Finite Group Databasebeta

← C5×#9973 #11932693

Subgroups — C5×#9973 #11932693

Order 1280.

632 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 138 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
1C2×C5×#483C212yesmaximal
2C5×#2659C211yesmaximal, characteristic
3C2×C5×#328C212yesmaximal
4C5×#1445C211yesmaximal, characteristic
5C5×#1280C211yesmaximal, characteristic
6C2×C5×C22⋊Q8C2212yes—
7C22×C5×C4⋊C4C2211yescharacteristic
8C5×#483—24no—
9C5×#483—24no—
10C2×C5×#106—22no—
11C2×C5×#103—22no—
12C2×C5×C22⋊C8C2212yes—
13C5×#398—22no—
14C5×#395—22no—
15C5×#380—22no—
16C2×C5×#95—22no—
17C2×C5×#95C2211yescharacteristic
18C2×C5×#95C2211yescharacteristic
19C5×#328—24no—
20#9973C511yesmaximal, characteristic, direct product factor, Sylow
21C22×C5×Q8D412yes—
22C23×C4×C5—21no—
23C23×C4×C5—21no—
24C23×C4×C5D412yes—
25C23×C4×C5C2311yescharacteristic
26C22×C5×C8—22no—
27C5×C22⋊Q8—22no—
28C5×C22⋊Q8—22no—
29C5×C22⋊Q8—22no—
30C5×C22⋊Q8—22no—
31C2×C5×C4⋊C4—22no—
32C2×C5×C4⋊C4—22no—
33C2×C5×C4⋊C4—22no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—22no—
36C2×C5×C4⋊C4—22no—
37C2×C5×C4⋊C4D412yes—
38C2×C5×C4⋊C4D412yes—
39C2×C5×C22⋊C4—22no—
40C5×#106—28no—
41C5×#103—28no—
42C5×C22⋊C8—22no—
43C5×C22⋊C8D414yes—
44C5×#95—24no—
45C5×#95—22no—
46C5×#95—22no—
47C5×#95—44no—
48C2×#483C2×C512yes—
49#2659C2×C511yescharacteristic
50C2×#328C2×C512yes—
51#1445C2×C511yescharacteristic
52#1280C2×C511yescharacteristic
53C24×C5C2×D411yescharacteristic
54C2×C5×Q8—22no—
55C2×C5×Q8—22no—
56C2×C5×Q8—44no—
57C22×C4×C5—22no—
58C22×C4×C5—22no—
59C22×C4×C5—22no—
60C22×C4×C5—22no—
61C22×C4×C5—22no—
62C22×C4×C5—22no—
63C22×C4×C5—42no—
64C22×C4×C5—42no—
65C22×C4×C5—42no—
66C22×C4×C5—41no—
67C22×C4×C5—42no—
68C22×C4×C5—41no—
69C22×C4×C5—41no—
70C22×C4×C5—41no—
71C22×C4×C5—42no—
72C22×C4×C5—42no—
73C22×C4×C5—42no—
74C22×C4×C5SD1614yes—
75C22×C4×C5C2×D412yes—
76C22×C4×C5C2×D411yescharacteristic
77C22×C4×C5C2×D412yes—
78C22×C4×C5#4111yescharacteristic
79C2×C5×C8—24no—
80C2×C5×C8—44no—
81C5×C4⋊C4—24no—
82C5×C4⋊C4—22no—
83C5×C4⋊C4—22no—
84C5×C4⋊C4—42no—
85C5×C4⋊C4—42no—
86C5×C4⋊C4—42no—
87C5×C4⋊C4—82no—
88C5×C4⋊C4—82no—
89C5×C22⋊C4—42no—
90C5×C22⋊C4—42no—
91C2×C22⋊Q8C22×C512yes—
92C22×C4⋊C4C22×C511yescharacteristic
93#483—24no—
94#483—24no—
95C2×#106—22no—
96C2×#103—22no—
97C2×C22⋊C8C22×C512yes—
98#398—22no—
99#395—22no—
100#380—22no—
101C2×#95—22no—
102C2×#95C22×C511yescharacteristic
103C2×#95C22×C511yescharacteristic
104#328—24no—
105C23×C5—21no—
106C23×C5—21no—
107C23×C5—22no—
108C23×C5#12011yescharacteristic
109C23×C5#12111yescharacteristic
110C23×C5#12711yescharacteristic
111C23×C5C2×SD1612yes—
112C23×C5#13712yes—
113C5×Q8—44no—
114C5×Q8—82no—
115C2×C4×C5—24no—
116C2×C4×C5—24no—
117C2×C4×C5—41no—
118C2×C4×C5—42no—
119C2×C4×C5—41no—
120C2×C4×C5—42no—
121C2×C4×C5—42no—
122C2×C4×C5—44no—
123C2×C4×C5—44no—
124C2×C4×C5—42no—
125C2×C4×C5—42no—
126C2×C4×C5—42no—
127C2×C4×C5—42no—
128C2×C4×C5—42no—
129C2×C4×C5—42no—
130C2×C4×C5—44no—
131C2×C4×C5—44no—
132C2×C4×C5—82no—
133C2×C4×C5—82no—
134C2×C4×C5—81no—
135C2×C4×C5—82no—
136C2×C4×C5—81no—
137C2×C4×C5—81no—
138C2×C4×C5—81no—
