Finite Group Databasebeta

← #12010338

Subgroups — #12010338

Order 1280.

472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 99 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#10614113C211yesmaximal, characteristic
2C5×#1459C211yesmaximal, characteristic
3#10602412C211yesmaximal, characteristic
4#10597941C214yesmaximal, complemented
5C2×C4×C5×D4C2211yescharacteristic
6C2×#4082—21no—
7C2×#4015C411yescharacteristic, complemented
8C2×C5×C22⋊C8—21no—
9C2×#3966—21no—
10#65501—21no—
11#65501—21no—
12#65501—21no—
13#65263—21no—
14#65242C412yescomplemented
15#65242C2212yes—
16C4×C4⋊Dic5C411yescharacteristic, complemented
17C5×#324—21no—
18C5×#323C2212yes—
19#64746C2212yes—
20#11878—51nomaximal, Sylow
21C22×C5×D4D411yescharacteristic
22C23×C4×C5D411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C22×Dic10—21no—
25C22×C5×C8—41no—
26C4×C5×D4—41no—
27C4×C5×D4—41no—
28C2×C5×C4⋊C4D411yescharacteristic
29C2×C5×C22⋊C4C2×C411yescharacteristic
30C2×C5×C22⋊C4C2311yescharacteristic
31C2×C42×C5C2×C411yescharacteristic
32C2×C22⋊Dic5—22no—
33C2×C22⋊Dic5—22no—
34C2×C22⋊Dic5—22no—
35#4082—42no—
36#4082—42no—
37C2×C4⋊Dic5—21no—
38C2×C4⋊Dic5—21no—
39C2×C4⋊Dic5—41no—
40C2×C4⋊Dic5C2×C412yes—
41C2×C4×Dic5—21no—
42#4015—41no—
43#4015—41no—
44C5×C22⋊C8—22no—
45C5×C22⋊C8—41no—
46#3966—42no—
47#3963—22no—
48#3963—22no—
49#3963—41no—
50#3963C2×C412yes—
51#2547—51no—
52#1799—51no—
53#1459D511yescharacteristic
54#1344—54no—
55C24×C5C22⋊C411yescharacteristic
56C24×C5C2×D411yescharacteristic
57C2×C5×D4—41no—
58C2×C5×D4—41no—
59C2×C5×D4D812yes—
60C2×C5×D4SD1612yes—
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×C5C22⋊C411yescharacteristic
68C22×C4×C5C22⋊C411yescharacteristic
69C22×C4×C5C22⋊C411yescharacteristic
70C22×C4×C5C22×C411yescharacteristic
71C22×C4×C5C2×D411yescharacteristic
72C22×Dic5—22no—
73C22×Dic5—22no—
74C22×Dic5—42no—
75C2×Dic10—42no—
76C2×Dic10—42no—
77C2×Dic10—42no—
78C2×C5×C8—42no—
79C2×C5×C8—82no—
80C5×C4⋊C4—41no—
81C5×C22⋊C4—41no—
82C5×C22⋊C4—41no—
83C42×C5—21no—
84C42×C5—21no—
85C22⋊Dic5—44no—
86C22⋊Dic5—42no—
87C22⋊Dic5—42no—
88C22⋊Dic5—42no—
89C22⋊Dic5—42no—
90C4⋊Dic5—42no—
91C4⋊Dic5—41no—
92C4⋊Dic5—41no—
93C4⋊Dic5—42no—
94C4⋊Dic5—82no—
95C4×Dic5—42no—
96C2×C4⋊Q8—51no—
97C2×#124—101no—
98C2×C4×D4C2×D511yescharacteristic
99C2×#99—101no—
100C2×C22⋊C8—21no—
101#397—52no—
102#397—52no—
103#391—101no—
104#380—101no—
105#380—101no—
106#380—101no—
107C4×C4⋊C4—51no—
108#342—52no—
109#324—21no—
110#323C2×D512yes—
111C23×C5—21no—
112C23×C5—21no—
113C23×C5—21no—
114C23×C5—21no—
115C23×C5—41no—
116C23×C5—41no—
117C23×C5—41no—
118C23×C5—41no—
119C23×C5#10212yes—
120C23×C5C2×C22⋊C411yescharacteristic
121C23×C5C2×D811yescharacteristic
122C23×C5C2×SD1611yescharacteristic
123C5×D4—42no—
124C5×D4—42no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—22no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—42no—
132C2×C4×C5—42no—
133C2×C4×C5—41no—
134C2×C4×C5—41no—
135C2×C4×C5—41no—
136C2×C4×C5—81no—
137C2×C4×C5—81no—
138C2×C4×C5#9911yescharacteristic
139C2×C4×C5#9911yescharacteristic
140C2×C4×C5#10212yes—
141C2×Dic5—42no—
142C2×Dic5—42no—
143C2×Dic5—42no—
144C2×Dic5—42no—
145C2×Dic5—42no—
146C2×Dic5—42no—
147C2×Dic5—82no—
148C2×Dic5—82no—
149C2×Dic5—82no—
150Dic10—84no—
151C5×C8—82no—
152C22×Q8—101no—
153C22×D4D2011yescharacteristic
154C23×C4D2011yescharacteristic
155C23×C4C22⋊D511yescharacteristic
156C22×C8—41no—
157C4⋊Q8—201no—
158C4⋊Q8—201no—
