Finite Group Databasebeta

← C13×#10037 #15696376

Subgroups — C13×#10037 #15696376

Order 3328.

476 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3162C211yesmaximal, characteristic
2C13×#3104C212yesmaximal
3C13×#1985C211yesmaximal, characteristic
4C13×#1481C212yesmaximal
5C13×#1275C211yesmaximal, characteristic
6C13×#533C2212yes—
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#501—22no—
9C13×#501—22no—
10C13×#484—22no—
11C13×#477—22no—
12C13×#462—22no—
13C13×#451—22no—
14C4×C13×Q16—24no—
15C13×#431C2212yes—
16C13×#427—22no—
17C2×C13×C4⋊C8C2211yescharacteristic
18C2×C13×#97C2211yescharacteristic
19C13×#336—22no—
20C13×Q8⋊C8—24no—
21C22×Q8×C13D411yescharacteristic
22C2×C13×Q16—24no—
23C22×C8×C13—21no—
24C22×C8×C13D412yes—
25C13×C4⋊Q8D412yes—
26C13×C4⋊Q8D412yes—
27C13×#125—22no—
28C13×C22⋊Q8—22no—
29C13×C22⋊Q8—22no—
30C4×Q8×C13—22no—
31C4×Q8×C13—22no—
32C4×Q8×C13—22no—
33C4×Q8×C13—22no—
34C13×#117—22no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C42×C13—21no—
38C2×C42×C13C2311yescharacteristic
39C13×#107—22no—
40C13×#107—22no—
41C13×#107—24no—
42C13×#106—24no—
43C13×C4⋊C8—22no—
44C13×C4⋊C8—22no—
45C13×#103—24no—
46C13×#103—24no—
47C13×C22⋊C8—22no—
48C13×#97—22no—
49C4×C8×C13D414yes—
50#10037C1311yesmaximal, characteristic, direct product factor, Sylow
51C2×Q8×C13—22no—
52C2×Q8×C13—22no—
53C2×Q8×C13—22no—
54C2×Q8×C13—42no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13C2×D411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13#4111yescharacteristic
60C13×Q16—48no—
61C2×C8×C13—22no—
62C2×C8×C13—22no—
63C2×C8×C13—24no—
64C2×C8×C13—41no—
65C2×C8×C13—42no—
66C2×C8×C13Q1614yescomplemented
67C13×C4⋊C4—22no—
68C13×C4⋊C4—22no—
69C13×C4⋊C4—22no—
70C13×C4⋊C4—22no—
71C13×C4⋊C4—22no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—42no—
74C13×C4⋊C4—42no—
75C13×C22⋊C4—42no—
76C42×C13—41no—
77C42×C13—41no—
78C42×C13—42no—
79C42×C13C2×D412yes—
80C42×C13C2×D412yes—
81#3162C2×C1311yescharacteristic
82#3104C2×C1312yes—
83#1985C2×C1311yescharacteristic
84#1481C2×C1312yes—
85#1275C2×C1311yescharacteristic
86C23×C13#12111yescharacteristic
87Q8×C13—24no—
88Q8×C13—42no—
89Q8×C13—44no—
90Q8×C13—44no—
91C2×C4×C13—22no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—42no—
97C2×C4×C13—41no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13#12012yes—
101C2×C4×C13#12011yescharacteristic
102C2×C4×C13#12112yes—
103C2×C4×C13#12711yescharacteristic
104C2×C4×C13C2×Q1612yes—
105C2×C4×C13#13712yes—
106C8×C13—24no—
107C8×C13—44no—
108C8×C13—81no—
109#533C22×C1312yes—
110C2×C4×Q8C22×C1311yescharacteristic
111#501—22no—
112#501—22no—
113#484—22no—
114#477—22no—
115#462—22no—
116#451—22no—
117C4×Q16—24no—
118#431C22×C1312yes—
119#427—22no—
120C2×C4⋊C8C22×C1311yescharacteristic
121C2×#97C22×C1311yescharacteristic
122#336—22no—
123Q8⋊C8—24no—
124C22×C13—21no—
125C22×C13—21no—
126C22×C13#39211yescharacteristic
127C22×C13#46212yes—
128C4×C13—22no—
129C4×C13—22no—
130C4×C13—42no—
131C4×C13—82no—
132C4×C13—81no—
133C4×C13—82no—
134C4×C13#45112yes—
135C4×C13#49411yescharacteristic
136C4×C13#49711yescharacteristic
137C22×Q8D4×C1311yescharacteristic
138C2×Q16—24no—
139C22×C8—21no—
140C22×C8D4×C1312yes—
141C4⋊Q8D4×C1312yes—
142C4⋊Q8D4×C1312yes—
143#125—22no—
144C22⋊Q8—22no—
145C22⋊Q8—22no—
146C4×Q8—22no—
147C4×Q8—22no—
148C4×Q8—22no—
149C4×Q8—22no—
150#117—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4D4×C1311yescharacteristic
153C2×C42—21no—
154C2×C42C23×C1311yescharacteristic
155#107—22no—
156#107—22no—
157#107—24no—
158#106—24no—
159C4⋊C8—22no—
160C4⋊C8—22no—
161#103—24no—
162#103—24no—
163C22⋊C8—22no—
164#97—22no—
165C4×C8D4×C1314yes—
166C2×C13—22no—
167C2×C13#201011yescharacteristic
168C2×C13#201611yescharacteristic
169C2×C13#201711yescharacteristic
170C2×Q8—22no—
171C2×Q8—22no—
172C2×Q8—22no—
173C2×Q8—42no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4C2×D4×C1311yescharacteristic
177C22×C4C2×D4×C1311yescharacteristic
178C22×C4C13×#4111yescharacteristic
179Q16—48no—
180C2×C8—22no—
181C2×C8—22no—
182C2×C8—24no—
183C2×C8—41no—
184C2×C8—42no—
185C2×C8C13×Q1614yescomplemented
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C22⋊C4—42no—
195C42—41no—
196C42—41no—
197C42—42no—
198C42C2×D4×C1312yes—
199C42C2×D4×C1312yes—
200C13#1003711yescharacteristic, direct product factor, Sylow
201C23C13×#12111yescharacteristic
202Q8—24no—
203Q8—42no—
204Q8—44no—
205Q8—44no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4C13×#12012yes—
216C2×C4C13×#12011yescharacteristic
217C2×C4C13×#12112yes—
218C2×C4C13×#12711yescharacteristic
219C2×C4C2×C13×Q1612yes—
220C2×C4C13×#13712yes—
221C8—24no—
222C8—44no—
223C8—81no—
224C22—21no—
225C22—21no—
226C22C13×#39211yescharacteristic
227C22C13×#46212yes—
228C4—22no—
229C4—22no—
230C4—42no—
231C4—82no—
232C4—81no—
233C4—82no—
234C4C13×#45112yes—
235C4C13×#49411yescharacteristic
236C4C13×#49711yescharacteristic
237C2—22no—
238C2C13×#201011yescharacteristic
239C2C13×#201611yescharacteristic
240C2C13×#201711yescharacteristic
subgroupG/H
centerC2×C4×C13#127
commutator, Frattini, cosocleC2×C42C23×C13
socleC22×C13#392
prime radicalC23×C13#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
50. #10037C13direct (N × H)
66. C2×C8×C13Q16semidirect
185. C2×C8C13×Q16semidirect
200. C13#10037direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31622
C13×#31042
C13×#19852
C13×#14812
C13×#12752
#1003713