Finite Group Databasebeta

← C5×#3118 #10616713

Subgroups — C5×#3118 #10616713

Order 640.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#542C211yesmaximal, characteristic, complemented
2C5×#518C211yesmaximal, characteristic, complemented
3C5×#485C211yesmaximal, characteristic, complemented
4C5×#482C211yesmaximal, characteristic, complemented
5C5×#476C211yesmaximal, characteristic, complemented
6C5×#474C211yesmaximal, characteristic, complemented
7C5×#463C211yesmaximal, characteristic, complemented
8C5×#463C211yesmaximal, characteristic, complemented
9C5×#450C211yesmaximal, characteristic, complemented
10C5×#447C211yesmaximal, characteristic
11C5×#442C211yesmaximal, characteristic, complemented
12C5×#440C211yesmaximal, characteristic, complemented
13C4×C5×SD16C211yesmaximal, characteristic, complemented
14C4×C5×D8C211yesmaximal, characteristic, complemented
15C5×#433C211yesmaximal, characteristic, complemented
16C22×C5×D4C2211yescharacteristic
17C2×C5×SD16C2211yescharacteristic
18C2×C5×SD16C2211yescharacteristic
19C2×C5×D8C2211yescharacteristic
20C2×C5×D8C2211yescharacteristic
21C5×C4⋊Q8C2211yescharacteristic, complemented
22C5×#126—21no—
23C5×#124—21no—
24C5×#124C2211yescharacteristic, complemented
25C5×#123—21no—
26C5×C22⋊Q8—21no—
27C5×C22⋊Q8C2211yescharacteristic
28C5×#121C2211yescharacteristic
29C4×C5×Q8C2211yescharacteristic, complemented
30C4×C5×D4—21no—
31C4×C5×D4—21no—
32C4×C5×D4C2211yescharacteristic
33C4×C5×D4C2211yescharacteristic
34C4×C5×D4C2211yescharacteristic
35C4×C5×D4C2211yescharacteristic
36C4×C5×D4C2211yescharacteristic, complemented
37C5×#117C2211yescharacteristic
38C5×#117C2211yescharacteristic
39C2×C5×C22⋊C4—21no—
40C2×C5×C22⋊C4—21no—
41C5×#107C2211yescharacteristic, complemented
42C5×#107C2211yescharacteristic, complemented
43C5×#106C2211yescharacteristic, complemented
44C5×#106C2211yescharacteristic, complemented
45C5×C4⋊C8C2211yescharacteristic, complemented
46C5×C4⋊C8C2211yescharacteristic, complemented
47C5×#103C2211yescharacteristic, complemented
48C5×#103C2211yescharacteristic, complemented
49C5×#102C2211yescharacteristic
50C5×#102C2211yescharacteristic
51C5×#102C2211yescharacteristic
52C5×#102C2211yescharacteristic
53C5×#102C2211yescharacteristic, complemented
54C5×#102C2211yescharacteristic, complemented
55C5×C22⋊C8C2211yescharacteristic
56C5×C22⋊C8C2211yescharacteristic
57C5×#97C2211yescharacteristic, complemented
58C4×C5×C8C2211yescharacteristic, complemented
59#3118C511yesmaximal, characteristic, direct product factor, Sylow
60C24×C5—21no—
61C2×C5×Q8—21no—
62C2×C5×Q8C2311yescharacteristic
63C2×C5×D4—22no—
64C2×C5×D4—22no—
65C2×C5×D4—21no—
66C2×C5×D4—21no—
67C2×C5×D4C2311yescharacteristic
68C2×C5×D4C2311yescharacteristic
69C2×C5×D4C2311yescharacteristic
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—21no—
73C22×C4×C5—21no—
74C22×C4×C5—21no—
75C22×C4×C5C2311yescharacteristic
76C5×SD16—22no—
77C5×SD16—22no—
78C5×D8—22no—
79C5×D8—22no—
80C2×C5×C8C2311yescharacteristic
81C2×C5×C8C2311yescharacteristic
82C2×C5×C8C2311yescharacteristic
83C2×C5×C8C2311yescharacteristic
84C5×C4⋊C4—21no—
85C5×C4⋊C4—21no—
86C5×C4⋊C4—21no—
87C5×C4⋊C4D411yescharacteristic
88C5×C4⋊C4D411yescharacteristic
89C5×C4⋊C4C2311yescharacteristic
90C5×C4⋊C4C2311yescharacteristic
91C5×C4⋊C4C2311yescharacteristic
92C5×C4⋊C4C2311yescharacteristic
93C5×C22⋊C4—21no—
94C5×C22⋊C4—21no—
95C5×C22⋊C4—21no—
96C5×C22⋊C4—21no—
97C5×C22⋊C4—21no—
98C5×C22⋊C4—21no—
99C5×C22⋊C4—21no—
100C5×C22⋊C4—21no—
101C5×C22⋊C4—21no—
102C5×C22⋊C4—21no—
103C5×C22⋊C4D411yescharacteristic
104C5×C22⋊C4D411yescharacteristic
105C42×C5—21no—
106C42×C5—21no—
107C42×C5C2311yescharacteristic
108C42×C5C2311yescharacteristic
