Finite Group Databasebeta

← C5×#7815 #11930535

Subgroups — C5×#7815 #11930535

Order 1280.

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

normal subgroups only

This group has 374 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×#2726C211yesmaximal, characteristic
2C5×#2099C211yesmaximal, characteristic
3C5×#2084C211yesmaximal, characteristic
4C5×#2084C211yesmaximal, characteristic
5C5×#1271C211yesmaximal, characteristic
6C5×#1271C211yesmaximal, characteristic
7C5×#1271C211yesmaximal, characteristic
8C2×C5×#125—21no—
9C2×C5×#106—21no—
10C2×C5×#106—21no—
11C5×#398—21no—
12C5×#398—21no—
13C5×#398—21no—
14C5×#389—21no—
15C5×#389C2211yescharacteristic
16C5×#389C2211yescharacteristic
17C5×#389C2211yescharacteristic
18C5×#387—21no—
19C5×#384C2211yescharacteristic
20C5×#340—21no—
21C5×#340—21no—
22C5×#340—21no—
23C5×#340—21no—
24C5×#336C2211yescharacteristic
25C5×#336C2211yescharacteristic
26C5×#336C2211yescharacteristic
27#7815C511yesmaximal, characteristic, direct product factor, Sylow
28C22×C5×C8—21no—
29C22×C5×C8—21no—
30C22×C5×C8—21no—
31C5×#125—42no—
32C5×#125—42no—
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⋊C4—21no—
40C2×C5×C4⋊C4—21no—
41C2×C5×C4⋊C4—21no—
42C2×C5×C4⋊C4—21no—
43C2×C5×C4⋊C4D411yescharacteristic
44C2×C5×C4⋊C4D411yescharacteristic
45C2×C5×C4⋊C4D411yescharacteristic
46C2×C5×C4⋊C4D411yescharacteristic
47C2×C5×C4⋊C4D411yescharacteristic
48C2×C5×C4⋊C4D411yescharacteristic
49C2×C42×C5—21no—
50C2×C42×C5C2311yescharacteristic
51C5×#106—42no—
52C5×#106—42no—
53C5×#95—21no—
54C5×#95—21no—
55C5×#95—21no—
56C5×#95—21no—
57C5×#95—21no—
58C5×#95—21no—
59#2726C2×C511yescharacteristic
60#2099C2×C511yescharacteristic
61#2084C2×C511yescharacteristic
62#2084C2×C511yescharacteristic
63#1271C2×C511yescharacteristic
64#1271C2×C511yescharacteristic
65#1271C2×C511yescharacteristic
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5—21no—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—41no—
73C22×C4×C5C2×D411yescharacteristic
74C22×C4×C5C2×D411yescharacteristic
75C22×C4×C5C2×D411yescharacteristic
76C2×C5×C8—22no—
77C2×C5×C8—22no—
78C2×C5×C8—41no—
79C2×C5×C8—41no—
80C2×C5×C8—41no—
81C2×C5×C8—41no—
82C2×C5×C8—41no—
83C2×C5×C8—41no—
84C2×C5×C8—41no—
85C5×C4⋊C4—21no—
86C5×C4⋊C4—21no—
87C5×C4⋊C4—21no—
88C5×C4⋊C4—21no—
89C5×C4⋊C4—41no—
90C5×C4⋊C4—41no—
91C5×C4⋊C4—41no—
92C5×C4⋊C4—42no—
93C5×C4⋊C4—42no—
94C5×C4⋊C4—42no—
95C5×C4⋊C4—42no—
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—41no—
104C5×C4⋊C4—41no—
105C5×C4⋊C4—41no—
106C5×C4⋊C4—81no—
107C5×C4⋊C4SD1612yes—
108C5×C4⋊C4SD1612yes—
109C42×C5—41no—
110C42×C5—42no—
111C2×#125—21no—
112C2×#106—21no—
113C2×#106—21no—
114#398—21no—
115#398—21no—
116#398—21no—
117#389—21no—
118#389C22×C511yescharacteristic
119#389C22×C511yescharacteristic
120#389C22×C511yescharacteristic
121#387—21no—
122#384C22×C511yescharacteristic
123#340—21no—
124#340—21no—
125#340—21no—
126#340—21no—
127#336C22×C511yescharacteristic
128#336C22×C511yescharacteristic
129#336C22×C511yescharacteristic
130C23×C5#12011yescharacteristic
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—22no—
