Finite Group Databasebeta

← #12009616

Subgroups — #12009616

Order 1280.

432 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 107 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#10613995C211yesmaximal, characteristic
2C5×#1458C211yesmaximal, characteristic
3#10602380C211yesmaximal, characteristic
4#10597950C214yesmaximal, complemented
5C2×C5×#117C2211yescharacteristic
6C22×#681—21no—
7C2×#4015C411yescharacteristic
8C5×#431—21no—
9#65501—21no—
10#65275C2212yes—
11#65268—21no—
12#65238C412yes—
13#65236—21no—
14#65225C411yescharacteristic
15#65217—21no—
16C5×#324C2212yes—
17C5×#323—21no—
18#64750—21no—
19#64750C2212yes—
20#11723—51nomaximal, Sylow
21C23×C4×C5D411yescharacteristic
22C22×Dic10—21no—
23C5×#117—41no—
24C5×#117—41no—
25C2×C5×C4⋊C4D411yescharacteristic
26C2×C5×C4⋊C4C2311yescharacteristic
27C2×C5×C22⋊C4C2×C411yescharacteristic
28C2×C5×C22⋊C4D411yescharacteristic
29C2×C42×C5C2×C411yescharacteristic
30C2×C42×C5D411yescharacteristic
31C2×C22⋊Dic5—22no—
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5C2×C412yes—
35C2×#683—22no—
36C2×#681—24no—
37C2×#681—22no—
38C2×#681—41no—
39C2×#681—42no—
40C22×#168—41no—
41#4015—41no—
42#4015—41no—
43C5×C4⋊C8—41no—
44C5×C22⋊C8—22no—
45C4×C5×C8—41no—
46#3963—21no—
47#3963—22no—
48#3963—22no—
49#3963C2×C412yes—
50#2628—51no—
51#1742—51no—
52#1458D511yescharacteristic
53#1353—54no—
54C24×C5C22⋊C411yescharacteristic
55C22×C4×C5—21no—
56C22×C4×C5—21no—
57C22×C4×C5—22no—
58C22×C4×C5C22⋊C411yescharacteristic
59C22×C4×C5C22⋊C411yescharacteristic
60C22×C4×C5C22⋊C411yescharacteristic
61C22×C4×C5SD1612yes—
62C22×C4×C5Q1612yes—
63C22×C4×C5C22×C411yescharacteristic
64C22×C4×C5C2×D411yescharacteristic
65C22×C4×C5C2×D411yescharacteristic
66C22×Dic5—22no—
67C22×Dic5—22no—
68C2×Dic10—42no—
69C2×Dic10—82no—
70C2×C5×C8—42no—
71C5×C4⋊C4—41no—
72C5×C4⋊C4—41no—
73C5×C22⋊C4—41no—
74C5×C22⋊C4—41no—
75C42×C5—21no—
76C42×C5—21no—
77C42×C5—21no—
78C42×C5—21no—
79C22⋊Dic5—82no—
80C4⋊Dic5—41no—
81C4⋊Dic5—41no—
82C4⋊Dic5—42no—
83C4⋊Dic5—42no—
84#683—82no—
85#681—24no—
86#681—44no—
87#681—42no—
88C2×#168—42no—
89C2×#168—44no—
90C22×M16—101no—
91C2×C4⋊Q8—51no—
92C2×#117C2×D511yescharacteristic
93#431—21no—
94#400—52no—
95#399—52no—
96#395—101no—
97#393—101no—
98#389—101no—
99#382—51no—
100#380—101no—
101#343—52no—
102#343—101no—
103#324C2×D512yes—
104#323—21no—
105C23×C5—21no—
106C23×C5—21no—
107C23×C5—41no—
108C23×C5—41no—
109C23×C5#10312yes—
110C23×C5C2×C22⋊C411yescharacteristic
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—22no—
114C2×C4×C5—22no—
115C2×C4×C5—22no—
116C2×C4×C5—22no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—41no—
122C2×C4×C5—41no—
123C2×C4×C5—41no—
124C2×C4×C5—41no—
125C2×C4×C5#9911yescharacteristic
126C2×C4×C5#9911yescharacteristic
127C2×C4×C5#10312yes—
128C2×C4×C5#10412yes—
129C2×C4×C5C2×SD1611yescharacteristic
130C2×C4×C5C2×Q1611yescharacteristic
131C2×Dic5—42no—
132C2×Dic5—42no—
133C2×Dic5—42no—
134C2×Dic5—42no—
135C2×Dic5—42no—
136C2×Dic5—42no—
137Dic10—84no—
138C5×C8—82no—
139#168—44no—
140C22×Q8—101no—
141C23×C4D2011yescharacteristic
142C2×M16—104no—
143C2×M16—102no—
144C2×M16—201no—
145C2×M16—202no—
