Finite Group Databasebeta

← C13×#12246 #15698585

Subgroups — C13×#12246 #15698585

Order 3328.

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

normal subgroups only

This group has 558 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×#2537C211yesmaximal, characteristic
2C13×#2060C211yesmaximal, characteristic, complemented
3C13×#1599C212yesmaximal, complemented
4C13×#1345C212yesmaximal, complemented
5C13×#1325C211yesmaximal, characteristic, complemented
6C13×#544C2211yescharacteristic
7C2×C13×#121—22no—
8C2×C4×D4×C13—21no—
9C13×#450—22no—
10C13×#428—21no—
11C13×#394—21no—
12C13×#394C2212yes—
13C13×#384C2211yescharacteristic
14C13×#380—22no—
15C13×#343C2211yescharacteristic
16C13×#339—21no—
17C13×#328—22no—
18C13×#324C2212yes—
19C22×D4×C13—21no—
20C22×D4×C13—21no—
21C22×D4×C13D412yes—
22C23×C4×C13—22no—
23C2×C13×SD16—42no—
24C2×C13×M16—21no—
25C13×C4⋊Q8—41no—
26C13×#125—41no—
27C13×C22⋊Q8—22no—
28C13×#121—48no—
29C4×D4×C13—42no—
30C4×D4×C13—42no—
31C13×#117—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C4⋊C4C2311yescharacteristic
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C42×C13D411yescharacteristic
40C13×#107—41no—
41C13×#106—41no—
42C13×#102—42no—
43C13×C22⋊C8—22no—
44C13×#95—21no—
45C13×#95D412yes—
46#12246C1311yesmaximal, characteristic, direct product factor, Sylow
47C24×C13—22no—
48C2×Q8×C13—22no—
49C2×D4×C13—24no—
50C2×D4×C13—42no—
51C2×D4×C13—42no—
52C2×D4×C13—42no—
53C2×D4×C13—44no—
54C2×D4×C13—44no—
55C2×D4×C13—81no—
56C22×C4×C13—21no—
57C22×C4×C13—22no—
58C22×C4×C13—21no—
59C22×C4×C13—44no—
60C22×C4×C13—44no—
61C22×C4×C13—44no—
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D412yes—
64C13×SD16—84no—
65C13×M16—22no—
66C13×M16—41no—
67C2×C8×C13—41no—
68C2×C8×C13—42no—
69C13×C4⋊C4—22no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—42no—
75C13×C4⋊C4—44no—
76C13×C4⋊C4—42no—
77C13×C22⋊C4—44no—
78C13×C22⋊C4—44no—
79C13×C22⋊C4—41no—
80C13×C22⋊C4—42no—
81C13×C22⋊C4—42no—
82C42×C13—21no—
83C42×C13—41no—
84C42×C13SD1612yescomplemented
85#2537C2×C1311yescharacteristic
86#2060C2×C1311yescharacteristic, complemented
87#1599C2×C1312yescomplemented
88#1345C2×C1312yescomplemented
89#1325C2×C1311yescharacteristic, complemented
90C23×C13—24no—
91C23×C13—42no—
92C23×C13—42no—
93C23×C13—42no—
94C23×C13—42no—
95C23×C13—42no—
96C23×C13—42no—
97C23×C13#12011yescharacteristic
98Q8×C13—82no—
99D4×C13—48no—
100D4×C13—44no—
101D4×C13—82no—
102D4×C13—84no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—22no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—88no—
118C2×C4×C13C2×SD1611yescharacteristic
119C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
120C8×C13—42no—
121C8×C13—82no—
122#544C22×C1311yescharacteristic
123C2×#121—22no—
124C2×C4×D4—21no—
125#450—22no—
126#428—21no—
127#394—21no—
128#394C22×C1312yes—
129#384C22×C1311yescharacteristic
130#380—22no—
131#343C22×C1311yescharacteristic
132#339—21no—
133#328—22no—
134#324C22×C1312yes—
135C22×C13—21no—
136C22×C13—21no—
137C22×C13—44no—
138C22×C13—44no—
139C22×C13—44no—
