Finite Group Databasebeta

← C13×#12123 #15698462

Subgroups — C13×#12123 #15698462

Order 3328.

570 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2840C211yesmaximal, characteristic, complemented
2C13×#2021C211yesmaximal, characteristic
3C13×#1601C212yesmaximal, complemented
4C13×#1351C212yesmaximal, complemented
5C13×#1316C211yesmaximal, characteristic, complemented
6C13×#534C2211yescharacteristic
7C2×C13×#120—21no—
8C13×#448—22no—
9C2×C13×#99—21no—
10C13×#393—22no—
11C13×#393—21no—
12C13×#393—22no—
13C13×#393C2212yes—
14C13×#379—21no—
15C13×#379C2211yescharacteristic
16C13×#342C2211yescharacteristic
17C13×#327—22no—
18C13×#323C2212yes—
19C25×C13D411yescharacteristic
20C22×Q8×C13—21no—
21C22×Q8×C13D412yescomplemented
22C22×D4×C13—21no—
23C22×D4×C13—41no—
24C2×C13×SD16—42no—
25C13×#123—41no—
26C13×#121—22no—
27C13×#120—42no—
28C13×#120—41no—
29C13×#120—42no—
30C2×C13×C22⋊C4—21no—
31C2×C13×C22⋊C4—21no—
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—41no—
37C2×C13×C22⋊C4D411yescharacteristic
38C2×C13×C22⋊C4C2311yescharacteristic
39C13×#103—42no—
40C13×#99—42no—
41C13×C22⋊C8—22no—
42C13×#95—21no—
43C13×#95—22no—
44C13×#95—22no—
45C13×#95D412yescomplemented
46#12123C1311yesmaximal, characteristic, direct product factor, Sylow
47C24×C13—21no—
48C24×C13—21no—
49C24×C13—21no—
50C24×C13—41no—
51C24×C13—41no—
52C24×C13—82no—
53C24×C13SD1612yescomplemented
54C24×C13C2×D411yescharacteristic
55C2×Q8×C13—42no—
56C2×Q8×C13—82no—
57C2×Q8×C13—82no—
58C2×Q8×C13—81no—
59C2×D4×C13—22no—
60C2×D4×C13—41no—
61C2×D4×C13—41no—
62C2×D4×C13—41no—
63C2×D4×C13—44no—
64C2×D4×C13—41no—
65C2×D4×C13—41no—
66C2×D4×C13—41no—
67C2×D4×C13—84no—
68C22×C4×C13—21no—
69C22×C4×C13—22no—
70C22×C4×C13—21no—
71C22×C4×C13—22no—
72C22×C4×C13—41no—
73C22×C4×C13C2×D412yes—
74C13×SD16—84no—
75C2×C8×C13—42no—
76C13×C4⋊C4—22no—
77C13×C22⋊C4—22no—
78C13×C22⋊C4—41no—
79C13×C22⋊C4—42no—
80C13×C22⋊C4—44no—
81C13×C22⋊C4—41no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—82no—
84C13×C22⋊C4—82no—
85C13×C22⋊C4—82no—
86C13×C22⋊C4—81no—
87C13×C22⋊C4—81no—
88#2840C2×C1311yescharacteristic, complemented
89#2021C2×C1311yescharacteristic
90#1601C2×C1312yescomplemented
91#1351C2×C1312yescomplemented
92#1316C2×C1311yescharacteristic, complemented
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—22no—
96C23×C13—42no—
97C23×C13—42no—
98C23×C13—42no—
99C23×C13—42no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13—44no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—81no—
107C23×C13—82no—
108C23×C13—82no—
109C23×C13—84no—
110C23×C13—82no—
111C23×C13—82no—
112C23×C13#12011yescharacteristic
113C23×C13C2×SD1611yescharacteristic
114C23×C13#13711yescharacteristic
115Q8×C13—44no—
116Q8×C13—82no—
117Q8×C13—84no—
118D4×C13—82no—
119D4×C13—81no—
120D4×C13—81no—
121D4×C13—88no—
122D4×C13—81no—
123D4×C13—81no—
124C2×C4×C13—22no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—41no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—42no—
136C2×C4×C13—41no—
137C2×C4×C13—42no—
138C2×C4×C13—82no—
139C8×C13—82no—
140#534C22×C1311yescharacteristic
141C2×#120—21no—
142#448—22no—
143C2×#99—21no—
144#393—22no—
145#393—21no—
146#393—22no—
147#393C22×C1312yes—
148#379—21no—
149#379C22×C1311yescharacteristic
150#342C22×C1311yescharacteristic
151#327—22no—
152#323C22×C1312yes—
153C22×C13—22no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—44no—
162C22×C13—42no—
163C22×C13—81no—
164C22×C13—82no—
165C22×C13—82no—
166C22×C13—84no—
