Finite Group Databasebeta

← C5×#10459 #11933179

Subgroups — C5×#10459 #11933179

Order 1280.

428 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3037C211yesmaximal, characteristic
2C5×#1801C211yesmaximal, characteristic, complemented
3C5×#1566C211yesmaximal, characteristic, complemented
4C5×#1547C211yesmaximal, characteristic
5C5×#1492C211yesmaximal, characteristic
6C2×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
7C5×#1292C211yesmaximal, characteristic, complemented
8C2×C5×#137—21no—
9C5×#532C2211yescharacteristic
10C2×C4×C5×Q8C2211yescharacteristic
11C5×#464—22no—
12C5×#462—21no—
13C5×#460—21no—
14C5×#423C2211yescharacteristic
15C5×#423C2211yescharacteristic
16C5×#423C2211yescharacteristic
17C2×C5×C4⋊C8C2211yescharacteristic
18C5×#417—21no—
19C2×C5×#101—21no—
20C2×C4×C5×C8C2211yescharacteristic
21C5×#343—21no—
22C5×#334—22no—
23C5×#332—21no—
24C5×#331—21no—
25C5×Q8⋊C8—21no—
26C5×Q8⋊C8—21no—
27C5×D4⋊C8—21no—
28C5×D4⋊C8—21no—
29#10459C511yesmaximal, characteristic, direct product factor, Sylow
30C2×C5×#41—21no—
31C22×C5×Q8D411yescharacteristic
32C5×#137—42no—
33C5×#137—42no—
34C2×C5×Q16—22no—
35C2×C5×SD16—22no—
36C2×C5×M16—21no—
37C2×C5×M16—21no—
38C2×C5×M16—21no—
39C22×C5×C8—21no—
40C22×C5×C8—21no—
41C5×C4⋊Q8D411yescharacteristic
42C5×#127D411yescharacteristic
43C5×#124—21no—
44C5×#121—21no—
45C5×#121—21no—
46C4×C5×Q8—21no—
47C4×C5×Q8—21no—
48C4×C5×Q8—21no—
49C4×C5×Q8—21no—
50C4×C5×D4—21no—
51C4×C5×D4—21no—
52C2×C5×C4⋊C4—21no—
53C2×C5×C4⋊C4D411yescharacteristic
54C2×C42×C5—21no—
55C2×C42×C5C2311yescharacteristic
56C5×C4⋊C8—21no—
57C5×C4⋊C8—21no—
58C5×C4⋊C8—21no—
59C5×C4⋊C8—21no—
60C5×C4⋊C8—21no—
61C5×C4⋊C8—21no—
62C5×C4⋊C8—21no—
63C5×C4⋊C8D412yes—
64C5×#103—22no—
65C5×#102—22no—
66C5×#101—42no—
67C4×C5×C8—21no—
68C4×C5×C8D411yescharacteristic
69C4×C5×C8D411yescharacteristic
70#3037C2×C511yescharacteristic
71#1801C2×C511yescharacteristic, complemented
72#1566C2×C511yescharacteristic, complemented
73#1547C2×C511yescharacteristic
74#1492C2×C511yescharacteristic
75C2×Q8⋊C8C2×C511yescharacteristic, complemented
76#1292C2×C511yescharacteristic, complemented
77C5×#41—41no—
78C5×#41—41no—
79C5×#41—41no—
80C5×#41—41no—
81C2×C5×Q8—21no—
82C2×C5×Q8—21no—
83C2×C5×Q8—21no—
84C2×C5×Q8—21no—
85C2×C5×Q8—21no—
86C2×C5×Q8—21no—
87C2×C5×Q8SD1612yes—
88C2×C5×D4—21no—
89C2×C5×D4—21no—
90C2×C5×D4—21no—
91C2×C5×D4—41no—
92C22×C4×C5—21no—
93C22×C4×C5—21no—
94C22×C4×C5—41no—
95C22×C4×C5C2×D411yescharacteristic
96C22×C4×C5#4111yescharacteristic
97C22×C4×C5#4111yescharacteristic
98C5×Q16—44no—
99C5×SD16—44no—
100C5×M16—41no—
101C5×M16—41no—
102C5×M16—41no—
103C5×M16—41no—
104C5×M16—41no—
105C5×M16—41no—
106C2×C5×C8—21no—
107C2×C5×C8—22no—
108C2×C5×C8—21no—
109C2×C5×C8—42no—
110C2×C5×C8—41no—
111C2×C5×C8—41no—
112C2×C5×C8—41no—
113C2×C5×C8—81no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—21no—
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×C5C2×D411yescharacteristic
127C42×C5#4111yescharacteristic
128C2×#137—21no—
129#532C22×C511yescharacteristic
130C2×C4×Q8C22×C511yescharacteristic
131#464—22no—
132#462—21no—
133#460—21no—
134#423C22×C511yescharacteristic
135#423C22×C511yescharacteristic
136#423C22×C511yescharacteristic
137C2×C4⋊C8C22×C511yescharacteristic
138#417—21no—
139C2×#101—21no—
140C2×C4×C8C22×C511yescharacteristic
141#343—21no—
142#334—22no—
143#332—21no—
144#331—21no—
145Q8⋊C8—21no—
146Q8⋊C8—21no—
147D4⋊C8—21no—
148D4⋊C8—21no—
149C23×C5—41no—
150C23×C5#12311yescharacteristic
151C5×Q8—22no—
152C5×Q8—22no—
153C5×Q8—41no—
154C5×Q8—41no—
155C5×Q8—41no—
156C5×Q8—41no—
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—22no—
167C2×C4×C5—41no—
168C2×C4×C5—41no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5—81no—
173C2×C4×C5—81no—
174C2×C4×C5—81no—
175C2×C4×C5#12011yescharacteristic
176C2×C4×C5#12111yescharacteristic
177C2×C4×C5#12111yescharacteristic
178C2×C4×C5#12111yescharacteristic
179C2×C4×C5#12311yescharacteristic
180C2×C4×C5#12411yescharacteristic
181C2×C4×C5C2×SD1611yescharacteristic
