Finite Group Databasebeta

← C59×#7338 #28419447

Subgroups — C59×#7338 #28419447

Order 15104.

490 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 46 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×#1781C211yesmaximal, characteristic
2C59×#1316C212yesmaximal, complemented
3C23×D4×C59C411yescharacteristic
4C2×#99×C59—22no—
5C59×#379C411yescharacteristic
6C59×#379C2211yescharacteristic
7C59×#323—22no—
8C25×C59C811yescharacteristic, complemented
9C25×C59C2×C411yescharacteristic
10C22×D4×C59—21no—
11C22×D4×C59—21no—
12C22×D4×C59—44no—
13C22×D4×C59—41no—
14C22×D4×C59—41no—
15C23×C4×C59C811yescharacteristic, complemented
16C2×C22⋊C4×C59—21no—
17C2×C22⋊C4×C59—41no—
18C2×C22⋊C4×C59—41no—
19C2×C22⋊C4×C59D412yes—
20#99×C59—44no—
21C22⋊C8×C59—42no—
22C24×C59—21no—
23C24×C59—21no—
24C24×C59—21no—
25C24×C59—41no—
26C24×C59—42no—
27C24×C59—42no—
28C24×C59—82no—
29C24×C59—82no—
30C24×C59C22⋊C411yescharacteristic
31C24×C59C2×C811yescharacteristic
32C24×C59M1611yescharacteristic
33C2×D4×C59—24no—
34C2×D4×C59—42no—
35C2×D4×C59—42no—
36C2×D4×C59—42no—
37C2×D4×C59—42no—
38C2×D4×C59—44no—
39C2×D4×C59—44no—
40C2×D4×C59—44no—
41C2×D4×C59—41no—
42C2×D4×C59—41no—
43C2×D4×C59—44no—
44C22×C4×C59—21no—
45C22×C4×C59—22no—
46C22×C4×C59—42no—
47C22×C4×C59—41no—
48C22×C4×C59—41no—
49C2×C8×C59—82no—
50C22⋊C4×C59—42no—
51C22⋊C4×C59—42no—
52C22⋊C4×C59—82no—
53C22⋊C4×C59—82no—
54C23×C59—21no—
55C23×C59—22no—
56C23×C59—22no—
57C23×C59—21no—
58C23×C59—41no—
59C23×C59—42no—
60C23×C59—42no—
61C23×C59—42no—
62C23×C59—41no—
63C23×C59—42no—
64C23×C59—41no—
65C23×C59—42no—
66C23×C59—42no—
67C23×C59—41no—
68C23×C59—42no—
69C23×C59—82no—
70C23×C59—81no—
71C23×C59—81no—
72C23×C59—81no—
73C23×C59—81no—
74C23×C59—82no—
75C23×C59—84no—
76C23×C59—84no—
77C23×C59—82no—
78C23×C59—84no—
79C23×C59—84no—
80C23×C59C22⋊C811yescharacteristic
81C23×C59#9911yescharacteristic
82C23×C59#10011yescharacteristic
83D4×C59—44no—
84D4×C59—48no—
85D4×C59—44no—
86C2×C4×C59—22no—
87C2×C4×C59—41no—
88C2×C4×C59—42no—
89C2×C4×C59—41no—
90C2×C4×C59—42no—
91C2×C4×C59—42no—
92C2×C4×C59—82no—
93C2×C4×C59—81no—
94C2×C4×C59—82no—
95C8×C59—162no—
96#7338C5911yesmaximal, characteristic, direct product factor, Sylow
97C22×C59—22no—
98C22×C59—21no—
99C22×C59—21no—
100C22×C59—41no—
101C22×C59—41no—
102C22×C59—41no—
103C22×C59—41no—
104C22×C59—41no—
105C22×C59—41no—
106C22×C59—42no—
107C22×C59—42no—
108C22×C59—41no—
109C22×C59—41no—
110C22×C59—42no—
111C22×C59—82no—
112C22×C59—84no—
113C22×C59—82no—
114C22×C59—84no—
115C22×C59—82no—
116C22×C59—82no—
117C22×C59—84no—
118C22×C59—82no—
119C22×C59—84no—
120C22×C59#32311yescharacteristic
121C22×C59AΣL(1,𝔽16)12yes—
122C4×C59—42no—
123C4×C59—82no—
124C4×C59—161no—
125#1781C2×C5911yescharacteristic
126#1316C2×C5912yescomplemented
127C2×C59—22no—
128C2×C59—21no—
