Finite Group Databasebeta

← C5×#9515 #11932235

Subgroups — C5×#9515 #11932235

Order 1280.

628 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2973C211yesmaximal, characteristic, complemented
2C5×#2534C211yesmaximal, characteristic
3C5×#1465C211yesmaximal, characteristic, complemented
4C5×#1462C212yesmaximal, complemented
5C5×#1305C212yesmaximal, complemented
6C2×C5×#123C411yescharacteristic
7C2×C5×#120C411yescharacteristic
8C2×C4×C5×D4C2211yescharacteristic
9C22×C5×C22⋊C4C2211yescharacteristic
10C5×#435—24no—
11C5×#432—21no—
12C5×#407C2212yes—
13C5×#407C2212yes—
14C2×C5×C22⋊C8—21no—
15C5×#396—21no—
16C5×#394—21no—
17C5×#388—21no—
18C5×#386—21no—
19C5×#381C411yescharacteristic
20C5×#380C2211yescharacteristic
21C5×#379C411yescharacteristic
22C5×#324—21no—
23C5×#323—24no—
24C5×#323—21no—
25#9515C511yesmaximal, characteristic, direct product factor, Sylow
26C25×C5C2×C411yescharacteristic
27C22×C5×D4—21no—
28C22×C5×D4C2×C411yescharacteristic
29C23×C4×C5C2×C411yescharacteristic
30C23×C4×C5D411yescharacteristic
31C23×C4×C5C2311yescharacteristic
32C2×C5×M16—22no—
33C2×C5×M16—22no—
34C22×C5×C8—22no—
35C5×#123—42no—
36C5×#120—42no—
37C4×C5×D4—22no—
38C4×C5×D4—22no—
39C2×C5×C4⋊C4—21no—
40C2×C5×C4⋊C4—21no—
41C2×C5×C4⋊C4D411yescharacteristic
42C2×C5×C22⋊C4—21no—
43C2×C5×C22⋊C4—21no—
44C2×C5×C22⋊C4—21no—
45C2×C5×C22⋊C4—21no—
46C2×C5×C22⋊C4—21no—
47C2×C5×C22⋊C4—22no—
48C2×C5×C22⋊C4—22no—
49C2×C5×C22⋊C4—21no—
50C2×C5×C22⋊C4C2×C411yescharacteristic
51C2×C5×C22⋊C4C2×C411yescharacteristic
52C2×C5×C22⋊C4C2×C411yescharacteristic
53C2×C5×C22⋊C4D411yescharacteristic
54C2×C42×C5D411yescharacteristic
55C5×C4⋊C8—22no—
56C5×C22⋊C8—22no—
57C5×C22⋊C8—22no—
58C5×C22⋊C8—22no—
59C5×C22⋊C8—22no—
60C5×C22⋊C8D414yescomplemented
61C5×#97—22no—
62C5×#95—21no—
63C5×#95—21no—
64C5×#95—21no—
65#2973C2×C511yescharacteristic, complemented
66#2534C2×C511yescharacteristic
67#1465C2×C511yescharacteristic, complemented
68#1462C2×C512yescomplemented
69#1305C2×C512yescomplemented
70C24×C5—21no—
71C24×C5—22no—
72C24×C5—42no—
73C24×C5—41no—
74C24×C5—41no—
75C24×C5—81no—
76C24×C5C22⋊C411yescharacteristic
77C24×C5C22×C411yescharacteristic
78C2×C5×D4—22no—
79C2×C5×D4—22no—
80C2×C5×D4—41no—
81C2×C5×D4—42no—
82C2×C5×D4—42no—
83C2×C5×D4—81no—
84C22×C4×C5—21no—
85C22×C4×C5—21no—
86C22×C4×C5—21no—
87C22×C4×C5—21no—
88C22×C4×C5—21no—
89C22×C4×C5—22no—
90C22×C4×C5—41no—
91C22×C4×C5—41no—
92C22×C4×C5—81no—
93C22×C4×C5—81no—
94C22×C4×C5C22⋊C411yescharacteristic
95C22×C4×C5C22⋊C411yescharacteristic
96C22×C4×C5C22⋊C411yescharacteristic
97C22×C4×C5C2×D412yes—
98C22×C4×C5C2×D411yescharacteristic
99C22×C4×C5C2×D411yescharacteristic
100C22×C4×C5#4112yes—
101C5×M16—82no—
102C5×M16—82no—
103C2×C5×C8—24no—
104C2×C5×C8—42no—
105C2×C5×C8—82no—
106C5×C4⋊C4—22no—
107C5×C4⋊C4—42no—
108C5×C4⋊C4—81no—
109C5×C22⋊C4—22no—
110C5×C22⋊C4—22no—
111C5×C22⋊C4—42no—
