Finite Group Databasebeta

← #11996692

Subgroups — #11996692

Order 1280.

514 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 109 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#10614991C211yesmaximal, characteristic
2#10611019C211yesmaximal, characteristic
3C5×#1548C211yesmaximal, characteristic, complemented
4#10602567C211yesmaximal, characteristic, complemented
5#10601320C211yesmaximal, characteristic
6#10598237C211yesmaximal, characteristic, complemented
7#10598206C211yesmaximal, characteristic, complemented
8C2×C5×C4⋊Q8C2211yescharacteristic
9C2×C4×D20C2211yescharacteristic
10C5×#431C2211yescharacteristic
11C5×#423C2211yescharacteristic
12#65520C414yes—
13C2×#3955—21no—
14#65277—21no—
15#65276—22no—
16#65266—21no—
17C4×C4⋊Dic5C2211yescharacteristic
18#65214C2211yescharacteristic
19#65213C2211yescharacteristic
20#65127—22no—
21#65015—22no—
22#64977—22no—
23C5×#333—22no—
24#64774—21no—
25#64766—22no—
26#9399—51nomaximal, Sylow
27C22×C5×Q8C2×C412yes—
28C22×D20D411yescharacteristic
29C22×C4×D5D412yes—
30C2×C5×M16—21no—
31C5×C4⋊Q8—21no—
32C5×C4⋊Q8—21no—
33C5×C4⋊Q8—21no—
34C5×C4⋊Q8—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4—21no—
37C2×C42×C5C2311yescharacteristic
38C2×#685—24no—
39C2×#685C2×C412yes—
40C2×C4⋊Dic5—21no—
41C2×C4⋊Dic5D411yescharacteristic
42C2×C4×Dic5—21no—
43C2×#681—21no—
44C2×#676—24no—
45C4×D20—21no—
46C4×D20—21no—
47C4×D20—21no—
48C4×D20—21no—
49C5×C4⋊C8—21no—
50C5×C4⋊C8—21no—
51C5×C4⋊C8D412yes—
52C5×C22⋊C8—21no—
53C4×C5×C8—21no—
54#3963—24no—
55#3963C2×C412yes—
56C22⋊#168—21no—
57#3955—42no—
58#3952—24no—
59C4⋊#168—21no—
60C4⋊#168—21no—
61C4⋊#168D412yes—
62C4×#168—21no—
63#2975—51no—
64#2563—51no—
65#1800—51no—
66#1548—51no—
67#1548D511yescharacteristic, complemented
68#1303—51no—
69#1303—51no—
70C23×D5C22⋊C412yes—
71C2×C5×Q8—22no—
72C2×C5×Q8—22no—
73C2×C5×Q8—82no—
74C22×C4×C5—22no—
75C22×C4×C5C22×C411yescharacteristic
76C22×C4×C5C2×D411yescharacteristic
77C22×C4×C5C2×D411yescharacteristic
78C22×Dic5—22no—
79C22×Dic5C22⋊C412yes—
80C2×D20—21no—
81C2×D20—21no—
82C2×D20—21no—
83C2×D20—21no—
84C2×D20—21no—
85C2×D20—21no—
86C2×C4×D5—22no—
87C2×C4×D5—22no—
88C2×C4×D5—44no—
89C5×M16—41no—
90C5×M16—41no—
91C2×C5×C8—22no—
92C2×C5×C8—41no—
93C5×C4⋊C4—41no—
94C5×C4⋊C4—41no—
95C5×C4⋊C4—41no—
96C5×C4⋊C4—41no—
97C42×C5C2×D411yescharacteristic
98C42×C5C2×D411yescharacteristic
99C42×C5#4111yescharacteristic
100C42×C5#4111yescharacteristic
101#685—22no—
102#685—22no—
103#685—84no—
104C4⋊Dic5—21no—
105C4⋊Dic5—21no—
106C4⋊Dic5—42no—
107C4×Dic5—41no—
108C4×Dic5—41no—
109#681—41no—
110#681—41no—
111C2×#168—22no—
112C2×#168—41no—
113#676—84no—
114C2×C4⋊Q8C2×D511yescharacteristic
115C2×C4×D4—51no—
116#436—102no—
117#436—102no—
118#431—51no—
119#431C2×D511yescharacteristic
120#423—51no—
121#423C2×D511yescharacteristic
122C2×#100—101no—
123#407—102no—
124#393—54no—
125#390—101no—
126#382—101no—
127#380—102no—
128C4×C4⋊C4—51no—
129#343—101no—
130#333—22no—
131#333—102no—
132C23×C5C2×C22⋊C411yescharacteristic
133C22×D5—22no—
134C22×D5—22no—
135C22×D5—22no—
136C22×D5—42no—
137C22×D5—42no—
138C5×Q8—82no—
139C5×Q8—82no—
140C2×C4×C5—22no—
141C2×C4×C5—41no—
142C2×C4×C5—44no—
143C2×C4×C5—42no—
144C2×C4×C5C4×D411yescharacteristic
145C2×C4×C5C4×D411yescharacteristic
146C2×C4×C5#12011yescharacteristic
147C2×C4×C5#12111yescharacteristic
148C2×C4×C5#12111yescharacteristic
149C2×C4×C5#12311yescharacteristic
150C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C5#13711yescharacteristic
152C2×C4×C5#13711yescharacteristic
153C2×C4×C5#13711yescharacteristic
154C2×Dic5—22no—
155C2×Dic5—42no—
156C2×Dic5—42no—
157C2×Dic5—42no—
158C2×Dic5—42no—
159D20—41no—
160D20—41no—
161D20—41no—
162D20—41no—
163C4×D5—44no—
164C4×D5—82no—
165C5×C8—42no—
166C5×C8—81no—
167#168—42no—
168#168—81no—
169C22×Q8C4×D512yes—
170C22×D4—51no—
171C23×C4—52no—
172C2×M16—21no—
