Finite Group Databasebeta

← C59×#11515 #28423624

Subgroups — C59×#11515 #28423624

Order 15104.

418 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2317C211yesmaximal, characteristic
2C59×#1464C212yesmaximal
3C59×#1324C214yesmaximal, complemented
4C2×#117×C59C411yescharacteristic
5C2×#117×C59C2211yescharacteristic
6C22×C4⋊C4×C59C411yescharacteristic
7C59×#432—22no—
8C59×#389—22no—
9C59×#385—22no—
10C59×#384C412yes—
11C59×#382C2212yes—
12C59×#324C2214yes—
13C59×#323—22no—
14C23×C4×C59—21no—
15C23×C4×C59C2×C411yescharacteristic
16#117×C59—24no—
17#117×C59—42no—
18C2×C4⋊C4×C59—21no—
19C2×C4⋊C4×C59—21no—
20C2×C4⋊C4×C59—24no—
21C2×C4⋊C4×C59—42no—
22C2×C4⋊C4×C59C2×C412yes—
23C2×C4⋊C4×C59C2×C411yescharacteristic
24C2×C4⋊C4×C59C2311yescharacteristic
25C2×C22⋊C4×C59—21no—
26C2×C22⋊C4×C59D412yes—
27C2×C42×C59C2×C412yes—
28C2×C42×C59D412yes—
29C4⋊C8×C59—42no—
30C22⋊C8×C59—24no—
31#97×C59—42no—
32#95×C59—24no—
33C24×C59C22⋊C411yescharacteristic
34C22×C4×C59—22no—
35C22×C4×C59—22no—
36C22×C4×C59—22no—
37C22×C4×C59—22no—
38C22×C4×C59—22no—
39C22×C4×C59—42no—
40C22×C4×C59—82no—
41C22×C4×C59C22⋊C412yes—
42C22×C4×C59C22⋊C411yescharacteristic
43C22×C4×C59C22×C411yescharacteristic
44C22×C4×C59C2×D412yes—
45C2×C8×C59—44no—
46C4⋊C4×C59—24no—
47C4⋊C4×C59—41no—
48C4⋊C4×C59—41no—
49C4⋊C4×C59—42no—
50C4⋊C4×C59—42no—
51C4⋊C4×C59—84no—
52C22⋊C4×C59—24no—
53C22⋊C4×C59—42no—
54C42×C59—22no—
55C42×C59—22no—
56C42×C59—22no—
57C42×C59M1614yes—
58C23×C59—21no—
59C23×C59—21no—
60C23×C59—41no—
61C23×C59—41no—
62C23×C59#10112yes—
63C23×C59C2×C22⋊C411yescharacteristic
64C2×C4×C59—28no—
65C2×C4×C59—21no—
66C2×C4×C59—21no—
67C2×C4×C59—21no—
68C2×C4×C59—21no—
69C2×C4×C59—24no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—42no—
73C2×C4×C59—42no—
74C2×C4×C59—42no—
75C2×C4×C59—42no—
76C2×C4×C59—44no—
77C2×C4×C59—42no—
78C2×C4×C59—84no—
79C2×C4×C59#9912yes—
80C2×C4×C59C2×M1612yes—
81C8×C59—84no—
82#11515C5911yesmaximal, characteristic, direct product factor, Sylow
83C22×C59—21no—
84C22×C59—21no—
85C22×C59—22no—
86C22×C59—42no—
87C22×C59—42no—
88C22×C59—41no—
89C22×C59—41no—
90C22×C59#40711yescharacteristic
91C22×C59C2×#9911yescharacteristic
92C22×C59C2×#10111yescharacteristic
93C4×C59—22no—
94C4×C59—22no—
95C4×C59—44no—
96C4×C59—42no—
97C4×C59—42no—
98C4×C59—82no—
99#2317C2×C5911yescharacteristic
100#1464C2×C5912yes—
101#1324C2×C5914yescomplemented
102C2×C59—21no—
103C2×C59—21no—
104C2×C59—42no—
105C2×C59#146311yescharacteristic
106C2×C59#212911yescharacteristic
107C2×C59#213411yescharacteristic
108C2×#117C4×C5911yescharacteristic
109C2×#117C22×C5911yescharacteristic
110C22×C4⋊C4C4×C5911yescharacteristic
111#432—22no—
112#389—22no—
113#385—22no—
114#384C4×C5912yes—
115#382C22×C5912yes—
116#324C22×C5914yes—
117#323—22no—
118C59#1151511yescharacteristic, direct product factor, Sylow
119C23×C4—21no—
120C23×C4C2×C4×C5911yescharacteristic
121#117—24no—
122#117—42no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—24no—
126C2×C4⋊C4—42no—
127C2×C4⋊C4C2×C4×C5912yes—
128C2×C4⋊C4C2×C4×C5911yescharacteristic
129C2×C4⋊C4C23×C5911yescharacteristic
130C2×C22⋊C4—21no—
131C2×C22⋊C4D4×C5912yes—
132C2×C42C2×C4×C5912yes—
133C2×C42D4×C5912yes—
134C4⋊C8—42no—
135C22⋊C8—24no—
136#97—42no—
137#95—24no—
138C24C22⋊C4×C5911yescharacteristic
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—42no—
145C22×C4—82no—
146C22×C4C22⋊C4×C5911yescharacteristic
147C22×C4C22⋊C4×C5912yes—
148C22×C4C22×C4×C5911yescharacteristic
149C22×C4C2×D4×C5912yes—
150C2×C8—44no—
151C4⋊C4—24no—
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C4⋊C4—84no—
157C22⋊C4—24no—
158C22⋊C4—42no—
159C42—22no—
160C42—22no—
161C42—22no—
162C42M16×C5914yes—
163C23—21no—
164C23—21no—
165C23—41no—
166C23—41no—
167C23#101×C5912yes—
168C23C2×C22⋊C4×C5911yescharacteristic
169C2×C4—28no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—44no—
182C2×C4—42no—
183C2×C4—84no—
184C2×C4#99×C5912yes—
185C2×C4C2×M16×C5912yes—
186C8—84no—
187C22—21no—
188C22—21no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22C59×#40711yescharacteristic
195C22C2×#99×C5911yescharacteristic
196C22C2×#101×C5911yescharacteristic
197C4—22no—
198C4—22no—
199C4—44no—
200C4—42no—
201C4—42no—
202C4—82no—
203C2—21no—
204C2—21no—
205C2—42no—
206C2C59×#146311yescharacteristic
207C2C59×#212911yescharacteristic
208C2C59×#213411yescharacteristic
subgroupG/H
center, socleC22×C59C2×#99
commutatorC22×C4C22×C4×C59
Frattini, cosocleC2×C4⋊C4C23×C59
prime radicalC24×C59C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C22×C4×C59 ◁ C2×#117×C59 ◁ G

Complements

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

NH ≅ G/Ntype
3. C59×#1324C2semidirect
82. #11515C59direct (N × H)
101. #1324C2×C59semidirect
118. C59#11515direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#23172
C59×#14642
C59×#13242
#1151559