167C22×C13—82no—
168C22×C13—82no—
169C22×C13—81no—
170C22×C13—82no—
171C22×C13—161no—
172C22×C13#44811yescharacteristic
173C22×C13#45311yescharacteristic
174C22×C13B(4,𝔽2)11yescharacteristic
175C4×C13—42no—
176C4×C13—81no—
177C4×C13—82no—
178C4×C13—82no—
179C4×C13—81no—
180C4×C13—82no—
181C25D4×C1311yescharacteristic
182C22×Q8—21no—
183C22×Q8D4×C1312yescomplemented
184C22×D4—21no—
185C22×D4—41no—
186C2×SD16—42no—
187#123—41no—
188#121—22no—
189#120—42no—
190#120—41no—
191#120—42no—
192C2×C22⋊C4—21no—
193C2×C22⋊C4—21no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—41no—
199C2×C22⋊C4D4×C1311yescharacteristic
200C2×C22⋊C4C23×C1311yescharacteristic
201#103—42no—
202#99—42no—
203C22⋊C8—22no—
204#95—21no—
205#95—22no—
206#95—22no—
207#95D4×C1312yescomplemented
208C2×C13—21no—
209C2×C13—21no—
210C2×C13—41no—
211C2×C13—41no—
212C2×C13—82no—
213C2×C13—161no—
214C2×C13#159611yescharacteristic
215C2×C13#219912yes—
216C24—21no—
217C24—21no—
218C24—21no—
219C24—41no—
220C24—41no—
221C24—82no—
222C24C13×SD1612yescomplemented
223C24C2×D4×C1311yescharacteristic
224C2×Q8—42no—
225C2×Q8—82no—
226C2×Q8—82no—
227C2×Q8—81no—
228C2×D4—22no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4—41no—
232C2×D4—44no—
233C2×D4—41no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4—84no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—41no—
242C22×C4C2×D4×C1312yes—
243SD16—84no—
244C2×C8—42no—
245C4⋊C4—22no—
246C22⋊C4—22no—
247C22⋊C4—41no—
248C22⋊C4—42no—
249C22⋊C4—44no—
250C22⋊C4—41no—
251C22⋊C4—41no—
252C22⋊C4—82no—
253C22⋊C4—82no—
254C22⋊C4—82no—
255C22⋊C4—81no—
256C22⋊C4—81no—
257C13#1212311yescharacteristic, direct product factor, Sylow
258C23—21no—
259C23—21no—
260C23—22no—
261C23—42no—
262C23—42no—
263C23—42no—
264C23—42no—
265C23—41no—
266C23—41no—
267C23—44no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23—81no—
272C23—82no—
273C23—82no—
274C23—82no—
275C23—84no—
276C23—82no—
277C23C13×#12011yescharacteristic
278C23C2×C13×SD1611yescharacteristic
279C23C13×#13711yescharacteristic
280Q8—44no—
281Q8—82no—
282Q8—84no—
283D4—82no—
284D4—81no—
285D4—81no—
286D4—88no—
287D4—81no—
288D4—81no—
289C2×C4—22no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—82no—
304C8—82no—
305C22—22no—
306C22—21no—
307C22—21no—
308C22—41no—
309C22—41no—
310C22—42no—
311C22—42no—
312C22—42no—
313C22—44no—
314C22—42no—
315C22—81no—
316C22—82no—
317C22—82no—
318C22—84no—
319C22—82no—
320C22—82no—
321C22—81no—
322C22—82no—
323C22—161no—
324C22C13×#44811yescharacteristic
325C22C13×#45311yescharacteristic
326C22C13×B(4,𝔽2)11yescharacteristic
327C4—42no—
328C4—81no—
329C4—82no—
330C4—82no—
331C4—81no—
332C4—82no—
333C2—21no—
334C2—21no—
335C2—41no—
336C2—41no—
337C2—82no—
338C2—161no—
339C2C13×#159611yescharacteristic
340C2C13×#219912yes—
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC13×#2021C2
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C2×C13×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2840C2semidirect
3. C13×#1601C2semidirect
4. C13×#1351C2semidirect
5. C13×#1316C2semidirect
21. C22×Q8×C13D4semidirect
45. C13×#95D4semidirect
46. #12123C13direct (N × H)
53. C24×C13SD16semidirect
88. #2840C2×C13semidirect
90. #1601C2×C13semidirect
91. #1351C2×C13semidirect
92. #1316C2×C13semidirect
183. C22×Q8D4×C13semidirect
207. #95D4×C13semidirect
222. C24C13×SD16semidirect
257. C13#12123direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28402
C13×#20212
C13×#16012
C13×#13512
C13×#13162
#1212313