112C5×C22⋊C4—42no—
113C5×C22⋊C4—42no—
114C5×C22⋊C4—41no—
115C5×C22⋊C4—42no—
116C5×C22⋊C4—41no—
117C5×C22⋊C4—41no—
118C5×C22⋊C4—41no—
119C5×C22⋊C4—81no—
120C42×C5—21no—
121C42×C5—21no—
122C2×#123C4×C511yescharacteristic
123C2×#120C4×C511yescharacteristic
124C2×C4×D4C22×C511yescharacteristic
125C22×C22⋊C4C22×C511yescharacteristic
126#435—24no—
127#432—21no—
128#407C22×C512yes—
129#407C22×C512yes—
130C2×C22⋊C8—21no—
131#396—21no—
132#394—21no—
133#388—21no—
134#386—21no—
135#381C4×C511yescharacteristic
136#380C22×C511yescharacteristic
137#379C4×C511yescharacteristic
138#324—21no—
139#323—21no—
140#323—24no—
141C23×C5—21no—
142C23×C5—21no—
143C23×C5—21no—
144C23×C5—21no—
145C23×C5—22no—
146C23×C5—24no—
147C23×C5—41no—
148C23×C5—41no—
149C23×C5—41no—
150C23×C5—41no—
151C23×C5—41no—
152C23×C5—41no—
153C23×C5—41no—
154C23×C5—42no—
155C23×C5—41no—
156C23×C5—41no—
157C23×C5—41no—
158C23×C5—82no—
159C23×C5—82no—
160C23×C5—84no—
161C23×C5—84no—
162C23×C5#10012yes—
163C23×C5C2×C22⋊C411yescharacteristic
164C23×C5C4×D412yes—
165C5×D4—44no—
166C5×D4—84no—
167C2×C4×C5—21no—
168C2×C4×C5—21no—
169C2×C4×C5—21no—
170C2×C4×C5—21no—
171C2×C4×C5—21no—
172C2×C4×C5—41no—
173C2×C4×C5—42no—
174C2×C4×C5—42no—
175C2×C4×C5—41no—
176C2×C4×C5—42no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—41no—
183C2×C4×C5—41no—
184C2×C4×C5—41no—
185C2×C4×C5—41no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—81no—
189C2×C4×C5—82no—
190C2×C4×C5#12011yescharacteristic
191C2×C4×C5#12112yes—
192C2×C4×C5#12311yescharacteristic
193C5×C8—44no—
194C5×C8—82no—
195C25C2×C4×C511yescharacteristic
196C22×D4—21no—
197C22×D4C2×C4×C511yescharacteristic
198C23×C4C2×C4×C511yescharacteristic
199C23×C4C5×D411yescharacteristic
200C23×C4C23×C511yescharacteristic
201C2×M16—22no—
202C2×M16—22no—
203C22×C8—22no—
204#123—42no—
205#120—42no—
206C4×D4—22no—
207C4×D4—22no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4C5×D411yescharacteristic
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—22no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4C2×C4×C511yescharacteristic
220C2×C22⋊C4C2×C4×C511yescharacteristic
221C2×C22⋊C4C2×C4×C511yescharacteristic
222C2×C22⋊C4C5×D411yescharacteristic
223C2×C42C5×D411yescharacteristic
224C4⋊C8—22no—
225C22⋊C8—22no—
226C22⋊C8—22no—
227C22⋊C8—22no—
228C22⋊C8—22no—
229C22⋊C8C5×D414yescomplemented
230#97—22no—
231#95—21no—
232#95—21no—
233#95—21no—
234C22×C5—21no—
235C22×C5—21no—
236C22×C5—22no—
237C22×C5—22no—
238C22×C5—22no—
239C22×C5—22no—
240C22×C5—42no—
241C22×C5—42no—
242C22×C5—42no—
243C22×C5—42no—
244C22×C5—42no—
245C22×C5—41no—
246C22×C5—41no—
247C22×C5—42no—
248C22×C5—81no—
249C22×C5—81no—
250C22×C5—81no—
251C22×C5—84no—
252C22×C5—84no—
253C22×C5—81no—
254C22×C5—81no—
255C22×C5#38611yescharacteristic
256C22×C5C2×#10011yescharacteristic
257C22×C5#41311yescharacteristic
258C4×C5—21no—
