Finite Group Databasebeta

← C13×#9937 #15696276

Subgroups — C13×#9937 #15696276

Order 3328.

526 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 102 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×#3195C211yesmaximal, characteristic
2C13×#3095C211yesmaximal, characteristic
3C13×#2625C211yesmaximal, characteristic
4C13×#1996C211yesmaximal, characteristic
5C13×#1826C211yesmaximal, characteristic
6C13×#1508C211yesmaximal, characteristic
7C13×#1305C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×C13×C22⋊Q8C2211yescharacteristic
10C2×C13×#117C2211yescharacteristic
11C13×#485—22no—
12C13×#484—21no—
13C13×#483—21no—
14C13×#483—21no—
15C13×#483—21no—
16C13×#470—22no—
17C13×#451—21no—
18C13×#451—21no—
19C13×#428—21no—
20C13×#419—21no—
21C13×#407C2211yescharacteristic
22C13×#407C2211yescharacteristic
23C13×#400—21no—
24C13×#398—21no—
25C13×#397—22no—
26C13×#391—21no—
27C13×#389—21no—
28C13×#380C2211yescharacteristic
29C4×C13×C22⋊C4C2211yescharacteristic
30C13×#342—22no—
31C13×#339—22no—
32C13×#328—22no—
33C22×Q8×C13D411yescharacteristic
34C22×Q8×C13D411yescharacteristic
35C23×C4×C13C2311yescharacteristic
36C2×C13×Q16—22no—
37C2×C13×M16—21no—
38C2×C13×M16D412yes—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8—21no—
43C13×C22⋊Q8—21no—
44C13×C22⋊Q8—21no—
45C13×C22⋊Q8—21no—
46C13×C22⋊Q8—21no—
47C13×#117—21no—
48C13×#117—21no—
49C13×#117—21no—
50C13×#117—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4D411yescharacteristic
56C2×C13×C4⋊C4D411yescharacteristic
57C2×C13×C4⋊C4D411yescharacteristic
58C2×C13×C4⋊C4D411yescharacteristic
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4D412yes—
64C2×C42×C13—21no—
65C2×C42×C13—21no—
66C13×#107—22no—
67C13×#106—22no—
68C13×#106—22no—
69C13×#103—22no—
70C13×#103—22no—
71C13×#103—22no—
72C13×#103—22no—
73C13×C22⋊C8—21no—
74C13×C22⋊C8—21no—
75C13×C22⋊C8—21no—
76C13×C22⋊C8D412yes—
77C13×#95—22no—
78C13×#95—22no—
79C13×#95—22no—
80C13×#95—21no—
81C13×#95—21no—
82#9937C1311yesmaximal, characteristic, direct product factor, Sylow
83C24×C13C2×D411yescharacteristic
84C2×Q8×C13—21no—
85C2×Q8×C13—21no—
86C2×Q8×C13—21no—
87C2×Q8×C13—21no—
88C2×Q8×C13—42no—
89C2×Q8×C13—42no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—22no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—42no—
98C22×C4×C13—41no—
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13#4111yescharacteristic
105C13×Q16—82no—
106C13×M16—42no—
107C13×M16—42no—
108C2×C8×C13—22no—
109C2×C8×C13—22no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—42no—
119C13×C4⋊C4—41no—
120C13×C4⋊C4—41no—
121C13×C4⋊C4—41no—
122C13×C4⋊C4—41no—
123C13×C4⋊C4—82no—
124C13×C22⋊C4—22no—
125C13×C22⋊C4—41no—
126C13×C22⋊C4—41no—
127C13×C22⋊C4—41no—
128C13×C22⋊C4—41no—
129C13×C22⋊C4—41no—
130C13×C22⋊C4—41no—
131C13×C22⋊C4—41no—
132C13×C22⋊C4—42no—
133C42×C13—42no—
134C42×C13—41no—
135C42×C13—41no—
136#3195C2×C1311yescharacteristic
137#3095C2×C1311yescharacteristic
138#2625C2×C1311yescharacteristic
139#1996C2×C1311yescharacteristic
140#1826C2×C1311yescharacteristic
141#1508C2×C1311yescharacteristic
142#1305C2×C1311yescharacteristic
143C23×C13—21no—
144C23×C13—21no—
145C23×C13—41no—
146C23×C13—41no—
147C23×C13#12011yescharacteristic
148C23×C13#12111yescharacteristic
149C23×C13#12711yescharacteristic
150Q8×C13—42no—
151Q8×C13—42no—
152Q8×C13—42no—
153Q8×C13—81no—
154C2×C4×C13—22no—
155C2×C4×C13—22no—
156C2×C4×C13—22no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—42no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13—42no—
164C2×C4×C13—42no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—42no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—81no—
177C2×C4×C13—81no—
178C2×C4×C13—81no—
179C2×C4×C13—81no—
180C2×C4×C13#12011yescharacteristic
181C2×C4×C13#12011yescharacteristic
182C2×C4×C13#12111yescharacteristic
