Finite Group Databasebeta

← C13×#7427 #15693766

Subgroups — C13×#7427 #15693766

Order 3328.

214 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 42 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×#2030C211yesmaximal, characteristic
2C13×#1317C211yesmaximal, characteristic
3C13×#1306C211yesmaximal, characteristic
4C13×#543C411yescharacteristic
5C13×#407—21no—
6C13×#381—21no—
7C13×#381C2211yescharacteristic
8C13×#342—21no—
9C13×#342C411yescharacteristic
10C13×#323—21no—
11C23×C4×C13D411yescharacteristic
12C2×C13×M16—41no—
13C13×C22⋊Q8—42no—
14C13×C22⋊Q8—41no—
15C2×C13×C22⋊C4—21no—
16C2×C13×C22⋊C4—21no—
17C2×C13×C22⋊C4C2×C411yescharacteristic
18C2×C13×C22⋊C4D411yescharacteristic
19C13×C22⋊C8—22no—
20C13×C22⋊C8—41no—
21C13×C22⋊C8—41no—
22C13×#95—41no—
23C13×#95—42no—
24#7427C1311yesmaximal, characteristic, direct product factor, Sylow
25C24×C13C22⋊C411yescharacteristic
26C2×Q8×C13—41no—
27C22×C4×C13—21no—
28C22×C4×C13—21no—
29C22×C4×C13—22no—
30C22×C4×C13—21no—
31C22×C4×C13—21no—
32C22×C4×C13—41no—
33C22×C4×C13—41no—
34C22×C4×C13—41no—
35C22×C4×C13SD1611yescharacteristic
36C22×C4×C13Q1611yescharacteristic
37C13×M16—81no—
38C13×M16—81no—
39C2×C8×C13—42no—
40C2×C8×C13—81no—
41C13×C4⋊C4—42no—
42C13×C4⋊C4—41no—
43C13×C22⋊C4—41no—
44C13×C22⋊C4—41no—
45C13×C22⋊C4—41no—
46C13×C22⋊C4—41no—
47C13×C22⋊C4—41no—
48C13×C22⋊C4—41no—
49#2030C2×C1311yescharacteristic
50#1317C2×C1311yescharacteristic
51#1306C2×C1311yescharacteristic
52C23×C13—21no—
53C23×C13—21no—
54C23×C13—81no—
55C23×C13#9911yescharacteristic
56C23×C13#10311yescharacteristic
57C23×C13#10411yescharacteristic
58Q8×C13—161no—
59C2×C4×C13—21no—
60C2×C4×C13—21no—
61C2×C4×C13—41no—
62C2×C4×C13—41no—
63C2×C4×C13—41no—
64C2×C4×C13—41no—
65C2×C4×C13—42no—
66C2×C4×C13—41no—
67C2×C4×C13—41no—
68C2×C4×C13—81no—
69C2×C4×C13—81no—
70C2×C4×C13—81no—
71C2×C4×C13—82no—
72C2×C4×C13—81no—
73C2×C4×C13—82no—
74C8×C13—82no—
75C8×C13—161no—
76#543C4×C1311yescharacteristic
77#407—21no—
78#381—21no—
79#381C22×C1311yescharacteristic
80#342—21no—
81#342C4×C1311yescharacteristic
82#323—21no—
83C22×C13—21no—
84C22×C13—21no—
85C22×C13—41no—
86C22×C13—41no—
87C22×C13—41no—
88C22×C13—42no—
89C22×C13—81no—
90C22×C13#32811yescharacteristic
91C22×C13AΣL(1,𝔽16)11yescharacteristic
92C22×C13#35411yescharacteristic
93C4×C13—41no—
94C4×C13—41no—
95C4×C13—81no—
96C4×C13—82no—
97C4×C13—81no—
98C4×C13—161no—
99C23×C4D4×C1311yescharacteristic
100C2×M16—41no—
101C22⋊Q8—42no—
102C22⋊Q8—41no—
103C2×C22⋊C4—21no—
104C2×C22⋊C4—21no—
105C2×C22⋊C4C2×C4×C1311yescharacteristic
106C2×C22⋊C4D4×C1311yescharacteristic
107C22⋊C8—22no—
108C22⋊C8—41no—
109C22⋊C8—41no—
110#95—41no—
111#95—42no—
112C2×C13—21no—
113C2×C13—21no—
114C2×C13—21no—
115C2×C13—41no—
116C2×C13—41no—
117C2×C13#135111yescharacteristic
118C24C13×C22⋊C411yescharacteristic
119C2×Q8—41no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—22no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—41no—
126C22×C4—41no—
127C22×C4—41no—
128C22×C4C13×SD1611yescharacteristic
129C22×C4C13×Q1611yescharacteristic
130M16—81no—
131M16—81no—
132C2×C8—42no—
133C2×C8—81no—
134C4⋊C4—42no—
135C4⋊C4—41no—
136C22⋊C4—41no—
137C22⋊C4—41no—
138C22⋊C4—41no—
139C22⋊C4—41no—
140C22⋊C4—41no—
141C22⋊C4—41no—
142C13#742711yescharacteristic, direct product factor, Sylow
143C23—21no—
144C23—21no—
145C23—81no—
146C23C13×#9911yescharacteristic
147C23C13×#10311yescharacteristic
148C23C13×#10411yescharacteristic
149Q8—161no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—81no—
162C2×C4—82no—
163C2×C4—81no—
164C2×C4—82no—
165C8—82no—
166C8—161no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—42no—
173C22—81no—
174C22C13×#32811yescharacteristic
175C22C13×AΣL(1,𝔽16)11yescharacteristic
176C22C13×#35411yescharacteristic
177C4—41no—
178C4—41no—
179C4—81no—
180C4—82no—
181C4—81no—
182C4—161no—
183C2—21no—
184C2—21no—
185C2—21no—
186C2—41no—
187C2—41no—
188C2C13×#135111yescharacteristic
subgroupG/H
center, socleC2×C13#1351
commutatorC2×C22⋊C4C2×C4×C13
Frattini, cosocle#381C22×C13
prime radicalC24×C13C22⋊C4
LCSG ▷ C2×C22⋊C4 ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C23×C13 ◁ C24×C13 ◁ C13×#381 ◁ G

Complements

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

NH ≅ G/Ntype
24. #7427C13direct (N × H)
142. C13#7427direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#20302
C13×#13172
C13×#13062
#742713