109#542C2×C511yescharacteristic, complemented
110#518C2×C511yescharacteristic, complemented
111#485C2×C511yescharacteristic, complemented
112#482C2×C511yescharacteristic, complemented
113#476C2×C511yescharacteristic, complemented
114#474C2×C511yescharacteristic, complemented
115#463C2×C511yescharacteristic, complemented
116#463C2×C511yescharacteristic, complemented
117#450C2×C511yescharacteristic, complemented
118#447C2×C511yescharacteristic
119#442C2×C511yescharacteristic, complemented
120#440C2×C511yescharacteristic, complemented
121C4×SD16C2×C511yescharacteristic, complemented
122C4×D8C2×C511yescharacteristic, complemented
123#433C2×C511yescharacteristic, complemented
124C23×C5—24no—
125C23×C5—21no—
126C23×C5—21no—
127C23×C5—21no—
128C23×C5—81no—
129C23×C5—81no—
130C23×C5C2×D411yescharacteristic
131C5×Q8—21no—
132C5×Q8—21no—
133C5×Q8—81no—
134C5×D4—24no—
135C5×D4—21no—
136C5×D4—21no—
137C5×D4—21no—
138C5×D4—21no—
139C5×D4—81no—
140C5×D4#4112yes—
141C5×D4#4112yes—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—81no—
150C2×C4×C5—81no—
151C2×C4×C5—81no—
152C2×C4×C5—81no—
153C2×C4×C5—81no—
154C2×C4×C5C2×D411yescharacteristic
155C2×C4×C5C2×D411yescharacteristic
156C2×C4×C5C2×D411yescharacteristic
157C2×C4×C5C2×D411yescharacteristic
158C2×C4×C5C2×D411yescharacteristic
159C2×C4×C5C2411yescharacteristic
160C5×C8—21no—
161C5×C8—21no—
162C5×C8—21no—
163C5×C8—21no—
164C22×D4C22×C511yescharacteristic
165C2×SD16C22×C511yescharacteristic
166C2×SD16C22×C511yescharacteristic
167C2×D8C22×C511yescharacteristic
168C2×D8C22×C511yescharacteristic
169C4⋊Q8C22×C511yescharacteristic, complemented
170#126—21no—
171#124—21no—
172#124C22×C511yescharacteristic, complemented
173#123—21no—
174C22⋊Q8—21no—
175C22⋊Q8C22×C511yescharacteristic
176#121C22×C511yescharacteristic
177C4×Q8C22×C511yescharacteristic, complemented
178C4×D4—21no—
179C4×D4—21no—
180C4×D4C22×C511yescharacteristic
181C4×D4C22×C511yescharacteristic
182C4×D4C22×C511yescharacteristic
183C4×D4C22×C511yescharacteristic
184C4×D4C22×C511yescharacteristic, complemented
185#117C22×C511yescharacteristic
186#117C22×C511yescharacteristic
187C2×C22⋊C4—21no—
188C2×C22⋊C4—21no—
189#107C22×C511yescharacteristic, complemented
190#107C22×C511yescharacteristic, complemented
191#106C22×C511yescharacteristic, complemented
192#106C22×C511yescharacteristic, complemented
193C4⋊C8C22×C511yescharacteristic, complemented
194C4⋊C8C22×C511yescharacteristic, complemented
195#103C22×C511yescharacteristic, complemented
196#103C22×C511yescharacteristic, complemented
197#102C22×C511yescharacteristic
198#102C22×C511yescharacteristic
199#102C22×C511yescharacteristic
200#102C22×C511yescharacteristic
201#102C22×C511yescharacteristic, complemented
202#102C22×C511yescharacteristic, complemented
203C22⋊C8C22×C511yescharacteristic
204C22⋊C8C22×C511yescharacteristic
205#97C22×C511yescharacteristic, complemented
206C4×C8C22×C511yescharacteristic, complemented
207C22×C5—21no—
208C22×C5—22no—
209C22×C5—22no—
210C22×C5—21no—
211C22×C5—21no—
212C22×C5—41no—
213C22×C5—41no—
214C22×C5—41no—
215C22×C5—41no—
216C22×C5—41no—
217C22×C5—41no—
218C22×C5—41no—
219C22×C5—84no—
220C22×C5C22×D411yescharacteristic
221C4×C5—21no—
222C4×C5—21no—
223C4×C5—21no—
224C4×C5—21no—
225C4×C5—21no—
226C4×C5—41no—
227C4×C5—41no—
228C4×C5—41no—
229C4×C5—41no—
230C4×C5—41no—
231C4×C5C2×#4111yescharacteristic
232C4×C5C2×#4111yescharacteristic
233C24—21no—
234C2×Q8—21no—
235C2×Q8C23×C511yescharacteristic
236C2×D4—22no—
237C2×D4—22no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4C23×C511yescharacteristic
241C2×D4C23×C511yescharacteristic
242C2×D4C23×C511yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4C23×C511yescharacteristic
