Finite Group Databasebeta

← C59×#11197 #28423306

Subgroups — C59×#11197 #28423306

Order 15104.

1134 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 238 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×#381C212yesmaximal
2C2×C59×#381C211yesmaximal, characteristic
3C2×C59×#342C214yesmaximal
4C24×C4×C59C2211yescharacteristic
5C22×C22⋊C4×C59C2212yes—
6C22×C22⋊C4×C59C2214yes—
7C59×#381—24no—
8C59×#381—28no—
9C2×#95×C59—24no—
10C2×#95×C59C414yescomplemented
11C59×#342—28no—
12C25×C59C2311yescharacteristic
13C23×C4×C59—24no—
14C23×C4×C59—24no—
15C23×C4×C59—24no—
16C23×C4×C59—24no—
17C23×C4×C59C2×C412yes—
18C23×C4×C59C2×C414yes—
19C23×C4×C59D414yes—
20C2×C22⋊C4×C59—24no—
21C2×C22⋊C4×C59—24no—
22C2×C22⋊C4×C59—24no—
23C2×C22⋊C4×C59—24no—
24C2×C22⋊C4×C59—24no—
25C2×C22⋊C4×C59—22no—
26C2×C22⋊C4×C59—22no—
27C2×C22⋊C4×C59—24no—
28C2×C22⋊C4×C59—24no—
29C2×C22⋊C4×C59D418yes—
30#95×C59—216no—
31#95×C59—28no—
32C24×C59—44no—
33C24×C59C22×C411yescharacteristic
34C24×C59C2×D412yes—
35C24×C59C2×D414yes—
36C24×C59#4114yes—
37C24×C59#4114yes—
38C22×C4×C59—24no—
39C22×C4×C59—28no—
40C22×C4×C59—24no—
41C22×C4×C59—28no—
42C22×C4×C59—28no—
43C22×C4×C59—24no—
44C22×C4×C59—24no—
45C22×C4×C59—28no—
46C22×C4×C59—28no—
47C22×C4×C59—44no—
48C22×C4×C59—44no—
49C22×C4×C59—44no—
50C22×C4×C59—44no—
51C22×C4×C59—416no—
52C22×C4×C59—44no—
53C22×C4×C59—44no—
54C22×C4×C59—48no—
55C22×C4×C59C22⋊C414yes—
56C22⋊C4×C59—28no—
57C22⋊C4×C59—28no—
58C22⋊C4×C59—42no—
59C22⋊C4×C59—44no—
60C22⋊C4×C59—44no—
61C22⋊C4×C59—42no—
62C22⋊C4×C59—44no—
63C23×C59—24no—
64C23×C59—28no—
65C23×C59—48no—
66C23×C59—48no—
67C23×C59—48no—
68C23×C59C2×C22⋊C411yescharacteristic
69C23×C59#11712yes—
70C23×C59C4×D414yes—
71C23×C59#12012yes—
72C23×C59#12114yes—
73C23×C59#12114yes—
74C23×C59#12314yes—
75C23×C59#12312yes—
76C23×C59#12314yes—
77C23×C59#12414yes—
78C23×C59#12614yes—
79C2×C4×C59—24no—
80C2×C4×C59—28no—
81C2×C4×C59—48no—
82C2×C4×C59—48no—
83C2×C4×C59—48no—
84C2×C4×C59—416no—
85C2×C4×C59—44no—
86C2×C4×C59—48no—
87C2×C4×C59—48no—
88C2×C4×C59—88no—
89C2×C4×C59—88no—
90C2×C4×C59—88no—
91#11197C5911yesmaximal, characteristic, direct product factor, Sylow
92C22×C59—28no—
93C22×C59—24no—
94C22×C59—24no—
95C22×C59—28no—
96C22×C59—28no—
97C22×C59—24no—
98C22×C59—44no—
99C22×C59—44no—
100C22×C59—44no—
101C22×C59—44no—
102C22×C59#38111yescharacteristic
103C22×C59#38612yes—
104C22×C59#38814yes—
105C22×C59#39414yes—
106C22×C59#39714yes—
107C22×C59#41014yes—
108C4×C59—44no—
109C4×C59—88no—
110C4×C59—84no—
111C2×#381C2×C5912yes—
112C2×#381C2×C5911yescharacteristic
113C2×#342C2×C5914yes—
114C2×C59—24no—
115C2×C59—24no—
