Finite Group Databasebeta

← C59×#13600 #28425709

Subgroups — C59×#13600 #28425709

Order 15104.

318 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3142C211yesmaximal, characteristic
2C59×#2132C212yesmaximal
3C59×#1413C214yesmaximal, complemented
4C59×#532C2211yescharacteristic
5C2×#125×C59C411yescharacteristic
6C59×#491C2212yes—
7C59×#490C412yes—
8C59×#488—22no—
9C59×#417—22no—
10C59×#413—22no—
11C4×M16×C59C411yescharacteristic
12C59×#356C2214yes—
13C59×#355—22no—
14C2×#41×C59D412yes—
15C2×M16×C59—21no—
16C2×M16×C59—42no—
17C4⋊Q8×C59C2311yescharacteristic
18#127×C59C2×C411yescharacteristic
19#125×C59—21no—
20#125×C59—41no—
21#125×C59C2×C412yes—
22#124×C59D412yes—
23#121×C59—41no—
24C4×D4×C59—41no—
25C2×C4⋊C4×C59—21no—
26C2×C4⋊C4×C59—41no—
27C2×C42×C59C2×C411yescharacteristic
28#103×C59—24no—
29#102×C59—24no—
30#101×C59—24no—
31#100×C59—42no—
32#97×C59C2×C412yes—
33C4×C8×C59—21no—
34#41×C59—42no—
35#41×C59—42no—
36C2×Q8×C59C2×D412yes—
37C2×D4×C59—22no—
38C2×D4×C59—41no—
39C2×D4×C59C22⋊C412yes—
40C22×C4×C59—21no—
41C22×C4×C59—22no—
42C22×C4×C59—41no—
43C22×C4×C59C22⋊C411yescharacteristic
44M16×C59—42no—
45M16×C59—44no—
46M16×C59—82no—
47C2×C8×C59—22no—
48C2×C8×C59—82no—
49C4⋊C4×C59—22no—
50C4⋊C4×C59—41no—
51C4⋊C4×C59—42no—
52C4⋊C4×C59—42no—
53C4⋊C4×C59—41no—
54C22⋊C4×C59—42no—
55C42×C59—21no—
56C42×C59C22⋊C411yescharacteristic
57C42×C59C22×C411yescharacteristic
58C23×C59—22no—
59C23×C59#9911yescharacteristic
60Q8×C59—42no—
61D4×C59—42no—
62D4×C59—82no—
63D4×C59—82no—
64C2×C4×C59—22no—
65C2×C4×C59—21no—
66C2×C4×C59—21no—
67C2×C4×C59—22no—
68C2×C4×C59—42no—
69C2×C4×C59—42no—
70C2×C4×C59—42no—
71C2×C4×C59—81no—
72C2×C4×C59—82no—
73C2×C4×C59#9911yescharacteristic
74C2×C4×C59C2×C22⋊C411yescharacteristic
75C8×C59—42no—
76C8×C59—84no—
77#13600C5911yesmaximal, characteristic, direct product factor, Sylow
78C22×C59—21no—
79C22×C59—41no—
80C22×C59—42no—
81C22×C59—82no—
82C22×C59C2×#9911yescharacteristic
83C4×C59—21no—
84C4×C59—41no—
85C4×C59—41no—
86C4×C59—42no—
87C4×C59—82no—
88C4×C59#35412yes—
89#3142C2×C5911yescharacteristic
90#2132C2×C5912yes—
91#1413C2×C5914yescomplemented
92C2×C59—21no—
93C2×C59—41no—
94C2×C59—82no—
95C2×C59C2×#35411yescharacteristic
96#532C22×C5911yescharacteristic
97C2×#125C4×C5911yescharacteristic
98#491C22×C5912yes—
99#490C4×C5912yes—
100#488—22no—
101#417—22no—
102#413—22no—
103C4×M16C4×C5911yescharacteristic
104#356C22×C5914yes—
105#355—22no—
106C59#1360011yescharacteristic, direct product factor, Sylow
107C2×#41D4×C5912yes—
108C2×M16—21no—
109C2×M16—42no—
110C4⋊Q8C23×C5911yescharacteristic
111#127C2×C4×C5911yescharacteristic
112#125—21no—
113#125—41no—
114#125C2×C4×C5912yes—
115#124D4×C5912yes—
116#121—41no—
117C4×D4—41no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—41no—
120C2×C42C2×C4×C5911yescharacteristic
121#103—24no—
122#102—24no—
123#101—24no—
124#100—42no—
125#97C2×C4×C5912yes—
126C4×C8—21no—
127#41—42no—
128#41—42no—
129C2×Q8C2×D4×C5912yes—
130C2×D4—22no—
131C2×D4—41no—
132C2×D4C22⋊C4×C5912yes—
133C22×C4—21no—
134C22×C4—22no—
135C22×C4—41no—
136C22×C4C22⋊C4×C5911yescharacteristic
137M16—42no—
138M16—44no—
139M16—82no—
140C2×C8—22no—
141C2×C8—82no—
142C4⋊C4—22no—
143C4⋊C4—41no—
144C4⋊C4—42no—
145C4⋊C4—42no—
146C4⋊C4—41no—
147C22⋊C4—42no—
148C42—21no—
149C42C22⋊C4×C5911yescharacteristic
150C42C22×C4×C5911yescharacteristic
151C23—22no—
152C23#99×C5911yescharacteristic
153Q8—42no—
154D4—42no—
155D4—82no—
156D4—82no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—81no—
165C2×C4—82no—
166C2×C4#99×C5911yescharacteristic
167C2×C4C2×C22⋊C4×C5911yescharacteristic
168C8—42no—
169C8—84no—
170C22—21no—
171C22—41no—
172C22—42no—
173C22—82no—
174C22C2×#99×C5911yescharacteristic
175C4—21no—
176C4—41no—
177C4—41no—
178C4—42no—
179C4—82no—
180C4C59×#35412yes—
181C2—21no—
182C2—41no—
183C2—82no—
184C2C2×C59×#35411yescharacteristic
subgroupG/H
center, socleC2×C59C2×#354
commutatorC42C22×C4×C59
Frattini, cosocleC4⋊Q8C23×C59
prime radicalC59×#532C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C59 ◁ C2×C4×C59 ◁ C22×C4×C59 ◁ C59×#532 ◁ G

Complements

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

NH ≅ G/Ntype
3. C59×#1413C2semidirect
77. #13600C59direct (N × H)
91. #1413C2×C59semidirect
106. C59#13600direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#31422
C59×#21322
C59×#14132
#1360059