Finite Group Databasebeta

← C13×#10386 #15696725

Subgroups — C13×#10386 #15696725

Order 3328.

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

normal subgroups only

This group has 602 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×#2607C211yesmaximal, characteristic, complemented
2C13×#1789C212yesmaximal
3C13×#1782C211yesmaximal, characteristic
4C13×#1306C211yesmaximal, characteristic, complemented
5C13×#1284C212yesmaximal, complemented
6C22×C13×#41C2211yescharacteristic
7C2×C13×#104—22no—
8C2×C13×#104—22no—
9C2×C13×#99—21no—
10C2×C13×#99—21no—
11C13×#407C2212yes—
12C13×#399—21no—
13C13×#393—21no—
14C13×#391—22no—
15C13×#387—22no—
16C13×#381C2211yescharacteristic
17C13×#381C2211yescharacteristic
18C4×C13×C22⋊C4C2212yes—
19C2×C13×#41—22no—
20C2×C13×#41—22no—
21C2×C13×#41—42no—
22C2×C13×#41—42no—
23C22×Q8×C13—21no—
24C22×Q8×C13Q811yescharacteristic, complemented
25C22×D4×C13—21no—
26C22×D4×C13Q811yescharacteristic, complemented
27C23×C4×C13—21no—
28C23×C4×C13C2311yescharacteristic
29C2×C13×M16—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4D411yescharacteristic
35C2×C13×C22⋊C4D411yescharacteristic
36C2×C42×C13D412yes—
37C2×C42×C13D412yes—
38C13×#104—44no—
39C13×#104—44no—
40C13×#99—42no—
41C13×#99—42no—
42C13×C22⋊C8—22no—
43C13×C22⋊C8—22no—
44C13×#95—21no—
45C13×#95—22no—
46C13×#95—21no—
47C13×#95—22no—
48C13×#95—22no—
49C13×#95—22no—
50#10386C1311yesmaximal, characteristic, direct product factor, Sylow
51C24×C13—21no—
52C24×C13C2×D411yescharacteristic
53C13×#41—24no—
54C13×#41—24no—
55C13×#41—42no—
56C13×#41—42no—
57C13×#41—44no—
58C13×#41—44no—
59C2×Q8×C13—22no—
60C2×Q8×C13—42no—
61C2×Q8×C13—44no—
62C2×Q8×C13—81no—
63C2×D4×C13—22no—
64C2×D4×C13—22no—
65C2×D4×C13—22no—
66C2×D4×C13—42no—
67C2×D4×C13—41no—
68C2×D4×C13—41no—
69C2×D4×C13—41no—
70C2×D4×C13—41no—
71C22×C4×C13—22no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—22no—
75C22×C4×C13—21no—
76C22×C4×C13—41no—
77C22×C4×C13—41no—
78C22×C4×C13—42no—
79C22×C4×C13—42no—
80C22×C4×C13—42no—
81C22×C4×C13—41no—
82C22×C4×C13C2×D412yes—
83C22×C4×C13C2×Q811yescharacteristic
84C22×C4×C13#4112yes—
85C22×C4×C13#4111yescharacteristic
86C13×M16—42no—
87C13×M16—42no—
88C2×C8×C13—42no—
89C13×C4⋊C4—44no—
90C13×C4⋊C4—81no—
91C13×C22⋊C4—44no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—41no—
96C42×C13—42no—
97C42×C13—42no—
98#2607C2×C1311yescharacteristic, complemented
99#1789C2×C1312yes—
100#1782C2×C1311yescharacteristic
101#1306C2×C1311yescharacteristic, complemented
102#1284C2×C1312yescomplemented
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—22no—
106C23×C13—42no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—82no—
110C23×C13#12011yescharacteristic
111C23×C13C22⋊Q811yescharacteristic
112C23×C13#12411yescharacteristic
113Q8×C13—24no—
114Q8×C13—42no—
115Q8×C13—84no—
116D4×C13—24no—
117D4×C13—42no—
118D4×C13—42no—
119D4×C13—42no—
120D4×C13—42no—
121D4×C13—42no—
122C2×C4×C13—22no—
123C2×C4×C13—22no—
124C2×C4×C13—24no—
125C2×C4×C13—22no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—42no—
129C2×C4×C13—44no—
130C2×C4×C13—44no—
131C2×C4×C13—41no—
132C2×C4×C13—42no—
133C2×C4×C13—41no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—81no—
143C2×C4×C13—82no—
144C2×C4×C13C22⋊Q812yes—
145C2×C4×C13#12412yes—
146C8×C13—82no—
147C22×#41C22×C1311yescharacteristic
148C2×#104—22no—
149C2×#104—22no—
150C2×#99—21no—
151C2×#99—21no—
152#407C22×C1312yes—
153#399—21no—
154#393—21no—
155#391—22no—
156#387—22no—
157#381C22×C1311yescharacteristic
158#381C22×C1311yescharacteristic
