Finite Group Databasebeta

← C5×#12236 #11934956

Subgroups — C5×#12236 #11934956

Order 1280.

324 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2794C211yesmaximal, characteristic
2C5×#2060C211yesmaximal, characteristic
3C5×#1617C211yesmaximal, characteristic
4C5×#1611C211yesmaximal, characteristic
5C5×#1353C211yesmaximal, characteristic
6C5×#1346C211yesmaximal, characteristic
7C5×#1325C211yesmaximal, characteristic
8C5×#544C2211yescharacteristic
9C5×#484—21no—
10C5×#483—21no—
11C5×#428—21no—
12C5×#400—21no—
13C5×#400—21no—
14C5×#400C2211yescharacteristic
15C5×#398C2211yescharacteristic
16C5×#387—21no—
17C5×#387—21no—
18C5×#387—21no—
19C5×#387—21no—
20C5×#384C2211yescharacteristic
21C5×#343C2211yescharacteristic
22C5×#339—21no—
23C5×#328—21no—
24C5×#328—21no—
25C5×#324C2211yescharacteristic
26C5×#324C2211yescharacteristic
27#12236C511yesmaximal, characteristic, direct product factor, Sylow
28C2×C5×M16—21no—
29C5×C4⋊Q8—41no—
30C5×#125—41no—
31C5×C22⋊Q8—21no—
32C5×C22⋊Q8—21no—
33C5×#117—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4—21no—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4D411yescharacteristic
39C2×C5×C4⋊C4D411yescharacteristic
40C2×C5×C4⋊C4D411yescharacteristic
41C2×C5×C4⋊C4C2311yescharacteristic
42C2×C42×C5—21no—
43C2×C42×C5D411yescharacteristic
44C5×#107—41no—
45C5×#107—41no—
46C5×#106—41no—
47C5×#106—41no—
48C5×#103—41no—
49C5×#103—41no—
50C5×C22⋊C8—21no—
51C5×C22⋊C8—21no—
52C5×#95—21no—
53C5×#95—21no—
54C5×#95—21no—
55C5×#95—21no—
56C5×#95—21no—
57C5×#95—21no—
58C5×#95—21no—
59C5×#95—21no—
60C5×#95—21no—
61C5×#95D411yescharacteristic
62C5×#95D411yescharacteristic
63#2794C2×C511yescharacteristic
64#2060C2×C511yescharacteristic
65#1617C2×C511yescharacteristic
66#1611C2×C511yescharacteristic
67#1353C2×C511yescharacteristic
68#1346C2×C511yescharacteristic
69#1325C2×C511yescharacteristic
70C2×C5×Q8—21no—
71C2×C5×Q8—21no—
72C22×C4×C5—21no—
73C22×C4×C5—21no—
74C22×C4×C5—21no—
75C22×C4×C5—21no—
76C22×C4×C5—21no—
77C22×C4×C5—21no—
78C22×C4×C5C2×D411yescharacteristic
79C22×C4×C5C2×D411yescharacteristic
80C22×C4×C5C2×D411yescharacteristic
81C5×M16—22no—
82C5×M16—41no—
83C2×C5×C8—41no—
84C2×C5×C8—41no—
85C2×C5×C8—41no—
86C5×C4⋊C4—21no—
87C5×C4⋊C4—21no—
88C5×C4⋊C4—21no—
89C5×C4⋊C4—21no—
90C5×C4⋊C4—41no—
91C5×C4⋊C4—41no—
92C5×C4⋊C4—41no—
93C5×C4⋊C4—41no—
94C5×C4⋊C4—42no—
95C5×C4⋊C4—42no—
96C5×C4⋊C4—42no—
97C5×C4⋊C4—41no—
98C5×C4⋊C4—41no—
99C5×C4⋊C4—41no—
100C5×C4⋊C4—41no—
101C5×C22⋊C4—41no—
102C42×C5—21no—
103C42×C5—21no—
104C42×C5—41no—
105C42×C5—81no—
106#544C22×C511yescharacteristic
107#484—21no—
108#483—21no—
109#428—21no—
110#400—21no—
111#400—21no—
112#400C22×C511yescharacteristic
113#398C22×C511yescharacteristic
114#387—21no—
115#387—21no—
116#387—21no—
117#387—21no—
118#384C22×C511yescharacteristic
119#343C22×C511yescharacteristic
120#339—21no—
121#328—21no—
122#328—21no—
123#324C22×C511yescharacteristic
124#324C22×C511yescharacteristic
125C23×C5#12011yescharacteristic
126C5×Q8—81no—
