Finite Group Databasebeta

← C13×#7430 #15693769

Subgroups — C13×#7430 #15693769

Order 3328.

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

normal subgroups only

This group has 236 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×#2027C211yesmaximal, characteristic
2C13×#1393C211yesmaximal, characteristic
3C13×#1270C211yesmaximal, characteristic
4C13×#544C411yescharacteristic, complemented
5C13×#418—21no—
6C2×C13×#99—21no—
7C13×#390C2211yescharacteristic
8C13×#343C411yescharacteristic, complemented
9C13×#339—21no—
10C13×#336—21no—
11C22×D4×C13D411yescharacteristic
12C2×C13×M16—21no—
13C22×C8×C13—41no—
14C13×C4⋊Q8—41no—
15C13×#125—41no—
16C13×C22⋊Q8—41no—
17C13×#117—21no—
18C2×C13×C4⋊C4C2×C411yescharacteristic
19C2×C13×C22⋊C4—41no—
20C2×C13×C22⋊C4—41no—
21C2×C42×C13D411yescharacteristic
22C13×#102—41no—
23C13×#102—41no—
24C13×#99—22no—
25C13×#99—41no—
26#7430C1311yesmaximal, characteristic, direct product factor, Sylow
27C24×C13—21no—
28C2×Q8×C13—41no—
29C2×D4×C13—21no—
30C2×D4×C13—41no—
31C2×D4×C13—41no—
32C2×D4×C13SD1611yescharacteristic
33C2×D4×C13Q1611yescharacteristic
34C22×C4×C13—21no—
35C22×C4×C13—21no—
36C22×C4×C13—81no—
37C22×C4×C13C22⋊C411yescharacteristic
38C13×M16—41no—
39C13×M16—41no—
40C2×C8×C13—41no—
41C2×C8×C13—42no—
42C2×C8×C13—81no—
43C2×C8×C13—81no—
44C13×C4⋊C4—21no—
45C13×C4⋊C4—21no—
46C13×C4⋊C4—41no—
47C13×C4⋊C4—41no—
48C13×C4⋊C4—42no—
49C13×C22⋊C4—41no—
50C13×C22⋊C4—42no—
51C13×C22⋊C4—81no—
52C13×C22⋊C4—81no—
53C13×C22⋊C4—81no—
54C42×C13—41no—
55C42×C13—41no—
56#2027C2×C1311yescharacteristic
57#1393C2×C1311yescharacteristic
58#1270C2×C1311yescharacteristic
59C23×C13—21no—
60C23×C13—21no—
61C23×C13—41no—
62C23×C13—41no—
63C23×C13—81no—
64C23×C13—81no—
65C23×C13#9911yescharacteristic
66Q8×C13—161no—
67D4×C13—41no—
68D4×C13—41no—
69D4×C13—81no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—41no—
75C2×C4×C13—41no—
76C2×C4×C13—41no—
77C2×C4×C13—41no—
78C2×C4×C13—41no—
79C2×C4×C13—81no—
80C2×C4×C13—82no—
81C2×C4×C13—161no—
82C2×C4×C13—161no—
83C2×C4×C13#10311yescharacteristic
84C2×C4×C13#10411yescharacteristic
85C8×C13—81no—
86C8×C13—82no—
87#544C4×C1311yescharacteristic, complemented
88#418—21no—
89C2×#99—21no—
90#390C22×C1311yescharacteristic
91#343C4×C1311yescharacteristic, complemented
92#339—21no—
93#336—21no—
94C22×C13—21no—
95C22×C13—21no—
96C22×C13—41no—
97C22×C13—41no—
98C22×C13—81no—
99C22×C13—81no—
100C22×C13—81no—
101C22×C13—81no—
102C22×C13—161no—
103C22×C13#32811yescharacteristic
104C22×C13AΣL(1,𝔽16)11yescharacteristic
105C22×C13#35411yescharacteristic
106C4×C13—21no—
107C4×C13—21no—
108C4×C13—41no—
109C4×C13—41no—
110C4×C13—81no—
111C4×C13—81no—
112C4×C13—81no—
113C4×C13—162no—
114C22×D4D4×C1311yescharacteristic
115C2×M16—21no—
116C22×C8—41no—
117C4⋊Q8—41no—
118#125—41no—
119C22⋊Q8—41no—
120#117—21no—
121C2×C4⋊C4C2×C4×C1311yescharacteristic
122C2×C22⋊C4—41no—
123C2×C22⋊C4—41no—
124C2×C42D4×C1311yescharacteristic
125#102—41no—
126#102—41no—
127#99—22no—
128#99—41no—
129C2×C13—21no—
130C2×C13—21no—
131C2×C13—81no—
132C2×C13—81no—
133C2×C13#135111yescharacteristic
134C2×C13#140211yescharacteristic
135C2×C13#140411yescharacteristic
136C24—21no—
137C2×Q8—41no—
138C2×D4—21no—
139C2×D4—41no—
140C2×D4—41no—
141C2×D4C13×SD1611yescharacteristic
142C2×D4C13×Q1611yescharacteristic
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—81no—
146C22×C4C13×C22⋊C411yescharacteristic
147M16—41no—
148M16—41no—
149C2×C8—41no—
150C2×C8—42no—
151C2×C8—81no—
152C2×C8—81no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—41no—
156C4⋊C4—41no—
157C4⋊C4—42no—
158C22⋊C4—41no—
159C22⋊C4—42no—
160C22⋊C4—81no—
161C22⋊C4—81no—
162C22⋊C4—81no—
163C42—41no—
164C42—41no—
165C13#743011yescharacteristic, direct product factor, Sylow
166C23—21no—
167C23—21no—
168C23—41no—
169C23—41no—
170C23—81no—
171C23—81no—
172C23C13×#9911yescharacteristic
173Q8—161no—
174D4—41no—
175D4—41no—
176D4—81no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—81no—
187C2×C4—82no—
188C2×C4—161no—
189C2×C4—161no—
190C2×C4C13×#10311yescharacteristic
191C2×C4C13×#10411yescharacteristic
192C8—81no—
193C8—82no—
194C22—21no—
195C22—21no—
196C22—41no—
197C22—41no—
198C22—81no—
199C22—81no—
200C22—81no—
201C22—81no—
202C22—161no—
203C22C13×#32811yescharacteristic
204C22C13×AΣL(1,𝔽16)11yescharacteristic
205C22C13×#35411yescharacteristic
206C4—21no—
207C4—21no—
208C4—41no—
209C4—41no—
210C4—81no—
211C4—81no—
212C4—81no—
213C4—162no—
214C2—21no—
215C2—21no—
216C2—81no—
217C2—81no—
218C2C13×#135111yescharacteristic
219C2C13×#140211yescharacteristic
220C2C13×#140411yescharacteristic
subgroupG/H
center, socleC22×C13AΣL(1,𝔽16)
commutatorC2×C4⋊C4C2×C4×C13
Frattini, cosocle#390C22×C13
prime radicalC22×D4×C13D4
LCSG ▷ C2×C4⋊C4 ▷ 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. C13×#544C4semidirect
8. C13×#343C4semidirect
26. #7430C13direct (N × H)
87. #544C4×C13semidirect
91. #343C4×C13semidirect
165. C13#7430direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#20272
C13×#13932
C13×#12702
#743013