Finite Group Databasebeta

← #12002974

Subgroups — #12002974

Order 1280.

376 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#65139C211yesmaximal, characteristic
2#10601573C211yesmaximal, characteristic
3#10601560C211yesmaximal, characteristic
4#10601321C211yesmaximal, characteristic
5#10601300C211yesmaximal, characteristic
6#10601215C211yesmaximal, characteristic
7C5×#1301C211yesmaximal, characteristic
8C2×#4015C2211yescharacteristic
9C2×C4×Dic10C2211yescharacteristic
10C5×#431C2211yescharacteristic
11C5×#423C2211yescharacteristic
12C2×C5×C4⋊C8C2211yescharacteristic
13C2×#3956—21no—
14C2×#3950—21no—
15C2×#3948—21no—
16#65214C2211yescharacteristic
17#65213C2211yescharacteristic
18#65139—22no—
19#65139—22no—
20#64774—21no—
21#64702—22no—
22#64701—22no—
23#64699—22no—
24#64676—22no—
25#10455—51nomaximal, Sylow
26C22×Dic10—21no—
27C22×Dic10D411yescharacteristic
28C2×C5×M16—21no—
29C22×C5×C8—21no—
30C2×C42×C5C2311yescharacteristic
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5D411yescharacteristic
34C2×#683—21no—
35C2×C4×Dic5—21no—
36C2×#681—21no—
37#4015—21no—
38#4015—21no—
39#4015—21no—
40#4015D412yes—
41C4×Dic10—21no—
42C4×Dic10—21no—
43C4×Dic10—21no—
44C4×Dic10—21no—
45C5×C4⋊C8—21no—
46C5×C4⋊C8—21no—
47C5×C4⋊C8—21no—
48C5×C4⋊C8—21no—
49C5×C4⋊C8D412yes—
50C5×C22⋊C8—21no—
51C4×C5×C8—21no—
52C22⋊#168—21no—
53#3956—42no—
54#3950—24no—
55#3948—24no—
56C4⋊#168—21no—
57C4⋊#168—21no—
58C4⋊#168D412yes—
59C4×#168—21no—
60C2×#477—51no—
61#1801—51no—
62#1571—51no—
63#1549—51no—
64#1548—51no—
65#1479—51no—
66#1301D511yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C22×C4×C5#4111yescharacteristic
69C22×C4×C5#4111yescharacteristic
70C22×Dic5—21no—
71C22×Dic5—21no—
72C22×Dic5—41no—
73C2×Dic10—21no—
74C2×Dic10—21no—
75C2×Dic10—21no—
76C2×Dic10—21no—
77C2×Dic10—21no—
78C2×Dic10—22no—
79C2×Dic10—41no—
80C2×Dic10—82no—
81C2×Dic10Q1612yes—
82C5×M16—41no—
83C5×M16—41no—
84C2×C5×C8—22no—
85C2×C5×C8—41no—
86C2×C5×C8—41no—
87C2×C5×C8—41no—
88C2×C5×C8—41no—
89C42×C5C2×D411yescharacteristic
90C42×C5C2×D411yescharacteristic
91C42×C5C2×D411yescharacteristic
92C42×C5#4111yescharacteristic
93C4⋊Dic5—22no—
94C4⋊Dic5—21no—
95C4⋊Dic5—21no—
96C4⋊Dic5—22no—
97C4⋊Dic5—41no—
98C4⋊Dic5—41no—
99#683—41no—
100#683—41no—
101C4×Dic5—41no—
102C4×Dic5—41no—
103#681—41no—
104#681—41no—
105C2×#168—22no—
106C2×#168—41no—
107C2×C4⋊Q8—51no—
108C2×C4×Q8—51no—
109#477—102no—
110#477—102no—
111#431—51no—
112#431C2×D511yescharacteristic
113C2×#107—101no—
114#423—51no—
115#423C2×D511yescharacteristic
116C2×C4⋊C8C2×D511yescharacteristic
117C2×#103—101no—
118C2×#101—101no—
119#343—101no—
120#335—102no—
121#333—102no—
122#332—102no—
123Q8⋊C8—102no—
124C23×C5#12311yescharacteristic
125C2×C4×C5—22no—
126C2×C4×C5—41no—
127C2×C4×C5#12011yescharacteristic
128C2×C4×C5#12111yescharacteristic
129C2×C4×C5#12111yescharacteristic
130C2×C4×C5#12111yescharacteristic
131C2×C4×C5#12311yescharacteristic
132C2×C4×C5#12411yescharacteristic
133C2×C4×C5C2×Q1611yescharacteristic
134C2×C4×C5#13511yescharacteristic
135C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C5#13711yescharacteristic
137C2×Dic5—22no—
138C2×Dic5—41no—
139C2×Dic5—41no—
140C2×Dic5—41no—
141C2×Dic5—42no—
142C2×Dic5—82no—
143C2×Dic5—81no—
144Dic10—22no—
145Dic10—22no—
146Dic10—41no—
147Dic10—41no—
148Dic10—82no—
149Dic10—82no—
150C5×C8—42no—
151C5×C8—81no—
152C5×C8—81no—
153#168—42no—
