Finite Group Databasebeta

← C5×#10503 #11933223

Subgroups — C5×#10503 #11933223

Order 1280.

428 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3226C211yesmaximal, characteristic
2C5×#1988C211yesmaximal, characteristic, complemented
3C5×#1980C211yesmaximal, characteristic
4C5×#1966C211yesmaximal, characteristic, complemented
5C5×#1565C211yesmaximal, characteristic, complemented
6C5×#1547C211yesmaximal, characteristic
7C5×#1303C211yesmaximal, characteristic, complemented
8C5×#532C2211yescharacteristic
9C2×C5×C4⋊Q8C2211yescharacteristic
10C5×#500—21no—
11C5×#486—21no—
12C5×#480—22no—
13C5×#474—21no—
14C5×#474—21no—
15C5×#431C2211yescharacteristic
16C5×#423C2211yescharacteristic
17C2×C5×C4⋊C8C2211yescharacteristic
18C2×C5×#104—21no—
19C2×C5×#104—21no—
20C2×C5×#101—21no—
21C2×C5×#101—21no—
22C4×C5×M16C2211yescharacteristic
23C4×C5×C4⋊C4C2211yescharacteristic
24C5×#340—22no—
25C5×#335—21no—
26C5×#334—21no—
27C5×#332—21no—
28C5×#331—21no—
29#10503C511yesmaximal, 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×#107—22no—
53C5×#107—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×#101—42no—
65C5×#101—42no—
66C5×C22⋊C8—21no—
67C5×#97—21no—
68C4×C5×C8—21no—
69C4×C5×C8—21no—
70C5×#95—21no—
71#3226C2×C511yescharacteristic
72#1988C2×C511yescharacteristic, complemented
73#1980C2×C511yescharacteristic
74#1966C2×C511yescharacteristic, complemented
75#1565C2×C511yescharacteristic, complemented
76#1547C2×C511yescharacteristic
77#1303C2×C511yescharacteristic, complemented
78C5×#41—41no—
79C5×#41—41no—
80C5×#41—41no—
81C5×#41—41no—
82C2×C5×Q8—21no—
83C2×C5×Q8—41no—
84C2×C5×Q8—41no—
85C2×C5×Q8—41no—
86C2×C5×Q8—41no—
87C2×C5×Q8—41no—
88C2×C5×Q8—41no—
89C2×C5×D4—21no—
90C2×C5×D4—21no—
91C2×C5×D4—21no—
92C2×C5×D4—41no—
93C22×C4×C5—22no—
94C22×C4×C5—41no—
95C22×C4×C5—41no—
96C22×C4×C5C2×D411yescharacteristic
97C22×C4×C5C2×D411yescharacteristic
98C22×C4×C5#4111yescharacteristic
99C5×M16—21no—
100C5×M16—21no—
101C5×M16—21no—
102C5×M16—41no—
103C5×M16—41no—
104C5×M16D812yes—
105C2×C5×C8—21no—
106C2×C5×C8—21no—
107C2×C5×C8—21no—
108C2×C5×C8—21no—
109C2×C5×C8—42no—
110C2×C5×C8—41no—
111C2×C5×C8—41no—
112C5×C4⋊C4—22no—
113C5×C4⋊C4—22no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—22no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—41no—
118C5×C4⋊C4—41no—
119C5×C4⋊C4—41no—
120C5×C22⋊C4—41no—
121C5×C22⋊C4—41no—
122C42×C5—41no—
123C42×C5—41no—
124C42×C5C2×D411yescharacteristic
125C42×C5C2×D411yescharacteristic
126C42×C5#4111yescharacteristic
127C42×C5#4111yescharacteristic
128#532C22×C511yescharacteristic
129C2×C4⋊Q8C22×C511yescharacteristic
130#500—21no—
131#486—21no—
132#480—22no—
133#474—21no—
134#474—21no—
135#431C22×C511yescharacteristic
136#423C22×C511yescharacteristic
137C2×C4⋊C8C22×C511yescharacteristic
138C2×#104—21no—
139C2×#104—21no—
140C2×#101—21no—
141C2×#101—21no—
142C4×M16C22×C511yescharacteristic
143C4×C4⋊C4C22×C511yescharacteristic
144#340—22no—
145#335—21no—
146#334—21no—
147#332—21no—
148#331—21no—
149C23×C5—41no—
150C23×C5#12111yescharacteristic
151C5×Q8—41no—
152C5×Q8—41no—
153C5×Q8—81no—
154C5×Q8—81no—
155C5×Q8—81no—
156C5×Q8—81no—
157C5×D4—41no—
158C5×D4—41no—
159C5×D4—41no—
160C5×D4—41no—
161C5×D4—81no—
162C5×D4—81no—
163C5×D4—81no—
164C2×C4×C5—21no—
165C2×C4×C5—21no—
166C2×C4×C5—41no—
167C2×C4×C5—42no—
168C2×C4×C5—41no—
169C2×C4×C5—42no—
170C2×C4×C5—42no—
171C2×C4×C5—42no—
172C2×C4×C5—81no—
173C2×C4×C5—81no—
174C2×C4×C5—81no—
175C2×C4×C5—81no—
176C2×C4×C5#12011yescharacteristic
177C2×C4×C5#12111yescharacteristic
178C2×C4×C5#12111yescharacteristic
179C2×C4×C5#12311yescharacteristic
180C2×C4×C5#12311yescharacteristic
181C2×C4×C5#12411yescharacteristic
182C2×C4×C5C2×D811yescharacteristic
183C2×C4×C5#13511yescharacteristic
184C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
186C5×C8—22no—
187C5×C8—41no—
188C5×C8—41no—
189C5×C8—41no—
