Finite Group Databasebeta

← #10608673

Subgroups — #10608673

Order 640.

454 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#394C211yesmaximal, characteristic
2#65510C211yesmaximal, characteristic
3#65509C211yesmaximal, characteristic
4#65270C211yesmaximal, characteristic, complemented
5#65267C211yesmaximal, characteristic, complemented
6#65241C211yesmaximal, characteristic, complemented
7#65241C211yesmaximal, characteristic, complemented
8#65234C211yesmaximal, characteristic, complemented
9#65234C211yesmaximal, characteristic, complemented
10#65234C211yesmaximal, characteristic, complemented
11#65233C211yesmaximal, characteristic, complemented
12#65231C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
14#64946C211yesmaximal, characteristic, complemented
15#64937C211yesmaximal, characteristic, complemented
16C22×C5×D4C2211yescharacteristic
17C23×Dic5C2211yescharacteristic
18C2×C5×C4⋊C4C2211yescharacteristic
19C2×C5×C22⋊C4C2211yescharacteristic
20C2×C5×C22⋊C4C2211yescharacteristic
21C2×C5×C22⋊C4C2211yescharacteristic
22C2×C5×C22⋊C4C2211yescharacteristic
23C2×C22⋊Dic5C2211yescharacteristic
24C2×C22⋊Dic5C2211yescharacteristic
25C2×C22⋊Dic5C2211yescharacteristic
26C2×C22⋊Dic5C2211yescharacteristic
27C2×C22⋊Dic5C2211yescharacteristic
28C2×C22⋊Dic5C2211yescharacteristic
29C2×C22⋊Dic5C2211yescharacteristic
30C2×C4⋊Dic5C2211yescharacteristic
31C2×#683C2211yescharacteristic
32C2×#683C2211yescharacteristic
33C2×#683C2211yescharacteristic
34C2×#683C2211yescharacteristic
35C2×C4×Dic5C2211yescharacteristic
36C2×C4×Dic5C2211yescharacteristic
37C2×C4×Dic5C2211yescharacteristic
38C2×C4×Dic5C2211yescharacteristic
39C5×#95C2211yescharacteristic
40#3963C2211yescharacteristic
41#3963C2211yescharacteristic
42#3963C2211yescharacteristic
43#3963C2211yescharacteristic
44#3963C2211yescharacteristic
45#3963C2211yescharacteristic
46#3963C2211yescharacteristic
47#3963C2211yescharacteristic
48#3963C2211yescharacteristic
49#3963C2211yescharacteristic
50#3963C2211yescharacteristic
51#2531—51nomaximal, Sylow
52C24×C5C2311yescharacteristic
53C24×C5C2311yescharacteristic
54C2×C5×D4—22no—
55C2×C5×D4—22no—
56C2×C5×D4—41no—
57C22×C4×C5C2311yescharacteristic
58C22×C4×C5C2311yescharacteristic
59C22×C4×C5C2311yescharacteristic
60C22×C4×C5C2311yescharacteristic
61C22×C4×C5C2311yescharacteristic
62C22×Dic5—22no—
63C22×Dic5—22no—
64C22×Dic5—41no—
65C22×Dic5C2311yescharacteristic
66C22×Dic5C2311yescharacteristic
67C22×Dic5C2311yescharacteristic
68C22×Dic5C2311yescharacteristic
69C22×Dic5C2311yescharacteristic
70C22×Dic5C2311yescharacteristic
71C22×Dic5C2311yescharacteristic
72C22×Dic5C2311yescharacteristic
73C5×C4⋊C4—22no—
74C5×C22⋊C4—22no—
75C5×C22⋊C4—41no—
76C5×C22⋊C4—41no—
77C5×C22⋊C4—41no—
78C22⋊Dic5—22no—
79C22⋊Dic5—22no—
80C22⋊Dic5—22no—
81C22⋊Dic5—22no—
