Finite Group Databasebeta

← #12074205

Subgroups — #12074205

Order 1280.

870 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 870 conjugacy classes of subgroups — too many to draw. Only its 191 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#10617704C211yesmaximal, characteristic
2C5×#2568C211yesmaximal, characteristic
3#10614955C212yesmaximal
4#10602417C211yesmaximal, characteristic
5#10600512C218yesmaximal
6#10600264C212yesmaximal
7C2×C5×C4⋊Q8C2211yescharacteristic
8C2×C4×C5×Q8C2211yescharacteristic
9#66146—21no—
10#65904—22no—
11#65903—24no—
12Q8×Dic10—22no—
13#65834—21no—
14#65834C2214yes—
15#65804—22no—
16#65804C2212yes—
17C5×#400C2214yes—
18C5×#391—21no—
19C5×#391—22no—
20C5×#382—21no—
21C4×C5×C4⋊C4C2211yescharacteristic
22#65382—22no—
23#65380—24no—
24#65367—22no—
25#65259C2218yes—
26#65214C2212yes—
27#64748C2214yes—
28#64672C2218yes—
29#18411—51nomaximal, Sylow
30C22×C5×Q8—21no—
31C22×C5×Q8D411yescharacteristic
32C5×C4⋊Q8—22no—
33C5×C4⋊Q8—22no—
34C4×C5×Q8—22no—
35C4×C5×Q8—22no—
36C2×C5×C4⋊C4—21no—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4D411yescharacteristic
39C2×C5×C4⋊C4C2312yes—
40C2×C5×C4⋊C4C2312yes—
41C2×C42×C5—21no—
42C2×C42×C5D412yes—
43C2×C42×C5C2311yescharacteristic
44Q8×Dic5—24no—
45Q8×Dic5—24no—
46#4072—24no—
47#4072—22no—
48#4070—22no—
49#4070—24no—
50#4070C2314yes—
51#4036—24no—
52#4036—28no—
53#4034—24no—
54#4034—28no—
55#4016—24no—
56#4016—22no—
57#4015—22no—
58#4015—22no—
59#4015D412yes—
60#4015D412yes—
61C4×Dic10—24no—
62C4×Dic10—24no—
63C4×Dic10—22no—
64C4×Dic10D414yes—
65C5×#95—24no—
66C5×#95—24no—
67C5×#95C2312yes—
68C22⋊#168C2314yes—
69#3942—28no—
70#3939—28no—
71C4⋊#168—22no—
72C4×#168—22no—
73#3502—51no—
74#3230—52no—
75#2568D511yescharacteristic
76#1617—58no—
77#1503—52no—
78#1461—51no—
79C2×C5×Q8—22no—
80C2×C5×Q8—22no—
81C2×C5×Q8—44no—
82C2×C5×Q8—41no—
83C2×C5×Q8—41no—
84C2×C5×Q8Q1614yes—
85C22×C4×C5—22no—
86C22×C4×C5—22no—
87C22×C4×C5C2×D411yescharacteristic
88C22×C4×C5C2×D412yes—
89C22×C4×C5C2×D412yes—
90C22×C4×C5C2×D411yescharacteristic
91C22×C4×C5C2411yescharacteristic
92C2×Dic10—22no—
93C2×Dic10—24no—
94C2×Dic10C2×D414yes—
95C5×C4⋊C4—22no—
96C5×C4⋊C4—24no—
97C5×C4⋊C4—24no—
98C5×C4⋊C4—42no—
99C5×C4⋊C4—42no—
100C42×C5—22no—
101C42×C5—22no—
102C42×C5—42no—
103C42×C5C2×D412yes—
104C42×C5C2×D412yes—
105C22⋊Dic5—24no—
106C4⋊Dic5—24no—
107C4⋊Dic5—24no—
108C4⋊Dic5—24no—
109C4⋊Dic5—22no—
110C4⋊Dic5—22no—
111C4⋊Dic5—22no—
112C4⋊Dic5C2×D414yes—
113#683—28no—
114#683—24no—
115#683—24no—
116C4×Dic5—28no—
117C4×Dic5—24no—
118C2×#168—24no—
119Q82—102no—
120#557—104no—
121#557—102no—
122#544—54no—
123#544—101no—
124#533—52no—
125#533—102no—
126C2×C4⋊Q8C2×D511yescharacteristic
127#519—101no—
128C2×C4×Q8C2×D511yescharacteristic
129#500—102no—
130#487—102no—
131#484—58no—
132#477—104no—
133#431—52no—
134#400C2×D514yes—
135#391—21no—
136#391—22no—
137#382—21no—
138C4×C4⋊C4C2×D511yescharacteristic
139#328—58no—
140#324—54no—
141C23×C5C22×D411yescharacteristic
142C5×Q8—28no—
143C5×Q8—82no—
144C5×Q8—82no—
145C2×C4×C5—22no—
146C2×C4×C5—22no—
147C2×C4×C5—22no—
148C2×C4×C5—22no—
149C2×C4×C5—41no—
150C2×C4×C5—42no—
151C2×C4×C5—42no—
152C2×C4×C5—42no—
153C2×C4×C5—44no—
154C2×C4×C5—42no—
155C2×C4×C5—42no—
156C2×C4×C5#12011yescharacteristic
157C2×C4×C5#12012yes—
158C2×C4×C5#12011yescharacteristic
159C2×C4×C5C2×Q1614yes—
160C2×C4×C5C2×Q1612yes—
161C2×C4×C5#13712yes—
162C2×C4×C5C22×D412yes—
