Finite Group Databasebeta

← #13026348

Subgroups — #13026348

Order 1280.

450 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic5×#131C211yesmaximal, characteristic
2C2×#64932C212yesmaximal
3#10604708C211yesmaximal, characteristic, complemented
4C2×#64888C211yesmaximal, characteristic, complemented
5#10598796C212yesmaximal, complemented
6C2×C5×#131C411yescharacteristic
7#41×Dic5C411yescharacteristic
8C2×#4094C2211yescharacteristic
9C2×#3998C2212yes—
10C22×#674C2212yes—
11#65411—21no—
12#65411C2211yescharacteristic
13M16×Dic5—21no—
14M16×Dic5C411yescharacteristic
15#65390—21no—
16#65390C411yescharacteristic
17C2×C8×Dic5—21no—
18C2×C8×Dic5C2211yescharacteristic
19#64932—24no—
20#64888—21no—
21#64888—21no—
22#64888—21no—
23#64888—21no—
24#12787—51nomaximal, Sylow
25C2×C5×#41C2×C411yescharacteristic
26C5×#131—22no—
27C5×#131—22no—
28C2×C5×M16—21no—
29C2×C5×M16C2×C411yescharacteristic
30C22×C5×C8—21no—
31C22×C5×C8C2×C411yescharacteristic
32#4094—21no—
33#4094—21no—
34#4094D412yes—
35#4094Q812yes—
36Q8×Dic5C811yescharacteristic
37Q8×Dic5C811yescharacteristic
38D4×Dic5—21no—
39D4×Dic5—21no—
40D4×Dic5C811yescharacteristic
41D4×Dic5C811yescharacteristic
42#4072—21no—
43#4072C2×C411yescharacteristic
44C2×C4×Dic5—21no—
45C2×C4×Dic5C2×C411yescharacteristic
46C2×#681—21no—
47C2×#681C2×C411yescharacteristic
48C22×#168—21no—
49C22×#168C2311yescharacteristic
50#3998—22no—
51#3998—22no—
52C2×#674—22no—
53C2×#674—22no—
54C2×#674—22no—
55C2×#674—22no—
56#3947—21no—
57#3947—21no—
58#3947—21no—
59C8×Dic5—21no—
60C8×Dic5—21no—
61C8×Dic5—21no—
62C8×Dic5D411yescharacteristic
63C8×Dic5D411yescharacteristic
64C8×Dic5D411yescharacteristic
65C8×Dic5D411yescharacteristic
66C4×#131—51no—
67#2150—51no—
68C2×C4⋊C16—51no—
69C2×#350—52no—
70#1379—52no—
71C5×#41—21no—
72C5×#41—21no—
73C5×#41C4⋊C412yes—
74C5×#41M1612yes—
75C2×C5×Q8C2×C811yescharacteristic
76C2×C5×D4—21no—
77C2×C5×D4C2×C811yescharacteristic
78C22×C4×C5—21no—
79C22×C4×C5C22×C411yescharacteristic
80C22×Dic5—21no—
81C22×Dic5—21no—
82C22×Dic5M1611yescharacteristic
83C22×Dic5M1611yescharacteristic
84C5×M16—24no—
85C5×M16—21no—
86C5×M16M1612yes—
87C2×C5×C8—24no—
88C2×C5×C8—21no—
89C2×C5×C8—21no—
90C2×C5×C8—21no—
91C2×C5×C8C22⋊C411yescharacteristic
92C2×C5×C8C22⋊C411yescharacteristic
93C22⋊Dic5—21no—
94C22⋊Dic5—21no—
95C22⋊Dic5—21no—
96C4⋊Dic5—21no—
97C4⋊Dic5—21no—
98C4⋊Dic5C2×C811yescharacteristic
99C4⋊Dic5C2×C811yescharacteristic
100C4×Dic5—21no—
101C4×Dic5—21no—
102C4×Dic5—21no—
103C4×Dic5C22⋊C411yescharacteristic
104C4×Dic5C22⋊C411yescharacteristic
105C4×Dic5C2×C811yescharacteristic
106C4×Dic5C2×C811yescharacteristic
107#681—21no—
108#681—22no—
109#681—22no—
110#681C4⋊C412yes—
111C2×#168—21no—
112C2×#168—22no—
