Finite Group Databasebeta

← C59×#21827 #28433936

Subgroups — C59×#21827 #28433936

Order 15104.

1130 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 366 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×#543C211yesmaximal, characteristic
2C59×#2312C212yesmaximal
3C59×#1996C218yesmaximal, complemented
4C59×#1819C214yesmaximal
5C59×#543—28no—
6C2×C22⋊Q8×C59C418yescomplemented
7C2×C22⋊Q8×C59C2214yes—
8C22×C22⋊C4×C59C2212yes—
9C22×C22⋊C4×C59C2211yescharacteristic
10C59×#388—28no—
11C59×#380C2214yes—
12C59×#379C2214yes—
13C4×C22⋊C4×C59C2214yes—
14C59×#342C22116yes—
15C25×C59C2311yescharacteristic
16C22×Q8×C59C2×C414yes—
17C23×C4×C59C2×C414yes—
18C23×C4×C59C2312yes—
19C22⋊Q8×C59—28no—
20C22⋊Q8×C59—28no—
21C22⋊Q8×C59—232no—
22C2×C4⋊C4×C59—24no—
23C2×C4⋊C4×C59C2×C4112yes—
24C2×C22⋊C4×C59—28no—
25C2×C22⋊C4×C59—24no—
26C2×C22⋊C4×C59—24no—
27C2×C22⋊C4×C59C2×C414yes—
28C2×C22⋊C4×C59C2×C414yes—
29C2×C22⋊C4×C59D418yes—
30C2×C22⋊C4×C59C2318yes—
31C2×C22⋊C4×C59C2314yes—
32C2×C42×C59—24no—
33#95×C59—24no—
34#95×C59—24no—
35C24×C59—24no—
36C24×C59—82no—
37C24×C59C22×C412yes—
38C24×C59C2×D414yes—
39C24×C59C2411yescharacteristic
40C2×Q8×C59—28no—
41C2×Q8×C59—84no—
42C22×C4×C59—28no—
43C22×C4×C59—28no—
44C22×C4×C59—82no—
45C22×C4×C59—84no—
46C22×C4×C59C22×C418yes—
47C22×C4×C59C22×C414yes—
48C22×C4×C59C2×D414yes—
49C22×C4×C59C2×D414yes—
50C4⋊C4×C59—224no—
51C4⋊C4×C59—84no—
52C22⋊C4×C59—28no—
53C22⋊C4×C59—28no—
54C22⋊C4×C59—216no—
55C22⋊C4×C59—84no—
56C22⋊C4×C59—84no—
57C22⋊C4×C59C22⋊C4116yes—
58C42×C59—84no—
59C23×C59—24no—
60C23×C59—28no—
61C23×C59—44no—
62C23×C59—42no—
63C23×C59—44no—
64C23×C59—44no—
65C23×C59—88no—
66C23×C59C2×C22⋊C414yes—
67C23×C59C23×C411yescharacteristic
68C23×C59C22×D412yes—
69C23×C592−1+414yes—
70Q8×C59—88no—
71C2×C4×C59—28no—
72C2×C4×C59—44no—
73C2×C4×C59—44no—
74C2×C4×C59—44no—
75C2×C4×C59—48no—
76C2×C4×C59—48no—
77C2×C4×C59—48no—
78C2×C4×C59—48no—
79C2×C4×C59—88no—
80C2×C4×C59C2×C22⋊C418yes—
81#21827C5911yesmaximal, characteristic, direct product factor, Sylow
82C22×C59—22no—
83C22×C59—22no—
84C22×C59—22no—
85C22×C59—24no—
86C22×C59—28no—
87C22×C59—44no—
88C22×C59—48no—
89C22×C59—88no—
90C22×C59C22×C22⋊C411yescharacteristic
91C22×C59#51912yes—
92C22×C59#53614yes—
93C4×C59—28no—
94C4×C59—48no—
95C4×C59—88no—
96C2×#543C2×C5911yescharacteristic
97#2312C2×C5912yes—
98#1996C2×C5918yescomplemented
99#1819C2×C5914yes—
100C2×C59—24no—
101C2×C59—22no—
102C2×C59—44no—
