Finite Group Databasebeta

← C13×#7428 #15693767

Subgroups — C13×#7428 #15693767

Order 3328.

226 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 46 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
1C13×#2025C211yesmaximal, characteristic
2C13×#1393C211yesmaximal, characteristic
3C13×#1318C211yesmaximal, characteristic
4C2×C13×#125C411yescharacteristic, complemented
5C2×C13×#102—21no—
6C2×C13×#99—21no—
7C13×#390C2211yescharacteristic
8C13×#340—21no—
9C13×#336C411yescharacteristic, complemented
10C13×#324—21no—
11C22×D4×C13D411yescharacteristic
12C22×C8×C13—21no—
13C13×#125—42no—
14C2×C13×C4⋊C4—21no—
15C2×C13×C4⋊C4—41no—
16C2×C13×C4⋊C4D411yescharacteristic
17C2×C13×C22⋊C4—41no—
18C2×C13×C22⋊C4—41no—
19C2×C42×C13C2×C411yescharacteristic
20C13×#102—42no—
21C13×#99—22no—
22C13×#99—41no—
23C13×C22⋊C8—41no—
24#7428C1311yesmaximal, characteristic, direct product factor, Sylow
25C24×C13—21no—
26C2×D4×C13—21no—
27C2×D4×C13—41no—
28C2×D4×C13—41no—
29C2×D4×C13SD1611yescharacteristic
30C2×D4×C13Q1611yescharacteristic
31C22×C4×C13—21no—
32C22×C4×C13—21no—
33C22×C4×C13—41no—
34C22×C4×C13—81no—
35C22×C4×C13C22⋊C411yescharacteristic
36C2×C8×C13—41no—
37C2×C8×C13—41no—
38C2×C8×C13—41no—
39C2×C8×C13—81no—
40C13×C4⋊C4—22no—
41C13×C4⋊C4—41no—
42C13×C4⋊C4—41no—
43C13×C4⋊C4—42no—
44C13×C4⋊C4—42no—
45C13×C22⋊C4—42no—
46C13×C22⋊C4—82no—
47C13×C22⋊C4—81no—
48C42×C13—41no—
49#2025C2×C1311yescharacteristic
50#1393C2×C1311yescharacteristic
51#1318C2×C1311yescharacteristic
52C23×C13—21no—
53C23×C13—21no—
54C23×C13—41no—
55C23×C13—41no—
56C23×C13—81no—
57C23×C13—81no—
58C23×C13#9911yescharacteristic
59D4×C13—41no—
60D4×C13—41no—
61D4×C13—81no—
62C2×C4×C13—21no—
63C2×C4×C13—21no—
64C2×C4×C13—41no—
65C2×C4×C13—41no—
66C2×C4×C13—41no—
67C2×C4×C13—42no—
68C2×C4×C13—41no—
69C2×C4×C13—81no—
70C2×C4×C13—81no—
71C2×C4×C13—81no—
72C2×C4×C13—82no—
73C2×C4×C13—161no—
74C2×C4×C13—161no—
75C2×C4×C13#10311yescharacteristic
76C2×C4×C13#10411yescharacteristic
77C8×C13—81no—
78C8×C13—161no—
79C2×#125C4×C1311yescharacteristic, complemented
80C2×#102—21no—
81C2×#99—21no—
82#390C22×C1311yescharacteristic
83#340—21no—
84#336C4×C1311yescharacteristic, complemented
85#324—21no—
86C22×C13—21no—
87C22×C13—21no—
88C22×C13—41no—
89C22×C13—41no—
90C22×C13—81no—
91C22×C13—81no—
92C22×C13—81no—
93C22×C13—81no—
94C22×C13—161no—
95C22×C13#32811yescharacteristic
96C22×C13AΣL(1,𝔽16)11yescharacteristic
97C22×C13#35411yescharacteristic
98C4×C13—21no—
99C4×C13—21no—
100C4×C13—81no—
101C4×C13—82no—
102C4×C13—81no—
103C4×C13—162no—
104C22×D4D4×C1311yescharacteristic
105C22×C8—21no—
106#125—42no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4D4×C1311yescharacteristic
110C2×C22⋊C4—41no—
111C2×C22⋊C4—41no—
112C2×C42C2×C4×C1311yescharacteristic
113#102—42no—
114#99—22no—
115#99—41no—
116C22⋊C8—41no—
117C2×C13—21no—
118C2×C13—21no—
119C2×C13—81no—
120C2×C13—81no—
121C2×C13#135111yescharacteristic
122C2×C13#141211yescharacteristic
123C2×C13#141411yescharacteristic
124C24—21no—
125C2×D4—21no—
126C2×D4—41no—
127C2×D4—41no—
128C2×D4C13×SD1611yescharacteristic
129C2×D4C13×Q1611yescharacteristic
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—41no—
133C22×C4—81no—
134C22×C4C13×C22⋊C411yescharacteristic
135C2×C8—41no—
136C2×C8—41no—
137C2×C8—41no—
138C2×C8—81no—
139C4⋊C4—22no—
140C4⋊C4—41no—
141C4⋊C4—41no—
142C4⋊C4—42no—
143C4⋊C4—42no—
144C22⋊C4—42no—
145C22⋊C4—82no—
146C22⋊C4—81no—
147C42—41no—
148C13#742811yescharacteristic, direct product factor, Sylow
149C23—21no—
150C23—21no—
151C23—41no—
152C23—41no—
153C23—81no—
154C23—81no—
155C23C13×#9911yescharacteristic
156D4—41no—
157D4—41no—
158D4—81no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—81no—
167C2×C4—81no—
168C2×C4—81no—
169C2×C4—82no—
170C2×C4—161no—
171C2×C4—161no—
172C2×C4C13×#10311yescharacteristic
173C2×C4C13×#10411yescharacteristic
174C8—81no—
175C8—161no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—81no—
181C22—81no—
182C22—81no—
183C22—81no—
184C22—161no—
185C22C13×#32811yescharacteristic
186C22C13×AΣL(1,𝔽16)11yescharacteristic
187C22C13×#35411yescharacteristic
188C4—21no—
189C4—21no—
190C4—81no—
191C4—82no—
192C4—81no—
193C4—162no—
194C2—21no—
195C2—21no—
196C2—81no—
197C2—81no—
198C2C13×#135111yescharacteristic
199C2C13×#141211yescharacteristic
200C2C13×#141411yescharacteristic
subgroupG/H
center, socleC22×C13#354
commutatorC2×C42C2×C4×C13
Frattini, cosocle#390C22×C13
prime radicalC22×D4×C13D4
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C22×C4×C13 ◁ C13×#390 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C13×#125C4semidirect
9. C13×#336C4semidirect
24. #7428C13direct (N × H)
79. C2×#125C4×C13semidirect
84. #336C4×C13semidirect
148. C13#7428direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#20252
C13×#13932
C13×#13182
#742813