Finite Group Databasebeta

← C13×#12261 #15698600

Subgroups — C13×#12261 #15698600

Order 3328.

330 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2844C211yesmaximal, characteristic
2C13×#2061C211yesmaximal, characteristic
3C13×#1617C212yesmaximal
4C13×#1353C212yesmaximal
5C13×#1324C211yesmaximal, characteristic
6C13×#544C2211yescharacteristic
7C13×#484—22no—
8C13×#428—21no—
9C13×#400—22no—
10C13×#400C2212yes—
11C13×#395—22no—
12C13×#395—21no—
13C13×#382—21no—
14C13×#382C2211yescharacteristic
15C13×#343C2211yescharacteristic
16C13×#339—21no—
17C13×#328—22no—
18C13×#324C2212yes—
19C22×Q8×C13—21no—
20C2×C13×M16—21no—
21C13×C4⋊Q8—41no—
22C13×#125—41no—
23C13×C22⋊Q8—22no—
24C13×#117—21no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4D412yes—
30C2×C13×C4⋊C4C2311yescharacteristic
31C2×C42×C13D411yescharacteristic
32C13×#107—41no—
33C13×#107—42no—
34C13×#106—41no—
35C13×#103—42no—
36C13×C22⋊C8—22no—
37C13×#95—22no—
38C13×#95—21no—
39C13×#95—22no—
40C13×#95—22no—
41C13×#95—22no—
42C13×#95D412yes—
43#12261C1311yesmaximal, characteristic, direct product factor, Sylow
44C2×Q8×C13—22no—
45C2×Q8×C13—82no—
46C2×Q8×C13—81no—
47C22×C4×C13—21no—
48C22×C4×C13—22no—
49C22×C4×C13—22no—
50C22×C4×C13—21no—
51C22×C4×C13C2×D411yescharacteristic
52C22×C4×C13C2×D412yes—
53C13×M16—22no—
54C13×M16—41no—
55C2×C8×C13—41no—
56C2×C8×C13—42no—
57C13×C4⋊C4—21no—
58C13×C4⋊C4—21no—
59C13×C4⋊C4—22no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—42no—
64C13×C4⋊C4—81no—
65C13×C4⋊C4—81no—
66C13×C4⋊C4—82no—
67C13×C22⋊C4—41no—
68C42×C13—21no—
69C42×C13—41no—
70C42×C13Q1612yes—
71#2844C2×C1311yescharacteristic
72#2061C2×C1311yescharacteristic
73#1617C2×C1312yes—
74#1353C2×C1312yes—
75#1324C2×C1311yescharacteristic
76C23×C13#12011yescharacteristic
77Q8×C13—82no—
78Q8×C13—84no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—41no—
84C2×C4×C13—41no—
85C2×C4×C13—42no—
86C2×C4×C13—42no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—42no—
95C2×C4×C13—41no—
96C2×C4×C13C2×Q1611yescharacteristic
97C2×C4×C13#13711yescharacteristic
98C8×C13—42no—
99C8×C13—82no—
100#544C22×C1311yescharacteristic
101#484—22no—
102#428—21no—
103#400—22no—
104#400C22×C1312yes—
105#395—22no—
106#395—21no—
107#382—21no—
108#382C22×C1311yescharacteristic
109#343C22×C1311yescharacteristic
110#339—21no—
111#328—22no—
112#324C22×C1312yes—
113C22×C13—21no—
114C22×C13—21no—
115C22×C13#45111yescharacteristic
116C22×C13#45611yescharacteristic
117C22×C13B(4,𝔽2)11yescharacteristic
118C4×C13—21no—
119C4×C13—21no—
120C4×C13—42no—
121C4×C13—42no—
122C4×C13—82no—
123C4×C13—81no—
124C4×C13—81no—
125C4×C13—82no—
126C4×C13—81no—
127C22×Q8—21no—
128C2×M16—21no—
129C4⋊Q8—41no—
130#125—41no—
131C22⋊Q8—22no—
132#117—21no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4D4×C1311yescharacteristic
137C2×C4⋊C4D4×C1312yes—
138C2×C4⋊C4C23×C1311yescharacteristic
139C2×C42D4×C1311yescharacteristic
140#107—41no—
141#107—42no—
142#106—41no—
143#103—42no—
144C22⋊C8—22no—
145#95—22no—
146#95—21no—
147#95—22no—
148#95—22no—
149#95—22no—
150#95D4×C1312yes—
151C2×C13—21no—
152C2×C13—21no—
153C2×C13#160511yescharacteristic
154C2×C13#220111yescharacteristic
155C2×C13#220211yescharacteristic
156C2×Q8—22no—
157C2×Q8—82no—
158C2×Q8—81no—
159C22×C4—21no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—21no—
163C22×C4C2×D4×C1311yescharacteristic
164C22×C4C2×D4×C1312yes—
165M16—22no—
166M16—41no—
167C2×C8—41no—
168C2×C8—42no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—22no—
172C4⋊C4—41no—
173C4⋊C4—42no—
174C4⋊C4—41no—
175C4⋊C4—42no—
176C4⋊C4—81no—
177C4⋊C4—81no—
178C4⋊C4—82no—
179C22⋊C4—41no—
180C42—21no—
181C42—41no—
182C42C13×Q1612yes—
183C13#1226111yescharacteristic, direct product factor, Sylow
184C23C13×#12011yescharacteristic
185Q8—82no—
186Q8—84no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—42no—
203C2×C4—41no—
204C2×C4C2×C13×Q1611yescharacteristic
205C2×C4C13×#13711yescharacteristic
206C8—42no—
207C8—82no—
208C22—21no—
209C22—21no—
210C22C13×#45111yescharacteristic
211C22C13×#45611yescharacteristic
212C22C13×B(4,𝔽2)11yescharacteristic
213C4—21no—
214C4—21no—
215C4—42no—
216C4—42no—
217C4—82no—
218C4—81no—
219C4—81no—
220C4—82no—
221C4—81no—
222C2—21no—
223C2—21no—
224C2C13×#160511yescharacteristic
225C2C13×#220111yescharacteristic
226C2C13×#220211yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC23×C13#120
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C2×C13×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
43. #12261C13direct (N × H)
183. C13#12261direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28442
C13×#20612
C13×#16172
C13×#13532
C13×#13242
#1226113