Finite Group Databasebeta

← C13×#12152 #15698491

Subgroups — C13×#12152 #15698491

Order 3328.

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

normal subgroups only

This group has 588 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×#2537C211yesmaximal, characteristic, complemented
2C13×#2039C211yesmaximal, characteristic, complemented
3C13×#1598C212yesmaximal, complemented
4C13×#1345C212yesmaximal, complemented
5C13×#1325C211yesmaximal, characteristic, complemented
6C13×#537C2211yescharacteristic
7C2×C13×#121—22no—
8C2×C4×D4×C13—21no—
9C13×#447—22no—
10C2×C13×#104—21no—
11C13×#417—21no—
12C13×#394—21no—
13C13×#394C2212yes—
14C13×#384C2211yescharacteristic
15C13×#380—22no—
16C13×#343C2211yescharacteristic
17C13×#327—22no—
18C13×#324C2212yes—
19C2×C13×#41—21no—
20C22×D4×C13—21no—
21C22×D4×C13—21no—
22C22×D4×C13D412yes—
23C23×C4×C13—22no—
24C2×C13×D8—42no—
25C2×C13×M16—21no—
26C13×C22⋊Q8—41no—
27C13×#121—22no—
28C13×#121—41no—
29C13×#121—48no—
30C4×D4×C13—42no—
31C4×D4×C13—42no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C4⋊C4C2311yescharacteristic
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C42×C13D411yescharacteristic
40C13×#104—42no—
41C13×#103—41no—
42C13×#102—42no—
43C13×#102—41no—
44C13×C22⋊C8—22no—
45C13×#95—21no—
46C13×#95D412yes—
47#12152C1311yesmaximal, characteristic, direct product factor, Sylow
48C24×C13—22no—
49C13×#41—41no—
50C13×#41—41no—
51C13×#41—41no—
52C13×#41—41no—
53C2×Q8×C13—21no—
54C2×D4×C13—24no—
55C2×D4×C13—21no—
56C2×D4×C13—22no—
57C2×D4×C13—42no—
58C2×D4×C13—42no—
59C2×D4×C13—42no—
60C2×D4×C13—44no—
61C2×D4×C13—44no—
62C2×D4×C13—41no—
63C2×D4×C13—81no—
64C22×C4×C13—21no—
65C22×C4×C13—22no—
66C22×C4×C13—21no—
67C22×C4×C13—44no—
68C22×C4×C13—44no—
69C22×C4×C13—41no—
70C22×C4×C13—44no—
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D412yes—
73C13×D8—84no—
74C13×M16—41no—
75C13×M16—41no—
76C2×C8×C13—42no—
77C2×C8×C13—41no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—44no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—44no—
85C13×C22⋊C4—44no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C42×C13—21no—
89C42×C13D812yescomplemented
90#2537C2×C1311yescharacteristic, complemented
91#2039C2×C1311yescharacteristic, complemented
92#1598C2×C1312yescomplemented
93#1345C2×C1312yescomplemented
94#1325C2×C1311yescharacteristic, complemented
95C23×C13—24no—
96C23×C13—42no—
97C23×C13—42no—
98C23×C13—42no—
99C23×C13—42no—
100C23×C13—42no—
101C23×C13—42no—
102C23×C13—41no—
103C23×C13#12011yescharacteristic
104Q8×C13—41no—
105Q8×C13—41no—
106D4×C13—48no—
107D4×C13—41no—
108D4×C13—41no—
109D4×C13—44no—
110D4×C13—82no—
111D4×C13—82no—
112D4×C13—84no—
113D4×C13—81no—
114D4×C13—81no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—22no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—88no—
129C2×C4×C13—81no—
130C2×C4×C13—81no—
131C2×C4×C13C2×D811yescharacteristic
132C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
133C8×C13—81no—
134C8×C13—82no—
135#537C22×C1311yescharacteristic
136C2×#121—22no—
137C2×C4×D4—21no—
138#447—22no—
139C2×#104—21no—
140#417—21no—
141#394—21no—
142#394C22×C1312yes—
143#384C22×C1311yescharacteristic
144#380—22no—
145#343C22×C1311yescharacteristic
146#327—22no—
147#324C22×C1312yes—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13—44no—
151C22×C13—44no—
152C22×C13—44no—
153C22×C13—82no—
154C22×C13—82no—
