Finite Group Databasebeta

← C13×#13463 #15699802

Subgroups — C13×#13463 #15699802

Order 3328.

484 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2804C211yesmaximal, characteristic
2C13×#1867C212yesmaximal
3C13×#1856C211yesmaximal, characteristic
4C13×#1393C211yesmaximal, characteristic
5C13×#1390C212yesmaximal
6C13×#518C2211yescharacteristic
7C13×#428—21no—
8C2×C13×#100C2211yescharacteristic
9C2×C13×#99C2212yes—
10C13×#400—21no—
11C13×#393—22no—
12C13×#391—21no—
13C13×#390C2211yescharacteristic
14C13×#386C2212yes—
15C13×#385—22no—
16C13×#385—22no—
17C13×#342—22no—
18C13×#339—21no—
19C22×Q8×C13—21no—
20C22×D4×C13C2311yescharacteristic
21C23×C4×C13D412yes—
22C2×C13×M16—21no—
23C4×D4×C13—41no—
24C4×D4×C13—41no—
25C13×#117—21no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—42no—
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4D412yes—
35C2×C42×C13D411yescharacteristic
36C13×#107—41no—
37C13×#106—41no—
38C13×#100—21no—
39C13×#100Q812yescomplemented
40C13×#99—22no—
41C13×#99Q814yescomplemented
42C13×#95—22no—
43C13×#95—22no—
44C13×#95—21no—
45C13×#95—22no—
46C13×#95—42no—
47#13463C1311yesmaximal, characteristic, direct product factor, Sylow
48C24×C13C2×D412yes—
49C2×Q8×C13—42no—
50C2×Q8×C13—81no—
51C2×Q8×C13—81no—
52C2×D4×C13—41no—
53C2×D4×C13—41no—
54C2×D4×C13C2×Q811yescharacteristic
55C2×D4×C13C2×Q812yes—
56C2×D4×C13#4111yescharacteristic
57C22×C4×C13—21no—
58C22×C4×C13—22no—
59C22×C4×C13—21no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13—82no—
66C22×C4×C13C2×D411yescharacteristic
67C13×M16—22no—
68C13×M16—41no—
69C2×C8×C13—41no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—81no—
74C13×C4⋊C4—81no—
75C13×C4⋊C4—84no—
76C13×C22⋊C4—24no—
77C13×C22⋊C4—44no—
78C13×C22⋊C4—42no—
79C13×C22⋊C4—42no—
80C13×C22⋊C4—41no—
81C13×C22⋊C4—42no—
82C13×C22⋊C4—82no—
83C42×C13—41no—
84C42×C13—41no—
85#2804C2×C1311yescharacteristic
86#1867C2×C1312yes—
87#1856C2×C1311yescharacteristic
88#1393C2×C1311yescharacteristic
89#1390C2×C1312yes—
90C23×C13—22no—
91C23×C13—22no—
92C23×C13—42no—
93C23×C13—42no—
94C23×C13#12011yescharacteristic
95C23×C13C22⋊Q812yes—
96C23×C13C4⋊Q812yes—
97Q8×C13—84no—
98D4×C13—41no—
99D4×C13—42no—
100D4×C13—41no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—22no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—44no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—44no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—82no—
119C2×C4×C13—82no—
120C2×C4×C13—82no—
121C2×C4×C13—82no—
122C2×C4×C13—82no—
123C2×C4×C13C22⋊Q811yescharacteristic
124C2×C4×C13C4⋊Q811yescharacteristic
125C8×C13—42no—
126#518C22×C1311yescharacteristic
127#428—21no—
128C2×#100C22×C1311yescharacteristic
129C2×#99C22×C1312yes—
130#400—21no—
131#393—22no—
132#391—21no—
133#390C22×C1311yescharacteristic
134#386C22×C1312yes—
135#385—22no—
136#385—22no—
137#342—22no—
138#339—21no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—22no—
142C22×C13—22no—
143C22×C13—42no—
144C22×C13—42no—
145C22×C13—42no—
146C22×C13—42no—
147C22×C13—82no—
148C22×C13#39511yescharacteristic
149C22×C13B(4,𝔽2)11yescharacteristic
150C22×C13#45811yescharacteristic
151C4×C13—21no—
152C4×C13—21no—
153C4×C13—42no—
154C4×C13—82no—
155C4×C13—84no—
156C4×C13—81no—
157C4×C13—81no—
158C4×C13—82no—
159C4×C13—81no—
160C22×Q8—21no—
161C22×D4C23×C1311yescharacteristic
162C23×C4D4×C1312yes—
163C2×M16—21no—
164C4×D4—41no—
165C4×D4—41no—
166#117—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4D4×C1311yescharacteristic
171C2×C22⋊C4—22no—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—22no—
175C2×C22⋊C4D4×C1312yes—
176C2×C42D4×C1311yescharacteristic
177#107—41no—
178#106—41no—
179#100—21no—
180#100Q8×C1312yescomplemented
181#99—22no—
182#99Q8×C1314yescomplemented
183#95—22no—
184#95—22no—
185#95—21no—
186#95—22no—
187#95—42no—
188C2×C13—21no—
189C2×C13—21no—
190C2×C13—42no—
191C2×C13—42no—
192C2×C13#206211yescharacteristic
193C2×C13#219811yescharacteristic
194C2×C13#219911yescharacteristic
195C24C2×D4×C1312yes—
196C2×Q8—42no—
197C2×Q8—81no—
198C2×Q8—81no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4C2×Q8×C1311yescharacteristic
202C2×D4C2×Q8×C1312yes—
203C2×D4C13×#4111yescharacteristic
204C22×C4—21no—
205C22×C4—22no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—82no—
213C22×C4C2×D4×C1311yescharacteristic
214M16—22no—
215M16—41no—
216C2×C8—41no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—41no—
220C4⋊C4—81no—
221C4⋊C4—81no—
222C4⋊C4—84no—
223C22⋊C4—24no—
224C22⋊C4—44no—
225C22⋊C4—42no—
226C22⋊C4—42no—
227C22⋊C4—41no—
228C22⋊C4—42no—
229C22⋊C4—82no—
230C42—41no—
231C42—41no—
232C13#1346311yescharacteristic, direct product factor, Sylow
233C23—22no—
234C23—22no—
235C23—42no—
236C23—42no—
237C23C13×#12011yescharacteristic
238C23C13×C22⋊Q812yes—
239C23C13×C4⋊Q812yes—
240Q8—84no—
241D4—41no—
242D4—42no—
243D4—41no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—44no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—44no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4—82no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4C13×C22⋊Q811yescharacteristic
267C2×C4C13×C4⋊Q811yescharacteristic
268C8—42no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—82no—
278C22C13×#39511yescharacteristic
279C22C13×B(4,𝔽2)11yescharacteristic
280C22C13×#45811yescharacteristic
281C4—21no—
282C4—21no—
283C4—42no—
284C4—82no—
285C4—84no—
286C4—81no—
287C4—81no—
288C4—82no—
289C4—81no—
290C2—21no—
291C2—21no—
292C2—42no—
293C2—42no—
294C2C13×#206211yescharacteristic
295C2C13×#219811yescharacteristic
296C2C13×#219911yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C13
prime radicalC22×D4×C13C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C22×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
39. C13×#100Q8semidirect
41. C13×#99Q8semidirect
47. #13463C13direct (N × H)
180. #100Q8×C13semidirect
182. #99Q8×C13semidirect
232. C13#13463direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28042
C13×#18672
C13×#18562
C13×#13932
C13×#13902
#1346313