Finite Group Databasebeta

← C5×#13329 #11936049

Subgroups — C5×#13329 #11936049

Order 1280.

578 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×Q32C211yesmaximal, characteristic, complemented
2C22×C5×SD32C211yesmaximal, characteristic
3C2×C5×#495C211yesmaximal, characteristic
4C2×C5×#358C211yesmaximal, characteristic, complemented
5C2×C5×#357C211yesmaximal, characteristic
6C5×#1969C211yesmaximal, characteristic, complemented
7C5×#1374C211yesmaximal, characteristic, complemented
8C22×C5×Q16C2211yescharacteristic
9C22×C5×Q16C2211yescharacteristic
10C22×C5×SD16—21no—
11C22×C5×D8C2211yescharacteristic
12C2×C5×#124—21no—
13C2×C5×Q32—22no—
14C2×C5×Q32—22no—
15C2×C5×Q32—22no—
16C2×C5×SD32—22no—
17C2×C5×SD32—22no—
18C2×C5×SD32—22no—
19C22×C5×C16C2211yescharacteristic
20C22×C5×C16C2211yescharacteristic
21C5×#495—22no—
22C5×#495—22no—
23C2×C5×#107C2211yescharacteristic
24C2×C5×#103—21no—
25C2×C4×C5×C8C2211yescharacteristic
26C5×#391—21no—
27C5×#358—22no—
28C5×#357—22no—
29#13329C511yesmaximal, characteristic, direct product factor, Sylow
30C22×C5×Q8—21no—
31C22×C5×Q8—21no—
32C22×C5×D4—21no—
33C2×C5×Q16—21no—
34C2×C5×Q16—21no—
35C2×C5×Q16—21no—
36C2×C5×Q16—21no—
37C2×C5×Q16—21no—
38C2×C5×Q16—21no—
39C2×C5×Q16—21no—
40C2×C5×Q16—21no—
41C2×C5×Q16—21no—
42C2×C5×Q16—21no—
43C2×C5×Q16D412yes—
44C2×C5×Q16D412yes—
45C2×C5×SD16—24no—
46C2×C5×SD16—42no—
47C2×C5×SD16—42no—
48C2×C5×D8—21no—
49C2×C5×D8—21no—
50C2×C5×D8—21no—
51C2×C5×D8—21no—
52C2×C5×D8—21no—
53C2×C5×D8D412yes—
54C22×C5×C8D411yescharacteristic
55C22×C5×C8C2311yescharacteristic
56C5×#124—24no—
57C5×#124—42no—
58C2×C5×C4⋊C4—21no—
59C2×C5×C22⋊C4—42no—
60C2×C42×C5D411yescharacteristic
61C5×Q32—28no—
62C5×SD32—28no—
63C2×C5×C16—21no—
64C2×C5×C16—21no—
65C2×C5×C16—21no—
66C2×C5×C16—21no—
67C2×C5×C16D412yes—
68C2×C5×C16D412yes—
69C5×#107—21no—
70C5×#107—21no—
71C5×#103—42no—
72C4×C5×C8—21no—
73C4×C5×C8—21no—
74C5×#95—42no—
75C22×Q32C2×C511yescharacteristic, complemented
76C22×SD32C2×C511yescharacteristic
77C2×#495C2×C511yescharacteristic
78C2×#358C2×C511yescharacteristic, complemented
79C2×#357C2×C511yescharacteristic
80#1969C2×C511yescharacteristic, complemented
81#1374C2×C511yescharacteristic, complemented
82C24×C5—41no—
83C2×C5×Q8—22no—
84C2×C5×Q8—22no—
85C2×C5×Q8—41no—
86C2×C5×Q8—41no—
87C2×C5×Q8—41no—
88C2×C5×Q8—41no—
89C2×C5×Q8—41no—
90C2×C5×Q8—41no—
91C2×C5×Q8—41no—
92C2×C5×Q8—41no—
93C2×C5×Q8—41no—
94C2×C5×Q8—41no—
95C2×C5×D4—22no—
96C2×C5×D4—41no—
97C2×C5×D4—41no—
98C2×C5×D4—41no—
99C2×C5×D4—41no—
100C2×C5×D4—41no—
101C22×C4×C5—41no—
102C22×C4×C5—41no—
103C22×C4×C5—41no—
104C22×C4×C5D812yes—
105C22×C4×C5C2×D411yescharacteristic
106C5×Q16—22no—
107C5×Q16—22no—
108C5×Q16—22no—
109C5×Q16—22no—
110C5×Q16—41no—
111C5×Q16—41no—
112C5×Q16—41no—
113C5×Q16—41no—
114C5×SD16—48no—
115C5×D8—22no—
116C5×D8—22no—
117C5×D8—41no—
