Finite Group Databasebeta

← C13×#10385 #15696724

Subgroups — C13×#10385 #15696724

Order 3328.

396 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2667C211yesmaximal, characteristic
2C13×#1996C211yesmaximal, characteristic
3C13×#1511C211yesmaximal, characteristic
4C13×#1508C211yesmaximal, characteristic
5C13×#1305C211yesmaximal, characteristic
6C13×#1297C211yesmaximal, characteristic
7C13×#1284C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C13×#407C2211yescharacteristic
10C13×#407C2211yescharacteristic
11C13×#399—21no—
12C13×#398—21no—
13C13×#398—21no—
14C13×#396—21no—
15C13×#389—21no—
16C13×#387—21no—
17C13×#381C2211yescharacteristic
18C13×#380C2211yescharacteristic
19C4×C13×C22⋊C4C2211yescharacteristic
20C4×C13×C22⋊C4C2211yescharacteristic
21C13×#342—21no—
22C13×#342—21no—
23C13×#328—21no—
24C13×#328—21no—
25C13×#328—21no—
26C13×#328—21no—
27C22×Q8×C13Q811yescharacteristic
28C23×C4×C13C2311yescharacteristic
29C2×C13×M16—21no—
30C2×C13×M16—21no—
31C13×C22⋊Q8—21no—
32C13×C22⋊Q8—21no—
33C13×C22⋊Q8—21no—
34C13×C22⋊Q8—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—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4Q811yescharacteristic
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4D411yescharacteristic
49C2×C13×C22⋊C4D411yescharacteristic
50C2×C42×C13—21no—
51C2×C42×C13—21no—
52C13×C22⋊C8—21no—
53C13×C22⋊C8—21no—
54C13×C22⋊C8—21no—
55C13×C22⋊C8—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95D411yescharacteristic
62C13×#95D411yescharacteristic
63C13×#95D411yescharacteristic
64C13×#95D411yescharacteristic
65#10385C1311yesmaximal, characteristic, direct product factor, Sylow
66C24×C13C2×D411yescharacteristic
67C2×Q8×C13—21no—
68C2×Q8×C13—21no—
69C2×Q8×C13—81no—
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—21no—
77C22×C4×C13—21no—
78C22×C4×C13—41no—
79C22×C4×C13—81no—
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×Q811yescharacteristic
83C22×C4×C13#4111yescharacteristic
84C22×C4×C13#4111yescharacteristic
85C22×C4×C13#4111yescharacteristic
86C13×M16—81no—
87C13×M16—81no—
88C2×C8×C13—41no—
89C2×C8×C13—41no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—42no—
93C13×C4⋊C4—42no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—81no—
97C13×C4⋊C4—81no—
98C13×C4⋊C4—81no—
99C13×C4⋊C4—81no—
100C13×C4⋊C4—81no—
101C13×C22⋊C4—22no—
102C13×C22⋊C4—42no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—81no—
109C42×C13—81no—
110C42×C13—81no—
111#2667C2×C1311yescharacteristic
112#1996C2×C1311yescharacteristic
113#1511C2×C1311yescharacteristic
114#1508C2×C1311yescharacteristic
115#1305C2×C1311yescharacteristic
116#1297C2×C1311yescharacteristic
117#1284C2×C1311yescharacteristic
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13#12011yescharacteristic
123C23×C13C22⋊Q811yescharacteristic
124C23×C13#12411yescharacteristic
125Q8×C13—81no—
126Q8×C13—81no—
127C2×C4×C13—22no—
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—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—42no—
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—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—81no—
155C2×C4×C13—81no—
156C2×C4×C13—81no—
157C2×C4×C13—81no—
158C2×C4×C13C22⋊Q811yescharacteristic
159C2×C4×C13C22⋊Q811yescharacteristic
160C2×C4×C13#12411yescharacteristic
161C2×C4×C13#12411yescharacteristic
162C8×C13—81no—
163C8×C13—81no—
164C2×C22⋊Q8C22×C1311yescharacteristic
165#407C22×C1311yescharacteristic
166#407C22×C1311yescharacteristic
167#399—21no—
168#398—21no—
169#398—21no—
170#396—21no—