82C22⋊Dic5—22no—
83C22⋊Dic5—41no—
84C22⋊Dic5—41no—
85C4⋊Dic5—41no—
86#683—22no—
87#683—41no—
88#683—41no—
89#683—41no—
90C4×Dic5—22no—
91C4×Dic5—22no—
92C4×Dic5—22no—
93C4×Dic5—41no—
94#398—51no—
95#397—51no—
96#397—51no—
97#394D511yescharacteristic
98#390—51no—
99#388—51no—
100#388—51no—
101#388—51no—
102#388—51no—
103#387—51no—
104#387—51no—
105#386—51no—
106#380—51no—
107C4×C22⋊C4—51no—
108#376—51no—
109C23×C5—21no—
110C23×C5—21no—
111C23×C5—21no—
112C23×C5—21no—
113C23×C5—21no—
114C23×C5—21no—
115C23×C5—21no—
116C23×C5—21no—
117C23×C5—21no—
118C23×C5—21no—
119C23×C5—21no—
120C23×C5—21no—
121C23×C5—21no—
122C23×C5#4112yes—
123C23×C5C2411yescharacteristic
124C5×D4—44no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5#4112yes—
140C2×Dic5—21no—
141C2×Dic5—21no—
142C2×Dic5—21no—
143C2×Dic5—21no—
144C2×Dic5—21no—
145C2×Dic5—21no—
146C2×Dic5—21no—
147C2×Dic5—21no—
148C2×Dic5—21no—
149C2×Dic5—21no—
150C2×Dic5—21no—
151C2×Dic5—21no—
152C2×Dic5—21no—
153C2×Dic5—21no—
154C2×Dic5—21no—
155C2×Dic5—21no—
156C2×Dic5—21no—
157C2×Dic5—21no—
158C2×Dic5—21no—
159C2×Dic5—21no—
160C2×Dic5—21no—
161C2×Dic5—44no—
162C2×Dic5#4112yes—
163C2×Dic5#4112yes—
164C2×Dic5#4112yes—
165C22×D4C2×D511yescharacteristic
166C23×C4—51no—
167C2×C4⋊C4—51no—
168C2×C4⋊C4—51no—
169C2×C4⋊C4—51no—
170C2×C4⋊C4—51no—
171C2×C4⋊C4—51no—
172C2×C4⋊C4C2×D511yescharacteristic
173C2×C22⋊C4—51no—
174C2×C22⋊C4—51no—
175C2×C22⋊C4—51no—
176C2×C22⋊C4—51no—
177C2×C22⋊C4—51no—
178C2×C22⋊C4—51no—
179C2×C22⋊C4—51no—
180C2×C22⋊C4C2×D511yescharacteristic
181C2×C22⋊C4C2×D511yescharacteristic
182C2×C22⋊C4C2×D511yescharacteristic
183C2×C22⋊C4C2×D511yescharacteristic
184C2×C42—51no—
185C2×C42—51no—
186C2×C42—51no—
187C2×C42—51no—
188#95—51no—
189#95—51no—
190#95—51no—
191#95—51no—
192#95—51no—
193#95—51no—
194#95—51no—
195#95—51no—
196#95—51no—
197#95—51no—
198#95—51no—
199#95C2×D511yescharacteristic
200C22×C5—22no—
201C22×C5—22no—
202C22×C5—22no—
203C22×C5—41no—
204C22×C5—41no—
205C22×C5—41no—
206C22×C5—41no—
207C22×C5—41no—
208C22×C5—41no—
209C22×C5—41no—
210C22×C5—41no—
211C22×C5—41no—
212C22×C5—41no—
213C22×C5—41no—
214C22×C5C2×#4111yescharacteristic
215C22×C5C2×#4111yescharacteristic
216C22×C5C2×#4111yescharacteristic
217C22×C5C2×#4111yescharacteristic
218C22×C5C2×#4111yescharacteristic
219C22×C5H(5,𝔽2)11yescharacteristic
220C22×C5H(5,𝔽2)11yescharacteristic
221C4×C5—22no—
222C4×C5—41no—
223C4×C5—41no—
224C4×C5—41no—
225C4×C5—41no—
226Dic5—22no—
227Dic5—22no—
228Dic5—22no—
229Dic5—41no—
230Dic5—41no—
231Dic5—41no—
232Dic5—41no—
233Dic5—41no—
234C24C22×D511yescharacteristic
235C24C22×D511yescharacteristic
236C2×D4—22no—
237C2×D4—22no—
238C2×D4—41no—
239C22×C4—51no—
240C22×C4—51no—
241C22×C4—51no—
242C22×C4—51no—
243C22×C4—51no—
244C22×C4—51no—
245C22×C4—51no—
246C22×C4—51no—
