Finite Group Databasebeta

← C59×#11520 #28423629

Subgroups — C59×#11520 #28423629

Order 15104.

418 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C59×#2317C211yesmaximal, characteristic
2C59×#1464C211yesmaximal, characteristic
3C59×#1464C211yesmaximal, characteristic
4C59×#1326C214yesmaximal
5C2×#117×C59C411yescharacteristic
6C2×#117×C59C2211yescharacteristic
7C22×C4⋊C4×C59C411yescharacteristic
8C59×#432—21no—
9C59×#432—21no—
10C59×#389—21no—
11C59×#389—21no—
12C59×#385C412yes—
13C59×#385C2212yes—
14C59×#384—21no—
15C59×#382—21no—
16C59×#324—21no—
17C59×#324—21no—
18C59×#323C2212yes—
19C59×#323C2212yes—
20C23×C4×C59C2×C411yescharacteristic
21C23×C4×C59C2×C412yes—
22#117×C59—24no—
23#117×C59—41no—
24#117×C59—41no—
25C2×C4⋊C4×C59—21no—
26C2×C4⋊C4×C59—21no—
27C2×C4⋊C4×C59—21no—
28C2×C4⋊C4×C59—22no—
29C2×C4⋊C4×C59—22no—
30C2×C4⋊C4×C59—41no—
31C2×C4⋊C4×C59—41no—
32C2×C4⋊C4×C59D411yescharacteristic
33C2×C4⋊C4×C59D411yescharacteristic
34C2×C22⋊C4×C59C2×C412yes—
35C2×C22⋊C4×C59C2×C411yescharacteristic
36C2×C22⋊C4×C59C2311yescharacteristic
37C2×C42×C59—21no—
38C2×C42×C59D411yescharacteristic
39C2×C42×C59D411yescharacteristic
40C4⋊C8×C59—41no—
41C4⋊C8×C59—41no—
42C22⋊C8×C59—22no—
43C22⋊C8×C59—22no—
44#97×C59—41no—
45#97×C59—41no—
46#95×C59—22no—
47#95×C59—22no—
48C24×C59C22×C411yescharacteristic
49C22×C4×C59—22no—
50C22×C4×C59—21no—
51C22×C4×C59—21no—
52C22×C4×C59—22no—
53C22×C4×C59—22no—
54C22×C4×C59—22no—
55C22×C4×C59—42no—
56C22×C4×C59—82no—
57C22×C4×C59C22⋊C411yescharacteristic
58C22×C4×C59C22⋊C411yescharacteristic
59C22×C4×C59C22⋊C411yescharacteristic
60C22×C4×C59C22⋊C411yescharacteristic
61C22×C4×C59C2×D411yescharacteristic
62C22×C4×C59C2×D411yescharacteristic
63C2×C8×C59—42no—
64C2×C8×C59—42no—
65C4⋊C4×C59—24no—
66C4⋊C4×C59—41no—
67C4⋊C4×C59—41no—
68C4⋊C4×C59—42no—
69C4⋊C4×C59—41no—
70C4⋊C4×C59—41no—
71C4⋊C4×C59—82no—
72C4⋊C4×C59—82no—
73C22⋊C4×C59—22no—
74C22⋊C4×C59—41no—
75C22⋊C4×C59—41no—
76C22⋊C4×C59M1614yes—
77C42×C59—24no—
78C42×C59—21no—
79C42×C59—21no—
80C42×C59—21no—
81C42×C59—21no—
82C23×C59—21no—
83C23×C59—21no—
84C23×C59—41no—
85C23×C59—41no—
86C23×C59C2×C22⋊C411yescharacteristic
87C23×C59C2×M1612yes—
88C2×C4×C59—24no—
89C2×C4×C59—24no—
90C2×C4×C59—21no—
91C2×C4×C59—21no—
92C2×C4×C59—21no—
93C2×C4×C59—21no—
94C2×C4×C59—24no—
95C2×C4×C59—21no—
96C2×C4×C59—21no—
97C2×C4×C59—21no—
98C2×C4×C59—21no—
99C2×C4×C59—42no—
100C2×C4×C59—42no—
101C2×C4×C59—41no—
102C2×C4×C59—41no—
103C2×C4×C59—41no—
104C2×C4×C59—41no—
105C2×C4×C59—42no—
106C2×C4×C59—42no—
107C2×C4×C59—42no—
108C2×C4×C59—84no—
109C2×C4×C59#9911yescharacteristic
110C2×C4×C59#9911yescharacteristic
111C2×C4×C59#10112yes—
112C8×C59—82no—
113C8×C59—82no—
114#11520C5911yesmaximal, characteristic, direct product factor, Sylow
115C22×C59—21no—
116C22×C59—21no—
117C22×C59—22no—
118C22×C59—42no—
119C22×C59—42no—
120C22×C59—41no—
121C22×C59—41no—
122C22×C59#40711yescharacteristic
123C22×C59C2×#9911yescharacteristic
124C22×C59C2×#10111yescharacteristic
125C4×C59—21no—
126C4×C59—21no—
127C4×C59—22no—
128C4×C59—44no—
129C4×C59—41no—
130C4×C59—41no—
131C4×C59—41no—
