Finite Group Databasebeta

← C5×#10493 #11933213

Subgroups — C5×#10493 #11933213

Order 1280.

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

normal subgroups only

This group has 372 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×#3209C211yesmaximal, characteristic
2C5×#1966C211yesmaximal, characteristic
3C5×#1574C211yesmaximal, characteristic
4C5×#1561C211yesmaximal, characteristic
5C5×#1548C211yesmaximal, characteristic
6C5×#1485C211yesmaximal, characteristic
7C5×#1299C211yesmaximal, characteristic
8C5×#533C2211yescharacteristic
9C2×C5×C4⋊Q8C2211yescharacteristic
10C5×#494—21no—
11C5×#487—21no—
12C5×#462—21no—
13C5×#462—21no—
14C5×#451—22no—
15C5×#431C2211yescharacteristic
16C5×#431C2211yescharacteristic
17C5×#423C2211yescharacteristic
18C5×#423C2211yescharacteristic
19C2×C5×#101—22no—
20C4×C5×M16C2211yescharacteristic
21C5×#335—21no—
22C5×#334—21no—
23C5×#333—22no—
24C5×#332—21no—
25C5×#332—21no—
26C5×Q8⋊C8—22no—
27#10493C511yesmaximal, characteristic, direct product factor, Sylow
28C22×C5×Q8D412yes—
29C2×C5×Q16—22no—
30C2×C5×Q16—22no—
31C2×C5×M16—21no—
32C2×C5×M16—21no—
33C2×C5×M16—21no—
34C5×C4⋊Q8—21no—
35C5×C4⋊Q8—21no—
36C5×C4⋊Q8—21no—
37C5×C4⋊Q8—21no—
38C5×C4⋊Q8D411yescharacteristic
39C5×C4⋊Q8D411yescharacteristic
40C5×#125—21no—
41C5×C22⋊Q8—21no—
42C5×C22⋊Q8—21no—
43C4×C5×Q8—21no—
44C4×C5×Q8—21no—
45C5×#117—21no—
46C2×C5×C4⋊C4—21no—
47C2×C5×C4⋊C4—21no—
48C2×C42×C5C2311yescharacteristic
49C5×C4⋊C8—21no—
50C5×C4⋊C8—21no—
51C5×C4⋊C8—21no—
52C5×C4⋊C8—21no—
53C5×C4⋊C8D412yes—
54C5×C4⋊C8D411yescharacteristic
55C5×C4⋊C8D411yescharacteristic
56C5×#103—22no—
57C5×#103—22no—
58C5×#101—44no—
59C5×C22⋊C8—21no—
60C5×C22⋊C8—21no—
61C5×#97—21no—
62C4×C5×C8—21no—
63C4×C5×C8—21no—
64C4×C5×C8—21no—
65#3209C2×C511yescharacteristic
66#1966C2×C511yescharacteristic
67#1574C2×C511yescharacteristic
68#1561C2×C511yescharacteristic
69#1548C2×C511yescharacteristic
70#1485C2×C511yescharacteristic
71#1299C2×C511yescharacteristic
72C2×C5×Q8—21no—
73C2×C5×Q8—22no—
74C2×C5×Q8—21no—
75C2×C5×Q8—22no—
76C2×C5×Q8—42no—
77C2×C5×Q8—42no—
78C22×C4×C5—22no—
79C22×C4×C5C2×D411yescharacteristic
80C22×C4×C5#4111yescharacteristic
81C22×C4×C5#4111yescharacteristic
82C5×Q16—82no—
83C5×Q16—82no—
84C5×M16—22no—
85C5×M16—41no—
86C5×M16—42no—
87C5×M16—81no—
88C2×C5×C8—21no—
89C2×C5×C8—21no—
90C2×C5×C8—22no—
91C2×C5×C8—41no—
92C2×C5×C8—41no—
93C2×C5×C8—41no—
94C5×C4⋊C4—21no—
95C5×C4⋊C4—21no—
96C5×C4⋊C4—21no—
97C5×C4⋊C4—21no—
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×C22⋊C4—41no—
105C42×C5—41no—
106C42×C5C2×D411yescharacteristic
107C42×C5C2×D411yescharacteristic
108C42×C5C2×D411yescharacteristic
109C42×C5#4111yescharacteristic
110#533C22×C511yescharacteristic
111C2×C4⋊Q8C22×C511yescharacteristic
112#494—21no—
113#487—21no—
114#462—21no—
115#462—21no—
116#451—22no—
117#431C22×C511yescharacteristic
118#431C22×C511yescharacteristic
119#423C22×C511yescharacteristic
120#423C22×C511yescharacteristic
121C2×#101—22no—
122C4×M16C22×C511yescharacteristic
123#335—21no—
124#334—21no—
125#333—22no—
126#332—21no—
127#332—21no—
128Q8⋊C8—22no—
129C23×C5#12311yescharacteristic
130C5×Q8—41no—
131C5×Q8—42no—
132C5×Q8—41no—
133C5×Q8—42no—
134C5×Q8—41no—
135C5×Q8—41no—
136C5×Q8—82no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5—22no—
142C2×C4×C5—44no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