247C22×C4—102no—
248C22×C4—102no—
249C22×C4—201no—
250C22×C4C22×D511yescharacteristic
251C22×C4C22×D511yescharacteristic
252C22×C4C22×D511yescharacteristic
253C22×C4C22×D511yescharacteristic
254C22×C4C22×D511yescharacteristic
255C4⋊C4—22no—
256C4⋊C4—102no—
257C4⋊C4—201no—
258C4⋊C4—201no—
259C4⋊C4—201no—
260C4⋊C4—201no—
261C22⋊C4—22no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—102no—
266C22⋊C4—102no—
267C22⋊C4—102no—
268C22⋊C4—102no—
269C22⋊C4—102no—
270C22⋊C4—201no—
271C22⋊C4—201no—
272C42—102no—
273C42—102no—
274C42—102no—
275C42—201no—
276C2×C5—42no—
277C2×C5—81no—
278C2×C5#52911yescharacteristic
279C2×C5#52911yescharacteristic
280C2×C5#54011yescharacteristic
281C2×C5#55111yescharacteristic
282C2×C5#55111yescharacteristic
283C2×C5#55311yescharacteristic
284C2×C5#55511yescharacteristic
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23#71112yes—
299C23C23×D511yescharacteristic
300D4—44no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—52no—
316C2×C4—52no—
317C2×C4—52no—
318C2×C4—101no—
319C2×C4—101no—
320C2×C4—101no—
321C2×C4—101no—
322C2×C4—101no—
323C2×C4—101no—
324C2×C4—101no—
325C2×C4—101no—
326C2×C4—101no—
327C2×C4—101no—
328C2×C4—101no—
329C2×C4—101no—
330C2×C4—101no—
331C2×C4—101no—
332C2×C4—101no—
333C2×C4—101no—
334C2×C4—101no—
335C2×C4—101no—
336C2×C4—101no—
337C2×C4—101no—
338C2×C4—101no—
339C2×C4—204no—
340C2×C4#71112yes—
341C5#253111yescharacteristic, complemented, Sylow
342C22—22no—
343C22—22no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22C2×#71111yescharacteristic
357C22C2×#71111yescharacteristic
358C22#414411yescharacteristic
359C22#414411yescharacteristic
360C22D5×#4111yescharacteristic
361C22D5×#4111yescharacteristic
362C22D5×#4111yescharacteristic
363C4—22no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—102no—
369C4—102no—
370C4—102no—
371C4—201no—
372C4—201no—
373C4—201no—
374C4—201no—
375C4—201no—
376C2—42no—
377C2—81no—
378C2#6592111yescharacteristic
379C2#6593511yescharacteristic
380C2#6594911yescharacteristic
381C2#6595011yescharacteristic
382C2#6598311yescharacteristic
383C2#6599311yescharacteristic
384C2#6601411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#394C2
prime radicalC22×C5×D4C22
hypercenter#394D5
hypocenterC5#2531
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
4. #65270C2semidirect
5. #65267C2semidirect
6. #65241C2semidirect
7. #65241C2semidirect
8. #65234C2semidirect
9. #65234C2semidirect
10. #65234C2semidirect
11. #65233C2semidirect
12. #65231C2semidirect
13. C22⋊C4×Dic5C2semidirect
14. #64946C2semidirect
15. #64937C2semidirect
341. C5#2531semidirect

Maximal subgroups

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

subgroupindex
C5×#3942
#655102
#655092
#652702
#652672
#652412
#652342
#652332
#652312
C22⋊C4×Dic52
#649462
#649372
#25315