Finite Group Databasebeta

← #13043556

Subgroups — #13043556

Order 1280.

646 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65791C211yesmaximal, characteristic, complemented
2C2×#65725C211yesmaximal, characteristic, complemented
3#10610720C211yesmaximal, characteristic
4#10605009C211yesmaximal, characteristic, complemented
5#10604745C211yesmaximal, characteristic, complemented
6#10604370C211yesmaximal, characteristic, complemented
7#10604366C211yesmaximal, characteristic, complemented
8#10604000C214yesmaximal, complemented
9#10603999C214yesmaximal, complemented
10#66156C411yescharacteristic
11C2×#4094C2211yescharacteristic
12C2×#4053C2211yescharacteristic
13#65791—21no—
14#65791—21no—
15#65791C2212yescomplemented
16#65791C2212yescomplemented
17C2×#3998—21no—
18C2×#3998C2211yescharacteristic
19C2×#3998C2211yescharacteristic
20C2×#3998C2211yescharacteristic
21C22×#674—21no—
22C22×#674C2211yescharacteristic
23#65725—21no—
24#65725—21no—
25#65725C2212yescomplemented
26#65725C2212yescomplemented
27C2×#3990—21no—
28C2×D5⋊C16—21no—
29C5×#421C411yescharacteristic
30#65413C411yescharacteristic
31#65294C411yescharacteristic
32#65286C2211yescharacteristic
33#65113C2214yes—
34#65112C414yes—
35#64932C2214yescomplemented
36#64898C2214yescomplemented
37#64861C2214yescomplemented
38#64859C2212yescomplemented
39C4×#674C2212yescomplemented
40#33441—51nomaximal, Sylow
41C2×C5×#41C2×C411yescharacteristic
42C2×#709C2×C411yescharacteristic
43C2×C5×M16C2×C411yescharacteristic
44C5×#117C2×C411yescharacteristic
45#4097C812yes—
46#4096C2×C414yes—
47#4095C812yes—
48#4094—21no—
49#4094—21no—
50#4094C2×C412yes—
51#4094C2312yes—
52#4088C812yes—
53#4078C812yes—
54C2×#681—21no—
55C2×#681C2×C411yescharacteristic
56C2×#681C2×C411yescharacteristic
57C22×#168—21no—
58C22×#168C2311yescharacteristic
59#4053—21no—
60#4053—21no—
61#4053C2×C412yes—
62#4053C2312yes—
63C2×#676—21no—
64C2×C8×D5—21no—
65#3998—21no—
66#3998—21no—
67#3998—21no—
68#3998—21no—
69#3998—22no—
70#3998—22no—
71#3998C2312yes—
72#3998C2312yes—
73C2×#674—21no—
74C2×#674—21no—
75C2×#674—22no—
76C2×#674—22no—
77C2×#674D411yescharacteristic
78C2×#674D411yescharacteristic
79C2×#674D411yescharacteristic
80C2×#674D411yescharacteristic
81C2×#674C2312yes—
82C2×#674C2311yescharacteristic
83C2×#674C2311yescharacteristic
84#3990—22no—
85#3990—22no—
86D5⋊C16—22no—
87D5⋊C16—22no—
88C5×#104C2×C414yes—
89#3954C2×C414yes—
90#3937C2×C414yes—
91#3935C2×C412yes—
92C4×#168C2312yes—
93C2×#504—51no—
94C2×#504—51no—
95#2955—51no—
96#2171—54no—
97#2170—54no—
98#2153—51no—
99#2117—51no—
100#2117—51no—
101#2108—51no—
102C5×#41—21no—
103C5×#41—21no—
104C5×#41C2×C812yes—
105C5×#41C22×C412yes—
106C2×C5×Q8C2×C811yescharacteristic
107C2×C5×D4—21no—
108C2×C5×D4C2×C811yescharacteristic
109C22×C4×C5—21no—
110C22×C4×C5C22×C411yescharacteristic
111C2×C22⋊D5—21no—
112#709—21no—
113#709—21no—
114#709C2×C812yes—
115#709C22×C412yes—
116C2×D20C2×C811yescharacteristic
117C2×C4×D5—21no—
118C2×Dic10C2×C811yescharacteristic
119C5×M16—21no—
120C5×M16C22×C412yes—
121C2×C5×C8—21no—
122C5×C4⋊C4—21no—
123C5×C22⋊C4—21no—
124C42×C5C22×C412yes—
