Finite Group Databasebeta

← C5×#10460 #11933180

Subgroups — C5×#10460 #11933180

Order 1280.

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×#3077C211yesmaximal, characteristic
2C5×#1800C211yesmaximal, characteristic
3C5×#1566C211yesmaximal, characteristic, complemented
4C5×#1550C211yesmaximal, characteristic, complemented
5C5×#1493C211yesmaximal, characteristic, complemented
6C2×C5×D4⋊C8C211yesmaximal, characteristic
7C5×#1292C211yesmaximal, characteristic, complemented
8C5×#533C2211yescharacteristic
9C2×C4×C5×D4C2211yescharacteristic
10C5×#478—22no—
11C5×#476—21no—
12C5×#474—21no—
13C5×#428—21no—
14C5×#423C2211yescharacteristic
15C5×#423C2211yescharacteristic
16C5×#423C2211yescharacteristic
17C2×C5×C4⋊C8C2211yescharacteristic
18C5×#418—21no—
19C2×C5×#100—21no—
20C2×C4×C5×C8C2211yescharacteristic
21C5×#343—21no—
22C5×#334—22no—
23C5×#333—21no—
24C5×#332—21no—
25C5×Q8⋊C8—21no—
26C5×Q8⋊C8—21no—
27C5×D4⋊C8—21no—
28C5×D4⋊C8—21no—
29#10460C511yesmaximal, characteristic, direct product factor, Sylow
30C22×C5×D4D411yescharacteristic
31C23×C4×C5—21no—
32C2×C5×M16—21no—
33C2×C5×M16—21no—
34C2×C5×M16—21no—
35C22×C5×C8—21no—
36C22×C5×C8—21no—
37C5×C4⋊Q8D411yescharacteristic
38C5×C4⋊Q8D411yescharacteristic
39C5×#125—21no—
40C5×C22⋊Q8—21no—
41C5×C22⋊Q8—21no—
42C4×C5×Q8—21no—
43C4×C5×Q8—21no—
44C4×C5×D4—21no—
45C4×C5×D4—21no—
46C4×C5×D4—21no—
47C4×C5×D4—21no—
48C5×#117—21no—
49C2×C5×C4⋊C4D411yescharacteristic
50C2×C5×C22⋊C4—21no—
51C2×C42×C5C2311yescharacteristic
52C5×#107—22no—
53C5×#106—22no—
54C5×C4⋊C8—21no—
55C5×C4⋊C8—21no—
56C5×C4⋊C8—21no—
57C5×C4⋊C8—21no—
58C5×C4⋊C8—21no—
59C5×C4⋊C8—21no—
60C5×C4⋊C8—21no—
61C5×C4⋊C8D412yes—
62C5×#102—22no—
63C5×#102—22no—
64C5×#100—42no—
65C4×C5×C8—21no—
66C4×C5×C8D411yescharacteristic
67C4×C5×C8D411yescharacteristic
68#3077C2×C511yescharacteristic
69#1800C2×C511yescharacteristic
70#1566C2×C511yescharacteristic, complemented
71#1550C2×C511yescharacteristic, complemented
72#1493C2×C511yescharacteristic, complemented
73C2×D4⋊C8C2×C511yescharacteristic
74#1292C2×C511yescharacteristic, complemented
75C24×C5—21no—
76C2×C5×Q8—21no—
77C2×C5×Q8—21no—
78C2×C5×D4—21no—
79C2×C5×D4—21no—
80C2×C5×D4—21no—
81C2×C5×D4—21no—
82C2×C5×D4—21no—
83C2×C5×D4SD1612yes—
84C22×C4×C5—21no—
85C22×C4×C5—41no—
86C22×C4×C5—41no—
87C22×C4×C5—81no—
88C22×C4×C5—81no—
89C22×C4×C5C2×D411yescharacteristic
90C22×C4×C5#4111yescharacteristic
91C22×C4×C5#4111yescharacteristic
92C5×M16—41no—
93C5×M16—41no—
94C5×M16—41no—
95C5×M16—41no—
96C5×M16—41no—
97C5×M16—41no—
98C2×C5×C8—21no—
99C2×C5×C8—22no—
100C2×C5×C8—21no—
101C2×C5×C8—42no—
102C2×C5×C8—41no—
103C2×C5×C8—41no—
104C2×C5×C8—41no—
105C2×C5×C8—81no—
106C5×C4⋊C4—21no—
107C5×C4⋊C4—21no—
