Finite Group Databasebeta

← C59×#7504 #28419613

Subgroups — C59×#7504 #28419613

Order 15104.

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

normal subgroups only

This group has 336 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×#353C212yesmaximal
2C59×#1961C211yesmaximal, characteristic
3C2×#127×C59C2211yescharacteristic
4C2×#102×C59—22no—
5C2×#99×C59—22no—
6C2×#97×C59C411yescharacteristic, complemented
7C59×#382C411yescharacteristic, complemented
8C59×#353—22no—
9C59×#353C414yescomplemented
10C22×D4×C59—41no—
11C22×D4×C59D412yes—
12C22×C8×C59—21no—
13#127×C59—41no—
14#127×C59C2×C412yes—
15#127×C59D411yescharacteristic
16#127×C59Q811yescharacteristic
17C2×C4⋊C4×C59—21no—
18C2×C22⋊C4×C59—42no—
19C2×C42×C59C2×C411yescharacteristic
20#102×C59—44no—
21#99×C59—24no—
22#99×C59—42no—
23#97×C59—41no—
24#95×C59—41no—
25C24×C59—22no—
26C2×D4×C59—22no—
27C2×D4×C59—42no—
28C2×D4×C59—42no—
29C2×D4×C59—42no—
30C2×D4×C59—41no—
31C2×D4×C59—41no—
32C2×D4×C59—84no—
33C2×D4×C59C22⋊C412yes—
34C2×D4×C59C4⋊C412yes—
35C22×C4×C59—21no—
36C22×C4×C59—41no—
37C22×C4×C59—82no—
38C22×C4×C59C22⋊C411yescharacteristic
39C2×C8×C59—22no—
40C2×C8×C59—41no—
41C2×C8×C59—41no—
42C4⋊C4×C59—42no—
43C22⋊C4×C59—44no—
44C22⋊C4×C59—82no—
45C42×C59—21no—
46C42×C59C4211yescharacteristic
47C42×C59C4⋊C411yescharacteristic
48C23×C59—22no—
49C23×C59—22no—
50C23×C59—42no—
51C23×C59—42no—
52C23×C59—84no—
53C23×C59#9911yescharacteristic
54D4×C59—42no—
55D4×C59—42no—
56D4×C59—82no—
57D4×C59—84no—
58D4×C59—82no—
59D4×C59—82no—
60C2×C4×C59—21no—
61C2×C4×C59—21no—
62C2×C4×C59—21no—
63C2×C4×C59—21no—
64C2×C4×C59—42no—
65C2×C4×C59—82no—
66C2×C4×C59—84no—
67C2×C4×C59—81no—
68C2×C4×C59—164no—
69C2×C4×C59#9511yescharacteristic
70C2×C4×C59#9911yescharacteristic
71C8×C59—42no—
72#7504C5911yesmaximal, characteristic, direct product factor, Sylow
73C22×C59—22no—
74C22×C59—42no—
75C22×C59—42no—
76C22×C59—82no—
77C22×C59—82no—
78C22×C59—84no—
79C22×C59—162no—
80C22×C59#34211yescharacteristic
81C22×C59#35311yescharacteristic
82C22×C59#35411yescharacteristic
83C4×C59—21no—
84C4×C59—21no—
85C4×C59—41no—
86C4×C59—41no—
87C4×C59—161no—
88C4×C59—164no—
89C2×#353C2×C5912yes—
90#1961C2×C5911yescharacteristic
91C2×C59—21no—
92C2×C59—21no—
93C2×C59—82no—
94C2×C59—82no—
95C2×C59#139311yescharacteristic
96C2×C59#141212yes—
97C2×#127C22×C5911yescharacteristic
98C2×#102—22no—
99C2×#99—22no—
100C2×#97C4×C5911yescharacteristic, complemented
101#382C4×C5911yescharacteristic, complemented
102#353—22no—
103#353C4×C5914yescomplemented
104C59#750411yescharacteristic, direct product factor, Sylow
105C22×D4—41no—
106C22×D4D4×C5912yes—
107C22×C8—21no—
108#127—41no—
109#127C2×C4×C5912yes—
110#127D4×C5911yescharacteristic
111#127Q8×C5911yescharacteristic
112C2×C4⋊C4—21no—
113C2×C22⋊C4—42no—
114C2×C42C2×C4×C5911yescharacteristic
115#102—44no—
116#99—24no—
117#99—42no—
118#97—41no—
119#95—41no—
120C24—22no—
121C2×D4—22no—
122C2×D4—42no—
123C2×D4—42no—
124C2×D4—42no—
125C2×D4—41no—
126C2×D4—41no—
127C2×D4—84no—
128C2×D4C22⋊C4×C5912yes—
129C2×D4C4⋊C4×C5912yes—
130C22×C4—21no—
131C22×C4—41no—
132C22×C4—82no—
133C22×C4C22⋊C4×C5911yescharacteristic
134C2×C8—22no—
135C2×C8—41no—
136C2×C8—41no—
137C4⋊C4—42no—
138C22⋊C4—44no—
139C22⋊C4—82no—
140C42—21no—
141C42C42×C5911yescharacteristic
142C42C4⋊C4×C5911yescharacteristic
143C23—22no—
144C23—22no—
145C23—42no—
146C23—42no—
147C23—84no—
148C23#99×C5911yescharacteristic
149D4—42no—
150D4—42no—
151D4—82no—
152D4—84no—
153D4—82no—
154D4—82no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—42no—
160C2×C4—82no—
161C2×C4—84no—
162C2×C4—81no—
163C2×C4—164no—
164C2×C4#95×C5911yescharacteristic
165C2×C4#99×C5911yescharacteristic
166C8—42no—
167C22—22no—
168C22—42no—
169C22—42no—
170C22—82no—
171C22—82no—
172C22—84no—
173C22—162no—
174C22C59×#34211yescharacteristic
175C22C59×#35311yescharacteristic
176C22C59×#35411yescharacteristic
177C4—21no—
178C4—21no—
179C4—41no—
180C4—41no—
181C4—161no—
182C4—164no—
183C2—21no—
184C2—21no—
185C2—82no—
186C2—82no—
187C2C59×#139311yescharacteristic
188C2C59×#141212yes—
subgroupG/H
center, socleC22×C59#354
commutatorC42C42×C59
Frattini, cosocleC2×#127C22×C59
prime radicalC2×#127×C59C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C59 ◁ C22×C4×C59 ◁ C2×#127×C59 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×#97×C59C4semidirect
7. C59×#382C4semidirect
9. C59×#353C4semidirect
72. #7504C59direct (N × H)
100. C2×#97C4×C59semidirect
101. #382C4×C59semidirect
103. #353C4×C59semidirect
104. C59#7504direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#3532
C59×#19612
#750459