Finite Group Databasebeta

← #10617291

Subgroups — #10617291

Order 640.

502 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4131C211yesmaximal, characteristic, complemented
2C2×D5⋊M16C211yesmaximal, characteristic, complemented
3#65990C211yesmaximal, characteristic
4#65775C211yesmaximal, characteristic, complemented
5C2×#4003C211yesmaximal, characteristic, complemented
6#65705C211yesmaximal, characteristic, complemented
7#65704C211yesmaximal, characteristic, complemented
8#65704C211yesmaximal, characteristic, complemented
9#65702C211yesmaximal, characteristic, complemented
10#65696C211yesmaximal, characteristic, complemented
11#65695C211yesmaximal, characteristic, complemented
12#65694C211yesmaximal, characteristic, complemented
13#65693C211yesmaximal, characteristic, complemented
14#65692C211yesmaximal, characteristic, complemented
15#65691C211yesmaximal, characteristic, complemented
16C2×#711C2211yescharacteristic
17C22×C4×D5C2211yescharacteristic
18C2×#704C2211yescharacteristic
19C2×#704C2211yescharacteristic
20C2×#704C2211yescharacteristic, complemented
21C22×#170C2211yescharacteristic
22C22×#170C2211yescharacteristic
23C22×#170C2211yescharacteristic, complemented
24#4131—24no—
25D5⋊M16—24no—
26C2×#700C2211yescharacteristic
27C2×#700C2211yescharacteristic
28C2×#700C2211yescharacteristic, complemented
29C2×D5⋊C8C2211yescharacteristic
30C2×D5⋊C8C2211yescharacteristic
31C2×D5⋊C8C2211yescharacteristic, complemented
32C5×#123C411yescharacteristic
33#4083C411yescharacteristic
34#4075C411yescharacteristic
35#4042C411yescharacteristic
36#4042C411yescharacteristic
37#4039C2211yescharacteristic
38#4039C2211yescharacteristic
39#4030C411yescharacteristic
40#4030C411yescharacteristic
41#4028C411yescharacteristic
42#4027C2211yescharacteristic
43#4027C2211yescharacteristic
44#4023C2211yescharacteristic
45C22⋊#170C2211yescharacteristic, complemented
46C22⋊#170C2211yescharacteristic, complemented
47#4004C2211yescharacteristic, complemented
48#4004C2211yescharacteristic, complemented
49#4003C2211yescharacteristic
50#4003C2211yescharacteristic
51#4003C2211yescharacteristic
52#4003C2211yescharacteristic
53#4003C2211yescharacteristic, complemented
54#4003C2211yescharacteristic, complemented
55#4002C2211yescharacteristic, complemented
56#4002C2211yescharacteristic, complemented
57C4⋊#170C2211yescharacteristic, complemented
58C4⋊#170C2211yescharacteristic, complemented
59C4×#170C2211yescharacteristic, complemented
60C4×#170C2211yescharacteristic, complemented
61#2933—51nomaximal, Sylow
62C23×D5C2×C411yescharacteristic
63C2×C5×D4C2×C411yescharacteristic
64C22×C4×C5C2×C411yescharacteristic
65C2×C22⋊D5C2×C411yescharacteristic
66C2×C22⋊D5C2×C411yescharacteristic
67C2×C22⋊D5C2×C411yescharacteristic
68C2×C22⋊D5C2×C411yescharacteristic
69C22×Dic5C2311yescharacteristic
70C22×Dic5C2311yescharacteristic
71#711—22no—
72#711—22no—
73C2×D20C2×C411yescharacteristic
74C2×D20C2×C411yescharacteristic
75C2×C4×D5—22no—
76C2×C4×D5—22no—
77C2×C4×D5C2×C411yescharacteristic
78C2×C4×D5C2×C411yescharacteristic
79C2×C4×D5C2311yescharacteristic
80C2×C4×D5C2311yescharacteristic
81C2×C4×D5C2311yescharacteristic
82C2×Dic10C2×C411yescharacteristic
83#704—22no—
84#704—22no—
85#704D414yescomplemented
86C2×#170—22no—
87C2×#170—22no—
88C2×#170—22no—
89C2×#170C2311yescharacteristic
90C2×#170C2311yescharacteristic
91C2×#170C2311yescharacteristic
92C2×#170C2311yescharacteristic
93C2×#170C2311yescharacteristic
94C2×#170C2311yescharacteristic
95C2×#170C2311yescharacteristic
96C2×#170C2311yescharacteristic
97#700—22no—
98#700—22no—