113C2×#168—22no—
114C2×#168C2×D411yescharacteristic
115C2×#168C2×D411yescharacteristic
116C2×#168C2×D411yescharacteristic
117C2×#168C2×Q811yescharacteristic
118C2×#168#4111yescharacteristic
119C2×#168#4111yescharacteristic
120#674—42no—
121#674—42no—
122C2×#131—51no—
123C2×#131AGL(1,𝔽5)11yescharacteristic
124C4×#41—51no—
125C2×M32—52no—
126C22×C16—52no—
127#405—51no—
128#405—51no—
129#405—101no—
130#405—101no—
131C4×M16—51no—
132C4×M16—101no—
133C2×C4×C8—51no—
134C2×C4×C8—101no—
135C4⋊C16—101no—
136C4⋊C16—101no—
137C4⋊C16—101no—
138C4⋊C16—101no—
139#350—104no—
140C23×C5—21no—
141C23×C5C2×M1611yescharacteristic
142C5×Q8—21no—
143C5×Q8C4⋊C812yes—
144C5×D4—22no—
145C5×D4—22no—
146C5×D4—21no—
147C5×D4C4⋊C812yes—
148C2×C4×C5—21no—
149C2×C4×C5—22no—
150C2×C4×C5—22no—
151C2×C4×C5C2×C22⋊C411yescharacteristic
152C2×C4×C5C2×C4⋊C411yescharacteristic
153C2×C4×C5#11711yescharacteristic
154C2×C4×C5C22×C811yescharacteristic
155C2×C4×C5C2×M1611yescharacteristic
156C2×C4×C5C2×M1611yescharacteristic
157C2×Dic5—22no—
158C2×Dic5—21no—
159C2×Dic5—21no—
160C2×Dic5—41no—
161C2×Dic5—42no—
162C2×Dic5—42no—
163C2×Dic5C22⋊C811yescharacteristic
164C2×Dic5C22⋊C811yescharacteristic
165C2×Dic5C22⋊C811yescharacteristic
166C2×Dic5C22⋊C811yescharacteristic
167C5×C8—21no—
168C5×C8—22no—
169C5×C8—21no—
170#168—22no—
171#168#12111yescharacteristic
172#168#12111yescharacteristic
173#168C22⋊Q811yescharacteristic
174#168C22⋊Q811yescharacteristic
175C2×#41C2×AGL(1,𝔽5)11yescharacteristic
176#131—22no—
177#131—22no—
178#131—52no—
179#131—52no—
180#131—101no—
181#131—101no—
182C2×M16—21no—
183C2×M16—51no—
184C2×M16—101no—
185C2×M16C2×AGL(1,𝔽5)11yescharacteristic
186C22×C8—21no—
187C22×C8—51no—
188C22×C8—101no—
189C22×C8C2×AGL(1,𝔽5)11yescharacteristic
190C4×Q8—51no—
191C4×Q8—51no—
192C4×D4—51no—
193C4×D4—51no—
194C4×D4—101no—
195C4×D4—101no—
196#117—51no—
197#117—101no—
198C2×C42—51no—
199C2×C42—101no—
200M32—102no—
201M32—102no—
202C2×C16—102no—
203C2×C16—102no—
204C2×C16—102no—
205C2×C16—102no—
206#97—101no—
207#97—101no—
208#97—101no—
209C4×C8—51no—
210C4×C8—51no—
211C4×C8—51no—
212C4×C8—51no—
213C4×C8—101no—
214C4×C8—101no—
215C4×C8—101no—
216C22×C5—21no—
217C22×C5—21no—
218C22×C5—22no—
219C22×C5—41no—
220C22×C5—41no—
221C22×C5C2×C22⋊C811yescharacteristic
222C22×C5#42311yescharacteristic
223C22×C5#43211yescharacteristic
224C4×C5—22no—
225C4×C5#38011yescharacteristic
226C4×C5#40711yescharacteristic
227C4×C5C2×C4⋊C811yescharacteristic
228C4×C5#43111yescharacteristic
229Dic5—21no—
230Dic5—21no—
231Dic5—21no—
232Dic5—41no—
233Dic5—41no—
234Dic5#35012yescomplemented
235#41—21no—
236#41—21no—
237#41C4⋊AGL(1,𝔽5)12yes—
238#41#70412yes—
239C2×Q8D5⋊C811yescharacteristic
240C2×D4—21no—
