Finite Group Databasebeta

← #11997170

Subgroups — #11997170

Order 1280.

602 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C5×#2535C211yesmaximal, characteristic
2#10614035C211yesmaximal, characteristic, complemented
3#10602410C211yesmaximal, characteristic, complemented
4#10602391C212yesmaximal, complemented
5#10598122C212yesmaximal, complemented
6C2×C5×#121—21no—
7C2×C4×C5×D4C2211yescharacteristic
8C2×C4×C5×D4C2211yescharacteristic
9C5×#397C412yes—
10C5×#392C412yes—
11C5×#386—22no—
12C5×#382C2211yescharacteristic
13C5×#380—21no—
14C2×#3965—21no—
15#65496—22no—
16#65301—24no—
17#65214C2212yes—
18#65213C2212yes—
19D4⋊#168—24no—
20#64750—21no—
21#9489—51nomaximal, Sylow
22C22×C5×D4—22no—
23C22×C5×D4C2×C411yescharacteristic
24C22×C5×D4D411yescharacteristic
25C23×C4×C5—21no—
26C23×C4×C5D412yes—
27C5×#121—44no—
28C4×C5×D4—22no—
29C4×C5×D4—22no—
30C4×C5×D4—22no—
31C4×C5×D4—22no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4C2×C411yescharacteristic
34C2×C5×C4⋊C4D411yescharacteristic
35C2×C5×C22⋊C4—22no—
36C2×C5×C22⋊C4—21no—
37C2×C5×C22⋊C4—22no—
38C2×C5×C22⋊C4C2×C412yes—
39C2×C42×C5C2311yescharacteristic
40C2×#681—24no—
41C2×#681—22no—
42C5×#95—22no—
43C5×#95—21no—
44C5×#95C2×C412yes—
45#3965—42no—
46C22⋊#168—24no—
47C22⋊#168—22no—
48C4⋊#168—22no—
49C4⋊#168—22no—
50C4⋊#168—22no—
51C4×#168D414yescomplemented
52#2975—51no—
53#2535D511yescharacteristic
54#1800—51no—
55#1486—52no—
56#1286—52no—
57C24×C5—21no—
58C24×C5C22⋊C412yes—
59C2×C5×D4—22no—
60C2×C5×D4—22no—
61C2×C5×D4—22no—
62C2×C5×D4—21no—
63C2×C5×D4—21no—
64C2×C5×D4—42no—
65C2×C5×D4—44no—
66C2×C5×D4—44no—
67C2×C5×D4—82no—
68C22×C4×C5—22no—
69C22×C4×C5—22no—
70C22×C4×C5—21no—
71C22×C4×C5—22no—
72C22×C4×C5—42no—
73C22×C4×C5—42no—
74C22×C4×C5—41no—
75C22×C4×C5—41no—
76C22×C4×C5—82no—
77C22×C4×C5C22⋊C412yes—
78C22×C4×C5C22×C411yescharacteristic
79C22×C4×C5C2×D411yescharacteristic
80C22×C4×C5C2×D411yescharacteristic
81C5×C4⋊C4—22no—
82C5×C4⋊C4—22no—
83C5×C4⋊C4—42no—
84C5×C22⋊C4—24no—
85C5×C22⋊C4—44no—
86C5×C22⋊C4—41no—
87C5×C22⋊C4—41no—
88C5×C22⋊C4—82no—
89C42×C5C2×D412yes—
90C42×C5#4112yes—
91#681—42no—
92#681—42no—
93#681—84no—
94C2×#168—24no—
95C2×#168—42no—
96C2×#121—21no—
97C2×C4×D4C2×D511yescharacteristic
98C2×C4×D4C2×D511yescharacteristic
99#436—104no—
100#431—52no—
101#423—52no—
102C2×#100—101no—
103#407—102no—
104#397Dic512yes—
105#392Dic512yes—
106#386—22no—
107#382C2×D511yescharacteristic
108#380—21no—
109#343—101no—
110D4⋊C8—104no—
111C23×C5—22no—
112C23×C5—22no—
113C23×C5—22no—
114C23×C5—22no—
115C23×C5—42no—
116C23×C5—42no—
117C23×C5—41no—
118C23×C5—41no—
119C23×C5—41no—
120C23×C5—41no—
121C23×C5—41no—
122C23×C5—41no—
123C23×C5C2×C22⋊C411yescharacteristic
124C5×D4—24no—
125C5×D4—42no—
126C5×D4—42no—
127C5×D4—42no—
128C5×D4—88no—
129C2×C4×C5—22no—
130C2×C4×C5—41no—
131C2×C4×C5—41no—
132C2×C4×C5—44no—
133C2×C4×C5—42no—
134C2×C4×C5—42no—
135C2×C4×C5—42no—
136C2×C4×C5—41no—
137C2×C4×C5—41no—
138C2×C4×C5—41no—
139C2×C4×C5—42no—
140C2×C4×C5—82no—
141C2×C4×C5—82no—
142C2×C4×C5—82no—
143C2×C4×C5C4×D412yes—
144C2×C4×C5#12011yescharacteristic
145C2×C4×C5#12112yes—
146C2×C4×C5#12311yescharacteristic
147C2×C4×C5AGL(1,ℤ/8)12yes—
148C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C5#13711yescharacteristic
150#168—44no—
151#168—82no—
152C22×D4—22no—
153C22×D4C2×Dic511yescharacteristic
154C22×D4C22⋊D511yescharacteristic
155C23×C4—21no—
156C23×C4C22⋊D512yes—
157C2×M16—104no—
158C2×M16—102no—
159#121—44no—
160C4×D4—22no—
161C4×D4—22no—
162C4×D4—22no—
163C4×D4—22no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4C2×Dic511yescharacteristic
