Finite Group Databasebeta

← #11995060

Subgroups — #11995060

Order 1280.

630 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 147 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×C5×#382C211yesmaximal, characteristic
2#10613806C211yesmaximal, characteristic
3#10602324C211yesmaximal, characteristic
4C2×#64672C212yesmaximal
5#10598103C212yesmaximal
6C22×C5×C4⋊C4—21no—
7C22×C42×C5C2211yescharacteristic
8C2×#4070C2211yescharacteristic
9C5×#382—24no—
10C2×C5×#95—21no—
11C2×C5×#95C2212yes—
12#65501C2211yescharacteristic
13#65500—21no—
14#65499—21no—
15C2×C22⋊#168C2212yes—
16#65222—22no—
17#65218C412yescomplemented
18#65217C412yescomplemented
19#64744—22no—
20#64672—24no—
21#9152—51nomaximal, Sylow
22C23×C4×C5—22no—
23C23×C4×C5D411yescharacteristic
24C23×C4×C5D411yescharacteristic
25C23×C4×C5C2311yescharacteristic
26C22×Dic10C2×C411yescharacteristic
27C2×C5×C4⋊C4—24no—
28C2×C5×C4⋊C4—42no—
29C2×C5×C4⋊C4—42no—
30C2×C42×C5—22no—
31C2×C42×C5—22no—
32C2×C42×C5C2×C412yes—
33C2×C42×C5D412yes—
34C2×C22⋊Dic5—21no—
35C2×C22⋊Dic5—21no—
36C2×C4⋊Dic5C2×C411yescharacteristic
37C2×C4⋊Dic5C2×C412yes—
38#4070—22no—
39#4070—22no—
40C2×#683—22no—
41C2×#683—21no—
42C22×#168—22no—
43C5×#95—24no—
44C5×#95—22no—
45C5×#95D414yes—
46#3963—22no—
47#3963—22no—
48#3963—22no—
49#3963—21no—
50C22⋊#168—22no—
51C22⋊#168—22no—
52#2855—51no—
53C2×#382D511yescharacteristic
54#1817—51no—
55C2×#328—52no—
56#1294—52no—
57C24×C5C2×D411yescharacteristic
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5—24no—
65C22×C4×C5—42no—
66C22×C4×C5—42no—
67C22×C4×C5—44no—
68C22×C4×C5—44no—
69C22×C4×C5—42no—
70C22×C4×C5—42no—
71C22×C4×C5C22⋊C412yes—
72C22×C4×C5C22⋊C412yes—
73C22×C4×C5SD1612yes—
74C22×C4×C5Q1612yes—
75C22×C4×C5C22×C411yescharacteristic
76C22×C4×C5C2×D411yescharacteristic
77C22×C4×C5C2×D412yes—
78C22×C4×C5#4112yes—
79C22×Dic5—21no—
80C22×Dic5—22no—
81C22×Dic5—21no—
82C2×Dic10—22no—
83C2×Dic10—42no—
84C5×C4⋊C4—48no—
85C42×C5—24no—
86C42×C5—24no—
87C22⋊Dic5—41no—
88C22⋊Dic5—41no—
89C22⋊Dic5—41no—
90C22⋊Dic5—41no—
91C4⋊Dic5—22no—
92C4⋊Dic5—42no—
93#683—44no—
94#683—42no—
95C2×#168—44no—
96C2×#168—42no—
97C2×C22⋊Q8—51no—
98C22×C4⋊C4—21no—
99C22×C42C2×D511yescharacteristic
100C2×C22⋊C8—52no—
101#391—52no—
102#389—52no—
103#387—102no—
104#385—101no—
105#382—24no—
106#381—101no—
107#380—51no—
108C2×#95—21no—
109C2×#95C2×D512yes—
110#336—102no—
111#328—104no—
112C23×C5—22no—
113C23×C5—22no—
114C23×C5C2×C22⋊C411yescharacteristic
115C23×C5#12011yescharacteristic
116C23×C5#12311yescharacteristic
117C23×C5C2×SD1611yescharacteristic
118C23×C5C2×Q1611yescharacteristic
119C23×C5AGL(1,ℤ/8)11yescharacteristic
120C23×C5#13711yescharacteristic
121C2×C4×C5—22no—
122C2×C4×C5—22no—
123C2×C4×C5—22no—
124C2×C4×C5—22no—
125C2×C4×C5—22no—
126C2×C4×C5—22no—
127C2×C4×C5—22no—
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5—22no—
131C2×C4×C5—22no—
132C2×C4×C5—42no—
133C2×C4×C5—42no—
134C2×C4×C5—42no—
135C2×C4×C5—42no—
136C2×C4×C5—44no—
137C2×C4×C5—44no—
138C2×C4×C5—44no—
139C2×C4×C5—84no—
140C2×C4×C5—84no—
141C2×C4×C5#10314yes—
142C2×C4×C5C4×D412yes—
143C2×C4×C5#12112yes—
144C2×Dic5—41no—
145C2×Dic5—41no—
146C2×Dic5—42no—
147C2×Dic5—42no—
148C2×Dic5—42no—
149C2×Dic5—42no—
150C2×Dic5—42no—
151Dic10—82no—
152#168—82no—
153C22×Q8—51no—
154C23×C4—22no—
155C23×C4C22⋊D511yescharacteristic
156C23×C4C22⋊D511yescharacteristic
157C23×C4C22×D511yescharacteristic
158C22×C8—102no—
159C22⋊Q8—102no—
160C22⋊Q8—102no—
161C2×C4⋊C4—24no—
