Finite Group Databasebeta

← C5×#10406 #11933126

Subgroups — C5×#10406 #11933126

Order 1280.

620 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2659C211yesmaximal, characteristic
2C5×#1872C212yesmaximal
3C2×C5×#328C212yesmaximal
4C5×#1444C211yesmaximal, characteristic
5C5×#1280C211yesmaximal, characteristic
6C2×C5×C22⋊Q8C2212yes—
7C22×C5×C4⋊C4—21no—
8C22×C5×C4⋊C4C2211yescharacteristic
9C2×C5×#103—22no—
10C2×C5×C22⋊C8C2212yes—
11C5×#398—22no—
12C5×#395—22no—
13C5×#380—21no—
14C5×#380—21no—
15C2×C5×#95—21no—
16C2×C5×#95C2211yescharacteristic
17C2×C5×#95C2211yescharacteristic
18C5×#340—22no—
19C5×#328—24no—
20#10406C511yesmaximal, characteristic, direct product factor, Sylow
21C22×C5×Q8D412yes—
22C23×C4×C5—21no—
23C23×C4×C5—21no—
24C23×C4×C5D411yescharacteristic
25C23×C4×C5D411yescharacteristic
26C23×C4×C5C2311yescharacteristic
27C22×C5×C8—22no—
28C5×C22⋊Q8—22no—
29C5×C22⋊Q8—22no—
30C5×C22⋊Q8—22no—
31C5×C22⋊Q8—22no—
32C2×C5×C4⋊C4—22no—
33C2×C5×C4⋊C4—22no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4—21no—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4—42no—
39C2×C5×C4⋊C4—42no—
40C2×C5×C4⋊C4—42no—
41C2×C5×C4⋊C4—42no—
42C2×C5×C4⋊C4D412yes—
43C2×C5×C22⋊C4—22no—
44C5×#103—44no—
45C5×C22⋊C8—22no—
46C5×C22⋊C8—22no—
47C5×#95—22no—
48C5×#95—22no—
49C5×#95—22no—
50C5×#95—21no—
51C5×#95—42no—
52C5×#95D412yes—
53#2659C2×C511yescharacteristic
54#1872C2×C512yes—
55C2×#328C2×C512yes—
56#1444C2×C511yescharacteristic
57#1280C2×C511yescharacteristic
58C24×C5C2×D411yescharacteristic
59C2×C5×Q8—22no—
60C2×C5×Q8—22no—
61C2×C5×Q8—42no—
62C2×C5×Q8—42no—
63C22×C4×C5—22no—
64C22×C4×C5—22no—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—22no—
68C22×C4×C5—21no—
69C22×C4×C5—21no—
70C22×C4×C5—22no—
71C22×C4×C5—22no—
72C22×C4×C5—22no—
73C22×C4×C5—41no—
74C22×C4×C5—41no—
75C22×C4×C5—41no—
76C22×C4×C5—41no—
77C22×C4×C5—41no—
78C22×C4×C5—41no—
79C22×C4×C5—41no—
80C22×C4×C5—41no—
81C22×C4×C5—41no—
82C22×C4×C5—41no—
83C22×C4×C5—41no—
84C22×C4×C5—41no—
85C22×C4×C5—41no—
86C22×C4×C5—41no—
87C22×C4×C5—41no—
88C22×C4×C5—41no—
89C22×C4×C5SD1612yes—
90C22×C4×C5Q1612yes—
91C22×C4×C5C2×D412yes—
92C22×C4×C5C2×D411yescharacteristic
93C22×C4×C5#4112yes—
94C22×C4×C5#4111yescharacteristic
95C2×C5×C8—42no—
96C2×C5×C8—42no—
97C2×C5×C8—42no—
98C5×C4⋊C4—24no—
99C5×C4⋊C4—22no—
100C5×C4⋊C4—22no—
101C5×C4⋊C4—42no—
102C5×C4⋊C4—48no—
103C5×C4⋊C4—42no—
104C5×C4⋊C4—42no—
105C5×C4⋊C4—81no—
106C5×C4⋊C4—81no—
107C5×C4⋊C4—81no—
108C5×C4⋊C4—81no—
109C5×C22⋊C4—42no—
110C5×C22⋊C4—42no—
111C2×C22⋊Q8C22×C512yes—
112C22×C4⋊C4—21no—
113C22×C4⋊C4C22×C511yescharacteristic
114C2×#103—22no—
115C2×C22⋊C8C22×C512yes—
116#398—22no—
117#395—22no—
118#380—21no—
119#380—21no—
120C2×#95—21no—
121C2×#95C22×C511yescharacteristic
122C2×#95C22×C511yescharacteristic
123#340—22no—
124#328—24no—
125C23×C5—21no—
126C23×C5—21no—
127C23×C5—21no—
128C23×C5—21no—
129C23×C5#12011yescharacteristic
130C23×C5#12111yescharacteristic
131C23×C5#12411yescharacteristic
132C23×C5C2×SD1611yescharacteristic
133C23×C5C2×Q1611yescharacteristic
134C23×C5#13711yescharacteristic
135C23×C5#13711yescharacteristic
136C5×Q8—44no—
137C5×Q8—82no—
138C2×C4×C5—22no—
139C2×C4×C5—22no—
140C2×C4×C5—24no—
141C2×C4×C5—22no—
142C2×C4×C5—22no—
143C2×C4×C5—41no—
144C2×C4×C5—42no—
145C2×C4×C5—41no—
146C2×C4×C5—42no—
147C2×C4×C5—42no—
148C2×C4×C5—42no—
149C2×C4×C5—42no—
150C2×C4×C5—42no—
151C2×C4×C5—41no—
152C2×C4×C5—41no—
153C2×C4×C5—41no—
154C2×C4×C5—41no—
155C2×C4×C5—42no—
156C2×C4×C5—42no—
157C2×C4×C5—42no—
158C2×C4×C5—42no—
159C2×C4×C5—42no—
160C2×C4×C5—42no—
161C2×C4×C5—42no—
162C2×C4×C5—42no—
163C2×C4×C5—42no—
164C2×C4×C5—42no—
165C2×C4×C5—42no—
166C2×C4×C5—42no—
167C2×C4×C5—81no—
168C2×C4×C5—81no—
169C2×C4×C5—81no—
170C2×C4×C5—81no—