125#689C2×C814yes—
126#688C2×C814yes—
127#687C2×C814yes—
128#686C2×C814yes—
129#681—21no—
130#681—22no—
131#681—22no—
132#681C2×C812yes—
133#681C2×C812yes—
134#681C22×C412yes—
135C2×#168—21no—
136C2×#168—22no—
137C2×#168—22no—
138C2×#168C22×C411yescharacteristic
139C2×#168C22×C412yes—
140C2×#168C2×D411yescharacteristic
141C2×#168C2×D411yescharacteristic
142C2×#168#4111yescharacteristic
143C2×#168#4111yescharacteristic
144C2×#168C2411yescharacteristic
145#676—22no—
146#676—22no—
147C8×D5—22no—
148C8×D5—22no—
149#674—22no—
150#674—22no—
151#674—22no—
152#674C2×D411yescharacteristic
153#674C2×D411yescharacteristic
154#674C2×D411yescharacteristic
155#674C2×D411yescharacteristic
156#575—51no—
157C2×#131—51no—
158C2×#131—51no—
159#504—52no—
160#504—52no—
161#504—52no—
162#504—52no—
163#504—101no—
164#504—101no—
165#504—101no—
166#504—101no—
167C2×M32—51no—
168C2×M32—51no—
169C2×M32—51no—
170C2×M32—101no—
171C2×M32—101no—
172C22×C16—51no—
173C22×C16—101no—
174C22×C16—101no—
175#444—54no—
176#443—54no—
177#430—51no—
178#421—51no—
179#421AGL(1,𝔽5)11yescharacteristic
180#405—51no—
181#364—54no—
182#350—54no—
183#350—54no—
184#346—52no—
185C4×C16—52no—
186C23×C5—21no—
187C23×C5#13111yescharacteristic
188C22×D5—21no—
189C5×Q8—21no—
190C5×Q8C22×C812yes—
191C5×D4—22no—
192C5×D4—22no—
193C5×D4—21no—
194C5×D4C22×C812yes—
195C2×C4×C5—21no—
196C2×C4×C5—22no—
197C2×C4×C5—22no—
198C2×C4×C5—22no—
199C2×C4×C5C4×D411yescharacteristic
200C2×C4×C5C4×D411yescharacteristic
201C2×C4×C5C22×C811yescharacteristic
202C2×C4×C5C22×C811yescharacteristic
203C2×C4×C5#13111yescharacteristic
204C2×C4×C5C23×C411yescharacteristic
205C22⋊D5—22no—
206C22⋊D5—22no—
207C2×Dic5—21no—
208D20—21no—
209D20C22×C812yes—
210C4×D5—22no—
211C4×D5—22no—
212Dic10—21no—
213Dic10C22×C812yes—
214C5×C8—22no—
215#168—22no—
216#168C4×D411yescharacteristic
217#168C4×D411yescharacteristic
218#168C22×C814yes—
219#168C22×D411yescharacteristic
220#168C2×#4111yescharacteristic
221C2×#41—51no—
222C2×#41C2×AGL(1,𝔽5)11yescharacteristic
223#137—52no—
224#137—52no—
225AGL(1,ℤ/8)—52no—
226AGL(1,ℤ/8)—52no—
227#135—54no—
228#131—52no—
229#131—52no—
230#131—52no—
231#131—52no—
232#131—101no—
233#131—101no—
234#131—101no—
235#131—101no—
236C2×M16—51no—
237C2×M16—51no—
238C2×M16—101no—
239C2×M16—101no—
240C2×M16C2×AGL(1,𝔽5)11yescharacteristic
241C22×C8—51no—
242C22×C8—101no—
243C22×C8—101no—
244#117C2×AGL(1,𝔽5)11yescharacteristic
245M32—52no—
246M32—52no—
247M32—102no—
248M32—102no—
249M32—102no—
250M32—102no—
251M32—101no—
252M32—101no—
253M32—101no—
254M32—101no—
255C2×C16—51no—
256C2×C16—51no—
257C2×C16—51no—
258C2×C16—51no—
259C2×C16—51no—
260C2×C16—51no—
261C2×C16—52no—
262C2×C16—102no—
263C2×C16—102no—
264C2×C16—102no—
265C2×C16—102no—
266C2×C16—101no—
267C2×C16—101no—
268#108—54no—
269#104—54no—
270#104C2×AGL(1,𝔽5)14yes—
271#97—52no—
272C4×C8—52no—
273C22×C5—22no—
274C22×C5—41no—
275C22×C5—42no—
276C22×C5C8×D411yescharacteristic
277C22×C5C8×D411yescharacteristic
278C22×C5C2×#13111yescharacteristic
279C2×D5—22no—
280C2×D5—42no—
281C4×C5—22no—
282C4×C5—42no—
283C4×C5C8×D411yescharacteristic
284C4×C5C8×D411yescharacteristic