140C22×C13—82no—
141C22×C13—82no—
142C22×C13—82no—
143C22×C13—82no—
144C22×C13#45011yescharacteristic
145C22×C13#45611yescharacteristic
146C22×C13B(4,𝔽2)11yescharacteristic
147C4×C13—24no—
148C4×C13—21no—
149C4×C13—21no—
150C4×C13—42no—
151C4×C13—82no—
152C4×C13—81no—
153C4×C13—81no—
154C4×C13—81no—
155C22×D4—21no—
156C22×D4—21no—
157C22×D4D4×C1312yes—
158C23×C4—22no—
159C2×SD16—42no—
160C2×M16—21no—
161C4⋊Q8—41no—
162#125—41no—
163C22⋊Q8—22no—
164#121—48no—
165C4×D4—42no—
166C4×D4—42no—
167#117—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4D4×C1311yescharacteristic
171C2×C4⋊C4C23×C1311yescharacteristic
172C2×C22⋊C4—22no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—22no—
175C2×C42D4×C1311yescharacteristic
176#107—41no—
177#106—41no—
178#102—42no—
179C22⋊C8—22no—
180#95—21no—
181#95D4×C1312yes—
182C2×C13—21no—
183C2×C13—21no—
184C2×C13—84no—
185C2×C13#160411yescharacteristic
186C2×C13#219611yescharacteristic
187C2×C13#220411yescharacteristic
188C24—22no—
189C2×Q8—22no—
190C2×D4—24no—
191C2×D4—42no—
192C2×D4—42no—
193C2×D4—42no—
194C2×D4—44no—
195C2×D4—44no—
196C2×D4—81no—
197C22×C4—21no—
198C22×C4—22no—
199C22×C4—21no—
200C22×C4—44no—
201C22×C4—44no—
202C22×C4—44no—
203C22×C4C2×D4×C1311yescharacteristic
204C22×C4C2×D4×C1312yes—
205SD16—84no—
206M16—22no—
207M16—41no—
208C2×C8—41no—
209C2×C8—42no—
210C4⋊C4—22no—
211C4⋊C4—21no—
212C4⋊C4—21no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—42no—
216C4⋊C4—44no—
217C4⋊C4—42no—
218C22⋊C4—44no—
219C22⋊C4—44no—
220C22⋊C4—41no—
221C22⋊C4—42no—
222C22⋊C4—42no—
223C42—21no—
224C42—41no—
225C42C13×SD1612yescomplemented
226C13#1224611yescharacteristic, direct product factor, Sylow
227C23—24no—
228C23—42no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—42no—
233C23—42no—
234C23C13×#12011yescharacteristic
235Q8—82no—
236D4—48no—
237D4—44no—
238D4—82no—
239D4—84no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—88no—
255C2×C4C2×C13×SD1611yescharacteristic
256C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
257C8—42no—
258C8—82no—
259C22—21no—
260C22—21no—
261C22—44no—
262C22—44no—
263C22—44no—
264C22—82no—
265C22—82no—
266C22—82no—
267C22—82no—
268C22C13×#45011yescharacteristic
269C22C13×#45611yescharacteristic
270C22C13×B(4,𝔽2)11yescharacteristic
271C4—24no—
272C4—21no—
273C4—21no—
274C4—42no—
275C4—82no—
276C4—81no—
277C4—81no—
278C4—81no—
279C2—21no—
280C2—21no—
281C2—84no—
282C2C13×#160411yescharacteristic
283C2C13×#219611yescharacteristic
284C2C13×#220411yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC13×#2537C2
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
2. C13×#2060C2semidirect
3. C13×#1599C2semidirect
4. C13×#1345C2semidirect
5. C13×#1325C2semidirect
46. #12246C13direct (N × H)
84. C42×C13SD16semidirect
86. #2060C2×C13semidirect
87. #1599C2×C13semidirect
88. #1345C2×C13semidirect
89. #1325C2×C13semidirect
225. C42C13×SD16semidirect
226. C13#12246direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25372
C13×#20602
C13×#15992
C13×#13452
C13×#13252
#1224613