Finite Group Databasebeta

← #11995070

Subgroups — #11995070

Order 1280.

902 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 902 conjugacy classes of subgroups — too many to draw. Only its 139 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×#381C211yesmaximal, characteristic
2#10615762C211yesmaximal, characteristic
3#10602919C211yesmaximal, characteristic
4C2×#64672C212yesmaximal, complemented
5#10598103C212yesmaximal, complemented
6C24×C4×C5C2211yescharacteristic
7C22×C5×C22⋊C4—21no—
8C2×#4070C412yescomplemented
9C2×#4070C2211yescharacteristic
10C5×#381—24no—
11C2×C5×#95—21no—
12C2×C5×#95C2212yes—
13#65536—21no—
14#65501C412yescomplemented
15#65501C2211yescharacteristic
16#65499—22no—
17#65499—21no—
18C2×C22⋊#168—22no—
19C2×C22⋊#168C2212yes—
20#64672—24no—
21#9154—51nomaximal, Sylow
22C25×C5D411yescharacteristic
23C23×C4×C5—22no—
24C23×C4×C5—22no—
25C23×C4×C5—22no—
26C23×C4×C5—44no—
27C23×C4×C5C2×C412yes—
28C23×C4×C5D412yes—
29C23×C4×C5D411yescharacteristic
30C23×C4×C5C2311yescharacteristic
31C22×Dic10C2×C411yescharacteristic
32C2×C5×C22⋊C4—24no—
33C2×C5×C22⋊C4—44no—
34C2×C22⋊Dic5—22no—
35C2×C22⋊Dic5—22no—
36C2×C22⋊Dic5—21no—
37C2×C22⋊Dic5—21no—
38C2×C4⋊Dic5C2×C411yescharacteristic
39C2×C4⋊Dic5C2×C412yes—
40#4070—22no—
41#4070—22no—
42#4070—44no—
43C2×#683—22no—
44C2×#683—21no—
45C22×#168—22no—
46C5×#95—24no—
47C5×#95—22no—
48C5×#95D414yes—
49#3963—22no—
50#3963—21no—
51C22⋊#168—22no—
52C22⋊#168—22no—
53C22⋊#168—44no—
54#2848—51no—
55C2×#381D511yescharacteristic
56#1779—51no—
57C2×#328—52no—
58#1294—52no—
59C24×C5—24no—
60C24×C5—21no—
61C24×C5—21no—
62C24×C5—22no—
63C24×C5—22no—
64C24×C5—42no—
65C24×C5C22⋊C412yes—
66C24×C5C2×D411yescharacteristic
67C22×C4×C5—24no—
68C22×C4×C5—24no—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—24no—
72C22×C4×C5—24no—
73C22×C4×C5—24no—
74C22×C4×C5—42no—
75C22×C4×C5—42no—
76C22×C4×C5—42no—
77C22×C4×C5—42no—
78C22×C4×C5—48no—
79C22×C4×C5—48no—
80C22×C4×C5—44no—
81C22×C4×C5—44no—
82C22×C4×C5—42no—
83C22×C4×C5—42no—
84C22×C4×C5C22⋊C412yes—
85C22×C4×C5C22×C411yescharacteristic
86C22×C4×C5C2×D411yescharacteristic
87C22×C4×C5C2×D412yes—
88C22×C4×C5#4112yes—
89C22×Dic5—21no—
90C22×Dic5—21no—
91C22×Dic5—22no—
92C2×Dic10—22no—
93C2×Dic10—42no—
94C5×C22⋊C4—48no—
95C22⋊Dic5—44no—
96C22⋊Dic5—44no—
97C22⋊Dic5—41no—
98C22⋊Dic5—41no—
99C22⋊Dic5—42no—
100C4⋊Dic5—22no—
101C4⋊Dic5—42no—
102#683—44no—
103#683—42no—
104C2×#168—44no—
105C2×#168—42no—
106C24×C4C2×D511yescharacteristic
107C2×C22⋊Q8—51no—
108C2×C22⋊Q8—52no—
109C22×C22⋊C4—21no—
110C2×C22⋊C8—52no—
111C2×C22⋊C8—102no—
112#385—102no—
113#385—101no—
114#381—24no—
115#380—52no—
116#380—51no—
117#379—101no—
118C2×#95—21no—
119C2×#95C2×D512yes—
120#328—104no—
121C23×C5—22no—
122C23×C5—22no—
123C23×C5—24no—
124C23×C5—24no—
125C23×C5—22no—
126C23×C5—22no—
127C23×C5—22no—
128C23×C5—22no—
129C23×C5—22no—
130C23×C5—22no—
131C23×C5—48no—
132C23×C5—48no—
133C23×C5—42no—
134C23×C5—42no—
135C23×C5—42no—
136C23×C5—42no—
137C23×C5#9914yes—
138C23×C5C2×C22⋊C411yescharacteristic
139C23×C5#12011yescharacteristic
140C23×C5#12311yescharacteristic
141C23×C5#13512yes—
142C23×C5#13712yes—
143C2×C4×C5—22no—
144C2×C4×C5—22no—
145C2×C4×C5—22no—
146C2×C4×C5—22no—
147C2×C4×C5—22no—
148C2×C4×C5—42no—
149C2×C4×C5—42no—
150C2×C4×C5—48no—
151C2×C4×C5—48no—
152C2×C4×C5—42no—
153C2×C4×C5—42no—
154C2×C4×C5—44no—
155C2×C4×C5—44no—
156C2×C4×C5—44no—
157C2×C4×C5—84no—
158C2×C4×C5—84no—
159C2×C4×C5C4×D412yes—
160C2×C4×C5#12112yes—
161C2×Dic5—41no—
162C2×Dic5—41no—
163C2×Dic5—42no—
164C2×Dic5—42no—
165C2×Dic5—42no—
166C2×Dic5—42no—
167C2×Dic5—42no—
168Dic10—82no—
169#168—82no—
170C25C22⋊D511yescharacteristic
171C22×Q8—51no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—44no—
176C23×C4C4×D512yes—
177C23×C4D2012yes—
