Finite Group Databasebeta

← C59×#7499 #28419608

Subgroups — C59×#7499 #28419608

Order 15104.

272 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 70 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×#356C212yesmaximal
2C59×#1956C211yesmaximal, characteristic
3C2×C4⋊Q8×C59C2211yescharacteristic
4C2×#103×C59—22no—
5C2×#101×C59—22no—
6C2×C4×C8×C59C411yescharacteristic
7C59×#384C411yescharacteristic
8C59×#356—22no—
9C59×#356C414yescomplemented
10C22×Q8×C59D412yes—
11C2×M16×C59—42no—
12C22×C8×C59—21no—
13C4⋊Q8×C59—41no—
14C4⋊Q8×C59C2×C412yes—
15C4⋊Q8×C59D411yescharacteristic
16C4⋊Q8×C59Q811yescharacteristic
17C2×C4⋊C4×C59—21no—
18C2×C4⋊C4×C59—41no—
19C2×C4⋊C4×C59—41no—
20C2×C42×C59C2×C411yescharacteristic
21#103×C59—44no—
22#101×C59—24no—
23#101×C59—42no—
24C4×C8×C59—41no—
25C2×Q8×C59—22no—
26C2×Q8×C59—42no—
27C2×Q8×C59—42no—
28C2×Q8×C59C22⋊C412yes—
29C2×Q8×C59C4⋊C412yes—
30C22×C4×C59—21no—
31C22×C4×C59—22no—
32C22×C4×C59—41no—
33C22×C4×C59C22⋊C411yescharacteristic
34M16×C59—44no—
35M16×C59—82no—
36C2×C8×C59—22no—
37C2×C8×C59—41no—
38C2×C8×C59—41no—
39C2×C8×C59—82no—
40C4⋊C4×C59—42no—
41C4⋊C4×C59—41no—
42C4⋊C4×C59—41no—
43C4⋊C4×C59—42no—
44C4⋊C4×C59—82no—
45C42×C59—21no—
46C42×C59C4211yescharacteristic
47C42×C59C4⋊C411yescharacteristic
48C23×C59#9911yescharacteristic
49Q8×C59—42no—
50Q8×C59—42no—
51Q8×C59—82no—
52C2×C4×C59—22no—
53C2×C4×C59—22no—
54C2×C4×C59—21no—
55C2×C4×C59—21no—
56C2×C4×C59—21no—
57C2×C4×C59—21no—
58C2×C4×C59—22no—
59C2×C4×C59—22no—
60C2×C4×C59—42no—
61C2×C4×C59—42no—
62C2×C4×C59—82no—
63C2×C4×C59—81no—
64C2×C4×C59#9511yescharacteristic
65C2×C4×C59#9911yescharacteristic
66C8×C59—42no—
67C8×C59—84no—
68#7499C5911yesmaximal, characteristic, direct product factor, Sylow
69C22×C59—21no—
70C22×C59—21no—
71C22×C59#34211yescharacteristic
72C22×C59#35311yescharacteristic
73C22×C59#35411yescharacteristic
74C4×C59—22no—
75C4×C59—22no—
76C4×C59—21no—
77C4×C59—21no—
78C4×C59—42no—
79C4×C59—42no—
80C4×C59—161no—
81C2×#356C2×C5912yes—
82#1956C2×C5911yescharacteristic
83C2×C59—21no—
84C2×C59—21no—
85C2×C59#139311yescharacteristic
86C2×C59#141011yescharacteristic
87C2×C59#141111yescharacteristic
88C2×C4⋊Q8C22×C5911yescharacteristic
89C2×#103—22no—
90C2×#101—22no—
91C2×C4×C8C4×C5911yescharacteristic
92#384C4×C5911yescharacteristic
93#356—22no—
94#356C4×C5914yescomplemented
95C59#749911yescharacteristic, direct product factor, Sylow
96C22×Q8D4×C5912yes—
97C2×M16—42no—
98C22×C8—21no—
99C4⋊Q8—41no—
100C4⋊Q8C2×C4×C5912yes—
101C4⋊Q8D4×C5911yescharacteristic
102C4⋊Q8Q8×C5911yescharacteristic
103C2×C4⋊C4—21no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—41no—
106C2×C42C2×C4×C5911yescharacteristic
107#103—44no—
108#101—24no—
109#101—42no—
110C4×C8—41no—
111C2×Q8—22no—
112C2×Q8—42no—
113C2×Q8—42no—
114C2×Q8C22⋊C4×C5912yes—
115C2×Q8C4⋊C4×C5912yes—
116C22×C4—21no—
117C22×C4—22no—
118C22×C4—41no—
119C22×C4C22⋊C4×C5911yescharacteristic
120M16—44no—
121M16—82no—
122C2×C8—22no—
123C2×C8—41no—
124C2×C8—41no—
125C2×C8—82no—
126C4⋊C4—42no—
127C4⋊C4—41no—
128C4⋊C4—41no—
129C4⋊C4—42no—
130C4⋊C4—82no—
131C42—21no—
132C42C42×C5911yescharacteristic
133C42C4⋊C4×C5911yescharacteristic
134C23#99×C5911yescharacteristic
135Q8—42no—
136Q8—42no—
137Q8—82no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4—82no—
149C2×C4—81no—
150C2×C4#95×C5911yescharacteristic
151C2×C4#99×C5911yescharacteristic
152C8—42no—
153C8—84no—
154C22—21no—
155C22—21no—
156C22C59×#34211yescharacteristic
157C22C59×#35311yescharacteristic
158C22C59×#35411yescharacteristic
159C4—22no—
160C4—22no—
161C4—21no—
162C4—21no—
163C4—42no—
164C4—42no—
165C4—161no—
166C2—21no—
167C2—21no—
168C2C59×#139311yescharacteristic
169C2C59×#141011yescharacteristic
170C2C59×#141111yescharacteristic
subgroupG/H
center, socleC22×C59#353
commutatorC42C42×C59
Frattini, cosocleC2×C4⋊Q8C22×C59
prime radicalC23×C59#99
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C59 ◁ C22×C4×C59 ◁ C2×C4⋊Q8×C59 ◁ G

Complements

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

NH ≅ G/Ntype
9. C59×#356C4semidirect
68. #7499C59direct (N × H)
94. #356C4×C59semidirect
95. C59#7499direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#3562
C59×#19562
#749959