241C2×D4D5⋊C811yescharacteristic
242C22×C4—21no—
243C22×C4—51no—
244C22×C4—51no—
245C22×C4—101no—
246C22×C4—101no—
247C22×C4C22×AGL(1,𝔽5)11yescharacteristic
248M16—24no—
249M16—21no—
250M16—52no—
251M16—102no—
252M16—102no—
253M16—101no—
254M16#70412yes—
255C2×C8—24no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—51no—
260C2×C8—51no—
261C2×C8—51no—
262C2×C8—51no—
263C2×C8—51no—
264C2×C8—51no—
265C2×C8—102no—
266C2×C8—102no—
267C2×C8—101no—
268C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
269C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
270C4⋊C4—51no—
271C4⋊C4—51no—
272C4⋊C4—101no—
273C4⋊C4—101no—
274C22⋊C4—101no—
275C22⋊C4—101no—
276C22⋊C4—101no—
277C42—51no—
278C42—51no—
279C42—51no—
280C42—51no—
281C42—101no—
282C42—101no—
283C42—101no—
284C16—202no—
285C16—202no—
286C2×C5—21no—
287C2×C5—21no—
288C2×C5—42no—
289C2×C5#179711yescharacteristic
290C2×C5C2×#35011yescharacteristic
291C2×C5#211711yescharacteristic
292C23—21no—
293C23D5⋊M1611yescharacteristic
294Q8—21no—
295Q8#400412yes—
296D4—22no—
297D4—22no—
298D4—21no—
299D4#400412yes—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—51no—
304C2×C4—51no—
305C2×C4—51no—
306C2×C4—51no—
307C2×C4—102no—
308C2×C4—101no—
309C2×C4—101no—
310C2×C4—202no—
311C2×C4—201no—
312C2×C4—202no—
313C2×C4C2×D5⋊C811yescharacteristic
314C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
315C2×C4#413011yescharacteristic
316C2×C4C2×#70411yescharacteristic
317C2×C4C2×#70411yescharacteristic
318C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
319C8—21no—
320C8—22no—
321C8—21no—
322C8—51no—
323C8—51no—
324C8—51no—
325C8—51no—
326C8—102no—
327C5#1278711yescharacteristic, complemented, Sylow
328C22—21no—
329C22—21no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22D5⋊(C22⋊C8)11yescharacteristic
334C22#6575711yescharacteristic
335C22#6575811yescharacteristic
336C4—22no—
337C4—52no—
338C4—101no—
339C4—101no—
340C4—101no—
341C4—201no—
342C4—201no—
343C4C2×#400411yescharacteristic
344C4#6575411yescharacteristic
345C4#6576511yescharacteristic
346C4#6579811yescharacteristic
347C2—21no—
348C2—21no—
349C2—42no—
350C2D5⋊#35011yescharacteristic
351C2#1060477611yescharacteristic
352C2#1060490011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×#131C4
socleC22×C5C2×C22⋊C8
prime radicalC2×C5×#41C2×C4
cosocleC22×#168C23
hypercenterC2×#131AGL(1,𝔽5)
hypocenterC5#12787
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
3. #10604708C2semidirect
4. C2×#64888C2semidirect
5. #10598796C2semidirect
234. Dic5#350semidirect
327. C5#12787semidirect

Maximal subgroups

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

subgroupindex
Dic5×#1312
C2×#649322
#106047082
C2×#648882
#105987962
#127875