Finite Group Databasebeta

← C5×#11732 #11934452

Subgroups — C5×#11732 #11934452

Order 1280.

442 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2633C211yesmaximal, characteristic
2C4×C5×#99C211yesmaximal, characteristic
3C5×#1459C211yesmaximal, characteristic
4C5×#1352C212yesmaximal, complemented
5C5×#1344C212yesmaximal, complemented
6C2×C5×#125C411yescharacteristic, complemented
7C2×C4×C5×D4C2211yescharacteristic
8C2×C5×#99—21no—
9C2×C5×C22⋊C8—21no—
10C5×#399C411yescharacteristic, complemented
11C5×#399C2211yescharacteristic
12C5×#398—21no—
13C5×#397C411yescharacteristic, complemented
14C5×#397C2211yescharacteristic
15C5×#394—21no—
16C5×#385—21no—
17C5×#385—21no—
18C5×#383C411yescharacteristic, complemented
19C4×C5×C22⋊C4—21no—
20C5×#342C2212yes—
21C5×#324—21no—
22C5×#323C2212yes—
23#11732C511yesmaximal, characteristic, direct product factor, Sylow
24C22×C5×D4D411yescharacteristic
25C23×C4×C5D411yescharacteristic
26C23×C4×C5D411yescharacteristic
27C22×C5×C8—41no—
28C5×#125—41no—
29C5×#125—41no—
30C4×C5×D4—41no—
31C4×C5×D4—41no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4C2×C411yescharacteristic
37C2×C5×C4⋊C4C2×C411yescharacteristic
38C2×C5×C4⋊C4D411yescharacteristic
39C2×C5×C22⋊C4—22no—
40C2×C5×C22⋊C4—21no—
41C2×C5×C22⋊C4—21no—
42C2×C5×C22⋊C4—21no—
43C2×C5×C22⋊C4—21no—
44C2×C5×C22⋊C4C2×C411yescharacteristic
45C2×C5×C22⋊C4C2311yescharacteristic
46C2×C42×C5—41no—
47C2×C42×C5C2×C411yescharacteristic
48C5×#99—24no—
49C5×C22⋊C8—22no—
50C5×C22⋊C8—41no—
51C5×#95—21no—
52C5×#95—21no—
53C5×#95—21no—
54C5×#95—21no—
55C5×#95—41no—
56C5×#95C2×C411yescharacteristic
57C5×#95C2×C411yescharacteristic
58#2633C2×C511yescharacteristic
59C4×#99C2×C511yescharacteristic
60#1459C2×C511yescharacteristic
61#1352C2×C512yescomplemented
62#1344C2×C512yescomplemented
63C24×C5C22⋊C411yescharacteristic
64C24×C5C2×D411yescharacteristic
65C2×C5×D4—22no—
66C2×C5×D4—22no—
67C2×C5×D4—41no—
68C22×C4×C5—21no—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—21no—
73C22×C4×C5—21no—
74C22×C4×C5—21no—
75C22×C4×C5—21no—
76C22×C4×C5—42no—
77C22×C4×C5—81no—
78C22×C4×C5—81no—
79C22×C4×C5C22⋊C411yescharacteristic
80C22×C4×C5C22⋊C411yescharacteristic
81C22×C4×C5C22⋊C411yescharacteristic
82C22×C4×C5C22×C411yescharacteristic
83C22×C4×C5C2×D411yescharacteristic
84C2×C5×C8—42no—
85C2×C5×C8—82no—
86C5×C4⋊C4—41no—
87C5×C4⋊C4—41no—
88C5×C4⋊C4—41no—
89C5×C4⋊C4—42no—
90C5×C4⋊C4—41no—
91C5×C4⋊C4—41no—
92C5×C4⋊C4—81no—
93C5×C4⋊C4—81no—
94C5×C22⋊C4—24no—
95C5×C22⋊C4—41no—
96C5×C22⋊C4—41no—
97C5×C22⋊C4—42no—
98C5×C22⋊C4—42no—
99C5×C22⋊C4—42no—
100C5×C22⋊C4—81no—
101C5×C22⋊C4—81no—
102C42×C5—21no—
103C42×C5—21no—
104C42×C5—82no—
105C2×#125C4×C511yescharacteristic, complemented
106C2×C4×D4C22×C511yescharacteristic
107C2×#99—21no—
108C2×C22⋊C8—21no—
109#399C4×C511yescharacteristic, complemented
110#399C22×C511yescharacteristic
111#398—21no—
112#397C4×C511yescharacteristic, complemented
113#397C22×C511yescharacteristic
114#394—21no—
115#385—21no—
116#385—21no—
117#383C4×C511yescharacteristic, complemented
118C4×C22⋊C4—21no—
119#342C22×C512yes—
120#324—21no—
121#323C22×C512yes—
122C23×C5—21no—
123C23×C5—21no—
124C23×C5—21no—
125C23×C5—21no—
126C23×C5—41no—
127C23×C5—41no—
128C23×C5—41no—
129C23×C5—41no—
130C23×C5#10412yes—
131C23×C5C2×C22⋊C411yescharacteristic
132C23×C5#13512yes—
133C5×D4—44no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5—41no—
141C2×C4×C5—42no—
142C2×C4×C5—42no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
145C2×C4×C5—41no—
146C2×C4×C5—44no—
147C2×C4×C5—41no—
148C2×C4×C5—41no—
149C2×C4×C5—41no—
150C2×C4×C5—41no—
151C2×C4×C5—41no—
152C2×C4×C5—41no—
153C2×C4×C5—41no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—81no—