155C22×C13—82no—
156C22×C13—82no—
157C22×C13—81no—
158C22×C13—81no—
159C22×C13—81no—
160C22×C13#44711yescharacteristic
161C22×C13#45411yescharacteristic
162C22×C13B(4,𝔽2)11yescharacteristic
163C4×C13—24no—
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—42no—
167C4×C13—82no—
168C4×C13—81no—
169C4×C13—81no—
170C2×#41—21no—
171C22×D4—21no—
172C22×D4—21no—
173C22×D4D4×C1312yes—
174C23×C4—22no—
175C2×D8—42no—
176C2×M16—21no—
177C22⋊Q8—41no—
178#121—22no—
179#121—41no—
180#121—48no—
181C4×D4—42no—
182C4×D4—42no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4D4×C1311yescharacteristic
186C2×C4⋊C4C23×C1311yescharacteristic
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—22no—
190C2×C42D4×C1311yescharacteristic
191#104—42no—
192#103—41no—
193#102—42no—
194#102—41no—
195C22⋊C8—22no—
196#95—21no—
197#95D4×C1312yes—
198C2×C13—21no—
199C2×C13—21no—
200C2×C13—84no—
201C2×C13—161no—
202C2×C13#159811yescharacteristic
203C2×C13#219611yescharacteristic
204C2×C13#220411yescharacteristic
205C24—22no—
206#41—41no—
207#41—41no—
208#41—41no—
209#41—41no—
210C2×Q8—21no—
211C2×D4—24no—
212C2×D4—21no—
213C2×D4—22no—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4—42no—
217C2×D4—44no—
218C2×D4—44no—
219C2×D4—41no—
220C2×D4—81no—
221C22×C4—21no—
222C22×C4—22no—
223C22×C4—21no—
224C22×C4—44no—
225C22×C4—44no—
226C22×C4—41no—
227C22×C4—44no—
228C22×C4C2×D4×C1311yescharacteristic
229C22×C4C2×D4×C1312yes—
230D8—84no—
231M16—41no—
232M16—41no—
233C2×C8—42no—
234C2×C8—41no—
235C4⋊C4—22no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C4⋊C4—44no—
240C22⋊C4—42no—
241C22⋊C4—44no—
242C22⋊C4—44no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C42—21no—
246C42C13×D812yescomplemented
247C13#1215211yescharacteristic, direct product factor, Sylow
248C23—24no—
249C23—42no—
250C23—42no—
251C23—42no—
252C23—42no—
253C23—42no—
254C23—42no—
255C23—41no—
256C23C13×#12011yescharacteristic
257Q8—41no—
258Q8—41no—
259D4—48no—
260D4—41no—
261D4—41no—
262D4—44no—
263D4—82no—
264D4—82no—
265D4—84no—
266D4—81no—
267D4—81no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—88no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4C2×C13×D811yescharacteristic
285C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
286C8—81no—
287C8—82no—
288C22—21no—
289C22—21no—
290C22—44no—
291C22—44no—
292C22—44no—
293C22—82no—
294C22—82no—
295C22—82no—
296C22—82no—
297C22—81no—
298C22—81no—
299C22—81no—
300C22C13×#44711yescharacteristic
301C22C13×#45411yescharacteristic
302C22C13×B(4,𝔽2)11yescharacteristic
303C4—24no—
304C4—21no—
305C4—21no—
306C4—42no—
307C4—82no—
308C4—81no—
309C4—81no—
310C2—21no—
311C2—21no—
312C2—84no—
313C2—161no—
314C2C13×#159811yescharacteristic
315C2C13×#219611yescharacteristic
316C2C13×#220411yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C13
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C2×C13×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2537C2semidirect
2. C13×#2039C2semidirect
3. C13×#1598C2semidirect
4. C13×#1345C2semidirect
5. C13×#1325C2semidirect
47. #12152C13direct (N × H)
89. C42×C13D8semidirect
90. #2537C2×C13semidirect
91. #2039C2×C13semidirect
92. #1598C2×C13semidirect
93. #1345C2×C13semidirect
94. #1325C2×C13semidirect
246. C42C13×D8semidirect
247. C13#12152direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25372
C13×#20392
C13×#15982
C13×#13452
C13×#13252
#1215213