Finite Group Databasebeta

← C59×#20360 #28432469

Subgroups — C59×#20360 #28432469

Order 15104.

1996 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#568C211yesmaximal, characteristic
2C2×C59×#568C211yesmaximal, characteristic
3C59×#3428C211yesmaximal, characteristic
4C2×C59×#344C2112yesmaximal, complemented
5C22×#41×C59C2211yescharacteristic
6C59×#568—24no—
7C59×#568—24no—
8C59×#568—24no—
9C59×#568C418yescomplemented
10C2×#131×C59—24no—
11C2×#131×C59C418yescomplemented
12C22×M16×C59C2216yes—
13C22×M16×C59C2216yes—
14C59×#520—24no—
15C59×#519C412yes—
16C59×#518C416yes—
17C4×#41×C59—24no—
18C2×#117×C59C2216yes—
19C59×#344C22116yes—
20C2×#41×C59C2×C414yes—
21C2×#41×C59C2×C414yes—
22C2×#41×C59D414yes—
23C2×#41×C59D414yes—
24C2×#41×C59D414yes—
25C2×#41×C59Q814yes—
26C22×Q8×C59C2×C411yescharacteristic
27C22×D4×C59C2×C413yes—
28C23×C4×C59C2313yes—
29#131×C59—232no—
30#131×C59—232no—
31C2×M16×C59—26no—
32C2×M16×C59—212no—
33C2×M16×C59—212no—
34C2×M16×C59—212no—
35C2×M16×C59C2×C4124yescomplemented
36C2×M16×C59C2×C4112yescomplemented
37C2×M16×C59C2314yes—
38C2×M16×C59C2314yes—
39C22×C8×C59—26no—
40C22×C8×C59C2×C4112yescomplemented
41C4×Q8×C59—28no—
42C4×D4×C59—224no—
43#117×C59—26no—
44#117×C59—26no—
45#117×C59C2×C4112yes—
46#117×C59C2314yes—
47C2×C4⋊C4×C59—26no—
48C2×C22⋊C4×C59C2×C4112yes—
49C2×C42×C59—26no—
50C24×C59C22×C413yes—
51#41×C59C22⋊C4116yes—
52#41×C59C22⋊C4116yes—
53#41×C59C4⋊C4116yes—
54#41×C59C4⋊C4116yes—
55C2×Q8×C59C4214yes—
56C2×Q8×C59C22⋊C414yes—
57C2×Q8×C59C4⋊C414yes—
58C2×D4×C59C42112yes—
59C2×D4×C59C22⋊C4112yes—
60C2×D4×C59C4⋊C4112yes—
61C22×C4×C59—212no—
62C22×C4×C59C22×C413yes—
63C22×C4×C59C22×C416yes—
64C22×C4×C59C22×C416yes—
65C22×C4×C59C2×D416yes—
66C22×C4×C59C2×D416yes—
67C22×C4×C59C2×D416yes—
68C22×C4×C59C2×Q816yes—
69C22×C4×C59C2411yescharacteristic
70M16×C59—224no—
71M16×C59—224no—
72M16×C59—24no—
73M16×C59—24no—
74M16×C59—24no—
75M16×C59C22×C418yes—
76C2×C8×C59—224no—
77C2×C8×C59—224no—
78C2×C8×C59—24no—
79C2×C8×C59C22×C418yes—
80C4⋊C4×C59—212no—
81C4⋊C4×C59—24no—
82C22⋊C4×C59—212no—
83C22⋊C4×C59C22×C418yes—
84C42×C59—212no—
85C42×C59—24no—
86C23×C59—83no—
87C23×C59C2×C4216yes—
88C23×C59C2×C22⋊C416yes—
89C23×C59C2×C4⋊C416yes—
90C23×C59C23×C411yescharacteristic
91Q8×C59#95116yes—
92D4×C59#95148yes—
93C2×C4×C59—28no—
94C2×C4×C59—812no—
95C2×C4×C59C2×C4216yes—
96C2×C4×C59C2×C22⋊C4112yes—
97C2×C4×C59C2×C22⋊C4112yes—
