Finite Group Databasebeta

← #12017957

Subgroups — #12017957

Order 1280.

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

normal subgroups only

This group has 488 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#10614105C211yesmaximal, characteristic
2C4×C5×#99C211yesmaximal, characteristic
3#10602410C211yesmaximal, characteristic
4#10598185C214yesmaximal
5C2×C4×C5×D4C2211yescharacteristic
6C22×C4⋊Dic5C411yescharacteristic, complemented
7C2×C5×#99C2212yes—
8C4×C5×C22⋊C4—21no—
9#65509C2212yes—
10C2×#3965C2212yes—
11#65501—21no—
12#65501C411yescharacteristic, complemented
13#65275—21no—
14#65238—21no—
15#65235C412yescomplemented
16#65217—21no—
17#65213—21no—
18C5×#342—21no—
19#64750—21no—
20#13295—51nomaximal, Sylow
21C22×C5×D4C2311yescharacteristic
22C23×C4×C5C2×C411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×Dic5C2×C412yes—
25C4×C5×D4—41no—
26C4×C5×D4—41no—
27C2×C5×C4⋊C4D411yescharacteristic
28C2×C5×C22⋊C4—22no—
29C2×C5×C22⋊C4C2×C411yescharacteristic
30C2×C5×C22⋊C4D411yescharacteristic
31C2×C42×C5—41no—
32C2×C42×C5D411yescharacteristic
33C2×C22⋊Dic5—22no—
34C2×C22⋊Dic5C2×C412yes—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—21no—
38C2×C4⋊Dic5—41no—
39C2×C4⋊Dic5—41no—
40C2×#683—22no—
41C2×#681—22no—
42C5×#99—22no—
43C5×#99Q814yes—
44C5×#95—41no—
45#3965—24no—
46#3963—22no—
47#3963—21no—
48#3963—22no—
49C4⋊#168—41no—
50C4⋊#168—41no—
51#2487—51no—
52#1800—51no—
53C4×#99D511yescharacteristic
54#1390—54no—
55C24×C5C22×C411yescharacteristic
56C24×C5C2×D411yescharacteristic
57C2×C5×D4—41no—
58C2×C5×D4—41no—
59C2×C5×D4C2×Q812yes—
60C2×C5×D4#4112yes—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5—21no—
65C22×C4×C5—42no—
66C22×C4×C5—42no—
67C22×C4×C5—42no—
68C22×C4×C5C22⋊C411yescharacteristic
69C22×C4×C5C22⋊C411yescharacteristic
70C22×C4×C5C22⋊C411yescharacteristic
71C22×C4×C5C22⋊C411yescharacteristic
72C22×C4×C5C2×D411yescharacteristic
73C22×Dic5—22no—
74C22×Dic5—22no—
75C22×Dic5—42no—
76C22×Dic5—82no—
77C5×C4⋊C4—41no—
78C5×C22⋊C4—24no—
79C5×C22⋊C4—41no—
80C5×C22⋊C4—41no—
81C5×C22⋊C4—42no—
82C42×C5—21no—
83C42×C5—21no—
84C42×C5—82no—
85C22⋊Dic5—42no—
86C22⋊Dic5—82no—
87C4⋊Dic5—42no—
88C4⋊Dic5—42no—
89C4⋊Dic5—41no—
90C4⋊Dic5—41no—
91#683—82no—
92#681—42no—
93#681—42no—
94C2×#168—42no—
95C2×C4×D4C2×D511yescharacteristic
96C22×C4⋊C4—51no—
97#423—101no—
98C2×#100—52no—
99C2×#99C2×D512yes—
100#400—101no—
101#399—101no—
102#389—101no—
103#386—52no—
104#385—52no—
105#380—51no—
106#380—101no—
107C4×C22⋊C4—21no—
108#343—101no—
109#342—21no—
110C23×C5—21no—
111C23×C5—21no—
112C23×C5—21no—
113C23×C5—21no—
114C23×C5—41no—
115C23×C5—41no—
116C23×C5—41no—
117C23×C5—41no—
118C23×C5C2×C22⋊C411yescharacteristic
119C23×C5C4×Q812yes—
120C23×C5C22⋊Q812yes—
121C5×D4—42no—
122C5×D4—42no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—22no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—42no—
130C2×C4×C5—42no—
131C2×C4×C5—42no—
132C2×C4×C5—41no—
133C2×C4×C5—41no—
134C2×C4×C5—41no—
135C2×C4×C5—44no—
136C2×C4×C5—81no—
137C2×C4×C5—82no—
138C2×C4×C5—82no—
139C2×C4×C5#9911yescharacteristic
140C2×C4×C5#9911yescharacteristic
141C2×C4×C5#12411yescharacteristic
142C2×C4×C5C4⋊Q811yescharacteristic
143C2×Dic5—42no—
144C2×Dic5—42no—
145C2×Dic5—42no—
146C2×Dic5—42no—
147C2×Dic5—42no—
148C2×Dic5—42no—
149C2×Dic5—84no—
150#168—82no—
151C22×D4C22×D511yescharacteristic
152C23×C4—52no—