285C4×C5C2×C4×D411yescharacteristic
286C4×C5C23×C811yescharacteristic
287Dic5—22no—
288#41—21no—
289#41—21no—
290#41—52no—
291#41—52no—
292#41—101no—
293#41—101no—
294#41D5⋊C812yes—
295#41C22×AGL(1,𝔽5)12yes—
296C2×Q8—51no—
297C2×Q8D5⋊C811yescharacteristic
298C2×D4—21no—
299C2×D4—51no—
300C2×D4—101no—
301C2×D4D5⋊C811yescharacteristic
302C22×C4—21no—
303C22×C4—101no—
304C22×C4C22×AGL(1,𝔽5)11yescharacteristic
305Q16—54no—
306SD16—54no—
307SD16—54no—
308D8—54no—
309M16—21no—
310M16—52no—
311M16—52no—
312M16—52no—
313M16—102no—
314M16—102no—
315M16—102no—
316M16—102no—
317M16—101no—
318M16C22×AGL(1,𝔽5)12yes—
319C2×C8—21no—
320C2×C8—51no—
321C2×C8—51no—
322C2×C8—51no—
323C2×C8—51no—
324C2×C8—51no—
325C2×C8—52no—
326C2×C8—51no—
327C2×C8—102no—
328C2×C8—102no—
329C2×C8—102no—
330C2×C8—102no—
331C2×C8—101no—
332C4⋊C4—21no—
333C22⋊C4—21no—
334C42C22×AGL(1,𝔽5)12yes—
335C16—51no—
336C16—51no—
337C16—51no—
338C16—51no—
339C16—102no—
340C16—102no—
341C16—102no—
342C2×C5—21no—
343C2×C5—21no—
344C2×C5—21no—
345C2×C5—42no—
346C2×C5C2×C8×D411yescharacteristic
347D5—42no—
348C23—21no—
349C23—101no—
350C23#413111yescharacteristic
351Q8—21no—
352Q8—52no—
353Q8—101no—
354Q8C2×D5⋊C812yes—
355D4—22no—
356D4—22no—
357D4—21no—
358D4—52no—
359D4—102no—
360D4—102no—
361D4—101no—
362D4C2×D5⋊C812yes—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—101no—
368C2×C4—102no—
369C2×C4—102no—
370C2×C4C2×D5⋊C811yescharacteristic
371C2×C4C2×D5⋊C811yescharacteristic
372C2×C4#413111yescharacteristic
373C2×C4D4×AGL(1,𝔽5)11yescharacteristic
374C2×C4D4×AGL(1,𝔽5)11yescharacteristic
375C2×C4C23×AGL(1,𝔽5)11yescharacteristic
376C8—22no—
377C8—54no—
378C8—51no—
379C8—51no—
380C8—51no—
381C8—51no—
382C8—102no—
383C5#3344111yescharacteristic, complemented, Sylow
384C22—22no—
385C22—41no—
386C22—42no—
387C22—102no—
388C22—202no—
389C22#6569211yescharacteristic
390C22#6569211yescharacteristic
391C22C2×#413111yescharacteristic
392C4—22no—
393C4—42no—
394C4—102no—
395C4#6569211yescharacteristic
396C4#6569211yescharacteristic
397C4C22×D5⋊C811yescharacteristic
398C4C2×D4×AGL(1,𝔽5)11yescharacteristic
399C2—21no—
400C2—21no—
401C2—21no—
402C2—42no—
403C2—202no—
404C2C2×#6569211yescharacteristic
subgroupG/H
centerC4C2×D4×AGL(1,𝔽5)
commutatorC4×C5C23×C8
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×#421C4
socleC2×C5C2×C8×D4
prime radical#66156C4
cosocleC2×#168C24
hypercenter#421AGL(1,𝔽5)
hypocenterC5#33441
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. C2×#65791C2semidirect
2. C2×#65725C2semidirect
4. #10605009C2semidirect
5. #10604745C2semidirect
6. #10604370C2semidirect
7. #10604366C2semidirect
8. #10604000C2semidirect
9. #10603999C2semidirect
15. #65791C22semidirect
16. #65791C22semidirect
25. #65725C22semidirect
26. #65725C22semidirect
35. #64932C22semidirect
36. #64898C22semidirect
37. #64861C22semidirect
38. #64859C22semidirect
39. C4×#674C22semidirect
383. C5#33441semidirect

Maximal subgroups

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

subgroupindex
C2×#657912
C2×#657252
#106107202
#106050092
#106047452
#106043702
#106043662
#106040002
#106039992
#334415