Finite Group Databasebeta

← C13×#11874 #15698213

Subgroups — C13×#11874 #15698213

Order 3328.

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

normal subgroups only

This group has 472 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×#2486C211yesmaximal, characteristic
2C13×#1799C211yesmaximal, characteristic
3C13×#1460C211yesmaximal, characteristic
4C13×#1344C214yesmaximal, complemented
5C2×C13×#123—21no—
6C2×C4×D4×C13C2211yescharacteristic
7C22×C13×C4⋊C4C411yescharacteristic, complemented
8C13×#431—21no—
9C2×C13×#99—21no—
10C13×#398C412yescomplemented
11C13×#397C2212yes—
12C13×#389—21no—
13C13×#381—21no—
14C13×#380—21no—
15C13×#380—21no—
16C13×#380C411yescharacteristic, complemented
17C13×#342C2212yes—
18C13×#323—21no—
19C13×#323C2212yes—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13—21no—
22C23×C4×C13C2×C411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C13×#123—42no—
25C13×#123—42no—
26C4×D4×C13—41no—
27C4×D4×C13—41no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—41no—
32C2×C13×C4⋊C4—41no—
33C2×C13×C4⋊C4—41no—
34C2×C13×C4⋊C4C2×C412yes—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4D411yescharacteristic
40C2×C13×C22⋊C4C2311yescharacteristic
41C2×C42×C13D411yescharacteristic
42C13×C4⋊C8—41no—
43C13×#99—42no—
44C13×C22⋊C8—22no—
45C4×C8×C13—41no—
46C13×#95—22no—
47C13×#95—22no—
48C13×#95—41no—
49C13×#95C2×C412yes—
50#11874C1311yesmaximal, characteristic, direct product factor, Sylow
51C24×C13C22⋊C411yescharacteristic
52C24×C13C2×D411yescharacteristic
53C2×D4×C13—41no—
54C2×D4×C13—41no—
55C2×D4×C13D812yes—
56C2×D4×C13SD1612yes—
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—42no—
68C22×C4×C13—42no—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C2×C8×C13—42no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—44no—
81C13×C4⋊C4—82no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—42no—
89C42×C13—21no—
90C42×C13—21no—
91#2486C2×C1311yescharacteristic
92#1799C2×C1311yescharacteristic
93#1460C2×C1311yescharacteristic
94#1344C2×C1314yescomplemented
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×C13#10212yes—
104C23×C13C2×C22⋊C411yescharacteristic
105C23×C13C2×D811yescharacteristic
106C23×C13C2×SD1611yescharacteristic
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×C13#10212yes—
135C8×C13—82no—
136C2×#123—21no—
137C2×C4×D4C22×C1311yescharacteristic
138C22×C4⋊C4C4×C1311yescharacteristic, complemented
139#431—21no—
140C2×#99—21no—
141#398C4×C1312yescomplemented
142#397C22×C1312yes—
143#389—21no—
144#381—21no—
145#380—21no—
146#380—21no—
147#380C4×C1311yescharacteristic, complemented
148#342C22×C1312yes—
149#323—21no—
150#323C22×C1312yes—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—22no—
154C22×C13—21no—
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×C13C2×#9911yescharacteristic
166C22×C13C2×#10211yescharacteristic
167C22×C13#42111yescharacteristic
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×D4D4×C1311yescharacteristic
178C23×C4—21no—
179C23×C4C2×C4×C1311yescharacteristic
180C23×C4D4×C1311yescharacteristic
181#123—42no—
182#123—42no—
183C4×D4—41no—
184C4×D4—41no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4—41no—
191C2×C4⋊C4C2×C4×C1312yes—
192C2×C4⋊C4C2×C4×C1311yescharacteristic
193C2×C22⋊C4—21no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4D4×C1311yescharacteristic
197C2×C22⋊C4C23×C1311yescharacteristic
198C2×C42D4×C1311yescharacteristic
199C4⋊C8—41no—
200#99—42no—
201C22⋊C8—22no—
202C4×C8—41no—
203#95—22no—
204#95—22no—
205#95—41no—
206#95C2×C4×C1312yes—
207C2×C13—21no—
208C2×C13—21no—
209C2×C13—41no—
210C2×C13—42no—
211C2×C13—41no—
212C2×C13#151911yescharacteristic
213C2×C13C2×#35211yescharacteristic
214C2×C13#212911yescharacteristic
215C24C13×C22⋊C411yescharacteristic
216C24C2×D4×C1311yescharacteristic
217C2×D4—41no—
218C2×D4—41no—
219C2×D4C13×D812yes—
220C2×D4C13×SD1612yes—
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—42no—
232C22×C4—42no—
233C22×C4C13×C22⋊C411yescharacteristic
234C22×C4C13×C22⋊C411yescharacteristic
235C22×C4C13×C22⋊C411yescharacteristic
236C22×C4C22×C4×C1311yescharacteristic
237C22×C4C2×D4×C1311yescharacteristic
238C2×C8—42no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—44no—
245C4⋊C4—82no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C42—21no—
254C42—21no—
255C13#1187411yescharacteristic, direct product factor, Sylow
256C23—21no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23C13×#10212yes—
265C23C2×C13×C22⋊C411yescharacteristic
266C23C2×C13×D811yescharacteristic
267C23C2×C13×SD1611yescharacteristic
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×#10212yes—
296C8—82no—
297C22—21no—
298C22—21no—
299C22—22no—
300C22—21no—
301C22—21no—
302C22—42no—
303C22—41no—
304C22—41no—
305C22—42no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—81no—
311C22C2×C13×#9911yescharacteristic
312C22C2×C13×#10211yescharacteristic
313C22C13×#42111yescharacteristic
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×#151911yescharacteristic
329C2C2×C13×#35211yescharacteristic
330C2C13×#212911yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC22×D4×C13D4
LCSG ▷ C22×C4 ▷ C23 ▷ 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
4. C13×#1344C2semidirect
7. C22×C13×C4⋊C4C4semidirect
10. C13×#398C4semidirect
16. C13×#380C4semidirect
50. #11874C13direct (N × H)
94. #1344C2×C13semidirect
138. C22×C4⋊C4C4×C13semidirect
141. #398C4×C13semidirect
147. #380C4×C13semidirect
255. C13#11874direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#24862
C13×#17992
C13×#14602
C13×#13442
#1187413