171#389—21no—
172#387—21no—
173#381C22×C1311yescharacteristic
174#380C22×C1311yescharacteristic
175C4×C22⋊C4C22×C1311yescharacteristic
176C4×C22⋊C4C22×C1311yescharacteristic
177#342—21no—
178#342—21no—
179#328—21no—
180#328—21no—
181#328—21no—
182#328—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—81no—
192C22×C13—81no—
193C22×C13#39311yescharacteristic
194C22×C13#45511yescharacteristic
195C22×C13#45611yescharacteristic
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—21no—
199C4×C13—21no—
200C4×C13—42no—
201C4×C13—81no—
202C4×C13—81no—
203C4×C13—81no—
204C4×C13—81no—
205C4×C13—81no—
206C4×C13—82no—
207C4×C13—81no—
208C4×C13—81no—
209C22×Q8Q8×C1311yescharacteristic
210C23×C4C23×C1311yescharacteristic
211C2×M16—21no—
212C2×M16—21no—
213C22⋊Q8—21no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4Q8×C1311yescharacteristic
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4D4×C1311yescharacteristic
231C2×C22⋊C4D4×C1311yescharacteristic
232C2×C42—21no—
233C2×C42—21no—
234C22⋊C8—21no—
235C22⋊C8—21no—
236C22⋊C8—21no—
237C22⋊C8—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95D4×C1311yescharacteristic
244#95D4×C1311yescharacteristic
245#95D4×C1311yescharacteristic
246#95D4×C1311yescharacteristic
247C2×C13—21no—
248C2×C13—21no—
249C2×C13—41no—
250C2×C13—41no—
251C2×C13#202811yescharacteristic
252C2×C13#203111yescharacteristic
253C2×C13#203211yescharacteristic
254C24C2×D4×C1311yescharacteristic
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—81no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—41no—
267C22×C4—81no—
268C22×C4C2×D4×C1311yescharacteristic
269C22×C4C2×D4×C1311yescharacteristic
270C22×C4C2×Q8×C1311yescharacteristic
271C22×C4C13×#4111yescharacteristic
272C22×C4C13×#4111yescharacteristic
273C22×C4C13×#4111yescharacteristic
274M16—81no—
275M16—81no—
276C2×C8—41no—
277C2×C8—41no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—81no—
285C4⋊C4—81no—
286C4⋊C4—81no—
287C4⋊C4—81no—
288C4⋊C4—81no—
289C22⋊C4—22no—
290C22⋊C4—42no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—81no—
297C42—81no—
298C42—81no—
299C13#1038511yescharacteristic, direct product factor, Sylow
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23C13×#12011yescharacteristic
305C23C13×C22⋊Q811yescharacteristic
306C23C13×#12411yescharacteristic
307Q8—81no—
308Q8—81no—
309C2×C4—22no—
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—42no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
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—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4C13×C22⋊Q811yescharacteristic
341C2×C4C13×C22⋊Q811yescharacteristic
342C2×C4C13×#12411yescharacteristic
343C2×C4C13×#12411yescharacteristic
344C8—81no—
345C8—81no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22C13×#39311yescharacteristic
357C22C13×#45511yescharacteristic
358C22C13×#45611yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—42no—
364C4—81no—
365C4—81no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4—82no—
370C4—81no—
371C4—81no—
372C2—21no—
373C2—21no—
374C2—41no—
375C2—41no—
376C2C13×#202811yescharacteristic
377C2C13×#203111yescharacteristic
378C2C13×#203211yescharacteristic
subgroupG/H
center, socleC22×C13#393
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC24×C13C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
65. #10385C13direct (N × H)
299. C13#10385direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26672
C13×#19962
C13×#15112
C13×#15082
C13×#13052
C13×#12972
C13×#12842
#1038513