99#700—22no—
100D5⋊C8—22no—
101D5⋊C8—22no—
102D5⋊C8—22no—
103C5×C4⋊C4C2×C411yescharacteristic
104C5×C4⋊C4C2×C411yescharacteristic
105C5×C22⋊C4C2×C411yescharacteristic
106C5×C22⋊C4C2×C411yescharacteristic
107C5×C22⋊C4C2×C411yescharacteristic
108C22⋊Dic5C2×C411yescharacteristic
109#685C2×C411yescharacteristic
110#685C2×C411yescharacteristic
111#685C2×C411yescharacteristic
112#685C2×C411yescharacteristic
113#685C2×C411yescharacteristic
114#685C2×C411yescharacteristic
115#683C2×C411yescharacteristic
116#683C2×C411yescharacteristic
117#683C2×C411yescharacteristic
118#683C2×C411yescharacteristic
119C4×Dic5C2311yescharacteristic
120C4×Dic5C2311yescharacteristic
121C2×#131—51no—
122C22×M16—51no—
123#525—51no—
124#436—51no—
125#436—51no—
126#435—51no—
127#435—51no—
128#435—51no—
129#435—51no—
130C8×D4—51no—
131C8×D4—51no—
132#424—51no—
133#408—51no—
134C2×C22⋊C8—51no—
135#405—51no—
136C23×C5C22×C411yescharacteristic
137C23×C5C22×C411yescharacteristic
138C22×D5—22no—
139C22×D5—22no—
140C22×D5—41no—
141C22×D5C22×C411yescharacteristic
142C22×D5C22×C411yescharacteristic
143C22×D5C22×C411yescharacteristic
144C5×D4—22no—
145C2×C4×C5—22no—
146C2×C4×C5C22×C411yescharacteristic
147C2×C4×C5C22×C411yescharacteristic
148C2×C4×C5C22×C411yescharacteristic
149C2×C4×C5C22×C411yescharacteristic
150C2×C4×C5C22×C411yescharacteristic
151C22⋊D5—22no—
152C22⋊D5—22no—
153C22⋊D5—22no—
154C22⋊D5—41no—
155C2×Dic5—21no—
156C2×Dic5—21no—
157C2×Dic5C22×C411yescharacteristic
158C2×Dic5C22×C411yescharacteristic
159C2×Dic5C22×C411yescharacteristic
160C2×Dic5C22×C411yescharacteristic
161C2×Dic5C2×D412yes—
162C2×Dic5#4112yes—
163C2×Dic5C2411yescharacteristic
164D20—22no—
165D20—41no—
166C4×D5—22no—
167C4×D5—22no—
168C4×D5—21no—
169C4×D5—21no—
170C4×D5—21no—
171C4×D5—21no—
172C4×D5—21no—
173C4×D5—21no—
174Dic10—22no—
175#170—21no—
176#170—21no—
177#170—21no—
178#170—21no—
179#170—21no—
180#170—21no—
181#170C2×D412yes—
182#170C2×D412yes—
183C2×#41—51no—
184C23×C4—51no—
185#131—104no—
186C2×M16—51no—
187C2×M16—51no—
188C2×M16—51no—
189C2×M16—51no—
190C2×M16—51no—
191C2×M16—51no—
192C2×M16—104no—
193C22×C8—51no—
194C22×C8—51no—
195C22×C8—51no—
196C22×C8—51no—
197C22×C8—51no—
198C22×C8—51no—
199#123—51no—
200#123AGL(1,𝔽5)11yescharacteristic
201C22⋊Q8—51no—
202C22⋊Q8—51no—
203#121—51no—
204#121—51no—
205#120—51no—
206#120—51no—
207C4×D4—51no—
208C4×D4—51no—
209C4×D4—51no—
210C4×D4—51no—
211#117—51no—
212C4⋊C8—51no—
213C4⋊C8—51no—
214C4⋊C8—51no—
215C4⋊C8—51no—
216C22⋊C8—51no—
217C22⋊C8—51no—
218C22⋊C8—51no—
219C22⋊C8—51no—
220C22⋊C8—51no—
221C22⋊C8—51no—
222C22⋊C8—51no—
223C22⋊C8—51no—
224#97—51no—
225#97—51no—
226C4×C8—51no—
227C4×C8—51no—
228C22×C5—21no—
229C22×C5—21no—
230C22×C5—21no—
231C22×C5—21no—
232C22×C5—21no—
233C22×C5C4×D412yes—
234C22×C5C23×C411yescharacteristic
235C2×D5—21no—
236C2×D5—21no—
237C2×D5—21no—
238C2×D5—21no—
239C2×D5—21no—
240C2×D5—21no—
241C2×D5—21no—
242C2×D5—21no—
243C2×D5—44no—
244C2×D5#13112yescomplemented
245C4×C5—21no—
246C4×C5—21no—
247C4×C5—21no—
248C4×C5—21no—
249C4×C5—21no—
250Dic5—21no—
251Dic5—21no—
252Dic5—21no—
253Dic5C4×D412yes—
254Dic5C22×D411yescharacteristic
255Dic5C2×#4111yescharacteristic
256C24—51no—
257#41—102no—
258#41—102no—
259C2×Q8—51no—
260C2×D4—51no—
261C2×D4—51no—
262C2×D4—51no—
263C2×D4—51no—
264C2×D4—51no—
265C2×D4—51no—
266C2×D4C2×AGL(1,𝔽5)11yescharacteristic
267C22×C4—51no—
268C22×C4—51no—
269C22×C4—51no—
270C22×C4—51no—
271C22×C4—51no—
272C22×C4—51no—
273C22×C4—51no—
274C22×C4—102no—
275C22×C4—102no—
276C22×C4C2×AGL(1,𝔽5)11yescharacteristic
277M16—54no—
278M16—102no—
279M16—102no—