116C2×C59—24no—
117C2×C59#144011yescharacteristic
118C2×C59#182012yes—
119C2×C59#189914yes—
120C24×C4C22×C5911yescharacteristic
121C22×C22⋊C4C22×C5912yes—
122C22×C22⋊C4C22×C5914yes—
123#381—24no—
124#381—28no—
125C2×#95—24no—
126C2×#95C4×C5914yescomplemented
127#342—28no—
128C59#1119711yescharacteristic, direct product factor, Sylow
129C25C23×C5911yescharacteristic
130C23×C4—24no—
131C23×C4—24no—
132C23×C4—24no—
133C23×C4—24no—
134C23×C4C2×C4×C5912yes—
135C23×C4C2×C4×C5914yes—
136C23×C4D4×C5914yes—
137C2×C22⋊C4—24no—
138C2×C22⋊C4—24no—
139C2×C22⋊C4—24no—
140C2×C22⋊C4—24no—
141C2×C22⋊C4—24no—
142C2×C22⋊C4—22no—
143C2×C22⋊C4—22no—
144C2×C22⋊C4—24no—
145C2×C22⋊C4—24no—
146C2×C22⋊C4D4×C5918yes—
147#95—216no—
148#95—28no—
149C24—44no—
150C24C22×C4×C5911yescharacteristic
151C24C2×D4×C5912yes—
152C24C2×D4×C5914yes—
153C24#41×C5914yes—
154C24#41×C5914yes—
155C22×C4—24no—
156C22×C4—28no—
157C22×C4—24no—
158C22×C4—28no—
159C22×C4—28no—
160C22×C4—24no—
161C22×C4—24no—
162C22×C4—28no—
163C22×C4—28no—
164C22×C4—44no—
165C22×C4—44no—
166C22×C4—44no—
167C22×C4—44no—
168C22×C4—416no—
169C22×C4—44no—
170C22×C4—44no—
171C22×C4—48no—
172C22×C4C22⋊C4×C5914yes—
173C22⋊C4—28no—
174C22⋊C4—28no—
175C22⋊C4—42no—
176C22⋊C4—44no—
177C22⋊C4—44no—
178C22⋊C4—42no—
179C22⋊C4—44no—
180C23—24no—
181C23—28no—
182C23—48no—
183C23—48no—
184C23—48no—
185C23C2×C22⋊C4×C5911yescharacteristic
186C23#117×C5912yes—
187C23C4×D4×C5914yes—
188C23#120×C5912yes—
189C23#121×C5914yes—
190C23#121×C5914yes—
191C23#123×C5914yes—
192C23#123×C5912yes—
193C23#123×C5914yes—
194C23#124×C5914yes—
195C23#126×C5914yes—
196C2×C4—24no—
197C2×C4—28no—
198C2×C4—48no—
199C2×C4—48no—
200C2×C4—48no—
201C2×C4—416no—
202C2×C4—44no—
203C2×C4—48no—
204C2×C4—48no—
205C2×C4—88no—
206C2×C4—88no—
207C2×C4—88no—
208C22—28no—
209C22—24no—
210C22—24no—
211C22—28no—
212C22—28no—
213C22—24no—
214C22—44no—
215C22—44no—
216C22—44no—
217C22—44no—
218C22C59×#38111yescharacteristic
219C22C59×#38612yes—
220C22C59×#38814yes—
221C22C59×#39414yes—
222C22C59×#39714yes—
223C22C59×#41014yes—
224C4—44no—
225C4—88no—
226C4—84no—
227C2—24no—
228C2—24no—
229C2—24no—
230C2C59×#144011yescharacteristic
231C2C59×#182012yes—
232C2C59×#189914yes—
subgroupG/H
center, socleC23×C59C2×C22⋊C4
commutatorC24C22×C4×C59
Frattini, cosocleC25C23×C59
prime radicalC25×C59C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C24×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
10. C2×#95×C59C4semidirect
91. #11197C59direct (N × H)
126. C2×#95C4×C59semidirect
128. C59#11197direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#3812
C2×C59×#3422
#1119759