163C2×Dic5—24no—
164C2×Dic5—24no—
165Dic10—44no—
166Dic10—44no—
167Dic10—84no—
168#168—44no—
169C22×Q8—21no—
170C22×Q8C22⋊D511yescharacteristic
171C4⋊Q8—22no—
172C4⋊Q8—22no—
173C4⋊Q8—52no—
174C4⋊Q8—52no—
175C4⋊Q8—102no—
176C4⋊Q8—102no—
177C4⋊Q8—108no—
178C4⋊Q8—104no—
179#125—104no—
180#125—108no—
181#125—104no—
182#125—102no—
183C22⋊Q8—54no—
184C22⋊Q8—102no—
185C22⋊Q8—104no—
186C4×Q8—22no—
187C4×Q8—22no—
188C4×Q8—54no—
189C4×Q8—104no—
190C4×Q8—104no—
191C4×Q8—104no—
192C4×Q8—104no—
193C4×Q8—102no—
194#117—102no—
195#117—104no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4C22⋊D511yescharacteristic
199C2×C4⋊C4C22×D512yes—
200C2×C4⋊C4C22×D512yes—
201C2×C42—21no—
202C2×C42C22⋊D512yes—
203C2×C42C22×D511yescharacteristic
204#107—108no—
205C4⋊C8—102no—
206#103—108no—
207C22⋊C8—54no—
208C4×C8—102no—
209#95—24no—
210#95—24no—
211#95C22×D512yes—
212C22×C5—21no—
213C22×C5—21no—
214C22×C5C2×#12011yescharacteristic
215C22×C5C22×Q1611yescharacteristic
216C22×C5C2×#13711yescharacteristic
217C4×C5—24no—
218C4×C5—21no—
219C4×C5—22no—
220C4×C5—42no—
221C4×C5—82no—
222C4×C5—82no—
223C4×C5#45114yes—
224C4×C5#45412yes—
225Dic5—44no—
226Dic5—44no—
227C2×Q8—22no—
228C2×Q8—22no—
229C2×Q8—44no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—54no—
233C2×Q8—104no—
234C2×Q8—102no—
235C2×Q8#68914yes—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4C2×C22⋊D511yescharacteristic
239C22×C4C2×C22⋊D512yes—
240C22×C4C2×C22⋊D512yes—
241C22×C4C2×C22⋊D511yescharacteristic
242C22×C4C23×D511yescharacteristic
243C2×C8—104no—
244C4⋊C4—24no—
245C4⋊C4—22no—
246C4⋊C4—24no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—54no—
250C4⋊C4—104no—
251C4⋊C4—104no—
252C4⋊C4—104no—
253C4⋊C4—108no—
254C4⋊C4—104no—
255C4⋊C4—102no—
256C4⋊C4—102no—
257C4⋊C4—104no—
258C4⋊C4—102no—
259C22⋊C4—104no—
260C42—22no—
261C42—22no—
262C42—42no—
263C42—108no—
264C42—104no—
265C42D4×D512yes—
266C42D4×D512yes—
267C2×C5—21no—
268C2×C5—21no—
269C2×C5C2×#45111yescharacteristic
270C2×C5C2×#45411yescharacteristic
271C2×C5#302811yescharacteristic
272C23C22×C22⋊D511yescharacteristic
273Q8—28no—
274Q8—82no—
275Q8—82no—
276Q8—204no—
277Q8—204no—
278Q8—404no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—44no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—104no—
291C2×C4—104no—
292C2×C4#408311yescharacteristic
293C2×C4#408312yes—
294C2×C4#408311yescharacteristic
295C2×C4C2×#68914yes—
296C2×C4C2×#68912yes—
297C2×C4#409712yes—
298C2×C4C2×D4×D512yes—
299C8—204no—
300C5#1841111yescharacteristic, complemented, Sylow
301C22—21no—
302C22—21no—
303C22C2×#408311yescharacteristic
304C22C22×#68911yescharacteristic
305C22C2×#409711yescharacteristic
306C4—22no—
307C4—21no—
308C4—24no—
309C4—42no—
310C4—82no—
311C4—82no—
312C4—204no—
313C4—204no—
314C4#6533914yes—
315C4#6535112yes—
316C2—21no—
317C2—21no—
318C2C2×#6533911yescharacteristic
319C2C2×#6535111yescharacteristic
320C2#1061514811yescharacteristic
subgroupG/H
centerC22C2×#4083
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC5×#2568C2
socleC22×C5C2×#120
prime radicalC23×C5C22×D4
hypercenter#2568D5
hypocenterC5#18411
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2568

Complements

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

NH ≅ G/Ntype
300. C5#18411semidirect

Maximal subgroups

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

subgroupindex
#106177042
C5×#25682
#106149552
#106024172
#106005122
#106002642
#184115