Finite Group Databasebeta

← C13×#13426 #15699765

Subgroups — C13×#13426 #15699765

Order 3328.

512 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2733C211yesmaximal, characteristic
2C2×C13×#355C212yesmaximal, complemented
3C13×#1888C212yesmaximal, complemented
4C13×#1857C211yesmaximal, characteristic, complemented
5C13×#1394C211yesmaximal, characteristic, complemented
6C2×C13×#124C2212yes—
7C13×#519C2211yescharacteristic
8C13×#428—21no—
9C13×#418—22no—
10C2×C13×#101C2212yes—
11C2×C13×#101C2211yescharacteristic
12C13×#394—21no—
13C13×#392—22no—
14C13×#391C2211yescharacteristic
15C13×#390—21no—
16C13×#388—22no—
17C13×#355—24no—
18C13×#339—21no—
19C13×#339—22no—
20C22×Q8×C13C2311yescharacteristic
21C22×D4×C13—21no—
22C22×D4×C13—21no—
23C22×D4×C13D412yes—
24C2×C13×M16—21no—
25C2×C13×M16—22no—
26C13×#124—22no—
27C13×#124—22no—
28C13×#124—22no—
29C13×#124—22no—
30C4×Q8×C13—41no—
31C4×Q8×C13—41no—
32C13×#117—22no—
33C13×#117—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C42×C13D412yes—
41C2×C42×C13D411yescharacteristic
42C13×#107—41no—
43C13×#106—41no—
44C13×#102—42no—
45C13×#102—42no—
46C13×#101—21no—
47C13×#101—22no—
48C13×#101—22no—
49C13×#101D412yescomplemented
50C13×#95—21no—
51C13×#95—22no—
52#13426C1311yesmaximal, characteristic, direct product factor, Sylow
53C24×C13—22no—
54C2×Q8×C13—41no—
55C2×Q8×C13—41no—
56C2×Q8×C13C2×D411yescharacteristic
57C2×Q8×C13#4111yescharacteristic
58C2×Q8×C13#4112yes—
59C2×D4×C13—22no—
60C2×D4×C13—22no—
61C2×D4×C13—42no—
62C2×D4×C13—42no—
63C2×D4×C13—42no—
64C2×D4×C13—81no—
65C2×D4×C13—81no—
66C2×D4×C13—82no—
67C2×D4×C13—81no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—22no—
71C22×C4×C13C2×D412yes—
72C22×C4×C13C2×D411yescharacteristic
73C13×M16—22no—
74C13×M16—41no—
75C13×M16—42no—
76C13×M16—42no—
77C2×C8×C13—41no—
78C2×C8×C13—42no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—81no—
85C13×C22⋊C4—44no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—42no—
89C13×C22⋊C4—42no—
90C13×C22⋊C4—42no—
91C13×C22⋊C4—82no—
92C42×C13—22no—
93C42×C13—22no—
94C42×C13—41no—
95C42×C13—41no—
96C42×C13—42no—
97#2733C2×C1311yescharacteristic
98C2×#355C2×C1312yescomplemented
99#1888C2×C1312yescomplemented
100#1857C2×C1311yescharacteristic, complemented
101#1394C2×C1311yescharacteristic, complemented
102C23×C13—42no—
103C23×C13—42no—
104C23×C13—42no—
105C23×C13—42no—
106C23×C13—42no—
107C23×C13—42no—
108C23×C13—42no—
109C23×C13#12011yescharacteristic
110Q8×C13—41no—
111Q8×C13—41no—
112Q8×C13—42no—
113D4×C13—44no—
114D4×C13—82no—
115D4×C13—84no—
116D4×C13—84no—
117C2×C4×C13—21no—
118C2×C4×C13—22no—
119C2×C4×C13—21no—
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13#12112yes—
132C2×C4×C13#12111yescharacteristic
133C2×C4×C13#12312yes—
134C2×C4×C13#12411yescharacteristic
135C8×C13—42no—
136C8×C13—82no—
137C2×#124C22×C1312yes—
138#519C22×C1311yescharacteristic
139#428—21no—
140#418—22no—
141C2×#101C22×C1312yes—
142C2×#101C22×C1311yescharacteristic
143#394—21no—
144#392—22no—
145#391C22×C1311yescharacteristic
146#390—21no—
147#388—22no—
148#355—24no—
149#339—21no—
150#339—22no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—82no—
154C22×C13—82no—
155C22×C13—82no—
156C22×C13—82no—
157C22×C13—82no—
158C22×C13—82no—
159C22×C13—82no—
