Finite Group Databasebeta

← C5×#10502 #11933222

Subgroups — C5×#10502 #11933222

Order 1280.

412 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×#3227C211yesmaximal, characteristic
2C5×#1997C211yesmaximal, characteristic, complemented
3C5×#1987C211yesmaximal, characteristic, complemented
4C5×#1980C211yesmaximal, characteristic
5C5×#1565C211yesmaximal, characteristic, complemented
6C5×#1547C211yesmaximal, characteristic
7C5×#1303C211yesmaximal, characteristic, complemented
8C5×#532C2211yescharacteristic
9C2×C5×C4⋊Q8C2211yescharacteristic
10C5×#498—21no—
11C5×#486—21no—
12C5×#481—22no—
13C5×#476—21no—
14C5×#476—21no—
15C5×#431C2211yescharacteristic
16C5×#423C2211yescharacteristic
17C2×C5×C4⋊C8C2211yescharacteristic
18C2×C5×#104—21no—
19C2×C5×#104—21no—
20C4×C5×M16C2211yescharacteristic
21C4×C5×C4⋊C4C2211yescharacteristic
22C5×#343—21no—
23C5×#343—21no—
24C5×#340—22no—
25C5×#335—21no—
26C5×#334—21no—
27C5×#332—21no—
28C5×#331—21no—
29#10502C511yesmaximal, characteristic, direct product factor, Sylow
30C2×C5×#41—21no—
31C22×C5×Q8—21no—
32C2×C5×M16—21no—
33C2×C5×M16D411yescharacteristic
34C2×C5×M16D411yescharacteristic
35C22×C5×C8—21no—
36C5×C4⋊Q8—21no—
37C5×C4⋊Q8—21no—
38C5×C4⋊Q8—21no—
39C5×C4⋊Q8—21no—
40C5×C4⋊Q8D411yescharacteristic
41C5×#127D411yescharacteristic
42C5×#124—21no—
43C5×#121—21no—
44C5×#121—21no—
45C4×C5×D4—21no—
46C4×C5×D4—21no—
47C2×C5×C4⋊C4—21no—
48C2×C5×C4⋊C4—21no—
49C2×C5×C4⋊C4D412yes—
50C2×C42×C5—21no—
51C2×C42×C5C2311yescharacteristic
52C5×#106—22no—
53C5×#106—22no—
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×#102—22no—
63C5×#102—22no—
64C5×C22⋊C8—21no—
65C5×#97—21no—
66C4×C5×C8—21no—
67C4×C5×C8—21no—
68C5×#95—21no—
69#3227C2×C511yescharacteristic
70#1997C2×C511yescharacteristic, complemented
71#1987C2×C511yescharacteristic, complemented
72#1980C2×C511yescharacteristic
73#1565C2×C511yescharacteristic, complemented
74#1547C2×C511yescharacteristic
75#1303C2×C511yescharacteristic, complemented
76C5×#41—41no—
77C5×#41—41no—
78C5×#41—41no—
79C5×#41—41no—
80C2×C5×Q8—21no—
81C2×C5×Q8—41no—
82C2×C5×Q8—41no—
83C2×C5×Q8—82no—
84C2×C5×D4—21no—
85C2×C5×D4—21no—
86C2×C5×D4—21no—
87C2×C5×D4—41no—
88C22×C4×C5—22no—
89C22×C4×C5—41no—
90C22×C4×C5—41no—
91C22×C4×C5C2×D411yescharacteristic
92C22×C4×C5C2×D411yescharacteristic
93C22×C4×C5#4111yescharacteristic
94C5×M16—21no—
95C5×M16—21no—
96C5×M16—21no—
97C5×M16—41no—
98C5×M16—41no—
99C5×M16SD1612yes—
100C2×C5×C8—21no—
101C2×C5×C8—21no—
102C2×C5×C8—21no—
103C2×C5×C8—21no—
104C2×C5×C8—42no—
105C2×C5×C8—41no—
106C2×C5×C8—41no—
107C5×C4⋊C4—22no—
108C5×C4⋊C4—22no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—22no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—41no—
113C5×C4⋊C4—41no—
114C5×C4⋊C4—41no—
115C5×C22⋊C4—41no—
116C5×C22⋊C4—41no—
117C42×C5—41no—
118C42×C5—41no—
119C42×C5C2×D411yescharacteristic
120C42×C5C2×D411yescharacteristic
121C42×C5#4111yescharacteristic
122C42×C5#4111yescharacteristic
123#532C22×C511yescharacteristic
124C2×C4⋊Q8C22×C511yescharacteristic
125#498—21no—
126#486—21no—
127#481—22no—
128#476—21no—
129#476—21no—
130#431C22×C511yescharacteristic
131#423C22×C511yescharacteristic
132C2×C4⋊C8C22×C511yescharacteristic
133C2×#104—21no—
134C2×#104—21no—
135C4×M16C22×C511yescharacteristic
136C4×C4⋊C4C22×C511yescharacteristic
137#343—21no—
138#343—21no—
139#340—22no—
140#335—21no—
141#334—21no—
142#332—21no—
143#331—21no—
144C23×C5—41no—
145C23×C5#12111yescharacteristic
146C5×Q8—41no—
147C5×Q8—41no—
148C5×Q8—82no—
149C5×Q8—82no—
150C5×D4—41no—
151C5×D4—41no—
152C5×D4—41no—
153C5×D4—41no—
154C5×D4—81no—
155C5×D4—81no—
156C5×D4—81no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—41no—
160C2×C4×C5—42no—
161C2×C4×C5—41no—
162C2×C4×C5—42no—
163C2×C4×C5—81no—
164C2×C4×C5—81no—
165C2×C4×C5—81no—
166C2×C4×C5—81no—
167C2×C4×C5—82no—
168C2×C4×C5#12011yescharacteristic
169C2×C4×C5#12111yescharacteristic
170C2×C4×C5#12111yescharacteristic
171C2×C4×C5#12311yescharacteristic
172C2×C4×C5#12311yescharacteristic