118C5×D8—41no—
119C2×C5×C8—21no—
120C2×C5×C8—21no—
121C2×C5×C8D812yes—
122C2×C5×C8C2×D411yescharacteristic
123C2×C5×C8C2×D411yescharacteristic
124C2×C5×C8C2×D411yescharacteristic
125C2×C5×C8C2×D411yescharacteristic
126C2×C5×C8C2×D411yescharacteristic
127C2×C5×C8#4111yescharacteristic
128C5×C4⋊C4—41no—
129C5×C4⋊C4—41no—
130C5×C22⋊C4—48no—
131C42×C5—21no—
132C42×C5—21no—
133C5×C16—22no—
134C5×C16—22no—
135C22×Q16C22×C511yescharacteristic
136C22×Q16C22×C511yescharacteristic
137C22×SD16—21no—
138C22×D8C22×C511yescharacteristic
139C2×#124—21no—
140C2×Q32—22no—
141C2×Q32—22no—
142C2×Q32—22no—
143C2×SD32—22no—
144C2×SD32—22no—
145C2×SD32—22no—
146C22×C16C22×C511yescharacteristic
147C22×C16C22×C511yescharacteristic
148#495—22no—
149#495—22no—
150C2×#107C22×C511yescharacteristic
151C2×#103—21no—
152C2×C4×C8C22×C511yescharacteristic
153#391—21no—
154#358—22no—
155#357—22no—
156C23×C5—42no—
157C23×C5—81no—
158C23×C5—81no—
159C23×C5—82no—
160C23×C5—82no—
161C23×C5C2×D811yescharacteristic
162C5×Q8—42no—
163C5×Q8—42no—
164C5×Q8—42no—
165C5×Q8—42no—
166C5×Q8—81no—
167C5×Q8—81no—
168C5×Q8—81no—
169C5×Q8—81no—
170C5×D4—42no—
171C5×D4—42no—
172C5×D4—81no—
173C5×D4—81no—
174C2×C4×C5—22no—
175C2×C4×C5—22no—
176C2×C4×C5—22no—
177C2×C4×C5—42no—
178C2×C4×C5—42no—
179C2×C4×C5—81no—
180C2×C4×C5—81no—
181C2×C4×C5—81no—
182C2×C4×C5—81no—
183C2×C4×C5—81no—
184C2×C4×C5—82no—
185C2×C4×C5#12011yescharacteristic
186C2×C4×C5#12111yescharacteristic
187C2×C4×C5#12711yescharacteristic
188C2×C4×C5C2×D811yescharacteristic
189C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
191C5×C8—22no—
192C5×C8#12011yescharacteristic
193C5×C8#12011yescharacteristic
194C5×C8#12111yescharacteristic
195C5×C8#12111yescharacteristic
196C22×Q8—21no—
197C22×Q8—21no—
198C22×D4—21no—
199C2×Q16—21no—
200C2×Q16—21no—
201C2×Q16—21no—
202C2×Q16—21no—
203C2×Q16—21no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16—21no—
209C2×Q16C5×D412yes—
210C2×Q16C5×D412yes—
211C2×SD16—24no—
212C2×SD16—42no—
213C2×SD16—42no—
214C2×D8—21no—
215C2×D8—21no—
216C2×D8—21no—
217C2×D8—21no—
218C2×D8—21no—
219C2×D8C5×D412yes—
220C22×C8C5×D411yescharacteristic
221C22×C8C23×C511yescharacteristic
222#124—24no—
223#124—42no—
224C2×C4⋊C4—21no—
225C2×C22⋊C4—42no—
226C2×C42C5×D411yescharacteristic
227Q32—28no—
228SD32—28no—
229C2×C16—21no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16C5×D412yes—
234C2×C16C5×D412yes—
235#107—21no—
236#107—21no—
237#103—42no—
238C4×C8—21no—
239C4×C8—21no—
240#95—42no—
241C22×C5—84no—
242C22×C5—82no—
243C22×C5—162no—
244C22×C5—161no—
245C22×C5—161no—
246C22×C5#44711yescharacteristic
247C22×C5#45911yescharacteristic
248C22×C5#49311yescharacteristic
249C22×C5#50812yes—
250C22×C5#51012yes—
251C4×C5—42no—
252C4×C5—82no—
253C4×C5—82no—
254C4×C5—161no—
255C4×C5#39211yescharacteristic
256C4×C5#44711yescharacteristic
