Finite Group Databasebeta

← C5×#10501 #11933221

Subgroups — C5×#10501 #11933221

Order 1280.

440 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3206C211yesmaximal, characteristic
2C5×#1997C211yesmaximal, characteristic, complemented
3C5×#1981C211yesmaximal, characteristic, complemented
4C5×#1980C211yesmaximal, characteristic
5C5×#1565C211yesmaximal, characteristic, complemented
6C5×#1547C211yesmaximal, characteristic
7C5×#1303C211yesmaximal, characteristic, complemented
8C5×#532C2211yescharacteristic
9C2×C5×C4⋊Q8C2211yescharacteristic
10C5×#492—21no—
11C5×#487—21no—
12C5×#461—21no—
13C5×#461—21no—
14C5×#448—22no—
15C5×#431C2211yescharacteristic
16C5×#423C2211yescharacteristic
17C2×C5×C4⋊C8C2211yescharacteristic
18C2×C5×#104—21no—
19C2×C5×#104—21no—
20C2×C5×#103—22no—
21C4×C5×M16C2211yescharacteristic
22C4×C5×C4⋊C4C2211yescharacteristic
23C5×#343—21no—
24C5×#343—21no—
25C5×#335—21no—
26C5×#334—21no—
27C5×#332—21no—
28C5×#331—21no—
29#10501C511yesmaximal, characteristic, direct product factor, Sylow
30C2×C5×#41—21no—
31C22×C5×Q8D412yes—
32C2×C5×SD16—22no—
33C2×C5×SD16—22no—
34C2×C5×M16—21no—
35C2×C5×M16D411yescharacteristic
36C2×C5×M16D411yescharacteristic
37C22×C5×C8—21no—
38C5×C4⋊Q8—21no—
39C5×C4⋊Q8—21no—
40C5×C4⋊Q8—21no—
41C5×C4⋊Q8—21no—
42C5×C4⋊Q8D411yescharacteristic
43C5×#127D411yescharacteristic
44C5×#124—21no—
45C5×#121—21no—
46C5×#121—21no—
47C4×C5×D4—21no—
48C4×C5×D4—21no—
49C2×C5×C4⋊C4—21no—
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4—21no—
52C2×C42×C5—21no—
53C2×C42×C5C2311yescharacteristic
54C5×C4⋊C8—21no—
55C5×C4⋊C8—21no—
56C5×C4⋊C8—21no—
57C5×C4⋊C8—21no—
58C5×C4⋊C8D411yescharacteristic
59C5×C4⋊C8D411yescharacteristic
60C5×#104—42no—
61C5×#104—42no—
62C5×#103—22no—
63C5×#103—22no—
64C5×#103—44no—
65C5×C22⋊C8—21no—
66C5×#97—21no—
67C4×C5×C8—21no—
68C4×C5×C8—21no—
69C5×#95—21no—
70#3206C2×C511yescharacteristic
71#1997C2×C511yescharacteristic, complemented
72#1981C2×C511yescharacteristic, complemented
73#1980C2×C511yescharacteristic
74#1565C2×C511yescharacteristic, complemented
75#1547C2×C511yescharacteristic
76#1303C2×C511yescharacteristic, complemented
77C5×#41—41no—
78C5×#41—41no—
79C5×#41—41no—
80C5×#41—41no—
81C2×C5×Q8—22no—
82C2×C5×Q8—21no—
83C2×C5×Q8—22no—
84C2×C5×Q8—42no—
85C2×C5×Q8—42no—
86C2×C5×D4—21no—
87C2×C5×D4—21no—
88C2×C5×D4—21no—
89C2×C5×D4—41no—
90C22×C4×C5—22no—
91C22×C4×C5—41no—
92C22×C4×C5—41no—
93C22×C4×C5C2×D411yescharacteristic
94C22×C4×C5C2×D411yescharacteristic
95C22×C4×C5#4111yescharacteristic
96C5×SD16—82no—
97C5×SD16—82no—
98C5×M16—21no—
99C5×M16—21no—
100C5×M16—21no—
101C5×M16—41no—
102C5×M16—41no—
103C5×M16SD1612yescomplemented
104C2×C5×C8—21no—
105C2×C5×C8—21no—
106C2×C5×C8—21no—
107C2×C5×C8—21no—
108C2×C5×C8—42no—
109C2×C5×C8—41no—
110C2×C5×C8—41no—
111C5×C4⋊C4—22no—
