Finite Group Databasebeta

← #11988198

Subgroups — #11988198

Order 1280.

416 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 91 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×#2726C211yesmaximal, characteristic
2#10600426C211yesmaximal, characteristic
3#10600398C211yesmaximal, characteristic
4#10600398C211yesmaximal, characteristic
5#10598129C211yesmaximal, characteristic
6#10598129C211yesmaximal, characteristic
7#10598129C211yesmaximal, characteristic
8C2×C5×#125—21no—
9C2×#4015C2211yescharacteristic
10C5×#398—21no—
11C5×#398—21no—
12C5×#398—21no—
13C5×#389—21no—
14C5×#389C2211yescharacteristic
15C5×#389C2211yescharacteristic
16C5×#389C2211yescharacteristic
17C5×#387—21no—
18C2×#3942—21no—
19C2×#3942—21no—
20C2×#3940—21no—
21C2×#3940—21no—
22#64749—21no—
23#64749—21no—
24#64744C2211yescharacteristic
25#64744C2211yescharacteristic
26#64744C2211yescharacteristic
27#7768—51nomaximal, Sylow
28C22×Dic10—21no—
29C5×#125—42no—
30C5×#125—42no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4—21no—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4D411yescharacteristic
39C2×C5×C4⋊C4D411yescharacteristic
40C2×C5×C4⋊C4D411yescharacteristic
41C2×C5×C4⋊C4D411yescharacteristic
42C2×C5×C4⋊C4D411yescharacteristic
43C2×C5×C4⋊C4D411yescharacteristic
44C2×C42×C5—21no—
45C2×C42×C5C2311yescharacteristic
46C2×C4⋊Dic5—21no—
47C2×C4⋊Dic5—21no—
48C22×#168—21no—
49C22×#168—21no—
50C22×#168—21no—
51#4015—42no—
52C5×#95—21no—
53C5×#95—21no—
54C5×#95—21no—
55C5×#95—21no—
56C5×#95—21no—
57C5×#95—21no—
58#3942—42no—
59#3942—42no—
60#3940—42no—
61#3940—42no—
62#2726D511yescharacteristic
63#2058—51no—
64#2058—51no—
65#2043—51no—
66#1271—51no—
67#1271—51no—
68#1271—51no—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—21no—
73C22×C4×C5—21no—
74C22×C4×C5—21no—
75C22×C4×C5C2×D411yescharacteristic
76C22×C4×C5C2×D411yescharacteristic
77C22×C4×C5C2×D411yescharacteristic
78C22×Dic5—41no—
79C2×Dic10—22no—
80C2×Dic10—41no—
81C2×Dic10—41no—
82C2×Dic10—41no—
83C2×Dic10—41no—
84C2×Dic10—41no—
85C5×C4⋊C4—21no—
86C5×C4⋊C4—21no—
87C5×C4⋊C4—21no—
88C5×C4⋊C4—21no—
89C5×C4⋊C4—41no—
90C5×C4⋊C4—41no—
91C5×C4⋊C4—41no—
92C5×C4⋊C4—42no—
93C5×C4⋊C4—42no—
94C5×C4⋊C4—42no—
95C5×C4⋊C4—41no—
96C5×C4⋊C4—41no—
97C5×C4⋊C4—41no—
98C5×C4⋊C4—41no—
99C5×C4⋊C4—41no—
100C5×C4⋊C4—41no—
101C5×C4⋊C4—81no—
102C5×C4⋊C4SD1612yes—
103C5×C4⋊C4SD1612yes—
104C42×C5—41no—
105C42×C5—42no—
106C4⋊Dic5—22no—
107C4⋊Dic5—22no—
108C4⋊Dic5—41no—
109C4⋊Dic5—41no—
110C2×#168—22no—
111C2×#168—22no—
112C2×#168—41no—
113C2×#168—41no—
114C2×#168—41no—
115C2×#168—41no—
116C2×#168—41no—
117C2×#168—41no—
118C2×#168—41no—
119C2×C4⋊Q8—51no—
120C2×#125—21no—
121C2×#106—101no—
122C2×#106—101no—
123C2×#103—101no—
124C2×#103—101no—
125#398—21no—
126#398—21no—
127#398—21no—
128#389—21no—
129#389C2×D511yescharacteristic
130#389C2×D511yescharacteristic
131#389C2×D511yescharacteristic
132#387—21no—
133#340—101no—
134#340—101no—
135#336—51no—
136#336—51no—
137#336—51no—
138C23×C5#12011yescharacteristic
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—22no—
146C2×C4×C5—22no—
147C2×C4×C5—41no—
148C2×C4×C5—41no—
149C2×C4×C5—41no—
150C2×C4×C5—41no—
151C2×C4×C5—41no—
152C2×C4×C5—41no—
153C2×C4×C5—41no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—41no—
163C2×C4×C5C2×SD1611yescharacteristic
164C2×C4×C5C2×SD1611yescharacteristic
165C2×C4×C5#13511yescharacteristic
166C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C5#13711yescharacteristic
168C2×C4×C5#13711yescharacteristic
169C2×Dic5—42no—