145C2×C4×C5—42no—
146C2×C4×C5#12011yescharacteristic
147C2×C4×C5#12111yescharacteristic
148C2×C4×C5#12111yescharacteristic
149C2×C4×C5#12111yescharacteristic
150C2×C4×C5#12311yescharacteristic
151C2×C4×C5#12411yescharacteristic
152C5×C8—42no—
153C5×C8—41no—
154C5×C8—41no—
155C5×C8—42no—
156C5×C8—81no—
157C5×C8—81no—
158C22×Q8C5×D412yes—
159C2×Q16—22no—
160C2×Q16—22no—
161C2×M16—21no—
162C2×M16—21no—
163C2×M16—21no—
164C4⋊Q8—21no—
165C4⋊Q8—21no—
166C4⋊Q8—21no—
167C4⋊Q8—21no—
168C4⋊Q8C5×D411yescharacteristic
169C4⋊Q8C5×D411yescharacteristic
170#125—21no—
171C22⋊Q8—21no—
172C22⋊Q8—21no—
173C4×Q8—21no—
174C4×Q8—21no—
175#117—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C42C23×C511yescharacteristic
179C4⋊C8—21no—
180C4⋊C8—21no—
181C4⋊C8—21no—
182C4⋊C8—21no—
183C4⋊C8C5×D412yes—
184C4⋊C8C5×D411yescharacteristic
185C4⋊C8C5×D411yescharacteristic
186#103—22no—
187#103—22no—
188#101—44no—
189C22⋊C8—21no—
190C22⋊C8—21no—
191#97—21no—
192C4×C8—21no—
193C4×C8—21no—
194C4×C8—21no—
195C22×C5—21no—
196C22×C5—21no—
197C22×C5—21no—
198C22×C5#39411yescharacteristic
199C4×C5—21no—
200C4×C5—21no—
201C4×C5—21no—
202C4×C5—81no—
203C4×C5—82no—
204C4×C5—81no—
205C4×C5#45311yescharacteristic
206C4×C5#45511yescharacteristic
207C4×C5#47111yescharacteristic
208C4×C5#47311yescharacteristic
209C4×C5#47312yes—
210C2×Q8—22no—
211C2×Q8—21no—
212C2×Q8—21no—
213C2×Q8—22no—
214C2×Q8—42no—
215C2×Q8—42no—
216C22×C4—22no—
217C22×C4C2×C5×D411yescharacteristic
218C22×C4C5×#4111yescharacteristic
219C22×C4C5×#4111yescharacteristic
220Q16—82no—
221Q16—82no—
222M16—22no—
223M16—41no—
224M16—42no—
225M16—81no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—22no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C22⋊C4—41no—
243C42—41no—
244C42C2×C5×D411yescharacteristic
245C42C2×C5×D411yescharacteristic
246C42C2×C5×D411yescharacteristic
247C42C5×#4111yescharacteristic
248C2×C5—41no—
249C2×C5#203711yescharacteristic
250C2×C5#204711yescharacteristic
251C2×C5#205211yescharacteristic
252C23C5×#12311yescharacteristic
253Q8—41no—
254Q8—42no—
255Q8—41no—
256Q8—42no—
257Q8—41no—
258Q8—41no—
259Q8—82no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—44no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4C5×#12011yescharacteristic
270C2×C4C5×#12111yescharacteristic
271C2×C4C5×#12111yescharacteristic
272C2×C4C5×#12111yescharacteristic
273C2×C4C5×#12311yescharacteristic
274C2×C4C5×#12411yescharacteristic
275C8—42no—
276C8—41no—
277C8—41no—
278C8—42no—
279C8—81no—
280C8—81no—
281C5#1049311yescharacteristic, direct product factor, Sylow
282C22—21no—
283C22—21no—
284C22—21no—
285C22C5×#39411yescharacteristic
286C4—21no—
287C4—21no—
288C4—21no—
289C4—82no—
290C4—81no—
291C4—81no—
292C4C5×#45311yescharacteristic
293C4C5×#45511yescharacteristic
294C4C5×#47111yescharacteristic
295C4C5×#47312yes—
296C4C5×#47311yescharacteristic
297C2—41no—
298C2C5×#203711yescharacteristic
299C2C5×#204711yescharacteristic
300C2C5×#205211yescharacteristic
subgroupG/H
center, socleC22×C5#394
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC23×C5#123
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
27. #10493C5direct (N × H)
281. C5#10493direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32092
C5×#19662
C5×#15742
C5×#15612
C5×#15482
C5×#14852
C5×#12992
#104935