127C5×Q8—81no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—22no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—41no—
134C2×C4×C5—41no—
135C2×C4×C5—41no—
136C2×C4×C5—41no—
137C2×C4×C5—41no—
138C2×C4×C5—41no—
139C2×C4×C5—41no—
140C2×C4×C5—41no—
141C2×C4×C5—41no—
142C2×C4×C5—41no—
143C2×C4×C5—42no—
144C2×C4×C5—41no—
145C2×C4×C5—41no—
146C2×C4×C5—41no—
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#13511yescharacteristic
154C2×C4×C5#13711yescharacteristic
155C5×C8—42no—
156C5×C8—81no—
157C5×C8—81no—
158C2×M16—21no—
159C4⋊Q8—41no—
160#125—41no—
161C22⋊Q8—21no—
162C22⋊Q8—21no—
163#117—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4C5×D411yescharacteristic
169C2×C4⋊C4C5×D411yescharacteristic
170C2×C4⋊C4C5×D411yescharacteristic
171C2×C4⋊C4C23×C511yescharacteristic
172C2×C42—21no—
173C2×C42C5×D411yescharacteristic
174#107—41no—
175#107—41no—
176#106—41no—
177#106—41no—
178#103—41no—
179#103—41no—
180C22⋊C8—21no—
181C22⋊C8—21no—
182#95—21no—
183#95—21no—
184#95—21no—
185#95—21no—
186#95—21no—
187#95—21no—
188#95—21no—
189#95—21no—
190#95—21no—
191#95C5×D411yescharacteristic
192#95C5×D411yescharacteristic
193C22×C5—21no—
194C22×C5—21no—
195C22×C5#45211yescharacteristic
196C22×C5#45611yescharacteristic
197C22×C5B(4,𝔽2)11yescharacteristic
198C4×C5—21no—
199C4×C5—21no—
200C4×C5—42no—
201C4×C5—41no—
202C4×C5—41no—
203C4×C5—81no—
204C4×C5—81no—
205C4×C5—81no—
206C4×C5—81no—
207C4×C5—81no—
208C4×C5—81no—
209C4×C5—81no—
210C2×Q8—21no—
211C2×Q8—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4C2×C5×D411yescharacteristic
219C22×C4C2×C5×D411yescharacteristic
220C22×C4C2×C5×D411yescharacteristic
221M16—22no—
222M16—41no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—41no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C22⋊C4—41no—
242C42—21no—
243C42—21no—
244C42—41no—
245C42—81no—
246C2×C5—21no—
247C2×C5—21no—
248C2×C5#160311yescharacteristic
249C2×C5#219811yescharacteristic
250C2×C5#220311yescharacteristic
251C23C5×#12011yescharacteristic
252Q8—81no—
253Q8—81no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4C5×#13511yescharacteristic
280C2×C4C5×#13711yescharacteristic
281C8—42no—
282C8—81no—
283C8—81no—
284C5#1223611yescharacteristic, direct product factor, Sylow
285C22—21no—
286C22—21no—
287C22C5×#45211yescharacteristic
288C22C5×#45611yescharacteristic
289C22C5×B(4,𝔽2)11yescharacteristic
290C4—21no—
291C4—21no—
292C4—42no—
293C4—41no—
294C4—41no—
295C4—81no—
296C4—81no—
297C4—81no—
298C4—81no—
299C4—81no—
300C4—81no—
301C4—81no—
302C2—21no—
303C2—21no—
304C2C5×#160311yescharacteristic
305C2C5×#219811yescharacteristic
306C2C5×#220311yescharacteristic
subgroupG/H
center, socleC22×C5B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C5
prime radicalC23×C5#120
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C5 ◁ C2×C5×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
27. #12236C5direct (N × H)
284. C5#12236direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#27942
C5×#20602
C5×#16172
C5×#16112
C5×#13532
C5×#13462
C5×#13252
#122365