160C22×C13#39411yescharacteristic
161C22×C13B(4,𝔽2)11yescharacteristic
162C22×C13#45811yescharacteristic
163C4×C13—21no—
164C4×C13—22no—
165C4×C13—22no—
166C4×C13—21no—
167C4×C13—42no—
168C4×C13—82no—
169C4×C13—81no—
170C4×C13—81no—
171C4×C13—81no—
172C22×Q8C23×C1311yescharacteristic
173C22×D4—21no—
174C22×D4—21no—
175C22×D4D4×C1312yes—
176C2×M16—21no—
177C2×M16—22no—
178#124—22no—
179#124—22no—
180#124—22no—
181#124—22no—
182C4×Q8—41no—
183C4×Q8—41no—
184#117—22no—
185#117—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4D4×C1311yescharacteristic
188C2×C22⋊C4—22no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—22no—
192C2×C42D4×C1312yes—
193C2×C42D4×C1311yescharacteristic
194#107—41no—
195#106—41no—
196#102—42no—
197#102—42no—
198#101—21no—
199#101—22no—
200#101—22no—
201#101D4×C1312yescomplemented
202#95—21no—
203#95—22no—
204C2×C13—21no—
205C2×C13—21no—
206C2×C13—162no—
207C2×C13#204411yescharacteristic
208C2×C13#220211yescharacteristic
209C2×C13#220411yescharacteristic
210C24—22no—
211C2×Q8—41no—
212C2×Q8—41no—
213C2×Q8C2×D4×C1311yescharacteristic
214C2×Q8C13×#4111yescharacteristic
215C2×Q8C13×#4112yes—
216C2×D4—22no—
217C2×D4—22no—
218C2×D4—42no—
219C2×D4—42no—
220C2×D4—42no—
221C2×D4—81no—
222C2×D4—81no—
223C2×D4—82no—
224C2×D4—81no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4C2×D4×C1312yes—
229C22×C4C2×D4×C1311yescharacteristic
230M16—22no—
231M16—41no—
232M16—42no—
233M16—42no—
234C2×C8—41no—
235C2×C8—42no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—41no—
241C4⋊C4—81no—
242C22⋊C4—44no—
243C22⋊C4—41no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C22⋊C4—42no—
248C22⋊C4—82no—
249C42—22no—
250C42—22no—
251C42—41no—
252C42—41no—
253C42—42no—
254C13#1342611yescharacteristic, direct product factor, Sylow
255C23—42no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—42no—
261C23—42no—
262C23C13×#12011yescharacteristic
263Q8—41no—
264Q8—41no—
265Q8—42no—
266D4—44no—
267D4—82no—
268D4—84no—
269D4—84no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4C13×#12112yes—
285C2×C4C13×#12111yescharacteristic
286C2×C4C13×#12312yes—
287C2×C4C13×#12411yescharacteristic
288C8—42no—
289C8—82no—
290C22—21no—
291C22—21no—
292C22—82no—
293C22—82no—
294C22—82no—
295C22—82no—
296C22—82no—
297C22—82no—
298C22—82no—
299C22C13×#39411yescharacteristic
300C22C13×B(4,𝔽2)11yescharacteristic
301C22C13×#45811yescharacteristic
302C4—21no—
303C4—22no—
304C4—22no—
305C4—21no—
306C4—42no—
307C4—82no—
308C4—81no—
309C4—81no—
310C4—81no—
311C2—21no—
312C2—21no—
313C2—162no—
314C2C13×#204411yescharacteristic
315C2C13×#220211yescharacteristic
316C2C13×#220411yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC22×Q8C23×C13
prime radicalC13×#2733C2
LCSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C22×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#355C2semidirect
3. C13×#1888C2semidirect
4. C13×#1857C2semidirect
5. C13×#1394C2semidirect
49. C13×#101D4semidirect
52. #13426C13direct (N × H)
98. C2×#355C2×C13semidirect
99. #1888C2×C13semidirect
100. #1857C2×C13semidirect
101. #1394C2×C13semidirect
201. #101D4×C13semidirect
254. C13#13426direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27332
C2×C13×#3552
C13×#18882
C13×#18572
C13×#13942
#1342613