162C2×C4⋊C4—42no—
163C2×C4⋊C4—42no—
164C2×C4⋊C4—51no—
165C2×C4⋊C4—52no—
166C2×C4⋊C4—102no—
167C2×C4⋊C4—101no—
168C2×C22⋊C4—101no—
169C2×C22⋊C4—101no—
170C2×C42—22no—
171C2×C42—22no—
172C2×C42C4×D512yes—
173C2×C42D2012yes—
174C22⋊C8—102no—
175C22⋊C8—102no—
176#95—24no—
177#95—22no—
178#95—102no—
179#95—102no—
180#95—102no—
181#95—101no—
182#95C22⋊D514yes—
183C22×C5—21no—
184C22×C5—21no—
185C22×C5—21no—
186C22×C5—21no—
187C22×C5—22no—
188C22×C5—22no—
189C22×C5—22no—
190C22×C5—22no—
191C22×C5#38611yescharacteristic
192C22×C5#41012yes—
193C22×C5C2×#10311yescharacteristic
194C22×C5#41711yescharacteristic
195C22×C5#42112yes—
196C22×C5#45011yescharacteristic
197C22×C5#45111yescharacteristic
198C22×C5#48311yescharacteristic
199C22×C5#48411yescharacteristic
200C4×C5—24no—
201C4×C5—22no—
202C4×C5—22no—
203C4×C5—42no—
204C4×C5—84no—
205Dic5—81no—
206Dic5—81no—
207Dic5—82no—
208C24C2×C22⋊D511yescharacteristic
209C2×Q8—102no—
210C2×Q8—202no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—24no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—44no—
221C22×C4—44no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—102no—
225C22×C4—101no—
226C22×C4—101no—
227C22×C4#68512yes—
228C22×C4#68512yes—
229C22×C4#68712yes—
230C22×C4#68912yes—
231C22×C4C2×C4×D511yescharacteristic
232C22×C4C2×D2011yescharacteristic
233C22×C4#70912yes—
234C22×C4C2×C22⋊D512yes—
235C2×C8—204no—
236C2×C8—202no—
237C4⋊C4—48no—
238C4⋊C4—102no—
239C4⋊C4—202no—
240C4⋊C4—204no—
241C4⋊C4—202no—
242C22⋊C4—201no—
243C22⋊C4—201no—
244C22⋊C4—201no—
245C22⋊C4—201no—
246C42—24no—
247C42—24no—
248C2×C5—21no—
249C2×C5—21no—
250C2×C5—21no—
251C2×C5—21no—
252C2×C5#151212yes—
253C2×C5#151812yes—
254C2×C5#187211yescharacteristic
255C2×C5#189711yescharacteristic
256C2×C5#189911yescharacteristic
257C23—22no—
258C23—22no—
259C23C2×#68511yescharacteristic
260C23#407511yescharacteristic
261C23#407811yescharacteristic
262C23C2×#68711yescharacteristic
263C23#408811yescharacteristic
264C23C2×#68911yescharacteristic
265C23#409911yescharacteristic
266Q8—402no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—44no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4—84no—
286C2×C4—84no—
287C2×C4—202no—
288C2×C4—202no—
289C2×C4—202no—
290C2×C4—202no—
291C2×C4—201no—
292C2×C4—201no—
293C2×C4—202no—
294C2×C4#394214yes—
295C2×C4C4×C22⋊D512yes—
296C2×C4#407612yes—
297C8—402no—
298C5#915211yescharacteristic, complemented, Sylow
299C22—21no—
300C22—21no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22—22no—
305C22—21no—
306C22—21no—
307C22#6525511yescharacteristic
308C22C2×#394211yescharacteristic
309C22#6525911yescharacteristic
310C22#6526011yescharacteristic
311C22#6529412yes—
312C22#6529512yes—
313C22#6550211yescharacteristic
314C22#6550711yescharacteristic
315C22#6551711yescharacteristic
316C4—24no—
317C4—22no—
318C4—22no—
319C4—42no—
320C4—84no—
321C4—401no—
322C4—402no—
323C4—401no—
324C2—21no—
325C2—21no—
326C2—21no—
327C2—21no—
328C2#1060033712yes—
329C2#1060033912yes—
330C2#1060235211yescharacteristic
331C2#1060238411yescharacteristic
332C2#1060238811yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#382C2
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenterC2×#382D5
hypocenterC5#9152
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
17. #65218C4semidirect
18. #65217C4semidirect
298. C5#9152semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3822
#106138062
#106023242
C2×#646722
#105981032
#91525