Finite Group Databasebeta

← C2×C59×#1324 #28423554

Subgroups — C2×C59×#1324 #28423554

Order 15104.

510 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 158 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×#382C211yesmaximal, characteristic
2C2×C59×#324C212yesmaximal
3C59×#1324C214yesmaximal, direct product factor
4C22×C4⋊C4×C59C411yescharacteristic
5C22×C4⋊C4×C59C2211yescharacteristic
6C22×C42×C59C411yescharacteristic
7C2×C22⋊C8×C59—22no—
8C59×#382—22no—
9C59×#382C412yes—
10C59×#382C2212yes—
11C2×#95×C59—22no—
12C59×#324—22no—
13C59×#324C2214yes—
14C23×C4×C59—21no—
15C23×C4×C59—21no—
16C23×C4×C59C2×C411yescharacteristic
17C23×C4×C59D412yes—
18C22×C8×C59—42no—
19C2×C4⋊C4×C59—21no—
20C2×C4⋊C4×C59—41no—
21C2×C4⋊C4×C59—41no—
22C2×C4⋊C4×C59—41no—
23C2×C4⋊C4×C59—41no—
24C2×C4⋊C4×C59C2×C412yes—
25C2×C4⋊C4×C59C2×C411yescharacteristic
26C2×C4⋊C4×C59D412yes—
27C2×C4⋊C4×C59C2311yescharacteristic
28C2×C42×C59—21no—
29C2×C42×C59—22no—
30C2×C42×C59C814yescomplemented
31C2×C42×C59C2×C412yes—
32C22⋊C8×C59—24no—
33C22⋊C8×C59—42no—
34#95×C59—24no—
35#95×C59—24no—
36C24×C59C22⋊C411yescharacteristic
37C22×C4×C59—21no—
38C22×C4×C59—21no—
39C22×C4×C59—22no—
40C22×C4×C59—24no—
41C22×C4×C59—22no—
42C22×C4×C59—22no—
43C22×C4×C59—22no—
44C22×C4×C59—22no—
45C22×C4×C59—42no—
46C22×C4×C59—42no—
47C22×C4×C59—44no—
48C22×C4×C59—44no—
49C22×C4×C59—41no—
50C22×C4×C59—41no—
51C22×C4×C59C22⋊C411yescharacteristic
52C22×C4×C59C22⋊C412yes—
53C22×C4×C59C2×C812yes—
54C22×C4×C59M1612yes—
55C22×C4×C59C22×C411yescharacteristic
56C22×C4×C59C2×D412yes—
57C2×C8×C59—44no—
58C2×C8×C59—84no—
59C4⋊C4×C59—41no—
60C4⋊C4×C59—42no—
61C4⋊C4×C59—41no—
62C4⋊C4×C59—42no—
63C4⋊C4×C59—42no—
64C42×C59—24no—
65C42×C59—22no—
66C42×C59C2×C814yescomplemented
67C23×C59—22no—
68C23×C59—22no—
69C23×C59C22⋊C812yes—
70C23×C59#9911yescharacteristic
71C23×C59#9911yescharacteristic
72C23×C59#10112yes—
73C23×C59C2×C22⋊C411yescharacteristic
74C2×C4×C59—22no—
75C2×C4×C59—22no—
76C2×C4×C59—22no—
77C2×C4×C59—22no—
78C2×C4×C59—21no—
79C2×C4×C59—21no—
80C2×C4×C59—21no—
81C2×C4×C59—21no—
82C2×C4×C59—24no—
83C2×C4×C59—22no—
84C2×C4×C59—22no—
85C2×C4×C59—48no—
86C2×C4×C59—42no—
87C2×C4×C59—42no—
88C2×C4×C59—44no—
89C2×C4×C59—42no—
90C2×C4×C59—42no—
91C2×C4×C59—44no—
92C2×C4×C59—42no—
93C2×C4×C59—82no—
94C2×C4×C59—82no—
95C2×C4×C59—82no—
96C2×C4×C59C22⋊C812yes—
97C2×C4×C59C22×C811yescharacteristic
98C2×C4×C59C2×M1611yescharacteristic
99C8×C59—84no—
100C2×#1324C5911yesmaximal, characteristic, direct product factor, Sylow
101C22×C59—24no—
102C22×C59—24no—
103C22×C59—21no—
104C22×C59—21no—
105C22×C59—21no—
106C22×C59—21no—
107C22×C59#32412yes—
108C22×C59#32412yes—
109C22×C59#35412yes—
110C22×C59#35512yes—
111C22×C59C2×C22⋊C811yescharacteristic
112C22×C59C2×#9911yescharacteristic
113C22×C59C2×#10111yescharacteristic
114C4×C59—22no—
115C4×C59—21no—
116C4×C59—21no—
117C4×C59—44no—
118C4×C59—42no—
119C4×C59—42no—
120C4×C59—82no—
121C2×#382C2×C5911yescharacteristic
122C2×#324C2×C5912yes—
123#1324C2×C5914yesdirect product factor
124C2×C59—21no—
125C2×C59—22no—
126C2×C59—21no—
127C2×C59#132414yesdirect product factor
128C2×C59C2×#32411yescharacteristic