178C23×C4C22⋊D511yescharacteristic
179C23×C4C22×D511yescharacteristic
180C22×C8—102no—
181C22⋊Q8—102no—
182C22⋊Q8—102no—
183C22⋊Q8—204no—
184C2×C4⋊C4—51no—
185C2×C4⋊C4—52no—
186C2×C4⋊C4—102no—
187C2×C4⋊C4—101no—
188C2×C22⋊C4—24no—
189C2×C22⋊C4—44no—
190C2×C22⋊C4—102no—
191C2×C22⋊C4—102no—
192C2×C22⋊C4—101no—
193C2×C22⋊C4—101no—
194C22⋊C8—102no—
195C22⋊C8—102no—
196C22⋊C8—204no—
197#95—24no—
198#95—22no—
199#95—102no—
200#95—101no—
201#95C22⋊D514yes—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5—21no—
205C22×C5—21no—
206C22×C5—24no—
207C22×C5—24no—
208C22×C5—24no—
209C22×C5—24no—
210C22×C5—24no—
211C22×C5—48no—
212C22×C5—48no—
213C22×C5—42no—
214C22×C5—42no—
215C22×C5—42no—
216C22×C5—42no—
217C22×C5#38611yescharacteristic
218C22×C5C2×#9912yes—
219C22×C5#41611yescharacteristic
220C22×C5#41911yescharacteristic
221C22×C5#42112yes—
222C22×C5#45212yes—
223C22×C5#48512yes—
224C4×C5—22no—
225C4×C5—22no—
226C4×C5—42no—
227C4×C5—84no—
228Dic5—81no—
229Dic5—81no—
230Dic5—82no—
231C24—21no—
232C24—24no—
233C24—21no—
234C24—22no—
235C24—22no—
236C24—42no—
237C24#68512yes—
238C24C2×C22⋊D511yescharacteristic
239C2×Q8—102no—
240C2×Q8—202no—
241C22×C4—21no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—21no—
245C22×C4—24no—
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—48no—
253C22×C4—48no—
254C22×C4—44no—
255C22×C4—44no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—102no—
259C22×C4—101no—
260C22×C4—101no—
261C22×C4#68512yes—
262C22×C4C2×C4×D511yescharacteristic
263C22×C4C2×D2011yescharacteristic
264C22×C4#70912yes—
265C22×C4C2×C22⋊D512yes—
266C2×C8—204no—
267C2×C8—202no—
268C4⋊C4—102no—
269C4⋊C4—202no—
270C4⋊C4—204no—
271C4⋊C4—202no—
272C22⋊C4—48no—
273C22⋊C4—204no—
274C22⋊C4—202no—
275C22⋊C4—201no—
276C22⋊C4—204no—
277C22⋊C4—201no—
278C2×C5—22no—
279C2×C5—22no—
280C2×C5—44no—
281C2×C5#151112yes—
282C2×C5#151612yes—
283C2×C5#187311yescharacteristic
284C2×C5#189711yescharacteristic
285C2×C5#189811yescharacteristic
286C23—22no—
287C23—22no—
288C23—24no—
289C23—24no—
290C23—22no—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—48no—
297C23—48no—
298C23—42no—
299C23—42no—
300C23—42no—
301C23—42no—
302C23#393814yes—
303C23C2×#68511yescharacteristic
304C23#407511yescharacteristic
305C23#409612yes—
306C23#409712yes—
307C23#409911yescharacteristic
308Q8—402no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—48no—
317C2×C4—48no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—84no—
324C2×C4—84no—
325C2×C4—202no—
326C2×C4—202no—
327C2×C4—202no—
328C2×C4—202no—
329C2×C4—202no—
330C2×C4—201no—
331C2×C4—201no—
332C2×C4C4×C22⋊D512yes—
333C2×C4#407612yes—
334C8—402no—
335C5#915411yescharacteristic, complemented, Sylow
336C22—21no—
337C22—21no—
338C22—24no—
339C22—24no—
340C22—21no—
341C22—21no—
342C22—24no—
343C22—24no—
344C22—24no—
345C22—48no—
346C22—48no—
347C22—42no—
348C22—42no—
349C22—42no—
350C22—42no—
351C22C2×#393812yes—
352C22#6528512yes—
353C22#6529111yescharacteristic
354C22#6529311yescharacteristic
355C22#6529412yes—
356C22#6550211yescharacteristic
357C22#6552812yes—
358C4—22no—
359C4—22no—
360C4—42no—
361C4—84no—
362C4—401no—
363C4—402no—
364C4—401no—
365C2—22no—
366C2—22no—
367C2—44no—
368C2#1060032512yes—
369C2#1060032612yes—
370C2#1060233611yescharacteristic
371C2#1060237811yescharacteristic
372C2#1060238411yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#381C2
socleC23×C5C2×C22⋊C4
prime radicalC25×C5D4
cosocleC23×C4×C5C23
hypercenterC2×#381D5
hypocenterC5#9154
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
4. C2×#64672C2semidirect
5. #10598103C2semidirect
8. C2×#4070C4semidirect
14. #65501C4semidirect
335. C5#9154semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3812
#106157622
#106029192
C2×#646722
#105981032
#91545