249SD16—22no—
250SD16—22no—
251D8—22no—
252D8—22no—
253C2×C8C23×C511yescharacteristic
254C2×C8C23×C511yescharacteristic
255C2×C8C23×C511yescharacteristic
256C2×C8C23×C511yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4C5×D411yescharacteristic
261C4⋊C4C5×D411yescharacteristic
262C4⋊C4C23×C511yescharacteristic
263C4⋊C4C23×C511yescharacteristic
264C4⋊C4C23×C511yescharacteristic
265C4⋊C4C23×C511yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4C5×D411yescharacteristic
277C22⋊C4C5×D411yescharacteristic
278C42—21no—
279C42—21no—
280C42C23×C511yescharacteristic
281C42C23×C511yescharacteristic
282C2×C5—41no—
283C2×C5—42no—
284C2×C5—42no—
285C2×C5—81no—
286C2×C5#52511yescharacteristic
287C2×C5#57611yescharacteristic
288C2×C5#57711yescharacteristic
289C23—24no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23C2×C5×D411yescharacteristic
296Q8—21no—
297Q8—21no—
298Q8—81no—
299D4—24no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—81no—
305D4C5×#4112yes—
306D4C5×#4112yes—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4C2×C5×D411yescharacteristic
320C2×C4C2×C5×D411yescharacteristic
321C2×C4C2×C5×D411yescharacteristic
322C2×C4C2×C5×D411yescharacteristic
323C2×C4C2×C5×D411yescharacteristic
324C2×C4C24×C511yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C5#311811yescharacteristic, direct product factor, Sylow
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—84no—
343C22C22×C5×D411yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4C2×C5×#4111yescharacteristic
355C4C2×C5×#4111yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—81no—
360C2C5×#52511yescharacteristic
361C2C5×#57611yescharacteristic
362C2C5×#57711yescharacteristic
subgroupG/H
center, socleC22×C5C22×D4
commutator, Frattini, cosocleC2×C4C24×C5
prime radicalC5×#447C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C5×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#542C2semidirect
2. C5×#518C2semidirect
3. C5×#485C2semidirect
4. C5×#482C2semidirect
5. C5×#476C2semidirect
6. C5×#474C2semidirect
7. C5×#463C2semidirect
8. C5×#463C2semidirect
9. C5×#450C2semidirect
11. C5×#442C2semidirect
12. C5×#440C2semidirect
13. C4×C5×SD16C2semidirect
14. C4×C5×D8C2semidirect
15. C5×#433C2semidirect
21. C5×C4⋊Q8C22semidirect
24. C5×#124C22semidirect
29. C4×C5×Q8C22semidirect
36. C4×C5×D4C22semidirect
41. C5×#107C22semidirect
42. C5×#107C22semidirect
43. C5×#106C22semidirect
44. C5×#106C22semidirect
45. C5×C4⋊C8C22semidirect
46. C5×C4⋊C8C22semidirect
47. C5×#103C22semidirect
48. C5×#103C22semidirect
53. C5×#102C22semidirect
54. C5×#102C22semidirect
57. C5×#97C22semidirect
58. C4×C5×C8C22semidirect
59. #3118C5direct (N × H)
109. #542C2×C5semidirect
110. #518C2×C5semidirect
111. #485C2×C5semidirect
112. #482C2×C5semidirect
113. #476C2×C5semidirect
114. #474C2×C5semidirect
115. #463C2×C5semidirect
116. #463C2×C5semidirect
117. #450C2×C5semidirect
119. #442C2×C5semidirect
120. #440C2×C5semidirect
121. C4×SD16C2×C5semidirect
122. C4×D8C2×C5semidirect
123. #433C2×C5semidirect
169. C4⋊Q8C22×C5semidirect
172. #124C22×C5semidirect
177. C4×Q8C22×C5semidirect
184. C4×D4C22×C5semidirect
189. #107C22×C5semidirect
190. #107C22×C5semidirect
191. #106C22×C5semidirect
192. #106C22×C5semidirect
193. C4⋊C8C22×C5semidirect
194. C4⋊C8C22×C5semidirect
195. #103C22×C5semidirect
196. #103C22×C5semidirect
201. #102C22×C5semidirect
202. #102C22×C5semidirect
205. #97C22×C5semidirect
206. C4×C8C22×C5semidirect
329. C5#3118direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#5422
C5×#5182
C5×#4852
C5×#4822
C5×#4762
C5×#4742
C5×#4632
C5×#4502
C5×#4472
C5×#4422
C5×#4402
C4×C5×SD162
C4×C5×D82
C5×#4332
#31185