173C2×M16—104no—
174C2×M16—101no—
175C4⋊Q8—21no—
176C4⋊Q8—21no—
177C4⋊Q8—21no—
178C4⋊Q8—21no—
179C4×D4—101no—
180C4×D4—101no—
181C4×D4—101no—
182C4×D4—101no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—51no—
186C2×C4⋊C4—101no—
187C2×C22⋊C4—52no—
188C2×C22⋊C4—104no—
189C2×C42—101no—
190C2×C42C22×D511yescharacteristic
191C4⋊C8—21no—
192C4⋊C8—21no—
193C4⋊C8—52no—
194C4⋊C8—101no—
195C4⋊C8—101no—
196C4⋊C8C22⋊D512yes—
197#100—202no—
198C22⋊C8—21no—
199C22⋊C8—104no—
200C22⋊C8—101no—
201C4×C8—21no—
202C4×C8—101no—
203#95—52no—
204#95—104no—
205C22×C5—21no—
206C22×C5—21no—
207C22×C5#38611yescharacteristic
208C22×C5#41711yescharacteristic
209C22×C5#41911yescharacteristic
210C2×D5—44no—
211C2×D5—42no—
212C2×D5—42no—
213C2×D5—42no—
214C2×D5—82no—
215C4×C5—21no—
216C4×C5—21no—
217C4×C5—21no—
218C4×C5—82no—
219C4×C5#45512yes—
220C4×C5#46811yescharacteristic
221C4×C5#46811yescharacteristic
222C4×C5#47011yescharacteristic
223C4×C5#47011yescharacteristic
224Dic5—42no—
225Dic5—82no—
226C24—52no—
227C2×Q8—22no—
228C2×Q8—22no—
229C2×Q8—82no—
230C2×D4—101no—
231C2×D4—101no—
232C2×D4—101no—
233C2×D4—101no—
234C2×D4—101no—
235C2×D4—101no—
236C22×C4—22no—
237C22×C4—52no—
238C22×C4—102no—
239C22×C4—102no—
240C22×C4—102no—
241C22×C4—204no—
242C22×C4C2×C4×D511yescharacteristic
243C22×C4D4×D511yescharacteristic
244C22×C4D4×D511yescharacteristic
245M16—41no—
246M16—41no—
247M16—201no—
248M16—201no—
249M16—404no—
250C2×C8—22no—
251C2×C8—41no—
252C2×C8—102no—
253C2×C8—201no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—101no—
259C4⋊C4—101no—
260C4⋊C4—202no—
261C22⋊C4—102no—
262C22⋊C4—102no—
263C22⋊C4—404no—
264C42—201no—
265C42—201no—
266C42#70911yescharacteristic
267C42D4×D511yescharacteristic
268C42#71111yescharacteristic
269C42C2×C22⋊D511yescharacteristic
270C2×C5—21no—
271C2×C5—21no—
272C2×C5#188511yescharacteristic
273C2×C5#189411yescharacteristic
274C2×C5#191411yescharacteristic
275D5—82no—
276C23—102no—
277C23—102no—
278C23—102no—
279C23—202no—
280C23—202no—
281C23D5×C22⋊C411yescharacteristic
282Q8—82no—
283Q8—82no—
284D4—201no—
285D4—201no—
286D4—201no—
287D4—201no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—44no—
291C2×C4—42no—
292C2×C4—102no—
293C2×C4—204no—
294C2×C4—202no—
295C2×C4—202no—
296C2×C4—202no—
297C2×C4—202no—
298C2×C4—402no—
299C2×C4#402711yescharacteristic
300C2×C4#402911yescharacteristic
301C2×C4#403011yescharacteristic
302C2×C4#406011yescharacteristic
303C2×C4#406111yescharacteristic
304C2×C4#406411yescharacteristic
305C2×C4#406411yescharacteristic
306C2×C4C4×C22⋊D511yescharacteristic
307C2×C4#408311yescharacteristic
308C2×C4#408411yescharacteristic
309C8—42no—
310C8—81no—
311C8—202no—
312C8—401no—
313C5#939911yescharacteristic, complemented, Sylow
314C22—21no—
315C22—21no—
316C22—204no—
317C22—202no—
318C22—202no—
319C22—202no—
320C22—402no—
321C22#6509111yescharacteristic
322C22#6509211yescharacteristic
323C22#6524511yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—82no—
328C4—202no—
329C4—402no—
330C4#6510111yescharacteristic
331C4#6510511yescharacteristic
332C4#6546311yescharacteristic
333C4#6547811yescharacteristic
334C4#6549112yes—
335C2—21no—
336C2—21no—
337C2—402no—
338C2#1060088211yescharacteristic
339C2#1060106411yescharacteristic
340C2#1060113611yescharacteristic
subgroupG/H
centerC22#65245
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1548C2
socleC22×C5#386
prime radicalC22×D20D4
cosocleC2×C42×C5C23
hypercenter#1548D5
hypocenterC5#9399
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
3. C5×#1548C2semidirect
4. #10602567C2semidirect
6. #10598237C2semidirect
7. #10598206C2semidirect
67. #1548D5semidirect
313. C5#9399semidirect

Maximal subgroups

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

subgroupindex
#106149912
#106110192
C5×#15482
#106025672
#106013202
#105982372
#105982062
#93995