159#124—202no—
160#124—202no—
161C4×D4—41no—
162C4×D4—41no—
163C2×C4⋊C4—52no—
164C2×C4⋊C4—101no—
165C2×C4⋊C4—101no—
166C2×C4⋊C4—201no—
167C2×C4⋊C4C22⋊D511yescharacteristic
168C2×C22⋊C4—102no—
169C2×C22⋊C4—102no—
170C2×C22⋊C4—102no—
171C2×C22⋊C4C4×D511yescharacteristic
172C2×C22⋊C4C22×D511yescharacteristic
173C2×C42—101no—
174C2×C42C4×D511yescharacteristic
175#99—202no—
176C22⋊C8—22no—
177C22⋊C8—41no—
178#95—52no—
179#95—102no—
180#95—102no—
181#95—201no—
182C22×C5—21no—
183C22×C5—21no—
184C22×C5—21no—
185C22×C5—22no—
186C22×C5—21no—
187C22×C5—42no—
188C22×C5—41no—
189C22×C5—41no—
190C22×C5—41no—
191C22×C5—41no—
192C22×C5—41no—
193C22×C5—41no—
194C22×C5—81no—
195C22×C5—81no—
196C22×C5C2×#9911yescharacteristic
197C22×C5C2×#10211yescharacteristic
198C22×C5#42111yescharacteristic
199C4×C5—21no—
200C4×C5—22no—
201C4×C5—41no—
202C4×C5—41no—
203C4×C5—41no—
204C4×C5#35412yes—
205Dic5—82no—
206Dic5—82no—
207Dic5—162no—
208C24#68511yescharacteristic
209C24C2×D2011yescharacteristic
210C2×Q8—202no—
211C2×Q8—202no—
212C2×Q8—202no—
213C2×D4—41no—
214C2×D4—41no—
215C2×D4#67712yes—
216C2×D4D4012yes—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—102no—
224C22×C4—102no—
225C22×C4—202no—
226C22×C4#68511yescharacteristic
227C22×C4#68511yescharacteristic
228C22×C4#68511yescharacteristic
229C22×C4C2×C4×D511yescharacteristic
230C22×C4C2×C22⋊D511yescharacteristic
231C2×C8—42no—
232C2×C8—82no—
233C4⋊C4—41no—
234C4⋊C4—202no—
235C4⋊C4—202no—
236C4⋊C4—201no—
237C4⋊C4—201no—
238C4⋊C4—402no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—204no—
242C22⋊C4—202no—
243C22⋊C4—202no—
244C22⋊C4—202no—
245C22⋊C4—202no—
246C42—21no—
247C42—21no—
248C42—202no—
249C2×C5—21no—
250C2×C5—21no—
251C2×C5—41no—
252C2×C5—42no—
253C2×C5—41no—
254C2×C5#151911yescharacteristic
255C2×C5#212311yescharacteristic
256C2×C5C2×#35411yescharacteristic
257C23—21no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23—41no—
265C23#395312yes—
266C23C2×#67711yescharacteristic
267C23C2×D4011yescharacteristic
268C23C2×#68511yescharacteristic
269Q8—404no—
270D4—42no—
271D4—42no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—202no—
286C2×C4—202no—
287C2×C4—202no—
288C2×C4—202no—
289C2×C4—202no—
290C2×C4—202no—
291C2×C4—402no—
292C2×C4—402no—
293C2×C4—402no—
294C2×C4#393811yescharacteristic
295C2×C4#393811yescharacteristic
296C2×C4#395312yes—
297C8—82no—
298C5#1187811yescharacteristic, complemented, Sylow
299C22—21no—
300C22—21no—
301C22—21no—
302C22—22no—
303C22—21no—
304C22—42no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22—81no—
312C22—81no—
313C22C2×#393811yescharacteristic
314C22C2×#395311yescharacteristic
315C22#6542811yescharacteristic
316C4—22no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—402no—
322C4—402no—
323C4—802no—
324C4#6469312yes—
325C2—21no—
326C2—21no—
327C2—41no—
328C2—42no—
329C2—41no—
330C2#1060073711yescharacteristic
331C2C2×#6469311yescharacteristic
332C2#1060094011yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C22⋊C4C22×D5
FittingC5×#1459C2
socleC22×C5C2×#99
prime radicalC22×C5×D4D4
cosocleC2×C5×C22⋊C4C23
hypercenter#1459D5
hypocenterC5#11878
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
4. #10597941C2semidirect
7. C2×#4015C4semidirect
14. #65242C4semidirect
16. C4×C4⋊Dic5C4semidirect
298. C5#11878semidirect

Maximal subgroups

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

subgroupindex
#106141132
C5×#14592
#106024122
#105979412
#118785