22no—
35C4⋊#170—22no—
36C4⋊#170—22no—
37C4⋊#170D412yes—
38C4⋊#170D412yes—
39C4×#170—22no—
40C4×#170—22no—
41#3956—24no—
42#3947—22no—
43C8×Dic5—22no—
44#2983—51no—
45#1984—51no—
46C4×#101—51no—
47#1565—52no—
48#1278—52no—
49C22×C4×C5C4⋊C412yes—
50C22×C4×C5C22×C411yescharacteristic
51C22×Dic5C4⋊C412yes—
52C22×Dic5C2×D411yescharacteristic
53C22×Dic5C2×Q811yescharacteristic
54C2×Dic10—22no—
55C2×Dic10—22no—
56C2×Dic10—21no—
57C2×Dic10—21no—
58C2×#170—22no—
59C2×#170—22no—
60C2×#170—22no—
61C2×#170—41no—
62C2×#170—41no—
63C2×#170—42no—
64C2×#170—41no—
65C5×M16—22no—
66C5×M16—22no—
67C2×C5×C8—22no—
68C5×C4⋊C4—22no—
69#683—24no—
70C4×Dic5—22no—
71C4×Dic5—22no—
72C4×Dic5C2×D412yes—
73C4×Dic5#4112yes—
74#681—22no—
75#681M1614yes—
76C2×#168—22no—
77C2×C4×Q8—51no—
78#446—102no—
79#446—102no—
80#432—102no—
81#431—52no—
82C2×C4⋊C8—51no—
83C2×#101—52no—
84C4×M16—52no—
85C2×C4×C8—51no—
86#343—51no—
87#343AGL(1,𝔽5)11yescharacteristic
88#336—102no—
89#335—102no—
90#334—102no—
91C23×C5C2×C4⋊C411yescharacteristic
92C2×C4×C5—22no—
93C2×C4×C5—42no—
94C2×C4×C5C4×D412yes—
95C2×C4×C5C2×M1612yes—
96C2×C4×C5#13111yescharacteristic
97C2×C4×C5#13111yescharacteristic
98C2×Dic5—21no—
99C2×Dic5—21no—
100C2×Dic5—22no—
101C2×Dic5—22no—
102C2×Dic5—22no—
103C2×Dic5—41no—
104C2×Dic5#12011yescharacteristic
105C2×Dic5C22⋊Q812yes—
106C2×Dic5#12311yescharacteristic
107Dic10—42no—
108Dic10—42no—
109#170—42no—
110#170—42no—
111#170—42no—
112#170—81no—
113C5×C8—42no—
114#168—24no—
115C22×Q8—51no—
116C2×M16—52no—
117C2×M16C2×AGL(1,𝔽5)12yes—
118C22×C8—101no—
119C22×C8—101no—
120C4×Q8—102no—
121C4×Q8—102no—
122C2×C4⋊C4—52no—
123C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
124C2×C42—51no—
125C2×C42—52no—
126C4⋊C8—52no—
127C4⋊C8—52no—
128C4⋊C8—102no—
129C4⋊C8—102no—
130C4⋊C8—102no—
131#101—104no—
132C22⋊C8—102no—
133#97—102no—
134#97—104no—
135C4×C8—102no—
136C4×C8—102no—
137C4×C8—102no—
138C22×C5—21no—
139C22×C5—21no—
140C22×C5#38511yescharacteristic
141C22×C5#42311yescharacteristic
142C22×C5#42411yescharacteristic
143C4×C5—42no—
144C4×C5#43512yes—
145C4×C5#43612yes—
146Dic5—21no—
147Dic5—22no—
148Dic5—42no—
149Dic5#45411yescharacteristic
150Dic5#45611yescharacteristic
151C2×Q8—102no—
152C2×Q8—101no—
153C2×Q8—102no—
154C2×Q8—101no—
155C22×C4—51no—
156C22×C4—51no—
157C22×C4—52no—
158C22×C4C4⋊AGL(1,𝔽5)12yes—
159C22×C4C22×AGL(1,𝔽5)11yescharacteristic
160M16—22no—
161M16—22no—
162M16—54no—
163M16—102no—
164C2×C8—22no—
165C2×C8—102no—
166C2×C8—102no—
167C2×C8—102no—
168C2×C8—102no—
169C2×C8—201no—
170C2×C8—201no—
171C2×C8—201no—
172C2×C8—202no—
173C4⋊C4—22no—
174C4⋊C4—104no—
175C42—52no—
176C42—52no—
177C42—102no—
178C42—102no—
179C2×C5—21no—
180C2×C5—21no—
181C2×C5#185111yescharacteristic
182C2×C5#185711yescharacteristic
183C2×C5#185811yescharacteristic
184C23C2×C4⋊AGL(1,𝔽5)11yescharacteristic
185Q8—202no—
186Q8—202no—
187C2×C4—22no—
188C2×C4—42no—
189C2×C4—51no—
190C2×C4—51no—
191C2×C4—52no—
192C2×C4—101no—
193C2×C4—101no—
194C2×C4—102no—
195C2×C4—102no—
196C2×C4—102no—
197C2×C4—201no—
198C2×C4D5⋊M1612yes—
199C2×C4#413111yescharacteristic
200C2×C4D4×AGL(1,𝔽5)12yes—
201C2×C4#413311yescharacteristic
202C8—42no—
203C8—104no—
204C8—202no—
205C8—202no—
206C8—202no—
207C8—401no—
208C5#883811yescharacteristic, complemented, Sylow
209C22—21no—
210C22—21no—
211C22#6568211yescharacteristic
212C22#6569911yescharacteristic
213C22#6570811yescharacteristic
214C4—42no—
215C4—51no—
216C4—51no—
217C4—102no—
218C4—101no—
219C4—202no—
220C4#6569512yes—
221C4#6570412yes—
222C2—21no—
223C2—21no—
224C2#1060378611yescharacteristic
225C2#1060392811yescharacteristic
226C2#1060393111yescharacteristic
subgroupG/H
centerC22#65699
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#343C4
socleC22×C5#385
prime radicalC23×C5C2×C4⋊C4
cosocleC2×C4×Dic5C23
hypercenter#343AGL(1,𝔽5)
hypocenterC5#8838
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
208. C5#8838semidirect

Maximal subgroups

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

subgroupindex
#106170952
#106047392
#106043302
#105997662
#105987872
#88385