Finite Group Databasebeta

← #11996086

Subgroups — #11996086

Order 1280.

464 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 105 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#10615081C211yesmaximal, characteristic
2#10611019C211yesmaximal, characteristic
3C5×#1481C211yesmaximal, characteristic, complemented
4#10602631C211yesmaximal, characteristic, complemented
5#10601273C211yesmaximal, characteristic
6#10598229C211yesmaximal, characteristic, complemented
7#10598198C211yesmaximal, characteristic, complemented
8C5×#533C2211yescharacteristic
9C2×C4×D20C2211yescharacteristic
10C5×#431C2211yescharacteristic
11C2×C5×C4⋊C8C2211yescharacteristic
12C2×#3953—21no—
13#65376C412yescomplemented
14#65373C412yescomplemented
15#65355—22no—
16#65290—21no—
17#65284—21no—
18#65225C2211yescharacteristic
19#65214C2211yescharacteristic
20#65213C2211yescharacteristic
21#65127—22no—
22#65015—22no—
23#64977—22no—
24C5×Q8⋊C8—22no—
25#64771—21no—
26#64758—22no—
27#9307—51nomaximal, Sylow
28C22×D20D411yescharacteristic
29C22×C4×D5—21no—
30C22×C5×C8—21no—
31C5×C4⋊Q8C2×C411yescharacteristic
32C5×C4⋊Q8C2×C411yescharacteristic
33C5×#125—21no—
34C5×C22⋊Q8—21no—
35C5×C22⋊Q8—21no—
36C4×C5×Q8—21no—
37C4×C5×Q8—21no—
38C5×#117—21no—
39C2×C42×C5C2311yescharacteristic
40C2×#685—21no—
41C2×C4⋊Dic5—21no—
42C2×C4⋊Dic5D411yescharacteristic
43C2×#681—21no—
44C2×#676—24no—
45C4×D20—21no—
46C4×D20—21no—
47C4×D20C2×C412yes—
48C4×D20D412yes—
49C5×C4⋊C8—21no—
50C5×C4⋊C8—21no—
51C5×C4⋊C8—21no—
52C5×C22⋊C8—21no—
53C4×C5×C8D412yes—
54#3963—21no—
55#3963—21no—
56C22⋊#168D412yes—
57#3953—42no—
58#3952—24no—
59#3941—22no—
60#3941—22no—
61#3940—22no—
62#3939—22no—
63C4⋊#168—21no—
64C4⋊#168—21no—
65C4⋊#168C2×C412yes—
66C4×#168—21no—
67#3077—51no—
68#2975—51no—
69#1804—51no—
70#1518—51no—
71#1481D511yescharacteristic, complemented
72#1301—51no—
73#1286—51no—
74C23×D5—21no—
75C2×C5×Q8—21no—
76C2×C5×Q8—21no—
77C22×C4×C5C2×D411yescharacteristic
78C22×C4×C5C2×D411yescharacteristic
79C22×C4×C5#4111yescharacteristic
80C22×Dic5—21no—
81C22×Dic5—41no—
82C2×D20—21no—
83C2×D20—21no—
84C2×D20—21no—
85C2×D20—21no—
86C2×D20—21no—
87C2×D20C22⋊C412yes—
88C2×C4×D5—22no—
89C2×C4×D5—22no—
90C2×C4×D5—82no—
91C2×C5×C8—22no—
92C2×C5×C8—41no—
93C2×C5×C8—41no—
94C2×C5×C8—41no—
95C5×C4⋊C4—21no—
96C5×C4⋊C4—21no—
97C5×C4⋊C4—21no—
98C5×C4⋊C4—21no—
99C5×C4⋊C4—41no—
100C5×C4⋊C4—41no—
101C5×C22⋊C4—41no—
102C42×C5—41no—
103C42×C5C22×C411yescharacteristic
104C42×C5C2×D411yescharacteristic
105C42×C5C2×D411yescharacteristic
106C42×C5#4111yescharacteristic
107#685—22no—
108#685—22no—
109C4⋊Dic5—21no—
110C4⋊Dic5—41no—
111C4⋊Dic5—41no—
112C4⋊Dic5C22⋊C412yes—
113#681—41no—
114#681—41no—
115C2×#168—22no—
116C2×#168—22no—
117#676—84no—
118#533C2×D511yescharacteristic
119C2×C4×D4—51no—
120#478—102no—
121#476—52no—
122#474—52no—
123#436—102no—
124#436—102no—
125#431—51no—
126#431C2×D511yescharacteristic
127#428—101no—
128#423—51no—
129C2×C4⋊C8C2×D511yescharacteristic
130#418—101no—
131C2×#102—101no—
132#407—102no—
133#382—51no—
134#340—101no—
135#328—102no—
136Q8⋊C8—22no—
137C23×C5#12111yescharacteristic
138C22×D5—22no—
139C22×D5—41no—
140C22×D5—41no—
141C22×D5—81no—
142C22×D5—81no—
143C5×Q8—42no—
144C5×Q8—81no—
145C2×C4×C5—41no—
146C2×C4×C5—41no—
147C2×C4×C5—41no—
148C2×C4×C5—41no—
149C2×C4×C5C2×C22⋊C411yescharacteristic
150C2×C4×C5C4×D411yescharacteristic
151C2×C4×C5C4×D411yescharacteristic
152C2×C4×C5#12011yescharacteristic
153C2×C4×C5#12111yescharacteristic
154C2×C4×C5#12311yescharacteristic
155C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C5#13711yescharacteristic
157C2×C4×C5#13711yescharacteristic
158C2×C4×C5#13711yescharacteristic
159C2×Dic5—22no—
160C2×Dic5—81no—
161C2×Dic5—81no—
162C2×Dic5—81no—
163C2×Dic5—81no—
164D20—22no—
165D20—22no—
166D20—41no—
167D20—41no—
168C4×D5—44no—
169C4×D5—82no—
170C5×C8—42no—
171C5×C8—81no—
172#168—42no—
173#168—42no—
174C22×D4—51no—
175C23×C4—101no—