182C2×C4×C5#13511yescharacteristic
183C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
185C5×C8—22no—
186C5×C8—41no—
187C5×C8—42no—
188C5×C8—81no—
189C5×C8—81no—
190C5×C8—81no—
191C2×#41—21no—
192C22×Q8C5×D411yescharacteristic
193#137—42no—
194#137—42no—
195C2×Q16—22no—
196C2×SD16—22no—
197C2×M16—21no—
198C2×M16—21no—
199C2×M16—21no—
200C22×C8—21no—
201C22×C8—21no—
202C4⋊Q8C5×D411yescharacteristic
203#127C5×D411yescharacteristic
204#124—21no—
205#121—21no—
206#121—21no—
207C4×Q8—21no—
208C4×Q8—21no—
209C4×Q8—21no—
210C4×Q8—21no—
211C4×D4—21no—
212C4×D4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C5×D411yescharacteristic
215C2×C42—21no—
216C2×C42C23×C511yescharacteristic
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8C5×D412yes—
225#103—22no—
226#102—22no—
227#101—42no—
228C4×C8—21no—
229C4×C8C5×D411yescharacteristic
230C4×C8C5×D411yescharacteristic
231C22×C5—21no—
232C22×C5—21no—
233C22×C5—81no—
234C22×C5—81no—
235C22×C5—81no—
236C22×C5#39411yescharacteristic
237C22×C5#48111yescharacteristic
238C22×C5#48211yescharacteristic
239C4×C5—21no—
240C4×C5—21no—
241C4×C5—21no—
242C4×C5—42no—
243C4×C5—81no—
244C4×C5—81no—
245C4×C5#44911yescharacteristic
246C4×C5#45011yescharacteristic
247C4×C5#46511yescharacteristic
248C4×C5#46911yescharacteristic
249C4×C5#47111yescharacteristic
250C4×C5#47311yescharacteristic
251#41—41no—
252#41—41no—
253#41—41no—
254#41—41no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8C5×SD1612yes—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—41no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4C2×C5×D411yescharacteristic
270C22×C4C5×#4111yescharacteristic
271C22×C4C5×#4111yescharacteristic
272Q16—44no—
273SD16—44no—
274M16—41no—
275M16—41no—
276M16—41no—
277M16—41no—
278M16—41no—
279M16—41no—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—21no—
283C2×C8—42no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—81no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C42—41no—
297C42—41no—
298C42C2×C5×D411yescharacteristic
299C42C2×C5×D411yescharacteristic
300C42C2×C5×D411yescharacteristic
301C42C5×#4111yescharacteristic
302C2×C5—21no—
303C2×C5—21no—
304C2×C5—161no—
305C2×C5#203411yescharacteristic
306C2×C5#205011yescharacteristic
307C2×C5#205211yescharacteristic
308C23—41no—
309C23C5×#12311yescharacteristic
310Q8—22no—
311Q8—22no—
312Q8—41no—
313Q8—41no—
314Q8—41no—
315Q8—41no—
316D4—41no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—81no—
321D4—81no—
322D4—81no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4C5×#12011yescharacteristic
335C2×C4C5×#12111yescharacteristic
336C2×C4C5×#12111yescharacteristic
337C2×C4C5×#12111yescharacteristic
338C2×C4C5×#12311yescharacteristic
339C2×C4C5×#12411yescharacteristic
340C2×C4C2×C5×SD1611yescharacteristic
341C2×C4C5×#13511yescharacteristic
342C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
343C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
344C8—22no—
345C8—41no—
346C8—42no—
347C8—81no—
348C8—81no—
349C8—81no—
350C5#1045911yescharacteristic, direct product factor, Sylow
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22C5×#39411yescharacteristic
357C22C5×#48111yescharacteristic
358C22C5×#48211yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—42no—
363C4—81no—
364C4—81no—
365C4C5×#44911yescharacteristic
366C4C5×#45011yescharacteristic
367C4C5×#46511yescharacteristic
368C4C5×#46911yescharacteristic
369C4C5×#47111yescharacteristic
370C4C5×#47311yescharacteristic
371C2—21no—
372C2—21no—
373C2—161no—
374C2C5×#203411yescharacteristic
375C2C5×#205011yescharacteristic
376C2C5×#205211yescharacteristic
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×#1801C2semidirect
3. C5×#1566C2semidirect
6. C2×C5×Q8⋊C8C2semidirect
7. C5×#1292C2semidirect
29. #10459C5direct (N × H)
71. #1801C2×C5semidirect
72. #1566C2×C5semidirect
75. C2×Q8⋊C8C2×C5semidirect
76. #1292C2×C5semidirect
350. C5#10459direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30372
C5×#18012
C5×#15662
C5×#15472
C5×#14922
C2×C5×Q8⋊C82
C5×#12922
#104595