Finite Group Databasebeta

← C13×#12252 #15698591

Subgroups — C13×#12252 #15698591

Order 3328.

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

normal subgroups only

This group has 452 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×#2677C211yesmaximal, characteristic
2C13×#2062C211yesmaximal, characteristic
3C13×#1614C211yesmaximal, characteristic
4C13×#1602C211yesmaximal, characteristic
5C13×#1352C211yesmaximal, characteristic
6C13×#1351C211yesmaximal, characteristic
7C13×#1326C211yesmaximal, characteristic
8C13×#543C2211yescharacteristic
9C2×C13×C4⋊Q8—21no—
10C2×C13×C22⋊Q8—21no—
11C13×#484—21no—
12C13×#451—21no—
13C13×#399C2211yescharacteristic
14C13×#398—21no—
15C13×#395—21no—
16C13×#393C2211yescharacteristic
17C13×#388—21no—
18C13×#387—21no—
19C13×#385—21no—
20C13×#385C2211yescharacteristic
21C13×#342—21no—
22C13×#342C2211yescharacteristic
23C13×#328—21no—
24C13×#328—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C22×Q8×C13—21no—
28C22×Q8×C13D411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C2×C13×Q16—41no—
31C13×C4⋊Q8—44no—
32C13×C22⋊Q8—21no—
33C13×C22⋊Q8—21no—
34C13×C22⋊Q8—41no—
35C13×C22⋊Q8—41no—
36C13×C22⋊Q8—44no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—41no—
44C2×C13×C4⋊C4D411yescharacteristic
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4D411yescharacteristic
50C2×C13×C22⋊C4C2311yescharacteristic
51C2×C42×C13—21no—
52C13×#107—41no—
53C13×#103—41no—
54C13×#103—41no—
55C13×C22⋊C8—21no—
56C13×C22⋊C8—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95—41no—
62C13×#95D411yescharacteristic
63C13×#95D411yescharacteristic
64#12252C1311yesmaximal, characteristic, direct product factor, Sylow
65C24×C13C2×D411yescharacteristic
66C2×Q8×C13—21no—
67C2×Q8×C13—21no—
68C2×Q8×C13—42no—
69C2×Q8×C13—42no—
70C2×Q8×C13—42no—
71C2×Q8×C13—41no—
72C2×Q8×C13—81no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—42no—
82C22×C4×C13—41no—
83C22×C4×C13—41no—
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C13×Q16—82no—
87C2×C8×C13—41no—
88C2×C8×C13—41no—
89C13×C4⋊C4—24no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—42no—
94C13×C4⋊C4—42no—
95C13×C4⋊C4—42no—
96C13×C4⋊C4—42no—
97C13×C4⋊C4—42no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—82no—
101C13×C22⋊C4—21no—
102C13×C22⋊C4—22no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—42no—
105C13×C22⋊C4—42no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4Q1612yescomplemented
110C42×C13—42no—
111#2677C2×C1311yescharacteristic
112#2062C2×C1311yescharacteristic
113#1614C2×C1311yescharacteristic
114#1602C2×C1311yescharacteristic
115#1352C2×C1311yescharacteristic
116#1351C2×C1311yescharacteristic
117#1326C2×C1311yescharacteristic
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13#12011yescharacteristic
123C23×C13C2×Q1611yescharacteristic
124C23×C13#13711yescharacteristic
125Q8×C13—42no—
126Q8×C13—81no—
127Q8×C13—84no—
128Q8×C13—81no—
129Q8×C13—81no—
130C2×C4×C13—22no—
131C2×C4×C13—22no—
132C2×C4×C13—22no—
133C2×C4×C13—22no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
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—42no—
147C2×C4×C13—42no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—81no—
157C2×C4×C13—81no—
158C2×C4×C13—81no—
159C2×C4×C13—81no—
160C2×C4×C13—81no—
161C8×C13—81no—
162C8×C13—81no—
163#543C22×C1311yescharacteristic