112C5×C4⋊C4—21no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—41no—
115C5×C4⋊C4—41no—
116C5×C4⋊C4—41no—
117C5×C4⋊C4—41no—
118C5×C4⋊C4—41no—
119C5×C22⋊C4—41no—
120C5×C22⋊C4—41no—
121C42×C5—41no—
122C42×C5—41no—
123C42×C5C2×D411yescharacteristic
124C42×C5C2×D411yescharacteristic
125C42×C5#4111yescharacteristic
126C42×C5#4111yescharacteristic
127#532C22×C511yescharacteristic
128C2×C4⋊Q8C22×C511yescharacteristic
129#492—21no—
130#487—21no—
131#461—21no—
132#461—21no—
133#448—22no—
134#431C22×C511yescharacteristic
135#423C22×C511yescharacteristic
136C2×C4⋊C8C22×C511yescharacteristic
137C2×#104—21no—
138C2×#104—21no—
139C2×#103—22no—
140C4×M16C22×C511yescharacteristic
141C4×C4⋊C4C22×C511yescharacteristic
142#343—21no—
143#343—21no—
144#335—21no—
145#334—21no—
146#332—21no—
147#331—21no—
148C23×C5—41no—
149C23×C5#12111yescharacteristic
150C5×Q8—44no—
151C5×Q8—42no—
152C5×Q8—42no—
153C5×Q8—41no—
154C5×Q8—41no—
155C5×D4—41no—
156C5×D4—41no—
157C5×D4—41no—
158C5×D4—41no—
159C5×D4—81no—
160C5×D4—81no—
161C5×D4—81no—
162C2×C4×C5—21no—
163C2×C4×C5—21no—
164C2×C4×C5—41no—
165C2×C4×C5—42no—
166C2×C4×C5—41no—
167C2×C4×C5—42no—
168C2×C4×C5—81no—
169C2×C4×C5—81no—
170C2×C4×C5—81no—
171C2×C4×C5—81no—
172C2×C4×C5—82no—
173C2×C4×C5#12011yescharacteristic
174C2×C4×C5#12111yescharacteristic
175C2×C4×C5#12111yescharacteristic
176C2×C4×C5#12311yescharacteristic
177C2×C4×C5#12311yescharacteristic
178C2×C4×C5#12411yescharacteristic
179C2×C4×C5C2×SD1611yescharacteristic
180C2×C4×C5#13511yescharacteristic
181C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C5#13711yescharacteristic
183C5×C8—22no—
184C5×C8—41no—
185C5×C8—41no—
186C5×C8—41no—
187C5×C8—81no—
188C5×C8—81no—
189C2×#41—21no—
190C22×Q8C5×D412yes—
191C2×SD16—22no—
192C2×SD16—22no—
193C2×M16—21no—
194C2×M16C5×D411yescharacteristic
195C2×M16C5×D411yescharacteristic
196C22×C8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8C5×D411yescharacteristic
202#127C5×D411yescharacteristic
203#124—21no—
204#121—21no—
205#121—21no—
206C4×D4—21no—
207C4×D4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C42—21no—
212C2×C42C23×C511yescharacteristic
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8C5×D411yescharacteristic
218C4⋊C8C5×D411yescharacteristic
219#104—42no—
220#104—42no—
221#103—22no—
222#103—22no—
223#103—44no—
224C22⋊C8—21no—
225#97—21no—
226C4×C8—21no—
227C4×C8—21no—
228#95—21no—
229C22×C5—21no—
230C22×C5—21no—
231C22×C5—81no—
232C22×C5—81no—
233C22×C5—81no—
234C22×C5#39411yescharacteristic
235C22×C5#46011yescharacteristic
236C22×C5#46411yescharacteristic
237C4×C5—21no—
238C4×C5—21no—
239C4×C5—21no—
240C4×C5—82no—
241C4×C5—81no—
242C4×C5—82no—
243C4×C5#45311yescharacteristic
244C4×C5#45511yescharacteristic
245C4×C5#46111yescharacteristic
246C4×C5#46311yescharacteristic
247C4×C5#46511yescharacteristic
248C4×C5#46811yescharacteristic
249#41—41no—