259C4×C5—22no—
260C4×C5—21no—
261C4×C5—41no—
262C4×C5—41no—
263C4×C5—41no—
264C4×C5—81no—
265C4×C5—81no—
266C4×C5—81no—
267C24—21no—
268C24—22no—
269C24—42no—
270C24—41no—
271C24—41no—
272C24—81no—
273C24C5×C22⋊C411yescharacteristic
274C24C22×C4×C511yescharacteristic
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—41no—
278C2×D4—42no—
279C2×D4—42no—
280C2×D4—81no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—81no—
290C22×C4—81no—
291C22×C4C5×C22⋊C411yescharacteristic
292C22×C4C5×C22⋊C411yescharacteristic
293C22×C4C5×C22⋊C411yescharacteristic
294C22×C4C2×C5×D412yes—
295C22×C4C2×C5×D411yescharacteristic
296C22×C4C2×C5×D411yescharacteristic
297C22×C4C5×#4112yes—
298M16—82no—
299M16—82no—
300C2×C8—24no—
301C2×C8—42no—
302C2×C8—82no—
303C4⋊C4—22no—
304C4⋊C4—42no—
305C4⋊C4—81no—
306C22⋊C4—22no—
307C22⋊C4—22no—
308C22⋊C4—42no—
309C22⋊C4—42no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—81no—
317C42—21no—
318C42—21no—
319C2×C5—21no—
320C2×C5—21no—
321C2×C5—42no—
322C2×C5—42no—
323C2×C5—82no—
324C2×C5#189111yescharacteristic
325C2×C5#190011yescharacteristic
326C2×C5#191311yescharacteristic
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—22no—
332C23—24no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—42no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—82no—
345C23—82no—
346C23—84no—
347C23—84no—
348C23C5×#10012yes—
349C23C2×C5×C22⋊C411yescharacteristic
350C23C4×C5×D412yes—
351D4—44no—
352D4—84no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—81no—
375C2×C4—82no—
376C2×C4C5×#12011yescharacteristic
377C2×C4C5×#12112yes—
378C2×C4C5×#12311yescharacteristic
379C8—44no—
380C8—82no—
381C5#951511yescharacteristic, direct product factor, Sylow
382C22—21no—
383C22—21no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—41no—
394C22—41no—
395C22—42no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—84no—
400C22—84no—
401C22—81no—
402C22—81no—
403C22C5×#38611yescharacteristic
404C22C2×C5×#10011yescharacteristic
405C22C5×#41311yescharacteristic
406C4—21no—
407C4—22no—
408C4—21no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—81no—
413C4—81no—
414C4—81no—
415C2—21no—
416C2—21no—
417C2—42no—
418C2—42no—
419C2—82no—
420C2C5×#189111yescharacteristic
421C2C5×#190011yescharacteristic
422C2C5×#191311yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC24C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC2×C5×#120C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#2973C2semidirect
3. C5×#1465C2semidirect
4. C5×#1462C2semidirect
5. C5×#1305C2semidirect
25. #9515C5direct (N × H)
60. C5×C22⋊C8D4semidirect
65. #2973C2×C5semidirect
67. #1465C2×C5semidirect
68. #1462C2×C5semidirect
69. #1305C2×C5semidirect
229. C22⋊C8C5×D4semidirect
381. C5#9515direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#29732
C5×#25342
C5×#14652
C5×#14622
C5×#13052
#95155