Finite Group Databasebeta

← #11991033

Subgroups — #11991033

Order 1280.

738 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 151 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×#556C211yesmaximal, characteristic
2#10602566C212yesmaximal, complemented
3#10602415C212yesmaximal, complemented
4#10602410C211yesmaximal, characteristic
5#10602394C211yesmaximal, characteristic
6C5×#556—24no—
7C5×#556—24no—
8C2×C5×C4⋊Q8C2211yescharacteristic
9C2×C5×#126—22no—
10C2×C5×#124—21no—
11C2×C5×C22⋊Q8C412yes—
12C2×C4×C5×Q8—21no—
13C2×C4×C5×Q8C2211yescharacteristic
14C2×C4×C5×D4C2211yescharacteristic
15C2×C5×#117C412yes—
16C2×#3965—21no—
17#65214C2212yes—
18#65213C2212yes—
19#64767—24no—
20Q8⋊#168—24no—
21#64750—21no—
22#64745—22no—
23#8389—51nomaximal, Sylow
24C22×C5×Q8—21no—
25C22×C5×Q8C2×C411yescharacteristic
26C22×C5×D4D411yescharacteristic
27C23×C4×C5C2×C412yes—
28C5×C4⋊Q8—22no—
29C5×C4⋊Q8D414yes—
30C5×#126—216no—
31C5×#124—28no—
32C5×C22⋊Q8—24no—
33C5×C22⋊Q8—24no—
34C4×C5×Q8—28no—
35C4×C5×Q8—22no—
36C4×C5×Q8D414yes—
37C4×C5×D4—22no—
38C4×C5×D4—22no—
39C5×#117—24no—
40C5×#117—24no—
41C2×C5×C4⋊C4—22no—
42C2×C5×C4⋊C4—21no—
43C2×C5×C4⋊C4—21no—
44C2×C5×C4⋊C4C2×C411yescharacteristic
45C2×C5×C4⋊C4C2×C412yes—
46C2×C5×C4⋊C4D411yescharacteristic
47C2×C5×C22⋊C4—22no—
48C2×C5×C22⋊C4—22no—
49C2×C5×C22⋊C4D412yes—
50C2×C42×C5—22no—
51C2×C42×C5—21no—
52C2×C42×C5C2311yescharacteristic
53C2×#681—22no—
54#3965—42no—
55C22⋊#168—22no—
56C4⋊#168—22no—
57C4⋊#168—22no—
58C4⋊#168—22no—
59C4×#168—22no—
60C2×#556D511yescharacteristic
61#1800—51no—
62#1546—52no—
63#1487—52no—
64#1460—51no—
65C24×C5C22⋊C412yes—
66C2×C5×Q8—21no—
67C2×C5×Q8—24no—
68C2×C5×Q8—42no—
69C2×C5×Q8—42no—
70C2×C5×Q8—41no—
71C2×C5×Q8—41no—
72C2×C5×Q8C22⋊C412yes—
73C2×C5×D4—22no—
74C2×C5×D4—22no—
75C2×C5×D4—21no—
76C2×C5×D4—21no—
77C22×C4×C5—21no—
78C22×C4×C5—21no—
79C22×C4×C5—22no—
80C22×C4×C5—22no—
81C22×C4×C5—22no—
82C22×C4×C5—44no—
83C22×C4×C5C22⋊C412yes—
84C22×C4×C5C22×C411yescharacteristic
85C22×C4×C5C2×D411yescharacteristic
86C22×C4×C5C2×D411yescharacteristic
87C5×C4⋊C4—28no—
88C5×C4⋊C4—21no—
89C5×C4⋊C4—22no—
90C5×C4⋊C4—24no—
91C5×C4⋊C4—24no—
92C5×C4⋊C4—22no—
93C5×C4⋊C4C22⋊C412yes—
94C5×C4⋊C4C22⋊C414yes—
95C5×C22⋊C4—28no—
96C5×C22⋊C4—28no—
97C5×C22⋊C4—24no—
98C42×C5—28no—
99C42×C5—24no—
100C42×C5C2×D412yes—
101C42×C5C2×D412yes—
102#681—42no—
103#681—42no—
104C2×#168—42no—
105C2×#168—42no—
106#556—24no—
107#556—24no—
108C2×C4⋊Q8C2×D511yescharacteristic
109C2×#126—22no—
110C2×#124—21no—
111C2×C22⋊Q8Dic512yes—
112C2×C4×Q8—21no—
113C2×C4×Q8C2×D511yescharacteristic
114C2×C4×D4C2×D511yescharacteristic
115C2×#117Dic512yes—
116#431—52no—
117#423—52no—
118C2×#100—101no—
119#343—101no—
120#332—104no—
121Q8⋊C8—104no—
122#323—102no—
123C23×C5—22no—
124C23×C5—22no—
125C23×C5—22no—
126C23×C5—42no—
127C23×C5—42no—
128C23×C5C2×C22⋊C411yescharacteristic
129C5×Q8—24no—
130C5×Q8—42no—
131C5×Q8—44no—
132C5×Q8—44no—
133C5×D4—42no—
134C5×D4—42no—
135C2×C4×C5—22no—
136C2×C4×C5—22no—
137C2×C4×C5—22no—
138C2×C4×C5—22no—
139C2×C4×C5—24no—
140C2×C4×C5—41no—
141C2×C4×C5—44no—
142C2×C4×C5—42no—
143C2×C4×C5—42no—
144C2×C4×C5—42no—
145C2×C4×C5—42no—
146C2×C4×C5—44no—
147C2×C4×C5—42no—
148C2×C4×C5C2×C22⋊C411yescharacteristic
149C2×C4×C5C2×C22⋊C411yescharacteristic
150C2×C4×C5#12012yes—
151C2×C4×C5#12012yes—
152C2×C4×C5#13512yes—
153C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C5#13711yescharacteristic
155#168—82no—