280M16—102no—
281M16—102no—
282M16—102no—
283C2×C8—51no—
284C2×C8—51no—
285C2×C8—51no—
286C2×C8—51no—
287C2×C8—51no—
288C2×C8—51no—
289C2×C8—51no—
290C2×C8—51no—
291C2×C8—102no—
292C2×C8—102no—
293C2×C8—102no—
294C2×C8—102no—
295C2×C8—102no—
296C2×C8—102no—
297C4⋊C4—51no—
298C4⋊C4—51no—
299C4⋊C4—51no—
300C4⋊C4—51no—
301C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
302C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
303C22⋊C4—51no—
304C22⋊C4—51no—
305C22⋊C4—51no—
306C22⋊C4—51no—
307C22⋊C4—51no—
308C22⋊C4—51no—
309C22⋊C4—51no—
310C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
311C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
312C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
313C42—51no—
314C42—51no—
315C2×C5—22no—
316C2×C5—41no—
317C2×C5C2×C4×D411yescharacteristic
318C2×C5C2×#13111yescharacteristic
319C2×C5#56811yescharacteristic
320D5—22no—
321D5—41no—
322D5—41no—
323C23—51no—
324C23—51no—
325C23—51no—
326C23—102no—
327C23—102no—
328C23—201no—
329C23C22×AGL(1,𝔽5)11yescharacteristic
330C23C22×AGL(1,𝔽5)11yescharacteristic
331Q8—102no—
332D4—22no—
333D4—102no—
334D4—102no—
335D4—102no—
336D4—102no—
337D4—201no—
338D4—201no—
339C2×C4—22no—
340C2×C4—52no—
341C2×C4—52no—
342C2×C4—51no—
343C2×C4—51no—
344C2×C4—51no—
345C2×C4—51no—
346C2×C4—51no—
347C2×C4—101no—
348C2×C4—101no—
349C2×C4—101no—
350C2×C4—101no—
351C2×C4—101no—
352C2×C4—102no—
353C2×C4—102no—
354C2×C4—101no—
355C2×C4—101no—
356C2×C4—101no—
357C2×C4C22×AGL(1,𝔽5)11yescharacteristic
358C2×C4C22×AGL(1,𝔽5)11yescharacteristic
359C2×C4C22×AGL(1,𝔽5)11yescharacteristic
360C2×C4C22×AGL(1,𝔽5)11yescharacteristic
361C2×C4C22×AGL(1,𝔽5)11yescharacteristic
362C8—52no—
363C8—52no—
364C8—101no—
365C8—101no—
366C8—101no—
367C8—101no—
368C8—101no—
369C8—101no—
370C5#293311yescharacteristic, complemented, Sylow
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—52no—
377C22—101no—
378C22—101no—
379C22—101no—
380C22—101no—
381C22—101no—
382C22—101no—
383C22—101no—
384C22—101no—
385C22—204no—
386C22D4×AGL(1,𝔽5)12yes—
387C22C23×AGL(1,𝔽5)11yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—51no—
394C4—51no—
395C4—52no—
396C4—101no—
397C4—101no—
398C4—101no—
399C2—22no—
400C2—41no—
401C2—102no—
402C2—201no—
403C2—201no—
404C2C2×D4×AGL(1,𝔽5)11yescharacteristic
405C2D5⋊#13111yescharacteristic
406C2#6626411yescharacteristic
subgroupG/H
center, FrattiniC22C23×AGL(1,𝔽5)
commutator, socleC22×C5C23×C4
FittingC5×#123C4
prime radical#65990C2
cosocleC2×Dic5C24
hypercenter#123AGL(1,𝔽5)
hypocenterC5#2933
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#4131C2semidirect
2. C2×D5⋊M16C2semidirect
4. #65775C2semidirect
5. C2×#4003C2semidirect
6. #65705C2semidirect
7. #65704C2semidirect
8. #65704C2semidirect
9. #65702C2semidirect
10. #65696C2semidirect
11. #65695C2semidirect
12. #65694C2semidirect
13. #65693C2semidirect
14. #65692C2semidirect
15. #65691C2semidirect
20. C2×#704C22semidirect
23. C22×#170C22semidirect
28. C2×#700C22semidirect
31. C2×D5⋊C8C22semidirect
45. C22⋊#170C22semidirect
46. C22⋊#170C22semidirect
47. #4004C22semidirect
48. #4004C22semidirect
53. #4003C22semidirect
54. #4003C22semidirect
55. #4002C22semidirect
56. #4002C22semidirect
57. C4⋊#170C22semidirect
58. C4⋊#170C22semidirect
59. C4×#170C22semidirect
60. C4×#170C22semidirect
85. #704D4semidirect
244. C2×D5#131semidirect
370. C5#2933semidirect

Maximal subgroups

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

subgroupindex
C2×#41312
C2×D5⋊M162
#659902
#657752
C2×#40032
#657052
#657042
#657022
#656962
#656952
#656942
#656932
#656922
#656912
#29335