Finite Group Databasebeta

← C5×#11502 #11934222

Subgroups — C5×#11502 #11934222

Order 1280.

714 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 714 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2308C211yesmaximal, characteristic
2C5×#1462C212yesmaximal, complemented
3C5×#1317C212yesmaximal, complemented
4C5×#1316C212yesmaximal, complemented
5C23×C5×D4C411yescharacteristic
6C22×C5×C22⋊C4C411yescharacteristic
7C22×C5×C22⋊C4C2211yescharacteristic
8C5×#407—22no—
9C5×#386—22no—
10C5×#386—22no—
11C5×#381C411yescharacteristic
12C5×#381C2211yescharacteristic
13C5×#379C411yescharacteristic
14C5×#379C2211yescharacteristic
15C5×#323—22no—
16C5×#323C2214yes—
17#11502C511yesmaximal, characteristic, direct product factor, Sylow
18C25×C5C2×C411yescharacteristic
19C25×C5C2×C411yescharacteristic
20C22×C5×D4—21no—
21C22×C5×D4—21no—
22C22×C5×D4—22no—
23C22×C5×D4—22no—
24C22×C5×D4—41no—
25C22×C5×D4—41no—
26C22×C5×D4—42no—
27C23×C4×C5—21no—
28C23×C4×C5C2×C411yescharacteristic
29C23×C4×C5D412yes—
30C2×C5×M16—42no—
31C2×C5×C22⋊C4—21no—
32C2×C5×C22⋊C4—22no—
33C2×C5×C22⋊C4—22no—
34C2×C5×C22⋊C4—41no—
35C2×C5×C22⋊C4—41no—
36C2×C5×C22⋊C4—42no—
37C2×C5×C22⋊C4C2×C411yescharacteristic
38C2×C5×C22⋊C4C2×C411yescharacteristic
39C2×C5×C22⋊C4C2×C411yescharacteristic
40C2×C5×C22⋊C4D412yes—
41C2×C5×C22⋊C4C2311yescharacteristic
42C5×C22⋊C8—24no—
43C5×C22⋊C8—42no—
44C5×#95—22no—
45C5×#95—22no—
46#2308C2×C511yescharacteristic
47#1462C2×C512yescomplemented
48#1317C2×C512yescomplemented
49#1316C2×C512yescomplemented
50C24×C5—21no—
51C24×C5—21no—
52C24×C5—22no—
53C24×C5—21no—
54C24×C5—21no—
55C24×C5—21no—
56C24×C5—21no—
57C24×C5—41no—
58C24×C5—41no—
59C24×C5—82no—
60C24×C5—82no—
61C24×C5C22⋊C411yescharacteristic
62C24×C5C22⋊C411yescharacteristic
63C24×C5M1612yescomplemented
64C24×C5C22×C411yescharacteristic
65C2×C5×D4—24no—
66C2×C5×D4—24no—
67C2×C5×D4—44no—
68C2×C5×D4—44no—
69C2×C5×D4—42no—
70C2×C5×D4—42no—
71C2×C5×D4—44no—
72C2×C5×D4—44no—
73C2×C5×D4—41no—
74C2×C5×D4—41no—
75C2×C5×D4—42no—
76C22×C4×C5—22no—
77C22×C4×C5—21no—
78C22×C4×C5—21no—
79C22×C4×C5—22no—
80C22×C4×C5—21no—
81C22×C4×C5—21no—
82C22×C4×C5—41no—
83C22×C4×C5—41no—
84C22×C4×C5—42no—
85C22×C4×C5—82no—
86C22×C4×C5—82no—
87C22×C4×C5C22⋊C412yes—
88C22×C4×C5M1612yescomplemented
89C22×C4×C5C2×D412yes—
90C5×M16—84no—
91C2×C5×C8—44no—
92C5×C22⋊C4—41no—
93C5×C22⋊C4—42no—
94C5×C22⋊C4—41no—
95C5×C22⋊C4—42no—
96C5×C22⋊C4—41no—
97C5×C22⋊C4—41no—
98C5×C22⋊C4—82no—
99C5×C22⋊C4—82no—
100C23×D4C4×C511yescharacteristic
101C22×C22⋊C4C4×C511yescharacteristic
102C22×C22⋊C4C22×C511yescharacteristic
103#407—22no—
104#386—22no—
105#386—22no—
106#381C4×C511yescharacteristic
