Finite Group Databasebeta

← C59×#18531 #28430640

Subgroups — C59×#18531 #28430640

Order 15104.

982 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 982 conjugacy classes of subgroups — too many to draw. Only its 230 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×C59×#559C211yesmaximal, characteristic
2C59×#3138C211yesmaximal, characteristic
3C59×#3113C212yesmaximal, complemented
4C59×#1640C218yesmaximal, complemented
5C59×#1555C211yesmaximal, characteristic
6C59×#1491C212yesmaximal, complemented
7C59×#559—22no—
8C59×#559—24no—
9C59×#559C2214yes—
10C59×#533C2211yescharacteristic
11C2×#127×C59C2211yescharacteristic
12C2×#124×C59—22no—
13C2×#123×C59—22no—
14C2×C4×Q8×C59C2212yes—
15C2×C4×D4×C59—22no—
16C59×#490—22no—
17C59×#486C2214yes—
18C59×#483—22no—
19C59×#475C2214yescomplemented
20C59×#462C2214yescomplemented
21C59×#451—22no—
22C59×#441—24no—
23C59×#432C2212yes—
24C59×#418—22no—
25C4×M16×C59C2211yescharacteristic
26C59×#331C2214yes—
27C59×Q8⋊C8C2218yescomplemented
28C22×Q8×C59D412yes—
29C22×D4×C59—22no—
30C22×D4×C59D412yes—
31C23×C4×C59—22no—
32C2×Q16×C59—24no—
33C2×M16×C59—21no—
34C4⋊Q8×C59C2312yes—
35#127×C59—22no—
36#127×C59D412yes—
37#127×C59C2312yes—
38#125×C59—21no—
39#124×C59—28no—
40#124×C59—28no—
41#123×C59—28no—
42#123×C59—28no—
43C22⋊Q8×C59—22no—
44C4×Q8×C59—22no—
45C4×Q8×C59—22no—
46C4×Q8×C59—22no—
47C4×Q8×C59D414yes—
48C4×Q8×C59C2314yes—
49C4×D4×C59—28no—
50C4×D4×C59—28no—
51#117×C59—21no—
52C2×C4⋊C4×C59—22no—
53C2×C4⋊C4×C59D412yes—
54C2×C22⋊C4×C59—24no—
55C2×C22⋊C4×C59—22no—
56C2×C42×C59—22no—
57C2×C42×C59C2311yescharacteristic
58#106×C59—24no—
59C4⋊C8×C59C2314yes—
60#103×C59—24no—
61#103×C59—24no—
62#102×C59—28no—
63C22⋊C8×C59—22no—
64#97×C59—21no—
65#97×C59—22no—
66C4×C8×C59C2312yes—
67C24×C59—22no—
68C2×Q8×C59—22no—
69C2×Q8×C59—22no—
70C2×Q8×C59—44no—
71C2×Q8×C59C2×D414yes—
72C2×D4×C59—24no—
73C2×D4×C59—22no—
74C2×D4×C59—24no—
75C2×D4×C59—48no—
76C2×D4×C59—44no—
77C2×D4×C59C2×D414yes—
78C22×C4×C59—22no—
79C22×C4×C59—22no—
80C22×C4×C59—28no—
81C22×C4×C59—84no—
82C22×C4×C59C2×D412yes—
83C22×C4×C59C2×D411yescharacteristic
84Q16×C59—48no—
85M16×C59—42no—
86C2×C8×C59—22no—
87C2×C8×C59—24no—
88C4⋊C4×C59—24no—
89C4⋊C4×C59—22no—
90C4⋊C4×C59—24no—
91C4⋊C4×C59—22no—
92C4⋊C4×C59—22no—
93C4⋊C4×C59—42no—
94C4⋊C4×C59C2×D414yes—
95C22⋊C4×C59—216no—
96C22⋊C4×C59—28no—
97C22⋊C4×C59—41no—
98C42×C59—24no—
99C42×C59—24no—
100C42×C59—41no—
101C42×C59C2×D412yes—
102C42×C59C2×D411yescharacteristic
103C42×C59C2411yescharacteristic
104C23×C59—24no—
105C23×C59—48no—
106C23×C59—44no—
107C23×C59#12011yescharacteristic
108Q8×C59—24no—
109Q8×C59—24no—
110Q8×C59—44no—
111Q8×C59—44no—
112D4×C59—44no—
113D4×C59—48no—
114D4×C59—48no—
115D4×C59—82no—
116C2×C4×C59—22no—
117C2×C4×C59—24no—
118C2×C4×C59—24no—
119C2×C4×C59—24no—
120C2×C4×C59—44no—
121C2×C4×C59—44no—
122C2×C4×C59—42no—
123C2×C4×C59—88no—
124C2×C4×C59#12012yes—
125C2×C4×C59#12011yescharacteristic
126C2×C4×C59C22×D411yescharacteristic
127C2×C4×C59C22×D412yes—
128C8×C59—42no—
129C8×C59—44no—
130#18531C5911yesmaximal, characteristic, direct product factor, Sylow
131C22×C59—22no—
132C22×C59—48no—
133C22×C59—44no—
134C22×C59—88no—
135C22×C59#45512yes—
136C22×C59C2×#12011yescharacteristic
137C4×C59—22no—
138C4×C59—21no—
139C4×C59—21no—
140C4×C59—44no—
141C4×C59—44no—
142C4×C59—82no—
143C4×C59#57514yes—
144C2×#559C2×C5911yescharacteristic
145#3138C2×C5911yescharacteristic
146#3113C2×C5912yescomplemented
