Finite Group Databasebeta

← C13×#12244 #15698583

Subgroups — C13×#12244 #15698583

Order 3328.

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

normal subgroups only

This group has 398 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×#2722C211yesmaximal, characteristic
2C13×#2062C211yesmaximal, characteristic
3C13×#1608C211yesmaximal, characteristic
4C13×#1608C211yesmaximal, characteristic
5C13×#1344C211yesmaximal, characteristic
6C13×#1344C211yesmaximal, characteristic
7C13×#1326C211yesmaximal, characteristic
8C13×#543C2211yescharacteristic
9C2×C13×#126—21no—
10C13×#483—21no—
11C13×#483—21no—
12C13×#398—21no—
13C13×#398—21no—
14C13×#397C2211yescharacteristic
15C13×#397C2211yescharacteristic
16C13×#389—21no—
17C13×#387—21no—
18C13×#385—21no—
19C13×#385C2211yescharacteristic
20C13×#380—21no—
21C13×#342—21no—
22C13×#342C2211yescharacteristic
23C13×#328—21no—
24C13×#328—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C23×C4×C13D411yescharacteristic
28C13×#126—42no—
29C13×#126—42no—
30C13×C22⋊Q8—21no—
31C13×C22⋊Q8—21no—
32C13×C22⋊Q8—41no—
33C13×C22⋊Q8—41no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—41no—
41C2×C13×C4⋊C4D411yescharacteristic
42C2×C13×C4⋊C4D411yescharacteristic
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4D411yescharacteristic
48C2×C13×C22⋊C4C2311yescharacteristic
49C2×C42×C13—21no—
50C13×#106—41no—
51C13×#106—41no—
52C13×#103—41no—
53C13×#103—41no—
54C13×C22⋊C8—21no—
55C13×C22⋊C8—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95—41no—
62C13×#95D411yescharacteristic
63C13×#95D411yescharacteristic
64#12244C1311yesmaximal, characteristic, direct product factor, Sylow
65C24×C13C2×D411yescharacteristic
66C2×Q8×C13—21no—
67C2×Q8×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—42no—
77C22×C4×C13—41no—
78C22×C4×C13—41no—
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C2×C8×C13—41no—
82C2×C8×C13—41no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—42no—
89C13×C4⋊C4—42no—
90C13×C4⋊C4—42no—
91C13×C4⋊C4—42no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—81no—
95C13×C4⋊C4—82no—
96C13×C22⋊C4—21no—
97C13×C22⋊C4—22no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4SD1612yes—
107C42×C13—42no—
108#2722C2×C1311yescharacteristic
109#2062C2×C1311yescharacteristic
110#1608C2×C1311yescharacteristic
111#1608C2×C1311yescharacteristic
112#1344C2×C1311yescharacteristic
113#1344C2×C1311yescharacteristic
114#1326C2×C1311yescharacteristic
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13#12011yescharacteristic
120C23×C13C2×SD1611yescharacteristic
121C23×C13AGL(1,ℤ/8)11yescharacteristic
122Q8×C13—81no—
123Q8×C13—81no—
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
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—41no—
149C2×C4×C13—41no—
150C2×C4×C13—81no—
151C2×C4×C13—81no—
152C2×C4×C13—81no—
153C2×C4×C13—81no—
154C2×C4×C13—81no—
155C8×C13—81no—
156C8×C13—81no—
157#543C22×C1311yescharacteristic
158C2×#126—21no—
159#483—21no—
160#483—21no—
161#398—21no—
162#398—21no—
163#397C22×C1311yescharacteristic
164#397C22×C1311yescharacteristic
165#389—21no—
166#387—21no—
167#385—21no—
168#385C22×C1311yescharacteristic
169#380—21no—
170#342—21no—
171#342C22×C1311yescharacteristic
172#328—21no—
173#328—21no—
174#323C22×C1311yescharacteristic
175#323C22×C1311yescharacteristic
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—81no—
185C22×C13#45011yescharacteristic
186C22×C13#45611yescharacteristic
187C22×C13B(4,𝔽2)11yescharacteristic
188C4×C13—42no—
189C4×C13—41no—
190C4×C13—42no—
191C4×C13—41no—
192C4×C13—81no—
193C4×C13—81no—
194C4×C13—82no—
195C4×C13—81no—
196C4×C13—81no—
197C4×C13—81no—
198C4×C13—81no—
199C23×C4D4×C1311yescharacteristic
200#126—42no—
201#126—42no—
202C22⋊Q8—21no—
203C22⋊Q8—21no—
204C22⋊Q8—41no—
205C22⋊Q8—41no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—41no—
213C2×C4⋊C4D4×C1311yescharacteristic
214C2×C4⋊C4D4×C1311yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4D4×C1311yescharacteristic
220C2×C22⋊C4C23×C1311yescharacteristic
221C2×C42—21no—
222#106—41no—
223#106—41no—
224#103—41no—
225#103—41no—
226C22⋊C8—21no—
227C22⋊C8—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—41no—
234#95D4×C1311yescharacteristic
235#95D4×C1311yescharacteristic
236C2×C13—21no—
237C2×C13—21no—
238C2×C13—41no—
239C2×C13—41no—
240C2×C13#160411yescharacteristic
241C2×C13#219711yescharacteristic
242C2×C13#220111yescharacteristic
243C24C2×D4×C1311yescharacteristic
244C2×Q8—21no—
245C2×Q8—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—42no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4C2×D4×C1311yescharacteristic
258C22×C4C2×D4×C1311yescharacteristic
259C2×C8—41no—
260C2×C8—41no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—81no—
273C4⋊C4—82no—
274C22⋊C4—21no—
275C22⋊C4—22no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4C13×SD1612yes—
285C42—42no—
286C13#1224411yescharacteristic, direct product factor, Sylow
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23C13×#12011yescharacteristic
292C23C2×C13×SD1611yescharacteristic
293C23C13×AGL(1,ℤ/8)11yescharacteristic
294Q8—81no—
295Q8—81no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—42no—
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—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C8—81no—
328C8—81no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22C13×#45011yescharacteristic
339C22C13×#45611yescharacteristic
340C22C13×B(4,𝔽2)11yescharacteristic
341C4—42no—
342C4—41no—
343C4—42no—
344C4—41no—
345C4—81no—
346C4—81no—
347C4—82no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—81no—
352C2—21no—
353C2—21no—
354C2—41no—
355C2—41no—
356C2C13×#160411yescharacteristic
357C2C13×#219711yescharacteristic
358C2C13×#220111yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC24×C13C2×D4
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
64. #12244C13direct (N × H)
286. C13#12244direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27222
C13×#20622
C13×#16082
C13×#13442
C13×#13262
#1224413