Finite Group Databasebeta

← #13023912

Subgroups — #13023912

Order 1280.

366 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C2×#65162C211yesmaximal, characteristic
2#10604709C211yesmaximal, characteristic
3#10604697C211yesmaximal, characteristic
4#10598610C214yesmaximal, complemented
5C22×Dic20C411yescharacteristic
6C2×#4033—21no—
7#65758—21no—
8C2×C5×#107C411yescharacteristic
9C2×C8×Dic5C2211yescharacteristic
10C2×#3942—21no—
11#65162—21no—
12#65162—21no—
13#65162C412yes—
14#65162C2212yes—
15C22⋊#674—21no—
16#64888—21no—
17#64885C2212yes—
18#64884—21no—
19#64882C2212yes—
20#11658—51nomaximal, Sylow
21C22×Dic10—21no—
22C2×#704—41no—
23C22×C5×C8C2×C411yescharacteristic
24C2×C5×C4⋊C4—21no—
25C2×#683—41no—
26C2×C4×Dic5—41no—
27C2×C4×Dic5D411yescharacteristic
28C22×#168D411yescharacteristic
29C2×Dic20—21no—
30C2×Dic20—24no—
31C2×Dic20C2×C412yes—
32#4033—22no—
33#4033—22no—
34#4033—41no—
35#4033—41no—
36#4004—41no—
37C4⋊#170—22no—
38C2×#674—22no—
39C5×#107—21no—
40C5×#107C2×C412yes—
41C8×Dic5C2×C411yescharacteristic
42C8×Dic5D411yescharacteristic
43C8×Dic5D411yescharacteristic
44C8×Dic5C2311yescharacteristic
45#3942—22no—
46#3942—22no—
47C2×C4×Q16—51no—
48#2162—51no—
49#1567—51no—
50#1332—54no—
51C22×C4×C5—41no—
52C22×C4×C5C22⋊C411yescharacteristic
53C22×Dic5—41no—
54C22×Dic5D811yescharacteristic
55C22×Dic5SD1611yescharacteristic
56C2×Dic10—24no—
57C2×Dic10—22no—
58C2×Dic10—42no—
59C2×Dic10—41no—
60#704—82no—
61C2×#170—42no—
62C2×C5×C8—22no—
63C2×C5×C8C22⋊C411yescharacteristic
64C2×C5×C8C22×C411yescharacteristic
65C5×C4⋊C4—22no—
66C5×C4⋊C4—41no—
67#683—42no—
68#683—42no—
69C4×Dic5—42no—
70C4×Dic5—42no—
71C4×Dic5C22⋊C411yescharacteristic
72C4×Dic5D811yescharacteristic
73C4×Dic5SD1611yescharacteristic
74C4×Dic5C2×D411yescharacteristic
75C2×#168—41no—
76C2×#168C22⋊C411yescharacteristic
77C2×#168C2×D411yescharacteristic
78Dic20—24no—
79Dic20—22no—
80Dic20M1614yescomplemented
81#674—42no—
82C22×Q16—51no—
83C2×C4×Q8—101no—
84C4×Q16—52no—
85C4×Q16—52no—
86C4×Q16—101no—
87C4×Q16—101no—
88C2×#107AGL(1,𝔽5)11yescharacteristic
89#423—101no—
90C2×#103—101no—
91C2×C4×C8—51no—
92C4⋊C16—101no—
93C22⋊C16—101no—
94C4×C16—52no—
95#335—52no—
96#335—101no—
97C23×C5#10211yescharacteristic
98C2×C4×C5—21no—
99C2×C4×C5—21no—
100C2×C4×C5—42no—
101C2×C4×C5—82no—
102C2×C4×C5#10211yescharacteristic
103C2×C4×C5C2×C22⋊C411yescharacteristic
104C2×Dic5—41no—
105C2×Dic5—44no—
106C2×Dic5—42no—
107C2×Dic5#10211yescharacteristic
108C2×Dic5#10211yescharacteristic
109C2×Dic5SD3212yes—
110C2×Dic5Q3212yes—
111C2×Dic5C2×D811yescharacteristic
112C2×Dic5C2×SD1611yescharacteristic
113Dic10—24no—
114Dic10—44no—
115Dic10—42no—
116#170—82no—
117C5×C8—21no—
118C5×C8C2×M1612yes—
119#168—21no—
120#168—21no—
121C22×Q8—101no—
122C2×Q16—52no—
123C2×Q16—104no—