147#1640C2×C5918yescomplemented
148#1555C2×C5911yescharacteristic
149#1491C2×C5912yescomplemented
150C2×C59—22no—
151C2×C59—84no—
152C2×C59#300512yes—
153C2×C59C2×#45511yescharacteristic
154#559—22no—
155#559—24no—
156#559C22×C5914yes—
157#533C22×C5911yescharacteristic
158C2×#127C22×C5911yescharacteristic
159C2×#124—22no—
160C2×#123—22no—
161C2×C4×Q8C22×C5912yes—
162C2×C4×D4—22no—
163#490—22no—
164#486C22×C5914yes—
165#483—22no—
166#475C22×C5914yescomplemented
167#462C22×C5914yescomplemented
168#451—22no—
169#441—24no—
170#432C22×C5912yes—
171#418—22no—
172C4×M16C22×C5911yescharacteristic
173#331C22×C5914yes—
174Q8⋊C8C22×C5918yescomplemented
175C59#1853111yescharacteristic, direct product factor, Sylow
176C22×Q8D4×C5912yes—
177C22×D4—22no—
178C22×D4D4×C5912yes—
179C23×C4—22no—
180C2×Q16—24no—
181C2×M16—21no—
182C4⋊Q8C23×C5912yes—
183#127—22no—
184#127D4×C5912yes—
185#127C23×C5912yes—
186#125—21no—
187#124—28no—
188#124—28no—
189#123—28no—
190#123—28no—
191C22⋊Q8—22no—
192C4×Q8—22no—
193C4×Q8—22no—
194C4×Q8—22no—
195C4×Q8D4×C5914yes—
196C4×Q8C23×C5914yes—
197C4×D4—28no—
198C4×D4—28no—
199#117—21no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4D4×C5912yes—
202C2×C22⋊C4—24no—
203C2×C22⋊C4—22no—
204C2×C42—22no—
205C2×C42C23×C5911yescharacteristic
206#106—24no—
207C4⋊C8C23×C5914yes—
208#103—24no—
209#103—24no—
210#102—28no—
211C22⋊C8—22no—
212#97—21no—
213#97—22no—
214C4×C8C23×C5912yes—
215C24—22no—
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—44no—
219C2×Q8C2×D4×C5914yes—
220C2×D4—24no—
221C2×D4—22no—
222C2×D4—24no—
223C2×D4—48no—
224C2×D4—44no—
225C2×D4C2×D4×C5914yes—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—28no—
229C22×C4—84no—
230C22×C4C2×D4×C5912yes—
231C22×C4C2×D4×C5911yescharacteristic
232Q16—48no—
233M16—42no—
234C2×C8—22no—
235C2×C8—24no—
236C4⋊C4—24no—
237C4⋊C4—22no—
238C4⋊C4—24no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—42no—
242C4⋊C4C2×D4×C5914yes—
243C22⋊C4—216no—
244C22⋊C4—28no—
245C22⋊C4—41no—
246C42—24no—
247C42—24no—
248C42—41no—
249C42C2×D4×C5912yes—
250C42C2×D4×C5911yescharacteristic
251C42C24×C5911yescharacteristic
252C23—24no—
253C23—48no—
254C23—44no—
255C23#120×C5911yescharacteristic
256Q8—24no—
257Q8—24no—
258Q8—44no—
259Q8—44no—
260D4—44no—
261D4—48no—
262D4—48no—
263D4—82no—
264C2×C4—22no—
265C2×C4—24no—
266C2×C4—24no—
267C2×C4—24no—
268C2×C4—44no—
269C2×C4—44no—
270C2×C4—42no—
271C2×C4—88no—
272C2×C4#120×C5912yes—
273C2×C4#120×C5911yescharacteristic
274C2×C4C22×D4×C5911yescharacteristic
275C2×C4C22×D4×C5912yes—
276C8—42no—
277C8—44no—
278C22—22no—
279C22—48no—
280C22—44no—
281C22—88no—
282C22C59×#45512yes—
283C22C2×#120×C5911yescharacteristic
284C4—22no—
285C4—21no—
286C4—21no—
287C4—44no—
288C4—44no—
289C4—82no—
290C4C59×#57514yes—
291C2—22no—
292C2—84no—
293C2C59×#300512yes—
294C2C2×C59×#45511yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC42C24×C59
prime radicalC2×#127×C59C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
3. C59×#3113C2semidirect
4. C59×#1640C2semidirect
6. C59×#1491C2semidirect
19. C59×#475C22semidirect
20. C59×#462C22semidirect
27. C59×Q8⋊C8C22semidirect
130. #18531C59direct (N × H)
146. #3113C2×C59semidirect
147. #1640C2×C59semidirect
149. #1491C2×C59semidirect
166. #475C22×C59semidirect
167. #462C22×C59semidirect
174. Q8⋊C8C22×C59semidirect
175. C59#18531direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#5592
C59×#31382
C59×#31132
C59×#16402
C59×#15552
C59×#14912
#1853159