129C2×C59—41no—
130C2×C59—42no—
131C2×C59—41no—
132C2×C59—81no—
133C2×C59—82no—
134C2×C59#131611yescharacteristic
135C23×D4C4×C5911yescharacteristic
136C2×#99—22no—
137#379C4×C5911yescharacteristic
138#379C22×C5911yescharacteristic
139#323—22no—
140C59#733811yescharacteristic, direct product factor, Sylow
141C25C8×C5911yescharacteristic, complemented
142C25C2×C4×C5911yescharacteristic
143C22×D4—21no—
144C22×D4—21no—
145C22×D4—44no—
146C22×D4—41no—
147C22×D4—41no—
148C23×C4C8×C5911yescharacteristic, complemented
149C2×C22⋊C4—21no—
150C2×C22⋊C4—41no—
151C2×C22⋊C4—41no—
152C2×C22⋊C4D4×C5912yes—
153#99—44no—
154C22⋊C8—42no—
155C24—21no—
156C24—21no—
157C24—21no—
158C24—41no—
159C24—42no—
160C24—42no—
161C24—82no—
162C24—82no—
163C24C22⋊C4×C5911yescharacteristic
164C24C2×C8×C5911yescharacteristic
165C24M16×C5911yescharacteristic
166C2×D4—24no—
167C2×D4—42no—
168C2×D4—42no—
169C2×D4—42no—
170C2×D4—42no—
171C2×D4—44no—
172C2×D4—44no—
173C2×D4—44no—
174C2×D4—41no—
175C2×D4—41no—
176C2×D4—44no—
177C22×C4—21no—
178C22×C4—22no—
179C22×C4—42no—
180C22×C4—41no—
181C22×C4—41no—
182C2×C8—82no—
183C22⋊C4—42no—
184C22⋊C4—42no—
185C22⋊C4—82no—
186C22⋊C4—82no—
187C23—21no—
188C23—22no—
189C23—22no—
190C23—21no—
191C23—41no—
192C23—42no—
193C23—42no—
194C23—42no—
195C23—41no—
196C23—42no—
197C23—41no—
198C23—42no—
199C23—42no—
200C23—42no—
201C23—41no—
202C23—82no—
203C23—81no—
204C23—81no—
205C23—81no—
206C23—81no—
207C23—82no—
208C23—84no—
209C23—84no—
210C23—82no—
211C23—84no—
212C23—84no—
213C23C22⋊C8×C5911yescharacteristic
214C23#99×C5911yescharacteristic
215C23#100×C5911yescharacteristic
216D4—44no—
217D4—48no—
218D4—44no—
219C2×C4—22no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—82no—
226C2×C4—81no—
227C2×C4—82no—
228C8—162no—
229C22—22no—
230C22—21no—
231C22—21no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—42no—
239C22—42no—
240C22—41no—
241C22—41no—
242C22—42no—
243C22—82no—
244C22—84no—
245C22—82no—
246C22—84no—
247C22—82no—
248C22—82no—
249C22—84no—
250C22—82no—
251C22—84no—
252C22C59×#32311yescharacteristic
253C22C59×AΣL(1,𝔽16)12yes—
254C4—42no—
255C4—82no—
256C4—161no—
257C2—22no—
258C2—21no—
259C2—41no—
260C2—42no—
261C2—41no—
262C2—81no—
263C2—82no—
264C2C59×#131611yescharacteristic
subgroupG/H
center, socleC2×C59#1316
commutatorC24C2×C8×C59
Frattini, cosocle#379C22×C59
prime radicalC23×D4×C59C4
LCSG ▷ C24 ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C59 ◁ C23×C59 ◁ C24×C59 ◁ C59×#379 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#1316C2semidirect
8. C25×C59C8semidirect
15. C23×C4×C59C8semidirect
96. #7338C59direct (N × H)
126. #1316C2×C59semidirect
140. C59#7338direct (N × H)
141. C25C8×C59semidirect
148. C23×C4C8×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#17812
C59×#13162
#733859