Finite Group Databasebeta

← #12015308

Subgroups — #12015308

Order 1280.

432 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 103 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#10614187C211yesmaximal, characteristic
2C5×#1801C211yesmaximal, characteristic
3#10602430C211yesmaximal, characteristic
4C2×#64698C212yesmaximal
5#10598190C212yesmaximal
6C2×C4×C5×Q8C2211yescharacteristic
7C2×#4090C2211yescharacteristic
8C2×C4×Dic10C411yescharacteristic
9C5×#423—21no—
10C2×C5×#101C2212yes—
11#65519C2211yescharacteristic
12C2×#3968C2212yes—
13#65267—21no—
14#65267—21no—
15#65266C411yescharacteristic
16#65263C411yescharacteristic
17#65222—21no—
18#65222—21no—
19#65221C411yescharacteristic
20#65213—21no—
21C5×#343—21no—
22#64750—21no—
23#64698—24no—
24#12804—51nomaximal, Sylow
25C22×C5×Q8C2311yescharacteristic
26C22×Dic10C2×C411yescharacteristic
27C2×C5×M16—22no—
28C4×C5×Q8—42no—
29C2×C5×C4⋊C4C2×C411yescharacteristic
30C2×C5×C4⋊C4D411yescharacteristic
31C2×C5×C4⋊C4D411yescharacteristic
32C2×C42×C5C2×C411yescharacteristic
33C2×C42×C5D411yescharacteristic
34C2×C42×C5D411yescharacteristic
35#4090—21no—
36#4090—21no—
37#4090D412yes—
38#4090Q812yes—
39C2×C4⋊Dic5C2×C411yescharacteristic
40C2×#683—21no—
41C2×#683—21no—
42C2×#683—21no—
43C2×C4×Dic5—21no—
44C2×C4×Dic5C2×C411yescharacteristic
45C2×C4×Dic5C2×C411yescharacteristic
46C2×#681—22no—
47C4×Dic10—42no—
48C5×C4⋊C8—42no—
49C5×#101—22no—
50C5×#101—22no—
51#3968—22no—
52#3968—22no—
53#3963—21no—
54#3963—21no—
55#3963—21no—
56#3963—21no—
57#3963—21no—
58#3963—21no—
59#3963—21no—
60#3963—21no—
61C4⋊#168—42no—
62#2327—51no—
63C2×#356—52no—
64#1801—51no—
65#1801D511yescharacteristic
66#1394—52no—
67C2×C5×Q8—41no—
68C2×C5×Q8—41no—
69C2×C5×Q8C2×D411yescharacteristic
70C2×C5×Q8C2×Q811yescharacteristic
71C2×C5×Q8#4111yescharacteristic
72C2×C5×Q8#4111yescharacteristic
73C22×C4×C5C22⋊C411yescharacteristic
74C22×C4×C5C22⋊C411yescharacteristic
75C22×C4×C5C22⋊C411yescharacteristic
76C22×C4×C5C22⋊C411yescharacteristic
77C22×C4×C5C22×C411yescharacteristic
78C22×C4×C5C2×D411yescharacteristic
79C22×C4×C5C2×D411yescharacteristic
80C22×Dic5—21no—
81C22×Dic5—21no—
82C22×Dic5—21no—
83C22×Dic5—21no—
84C2×Dic10—21no—
85C2×Dic10—41no—
86C2×Dic10—41no—
87C2×Dic10C4⋊C412yes—
88C5×M16—42no—
89C5×M16—42no—
90C2×C5×C8—42no—
91C5×C4⋊C4—41no—
92C5×C4⋊C4—41no—
93C5×C4⋊C4—41no—
94C42×C5—22no—
95C42×C5—22no—
96C42×C5—22no—
97C4⋊Dic5—41no—
98#683—22no—
99#683—22no—
100#683—22no—
101#683—22no—
102#683—42no—
103C4×Dic5—21no—
104C4×Dic5—42no—
105C4×Dic5—41no—
106C4×Dic5C4⋊C412yes—
107#681—42no—
108#681—42no—
109C2×#168—42no—
110C2×C4⋊Q8—51no—
111C2×C4×Q8—51no—
112C2×C4×Q8C2×D511yescharacteristic
113#423—21no—
114#423—101no—
115C2×#101—52no—
116C2×#101C2×D512yes—
117#391—51no—
118#391—51no—
119#387—101no—
120#387—101no—
121#387—101no—
122#387—101no—
123#382—51no—
124#376—51no—
125#356—104no—
126#343—21no—
127#343—101no—
128C23×C5C2×C22⋊C411yescharacteristic
129C5×Q8—41no—
130C5×Q8—41no—
131C5×Q8—41no—
132C5×Q8—41no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5—21no—
142C2×C4×C5—41no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
145C2×C4×C5—41no—
146C2×C4×C5#9912yes—
147C2×C4×C5C2×C4⋊C411yescharacteristic
148C2×C4×C5#11711yescharacteristic
149C2×C4×C5#12111yescharacteristic
150C2×C4×C5#12111yescharacteristic
151C2×C4×C5C22⋊Q811yescharacteristic
152C2×C4×C5C22⋊Q811yescharacteristic
153C2×Dic5—22no—
154C2×Dic5—22no—
155C2×Dic5—41no—
156C2×Dic5—41no—
157C2×Dic5—41no—
158C2×Dic5—41no—
159C2×Dic5—41no—
160C2×Dic5—41no—
161C2×Dic5—42no—
162C2×Dic5—41no—