170C2×Dic5—81no—
171C2×Dic5—81no—
172Dic10—42no—
173Dic10—42no—
174Dic10—81no—
175Dic10—81no—
176#168—42no—
177#168—42no—
178#168—81no—
179C22×Q8—101no—
180C22×C8—101no—
181C22×C8—101no—
182C22×C8—101no—
183C4⋊Q8—202no—
184#125—42no—
185#125—42no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—101no—
194C2×C4⋊C4—101no—
195C2×C4⋊C4C22⋊D511yescharacteristic
196C2×C4⋊C4C22⋊D511yescharacteristic
197C2×C4⋊C4C22⋊D511yescharacteristic
198C2×C4⋊C4C22⋊D511yescharacteristic
199C2×C4⋊C4C22⋊D511yescharacteristic
200C2×C4⋊C4C22⋊D511yescharacteristic
201C2×C42—21no—
202C2×C42C22×D511yescharacteristic
203#106—202no—
204#106—202no—
205#103—202no—
206#103—202no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213C22×C5#44811yescharacteristic
214C22×C5#45011yescharacteristic
215C22×C5#45211yescharacteristic
216C22×C5#45411yescharacteristic
217C22×C5#45611yescharacteristic
218C22×C5#45611yescharacteristic
219C22×C5B(4,𝔽2)11yescharacteristic
220C4×C5—21no—
221C4×C5—21no—
222C4×C5—21no—
223C4×C5—21no—
224C4×C5—21no—
225C4×C5—21no—
226C4×C5—42no—
227C4×C5—42no—
228C4×C5—81no—
229C4×C5—81no—
230C4×C5—81no—
231C4×C5—81no—
232Dic5—82no—
233C2×Q8—102no—
234C2×Q8—201no—
235C2×Q8—201no—
236C2×Q8—201no—
237C2×Q8—201no—
238C2×Q8—201no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—201no—
246C22×C4C2×C22⋊D511yescharacteristic
247C22×C4C2×C22⋊D511yescharacteristic
248C22×C4C2×C22⋊D511yescharacteristic
249C2×C8—102no—
250C2×C8—102no—
251C2×C8—201no—
252C2×C8—201no—
253C2×C8—201no—
254C2×C8—201no—
255C2×C8—201no—
256C2×C8—201no—
257C2×C8—201no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—81no—
275C4⋊C4—102no—
276C4⋊C4—102no—
277C4⋊C4—201no—
278C4⋊C4—201no—
279C4⋊C4#68712yes—
280C4⋊C4#68812yes—
281C42—41no—
282C42—42no—
283C2×C5#159911yescharacteristic
284C2×C5#160311yescharacteristic
285C2×C5#160411yescharacteristic
286C2×C5#163511yescharacteristic
287C2×C5#165111yescharacteristic
288C2×C5#165311yescharacteristic
289C2×C5#166311yescharacteristic
290C23#409911yescharacteristic
291Q8—202no—
292Q8—202no—
293Q8—401no—
294Q8—401no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—202no—
320C2×C4—401no—
321C2×C4—401no—
322C2×C4#407811yescharacteristic
323C2×C4C2×#68711yescharacteristic
324C2×C4C2×#68811yescharacteristic
325C2×C4#408811yescharacteristic
326C2×C4#409611yescharacteristic
327C2×C4#409711yescharacteristic
328C8—202no—
329C8—202no—
330C8—401no—
331C5#776811yescharacteristic, complemented, Sylow
332C22#6550711yescharacteristic
333C22#6551611yescharacteristic
334C22#6552811yescharacteristic
335C22#6553311yescharacteristic
336C22#6553411yescharacteristic
337C22#6553511yescharacteristic
338C22#6553511yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—42no—
346C4—42no—
347C4—81no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—402no—
352C2#1060267311yescharacteristic
353C2#1060268211yescharacteristic
354C2#1060269511yescharacteristic
355C2#1060270411yescharacteristic
356C2#1060271011yescharacteristic
357C2#1060273111yescharacteristic
358C2#1060275411yescharacteristic
subgroupG/H
centerC23#4099
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#2726C2
socle, prime radicalC23×C5#120
hypercenter#2726D5
hypocenterC5#7768
LCSG ▷ C2×C42×C5 ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2726

Complements

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

NH ≅ G/Ntype
331. C5#7768semidirect

Maximal subgroups

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

subgroupindex
C5×#27262
#106004262
#106003982
#105981292
#77685