107#381C22×C511yescharacteristic
108#379C4×C511yescharacteristic
109#379C22×C511yescharacteristic
110#323—22no—
111#323C22×C514yes—
112C23×C5—22no—
113C23×C5—22no—
114C23×C5—22no—
115C23×C5—22no—
116C23×C5—21no—
117C23×C5—21no—
118C23×C5—21no—
119C23×C5—21no—
120C23×C5—21no—
121C23×C5—21no—
122C23×C5—22no—
123C23×C5—42no—
124C23×C5—42no—
125C23×C5—42no—
126C23×C5—42no—
127C23×C5—42no—
128C23×C5—42no—
129C23×C5—42no—
130C23×C5—41no—
131C23×C5—41no—
132C23×C5—82no—
133C23×C5—82no—
134C23×C5—82no—
135C23×C5—84no—
136C23×C5—82no—
137C23×C5—82no—
138C23×C5—82no—
139C23×C5—84no—
140C23×C5—84no—
141C23×C5#9911yescharacteristic
142C23×C5#9911yescharacteristic
143C23×C5#10012yes—
144C23×C5C2×C22⋊C411yescharacteristic
145C23×C5C2×M1611yescharacteristic
146C23×C5C2×M1611yescharacteristic
147C5×D4—44no—
148C5×D4—44no—
149C5×D4—48no—
150C2×C4×C5—22no—
151C2×C4×C5—22no—
152C2×C4×C5—22no—
153C2×C4×C5—44no—
154C2×C4×C5—42no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—42no—
158C2×C4×C5—42no—
159C2×C4×C5—42no—
160C2×C4×C5—42no—
161C2×C4×C5—42no—
162C2×C4×C5—41no—
163C2×C4×C5—41no—
164C2×C4×C5—82no—
165C2×C4×C5—84no—
166C5×C8—84no—
167C25C2×C4×C511yescharacteristic
168C25C2×C4×C511yescharacteristic
169C22×D4—21no—
170C22×D4—21no—
171C22×D4—22no—
172C22×D4—22no—
173C22×D4—41no—
174C22×D4—41no—
175C22×D4—42no—
176C23×C4—21no—
177C23×C4C2×C4×C511yescharacteristic
178C23×C4C5×D412yes—
179C2×M16—42no—
180C2×C22⋊C4—21no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4—22no—
183C2×C22⋊C4—41no—
184C2×C22⋊C4—41no—
185C2×C22⋊C4—42no—
186C2×C22⋊C4C2×C4×C511yescharacteristic
187C2×C22⋊C4C2×C4×C511yescharacteristic
188C2×C22⋊C4C2×C4×C511yescharacteristic
189C2×C22⋊C4C5×D412yes—
190C2×C22⋊C4C23×C511yescharacteristic
191C22⋊C8—24no—
192C22⋊C8—42no—
193#95—22no—
194#95—22no—
195C22×C5—22no—
196C22×C5—22no—
197C22×C5—22no—
198C22×C5—21no—
199C22×C5—21no—
200C22×C5—21no—
201C22×C5—21no—
202C22×C5—22no—
203C22×C5—42no—
204C22×C5—41no—
205C22×C5—41no—
206C22×C5—42no—
207C22×C5—42no—
208C22×C5—42no—
209C22×C5—42no—
210C22×C5—42no—
211C22×C5—42no—
212C22×C5—42no—
213C22×C5—42no—
214C22×C5—42no—
215C22×C5—82no—
216C22×C5—82no—
217C22×C5—82no—
218C22×C5—82no—
219C22×C5—82no—
220C22×C5—84no—
221C22×C5—84no—
222C22×C5—82no—
223C22×C5#40711yescharacteristic
224C22×C5C2×#9911yescharacteristic
225C22×C5C2×#10011yescharacteristic
226C4×C5—42no—
227C4×C5—42no—
228C4×C5—42no—
229C4×C5—81no—
230C4×C5—81no—
231C24—21no—
232C24—21no—
233C24—21no—
234C24—21no—
235C24—22no—
236C24—21no—
237C24—21no—
238C24—41no—
239C24—41no—
240C24—82no—
241C24—82no—
242C24C5×C22⋊C411yescharacteristic
243C24C5×C22⋊C411yescharacteristic
244C24C5×M1612yescomplemented
