Finite Group Databasebeta

← C59×#8326 #28420435

Subgroups — C59×#8326 #28420435

Order 15104.

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

normal subgroups only

This group has 812 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×#540C211yesmaximal, characteristic
2C59×#1478C214yesmaximal, complemented
3C59×#1458C212yesmaximal, complemented
4C59×#540—28no—
5C2×#127×C59C411yescharacteristic
6C2×#125×C59C411yescharacteristic
7C2×#123×C59—22no—
8C2×#121×C59—22no—
9C2×#121×C59C412yes—
10C2×C4×D4×C59C2212yes—
11C2×#117×C59C2211yescharacteristic
12C59×#431C2214yes—
13C59×D4⋊C8—28no—
14C59×#324—22no—
15C59×#323—22no—
16C22×D4×C59—22no—
17C22×D4×C59—22no—
18C22×D4×C59C2×C412yes—
19C23×C4×C59—22no—
20C23×C4×C59C2×C411yescharacteristic
21#127×C59—24no—
22#125×C59—24no—
23#123×C59—216no—
24#121×C59—216no—
25#121×C59—24no—
26#121×C59—24no—
27C4×D4×C59—24no—
28C4×D4×C59D418yes—
29#117×C59—24no—
30C2×C4⋊C4×C59—22no—
31C2×C4⋊C4×C59C2×C412yes—
32C2×C4⋊C4×C59D412yes—
33C2×C22⋊C4×C59—22no—
34C2×C22⋊C4×C59—22no—
35C2×C22⋊C4×C59D412yes—
36C2×C42×C59C2×C411yescharacteristic
37C2×C42×C59C2311yescharacteristic
38C4⋊C8×C59—24no—
39C22⋊C8×C59—24no—
40C4×C8×C59—24no—
41C24×C59—22no—
42C24×C59C22⋊C411yescharacteristic
43C2×D4×C59—28no—
44C2×D4×C59—28no—
45C2×D4×C59—22no—
46C2×D4×C59—28no—
47C2×D4×C59—84no—
48C2×D4×C59—84no—
49C2×D4×C59C22⋊C414yes—
50C22×C4×C59—22no—
51C22×C4×C59—22no—
52C22×C4×C59—24no—
53C22×C4×C59—28no—
54C22×C4×C59—84no—
55C22×C4×C59C22⋊C411yescharacteristic
56C22×C4×C59C22⋊C412yes—
57C22×C4×C59C22×C411yescharacteristic
58C22×C4×C59C2×D412yes—
59C2×C8×C59—44no—
60C4⋊C4×C59—28no—
61C4⋊C4×C59—22no—
62C4⋊C4×C59—24no—
63C4⋊C4×C59C22⋊C414yes—
64C22⋊C4×C59—28no—
65C22⋊C4×C59—28no—
66C22⋊C4×C59—24no—
67C42×C59—22no—
68C42×C59C2×D414yes—
69C23×C59—21no—
70C23×C59—24no—
71C23×C59—22no—
72C23×C59—44no—
73C23×C59—44no—
74C23×C59—42no—
75C23×C59—44no—
76C23×C59C2×C22⋊C411yescharacteristic
77D4×C59—28no—
78D4×C59—44no—
79D4×C59—88no—
80D4×C59—88no—
81C2×C4×C59—22no—
82C2×C4×C59—21no—
83C2×C4×C59—24no—
84C2×C4×C59—22no—
85C2×C4×C59—42no—
86C2×C4×C59—44no—
87C2×C4×C59—44no—
88C2×C4×C59—42no—
89C2×C4×C59—88no—
90C2×C4×C59C2×C22⋊C412yes—
91C2×C4×C59#12014yes—
92C2×C4×C59#13114yes—
93C8×C59—84no—
94#8326C5911yesmaximal, characteristic, direct product factor, Sylow
95C22×C59—22no—
96C22×C59—44no—
97C22×C59—42no—
98C22×C59—44no—
99C22×C59—41no—
100C22×C59—44no—
101C22×C59—82no—
102C22×C59—88no—
103C22×C59#37911yescharacteristic
104C22×C59#40812yes—
105C4×C59—24no—
106C4×C59—44no—
107C4×C59—42no—
108C4×C59—41no—
109C4×C59#40814yes—
110C2×#540C2×C5911yescharacteristic
111#1478C2×C5914yescomplemented
112#1458C2×C5912yescomplemented