164C2×C4⋊Q8—21no—
165C2×C22⋊Q8—21no—
166#484—21no—
167#451—21no—
168#399C22×C1311yescharacteristic
169#398—21no—
170#395—21no—
171#393C22×C1311yescharacteristic
172#388—21no—
173#387—21no—
174#385—21no—
175#385C22×C1311yescharacteristic
176#342—21no—
177#342C22×C1311yescharacteristic
178#328—21no—
179#328—21no—
180#323C22×C1311yescharacteristic
181#323C22×C1311yescharacteristic
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—81no—
191C22×C13#45111yescharacteristic
192C22×C13#45611yescharacteristic
193C22×C13B(4,𝔽2)11yescharacteristic
194C4×C13—42no—
195C4×C13—42no—
196C4×C13—41no—
197C4×C13—42no—
198C4×C13—42no—
199C4×C13—41no—
200C4×C13—81no—
201C4×C13—82no—
202C4×C13—81no—
203C4×C13—81no—
204C4×C13—81no—
205C22×Q8—21no—
206C22×Q8D4×C1311yescharacteristic
207C23×C4D4×C1311yescharacteristic
208C2×Q16—41no—
209C4⋊Q8—44no—
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C22⋊Q8—41no—
213C22⋊Q8—41no—
214C22⋊Q8—44no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—41no—
222C2×C4⋊C4D4×C1311yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4D4×C1311yescharacteristic
228C2×C22⋊C4C23×C1311yescharacteristic
229C2×C42—21no—
230#107—41no—
231#103—41no—
232#103—41no—
233C22⋊C8—21no—
234C22⋊C8—21no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—41no—
240#95D4×C1311yescharacteristic
241#95D4×C1311yescharacteristic
242C2×C13—21no—
243C2×C13—21no—
244C2×C13—41no—
245C2×C13—41no—
246C2×C13#160511yescharacteristic
247C2×C13#219611yescharacteristic
248C2×C13#220111yescharacteristic
249C24C2×D4×C1311yescharacteristic
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—42no—
253C2×Q8—42no—
254C2×Q8—42no—
255C2×Q8—41no—
256C2×Q8—81no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—42no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4C2×D4×C1311yescharacteristic
269C22×C4C2×D4×C1311yescharacteristic
270Q16—82no—
271C2×C8—41no—
272C2×C8—41no—
273C4⋊C4—24no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—41no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—82no—
285C22⋊C4—21no—
286C22⋊C4—22no—
287C22⋊C4—41no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4C13×Q1612yescomplemented
294C42—42no—
295C13#1225211yescharacteristic, direct product factor, Sylow
296C23—21no—
297C23—21no—
298C23—41no—
299C23—41no—
300C23C13×#12011yescharacteristic
301C23C2×C13×Q1611yescharacteristic
302C23C13×#13711yescharacteristic
303Q8—42no—
304Q8—81no—
305Q8—84no—
306Q8—81no—
307Q8—81no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
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—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C8—81no—
340C8—81no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22C13×#45111yescharacteristic
351C22C13×#45611yescharacteristic
352C22C13×B(4,𝔽2)11yescharacteristic
353C4—42no—
354C4—42no—
355C4—41no—
356C4—42no—
357C4—42no—
358C4—41no—
359C4—81no—
360C4—82no—
361C4—81no—
362C4—81no—
363C4—81no—
364C2—21no—
365C2—21no—
366C2—41no—
367C2—41no—
368C2C13×#160511yescharacteristic
369C2C13×#219611yescharacteristic
370C2C13×#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. #12252C13direct (N × H)
109. C13×C22⋊C4Q16semidirect
293. C22⋊C4C13×Q16semidirect
295. C13#12252direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26772
C13×#20622
C13×#16142
C13×#16022
C13×#13522
C13×#13512
C13×#13262
#1225213