98C2×C4×C59C2×C22⋊C416yes—
99C2×C4×C59C2×C4⋊C4112yes—
100C2×C4×C59C2×C4⋊C4112yes—
101C2×C4×C59C2×C4⋊C416yes—
102C2×C4×C59C23×C411yescharacteristic
103C2×C4×C59C23×C411yescharacteristic
104C2×C4×C59C22×D411yescharacteristic
105C2×C4×C59C22×D411yescharacteristic
106C2×C4×C59C22×D411yescharacteristic
107C2×C4×C59C22×Q811yescharacteristic
108C8×C59—28no—
109C8×C59—28no—
110#20360C5911yesmaximal, characteristic, direct product factor, Sylow
111C22×C59—46no—
112C22×C59—41no—
113C22×C59—46no—
114C22×C59—46no—
115C22×C59C2×#95112yes—
116C22×C59C22×C4211yescharacteristic
117C22×C59C22×C22⋊C411yescharacteristic
118C22×C59C22×C4⋊C411yescharacteristic
119C4×C59—48no—
120C4×C59C2×#95112yes—
121C4×C59C22×C22⋊C411yescharacteristic
122C4×C59C22×C22⋊C411yescharacteristic
123C4×C59C22×C4⋊C411yescharacteristic
124C4×C59C22×C4⋊C411yescharacteristic
125C2×#568C2×C5911yescharacteristic
126C2×#568C2×C5911yescharacteristic
127#3428C2×C5911yescharacteristic
128C2×#344C2×C59112yescomplemented
129C2×C59—21no—
130C2×C59—21no—
131C2×C59—21no—
132C2×C59—212no—
133C2×C59C22×#9511yescharacteristic
134C22×#41C22×C5911yescharacteristic
135#568—24no—
136#568—24no—
137#568—24no—
138#568C4×C5918yescomplemented
139C2×#131—24no—
140C2×#131C4×C5918yescomplemented
141C22×M16C22×C5916yes—
142C22×M16C22×C5916yes—
143#520—24no—
144#519C4×C5912yes—
145#518C4×C5916yes—
146C4×#41—24no—
147C2×#117C22×C5916yes—
148#344C22×C59116yes—
149C59#2036011yescharacteristic, direct product factor, Sylow
150C2×#41C2×C4×C5914yes—
151C2×#41C2×C4×C5914yes—
152C2×#41D4×C5914yes—
153C2×#41D4×C5914yes—
154C2×#41D4×C5914yes—
155C2×#41Q8×C5914yes—
156C22×Q8C2×C4×C5911yescharacteristic
157C22×D4C2×C4×C5913yes—
158C23×C4C23×C5913yes—
159#131—232no—
160#131—232no—
161C2×M16—26no—
162C2×M16—212no—
163C2×M16—212no—
164C2×M16—212no—
165C2×M16C2×C4×C59124yescomplemented
166C2×M16C2×C4×C59112yescomplemented
167C2×M16C23×C5914yes—
168C2×M16C23×C5914yes—
169C22×C8—26no—
170C22×C8C2×C4×C59112yescomplemented
171C4×Q8—28no—
172C4×D4—224no—
173#117—26no—
174#117—26no—
175#117C2×C4×C59112yes—
176#117C23×C5914yes—
177C2×C4⋊C4—26no—
178C2×C22⋊C4C2×C4×C59112yes—
179C2×C42—26no—
180C24C22×C4×C5913yes—
181#41C22⋊C4×C59116yes—
182#41C22⋊C4×C59116yes—
183#41C4⋊C4×C59116yes—
184#41C4⋊C4×C59116yes—
185C2×Q8C42×C5914yes—
186C2×Q8C22⋊C4×C5914yes—
187C2×Q8C4⋊C4×C5914yes—
188C2×D4C42×C59112yes—
189C2×D4C22⋊C4×C59112yes—