139C2×C4×C5#12012yes—
140C2×C4×C5#12112yes—
141C5×C8—44no—
142C22×Q8C5×D412yes—
143C23×C4—21no—
144C23×C4—21no—
145C23×C4C5×D412yes—
146C23×C4C23×C511yescharacteristic
147C22×C8—22no—
148C22⋊Q8—22no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C22⋊Q8—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4C5×D412yes—
159C2×C4⋊C4C5×D412yes—
160C2×C22⋊C4—22no—
161#106—28no—
162#103—28no—
163C22⋊C8—22no—
164C22⋊C8C5×D414yes—
165#95—24no—
166#95—22no—
167#95—22no—
168#95—44no—
169C22×C5—22no—
170C22×C5—22no—
171C22×C5—22no—
172C22×C5—22no—
173C22×C5—21no—
174C22×C5—21no—
175C22×C5—21no—
176C22×C5—21no—
177C22×C5#39211yescharacteristic
178C22×C5#44812yes—
179C22×C5#45511yescharacteristic
180C22×C5#45611yescharacteristic
181C22×C5#45812yes—
182C22×C5#46112yes—
183C22×C5#49211yescharacteristic
184C22×C5#49711yescharacteristic
185C4×C5—22no—
186C4×C5—22no—
187C4×C5—44no—
188C4×C5—82no—
189C4×C5—82no—
190C4×C5—82no—
191C4×C5—82no—
192C24C2×C5×D411yescharacteristic
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—44no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—41no—
206C22×C4—42no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4C5×SD1614yes—
214C22×C4C2×C5×D412yes—
215C22×C4C2×C5×D411yescharacteristic
216C22×C4C2×C5×D412yes—
217C22×C4C5×#4111yescharacteristic
218C2×C8—24no—
219C2×C8—44no—
220C4⋊C4—24no—
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—82no—
227C4⋊C4—82no—
228C22⋊C4—42no—
229C22⋊C4—42no—
230C2×C5—21no—
231C2×C5—22no—
232C2×C5—21no—
233C2×C5#160812yes—
234C2×C5#161112yes—
235C2×C5#200711yescharacteristic
236C2×C5#201311yescharacteristic
237C2×C5#202211yescharacteristic
238C23—21no—
239C23—21no—
240C23—22no—
241C23C5×#12011yescharacteristic
242C23C5×#12111yescharacteristic
243C23C5×#12711yescharacteristic
244C23C2×C5×SD1612yes—
245C23C5×#13712yes—
246Q8—44no—
247Q8—82no—
248C2×C4—24no—
249C2×C4—24no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—44no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—44no—
264C2×C4—44no—
265C2×C4—82no—
266C2×C4—81no—
267C2×C4—82no—
268C2×C4—82no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4C5×#12012yes—
273C2×C4C5×#12112yes—
274C8—44no—
275C5#997311yescharacteristic, direct product factor, Sylow
276C22—21no—
277C22—21no—
278C22—22no—
279C22—22no—
280C22—22no—
281C22—22no—
282C22—21no—
283C22—21no—
284C22C5×#39211yescharacteristic
285C22C5×#44812yes—
286C22C5×#45511yescharacteristic
287C22C5×#45611yescharacteristic
288C22C5×#45812yes—
289C22C5×#46112yes—
290C22C5×#49211yescharacteristic
291C22C5×#49711yescharacteristic
292C4—22no—
293C4—22no—
294C4—44no—
295C4—82no—
296C4—82no—
297C4—82no—
298C4—82no—
299C2—21no—
300C2—22no—
301C2—21no—
302C2C5×#160812yes—
303C2C5×#161112yes—
304C2C5×#200711yescharacteristic
305C2C5×#201311yescharacteristic
306C2C5×#202211yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutator, Frattini, cosocleC23×C4C23×C5
prime radicalC24×C5C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
20. #9973C5direct (N × H)
275. C5#9973direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4832
C5×#26592
C2×C5×#3282
C5×#14452
C5×#12802
#99735