171C2×C4×C5—81no—
172C2×C4×C5—81no—
173C2×C4×C5#12112yes—
174C2×C4×C5#12312yes—
175C5×C8—82no—
176C22×Q8C5×D412yes—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4C5×D411yescharacteristic
180C23×C4C5×D411yescharacteristic
181C23×C4C23×C511yescharacteristic
182C22×C8—22no—
183C22⋊Q8—22no—
184C22⋊Q8—22no—
185C22⋊Q8—22no—
186C22⋊Q8—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—42no—
194C2×C4⋊C4—42no—
195C2×C4⋊C4—42no—
196C2×C4⋊C4—42no—
197C2×C4⋊C4C5×D412yes—
198C2×C22⋊C4—22no—
199#103—44no—
200C22⋊C8—22no—
201C22⋊C8—22no—
202#95—22no—
203#95—22no—
204#95—22no—
205#95—21no—
206#95—42no—
207#95C5×D412yes—
208C22×C5—21no—
209C22×C5—21no—
210C22×C5—21no—
211C22×C5—21no—
212C22×C5—21no—
213C22×C5—21no—
214C22×C5—21no—
215C22×C5—21no—
216C22×C5—21no—
217C22×C5—21no—
218C22×C5—21no—
219C22×C5—21no—
220C22×C5#39411yescharacteristic
221C22×C5#44811yescharacteristic
222C22×C5#45111yescharacteristic
223C22×C5#45311yescharacteristic
224C22×C5#45611yescharacteristic
225C22×C5B(4,𝔽2)11yescharacteristic
226C22×C5#45811yescharacteristic
227C22×C5#46111yescharacteristic
228C22×C5#46211yescharacteristic
229C22×C5#48711yescharacteristic
230C22×C5#49111yescharacteristic
231C4×C5—22no—
232C4×C5—22no—
233C4×C5—44no—
234C4×C5—42no—
235C4×C5—42no—
236C4×C5—82no—
237C4×C5—82no—
238C4×C5—82no—
239C24C2×C5×D411yescharacteristic
240C2×Q8—22no—
241C2×Q8—22no—
242C2×Q8—42no—
243C2×Q8—42no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4C5×SD1612yes—
271C22×C4C5×Q1612yes—
272C22×C4C2×C5×D412yes—
273C22×C4C2×C5×D411yescharacteristic
274C22×C4C5×#4112yes—
275C22×C4C5×#4111yescharacteristic
276C2×C8—42no—
277C2×C8—42no—
278C2×C8—42no—
279C4⋊C4—24no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—42no—
283C4⋊C4—48no—
284C4⋊C4—42no—
285C4⋊C4—42no—
286C4⋊C4—81no—
287C4⋊C4—81no—
288C4⋊C4—81no—
289C4⋊C4—81no—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C2×C5—21no—
293C2×C5—21no—
294C2×C5—21no—
295C2×C5—21no—
296C2×C5#159611yescharacteristic
297C2×C5#160511yescharacteristic
298C2×C5#161111yescharacteristic
299C2×C5#161411yescharacteristic
300C2×C5#203911yescharacteristic
301C2×C5#204311yescharacteristic
302C2×C5#204411yescharacteristic
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23C5×#12011yescharacteristic
308C23C5×#12111yescharacteristic
309C23C5×#12411yescharacteristic
310C23C2×C5×SD1611yescharacteristic
311C23C2×C5×Q1611yescharacteristic
312C23C5×#13711yescharacteristic
313C23C5×#13711yescharacteristic
314Q8—44no—
315Q8—82no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4C5×#12112yes—
352C2×C4C5×#12312yes—
353C8—82no—
354C5#1040611yescharacteristic, direct product factor, Sylow
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22C5×#39411yescharacteristic
368C22C5×#44811yescharacteristic
369C22C5×#45111yescharacteristic
370C22C5×#45311yescharacteristic
371C22C5×#45611yescharacteristic
372C22C5×B(4,𝔽2)11yescharacteristic
373C22C5×#45811yescharacteristic
374C22C5×#46111yescharacteristic
375C22C5×#46211yescharacteristic
376C22C5×#48711yescharacteristic
377C22C5×#49111yescharacteristic
378C4—22no—
379C4—22no—
380C4—44no—
381C4—42no—
382C4—42no—
383C4—82no—
384C4—82no—
385C4—82no—
386C2—21no—
387C2—21no—
388C2—21no—
389C2—21no—
390C2C5×#159611yescharacteristic
391C2C5×#160511yescharacteristic
392C2C5×#161111yescharacteristic
393C2C5×#161411yescharacteristic
394C2C5×#203911yescharacteristic
395C2C5×#204311yescharacteristic
396C2C5×#204411yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutator, Frattini, cosocleC23×C4C23×C5
prime radicalC24×C5C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
20. #10406C5direct (N × H)
354. C5#10406direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#26592
C5×#18722
C2×C5×#3282
C5×#14442
C5×#12802
#104065