183C2×C4×C13#12111yescharacteristic
184C8×C13—42no—
185C8×C13—42no—
186C2×C22⋊Q8C22×C1311yescharacteristic
187C2×C22⋊Q8C22×C1311yescharacteristic
188C2×#117C22×C1311yescharacteristic
189#485—22no—
190#484—21no—
191#483—21no—
192#483—21no—
193#483—21no—
194#470—22no—
195#451—21no—
196#451—21no—
197#428—21no—
198#419—21no—
199#407C22×C1311yescharacteristic
200#407C22×C1311yescharacteristic
201#400—21no—
202#398—21no—
203#397—22no—
204#391—21no—
205#389—21no—
206#380C22×C1311yescharacteristic
207C4×C22⋊C4C22×C1311yescharacteristic
208#342—22no—
209#339—22no—
210#328—22no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—81no—
220C22×C13—81no—
221C22×C13#39211yescharacteristic
222C22×C13#45511yescharacteristic
223C22×C13#45611yescharacteristic
224C4×C13—21no—
225C4×C13—21no—
226C4×C13—21no—
227C4×C13—82no—
228C4×C13—82no—
229C4×C13—81no—
230C4×C13—81no—
231C4×C13—81no—
232C4×C13—81no—
233C4×C13—81no—
234C4×C13—81no—
235C4×C13#45812yes—
236C22×Q8D4×C1311yescharacteristic
237C22×Q8D4×C1311yescharacteristic
238C23×C4C23×C1311yescharacteristic
239C2×Q16—22no—
240C2×M16—21no—
241C2×M16D4×C1312yes—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250#117—21no—
251#117—21no—
252#117—21no—
253#117—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4D4×C1311yescharacteristic
259C2×C4⋊C4D4×C1311yescharacteristic
260C2×C4⋊C4D4×C1311yescharacteristic
261C2×C4⋊C4D4×C1311yescharacteristic
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4D4×C1312yes—
267C2×C42—21no—
268C2×C42—21no—
269#107—22no—
270#106—22no—
271#106—22no—
272#103—22no—
273#103—22no—
274#103—22no—
275#103—22no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C22⋊C8D4×C1312yes—
280#95—22no—
281#95—22no—
282#95—22no—
283#95—21no—
284#95—21no—
285C2×C13—21no—
286C2×C13—21no—
287C2×C13—41no—
288C2×C13—41no—
289C2×C13#200711yescharacteristic
290C2×C13#200911yescharacteristic
291C2×C13#202211yescharacteristic
292C24C2×D4×C1311yescharacteristic
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—42no—
298C2×Q8—42no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—42no—
307C22×C4—41no—
308C22×C4C2×D4×C1311yescharacteristic
309C22×C4C2×D4×C1311yescharacteristic
310C22×C4C2×D4×C1311yescharacteristic
311C22×C4C2×D4×C1311yescharacteristic
312C22×C4C2×D4×C1311yescharacteristic
313C22×C4C13×#4111yescharacteristic
314Q16—82no—
315M16—42no—
316M16—42no—
317C2×C8—22no—
318C2×C8—22no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—42no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—82no—
333C22⋊C4—22no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—42no—
342C42—42no—
343C42—41no—
344C42—41no—
345C13#993711yescharacteristic, direct product factor, Sylow
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23C13×#12011yescharacteristic
351C23C13×#12111yescharacteristic
352C23C13×#12711yescharacteristic
353Q8—42no—
354Q8—42no—
355Q8—42no—
356Q8—81no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4C13×#12011yescharacteristic
384C2×C4C13×#12011yescharacteristic
385C2×C4C13×#12111yescharacteristic
386C2×C4C13×#12111yescharacteristic
387C8—42no—
388C8—42no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—81no—
398C22—81no—
399C22C13×#39211yescharacteristic
400C22C13×#45511yescharacteristic
401C22C13×#45611yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—82no—
406C4—82no—
407C4—81no—
408C4—81no—
409C4—81no—
410C4—81no—
411C4—81no—
412C4—81no—
413C4C13×#45812yes—
414C2—21no—
415C2—21no—
416C2—41no—
417C2—41no—
418C2C13×#200711yescharacteristic
419C2C13×#200911yescharacteristic
420C2C13×#202211yescharacteristic
subgroupG/H
center, socleC22×C13#392
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
82. #9937C13direct (N × H)
345. C13#9937direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31952
C13×#30952
C13×#26252
C13×#19962
C13×#18262
C13×#15082
C13×#13052
#993713