Finite Group Databasebeta

← C5×#13228 #11935948

Subgroups — C5×#13228 #11935948

Order 1280.

490 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×#2545C211yesmaximal, characteristic
2C2×C5×#356C212yesmaximal, complemented
3C2×C5×#355C212yesmaximal
4C5×#1801C211yesmaximal, characteristic, complemented
5C4×C5×#101C211yesmaximal, characteristic, complemented
6C2×C5×C4⋊Q8C2211yescharacteristic
7C2×C5×#124C411yescharacteristic
8C2×C5×#124C2211yescharacteristic
9C2×C4×C5×Q8C2211yescharacteristic
10C5×#423—21no—
11C2×C5×#101C2212yes—
12C2×C5×#101C2212yes—
13C4×C5×M16—21no—
14C5×#396—21no—
15C5×#396—21no—
16C5×#391C411yescharacteristic
17C5×#390C411yescharacteristic
18C5×#388—21no—
19C5×#388—21no—
20C4×C5×C4⋊C4C411yescharacteristic
21C5×#356—24no—
22C5×#355—24no—
23C5×#343—21no—
24C5×#343—21no—
25#13228C511yesmaximal, characteristic, direct product factor, Sylow
26C22×C5×Q8C2×C411yescharacteristic
27C22×C5×Q8C2311yescharacteristic
28C22×C5×D4C2×C411yescharacteristic
29C2×C5×M16—22no—
30C2×C5×M16—22no—
31C5×C4⋊Q8—22no—
32C5×C4⋊Q8—22no—
33C5×#124—22no—
34C5×#124—22no—
35C5×#124—41no—
36C5×#124—41no—
37C4×C5×Q8—41no—
38C4×C5×Q8—41no—
39C2×C5×C4⋊C4—21no—
40C2×C5×C4⋊C4—21no—
41C2×C5×C4⋊C4—21no—
42C2×C5×C4⋊C4C2×C411yescharacteristic
43C2×C5×C4⋊C4D411yescharacteristic
44C2×C5×C4⋊C4D411yescharacteristic
45C2×C5×C22⋊C4—21no—
46C2×C5×C22⋊C4—21no—
47C2×C5×C22⋊C4—21no—
48C2×C5×C22⋊C4—21no—
49C2×C5×C22⋊C4—21no—
50C2×C5×C22⋊C4—21no—
51C2×C42×C5C2×C411yescharacteristic
52C2×C42×C5C2×C411yescharacteristic
53C2×C42×C5C2×C411yescharacteristic
54C2×C42×C5D411yescharacteristic
55C2×C42×C5D411yescharacteristic
56C5×C4⋊C8—41no—
57C5×C4⋊C8—41no—
58C5×#101—22no—
59C5×#101—22no—
60C5×#101—22no—
61C5×#101D414yes—
62C5×#97—41no—
63C4×C5×C8—41no—
64C5×#95—21no—
65C5×#95—21no—
66C5×#95—21no—
67#2545C2×C511yescharacteristic
68C2×#356C2×C512yescomplemented
69C2×#355C2×C512yes—
70#1801C2×C511yescharacteristic, complemented
71C4×#101C2×C511yescharacteristic, complemented
72C24×C5—21no—
73C2×C5×Q8—22no—
74C2×C5×Q8—41no—
75C2×C5×Q8—41no—
76C2×C5×Q8—41no—
77C2×C5×Q8—41no—
78C2×C5×Q8C2×D412yes—
79C2×C5×Q8#4112yes—
80C2×C5×D4—22no—
81C2×C5×D4—41no—
82C2×C5×D4—41no—
83C22×C4×C5—21no—
84C22×C4×C5—21no—
85C22×C4×C5—21no—
86C22×C4×C5C22⋊C411yescharacteristic
87C22×C4×C5C22⋊C411yescharacteristic
88C22×C4×C5C22⋊C411yescharacteristic
89C22×C4×C5C22⋊C411yescharacteristic
90C22×C4×C5C22×C411yescharacteristic
91C22×C4×C5C2×D411yescharacteristic
92C22×C4×C5C2×D411yescharacteristic
93C5×M16—24no—
94C5×M16—42no—
95C5×M16—42no—
96C5×M16—42no—
97C2×C5×C8—42no—
98C2×C5×C8—42no—
99C5×C4⋊C4—41no—
100C5×C4⋊C4—41no—
101C5×C4⋊C4—41no—
102C5×C4⋊C4—42no—
103C5×C4⋊C4—42no—
104C5×C4⋊C4—41no—
105C5×C4⋊C4—41no—
106C5×C22⋊C4—42no—
107C5×C22⋊C4—42no—
108C5×C22⋊C4—42no—
109C5×C22⋊C4—41no—
110C5×C22⋊C4—41no—
111C5×C22⋊C4—42no—
112C5×C22⋊C4—41no—
113C5×C22⋊C4—41no—
114C42×C5—21no—
115C42×C5—21no—
116C42×C5—21no—
117C42×C5—21no—
118C42×C5—21no—
119C42×C5—21no—
120C42×C5—22no—
121C42×C5—22no—
122C2×C4⋊Q8C22×C511yescharacteristic
123C2×#124C4×C511yescharacteristic
124C2×#124C22×C511yescharacteristic
125C2×C4×Q8C22×C511yescharacteristic
126#423—21no—
127C2×#101C22×C512yes—
128C2×#101C22×C512yes—
129C4×M16—21no—
130#396—21no—
131#396—21no—
132#391C4×C511yescharacteristic
133#390C4×C511yescharacteristic
134#388—21no—
135#388—21no—
136C4×C4⋊C4C4×C511yescharacteristic
137#356—24no—
138#355—24no—
139#343—21no—
140#343—21no—
141C23×C5—41no—
142C23×C5—41no—
143C23×C5—41no—
144C23×C5—41no—
145C23×C5—41no—
146C23×C5—41no—
147C23×C5—41no—
148C23×C5C2×C22⋊C411yescharacteristic
149C5×Q8—42no—
150C5×Q8—42no—
151C5×Q8—82no—
152C5×D4—82no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—21no—
156C2×C4×C5—21no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—22no—
160C2×C4×C5—21no—
161C2×C4×C5—21no—
