Finite Group Databasebeta

← C13×#13292 #15699631

Subgroups — C13×#13292 #15699631

Order 3328.

484 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2487C211yesmaximal, characteristic
2C13×#1799C211yesmaximal, characteristic
3C4×C13×#100C211yesmaximal, characteristic
4C13×#1390C214yesmaximal
5C2×C4×D4×C13C2211yescharacteristic
6C22×C13×C4⋊C4C411yescharacteristic, complemented
7C2×C13×#100C2212yes—
8C2×C13×#99C2212yes—
9C4×C13×M16—21no—
10C13×#400—21no—
11C13×#399—21no—
12C13×#389—21no—
13C13×#386C2212yes—
14C13×#385C412yescomplemented
15C13×#380—21no—
16C13×#380—21no—
17C13×#380C411yescharacteristic, complemented
18C13×#343—21no—
19C13×#342—21no—
20C22×D4×C13C2311yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13C2×C412yes—
23C23×C4×C13D411yescharacteristic
24C2×C13×M16—22no—
25C4×D4×C13—41no—
26C4×D4×C13—41no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—41no—
32C2×C13×C4⋊C4—41no—
33C2×C13×C4⋊C4—41no—
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4C2×C412yes—
38C2×C13×C22⋊C4C2×C411yescharacteristic
39C2×C13×C22⋊C4D411yescharacteristic
40C2×C42×C13D411yescharacteristic
41C13×#100—22no—
42C13×#100Q814yes—
43C13×#99—24no—
44C13×#97—41no—
45C4×C8×C13—41no—
46C13×#95—22no—
47C13×#95—21no—
48C13×#95—22no—
49C13×#95—41no—
50#13292C1311yesmaximal, characteristic, direct product factor, Sylow
51C24×C13C22×C411yescharacteristic
52C24×C13C2×D411yescharacteristic
53C2×D4×C13—41no—
54C2×D4×C13—41no—
55C2×D4×C13C2×Q812yes—
56C2×D4×C13#4112yes—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13—42no—
67C22×C4×C13—82no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C13×M16—24no—
74C13×M16—42no—
75C2×C8×C13—42no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—82no—
82C13×C4⋊C4—82no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—82no—
89C42×C13—21no—
90C42×C13—21no—
91#2487C2×C1311yescharacteristic
92#1799C2×C1311yescharacteristic
93C4×#100C2×C1311yescharacteristic
94#1390C2×C1314yes—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13C2×C22⋊C411yescharacteristic
104C23×C13C4×Q812yes—
105C23×C13#12411yescharacteristic
106C23×C13C4⋊Q811yescharacteristic
107D4×C13—42no—
108D4×C13—42no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—22no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—81no—
128C2×C4×C13—84no—
129C2×C4×C13—82no—
130C2×C4×C13—82no—
131C2×C4×C13—82no—
132C2×C4×C13#9911yescharacteristic
133C2×C4×C13#9911yescharacteristic
134C2×C4×C13C22⋊Q812yes—
135C8×C13—44no—
136C2×C4×D4C22×C1311yescharacteristic
137C22×C4⋊C4C4×C1311yescharacteristic, complemented
138C2×#100C22×C1312yes—
139C2×#99C22×C1312yes—
140C4×M16—21no—
141#400—21no—
142#399—21no—
143#389—21no—
144#386C22×C1312yes—
145#385C4×C1312yescomplemented
146#380—21no—
147#380—21no—
148#380C4×C1311yescharacteristic, complemented
149#343—21no—
150#342—21no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—22no—
155C22×C13—21no—
156C22×C13—42no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—42no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—81no—
165C22×C13#39111yescharacteristic
166C22×C13C2×#9911yescharacteristic
167C22×C13#41011yescharacteristic
168C4×C13—21no—
169C4×C13—22no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—82no—
174C4×C13—82no—
175C4×C13—162no—
176C4×C13#35212yes—
177C22×D4C23×C1311yescharacteristic
178C23×C4C2×C4×C1311yescharacteristic
179C23×C4C2×C4×C1312yes—
180C23×C4D4×C1311yescharacteristic
181C2×M16—22no—
182C4×D4—41no—
183C4×D4—41no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4—41no—
191C2×C4⋊C4D4×C1311yescharacteristic
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4C2×C4×C1312yes—
195C2×C22⋊C4C2×C4×C1311yescharacteristic
196C2×C22⋊C4D4×C1311yescharacteristic
197C2×C42D4×C1311yescharacteristic
198#100—22no—
199#100Q8×C1314yes—
200#99—24no—
201#97—41no—
202C4×C8—41no—
203#95—22no—
204#95—21no—
205#95—22no—
206#95—41no—
207C2×C13—21no—
208C2×C13—21no—
209C2×C13—41no—
210C2×C13—42no—
211C2×C13—41no—
212C2×C13#199611yescharacteristic
213C2×C13C2×#35211yescharacteristic
214C2×C13#212211yescharacteristic
215C24C22×C4×C1311yescharacteristic
216C24C2×D4×C1311yescharacteristic
217C2×D4—41no—
218C2×D4—41no—
219C2×D4C2×Q8×C1312yes—
220C2×D4C13×#4112yes—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—82no—
232C22×C4C13×C22⋊C411yescharacteristic
233C22×C4C13×C22⋊C411yescharacteristic
234C22×C4C13×C22⋊C411yescharacteristic
235C22×C4C13×C22⋊C411yescharacteristic
236C22×C4C2×D4×C1311yescharacteristic
237M16—24no—
238M16—42no—
239C2×C8—42no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—82no—
246C4⋊C4—82no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—82no—
253C42—21no—
254C42—21no—
255C13#1329211yescharacteristic, direct product factor, Sylow
256C23—21no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23C2×C13×C22⋊C411yescharacteristic
265C23C4×Q8×C1312yes—
266C23C13×#12411yescharacteristic
267C23C13×C4⋊Q811yescharacteristic
268D4—42no—
269D4—42no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—81no—
289C2×C4—84no—
290C2×C4—82no—
291C2×C4—82no—
292C2×C4—82no—
293C2×C4C13×#9911yescharacteristic
294C2×C4C13×#9911yescharacteristic
295C2×C4C13×C22⋊Q812yes—
296C8—44no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—22no—
301C22—21no—
302C22—42no—
303C22—41no—
304C22—41no—
305C22—42no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—81no—
311C22C13×#39111yescharacteristic
312C22C2×C13×#9911yescharacteristic
313C22C13×#41011yescharacteristic
314C4—22no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—82no—
320C4—82no—
321C4—162no—
322C4C13×#35212yes—
323C2—21no—
324C2—21no—
325C2—41no—
326C2—42no—
327C2—41no—
328C2C13×#199611yescharacteristic
329C2C2×C13×#35211yescharacteristic
330C2C13×#212211yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC22×D4×C13C23
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
6. C22×C13×C4⋊C4C4semidirect
14. C13×#385C4semidirect
17. C13×#380C4semidirect
50. #13292C13direct (N × H)
137. C22×C4⋊C4C4×C13semidirect
145. #385C4×C13semidirect
148. #380C4×C13semidirect
255. C13#13292direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#24872
C13×#17992
C4×C13×#1002
C13×#13902
#1329213