146C22×C8—201no—
147C4⋊Q8—201no—
148C4⋊Q8—201no—
149#117—41no—
150#117—41no—
151C2×C4⋊C4—52no—
152C2×C4⋊C4—101no—
153C2×C4⋊C4—101no—
154C2×C4⋊C4—102no—
155C2×C4⋊C4D2011yescharacteristic
156C2×C4⋊C4C22×D511yescharacteristic
157C2×C22⋊C4—102no—
158C2×C22⋊C4C4×D511yescharacteristic
159C2×C22⋊C4C22⋊D511yescharacteristic
160C2×C42C4×D511yescharacteristic
161C2×C42C22⋊D511yescharacteristic
162C4⋊C8—41no—
163C22⋊C8—22no—
164C4×C8—41no—
165#95—52no—
166#95—101no—
167#95—102no—
168#95—102no—
169C22×C5—21no—
170C22×C5—21no—
171C22×C5—22no—
172C22×C5—42no—
173C22×C5—41no—
174C22×C5—41no—
175C22×C5—81no—
176C22×C5C2×#9911yescharacteristic
177C22×C5C2×#10311yescharacteristic
178C22×C5C2×#10411yescharacteristic
179C4×C5—21no—
180C4×C5—21no—
181C4×C5—41no—
182C4×C5—41no—
183C4×C5—41no—
184C4×C5—41no—
185C4×C5#32812yes—
186C4×C5#32812yes—
187Dic5—82no—
188Dic5—82no—
189C24#68511yescharacteristic
190C2×Q8—202no—
191C2×Q8—402no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—22no—
195C22×C4—102no—
196C22×C4—102no—
197C22×C4#67712yes—
198C22×C4Dic2012yes—
199C22×C4#68511yescharacteristic
200C22×C4#68511yescharacteristic
201C22×C4#68511yescharacteristic
202C22×C4C2×C4×D511yescharacteristic
203C22×C4C2×D2011yescharacteristic
204C22×C4C2×C22⋊D511yescharacteristic
205M16—104no—
206M16—204no—
207M16—202no—
208C2×C8—42no—
209C2×C8—202no—
210C2×C8—204no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—202no—
214C4⋊C4—201no—
215C4⋊C4—201no—
216C4⋊C4—202no—
217C4⋊C4—402no—
218C22⋊C4—41no—
219C22⋊C4—41no—
220C22⋊C4—402no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C2×C5—21no—
226C2×C5—21no—
227C2×C5—42no—
228C2×C5C2×#32811yescharacteristic
229C2×C5#212311yescharacteristic
230C2×C5#213411yescharacteristic
231C23—21no—
232C23—21no—
233C23—41no—
234C23—41no—
235C23#394812yes—
236C23C2×#68511yescharacteristic
237Q8—404no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—202no—
253C2×C4—202no—
254C2×C4—202no—
255C2×C4—202no—
256C2×C4—202no—
257C2×C4—202no—
258C2×C4#393811yescharacteristic
259C2×C4#393811yescharacteristic
260C2×C4#394812yes—
261C2×C4#395712yes—
262C2×C4C2×#67711yescharacteristic
263C2×C4C2×Dic2011yescharacteristic
264C8—82no—
265C8—204no—
266C5#1172311yescharacteristic, complemented, Sylow
267C22—21no—
268C22—21no—
269C22—22no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—81no—
274C22C2×#393811yescharacteristic
275C22C2×#394811yescharacteristic
276C22C2×#395711yescharacteristic
277C4—21no—
278C4—21no—
279C4—41no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—402no—
284C4—402no—
285C4#6468712yes—
286C4#6468712yes—
287C2—21no—
288C2—21no—
289C2—42no—
290C2C2×#6468711yescharacteristic
291C2#1060085111yescharacteristic
292C2#1060094211yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#1458C2
socleC22×C5C2×#99
prime radicalC24×C5C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#1458D5
hypocenterC5#11723
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
4. #10597950C2semidirect
266. C5#11723semidirect

Maximal subgroups

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

subgroupindex
#106139952
C5×#14582
#106023802
#105979502
#117235