Finite Group Databasebeta

← C5×#12095 #11934815

Subgroups — C5×#12095 #11934815

Order 1280.

458 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2817C211yesmaximal, characteristic, complemented
2C5×#2022C211yesmaximal, characteristic
3C5×#1607C212yesmaximal
4C5×#1344C212yesmaximal, complemented
5C5×#1317C211yesmaximal, characteristic, complemented
6C5×#534C2211yescharacteristic
7C2×C5×#123—21no—
8C2×C5×C22⋊Q8—21no—
9C5×#480—22no—
10C2×C5×#99—21no—
11C5×#400—22no—
12C5×#397—21no—
13C5×#397C2212yes—
14C5×#395—22no—
15C5×#381C2211yescharacteristic
16C5×#342C2211yescharacteristic
17C5×#327—22no—
18C5×#323C2212yes—
19#12095C511yesmaximal, characteristic, direct product factor, Sylow
20C22×C5×Q8—21no—
21C22×C5×D4—21no—
22C23×C4×C5D411yescharacteristic
23C5×#123—42no—
24C5×#123—41no—
25C5×#123—42no—
26C5×C22⋊Q8—42no—
27C5×C22⋊Q8—42no—
28C5×#121—22no—
29C5×#120—41no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—41no—
34C2×C5×C4⋊C4D412yes—
35C2×C5×C22⋊C4—21no—
36C2×C5×C22⋊C4—22no—
37C2×C5×C22⋊C4—41no—
38C2×C5×C22⋊C4D411yescharacteristic
39C2×C5×C22⋊C4C2311yescharacteristic
40C5×#107—42no—
41C5×#102—42no—
42C5×#99—42no—
43C5×C22⋊C8—22no—
44C5×#95—22no—
45C5×#95—21no—
46C5×#95—22no—
47C5×#95—22no—
48C5×#95D412yes—
49#2817C2×C511yescharacteristic, complemented
50#2022C2×C511yescharacteristic
51#1607C2×C512yes—
52#1344C2×C512yescomplemented
53#1317C2×C511yescharacteristic, complemented
54C24×C5—21no—
55C24×C5C2×D411yescharacteristic
56C2×C5×Q8—42no—
57C2×C5×Q8—81no—
58C2×C5×Q8—81no—
59C2×C5×D4—22no—
60C2×C5×D4—41no—
61C2×C5×D4—41no—
62C2×C5×D4—41no—
63C2×C5×D4—41no—
64C2×C5×D4—41no—
65C2×C5×D4—41no—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5—21no—
69C22×C4×C5—22no—
70C22×C4×C5—22no—
71C22×C4×C5—21no—
72C22×C4×C5—41no—
73C22×C4×C5—41no—
74C22×C4×C5—41no—
75C22×C4×C5D812yes—
76C22×C4×C5C2×D412yes—
77C2×C5×C8—42no—
78C5×C4⋊C4—22no—
79C5×C4⋊C4—42no—
80C5×C4⋊C4—42no—
81C5×C4⋊C4—44no—
82C5×C4⋊C4—44no—
83C5×C4⋊C4—81no—
84C5×C22⋊C4—22no—
85C5×C22⋊C4—41no—
86C5×C22⋊C4—42no—
87C5×C22⋊C4—44no—
88C5×C22⋊C4—42no—
89C5×C22⋊C4—41no—
90C5×C22⋊C4—42no—
91C5×C22⋊C4—41no—
92#534C22×C511yescharacteristic
93C2×#123—21no—
94C2×C22⋊Q8—21no—
95#480—22no—
96C2×#99—21no—
97#400—22no—
98#397—21no—
99#397C22×C512yes—
100#395—22no—
101#381C22×C511yescharacteristic
102#342C22×C511yescharacteristic
103#327—22no—
104#323C22×C512yes—
105C23×C5—21no—
106C23×C5—21no—
107C23×C5—42no—
108C23×C5—41no—
109C23×C5—41no—
110C23×C5—41no—
111C23×C5—82no—
112C23×C5#12011yescharacteristic
113C23×C5C2×D811yescharacteristic
114C23×C5AGL(1,ℤ/8)11yescharacteristic
115C5×Q8—84no—
116C5×D4—82no—
117C5×D4—81no—
118C5×D4—81no—
119C5×D4—81no—
120C5×D4—81no—
121C2×C4×C5—22no—
122C2×C4×C5—22no—
123C2×C4×C5—41no—
124C2×C4×C5—41no—
125C2×C4×C5—42no—
126C2×C4×C5—42no—
127C2×C4×C5—42no—
128C2×C4×C5—41no—
129C2×C4×C5—44no—
130C2×C4×C5—42no—
131C2×C4×C5—41no—
132C2×C4×C5—42no—
133C2×C4×C5—42no—
134C2×C4×C5—41no—
135C2×C4×C5—42no—
136C2×C4×C5—41no—
137C2×C4×C5—42no—
138C2×C4×C5—81no—
139C2×C4×C5—82no—
