Finite Group Databasebeta

← C5×#7813 #11930533

Subgroups — C5×#7813 #11930533

Order 1280.

350 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2809C211yesmaximal, characteristic
2C5×#2099C211yesmaximal, characteristic
3C5×#2084C211yesmaximal, characteristic
4C5×#2072C211yesmaximal, characteristic
5C5×#1272C211yesmaximal, characteristic
6C5×#1271C211yesmaximal, characteristic
7C5×#1271C211yesmaximal, characteristic
8C2×C5×#106—21no—
9C2×C5×#103—21no—
10C5×#400—21no—
11C5×#398—21no—
12C5×#398—21no—
13C5×#391—21no—
14C5×#391C2211yescharacteristic
15C5×#389C2211yescharacteristic
16C5×#389C2211yescharacteristic
17C5×#387—21no—
18C5×#387—21no—
19C5×#384C2211yescharacteristic
20C5×#340—21no—
21C5×#340—21no—
22C5×#340—21no—
23C5×#340—21no—
24C5×#336C2211yescharacteristic
25C5×#336C2211yescharacteristic
26C5×#336C2211yescharacteristic
27#7813C511yesmaximal, characteristic, direct product factor, Sylow
28C22×C5×Q8D411yescharacteristic
29C22×C5×C8—21no—
30C22×C5×C8—21no—
31C22×C5×C8—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4—21no—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4—21no—
39C2×C5×C4⋊C4D411yescharacteristic
40C2×C5×C4⋊C4D411yescharacteristic
41C2×C5×C4⋊C4D411yescharacteristic
42C2×C5×C4⋊C4D411yescharacteristic
43C2×C5×C4⋊C4D411yescharacteristic
44C2×C42×C5—21no—
45C2×C42×C5C2311yescharacteristic
46C5×#106—42no—
47C5×#103—42no—
48C5×#95—21no—
49C5×#95—21no—
50C5×#95—21no—
51C5×#95—21no—
52C5×#95—21no—
53C5×#95—21no—
54C5×#95—21no—
55C5×#95—21no—
56C5×#95—21no—
57#2809C2×C511yescharacteristic
58#2099C2×C511yescharacteristic
59#2084C2×C511yescharacteristic
60#2072C2×C511yescharacteristic
61#1272C2×C511yescharacteristic
62#1271C2×C511yescharacteristic
63#1271C2×C511yescharacteristic
64C2×C5×Q8—21no—
65C2×C5×Q8—41no—
66C2×C5×Q8—41no—
67C2×C5×Q8SD1612yes—
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—41no—
75C22×C4×C5C2×D411yescharacteristic
76C22×C4×C5C2×D411yescharacteristic
77C22×C4×C5C2×D411yescharacteristic
78C2×C5×C8—22no—
79C2×C5×C8—41no—
80C2×C5×C8—41no—
81C2×C5×C8—41no—
82C2×C5×C8—41no—
83C2×C5×C8—41no—
84C2×C5×C8—41no—
85C2×C5×C8—41no—
86C2×C5×C8—41no—
87C5×C4⋊C4—21no—
88C5×C4⋊C4—21no—
89C5×C4⋊C4—21no—
90C5×C4⋊C4—21no—
91C5×C4⋊C4—41no—
92C5×C4⋊C4—41no—
93C5×C4⋊C4—41no—
94C5×C4⋊C4—42no—
95C5×C4⋊C4—41no—
96C5×C4⋊C4—41no—
97C5×C4⋊C4—41no—
98C5×C4⋊C4—41no—
99C5×C4⋊C4—41no—
100C5×C4⋊C4—41no—
101C5×C4⋊C4—41no—
102C5×C4⋊C4—41no—
103C5×C4⋊C4—81no—
104C5×C4⋊C4—81no—
105C42×C5—41no—
106C42×C5—81no—
107C2×#106—21no—
108C2×#103—21no—
109#400—21no—
110#398—21no—
111#398—21no—
112#391—21no—
113#391C22×C511yescharacteristic
114#389C22×C511yescharacteristic
115#389C22×C511yescharacteristic
116#387—21no—
117#387—21no—
118#384C22×C511yescharacteristic
119#340—21no—
120#340—21no—
121#340—21no—
122#340—21no—
123#336C22×C511yescharacteristic
124#336C22×C511yescharacteristic
125#336C22×C511yescharacteristic
126C23×C5#12011yescharacteristic
127C5×Q8—42no—
128C5×Q8—81no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—22no—
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—41no—
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—81no—
154C2×C4×C5—81no—
155C2×C4×C5—81no—
