Finite Group Databasebeta

← C13×#12181 #15698520

Subgroups — C13×#12181 #15698520

Order 3328.

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

normal subgroups only

This group has 372 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×#2571C211yesmaximal, characteristic, complemented
2C13×#2039C211yesmaximal, characteristic
3C13×#1616C212yesmaximal
4C13×#1353C212yesmaximal, complemented
5C13×#1325C211yesmaximal, characteristic, complemented
6C13×#537C2211yescharacteristic
7C13×#481—22no—
8C2×C13×#104—21no—
9C13×#417—21no—
10C13×#400—21no—
11C13×#400C2212yes—
12C13×#389—22no—
13C13×#384C2211yescharacteristic
14C13×#382—22no—
15C4×C13×C4⋊C4—21no—
16C13×#343C2211yescharacteristic
17C13×#327—22no—
18C13×#324C2212yes—
19C2×C13×#41—21no—
20C2×C13×M16—21no—
21C13×C22⋊Q8—41no—
22C13×#121—22no—
23C13×#121—41no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4D412yes—
30C2×C13×C4⋊C4C2311yescharacteristic
31C2×C42×C13—22no—
32C2×C42×C13D411yescharacteristic
33C13×#106—42no—
34C13×#104—42no—
35C13×#103—41no—
36C13×#102—41no—
37C13×#102—42no—
38C13×C22⋊C8—22no—
39C13×#95—21no—
40C13×#95—22no—
41C13×#95—22no—
42C13×#95—22no—
43C13×#95D412yes—
44#12181C1311yesmaximal, characteristic, direct product factor, Sylow
45C13×#41—41no—
46C13×#41—41no—
47C13×#41—41no—
48C13×#41—41no—
49C2×Q8×C13—21no—
50C2×D4×C13—21no—
51C2×D4×C13—22no—
52C2×D4×C13—41no—
53C22×C4×C13—21no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—21no—
57C22×C4×C13—41no—
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D412yes—
60C13×M16—41no—
61C13×M16—41no—
62C2×C8×C13—42no—
63C2×C8×C13—41no—
64C13×C4⋊C4—22no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—42no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—44no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—81no—
72C13×C22⋊C4—42no—
73C42×C13—21no—
74C42×C13—44no—
75C42×C13SD1612yes—
76#2571C2×C1311yescharacteristic, complemented
77#2039C2×C1311yescharacteristic
78#1616C2×C1312yes—
79#1353C2×C1312yescomplemented
80#1325C2×C1311yescharacteristic, complemented
81C23×C13—41no—
82C23×C13#12011yescharacteristic
83Q8×C13—41no—
84Q8×C13—41no—
85D4×C13—41no—
86D4×C13—41no—
87D4×C13—82no—
88D4×C13—81no—
89D4×C13—81no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—42no—
106C2×C4×C13—81no—
107C2×C4×C13—81no—
108C2×C4×C13C2×SD1611yescharacteristic
109C2×C4×C13#13711yescharacteristic
110C8×C13—81no—
111C8×C13—82no—
112#537C22×C1311yescharacteristic
113#481—22no—
114C2×#104—21no—
115#417—21no—
116#400—21no—
117#400C22×C1312yes—
118#389—22no—
119#384C22×C1311yescharacteristic
120#382—22no—
121C4×C4⋊C4—21no—
122#343C22×C1311yescharacteristic
123#327—22no—
124#324C22×C1312yes—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13—81no—
128C22×C13—81no—
129C22×C13—81no—
130C22×C13#44811yescharacteristic
131C22×C13#45411yescharacteristic
132C22×C13B(4,𝔽2)11yescharacteristic
133C4×C13—24no—
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—42no—
137C4×C13—82no—
138C4×C13—81no—
139C4×C13—81no—
140C4×C13—82no—
141C2×#41—21no—
142C2×M16—21no—
143C22⋊Q8—41no—
144#121—22no—
145#121—41no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4D4×C1311yescharacteristic
151C2×C4⋊C4D4×C1312yes—
152C2×C4⋊C4C23×C1311yescharacteristic
153C2×C42—22no—
154C2×C42D4×C1311yescharacteristic
155#106—42no—
156#104—42no—
157#103—41no—
158#102—41no—
159#102—42no—
160C22⋊C8—22no—
161#95—21no—
162#95—22no—
163#95—22no—
164#95—22no—
165#95D4×C1312yes—
166C2×C13—21no—
167C2×C13—21no—
168C2×C13—161no—
169C2×C13#159911yescharacteristic
170C2×C13#219811yescharacteristic
171C2×C13#220411yescharacteristic
172#41—41no—
173#41—41no—
174#41—41no—
175#41—41no—
176C2×Q8—21no—
177C2×D4—21no—
178C2×D4—22no—
179C2×D4—41no—
180C22×C4—21no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—21no—
184C22×C4—41no—
185C22×C4C2×D4×C1311yescharacteristic
186C22×C4C2×D4×C1312yes—
187M16—41no—
188M16—41no—
189C2×C8—42no—
190C2×C8—41no—
191C4⋊C4—22no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—44no—
197C4⋊C4—42no—
198C4⋊C4—81no—
199C22⋊C4—42no—
200C42—21no—
201C42—44no—
202C42C13×SD1612yes—
203C13#1218111yescharacteristic, direct product factor, Sylow
204C23—41no—
205C23C13×#12011yescharacteristic
206Q8—41no—
207Q8—41no—
208D4—41no—
209D4—41no—
210D4—82no—
211D4—81no—
212D4—81no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—81no—
230C2×C4—81no—
231C2×C4C2×C13×SD1611yescharacteristic
232C2×C4C13×#13711yescharacteristic
233C8—81no—
234C8—82no—
235C22—21no—
236C22—21no—
237C22—81no—
238C22—81no—
239C22—81no—
240C22C13×#44811yescharacteristic
241C22C13×#45411yescharacteristic
242C22C13×B(4,𝔽2)11yescharacteristic
243C4—24no—
244C4—21no—
245C4—21no—
246C4—42no—
247C4—82no—
248C4—81no—
249C4—81no—
250C4—82no—
251C2—21no—
252C2—21no—
253C2—161no—
254C2C13×#159911yescharacteristic
255C2C13×#219811yescharacteristic
256C2C13×#220411yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC13×#537C22
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
1. C13×#2571C2semidirect
4. C13×#1353C2semidirect
5. C13×#1325C2semidirect
44. #12181C13direct (N × H)
76. #2571C2×C13semidirect
79. #1353C2×C13semidirect
80. #1325C2×C13semidirect
203. C13#12181direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25712
C13×#20392
C13×#16162
C13×#13532
C13×#13252
#1218113