190C5×C8—81no—
191C5×C8—81no—
192C2×#41—21no—
193C22×Q8—21no—
194C2×M16—21no—
195C2×M16C5×D411yescharacteristic
196C2×M16C5×D411yescharacteristic
197C22×C8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8C5×D411yescharacteristic
203#127C5×D411yescharacteristic
204#124—21no—
205#121—21no—
206#121—21no—
207C4×D4—21no—
208C4×D4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4C5×D412yes—
212C2×C42—21no—
213C2×C42C23×C511yescharacteristic
214#107—22no—
215#107—22no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8C5×D411yescharacteristic
221C4⋊C8C5×D411yescharacteristic
222#104—42no—
223#104—42no—
224#102—22no—
225#102—22no—
226#101—42no—
227#101—42no—
228C22⋊C8—21no—
229#97—21no—
230C4×C8—21no—
231C4×C8—21no—
232#95—21no—
233C22×C5—21no—
234C22×C5—21no—
235C22×C5—81no—
236C22×C5—81no—
237C22×C5—81no—
238C22×C5#39411yescharacteristic
239C22×C5#45911yescharacteristic
240C22×C5#46311yescharacteristic
241C4×C5—21no—
242C4×C5—21no—
243C4×C5—21no—
244C4×C5—82no—
245C4×C5—82no—
246C4×C5—81no—
247C4×C5#45411yescharacteristic
248C4×C5#45611yescharacteristic
249C4×C5#45911yescharacteristic
250C4×C5#46311yescharacteristic
251C4×C5#46611yescharacteristic
252C4×C5#46911yescharacteristic
253#41—41no—
254#41—41no—
255#41—41no—
256#41—41no—
257C2×Q8—21no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—41no—
268C22×C4—22no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4C2×C5×D411yescharacteristic
272C22×C4C2×C5×D411yescharacteristic
273C22×C4C5×#4111yescharacteristic
274M16—21no—
275M16—21no—
276M16—21no—
277M16—41no—
278M16—41no—
279M16C5×D812yes—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—42no—
285C2×C8—41no—
286C2×C8—41no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—21no—
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C42—41no—
298C42—41no—
299C42C2×C5×D411yescharacteristic
300C42C2×C5×D411yescharacteristic
301C42C5×#4111yescharacteristic
302C42C5×#4111yescharacteristic
303C2×C5—21no—
304C2×C5—21no—
305C2×C5—161no—
306C2×C5#203811yescharacteristic
307C2×C5#204911yescharacteristic
308C2×C5#205411yescharacteristic
309C23—41no—
310C23C5×#12111yescharacteristic
311Q8—41no—
312Q8—41no—
313Q8—81no—
314Q8—81no—
315Q8—81no—
316Q8—81no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—81no—
322D4—81no—
323D4—81no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4C5×#12011yescharacteristic
337C2×C4C5×#12111yescharacteristic
338C2×C4C5×#12111yescharacteristic
339C2×C4C5×#12311yescharacteristic
340C2×C4C5×#12311yescharacteristic
341C2×C4C5×#12411yescharacteristic
342C2×C4C2×C5×D811yescharacteristic
343C2×C4C5×#13511yescharacteristic
344C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
345C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
346C8—22no—
347C8—41no—
348C8—41no—
349C8—41no—
350C8—81no—
351C8—81no—
352C5#1050311yescharacteristic, direct product factor, Sylow
353C22—21no—
354C22—21no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22C5×#39411yescharacteristic
359C22C5×#45911yescharacteristic
360C22C5×#46311yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—82no—
365C4—82no—
366C4—81no—
367C4C5×#45411yescharacteristic
368C4C5×#45611yescharacteristic
369C4C5×#45911yescharacteristic
370C4C5×#46311yescharacteristic
371C4C5×#46611yescharacteristic
372C4C5×#46911yescharacteristic
373C2—21no—
374C2—21no—
375C2—161no—
376C2C5×#203811yescharacteristic
377C2C5×#204911yescharacteristic
378C2C5×#205411yescharacteristic
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×#1988C2semidirect
4. C5×#1966C2semidirect
5. C5×#1565C2semidirect
7. C5×#1303C2semidirect
29. #10503C5direct (N × H)
72. #1988C2×C5semidirect
74. #1966C2×C5semidirect
75. #1565C2×C5semidirect
77. #1303C2×C5semidirect
352. C5#10503direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32262
C5×#19882
C5×#19802
C5×#19662
C5×#15652
C5×#15472
C5×#13032
#105035