124C2×Q16—101no—
125C2×M16—201no—
126C22×C8—51no—
127C22×C8C2×AGL(1,𝔽5)11yescharacteristic
128C4×Q8—102no—
129C4×Q8—102no—
130C4×Q8—201no—
131C4×Q8—201no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—201no—
134C2×C42—51no—
135C2×C42—201no—
136C2×C16—102no—
137#107—21no—
138#107C2×AGL(1,𝔽5)12yes—
139C4⋊C8—102no—
140C4⋊C8—201no—
141#103—102no—
142#103—102no—
143C4×C8—51no—
144C4×C8—51no—
145C4×C8—51no—
146C4×C8—51no—
147C22×C5—21no—
148C22×C5—21no—
149C22×C5#35812yes—
150C22×C5C2×#10211yescharacteristic
151C4×C5—21no—
152C4×C5—82no—
153C4×C5#40711yescharacteristic
154C4×C5#42111yescharacteristic
155Dic5—21no—
156Dic5—21no—
157Dic5—44no—
158Dic5#35812yes—
159Dic5C2×SD3211yescharacteristic
160Dic5C2×Q3211yescharacteristic
161C2×Q8—104no—
162C2×Q8—102no—
163C2×Q8—202no—
164C2×Q8—201no—
165C22×C4—41no—
166C22×C4—51no—
167C22×C4—51no—
168C22×C4—201no—
169C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
170Q16—54no—
171Q16—104no—
172Q16—102no—
173M16—402no—
174C2×C8—22no—
175C2×C8—51no—
176C2×C8—51no—
177C2×C8—201no—
178C2×C8—202no—
179C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
180C2×C8C22×AGL(1,𝔽5)11yescharacteristic
181C4⋊C4—22no—
182C4⋊C4—41no—
183C4⋊C4—202no—
184C4⋊C4—202no—
185C42—51no—
186C42—51no—
187C42—51no—
188C42—51no—
189C42—202no—
190C42—202no—
191C16—202no—
192C2×C5—22no—
193C2×C5#148611yescharacteristic
194C2×C5C2×#35811yescharacteristic
195C2×C5#214311yescharacteristic
196C23#400711yescharacteristic
197Q8—104no—
198Q8—204no—
199Q8—202no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—42no—
203C2×C4—52no—
204C2×C4—52no—
205C2×C4—51no—
206C2×C4—51no—
207C2×C4—51no—
208C2×C4—51no—
209C2×C4—82no—
210C2×C4—201no—
211C2×C4—204no—
212C2×C4—202no—
213C2×C4#400711yescharacteristic
214C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
215C8—21no—
216C8—101no—
217C8—101no—
218C8—402no—
219C8D5⋊M1612yes—
220C5#1165811yescharacteristic, complemented, Sylow
221C22—21no—
222C22—21no—
223C22#6490812yes—
224C22C2×#400711yescharacteristic
225C4—21no—
226C4—51no—
227C4—52no—
228C4—51no—
229C4—82no—
230C4—101no—
231C4—101no—
232C4—204no—
233C4#6575511yescharacteristic
234C4#6578411yescharacteristic
235C2—22no—
236C2#1060427211yescharacteristic
237C2#1060478811yescharacteristic
238C2C2×#6490811yescharacteristic
subgroupG/H
centerC22C2×#4007
commutatorC2×C5×C8C22×C4
FrattiniC2×C8C22×AGL(1,𝔽5)
FittingC2×C5×#107C4
socleC22×C5C2×#102
prime radicalC23×C5#102
cosocleC8×Dic5C23
hypercenterC2×#107AGL(1,𝔽5)
hypocenterC5#11658
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
4. #10598610C2semidirect
80. Dic20M16semidirect
220. C5#11658semidirect

Maximal subgroups

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

subgroupindex
C2×#651622
#106047092
#106046972
#105986102
#116585