159C4×C22⋊C4C22×C1312yes—
160C22×C13—22no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—22no—
164C22×C13—22no—
165C22×C13—42no—
166C22×C13—81no—
167C22×C13—81no—
168C22×C13—82no—
169C22×C13—82no—
170C22×C13—82no—
171C22×C13#39311yescharacteristic
172C22×C13B(4,𝔽2)11yescharacteristic
173C22×C13B(4,𝔽2)11yescharacteristic
174C4×C13—22no—
175C4×C13—22no—
176C4×C13—44no—
177C4×C13—42no—
178C4×C13—82no—
179C4×C13—81no—
180C4×C13—81no—
181C4×C13—161no—
182C2×#41—22no—
183C2×#41—22no—
184C2×#41—42no—
185C2×#41—42no—
186C22×Q8—21no—
187C22×Q8Q8×C1311yescharacteristic, complemented
188C22×D4—21no—
189C22×D4Q8×C1311yescharacteristic, complemented
190C23×C4—21no—
191C23×C4C23×C1311yescharacteristic
192C2×M16—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—21no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—21no—
197C2×C22⋊C4D4×C1311yescharacteristic
198C2×C22⋊C4D4×C1311yescharacteristic
199C2×C42D4×C1312yes—
200C2×C42D4×C1312yes—
201#104—44no—
202#104—44no—
203#99—42no—
204#99—42no—
205C22⋊C8—22no—
206C22⋊C8—22no—
207#95—21no—
208#95—22no—
209#95—21no—
210#95—22no—
211#95—22no—
212#95—22no—
213C2×C13—21no—
214C2×C13—21no—
215C2×C13—41no—
216C2×C13—41no—
217C2×C13—82no—
218C2×C13#202911yescharacteristic
219C2×C13#203112yes—
220C24—21no—
221C24C2×D4×C1311yescharacteristic
222#41—24no—
223#41—24no—
224#41—42no—
225#41—42no—
226#41—44no—
227#41—44no—
228C2×Q8—22no—
229C2×Q8—42no—
230C2×Q8—44no—
231C2×Q8—81no—
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—22no—
235C2×D4—42no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—41no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—41no—
251C22×C4C2×D4×C1312yes—
252C22×C4C2×Q8×C1311yescharacteristic
253C22×C4C13×#4112yes—
254C22×C4C13×#4111yescharacteristic
255M16—42no—
256M16—42no—
257C2×C8—42no—
258C4⋊C4—44no—
259C4⋊C4—81no—
260C22⋊C4—44no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C42—42no—
266C42—42no—
267C13#1038611yescharacteristic, direct product factor, Sylow
268C23—21no—
269C23—21no—
270C23—22no—
271C23—42no—
272C23—41no—
273C23—41no—
274C23—82no—
275C23C13×#12011yescharacteristic
276C23C13×C22⋊Q811yescharacteristic
277C23C13×#12411yescharacteristic
278Q8—24no—
279Q8—42no—
280Q8—84no—
281D4—24no—
282D4—42no—
283D4—42no—
284D4—42no—
285D4—42no—
286D4—42no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—24no—
290C2×C4—22no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—81no—
308C2×C4—82no—
309C2×C4C13×C22⋊Q812yes—
310C2×C4C13×#12412yes—
311C8—82no—
312C22—22no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—22no—
317C22—42no—
318C22—81no—
319C22—81no—
320C22—82no—
321C22—82no—
322C22—82no—
323C22C13×#39311yescharacteristic
324C22C13×B(4,𝔽2)11yescharacteristic
325C22C13×B(4,𝔽2)11yescharacteristic
326C4—22no—
327C4—22no—
328C4—44no—
329C4—42no—
330C4—82no—
331C4—81no—
332C4—81no—
333C4—161no—
334C2—21no—
335C2—21no—
336C2—41no—
337C2—41no—
338C2—82no—
339C2C13×#202911yescharacteristic
340C2C13×#203112yes—
subgroupG/H
center, socleC22×C13#393
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC22×C13×#41C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2607C2semidirect
4. C13×#1306C2semidirect
5. C13×#1284C2semidirect
24. C22×Q8×C13Q8semidirect
26. C22×D4×C13Q8semidirect
50. #10386C13direct (N × H)
98. #2607C2×C13semidirect
101. #1306C2×C13semidirect
102. #1284C2×C13semidirect
187. C22×Q8Q8×C13semidirect
189. C22×D4Q8×C13semidirect
267. C13#10386direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26072
C13×#17892
C13×#17822
C13×#13062
C13×#12842
#1038613