160C2×C4×C5—81no—
161C2×C4×C5—82no—
162C2×C4×C5—82no—
163C2×C4×C5#9911yescharacteristic
164C2×C4×C5#9911yescharacteristic
165C5×C8—82no—
166C22×D4C5×D411yescharacteristic
167C23×C4C5×D411yescharacteristic
168C23×C4C5×D411yescharacteristic
169C22×C8—41no—
170#125—41no—
171#125—41no—
172C4×D4—41no—
173C4×D4—41no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4C2×C4×C511yescharacteristic
179C2×C4⋊C4C2×C4×C511yescharacteristic
180C2×C4⋊C4C5×D411yescharacteristic
181C2×C22⋊C4—22no—
182C2×C22⋊C4—21no—
183C2×C22⋊C4—21no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4—21no—
186C2×C22⋊C4C2×C4×C511yescharacteristic
187C2×C22⋊C4C23×C511yescharacteristic
188C2×C42—41no—
189C2×C42C2×C4×C511yescharacteristic
190#99—24no—
191C22⋊C8—22no—
192C22⋊C8—41no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—41no—
198#95C2×C4×C511yescharacteristic
199#95C2×C4×C511yescharacteristic
200C22×C5—21no—
201C22×C5—21no—
202C22×C5—22no—
203C22×C5—22no—
204C22×C5—42no—
205C22×C5—42no—
206C22×C5—41no—
207C22×C5—41no—
208C22×C5—41no—
209C22×C5—41no—
210C22×C5—81no—
211C22×C5—81no—
212C22×C5C2×#9911yescharacteristic
213C22×C5#41611yescharacteristic
214C22×C5C2×#10411yescharacteristic
215C4×C5—21no—
216C4×C5—21no—
217C4×C5—41no—
218C4×C5—41no—
219C4×C5—41no—
220C4×C5—41no—
221C4×C5—81no—
222C4×C5—81no—
223C4×C5—84no—
224C4×C5—81no—
225C4×C5—81no—
226C24C5×C22⋊C411yescharacteristic
227C24C2×C5×D411yescharacteristic
228C2×D4—22no—
229C2×D4—22no—
230C2×D4—41no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—42no—
240C22×C4—81no—
241C22×C4—81no—
242C22×C4C5×C22⋊C411yescharacteristic
243C22×C4C5×C22⋊C411yescharacteristic
244C22×C4C5×C22⋊C411yescharacteristic
245C22×C4C22×C4×C511yescharacteristic
246C22×C4C2×C5×D411yescharacteristic
247C2×C8—42no—
248C2×C8—82no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—81no—
256C4⋊C4—81no—
257C22⋊C4—24no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C22⋊C4—81no—
264C22⋊C4—81no—
265C42—21no—
266C42—21no—
267C42—82no—
268C2×C5—21no—
269C2×C5—21no—
270C2×C5—42no—
271C2×C5—42no—
272C2×C5#150111yescharacteristic
273C2×C5#212311yescharacteristic
274C2×C5#212711yescharacteristic
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23C5×#10412yes—
284C23C2×C5×C22⋊C411yescharacteristic
285C23C5×#13512yes—
286D4—44no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—44no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—82no—
315C2×C4—82no—
316C2×C4C5×#9911yescharacteristic
317C2×C4C5×#9911yescharacteristic
318C8—82no—
319C5#1173211yescharacteristic, direct product factor, Sylow
320C22—21no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—42no—
325C22—42no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22—81no—
332C22C2×C5×#9911yescharacteristic
333C22C5×#41611yescharacteristic
334C22C2×C5×#10411yescharacteristic
335C4—21no—
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—84no—
344C4—81no—
345C4—81no—
346C2—21no—
347C2—21no—
348C2—42no—
349C2—42no—
350C2C5×#150111yescharacteristic
351C2C5×#212311yescharacteristic
352C2C5×#212711yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C22⋊C4C23×C5
prime radicalC22×C5×D4D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#1352C2semidirect
5. C5×#1344C2semidirect
6. C2×C5×#125C4semidirect
10. C5×#399C4semidirect
13. C5×#397C4semidirect
18. C5×#383C4semidirect
23. #11732C5direct (N × H)
61. #1352C2×C5semidirect
62. #1344C2×C5semidirect
105. C2×#125C4×C5semidirect
109. #399C4×C5semidirect
112. #397C4×C5semidirect
117. #383C4×C5semidirect
319. C5#11732direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#26332
C4×C5×#992
C5×#14592
C5×#13522
C5×#13442
#117325