103C2×C59#231011yescharacteristic
104C2×C59#288312yes—
105#543—28no—
106C2×C22⋊Q8C4×C5918yescomplemented
107C2×C22⋊Q8C22×C5914yes—
108C22×C22⋊C4C22×C5912yes—
109C22×C22⋊C4C22×C5911yescharacteristic
110#388—28no—
111#380C22×C5914yes—
112#379C22×C5914yes—
113C4×C22⋊C4C22×C5914yes—
114#342C22×C59116yes—
115C59#2182711yescharacteristic, direct product factor, Sylow
116C25C23×C5911yescharacteristic
117C22×Q8C2×C4×C5914yes—
118C23×C4C2×C4×C5914yes—
119C23×C4C23×C5912yes—
120C22⋊Q8—28no—
121C22⋊Q8—28no—
122C22⋊Q8—232no—
123C2×C4⋊C4—24no—
124C2×C4⋊C4C2×C4×C59112yes—
125C2×C22⋊C4—28no—
126C2×C22⋊C4—24no—
127C2×C22⋊C4—24no—
128C2×C22⋊C4C2×C4×C5914yes—
129C2×C22⋊C4C2×C4×C5914yes—
130C2×C22⋊C4D4×C5918yes—
131C2×C22⋊C4C23×C5918yes—
132C2×C22⋊C4C23×C5914yes—
133C2×C42—24no—
134#95—24no—
135#95—24no—
136C24—24no—
137C24—82no—
138C24C22×C4×C5912yes—
139C24C2×D4×C5914yes—
140C24C24×C5911yescharacteristic
141C2×Q8—28no—
142C2×Q8—84no—
143C22×C4—28no—
144C22×C4—28no—
145C22×C4—82no—
146C22×C4—84no—
147C22×C4C22×C4×C5918yes—
148C22×C4C22×C4×C5914yes—
149C22×C4C2×D4×C5914yes—
150C22×C4C2×D4×C5914yes—
151C4⋊C4—224no—
152C4⋊C4—84no—
153C22⋊C4—28no—
154C22⋊C4—28no—
155C22⋊C4—216no—
156C22⋊C4—84no—
157C22⋊C4—84no—
158C22⋊C4C22⋊C4×C59116yes—
159C42—84no—
160C23—24no—
161C23—28no—
162C23—44no—
163C23—42no—
164C23—44no—
165C23—44no—
166C23—88no—
167C23C2×C22⋊C4×C5914yes—
168C23C23×C4×C5911yescharacteristic
169C23C22×D4×C5912yes—
170C232−1+4×C5914yes—
171Q8—88no—
172C2×C4—28no—
173C2×C4—44no—
174C2×C4—44no—
175C2×C4—44no—
176C2×C4—48no—
177C2×C4—48no—
178C2×C4—48no—
179C2×C4—48no—
180C2×C4—88no—
181C2×C4C2×C22⋊C4×C5918yes—
182C22—22no—
183C22—22no—
184C22—22no—
185C22—24no—
186C22—28no—
187C22—44no—
188C22—48no—
189C22—88no—
190C22C22×C22⋊C4×C5911yescharacteristic
191C22C59×#51912yes—
192C22C59×#53614yes—
193C4—28no—
194C4—48no—
195C4—88no—
196C2—24no—
197C2—22no—
198C2—44no—
199C2C59×#231011yescharacteristic
200C2C59×#288312yes—
subgroupG/H
center, socleC22×C59C22×C22⋊C4
commutatorC23C23×C4×C59
Frattini, cosocleC24C24×C59
prime radicalC25×C59C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C22×C22⋊C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
3. C59×#1996C2semidirect
6. C2×C22⋊Q8×C59C4semidirect
81. #21827C59direct (N × H)
98. #1996C2×C59semidirect
106. C2×C22⋊Q8C4×C59semidirect
115. C59#21827direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#5432
C59×#23122
C59×#19962
C59×#18192
#2182759