108C5×C4⋊C4—21no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—21no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—41no—
113C5×C4⋊C4—41no—
114C5×C22⋊C4—41no—
115C5×C22⋊C4—41no—
116C5×C22⋊C4—41no—
117C42×C5—41no—
118C42×C5C2×D411yescharacteristic
119C42×C5C2×D411yescharacteristic
120C42×C5C2×D411yescharacteristic
121C42×C5#4111yescharacteristic
122#533C22×C511yescharacteristic
123C2×C4×D4C22×C511yescharacteristic
124#478—22no—
125#476—21no—
126#474—21no—
127#428—21no—
128#423C22×C511yescharacteristic
129#423C22×C511yescharacteristic
130#423C22×C511yescharacteristic
131C2×C4⋊C8C22×C511yescharacteristic
132#418—21no—
133C2×#100—21no—
134C2×C4×C8C22×C511yescharacteristic
135#343—21no—
136#334—22no—
137#333—21no—
138#332—21no—
139Q8⋊C8—21no—
140Q8⋊C8—21no—
141D4⋊C8—21no—
142D4⋊C8—21no—
143C23×C5—22no—
144C23×C5—41no—
145C23×C5—41no—
146C23×C5—81no—
147C23×C5—81no—
148C23×C5#12311yescharacteristic
149C5×Q8—41no—
150C5×Q8—41no—
151C5×Q8—81no—
152C5×D4—22no—
153C5×D4—22no—
154C5×D4—41no—
155C5×D4—41no—
156C2×C4×C5—21no—
157C2×C4×C5—21no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—82no—
163C2×C4×C5—81no—
164C2×C4×C5—81no—
165C2×C4×C5—81no—
166C2×C4×C5#12011yescharacteristic
167C2×C4×C5#12111yescharacteristic
168C2×C4×C5#12111yescharacteristic
169C2×C4×C5#12111yescharacteristic
170C2×C4×C5#12311yescharacteristic
171C2×C4×C5#12411yescharacteristic
172C2×C4×C5C2×SD1611yescharacteristic
173C2×C4×C5#13511yescharacteristic
174C2×C4×C5#13711yescharacteristic
175C2×C4×C5#13711yescharacteristic
176C5×C8—22no—
177C5×C8—41no—
178C5×C8—42no—
179C5×C8—81no—
180C5×C8—81no—
181C5×C8—81no—
182C22×D4C5×D411yescharacteristic
183C23×C4—21no—
184C2×M16—21no—
185C2×M16—21no—
186C2×M16—21no—
187C22×C8—21no—
188C22×C8—21no—
189C4⋊Q8C5×D411yescharacteristic
190C4⋊Q8C5×D411yescharacteristic
191#125—21no—
192C22⋊Q8—21no—
193C22⋊Q8—21no—
194C4×Q8—21no—
195C4×Q8—21no—
196C4×D4—21no—
197C4×D4—21no—
198C4×D4—21no—
199C4×D4—21no—
200#117—21no—
201C2×C4⋊C4C5×D411yescharacteristic
202C2×C22⋊C4—21no—
203C2×C42C23×C511yescharacteristic
204#107—22no—
205#106—22no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8C5×D412yes—
214#102—22no—
215#102—22no—
216#100—42no—
217C4×C8—21no—
218C4×C8C5×D411yescharacteristic
219C4×C8C5×D411yescharacteristic
220C22×C5—21no—
221C22×C5—21no—
222C22×C5—42no—
223C22×C5—82no—
224C22×C5—82no—
225C22×C5—81no—
226C22×C5—81no—
227C22×C5#39411yescharacteristic
228C22×C5#48311yescharacteristic
229C22×C5#48511yescharacteristic
230C4×C5—21no—
231C4×C5—21no—
232C4×C5—21no—
233C4×C5—81no—
234C4×C5—81no—
235C4×C5—81no—
236C4×C5#44811yescharacteristic
237C4×C5#45211yescharacteristic
238C4×C5#46511yescharacteristic
239C4×C5#47011yescharacteristic