156#168—82no—
157C22×Q8—21no—
158C22×Q8C2×Dic511yescharacteristic
159C22×D4C22⋊D511yescharacteristic
160C23×C4C2×Dic512yes—
161C2×M16—102no—
162C4⋊Q8—22no—
163C4⋊Q8C22⋊D514yes—
164#126—216no—
165#124—28no—
166C22⋊Q8—24no—
167C22⋊Q8—24no—
168C4×Q8—28no—
169C4×Q8—22no—
170C4×Q8C22⋊D514yes—
171C4×D4—22no—
172C4×D4—22no—
173#117—24no—
174#117—24no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4C2×Dic511yescharacteristic
179C2×C4⋊C4C2×Dic512yes—
180C2×C4⋊C4C22⋊D511yescharacteristic
181C2×C22⋊C4—22no—
182C2×C22⋊C4—22no—
183C2×C22⋊C4C22⋊D512yes—
184C2×C42—22no—
185C2×C42—21no—
186C2×C42C22×D511yescharacteristic
187C4⋊C8—102no—
188C4⋊C8—102no—
189C4⋊C8—102no—
190#100—202no—
191C22⋊C8—102no—
192C4×C8—102no—
193C22×C5—21no—
194C22×C5—21no—
195C22×C5—42no—
196C22×C5—42no—
197C22×C5—42no—
198C22×C5—82no—
199C22×C5—82no—
200C22×C5#37911yescharacteristic
201C22×C5#41611yescharacteristic
202C22×C5#41711yescharacteristic
203C4×C5—22no—
204C4×C5—21no—
205C4×C5—42no—
206C4×C5—42no—
207C4×C5—42no—
208C4×C5—44no—
209C4×C5#41312yes—
210C4×C5#44912yes—
211C4×C5#45212yes—
212C24C22⋊Dic512yes—
213C2×Q8—21no—
214C2×Q8—24no—
215C2×Q8—42no—
216C2×Q8—42no—
217C2×Q8—41no—
218C2×Q8—41no—
219C2×Q8C22⋊Dic512yes—
220C2×D4—22no—
221C2×D4—21no—
222C2×D4—22no—
223C2×D4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—44no—
230C22×C4C22⋊Dic512yes—
231C22×C4C22×Dic511yescharacteristic
232C22×C4C2×C22⋊D511yescharacteristic
233C22×C4C2×C22⋊D511yescharacteristic
234M16—202no—
235M16—202no—
236C2×C8—202no—
237C2×C8—202no—
238C4⋊C4—28no—
239C4⋊C4—21no—
240C4⋊C4—22no—
241C4⋊C4—24no—
242C4⋊C4—24no—
243C4⋊C4—22no—
244C4⋊C4C22⋊Dic512yes—
245C4⋊C4C22⋊Dic514yes—
246C22⋊C4—28no—
247C22⋊C4—28no—
248C22⋊C4—24no—
249C42—28no—
250C42—24no—
251C42C2×C22⋊D512yes—
252C42C2×C22⋊D512yes—
253C2×C5—21no—
254C2×C5—21no—
255C2×C5—82no—
256C2×C5#178511yescharacteristic
257C2×C5#178811yescharacteristic
258C2×C5#179611yescharacteristic
259C23—22no—
260C23—22no—
261C23—22no—
262C23—42no—
263C23—42no—
264C23C2×C22⋊Dic511yescharacteristic
265Q8—24no—
266Q8—42no—
267Q8—44no—
268Q8—44no—
269D4—42no—
270D4—42no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—24no—
276C2×C4—41no—
277C2×C4—44no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—44no—
283C2×C4—42no—
284C2×C4#409511yescharacteristic
285C2×C4#409612yes—
286C2×C4#409711yescharacteristic
287C2×C4C2×C22⋊Dic511yescharacteristic
288C2×C4C2×C22⋊Dic511yescharacteristic
289C2×C4#409912yes—
290C2×C4#409912yes—
291C8—402no—
292C8—402no—
293C5#838911yescharacteristic, complemented, Sylow
294C22—21no—
295C22—21no—
296C22—42no—
297C22—42no—
298C22—42no—
299C22—82no—
300C22—82no—
301C22#6552111yescharacteristic
302C22#6552211yescharacteristic
303C22#6553611yescharacteristic
304C4—21no—
305C4—22no—
306C4—44no—
307C4—42no—
308C4—42no—
309C4—42no—
310C4#6552612yes—
311C4#6552712yes—
312C4#6552812yes—
313C2—21no—
314C2—21no—
315C2—82no—
316C2#1060292811yescharacteristic
317C2#1060293011yescharacteristic
318C2#1060293711yescharacteristic
subgroupG/H
centerC22#65536
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC2×C5×#556C2
socleC22×C5#379
prime radicalC22×C5×D4D4
cosocleC2×C42×C5C23
hypercenterC2×#556D5
hypocenterC5#8389
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
2. #10602566C2semidirect
3. #10602415C2semidirect
293. C5#8389semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#5562
#106025662
#106024152
#106024102
#106023942
#83895