190C2×D4C4⋊C4×C59112yes—
191C22×C4—212no—
192C22×C4C22×C4×C5913yes—
193C22×C4C22×C4×C5916yes—
194C22×C4C22×C4×C5916yes—
195C22×C4C2×D4×C5916yes—
196C22×C4C2×D4×C5916yes—
197C22×C4C2×D4×C5916yes—
198C22×C4C2×Q8×C5916yes—
199C22×C4C24×C5911yescharacteristic
200M16—224no—
201M16—224no—
202M16—24no—
203M16—24no—
204M16—24no—
205M16C22×C4×C5918yes—
206C2×C8—224no—
207C2×C8—224no—
208C2×C8—24no—
209C2×C8C22×C4×C5918yes—
210C4⋊C4—212no—
211C4⋊C4—24no—
212C22⋊C4—212no—
213C22⋊C4C22×C4×C5918yes—
214C42—212no—
215C42—24no—
216C23—83no—
217C23C2×C42×C5916yes—
218C23C2×C22⋊C4×C5916yes—
219C23C2×C4⋊C4×C5916yes—
220C23C23×C4×C5911yescharacteristic
221Q8#95×C59116yes—
222D4#95×C59148yes—
223C2×C4—28no—
224C2×C4—812no—
225C2×C4C2×C42×C5916yes—
226C2×C4C2×C22⋊C4×C5916yes—
227C2×C4C2×C22⋊C4×C59112yes—
228C2×C4C2×C22⋊C4×C59112yes—
229C2×C4C2×C4⋊C4×C5916yes—
230C2×C4C2×C4⋊C4×C59112yes—
231C2×C4C2×C4⋊C4×C59112yes—
232C2×C4C23×C4×C5911yescharacteristic
233C2×C4C23×C4×C5911yescharacteristic
234C2×C4C22×D4×C5911yescharacteristic
235C2×C4C22×D4×C5911yescharacteristic
236C2×C4C22×D4×C5911yescharacteristic
237C2×C4C22×Q8×C5911yescharacteristic
238C8—28no—
239C8—28no—
240C22—46no—
241C22—41no—
242C22—46no—
243C22—46no—
244C22C2×#95×C59112yes—
245C22C22×C42×C5911yescharacteristic
246C22C22×C22⋊C4×C5911yescharacteristic
247C22C22×C4⋊C4×C5911yescharacteristic
248C4—48no—
249C4C2×#95×C59112yes—
250C4C22×C22⋊C4×C5911yescharacteristic
251C4C22×C22⋊C4×C5911yescharacteristic
252C4C22×C4⋊C4×C5911yescharacteristic
253C4C22×C4⋊C4×C5911yescharacteristic
254C2—21no—
255C2—21no—
256C2—21no—
257C2—212no—
258C2C22×#95×C5911yescharacteristic
subgroupG/H
centerC4×C59C22×C22⋊C4
commutatorC22C22×C42×C59
Frattini, cosocleC22×C4C24×C59
socleC2×C59C22×#95
prime radicalC22×#41×C59C22
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C59 ◁ C22×#41×C59 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C59×#344C2semidirect
9. C59×#568C4semidirect
11. C2×#131×C59C4semidirect
35. C2×M16×C59C2×C4semidirect
36. C2×M16×C59C2×C4semidirect
40. C22×C8×C59C2×C4semidirect
110. #20360C59direct (N × H)
128. C2×#344C2×C59semidirect
138. #568C4×C59semidirect
140. C2×#131C4×C59semidirect
149. C59#20360direct (N × H)
165. C2×M16C2×C4×C59semidirect
166. C2×M16C2×C4×C59semidirect
170. C22×C8C2×C4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#5682
C59×#34282
C2×C59×#3442
#2036059