154#168—81no—
155C22×Q8—51no—
156C22×Q8—101no—
157C2×M16—21no—
158C2×M16—101no—
159C22×C8—21no—
160C4⋊Q8—52no—
161C4⋊Q8—101no—
162C4⋊Q8—101no—
163C4⋊Q8—101no—
164C4×Q8—101no—
165C4×Q8—101no—
166C4×Q8—101no—
167C4×Q8—101no—
168C2×C4⋊C4—51no—
169C2×C4⋊C4—101no—
170C2×C4⋊C4—101no—
171C2×C4⋊C4—101no—
172C2×C42—101no—
173C2×C42C22×D511yescharacteristic
174#107—104no—
175C4⋊C8—21no—
176C4⋊C8—21no—
177C4⋊C8—21no—
178C4⋊C8—21no—
179C4⋊C8—52no—
180C4⋊C8—101no—
181C4⋊C8—101no—
182C4⋊C8D2012yes—
183#103—104no—
184#101—202no—
185C22⋊C8—21no—
186C22⋊C8—101no—
187C4×C8—21no—
188C4×C8—101no—
189C22×C5—21no—
190C22×C5—21no—
191C22×C5#39411yescharacteristic
192C22×C5#48411yescharacteristic
193C22×C5#48511yescharacteristic
194C4×C5—21no—
195C4×C5—21no—
196C4×C5—21no—
197C4×C5#44911yescharacteristic
198C4×C5#45111yescharacteristic
199C4×C5#46711yescharacteristic
200C4×C5#46811yescharacteristic
201C4×C5#47312yes—
202Dic5—42no—
203Dic5—82no—
204Dic5—81no—
205C2×Q8—52no—
206C2×Q8—101no—
207C2×Q8—101no—
208C2×Q8—101no—
209C2×Q8—102no—
210C2×Q8—101no—
211C2×Q8—101no—
212C2×Q8—201no—
213C2×Q8—402no—
214C22×C4—101no—
215C22×C4—101no—
216C22×C4—201no—
217C22×C4#70911yescharacteristic
218C22×C4D4×D511yescharacteristic
219C22×C4#71311yescharacteristic
220M16—41no—
221M16—41no—
222M16—201no—
223M16—201no—
224C2×C8—22no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—102no—
230C2×C8—201no—
231C4⋊C4—102no—
232C4⋊C4—101no—
233C4⋊C4—101no—
234C4⋊C4—102no—
235C4⋊C4—201no—
236C4⋊C4—201no—
237C4⋊C4—201no—
238C4⋊C4—201no—
239C42—201no—
240C42—201no—
241C42C2×D2011yescharacteristic
242C42#70911yescharacteristic
243C42D4×D511yescharacteristic
244C42D4×D511yescharacteristic
245C2×C5—21no—
246C2×C5—21no—
247C2×C5#203611yescharacteristic
248C2×C5#204711yescharacteristic
249C2×C5#204811yescharacteristic
250C23#404011yescharacteristic
251Q8—102no—
252Q8—102no—
253Q8—201no—
254Q8—201no—
255Q8—402no—
256Q8—402no—
257C2×C4—22no—
258C2×C4—41no—
259C2×C4—102no—
260C2×C4—201no—
261C2×C4—201no—
262C2×C4—201no—
263C2×C4—202no—
264C2×C4—402no—
265C2×C4—401no—
266C2×C4#402111yescharacteristic
267C2×C4#402811yescharacteristic
268C2×C4#403011yescharacteristic
269C2×C4#403011yescharacteristic
270C2×C4#404011yescharacteristic
271C2×C4#404111yescharacteristic
272C2×C4#405711yescharacteristic
273C2×C4#406111yescharacteristic
274C2×C4#406211yescharacteristic
275C2×C4D5×Q1611yescharacteristic
276C8—42no—
277C8—81no—
278C8—81no—
279C8—202no—
280C8—401no—
281C5#1045511yescharacteristic, complemented, Sylow
282C22—21no—
283C22—21no—
284C22#6496111yescharacteristic
285C22#6515611yescharacteristic
286C22#6517311yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—202no—
291C4—402no—
292C4—401no—
293C4#6506911yescharacteristic
294C4#6507011yescharacteristic
295C4#6509711yescharacteristic
296C4#6510211yescharacteristic
297C4#6518512yes—
298C2—21no—
299C2—21no—
300C2#1059961811yescharacteristic
301C2#1059972711yescharacteristic
302C2#1059981111yescharacteristic
subgroupG/H
centerC22#64961
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1301C2
socleC22×C5#394
prime radicalC23×C5#123
hypercenter#1301D5
hypocenterC5#10455
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
281. C5#10455semidirect

Maximal subgroups

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

subgroupindex
C2×#651392
#106015732
#106015602
#106013212
#106013002
#106012152
C5×#13012
#104555