138C2×C4×C5—22no—
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—41no—
154C2×C4×C5—41no—
155C2×C4×C5—81no—
156C2×C4×C5—81no—
157C2×C4×C5—81no—
158C2×C4×C5C2×SD1611yescharacteristic
159C2×C4×C5C2×SD1611yescharacteristic
160C2×C4×C5#13511yescharacteristic
161C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C5#13711yescharacteristic
164C5×C8—42no—
165C5×C8—42no—
166C5×C8—81no—
167C22×C8—21no—
168C22×C8—21no—
169C22×C8—21no—
170#125—42no—
171#125—42no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4C5×D411yescharacteristic
183C2×C4⋊C4C5×D411yescharacteristic
184C2×C4⋊C4C5×D411yescharacteristic
185C2×C4⋊C4C5×D411yescharacteristic
186C2×C4⋊C4C5×D411yescharacteristic
187C2×C4⋊C4C5×D411yescharacteristic
188C2×C42—21no—
189C2×C42C23×C511yescharacteristic
190#106—42no—
191#106—42no—
192#95—21no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198C22×C5#44811yescharacteristic
199C22×C5#44911yescharacteristic
200C22×C5#45011yescharacteristic
201C22×C5#45411yescharacteristic
202C22×C5#45611yescharacteristic
203C22×C5#45611yescharacteristic
204C22×C5#45811yescharacteristic
205C4×C5—21no—
206C4×C5—21no—
207C4×C5—21no—
208C4×C5—21no—
209C4×C5—21no—
210C4×C5—21no—
211C4×C5—42no—
212C4×C5—42no—
213C4×C5—81no—
214C4×C5—81no—
215C4×C5—81no—
216C4×C5—81no—
217C4×C5—161no—
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—22no—
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—42no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—81no—
259C4⋊C4C5×SD1612yes—
260C4⋊C4C5×SD1612yes—
261C42—41no—
262C42—42no—
263C2×C5#160911yescharacteristic
264C2×C5#161111yescharacteristic
265C2×C5#161611yescharacteristic
266C2×C5#162611yescharacteristic
267C2×C5#165111yescharacteristic
268C2×C5#165411yescharacteristic
269C2×C5#166311yescharacteristic
270C23C5×#12011yescharacteristic
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—22no—
278C2×C4—22no—
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—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4C2×C5×SD1611yescharacteristic
299C2×C4C2×C5×SD1611yescharacteristic
300C2×C4C5×#13511yescharacteristic
301C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
302C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
303C2×C4C5×#13711yescharacteristic
304C8—42no—
305C8—42no—
306C8—81no—
307C5#781511yescharacteristic, direct product factor, Sylow
308C22C5×#44811yescharacteristic
309C22C5×#44911yescharacteristic
310C22C5×#45011yescharacteristic
311C22C5×#45411yescharacteristic
312C22C5×#45611yescharacteristic
313C22C5×#45611yescharacteristic
314C22C5×#45811yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—42no—
322C4—42no—
323C4—81no—
324C4—81no—
325C4—81no—
326C4—81no—
327C4—161no—
328C2C5×#160911yescharacteristic
329C2C5×#161111yescharacteristic
330C2C5×#161611yescharacteristic
331C2C5×#162611yescharacteristic
332C2C5×#165111yescharacteristic
333C2C5×#165411yescharacteristic
334C2C5×#166311yescharacteristic
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. #7815C5direct (N × H)
307. C5#7815direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#27262
C5×#20992
C5×#20842
C5×#12712
#78155