163C2×Dic5—41no—
164Dic10—42no—
165Dic10—42no—
166C5×C8—82no—
167#168—82no—
168C22×Q8—51no—
169C22×Q8C22×D511yescharacteristic
170C2×M16—22no—
171C2×M16—102no—
172C4⋊Q8—52no—
173C4⋊Q8—52no—
174C4⋊Q8—101no—
175C4⋊Q8—101no—
176C4×Q8—42no—
177C4×Q8—202no—
178C2×C4⋊C4—51no—
179C2×C4⋊C4—101no—
180C2×C4⋊C4—101no—
181C2×C4⋊C4—101no—
182C2×C4⋊C4C4×D511yescharacteristic
183C2×C4⋊C4D2011yescharacteristic
184C2×C4⋊C4C22⋊D511yescharacteristic
185C2×C42—51no—
186C2×C42—51no—
187C2×C42—101no—
188C2×C42C4×D511yescharacteristic
189C2×C42D2011yescharacteristic
190C2×C42C22⋊D511yescharacteristic
191C4⋊C8—42no—
192C4⋊C8—202no—
193#101—22no—
194#101—22no—
195#101—102no—
196#101—102no—
197#95—101no—
198#95—101no—
199#95—101no—
200#95—101no—
201#95—101no—
202#95—101no—
203#95—101no—
204#95—101no—
205C22×C5—21no—
206C22×C5—21no—
207C22×C5#38011yescharacteristic
208C22×C5C2×#9911yescharacteristic
209C22×C5#41011yescharacteristic
210C4×C5—21no—
211C4×C5—21no—
212C4×C5—21no—
213C4×C5—21no—
214C4×C5—21no—
215C4×C5—21no—
216C4×C5—22no—
217C4×C5—41no—
218C4×C5—41no—
219C4×C5—41no—
220Dic5—42no—
221Dic5—42no—
222Dic5—81no—
223Dic5—81no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8—52no—
227C2×Q8—101no—
228C2×Q8—201no—
229C2×Q8—201no—
230C2×Q8D4×D511yescharacteristic
231C2×Q8#71111yescharacteristic
232C2×Q8Q8×D511yescharacteristic
233C2×Q8#71311yescharacteristic
234C22×C4—101no—
235C22×C4—101no—
236C22×C4—101no—
237C22×C4—101no—
238C22×C4#68511yescharacteristic
239C22×C4#68511yescharacteristic
240C22×C4#68511yescharacteristic
241C22×C4#68511yescharacteristic
242C22×C4C2×C4×D511yescharacteristic
243C22×C4C2×D2011yescharacteristic
244C22×C4C2×C22⋊D511yescharacteristic
245M16—42no—
246M16—42no—
247M16—202no—
248M16—202no—
249C2×C8—42no—
250C2×C8—202no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—102no—
255C4⋊C4—102no—
256C4⋊C4—102no—
257C4⋊C4—102no—
258C4⋊C4—201no—
259C4⋊C4—202no—
260C42—22no—
261C42—22no—
262C42—22no—
263C42—52no—
264C42—101no—
265C42—201no—
266C42—202no—
267C2×C5—21no—
268C2×C5—21no—
269C2×C5#179911yescharacteristic
270C2×C5#213311yescharacteristic
271C2×C5#213511yescharacteristic
272C23C2×#68511yescharacteristic
273Q8—41no—
274Q8—41no—
275Q8—41no—
276Q8—41no—
277Q8—202no—
278Q8—202no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—102no—
293C2×C4—102no—
294C2×C4—201no—
295C2×C4—201no—
296C2×C4—201no—
297C2×C4—201no—
298C2×C4—201no—
299C2×C4—201no—
300C2×C4—202no—
301C2×C4—201no—
302C2×C4—201no—
303C2×C4#393812yes—
304C2×C4D5×C4⋊C411yescharacteristic
305C2×C4#403811yescharacteristic
306C2×C4#404111yescharacteristic
307C2×C4#404311yescharacteristic
308C2×C4#408411yescharacteristic
309C2×C4#409211yescharacteristic
310C8—82no—
311C8—402no—
312C5#1280411yescharacteristic, complemented, Sylow
313C22—21no—
314C22—21no—
315C22C2×#393811yescharacteristic
316C22#6527611yescharacteristic
317C22#6529511yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—22no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—202no—
329C4—202no—
330C4—401no—
331C4—401no—
332C2—21no—
333C2—21no—
334C2#1060032311yescharacteristic
335C2#1060092111yescharacteristic
336C2#1060094311yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC22×Q8C22×D5
FittingC5×#1801C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC22×C5×Q8C23
hypercenter#1801D5
hypocenterC5#12804
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
312. C5#12804semidirect

Maximal subgroups

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

subgroupindex
#106141872
C5×#18012
#106024302
C2×#646982
#105981902
#128045