153C23×C4C4×D511yescharacteristic
154C23×C4C22⋊D511yescharacteristic
155C2×M16—102no—
156C4×D4—41no—
157C4×D4—41no—
158C2×C4⋊C4—101no—
159C2×C4⋊C4—101no—
160C2×C4⋊C4—101no—
161C2×C4⋊C4—102no—
162C2×C4⋊C4—201no—
163C2×C4⋊C4—201no—
164C2×C4⋊C4D2011yescharacteristic
165C2×C22⋊C4—22no—
166C2×C22⋊C4—52no—
167C2×C22⋊C4—102no—
168C2×C22⋊C4C4×D511yescharacteristic
169C2×C22⋊C4C22⋊D511yescharacteristic
170C2×C42—41no—
171C2×C42D2011yescharacteristic
172C4⋊C8—201no—
173C4⋊C8—201no—
174#100—104no—
175#99—22no—
176#99Dic1014yes—
177#95—41no—
178#95—101no—
179#95—102no—
180#95—102no—
181C22×C5—21no—
182C22×C5—21no—
183C22×C5—22no—
184C22×C5—22no—
185C22×C5—42no—
186C22×C5—42no—
187C22×C5—42no—
188C22×C5—41no—
189C22×C5—41no—
190C22×C5—41no—
191C22×C5—41no—
192C22×C5—81no—
193C22×C5#39111yescharacteristic
194C22×C5C2×#9911yescharacteristic
195C22×C5#41011yescharacteristic
196C4×C5—21no—
197C4×C5—21no—
198C4×C5—21no—
199C4×C5—41no—
200C4×C5—41no—
201C4×C5—41no—
202C4×C5—84no—
203C4×C5#35212yes—
204Dic5—82no—
205Dic5—82no—
206C24C2×C4×D511yescharacteristic
207C24C2×C22⋊D511yescharacteristic
208C2×D4—41no—
209C2×D4—41no—
210C2×D4C2×Dic1012yes—
211C2×D4#70912yes—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—102no—
220C22×C4—102no—
221C22×C4—202no—
222C22×C4—402no—
223C22×C4#68511yescharacteristic
224C22×C4#68511yescharacteristic
225C22×C4#68511yescharacteristic
226C22×C4#68511yescharacteristic
227C22×C4C2×D2011yescharacteristic
228M16—202no—
229M16—202no—
230C2×C8—202no—
231C4⋊C4—41no—
232C4⋊C4—202no—
233C4⋊C4—202no—
234C4⋊C4—201no—
235C4⋊C4—201no—
236C4⋊C4—402no—
237C22⋊C4—24no—
238C22⋊C4—41no—
239C22⋊C4—41no—
240C22⋊C4—42no—
241C22⋊C4—202no—
242C22⋊C4—402no—
243C42—21no—
244C42—21no—
245C42—82no—
246C2×C5—21no—
247C2×C5—21no—
248C2×C5—42no—
249C2×C5—42no—
250C2×C5#199611yescharacteristic
251C2×C5C2×#35211yescharacteristic
252C2×C5#212211yescharacteristic
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23C4×Dic1012yes—
262C23#407012yes—
263C23C2×#68511yescharacteristic
264D4—42no—
265D4—42no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—44no—
279C2×C4—81no—
280C2×C4—82no—
281C2×C4—82no—
282C2×C4—202no—
283C2×C4—202no—
284C2×C4—202no—
285C2×C4—202no—
286C2×C4—202no—
287C2×C4—202no—
288C2×C4—404no—
289C2×C4#393811yescharacteristic
290C2×C4#393811yescharacteristic
291C2×C4#401511yescharacteristic
292C2×C4#402111yescharacteristic
293C8—402no—
294C5#1329511yescharacteristic, complemented, Sylow
295C22—21no—
296C22—21no—
297C22—22no—
298C22—22no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—81no—
307C22#6521811yescharacteristic
308C22C2×#393811yescharacteristic
309C22#6529511yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—84no—
317C4—402no—
318C4—402no—
319C4#6469212yes—
320C2—21no—
321C2—21no—
322C2—42no—
323C2—42no—
324C2#1060025011yescharacteristic
325C2C2×#6469211yescharacteristic
326C2#1060085011yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC24×C5C22×C4
FrattiniC22×D4C22×D5
FittingC4×C5×#99C2
socleC22×C5C2×#99
prime radical, cosocleC22×C5×D4C23
hypercenterC4×#99D5
hypocenterC5#13295
LCSG ▷ C24×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
6. C22×C4⋊Dic5C4semidirect
12. #65501C4semidirect
15. #65235C4semidirect
294. C5#13295semidirect

Maximal subgroups

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

subgroupindex
#106141052
C4×C5×#992
#106024102
#105981852
#132955