Finite Group Databasebeta

← C13×#12235 #15698574

Subgroups — C13×#12235 #15698574

Order 3328.

382 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2782C211yesmaximal, characteristic
2C13×#2061C211yesmaximal, characteristic, complemented
3C13×#1617C211yesmaximal, characteristic, complemented
4C13×#1599C211yesmaximal, characteristic
5C13×#1353C211yesmaximal, characteristic, complemented
6C13×#1345C211yesmaximal, characteristic
7C13×#1324C211yesmaximal, characteristic, complemented
8C13×#544C2211yescharacteristic
9C13×#484—21no—
10C13×#450—21no—
11C13×#428—21no—
12C13×#400—21no—
13C13×#400C2211yescharacteristic
14C13×#397—21no—
15C13×#394C2211yescharacteristic
16C13×#388—21no—
17C13×#386—21no—
18C13×#385—21no—
19C13×#385—21no—
20C13×#382C2211yescharacteristic
21C13×#343C2211yescharacteristic
22C13×#339—21no—
23C13×#328—21no—
24C13×#328—21no—
25C13×#324C2211yescharacteristic
26C13×#324C2211yescharacteristic
27C22×D4×C13D411yescharacteristic
28C23×C4×C13—21no—
29C2×C13×SD16—41no—
30C2×C13×M16—21no—
31C13×C4⋊Q8—41no—
32C13×#125—41no—
33C13×C22⋊Q8—21no—
34C13×C22⋊Q8—21no—
35C13×#117—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C4⋊C4C2311yescharacteristic
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C42×C13D411yescharacteristic
47C13×#107—41no—
48C13×#107—41no—
49C13×#106—41no—
50C13×#103—41no—
51C13×#102—41no—
52C13×C22⋊C8—21no—
53C13×C22⋊C8—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95D411yescharacteristic
61C13×#95D411yescharacteristic
62#12235C1311yesmaximal, characteristic, direct product factor, Sylow
63C24×C13—21no—
64C2×Q8×C13—21no—
65C2×Q8×C13—21no—
66C2×D4×C13—41no—
67C2×D4×C13—42no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—81no—
74C22×C4×C13—81no—
75C22×C4×C13—81no—
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C13×SD16—82no—
80C13×M16—22no—
81C13×M16—41no—
82C2×C8×C13—41no—
83C2×C8×C13—41no—
84C2×C8×C13—41no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—81no—
95C13×C4⋊C4—81no—
96C13×C22⋊C4—42no—
97C13×C22⋊C4—42no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—81no—
102C13×C22⋊C4—81no—
103C42×C13—21no—
104C42×C13—21no—
105C42×C13—41no—
106#2782C2×C1311yescharacteristic
107#2061C2×C1311yescharacteristic, complemented
108#1617C2×C1311yescharacteristic, complemented
109#1599C2×C1311yescharacteristic
110#1353C2×C1311yescharacteristic, complemented
111#1345C2×C1311yescharacteristic
112#1324C2×C1311yescharacteristic, complemented
113C23×C13—22no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13#12011yescharacteristic
121Q8×C13—81no—
122Q8×C13—81no—
123D4×C13—42no—
124D4×C13—81no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—84no—
149C2×C4×C13#13511yescharacteristic
150C2×C4×C13#13711yescharacteristic
151C8×C13—42no—
152C8×C13—81no—
153C8×C13—81no—
154#544C22×C1311yescharacteristic
155#484—21no—
156#450—21no—
157#428—21no—
158#400—21no—
159#400C22×C1311yescharacteristic
160#397—21no—
161#394C22×C1311yescharacteristic
162#388—21no—
163#386—21no—
164#385—21no—
165#385—21no—
166#382C22×C1311yescharacteristic
167#343C22×C1311yescharacteristic
168#339—21no—
169#328—21no—
170#328—21no—
171#324C22×C1311yescharacteristic
172#324C22×C1311yescharacteristic
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—42no—
176C22×C13—42no—
177C22×C13—42no—
178C22×C13—81no—
179C22×C13—81no—
180C22×C13—81no—
181C22×C13—81no—
182C22×C13#45211yescharacteristic
183C22×C13#45611yescharacteristic
184C22×C13B(4,𝔽2)11yescharacteristic
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13—81no—
190C4×C13—81no—
191C4×C13—81no—
192C4×C13—81no—
193C4×C13—81no—
194C4×C13—81no—
195C4×C13—81no—
196C22×D4D4×C1311yescharacteristic
197C23×C4—21no—
198C2×SD16—41no—
199C2×M16—21no—
200C4⋊Q8—41no—
201#125—41no—
202C22⋊Q8—21no—
203C22⋊Q8—21no—
204#117—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4D4×C1311yescharacteristic
208C2×C4⋊C4D4×C1311yescharacteristic
209C2×C4⋊C4C23×C1311yescharacteristic
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C42D4×C1311yescharacteristic
216#107—41no—
217#107—41no—
218#106—41no—
219#103—41no—
220#102—41no—
221C22⋊C8—21no—
222C22⋊C8—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95D4×C1311yescharacteristic
230#95D4×C1311yescharacteristic
231C2×C13—21no—
232C2×C13—21no—
233C2×C13—82no—
234C2×C13#160311yescharacteristic
235C2×C13#219711yescharacteristic
236C2×C13#220211yescharacteristic
237C24—21no—
238C2×Q8—21no—
239C2×Q8—21no—
240C2×D4—41no—
241C2×D4—42no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—81no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4C2×D4×C1311yescharacteristic
251C22×C4C2×D4×C1311yescharacteristic
252C22×C4C2×D4×C1311yescharacteristic
253SD16—82no—
254M16—22no—
255M16—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—81no—
269C4⋊C4—81no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—81no—
276C22⋊C4—81no—
277C42—21no—
278C42—21no—
279C42—41no—
280C13#1223511yescharacteristic, direct product factor, Sylow
281C23—22no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23C13×#12011yescharacteristic
289Q8—81no—
290Q8—81no—
291D4—42no—
292D4—81no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—84no—
317C2×C4C13×#13511yescharacteristic
318C2×C4C13×#13711yescharacteristic
319C8—42no—
320C8—81no—
321C8—81no—
322C22—21no—
323C22—21no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22C13×#45211yescharacteristic
332C22C13×#45611yescharacteristic
333C22C13×B(4,𝔽2)11yescharacteristic
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—81no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—81no—
345C2—21no—
346C2—21no—
347C2—82no—
348C2C13×#160311yescharacteristic
349C2C13×#219711yescharacteristic
350C2C13×#220211yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC22×D4×C13D4
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
2. C13×#2061C2semidirect
3. C13×#1617C2semidirect
5. C13×#1353C2semidirect
7. C13×#1324C2semidirect
62. #12235C13direct (N × H)
107. #2061C2×C13semidirect
108. #1617C2×C13semidirect
110. #1353C2×C13semidirect
112. #1324C2×C13semidirect
280. C13#12235direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27822
C13×#20612
C13×#16172
C13×#15992
C13×#13532
C13×#13452
C13×#13242
#1223513