132C4×C59—41no—
133C4×C59—82no—
134#2317C2×C5911yescharacteristic
135#1464C2×C5911yescharacteristic
136#1464C2×C5911yescharacteristic
137#1326C2×C5914yes—
138C2×C59—21no—
139C2×C59—21no—
140C2×C59—42no—
141C2×C59#146311yescharacteristic
142C2×C59#212211yescharacteristic
143C2×C59#212311yescharacteristic
144C2×#117C4×C5911yescharacteristic
145C2×#117C22×C5911yescharacteristic
146C22×C4⋊C4C4×C5911yescharacteristic
147#432—21no—
148#432—21no—
149#389—21no—
150#389—21no—
151#385C4×C5912yes—
152#385C22×C5912yes—
153#384—21no—
154#382—21no—
155#324—21no—
156#324—21no—
157#323C22×C5912yes—
158#323C22×C5912yes—
159C59#1152011yescharacteristic, direct product factor, Sylow
160C23×C4C2×C4×C5911yescharacteristic
161C23×C4C2×C4×C5912yes—
162#117—24no—
163#117—41no—
164#117—41no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4D4×C5911yescharacteristic
173C2×C4⋊C4D4×C5911yescharacteristic
174C2×C22⋊C4C2×C4×C5912yes—
175C2×C22⋊C4C2×C4×C5911yescharacteristic
176C2×C22⋊C4C23×C5911yescharacteristic
177C2×C42—21no—
178C2×C42D4×C5911yescharacteristic
179C2×C42D4×C5911yescharacteristic
180C4⋊C8—41no—
181C4⋊C8—41no—
182C22⋊C8—22no—
183C22⋊C8—22no—
184#97—41no—
185#97—41no—
186#95—22no—
187#95—22no—
188C24C22×C4×C5911yescharacteristic
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—42no—
196C22×C4—82no—
197C22×C4C22⋊C4×C5911yescharacteristic
198C22×C4C22⋊C4×C5911yescharacteristic
199C22×C4C22⋊C4×C5911yescharacteristic
200C22×C4C22⋊C4×C5911yescharacteristic
201C22×C4C2×D4×C5911yescharacteristic
202C22×C4C2×D4×C5911yescharacteristic
203C2×C8—42no—
204C2×C8—42no—
205C4⋊C4—24no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—42no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—82no—
212C4⋊C4—82no—
213C22⋊C4—22no—
214C22⋊C4—41no—
215C22⋊C4—41no—
216C22⋊C4M16×C5914yes—
217C42—24no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—21no—
222C23—21no—
223C23—21no—
224C23—41no—
225C23—41no—
226C23C2×C22⋊C4×C5911yescharacteristic
227C23C2×M16×C5912yes—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—24no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—84no—
249C2×C4#99×C5911yescharacteristic
250C2×C4#99×C5911yescharacteristic
251C2×C4#101×C5912yes—
252C8—82no—
253C8—82no—
254C22—21no—
255C22—21no—
256C22—22no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22C59×#40711yescharacteristic
262C22C2×#99×C5911yescharacteristic
263C22C2×#101×C5911yescharacteristic
264C4—21no—
265C4—21no—
266C4—22no—
267C4—44no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—82no—
273C2—21no—
274C2—21no—
275C2—42no—
276C2C59×#146311yescharacteristic
277C2C59×#212211yescharacteristic
278C2C59×#212311yescharacteristic
subgroupG/H
center, socleC22×C59C2×#99
commutatorC24C22×C4×C59
Frattini, cosocleC2×C22⋊C4C23×C59
prime radicalC24×C59C22×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C22×C4×C59 ◁ C2×#117×C59 ◁ G

Complements

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

NH ≅ G/Ntype
114. #11520C59direct (N × H)
159. C59#11520direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#23172
C59×#14642
C59×#13262
#1152059