173C2×C4×C5#12411yescharacteristic
174C2×C4×C5C2×SD1611yescharacteristic
175C2×C4×C5#13511yescharacteristic
176C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C5#13711yescharacteristic
178C5×C8—22no—
179C5×C8—41no—
180C5×C8—41no—
181C5×C8—41no—
182C5×C8—81no—
183C5×C8—81no—
184C2×#41—21no—
185C22×Q8—21no—
186C2×M16—21no—
187C2×M16C5×D411yescharacteristic
188C2×M16C5×D411yescharacteristic
189C22×C8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8C5×D411yescharacteristic
195#127C5×D411yescharacteristic
196#124—21no—
197#121—21no—
198#121—21no—
199C4×D4—21no—
200C4×D4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4C5×D412yes—
204C2×C42—21no—
205C2×C42C23×C511yescharacteristic
206#106—22no—
207#106—22no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8C5×D411yescharacteristic
213C4⋊C8C5×D411yescharacteristic
214#104—42no—
215#104—42no—
216#102—22no—
217#102—22no—
218C22⋊C8—21no—
219#97—21no—
220C4×C8—21no—
221C4×C8—21no—
222#95—21no—
223C22×C5—21no—
224C22×C5—21no—
225C22×C5—81no—
226C22×C5—81no—
227C22×C5—81no—
228C22×C5#39411yescharacteristic
229C22×C5#46011yescharacteristic
230C22×C5#46411yescharacteristic
231C4×C5—21no—
232C4×C5—21no—
233C4×C5—21no—
234C4×C5—82no—
235C4×C5—82no—
236C4×C5—81no—
237C4×C5#45411yescharacteristic
238C4×C5#45611yescharacteristic
239C4×C5#46111yescharacteristic
240C4×C5#46311yescharacteristic
241C4×C5#46511yescharacteristic
242C4×C5#46811yescharacteristic
243#41—41no—
244#41—41no—
245#41—41no—
246#41—41no—
247C2×Q8—21no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—82no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C22×C4—22no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4C2×C5×D411yescharacteristic
259C22×C4C2×C5×D411yescharacteristic
260C22×C4C5×#4111yescharacteristic
261M16—21no—
262M16—21no—
263M16—21no—
264M16—41no—
265M16—41no—
266M16C5×SD1612yes—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—42no—
272C2×C8—41no—
273C2×C8—41no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C42—41no—
285C42—41no—
286C42C2×C5×D411yescharacteristic
287C42C2×C5×D411yescharacteristic
288C42C5×#4111yescharacteristic
289C42C5×#4111yescharacteristic
290C2×C5—21no—
291C2×C5—21no—
292C2×C5—161no—
293C2×C5#203811yescharacteristic
294C2×C5#204811yescharacteristic
295C2×C5#205511yescharacteristic
296C23—41no—
297C23C5×#12111yescharacteristic
298Q8—41no—
299Q8—41no—
300Q8—82no—
301Q8—82no—
302D4—41no—
303D4—41no—
304D4—41no—
305D4—41no—
306D4—81no—
307D4—81no—
308D4—81no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—82no—
320C2×C4C5×#12011yescharacteristic
321C2×C4C5×#12111yescharacteristic
322C2×C4C5×#12111yescharacteristic
323C2×C4C5×#12311yescharacteristic
324C2×C4C5×#12311yescharacteristic
325C2×C4C5×#12411yescharacteristic
326C2×C4C2×C5×SD1611yescharacteristic
327C2×C4C5×#13511yescharacteristic
328C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
329C2×C4C5×#13711yescharacteristic
330C8—22no—
331C8—41no—
332C8—41no—
333C8—41no—
334C8—81no—
335C8—81no—
336C5#1050211yescharacteristic, direct product factor, Sylow
337C22—21no—
338C22—21no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22C5×#39411yescharacteristic
343C22C5×#46011yescharacteristic
344C22C5×#46411yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—82no—
349C4—82no—
350C4—81no—
351C4C5×#45411yescharacteristic
352C4C5×#45611yescharacteristic
353C4C5×#46111yescharacteristic
354C4C5×#46311yescharacteristic
355C4C5×#46511yescharacteristic
356C4C5×#46811yescharacteristic
357C2—21no—
358C2—21no—
359C2—161no—
360C2C5×#203811yescharacteristic
361C2C5×#204811yescharacteristic
362C2C5×#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×#1987C2semidirect
5. C5×#1565C2semidirect
7. C5×#1303C2semidirect
29. #10502C5direct (N × H)
70. #1997C2×C5semidirect
71. #1987C2×C5semidirect
73. #1565C2×C5semidirect
75. #1303C2×C5semidirect
336. C5#10502direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32272
C5×#19972
C5×#19872
C5×#19802
C5×#15652
C5×#15472
C5×#13032
#105025