Finite Group Databasebeta

← #11997074

Subgroups — #11997074

Order 1280.

598 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 135 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×#2972C211yesmaximal, characteristic
2#10614104C211yesmaximal, characteristic
3#10602412C211yesmaximal, characteristic
4#10600717C212yesmaximal, complemented
5#10598167C212yesmaximal, complemented
6C2×C4×C5×D4C2211yescharacteristic
7C2×#4081—21no—
8C22×C4⋊Dic5C2211yescharacteristic
9C5×C8×D4—24no—
10C5×#431—21no—
11C2×C5×C22⋊C8—21no—
12C2×C5×C22⋊C8C2212yes—
13C2×#3966—21no—
14#65501—21no—
15#65501C2212yes—
16#65501C2211yescharacteristic
17#65272C412yescomplemented
18#65242C412yescomplemented
19#65232—21no—
20#65217—21no—
21#64771—24no—
22#64746—21no—
23#9470—51nomaximal, Sylow
24C22×C5×D4D411yescharacteristic
25C23×C4×C5D411yescharacteristic
26C23×C4×C5C2311yescharacteristic
27C23×Dic5—21no—
28C22×C5×C8—22no—
29C22×C5×C8D414yes—
30C4×C5×D4—22no—
31C4×C5×D4—22no—
32C2×C5×C4⋊C4C2×C411yescharacteristic
33C2×C5×C22⋊C4C2×C411yescharacteristic
34C2×C5×C22⋊C4D411yescharacteristic
35C2×C42×C5D411yescharacteristic
36C2×C22⋊Dic5—22no—
37C2×C22⋊Dic5—21no—
38C2×C22⋊Dic5—22no—
39#4081—42no—
40#4081—42no—
41C2×C4⋊Dic5—22no—
42C2×C4⋊Dic5—22no—
43C2×C4⋊Dic5—21no—
44C2×C4⋊Dic5—21no—
45C2×C4⋊Dic5—22no—
46C2×C4⋊Dic5C2×C412yes—
47C2×#683—22no—
48C5×C4⋊C8—22no—
49C5×C22⋊C8—22no—
50C5×C22⋊C8—22no—
51C5×C22⋊C8—22no—
52C4×C5×C8—22no—
53#3966—42no—
54#3963—22no—
55#3963—22no—
56#3963—22no—
57#3963C2×C412yes—
58#2972D511yescharacteristic
59#2486—51no—
60#1823—52no—
61#1799—51no—
62#1289—52no—
63C24×C5C22⋊C411yescharacteristic
64C24×C5C2×D411yescharacteristic
65C2×C5×D4—22no—
66C2×C5×D4—22no—
67C2×C5×D4D812yes—
68C2×C5×D4SD1612yes—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—42no—
72C22×C4×C5—42no—
73C22×C4×C5C22⋊C411yescharacteristic
74C22×C4×C5C22⋊C411yescharacteristic
75C22×C4×C5C22⋊C411yescharacteristic
76C22×C4×C5C22×C411yescharacteristic
77C22×C4×C5C2×D412yes—
78C22×C4×C5C2×D411yescharacteristic
79C22×C4×C5#4112yes—
80C22×Dic5—22no—
81C22×Dic5—22no—
82C22×Dic5—42no—
83C22×Dic5—41no—
84C22×Dic5—41no—
85C22×Dic5—42no—
86C22×Dic5—42no—
87C2×C5×C8—24no—
88C2×C5×C8—44no—
89C2×C5×C8—82no—
90C5×C4⋊C4—22no—
91C5×C22⋊C4—22no—
92C5×C22⋊C4—22no—
93C42×C5—21no—
94C42×C5—21no—
95C22⋊Dic5—44no—
96C22⋊Dic5—41no—
97C22⋊Dic5—41no—
98C22⋊Dic5—42no—
99C22⋊Dic5—42no—
100C4⋊Dic5—24no—
101C4⋊Dic5—42no—
102C4⋊Dic5—41no—
103C4⋊Dic5—41no—
104C4⋊Dic5—44no—
105#683—44no—
106C2×#123—101no—
107C2×C4×D4C2×D511yescharacteristic
108C22×C4⋊C4—51no—
109C8×D4—24no—
110#431—21no—
111C2×#99—101no—
112C2×C22⋊C8—21no—
113C2×C22⋊C8C2×D512yes—
114#398—52no—
115#397—52no—
116#389—101no—
117#381—101no—
118#380—51no—
119#380—52no—
120#380—101no—
121#342—101no—
122#340—104no—
123C23×C5—21no—
124C23×C5—21no—
125C23×C5—41no—
126C23×C5—41no—
127C23×C5—41no—
128C23×C5—41no—
129C23×C5#10212yes—
130C23×C5C2×C22⋊C411yescharacteristic
131C23×C5#12112yes—
132C23×C5C2×D811yescharacteristic
133C23×C5C2×SD1611yescharacteristic
134C23×C5#13512yes—
135C5×D4—24no—
136C5×D4—24no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—24no—
140C2×C4×C5—22no—
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—41no—
144C2×C4×C5—42no—
145C2×C4×C5—42no—
146C2×C4×C5—41no—
147C2×C4×C5—41no—
148C2×C4×C5—81no—
149C2×C4×C5#10212yes—
150C2×C4×C5C4×D412yes—
151C2×C4×C5#12011yescharacteristic
152C2×C4×C5#12311yescharacteristic
153C2×Dic5—42no—
154C2×Dic5—42no—
155C2×Dic5—42no—
156C2×Dic5—42no—
157C2×Dic5—42no—
158C2×Dic5—42no—
159C2×Dic5—82no—
160C2×Dic5—82no—
161C2×Dic5—82no—
162C2×Dic5—82no—
163C2×Dic5—82no—
164C5×C8—44no—
165C22×D4D2011yescharacteristic
166C23×C4—101no—
167C23×C4C22⋊D511yescharacteristic
168C23×C4C22×D511yescharacteristic
169C22×C8—22no—
170C22×C8C22⋊D514yes—
171#123—202no—
172#123—202no—
173C4×D4—22no—