162C2×C4×C5—21no—
163C2×C4×C5—41no—
164C2×C4×C5—41no—
165C2×C4×C5—41no—
166C2×C4×C5—41no—
167C2×C4×C5—41no—
168C2×C4×C5—41no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5#9911yescharacteristic
176C2×C4×C5#9911yescharacteristic
177C2×C4×C5C4×D412yes—
178C2×C4×C5#12112yes—
179C2×C4×C5#12411yescharacteristic
180C2×C4×C5#12711yescharacteristic
181C5×C8—44no—
182C5×C8—82no—
183C22×Q8C2×C4×C511yescharacteristic
184C22×Q8C23×C511yescharacteristic
185C22×D4C2×C4×C511yescharacteristic
186C2×M16—22no—
187C2×M16—22no—
188C4⋊Q8—22no—
189C4⋊Q8—22no—
190#124—22no—
191#124—22no—
192#124—41no—
193#124—41no—
194C4×Q8—41no—
195C4×Q8—41no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4C2×C4×C511yescharacteristic
200C2×C4⋊C4C5×D411yescharacteristic
201C2×C4⋊C4C5×D411yescharacteristic
202C2×C22⋊C4—21no—
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C42C2×C4×C511yescharacteristic
209C2×C42C2×C4×C511yescharacteristic
210C2×C42C2×C4×C511yescharacteristic
211C2×C42C5×D411yescharacteristic
212C2×C42C5×D411yescharacteristic
213C4⋊C8—41no—
214C4⋊C8—41no—
215#101—22no—
216#101—22no—
217#101—22no—
218#101C5×D414yes—
219#97—41no—
220C4×C8—41no—
221#95—21no—
222#95—21no—
223#95—21no—
224C22×C5—21no—
225C22×C5—21no—
226C22×C5—81no—
227C22×C5—81no—
228C22×C5—81no—
229C22×C5—81no—
230C22×C5—81no—
231C22×C5—81no—
232C22×C5—81no—
233C22×C5#39011yescharacteristic
234C22×C5C2×#9911yescharacteristic
235C22×C5#41011yescharacteristic
236C4×C5—21no—
237C4×C5—21no—
238C4×C5—22no—
239C4×C5—21no—
240C4×C5—22no—
241C4×C5—21no—
242C4×C5—42no—
243C4×C5—41no—
244C4×C5—41no—
245C4×C5—41no—
246C4×C5—81no—
247C4×C5—81no—
248C24—21no—
249C2×Q8—22no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8C2×C5×D412yes—
255C2×Q8C5×#4112yes—
256C2×D4—22no—
257C2×D4—41no—
258C2×D4—41no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4C5×C22⋊C411yescharacteristic
263C22×C4C5×C22⋊C411yescharacteristic
264C22×C4C5×C22⋊C411yescharacteristic
265C22×C4C5×C22⋊C411yescharacteristic
266C22×C4C22×C4×C511yescharacteristic
267C22×C4C2×C5×D411yescharacteristic
268C22×C4C2×C5×D411yescharacteristic
269M16—24no—
270M16—42no—
271M16—42no—
272M16—42no—
273C2×C8—42no—
274C2×C8—42no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C42—21no—
291C42—21no—
292C42—21no—
293C42—21no—
294C42—21no—
295C42—21no—
296C42—22no—
297C42—22no—
298C2×C5—21no—
299C2×C5—21no—
300C2×C5—161no—
301C2×C5#196411yescharacteristic
302C2×C5#213211yescharacteristic
303C2×C5#213311yescharacteristic
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23C2×C5×C22⋊C411yescharacteristic
312Q8—42no—
313Q8—42no—
314Q8—82no—
315D4—82no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4C5×#9911yescharacteristic
339C2×C4C5×#9911yescharacteristic
340C2×C4C4×C5×D412yes—
341C2×C4C5×#12112yes—
342C2×C4C5×#12411yescharacteristic
343C2×C4C5×#12711yescharacteristic
344C8—44no—
345C8—82no—
346C5#1322811yescharacteristic, direct product factor, Sylow
347C22—21no—
348C22—21no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22C5×#39011yescharacteristic
357C22C2×C5×#9911yescharacteristic
358C22C5×#41011yescharacteristic
359C4—21no—
360C4—21no—
361C4—22no—
362C4—21no—
363C4—22no—
364C4—21no—
365C4—42no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—81no—
370C4—81no—
371C2—21no—
372C2—21no—
373C2—161no—
374C2C5×#196411yescharacteristic
375C2C5×#213211yescharacteristic
376C2C5×#213311yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC22×Q8C23×C5
prime radicalC22×C5×D4C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#356C2semidirect
4. C5×#1801C2semidirect
5. C4×C5×#101C2semidirect
25. #13228C5direct (N × H)
68. C2×#356C2×C5semidirect
70. #1801C2×C5semidirect
71. C4×#101C2×C5semidirect
346. C5#13228direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#25452
C2×C5×#3562
C2×C5×#3552
C5×#18012
C4×C5×#1012
#132285