Finite Group Databasebeta

← C13×#12964 #15699303

Subgroups — C13×#12964 #15699303

Order 3328.

672 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2366C211yesmaximal, characteristic
2C2×C13×#353C211yesmaximal, characteristic
3C13×#1887C211yesmaximal, characteristic
4C13×#1867C212yesmaximal, complemented
5C13×#1390C212yesmaximal, complemented
6C2×C13×#127C2211yescharacteristic
7C13×#518C2211yescharacteristic
8C2×C4×D4×C13—22no—
9C13×#418—21no—
10C2×C13×#100C2211yescharacteristic
11C2×C13×#99C2212yes—
12C13×#390—22no—
13C13×#386—21no—
14C13×#386C2212yes—
15C13×#385—22no—
16C4×C13×C4⋊C4—21no—
17C13×#353C414yescomplemented
18C13×#342—22no—
19C13×#339—21no—
20C22×D4×C13—22no—
21C22×D4×C13D411yescharacteristic
22C22×D4×C13C2311yescharacteristic
23C23×C4×C13—21no—
24C23×C4×C13D412yes—
25C2×C13×M16—21no—
26C13×#127—22no—
27C13×#127C2×C412yes—
28C13×#127Q812yes—
29C4×D4×C13—41no—
30C4×D4×C13—41no—
31C4×D4×C13—48no—
32C13×#117—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—42no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4D412yes—
42C2×C42×C13—22no—
43C2×C42×C13D411yescharacteristic
44C13×#102—41no—
45C13×#102—41no—
46C13×#100—22no—
47C13×#99—22no—
48C13×#99C2×C414yescomplemented
49C13×#95—22no—
50C13×#95—42no—
51#12964C1311yesmaximal, characteristic, direct product factor, Sylow
52C24×C13—21no—
53C24×C13C2×D412yes—
54C2×D4×C13—24no—
55C2×D4×C13—24no—
56C2×D4×C13—21no—
57C2×D4×C13—41no—
58C2×D4×C13—41no—
59C2×D4×C13—44no—
60C2×D4×C13—44no—
61C2×D4×C13—41no—
62C2×D4×C13—41no—
63C2×D4×C13C4⋊C412yescomplemented
64C2×D4×C13C22×C411yescharacteristic
65C2×D4×C13C2×Q811yescharacteristic
66C2×D4×C13#4112yes—
67C22×C4×C13—21no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—44no—
73C22×C4×C13—44no—
74C22×C4×C13—42no—
75C22×C4×C13—42no—
76C22×C4×C13—81no—
77C22×C4×C13C2×D411yescharacteristic
78C13×M16—41no—
79C13×M16—41no—
80C2×C8×C13—41no—
81C13×C4⋊C4—24no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—42no—
85C13×C4⋊C4—84no—
86C13×C22⋊C4—24no—
87C13×C22⋊C4—44no—
88C13×C22⋊C4—44no—
89C13×C22⋊C4—42no—
90C13×C22⋊C4—42no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—42no—
93C13×C22⋊C4—81no—
94C42×C13—21no—
95C42×C13—44no—
96C42×C13—41no—
97C42×C13C4⋊C412yescomplemented
98#2366C2×C1311yescharacteristic
99C2×#353C2×C1311yescharacteristic
100#1887C2×C1311yescharacteristic
101#1867C2×C1312yescomplemented
102#1390C2×C1312yescomplemented
103C23×C13—22no—
104C23×C13—22no—
105C23×C13—22no—
106C23×C13—42no—
107C23×C13—42no—
108C23×C13—42no—
109C23×C13—42no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13C4×D412yes—
113C23×C13#12011yescharacteristic
114C23×C13C22⋊Q812yes—
115D4×C13—41no—
116D4×C13—41no—
117D4×C13—42no—
118D4×C13—48no—
119D4×C13—48no—
120D4×C13—42no—
121D4×C13—81no—
122C2×C4×C13—22no—
123C2×C4×C13—22no—
124C2×C4×C13—22no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—24no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—44no—
131C2×C4×C13—42no—
132C2×C4×C13—44no—
133C2×C4×C13—42no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—42no—
137C2×C4×C13—82no—
138C2×C4×C13—84no—
139C2×C4×C13—82no—
140C2×C4×C13—82no—
141C2×C4×C13—82no—
142C2×C4×C13—82no—
143C2×C4×C13C2×C4⋊C411yescharacteristic
144C2×C4×C13#12311yescharacteristic
145C8×C13—81no—
146C2×#127C22×C1311yescharacteristic
147#518C22×C1311yescharacteristic
148C2×C4×D4—22no—
149#418—21no—
150C2×#100C22×C1311yescharacteristic
151C2×#99C22×C1312yes—
152#390—22no—
153#386—21no—
154#386C22×C1312yes—
155#385—22no—
156C4×C4⋊C4—21no—
157#353C4×C1314yescomplemented
158#342—22no—
159#339—21no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—22no—
163C22×C13—22no—
164C22×C13—42no—
165C22×C13—42no—
166C22×C13—44no—
167C22×C13—42no—
168C22×C13—42no—
169C22×C13—42no—
170C22×C13—82no—
171C22×C13—82no—