245C24C22×C4×C511yescharacteristic
246C2×D4—24no—
247C2×D4—24no—
248C2×D4—44no—
249C2×D4—44no—
250C2×D4—42no—
251C2×D4—42no—
252C2×D4—44no—
253C2×D4—44no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—42no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—42no—
266C22×C4—82no—
267C22×C4—82no—
268C22×C4C5×C22⋊C412yes—
269C22×C4C5×M1612yescomplemented
270C22×C4C2×C5×D412yes—
271M16—84no—
272C2×C8—44no—
273C22⋊C4—41no—
274C22⋊C4—42no—
275C22⋊C4—41no—
276C22⋊C4—42no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—82no—
280C22⋊C4—82no—
281C2×C5—21no—
282C2×C5—21no—
283C2×C5—41no—
284C2×C5—41no—
285C2×C5—42no—
286C2×C5—41no—
287C2×C5—41no—
288C2×C5—82no—
289C2×C5#146211yescharacteristic
290C2×C5#212112yes—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—22no—
302C23—42no—
303C23—42no—
304C23—42no—
305C23—42no—
306C23—42no—
307C23—42no—
308C23—42no—
309C23—41no—
310C23—41no—
311C23—82no—
312C23—82no—
313C23—82no—
314C23—84no—
315C23—82no—
316C23—82no—
317C23—82no—
318C23—84no—
319C23—84no—
320C23C5×#9911yescharacteristic
321C23C5×#9911yescharacteristic
322C23C5×#10012yes—
323C23C2×C5×C22⋊C411yescharacteristic
324C23C2×C5×M1611yescharacteristic
325C23C2×C5×M1611yescharacteristic
326D4—44no—
327D4—44no—
328D4—48no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—82no—
344C2×C4—84no—
345C8—84no—
346C5#1150211yescharacteristic, direct product factor, Sylow
347C22—22no—
348C22—22no—
349C22—22no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—22no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22—42no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—42no—
367C22—82no—
368C22—82no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22—84no—
373C22—84no—
374C22—82no—
375C22C5×#40711yescharacteristic
376C22C2×C5×#9911yescharacteristic
377C22C2×C5×#10011yescharacteristic
378C4—42no—
379C4—42no—
380C4—42no—
381C4—81no—
382C4—81no—
383C2—21no—
384C2—21no—
385C2—41no—
386C2—41no—
387C2—41no—
388C2—41no—
389C2—42no—
390C2—82no—
391C2C5×#146211yescharacteristic
392C2C5×#212112yes—
subgroupG/H
center, socleC22×C5C2×#99
commutatorC24C22×C4×C5
Frattini, cosocleC2×C22⋊C4C23×C5
prime radicalC23×C5×D4C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C24×C5 ◁ C22×C5×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1462C2semidirect
3. C5×#1317C2semidirect
4. C5×#1316C2semidirect
17. #11502C5direct (N × H)
47. #1462C2×C5semidirect
48. #1317C2×C5semidirect
49. #1316C2×C5semidirect
63. C24×C5M16semidirect
88. C22×C4×C5M16semidirect
244. C24C5×M16semidirect
269. C22×C4C5×M16semidirect
346. C5#11502direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#23082
C5×#14622
C5×#13172
C5×#13162
#115025