156C2×C4×C5C2×SD1611yescharacteristic
157C2×C4×C5#13511yescharacteristic
158C2×C4×C5#13511yescharacteristic
159C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C5#13711yescharacteristic
161C2×C4×C5#13711yescharacteristic
162C5×C8—42no—
163C5×C8—81no—
164C5×C8—81no—
165C22×Q8C5×D411yescharacteristic
166C22×C8—21no—
167C22×C8—21no—
168C22×C8—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4C5×D411yescharacteristic
177C2×C4⋊C4C5×D411yescharacteristic
178C2×C4⋊C4C5×D411yescharacteristic
179C2×C4⋊C4C5×D411yescharacteristic
180C2×C4⋊C4C5×D411yescharacteristic
181C2×C42—21no—
182C2×C42C23×C511yescharacteristic
183#106—42no—
184#103—42no—
185#95—21no—
186#95—21no—
187#95—21no—
188#95—21no—
189#95—21no—
190#95—21no—
191#95—21no—
192#95—21no—
193#95—21no—
194C22×C5#44811yescharacteristic
195C22×C5#44911yescharacteristic
196C22×C5#45211yescharacteristic
197C22×C5#45411yescharacteristic
198C22×C5#45511yescharacteristic
199C22×C5#45611yescharacteristic
200C22×C5#45811yescharacteristic
201C4×C5—21no—
202C4×C5—21no—
203C4×C5—21no—
204C4×C5—21no—
205C4×C5—21no—
206C4×C5—21no—
207C4×C5—42no—
208C4×C5—81no—
209C4×C5—81no—
210C4×C5—81no—
211C4×C5—81no—
212C4×C5—81no—
213C4×C5—161no—
214C2×Q8—21no—
215C2×Q8—41no—
216C2×Q8—41no—
217C2×Q8C5×SD1612yes—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4C2×C5×D411yescharacteristic
226C22×C4C2×C5×D411yescharacteristic
227C22×C4C2×C5×D411yescharacteristic
228C2×C8—22no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—42no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—81no—
254C4⋊C4—81no—
255C42—41no—
256C42—81no—
257C2×C5#160811yescharacteristic
258C2×C5#160911yescharacteristic
259C2×C5#161511yescharacteristic
260C2×C5#162611yescharacteristic
261C2×C5#164611yescharacteristic
262C2×C5#165311yescharacteristic
263C2×C5#166411yescharacteristic
264C23C5×#12011yescharacteristic
265Q8—42no—
266Q8—81no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4C2×C5×SD1611yescharacteristic
295C2×C4C5×#13511yescharacteristic
296C2×C4C5×#13511yescharacteristic
297C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
298C2×C4C5×#13711yescharacteristic
299C2×C4C5×#13711yescharacteristic
300C8—42no—
301C8—81no—
302C8—81no—
303C5#781311yescharacteristic, direct product factor, Sylow
304C22C5×#44811yescharacteristic
305C22C5×#44911yescharacteristic
306C22C5×#45211yescharacteristic
307C22C5×#45411yescharacteristic
308C22C5×#45511yescharacteristic
309C22C5×#45611yescharacteristic
310C22C5×#45811yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—42no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—81no—
322C4—81no—
323C4—161no—
324C2C5×#160811yescharacteristic
325C2C5×#160911yescharacteristic
326C2C5×#161511yescharacteristic
327C2C5×#162611yescharacteristic
328C2C5×#164611yescharacteristic
329C2C5×#165311yescharacteristic
330C2C5×#166411yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C5#120
commutator, Frattini, cosocleC2×C42C23×C5
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
27. #7813C5direct (N × H)
303. C5#7813direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#28092
C5×#20992
C5×#20842
C5×#20722
C5×#12722
C5×#12712
#78135