Finite Group Databasebeta

← C13×#10087 #15696426

Subgroups — C13×#10087 #15696426

Order 3328.

500 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C2×C13×#501C212yesmaximal
2C13×#2822C211yesmaximal, characteristic
3C13×#1960C211yesmaximal, characteristic
4C2×C13×#330C212yesmaximal
5C13×#1295C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C13×#125C2212yes—
8C13×#501—24no—
9C13×#501—24no—
10C2×C13×#107—22no—
11C2×C13×#106—22no—
12C2×C13×#103—22no—
13C2×C13×#97C2211yescharacteristic
14C2×C13×#97C2212yes—
15C13×#400—22no—
16C13×#398—22no—
17C13×#398—22no—
18C13×#382C2211yescharacteristic
19C13×#330—24no—
20C22×Q8×C13—21no—
21C22×C8×C13—22no—
22C22×C8×C13—21no—
23C13×C4⋊Q8—22no—
24C13×C4⋊Q8—21no—
25C13×C4⋊Q8D412yes—
26C13×#125—22no—
27C13×#125—22no—
28C13×#125—22no—
29C13×#125—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4D412yes—
35C2×C13×C4⋊C4D412yes—
36C2×C13×C4⋊C4D412yes—
37C2×C42×C13C2311yescharacteristic
38C13×#107—28no—
39C13×#106—28no—
40C13×#103—44no—
41C13×#97—22no—
42C13×#97—22no—
43C13×#97D414yes—
44C13×#95—24no—
45C13×#95—22no—
46C13×#95—22no—
47#10087C1311yesmaximal, characteristic, direct product factor, Sylow
48C2×Q8×C13—22no—
49C2×Q8×C13—42no—
50C2×Q8×C13—42no—
51C2×Q8×C13—41no—
52C22×C4×C13—22no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13—41no—
56C22×C4×C13C2×D412yes—
57C22×C4×C13C2×D411yescharacteristic
58C2×C8×C13—28no—
59C2×C8×C13—24no—
60C2×C8×C13—22no—
61C2×C8×C13—41no—
62C2×C8×C13—41no—
63C13×C4⋊C4—22no—
64C13×C4⋊C4—24no—
65C13×C4⋊C4—22no—
66C13×C4⋊C4—22no—
67C13×C4⋊C4—22no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—42no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—42no—
74C13×C4⋊C4—82no—
75C42×C13C2×D411yescharacteristic
76C42×C13C2×D412yes—
77C42×C13#4111yescharacteristic
78C2×#501C2×C1312yes—
79#2822C2×C1311yescharacteristic
80#1960C2×C1311yescharacteristic
81C2×#330C2×C1312yes—
82#1295C2×C1311yescharacteristic
83C23×C13#12011yescharacteristic
84Q8×C13—44no—
85Q8×C13—82no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—24no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—44no—
96C2×C4×C13—44no—
97C2×C4×C13—81no—
98C2×C4×C13—81no—
99C2×C4×C13#12012yes—
100C2×C4×C13#12112yes—
101C2×C4×C13#12111yescharacteristic
102C2×C4×C13#12711yescharacteristic
103C8×C13—28no—
104C8×C13—42no—
105C2×C4⋊Q8C22×C1311yescharacteristic
106C2×#125C22×C1312yes—
107#501—24no—
108#501—24no—
109C2×#107—22no—
110C2×#106—22no—
111C2×#103—22no—
112C2×#97C22×C1311yescharacteristic
113C2×#97C22×C1312yes—
114#400—22no—
115#398—22no—
116#398—22no—
117#382C22×C1311yescharacteristic
118#330—24no—
119C22×C13#39211yescharacteristic
120C22×C13#45311yescharacteristic
121C22×C13#45411yescharacteristic
122C22×C13#45614yes—
123C4×C13—22no—
124C4×C13—22no—
125C4×C13—21no—
126C4×C13—21no—
127C4×C13—82no—
128C4×C13—82no—
129C4×C13—82no—
130C4×C13—82no—
131C22×Q8—21no—
132C22×C8—22no—
133C22×C8—21no—
134C4⋊Q8—22no—
135C4⋊Q8—21no—
136C4⋊Q8D4×C1312yes—
137#125—22no—
138#125—22no—
139#125—22no—
140#125—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4D4×C1312yes—
146C2×C4⋊C4D4×C1312yes—
147C2×C4⋊C4D4×C1312yes—
148C2×C42C23×C1311yescharacteristic
149#107—28no—
150#106—28no—
151#103—44no—
152#97—22no—
153#97—22no—
154#97D4×C1314yes—
155#95—24no—
156#95—22no—
157#95—22no—
158C2×C13#166012yes—
159C2×C13#166312yes—
160C2×C13#200512yes—
161C2×C13#200611yescharacteristic
162C2×Q8—22no—
163C2×Q8—42no—
164C2×Q8—42no—
165C2×Q8—41no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—41no—
170C22×C4C2×D4×C1312yes—
171C22×C4C2×D4×C1311yescharacteristic
172C2×C8—28no—
173C2×C8—24no—
174C2×C8—22no—
175C2×C8—41no—
176C2×C8—41no—
177C4⋊C4—22no—
178C4⋊C4—24no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—82no—
189C42C2×D4×C1311yescharacteristic
190C42C2×D4×C1312yes—
191C42C13×#4111yescharacteristic
192C13#1008711yescharacteristic, direct product factor, Sylow
193C23C13×#12011yescharacteristic
194Q8—44no—
195Q8—82no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—24no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—44no—
206C2×C4—44no—
207C2×C4—81no—
208C2×C4—81no—
209C2×C4C13×#12012yes—
210C2×C4C13×#12112yes—
211C2×C4C13×#12111yescharacteristic
212C2×C4C13×#12711yescharacteristic
213C8—28no—
214C8—42no—
215C22C13×#39211yescharacteristic
216C22C13×#45311yescharacteristic
217C22C13×#45411yescharacteristic
218C22C13×#45614yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—82no—
225C4—82no—
226C4—82no—
227C2C13×#166012yes—
228C2C13×#166312yes—
229C2C13×#200512yes—
230C2C13×#200611yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C13#120
commutator, Frattini, cosocleC2×C42C23×C13
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
47. #10087C13direct (N × H)
192. C13#10087direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5012
C13×#28222
C13×#19602
C2×C13×#3302
C13×#12952
#1008713