240C4×C5#47111yescharacteristic
241C4×C5#47211yescharacteristic
242C24—21no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4C5×SD1612yes—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—81no—
255C22×C4—81no—
256C22×C4C2×C5×D411yescharacteristic
257C22×C4C5×#4111yescharacteristic
258C22×C4C5×#4111yescharacteristic
259M16—41no—
260M16—41no—
261M16—41no—
262M16—41no—
263M16—41no—
264M16—41no—
265C2×C8—21no—
266C2×C8—22no—
267C2×C8—21no—
268C2×C8—42no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—81no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C42—41no—
285C42C2×C5×D411yescharacteristic
286C42C2×C5×D411yescharacteristic
287C42C2×C5×D411yescharacteristic
288C42C5×#4111yescharacteristic
289C2×C5—21no—
290C2×C5—21no—
291C2×C5—82no—
292C2×C5#203511yescharacteristic
293C2×C5#205011yescharacteristic
294C2×C5#205111yescharacteristic
295C23—22no—
296C23—41no—
297C23—41no—
298C23—81no—
299C23—81no—
300C23C5×#12311yescharacteristic
301Q8—41no—
302Q8—41no—
303Q8—81no—
304D4—22no—
305D4—22no—
306D4—41no—
307D4—41no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—82no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4C5×#12011yescharacteristic
319C2×C4C5×#12111yescharacteristic
320C2×C4C5×#12111yescharacteristic
321C2×C4C5×#12111yescharacteristic
322C2×C4C5×#12311yescharacteristic
323C2×C4C5×#12411yescharacteristic
324C2×C4C2×C5×SD1611yescharacteristic
325C2×C4C5×#13511yescharacteristic
326C2×C4C5×#13711yescharacteristic
327C2×C4C5×#13711yescharacteristic
328C8—22no—
329C8—41no—
330C8—42no—
331C8—81no—
332C8—81no—
333C8—81no—
334C5#1046011yescharacteristic, direct product factor, Sylow
335C22—21no—
336C22—21no—
337C22—42no—
338C22—82no—
339C22—82no—
340C22—81no—
341C22—81no—
342C22C5×#39411yescharacteristic
343C22C5×#48311yescharacteristic
344C22C5×#48511yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4C5×#44811yescharacteristic
352C4C5×#45211yescharacteristic
353C4C5×#46511yescharacteristic
354C4C5×#47011yescharacteristic
355C4C5×#47111yescharacteristic
356C4C5×#47211yescharacteristic
357C2—21no—
358C2—21no—
359C2—82no—
360C2C5×#203511yescharacteristic
361C2C5×#205011yescharacteristic
362C2C5×#205111yescharacteristic
subgroupG/H
center, socleC22×C5#394
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC22×C5×D4D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1566C2semidirect
4. C5×#1550C2semidirect
5. C5×#1493C2semidirect
7. C5×#1292C2semidirect
29. #10460C5direct (N × H)
70. #1566C2×C5semidirect
71. #1550C2×C5semidirect
72. #1493C2×C5semidirect
74. #1292C2×C5semidirect
334. C5#10460direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30772
C5×#18002
C5×#15662
C5×#15502
C5×#14932
C2×C5×D4⋊C82
C5×#12922
#104605