176C2×M16—104no—
177C2×M16—101no—
178C22×C8—21no—
179C4⋊Q8C4×D511yescharacteristic
180C4⋊Q8C4×D511yescharacteristic
181#125—21no—
182C22⋊Q8—21no—
183C22⋊Q8—21no—
184C4×Q8—21no—
185C4×Q8—21no—
186C4×D4—52no—
187C4×D4—52no—
188C4×D4—101no—
189C4×D4—101no—
190#117—21no—
191C2×C4⋊C4—51no—
192C2×C4⋊C4—101no—
193C2×C22⋊C4—101no—
194C2×C42C22×D511yescharacteristic
195#107—102no—
196#106—102no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8—52no—
201C4⋊C8—101no—
202C4⋊C8—101no—
203#102—102no—
204#102—102no—
205#102—202no—
206C22⋊C8—21no—
207C22⋊C8—52no—
208C22⋊C8—104no—
209C4×C8—101no—
210C4×C8C22⋊D512yes—
211#95—101no—
212#95—101no—
213C22×C5—21no—
214C22×C5—21no—
215C22×C5#38611yescharacteristic
216C22×C5#46811yescharacteristic
217C22×C5#47011yescharacteristic
218C2×D5—42no—
219C2×D5—42no—
220C2×D5—42no—
221C2×D5—82no—
222C2×D5—82no—
223C4×C5—21no—
224C4×C5—21no—
225C4×C5—21no—
226C4×C5—21no—
227C4×C5—81no—
228C4×C5—81no—
229C4×C5#41711yescharacteristic
230C4×C5#41911yescharacteristic
231C4×C5#46811yescharacteristic
232C4×C5#47011yescharacteristic
233Dic5—42no—
234Dic5—161no—
235C24—101no—
236C2×Q8—21no—
237C2×Q8—21no—
238C2×D4—52no—
239C2×D4—101no—
240C2×D4—101no—
241C2×D4—101no—
242C2×D4—101no—
243C2×D4—101no—
244C22×C4—101no—
245C22×C4—102no—
246C22×C4—102no—
247C22×C4—201no—
248C22×C4—402no—
249C22×C4#70911yescharacteristic
250C22×C4D4×D511yescharacteristic
251C22×C4D4×D511yescharacteristic
252M16—201no—
253M16—201no—
254M16—404no—
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—102no—
260C2×C8—102no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—52no—
268C4⋊C4—101no—
269C4⋊C4—201no—
270C4⋊C4—201no—
271C22⋊C4—41no—
272C22⋊C4—102no—
273C22⋊C4—102no—
274C42—41no—
275C42C2×C4×D511yescharacteristic
276C42D4×D511yescharacteristic
277C42#71111yescharacteristic
278C42C2×C22⋊D511yescharacteristic
279C2×C5—21no—
280C2×C5—21no—
281C2×C5#188111yescharacteristic
282C2×C5#189411yescharacteristic
283C2×C5#190411yescharacteristic
284D5—82no—
285C23—102no—
286C23—201no—
287C23—201no—
288C23—401no—
289C23—401no—
290C23#403011yescharacteristic
291Q8—42no—
292Q8—81no—
293D4—102no—
294D4—102no—
295D4—201no—
296D4—201no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—102no—
302C2×C4—204no—
303C2×C4—402no—
304C2×C4—401no—
305C2×C4—401no—
306C2×C4—401no—
307C2×C4—401no—
308C2×C4D5×C22⋊C411yescharacteristic
309C2×C4#402711yescharacteristic
310C2×C4#402911yescharacteristic
311C2×C4#406011yescharacteristic
312C2×C4#406111yescharacteristic
313C2×C4#406411yescharacteristic
314C2×C4#406411yescharacteristic
315C2×C4C4×C22⋊D511yescharacteristic
316C2×C4#408311yescharacteristic
317C2×C4#408411yescharacteristic
318C8—42no—
319C8—81no—
320C8—202no—
321C8—202no—
322C5#930711yescharacteristic, complemented, Sylow
323C22—21no—
324C22—21no—
325C22—202no—
326C22—202no—
327C22—202no—
328C22—402no—
329C22—402no—
330C22#6510111yescharacteristic
331C22#6510511yescharacteristic
332C22#6524511yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—81no—
338C4—81no—
339C4—202no—
340C4—801no—
341C4#6509111yescharacteristic
342C4#6509211yescharacteristic
343C4#6546311yescharacteristic
344C4#6547811yescharacteristic
345C2—21no—
346C2—21no—
347C2—402no—
348C2#1060080511yescharacteristic
349C2#1060106411yescharacteristic
350C2#1060120011yescharacteristic
subgroupG/H
centerC22#65245
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1481C2
socleC22×C5#386
prime radicalC22×D20D4
cosocleC2×C42×C5C23
hypercenter#1481D5
hypocenterC5#9307
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
3. C5×#1481C2semidirect
4. #10602631C2semidirect
6. #10598229C2semidirect
7. #10598198C2semidirect
13. #65376C4semidirect
14. #65373C4semidirect
71. #1481D5semidirect
322. C5#9307semidirect

Maximal subgroups

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

subgroupindex
#106150812
#106110192
C5×#14812
#106026312
#106012732
#105982292
#105981982
#93075