250#41—41no—
251#41—41no—
252#41—41no—
253C2×Q8—22no—
254C2×Q8—21no—
255C2×Q8—22no—
256C2×Q8—42no—
257C2×Q8—42no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C22×C4—22no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4C2×C5×D411yescharacteristic
266C22×C4C2×C5×D411yescharacteristic
267C22×C4C5×#4111yescharacteristic
268SD16—82no—
269SD16—82no—
270M16—21no—
271M16—21no—
272M16—21no—
273M16—41no—
274M16—41no—
275M16C5×SD1612yescomplemented
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—42no—
281C2×C8—41no—
282C2×C8—41no—
283C4⋊C4—22no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C42—41no—
294C42—41no—
295C42C2×C5×D411yescharacteristic
296C42C2×C5×D411yescharacteristic
297C42C5×#4111yescharacteristic
298C42C5×#4111yescharacteristic
299C2×C5—21no—
300C2×C5—21no—
301C2×C5—161no—
302C2×C5#203711yescharacteristic
303C2×C5#204911yescharacteristic
304C2×C5#205511yescharacteristic
305C23—41no—
306C23C5×#12111yescharacteristic
307Q8—44no—
308Q8—42no—
309Q8—42no—
310Q8—41no—
311Q8—41no—
312D4—41no—
313D4—41no—
314D4—41no—
315D4—41no—
316D4—81no—
317D4—81no—
318D4—81no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—82no—
330C2×C4C5×#12011yescharacteristic
331C2×C4C5×#12111yescharacteristic
332C2×C4C5×#12111yescharacteristic
333C2×C4C5×#12311yescharacteristic
334C2×C4C5×#12311yescharacteristic
335C2×C4C5×#12411yescharacteristic
336C2×C4C2×C5×SD1611yescharacteristic
337C2×C4C5×#13511yescharacteristic
338C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
339C2×C4C5×#13711yescharacteristic
340C8—22no—
341C8—41no—
342C8—41no—
343C8—41no—
344C8—81no—
345C8—81no—
346C5#1050111yescharacteristic, direct product factor, Sylow
347C22—21no—
348C22—21no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22C5×#39411yescharacteristic
353C22C5×#46011yescharacteristic
354C22C5×#46411yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—82no—
359C4—82no—
360C4—81no—
361C4C5×#45311yescharacteristic
362C4C5×#45511yescharacteristic
363C4C5×#46111yescharacteristic
364C4C5×#46311yescharacteristic
365C4C5×#46511yescharacteristic
366C4C5×#46811yescharacteristic
367C2—21no—
368C2—21no—
369C2—161no—
370C2C5×#203711yescharacteristic
371C2C5×#204911yescharacteristic
372C2C5×#205511yescharacteristic
subgroupG/H
center, socleC22×C5#394
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC5×#532C22
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
2. C5×#1997C2semidirect
3. C5×#1981C2semidirect
5. C5×#1565C2semidirect
7. C5×#1303C2semidirect
29. #10501C5direct (N × H)
71. #1997C2×C5semidirect
72. #1981C2×C5semidirect
74. #1565C2×C5semidirect
76. #1303C2×C5semidirect
103. C5×M16SD16semidirect
275. M16C5×SD16semidirect
346. C5#10501direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32062
C5×#19972
C5×#19812
C5×#19802
C5×#15652
C5×#15472
C5×#13032
#105015