257C4×C5#45911yescharacteristic
258C4×C5#49611yescharacteristic
259C24—41no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×D4—22no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4C5×D812yes—
282C22×C4C2×C5×D411yescharacteristic
283Q16—22no—
284Q16—22no—
285Q16—22no—
286Q16—22no—
287Q16—41no—
288Q16—41no—
289Q16—41no—
290Q16—41no—
291SD16—48no—
292D8—22no—
293D8—22no—
294D8—41no—
295D8—41no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8C5×D812yes—
299C2×C8C2×C5×D411yescharacteristic
300C2×C8C2×C5×D411yescharacteristic
301C2×C8C2×C5×D411yescharacteristic
302C2×C8C2×C5×D411yescharacteristic
303C2×C8C2×C5×D411yescharacteristic
304C2×C8C5×#4111yescharacteristic
305C4⋊C4—41no—
306C4⋊C4—41no—
307C22⋊C4—48no—
308C42—21no—
309C42—21no—
310C16—22no—
311C16—22no—
312C2×C5—162no—
313C2×C5#201111yescharacteristic
314C2×C5#218912yes—
315C2×C5#221112yes—
316C2×C5#224911yescharacteristic
317C2×C5#225111yescharacteristic
318C23—42no—
319C23—81no—
320C23—81no—
321C23—82no—
322C23—82no—
323C23C2×C5×D811yescharacteristic
324Q8—42no—
325Q8—42no—
326Q8—42no—
327Q8—42no—
328Q8—81no—
329Q8—81no—
330Q8—81no—
331Q8—81no—
332D4—42no—
333D4—42no—
334D4—81no—
335D4—81no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—82no—
347C2×C4C5×#12011yescharacteristic
348C2×C4C5×#12111yescharacteristic
349C2×C4C5×#12711yescharacteristic
350C2×C4C2×C5×D811yescharacteristic
351C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
352C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
353C8—22no—
354C8C5×#12011yescharacteristic
355C8C5×#12011yescharacteristic
356C8C5×#12111yescharacteristic
357C8C5×#12111yescharacteristic
358C5#1332911yescharacteristic, direct product factor, Sylow
359C22—84no—
360C22—82no—
361C22—162no—
362C22—161no—
363C22—161no—
364C22C5×#44711yescharacteristic
365C22C5×#45911yescharacteristic
366C22C5×#49311yescharacteristic
367C22C5×#50812yes—
368C22C5×#51012yes—
369C4—42no—
370C4—82no—
371C4—82no—
372C4—161no—
373C4C5×#39211yescharacteristic
374C4C5×#44711yescharacteristic
375C4C5×#45911yescharacteristic
376C4C5×#49611yescharacteristic
377C2—162no—
378C2C5×#201111yescharacteristic
379C2C5×#218912yes—
380C2C5×#221112yes—
381C2C5×#224911yescharacteristic
382C2C5×#225111yescharacteristic
subgroupG/H
center, socleC23×C5C2×D8
commutator, Frattini, cosocleC22×C8C23×C5
prime radicalC22×C5×D8C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ C2×C4×C5×C8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C5×Q32C2semidirect
4. C2×C5×#358C2semidirect
6. C5×#1969C2semidirect
7. C5×#1374C2semidirect
29. #13329C5direct (N × H)
75. C22×Q32C2×C5semidirect
78. C2×#358C2×C5semidirect
80. #1969C2×C5semidirect
81. #1374C2×C5semidirect
358. C5#13329direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×Q322
C22×C5×SD322
C2×C5×#4952
C2×C5×#3582
C2×C5×#3572
C5×#19692
C5×#13742
#133295