166C2×C4⋊C4C22⋊D511yescharacteristic
167C2×C22⋊C4—22no—
168C2×C22⋊C4—21no—
169C2×C22⋊C4—22no—
170C2×C22⋊C4C2×Dic512yes—
171C2×C42C22×D511yescharacteristic
172C4⋊C8—102no—
173C4⋊C8—102no—
174C4⋊C8—102no—
175#100—202no—
176C22⋊C8—104no—
177C22⋊C8—102no—
178C4×C8—54no—
179#95—22no—
180#95—21no—
181#95C2×Dic512yes—
182C22×C5—21no—
183C22×C5—21no—
184C22×C5—42no—
185C22×C5—44no—
186C22×C5—42no—
187C22×C5—42no—
188C22×C5—42no—
189C22×C5—42no—
190C22×C5—42no—
191C22×C5—82no—
192C22×C5—81no—
193C22×C5—81no—
194C22×C5—81no—
195C22×C5—81no—
196C22×C5#38611yescharacteristic
197C22×C5#41711yescharacteristic
198C22×C5#41811yescharacteristic
199C4×C5—22no—
200C4×C5—21no—
201C4×C5—21no—
202C4×C5—42no—
203C4×C5—82no—
204C4×C5—81no—
205C4×C5#46812yes—
206C4×C5#46912yes—
207C24—21no—
208C24C22⋊Dic512yes—
209C2×D4—21no—
210C2×D4—22no—
211C2×D4—22no—
212C2×D4—22no—
213C2×D4—21no—
214C2×D4—42no—
215C2×D4—44no—
216C2×D4—44no—
217C2×D4—82no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—21no—
222C22×C4—41no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—41no—
226C22×C4—82no—
227C22×C4C22⋊Dic512yes—
228C22×C4C22×Dic511yescharacteristic
229C22×C4C2×C22⋊D511yescharacteristic
230C22×C4C2×C22⋊D511yescharacteristic
231M16—202no—
232M16—202no—
233M16—404no—
234C2×C8—104no—
235C2×C8—202no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—42no—
239C22⋊C4—24no—
240C22⋊C4—44no—
241C22⋊C4—41no—
242C22⋊C4—41no—
243C22⋊C4—82no—
244C42D4×D512yes—
245C42#71112yes—
246C2×C5—21no—
247C2×C5—21no—
248C2×C5—82no—
249C2×C5—82no—
250C2×C5#189111yescharacteristic
251C2×C5#189511yescharacteristic
252C2×C5#191111yescharacteristic
253C23—22no—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—42no—
258C23—42no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23—41no—
265C23C2×C22⋊Dic511yescharacteristic
266D4—24no—
267D4—42no—
268D4—42no—
269D4—42no—
270D4—88no—
271C2×C4—22no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—44no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—82no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4#407812yes—
286C2×C4D4×Dic512yes—
287C2×C4#408111yescharacteristic
288C2×C4#408311yescharacteristic
289C2×C4#408512yes—
290C2×C4#409511yescharacteristic
291C2×C4#409711yescharacteristic
292C8—204no—
293C8—402no—
294C5#948911yescharacteristic, complemented, Sylow
295C22—21no—
296C22—21no—
297C22—42no—
298C22—44no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—42no—
303C22—42no—
304C22—82no—
305C22—81no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22#6550411yescharacteristic
310C22#6550911yescharacteristic
311C22#6552111yescharacteristic
312C4—22no—
313C4—21no—
314C4—21no—
315C4—42no—
316C4—82no—
317C4—81no—
318C4#6532812yes—
319C4#6533112yes—
320C2—21no—
321C2—21no—
322C2—82no—
323C2—82no—
324C2#1060247511yescharacteristic
325C2#1060250711yescharacteristic
326C2#1060264611yescharacteristic
subgroupG/H
centerC22#65509
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
Fitting, prime radicalC5×#2535C2
socleC22×C5#386
cosocleC2×C42×C5C23
hypercenter#2535D5
hypocenterC5#9489
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2535

Complements

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

NH ≅ G/Ntype
2. #10614035C2semidirect
3. #10602410C2semidirect
4. #10602391C2semidirect
5. #10598122C2semidirect
51. C4×#168D4semidirect
294. C5#9489semidirect

Maximal subgroups

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

subgroupindex
C5×#25352
#106140352
#106024102
#106023912
#105981222
#94895