172C22×C13—81no—
173C22×C13—81no—
174C22×C13#38511yescharacteristic
175C22×C13B(4,𝔽2)11yescharacteristic
176C22×C13#45811yescharacteristic
177C4×C13—24no—
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—44no—
181C4×C13—82no—
182C4×C13—84no—
183C4×C13—81no—
184C4×C13—81no—
185C22×D4—22no—
186C22×D4D4×C1311yescharacteristic
187C22×D4C23×C1311yescharacteristic
188C23×C4—21no—
189C23×C4D4×C1312yes—
190C2×M16—21no—
191#127—22no—
192#127C2×C4×C1312yes—
193#127Q8×C1312yes—
194C4×D4—41no—
195C4×D4—41no—
196C4×D4—48no—
197#117—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—42no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4D4×C1312yes—
207C2×C42—22no—
208C2×C42D4×C1311yescharacteristic
209#102—41no—
210#102—41no—
211#100—22no—
212#99—22no—
213#99C2×C4×C1314yescomplemented
214#95—22no—
215#95—42no—
216C2×C13—21no—
217C2×C13—21no—
218C2×C13—42no—
219C2×C13—42no—
220C2×C13—82no—
221C2×C13#186711yescharacteristic
222C2×C13#219611yescharacteristic
223C2×C13#219811yescharacteristic
224C24—21no—
225C24C2×D4×C1312yes—
226C2×D4—24no—
227C2×D4—24no—
228C2×D4—21no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4—44no—
232C2×D4—44no—
233C2×D4—41no—
234C2×D4—41no—
235C2×D4C13×C4⋊C412yescomplemented
236C2×D4C22×C4×C1311yescharacteristic
237C2×D4C2×Q8×C1311yescharacteristic
238C2×D4C13×#4112yes—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—44no—
245C22×C4—44no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—81no—
249C22×C4C2×D4×C1311yescharacteristic
250M16—41no—
251M16—41no—
252C2×C8—41no—
253C4⋊C4—24no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—42no—
257C4⋊C4—84no—
258C22⋊C4—24no—
259C22⋊C4—44no—
260C22⋊C4—44no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C22⋊C4—41no—
264C22⋊C4—42no—
265C22⋊C4—81no—
266C42—21no—
267C42—44no—
268C42—41no—
269C42C13×C4⋊C412yescomplemented
270C13#1296411yescharacteristic, direct product factor, Sylow
271C23—22no—
272C23—22no—
273C23—22no—
274C23—42no—
275C23—42no—
276C23—42no—
277C23—42no—
278C23—41no—
279C23—41no—
280C23C4×D4×C1312yes—
281C23C13×#12011yescharacteristic
282C23C13×C22⋊Q812yes—
283D4—41no—
284D4—41no—
285D4—42no—
286D4—42no—
287D4—48no—
288D4—48no—
289D4—81no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—24no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—44no—
299C2×C4—42no—
300C2×C4—44no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—82no—
306C2×C4—84no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4C2×C13×C4⋊C411yescharacteristic
312C2×C4C13×#12311yescharacteristic
313C8—81no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—22no—
318C22—42no—
319C22—42no—
320C22—44no—
321C22—42no—
322C22—42no—
323C22—42no—
324C22—82no—
325C22—82no—
326C22—81no—
327C22—81no—
328C22C13×#38511yescharacteristic
329C22C13×B(4,𝔽2)11yescharacteristic
330C22C13×#45811yescharacteristic
331C4—24no—
332C4—21no—
333C4—21no—
334C4—44no—
335C4—82no—
336C4—84no—
337C4—81no—
338C4—81no—
339C2—21no—
340C2—21no—
341C2—42no—
342C2—42no—
343C2—82no—
344C2C13×#186711yescharacteristic
345C2C13×#219611yescharacteristic
346C2C13×#219811yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutatorC2×D4C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC2×C13×#127C22
LCSG ▷ C2×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
4. C13×#1867C2semidirect
5. C13×#1390C2semidirect
17. C13×#353C4semidirect
48. C13×#99C2×C4semidirect
51. #12964C13direct (N × H)
63. C2×D4×C13C4⋊C4semidirect
97. C42×C13C4⋊C4semidirect
101. #1867C2×C13semidirect
102. #1390C2×C13semidirect
157. #353C4×C13semidirect
213. #99C2×C4×C13semidirect
235. C2×D4C13×C4⋊C4semidirect
269. C42C13×C4⋊C4semidirect
270. C13#12964direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#23662
C2×C13×#3532
C13×#18872
C13×#18672
C13×#13902
#1296413