174C4×D4—22no—
175C2×C4⋊C4—52no—
176C2×C4⋊C4—102no—
177C2×C4⋊C4—102no—
178C2×C4⋊C4—102no—
179C2×C4⋊C4—101no—
180C2×C4⋊C4—101no—
181C2×C4⋊C4—102no—
182C2×C4⋊C4C4×D511yescharacteristic
183C2×C22⋊C4—102no—
184C2×C22⋊C4—101no—
185C2×C22⋊C4—102no—
186C2×C22⋊C4C4×D511yescharacteristic
187C2×C22⋊C4D2011yescharacteristic
188C2×C42C22⋊D511yescharacteristic
189C4⋊C8—22no—
190#99—202no—
191C22⋊C8—22no—
192C22⋊C8—22no—
193C22⋊C8—22no—
194C4×C8—22no—
195#95—52no—
196#95—102no—
197#95—102no—
198#95—102no—
199C22×C5—21no—
200C22×C5—22no—
201C22×C5—21no—
202C22×C5—22no—
203C22×C5—22no—
204C22×C5—41no—
205C22×C5—41no—
206C22×C5—42no—
207C22×C5—42no—
208C22×C5—41no—
209C22×C5—41no—
210C22×C5—81no—
211C22×C5#38611yescharacteristic
212C22×C5C2×#10211yescharacteristic
213C22×C5#41611yescharacteristic
214C22×C5#46512yes—
215C22×C5#46612yes—
216C4×C5—21no—
217C4×C5—22no—
218C4×C5—22no—
219C4×C5—41no—
220C4×C5—41no—
221C4×C5#45812yes—
222Dic5—82no—
223Dic5—82no—
224Dic5—162no—
225C24#68511yescharacteristic
226C24C2×D2011yescharacteristic
227C2×D4—22no—
228C2×D4—22no—
229C2×D4#67712yes—
230C2×D4D4012yes—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—102no—
236C22×C4—102no—
237C22×C4—201no—
238C22×C4—201no—
239C22×C4—202no—
240C22×C4—202no—
241C22×C4—202no—
242C22×C4#68511yescharacteristic
243C22×C4#68511yescharacteristic
244C22×C4#68511yescharacteristic
245C22×C4C2×C4×D511yescharacteristic
246C22×C4#70912yes—
247C22×C4C2×C22⋊D512yes—
248C22×C4C2×C22⋊D511yescharacteristic
249C2×C8—24no—
250C2×C8—44no—
251C2×C8—82no—
252C4⋊C4—22no—
253C4⋊C4—104no—
254C4⋊C4—202no—
255C4⋊C4—204no—
256C4⋊C4—201no—
257C4⋊C4—204no—
258C4⋊C4—201no—
259C22⋊C4—22no—
260C22⋊C4—22no—
261C22⋊C4—204no—
262C22⋊C4—201no—
263C22⋊C4—201no—
264C22⋊C4—202no—
265C22⋊C4—202no—
266C42—21no—
267C42—21no—
268C2×C5—21no—
269C2×C5—22no—
270C2×C5—21no—
271C2×C5—22no—
272C2×C5—42no—
273C2×C5#189011yescharacteristic
274C2×C5#189311yescharacteristic
275C2×C5#190911yescharacteristic
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23#395312yes—
283C23C2×#67711yescharacteristic
284C23C2×D4011yescharacteristic
285C23#405012yes—
286C23C2×#68511yescharacteristic
287C23#407612yes—
288D4—24no—
289D4—24no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—24no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—81no—
302C2×C4—202no—
303C2×C4—202no—
304C2×C4—202no—
305C2×C4—202no—
306C2×C4—202no—
307C2×C4—202no—
308C2×C4—402no—
309C2×C4—402no—
310C2×C4—402no—
311C2×C4—402no—
312C2×C4—402no—
313C2×C4#395312yes—
314C2×C4C4×C22⋊D512yes—
315C2×C4#407511yescharacteristic
316C2×C4#409911yescharacteristic
317C8—44no—
318C5#947011yescharacteristic, complemented, Sylow
319C22—21no—
320C22—22no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—42no—
327C22—42no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22C2×#395311yescharacteristic
332C22#6540211yescharacteristic
333C22#6540312yes—
334C22#6540412yes—
335C22#6550211yescharacteristic
336C4—22no—
337C4—21no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—402no—
342C4—402no—
343C4—802no—
344C4#6553212yes—
345C2—21no—
346C2—22no—
347C2—21no—
348C2—22no—
349C2—42no—
350C2#1060244811yescharacteristic
351C2#1060276611yescharacteristic
352C2#1060281711yescharacteristic
subgroupG/H
centerC22#65502
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×#2972C2
socleC22×C5#386
prime radicalC22×C5×D4D4
cosocleC23×C4×C5C23
hypercenter#2972D5
hypocenterC5#9470
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2972

Complements

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

NH ≅ G/Ntype
4. #10600717C2semidirect
5. #10598167C2semidirect
17. #65272C4semidirect
18. #65242C4semidirect
318. C5#9470semidirect

Maximal subgroups

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

subgroupindex
C5×#29722
#106141042
#106024122
#106007172
#105981672
#94705