129C2×C59C2×#35411yescharacteristic
130C2×C59C2×#35511yescharacteristic
131C22×C4⋊C4C4×C5911yescharacteristic
132C22×C4⋊C4C22×C5911yescharacteristic
133C22×C42C4×C5911yescharacteristic
134C2×C22⋊C8—22no—
135#382—22no—
136#382C4×C5912yes—
137#382C22×C5912yes—
138C2×#95—22no—
139#324—22no—
140#324C22×C5914yes—
141C59C2×#132411yescharacteristic, direct product factor, Sylow
142C23×C4—21no—
143C23×C4—21no—
144C23×C4C2×C4×C5911yescharacteristic
145C23×C4D4×C5912yes—
146C22×C8—42no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4C2×C4×C5912yes—
153C2×C4⋊C4C2×C4×C5911yescharacteristic
154C2×C4⋊C4D4×C5912yes—
155C2×C4⋊C4C23×C5911yescharacteristic
156C2×C42—21no—
157C2×C42—22no—
158C2×C42C8×C5914yescomplemented
159C2×C42C2×C4×C5912yes—
160C22⋊C8—24no—
161C22⋊C8—42no—
162#95—24no—
163#95—24no—
164C24C22⋊C4×C5911yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—22no—
168C22×C4—24no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4—44no—
176C22×C4—44no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4C22⋊C4×C5911yescharacteristic
180C22×C4C22⋊C4×C5912yes—
181C22×C4C2×C8×C5912yes—
182C22×C4M16×C5912yes—
183C22×C4C22×C4×C5911yescharacteristic
184C22×C4C2×D4×C5912yes—
185C2×C8—44no—
186C2×C8—84no—
187C4⋊C4—41no—
188C4⋊C4—42no—
189C4⋊C4—41no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C42—24no—
193C42—22no—
194C42C2×C8×C5914yescomplemented
195C23—22no—
196C23—22no—
197C23C22⋊C8×C5912yes—
198C23#99×C5911yescharacteristic
199C23#99×C5911yescharacteristic
200C23#101×C5912yes—
201C23C2×C22⋊C4×C5911yescharacteristic
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—24no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—48no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—44no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—44no—
220C2×C4—42no—
221C2×C4—82no—
222C2×C4—82no—
223C2×C4—82no—
224C2×C4C22⋊C8×C5912yes—
225C2×C4C22×C8×C5911yescharacteristic
226C2×C4C2×M16×C5911yescharacteristic
227C8—84no—
228C22—24no—
229C22—24no—
230C22—21no—
231C22—21no—
232C22—21no—
233C22—21no—
234C22C59×#32412yes—
235C22C59×#32412yes—
236C22C59×#35412yes—
237C22C59×#35512yes—
238C22C2×C22⋊C8×C5911yescharacteristic
239C22C2×#99×C5911yescharacteristic
240C22C2×#101×C5911yescharacteristic
241C4—22no—
242C4—21no—
243C4—21no—
244C4—44no—
245C4—42no—
246C4—42no—
247C4—82no—
248C2—21no—
249C2—21no—
250C2—22no—
251C2C59×#132414yesdirect product factor
252C2C2×C59×#32411yescharacteristic
253C2C2×C59×#35411yescharacteristic
254C2C2×C59×#35511yescharacteristic
subgroupG/H
center, socleC23×C59#99
commutatorC2×C4C22×C8×C59
Frattini, cosocleC2×C4⋊C4C23×C59
prime radicalC24×C59C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C24×C59 ◁ C22×C4⋊C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
3. C59×#1324C2direct (N × H)
30. C2×C42×C59C8semidirect
66. C42×C59C2×C8semidirect
100. C2×#1324C59direct (N × H)
123. #1324C2×C59direct (N × H)
127. C2×C59#1324direct (N × H)
141. C59C2×#1324direct (N × H)
158. C2×C42C8×C59semidirect
194. C42C2×C8×C59semidirect
251. C2C59×#1324direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#3822
C2×C59×#3242
C59×#13242
C2×#132459