113C2×C59—22no—
114C2×C59—81no—
115C2×C59—84no—
116C2×C59#178011yescharacteristic
117C2×C59#179512yes—
118#540—28no—
119C2×#127C4×C5911yescharacteristic
120C2×#125C4×C5911yescharacteristic
121C2×#123—22no—
122C2×#121—22no—
123C2×#121C4×C5912yes—
124C2×C4×D4C22×C5912yes—
125C2×#117C22×C5911yescharacteristic
126#431C22×C5914yes—
127D4⋊C8—28no—
128#324—22no—
129#323—22no—
130C59#832611yescharacteristic, direct product factor, Sylow
131C22×D4—22no—
132C22×D4—22no—
133C22×D4C2×C4×C5912yes—
134C23×C4—22no—
135C23×C4C2×C4×C5911yescharacteristic
136#127—24no—
137#125—24no—
138#123—216no—
139#121—216no—
140#121—24no—
141#121—24no—
142C4×D4—24no—
143C4×D4D4×C5918yes—
144#117—24no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4C2×C4×C5912yes—
147C2×C4⋊C4D4×C5912yes—
148C2×C22⋊C4—22no—
149C2×C22⋊C4—22no—
150C2×C22⋊C4D4×C5912yes—
151C2×C42C2×C4×C5911yescharacteristic
152C2×C42C23×C5911yescharacteristic
153C4⋊C8—24no—
154C22⋊C8—24no—
155C4×C8—24no—
156C24—22no—
157C24C22⋊C4×C5911yescharacteristic
158C2×D4—28no—
159C2×D4—28no—
160C2×D4—22no—
161C2×D4—28no—
162C2×D4—84no—
163C2×D4—84no—
164C2×D4C22⋊C4×C5914yes—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—24no—
168C22×C4—28no—
169C22×C4—84no—
170C22×C4C22⋊C4×C5911yescharacteristic
171C22×C4C22⋊C4×C5912yes—
172C22×C4C22×C4×C5911yescharacteristic
173C22×C4C2×D4×C5912yes—
174C2×C8—44no—
175C4⋊C4—28no—
176C4⋊C4—22no—
177C4⋊C4—24no—
178C4⋊C4C22⋊C4×C5914yes—
179C22⋊C4—28no—
180C22⋊C4—28no—
181C22⋊C4—24no—
182C42—22no—
183C42C2×D4×C5914yes—
184C23—21no—
185C23—24no—
186C23—22no—
187C23—44no—
188C23—44no—
189C23—42no—
190C23—44no—
191C23C2×C22⋊C4×C5911yescharacteristic
192D4—28no—
193D4—44no—
194D4—88no—
195D4—88no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—24no—
199C2×C4—22no—
200C2×C4—42no—
201C2×C4—44no—
202C2×C4—44no—
203C2×C4—42no—
204C2×C4—88no—
205C2×C4C2×C22⋊C4×C5912yes—
206C2×C4#120×C5914yes—
207C2×C4#131×C5914yes—
208C8—84no—
209C22—22no—
210C22—41no—
211C22—44no—
212C22—44no—
213C22—44no—
214C22—42no—
215C22—82no—
216C22—88no—
217C22C59×#37911yescharacteristic
218C22C59×#40812yes—
219C4—24no—
220C4—41no—
221C4—44no—
222C4—42no—
223C4C59×#40814yes—
224C2—22no—
225C2—84no—
226C2—81no—
227C2C59×#178011yescharacteristic
228C2C59×#179512yes—
subgroupG/H
center, socleC22×C59#379
commutatorC22×C4C22×C4×C59
Frattini, cosocleC2×C42C23×C59
prime radicalC2×C59×#540C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#1478C2semidirect
3. C59×#1458C2semidirect
94. #8326C59direct (N × H)
111. #1478C2×C59semidirect
112. #1458C2×C59semidirect
130. C59#8326direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#5402
C59×#14782
C59×#14582
#832659