140C5×C8—82no—
141C22×Q8—21no—
142C22×D4—21no—
143C23×C4C5×D411yescharacteristic
144#123—42no—
145#123—41no—
146#123—42no—
147C22⋊Q8—42no—
148C22⋊Q8—42no—
149#121—22no—
150#120—41no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4C5×D412yes—
156C2×C22⋊C4—21no—
157C2×C22⋊C4—22no—
158C2×C22⋊C4—41no—
159C2×C22⋊C4C5×D411yescharacteristic
160C2×C22⋊C4C23×C511yescharacteristic
161#107—42no—
162#102—42no—
163#99—42no—
164C22⋊C8—22no—
165#95—22no—
166#95—21no—
167#95—22no—
168#95—22no—
169#95C5×D412yes—
170C22×C5—22no—
171C22×C5—21no—
172C22×C5—21no—
173C22×C5—41no—
174C22×C5—41no—
175C22×C5—42no—
176C22×C5—81no—
177C22×C5—82no—
178C22×C5—81no—
179C22×C5—82no—
180C22×C5—161no—
181C22×C5#44711yescharacteristic
182C22×C5#45311yescharacteristic
183C22×C5B(4,𝔽2)11yescharacteristic
184C4×C5—42no—
185C4×C5—42no—
186C4×C5—82no—
187C4×C5—81no—
188C4×C5—82no—
189C4×C5—81no—
190C4×C5—82no—
191C24—21no—
192C24C2×C5×D411yescharacteristic
193C2×Q8—42no—
194C2×Q8—81no—
195C2×Q8—81no—
196C2×D4—22no—
197C2×D4—41no—
198C2×D4—41no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4—41no—
202C2×D4—41no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4C5×D812yes—
213C22×C4C2×C5×D412yes—
214C2×C8—42no—
215C4⋊C4—22no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C4⋊C4—44no—
219C4⋊C4—44no—
220C4⋊C4—81no—
221C22⋊C4—22no—
222C22⋊C4—41no—
223C22⋊C4—42no—
224C22⋊C4—44no—
225C22⋊C4—42no—
226C22⋊C4—41no—
227C22⋊C4—42no—
228C22⋊C4—41no—
229C2×C5—21no—
230C2×C5—21no—
231C2×C5—41no—
232C2×C5—41no—
233C2×C5—161no—
234C2×C5#159511yescharacteristic
235C2×C5#220112yes—
236C23—21no—
237C23—21no—
238C23—42no—
239C23—41no—
240C23—41no—
241C23—41no—
242C23—82no—
243C23C5×#12011yescharacteristic
244C23C2×C5×D811yescharacteristic
245C23C5×AGL(1,ℤ/8)11yescharacteristic
246Q8—84no—
247D4—82no—
248D4—81no—
249D4—81no—
250D4—81no—
251D4—81no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—44no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—81no—
270C2×C4—82no—
271C8—82no—
272C5#1209511yescharacteristic, direct product factor, Sylow
273C22—22no—
274C22—21no—
275C22—21no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—81no—
280C22—82no—
281C22—81no—
282C22—82no—
283C22—161no—
284C22C5×#44711yescharacteristic
285C22C5×#45311yescharacteristic
286C22C5×B(4,𝔽2)11yescharacteristic
287C4—42no—
288C4—42no—
289C4—82no—
290C4—81no—
291C4—82no—
292C4—81no—
293C4—82no—
294C2—21no—
295C2—21no—
296C2—41no—
297C2—41no—
298C2—161no—
299C2C5×#159511yescharacteristic
300C2C5×#220112yes—
subgroupG/H
center, socleC22×C5B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C5
prime radicalC5×#534C22
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C5 ◁ C2×C5×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#2817C2semidirect
4. C5×#1344C2semidirect
5. C5×#1317C2semidirect
19. #12095C5direct (N × H)
49. #2817C2×C5semidirect
52. #1344C2×C5semidirect
53. #1317C2×C5semidirect
272. C5#12095direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#28172
C5×#20222
C5×#16072
C5×#13442
C5×#13172
#120955