Finite Group Databasebeta

← C13×#13425 #15699764

Subgroups — C13×#13425 #15699764

Order 3328.

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

normal subgroups only

This group has 508 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×#2717C211yesmaximal, characteristic
2C2×C13×#354C211yesmaximal, characteristic
3C2×C13×#352C211yesmaximal, characteristic
4C13×#1890C211yesmaximal, characteristic
5C13×#1885C211yesmaximal, characteristic
6C13×#1867C211yesmaximal, characteristic
7C13×#1390C211yesmaximal, characteristic
8C2×C13×#124C2211yescharacteristic
9C2×C13×#123C2211yescharacteristic
10C13×#518C2211yescharacteristic
11C13×#419—21no—
12C2×C13×#100C2211yescharacteristic
13C2×C13×#99C2211yescharacteristic
14C2×C13×#99C2211yescharacteristic
15C13×#397—21no—
16C13×#397—21no—
17C13×#395—21no—
18C13×#387—21no—
19C13×#386C2211yescharacteristic
20C13×#385—21no—
21C13×#385—21no—
22C13×#381—21no—
23C13×#380—21no—
24C13×#354—22no—
25C13×#352—22no—
26C13×#342—21no—
27C13×#342—21no—
28C13×#339—21no—
29C22×Q8×C13D411yescharacteristic
30C22×D4×C13C2311yescharacteristic
31C23×C4×C13D411yescharacteristic
32C23×C4×C13D411yescharacteristic
33C2×C13×M16—21no—
34C13×#124—21no—
35C13×#124—21no—
36C13×#124—21no—
37C13×#124—21no—
38C13×#123—21no—
39C13×#123—21no—
40C13×#123—21no—
41C13×#123—21no—
42C4×D4×C13—41no—
43C4×D4×C13—41no—
44C13×#117—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—41no—
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4—21no—
53C2×C13×C22⋊C4—21no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—21no—
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4D411yescharacteristic
59C2×C13×C22⋊C4D411yescharacteristic
60C2×C42×C13D411yescharacteristic
61C13×#103—41no—
62C13×#103—41no—
63C13×#100—21no—
64C13×#100—21no—
65C13×#99—21no—
66C13×#99—21no—
67C13×#99—21no—
68C13×#99D412yes—
69C13×#95—21no—
70C13×#95—21no—
71C13×#95—21no—
72C13×#95—21no—
73C13×#95—21no—
74C13×#95—21no—
75C13×#95—41no—
76C13×#95—41no—
77C13×#95—41no—
78#13425C1311yesmaximal, characteristic, direct product factor, Sylow
79C24×C13C2×D411yescharacteristic
80C24×C13C2×D411yescharacteristic
81C2×Q8×C13—21no—
82C2×Q8×C13—21no—
83C2×Q8×C13—41no—
84C2×Q8×C13—41no—
85C2×D4×C13—41no—
86C2×D4×C13—41no—
87C2×D4×C13C2×D411yescharacteristic
88C2×D4×C13#4111yescharacteristic
89C2×D4×C13#4111yescharacteristic
90C2×D4×C13#4111yescharacteristic
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—42no—
104C22×C4×C13—41no—
105C22×C4×C13—41no—
106C22×C4×C13—41no—
107C22×C4×C13—41no—
108C22×C4×C13—41no—
109C22×C4×C13C2×D411yescharacteristic
110C13×M16—41no—
111C13×M16—41no—
112C2×C8×C13—41no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—42no—
116C13×C4⋊C4—41no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4—81no—
119C13×C4⋊C4—81no—
120C13×C4⋊C4—82no—
121C13×C22⋊C4—22no—
122C13×C22⋊C4—21no—
123C13×C22⋊C4—21no—
124C13×C22⋊C4—42no—
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—41no—
133C13×C22⋊C4—41no—
134C13×C22⋊C4—41no—
135C13×C22⋊C4—41no—
136C13×C22⋊C4—41no—
137C13×C22⋊C4—41no—
138C42×C13—21no—
139C42×C13—21no—
140C42×C13—41no—
141#2717C2×C1311yescharacteristic
142C2×#354C2×C1311yescharacteristic
143C2×#352C2×C1311yescharacteristic
144#1890C2×C1311yescharacteristic
145#1885C2×C1311yescharacteristic
146#1867C2×C1311yescharacteristic
147#1390C2×C1311yescharacteristic
148C23×C13—21no—
149C23×C13—21no—
150C23×C13—21no—
151C23×C13—21no—
152C23×C13—41no—
153C23×C13—41no—
154C23×C13—41no—
155C23×C13—41no—
156C23×C13#12011yescharacteristic
157C23×C13#12111yescharacteristic
158C23×C13#12111yescharacteristic
159C23×C13#12311yescharacteristic
160C23×C13#12411yescharacteristic
161Q8×C13—42no—
162Q8×C13—81no—
163D4×C13—41no—
164D4×C13—41no—
165D4×C13—41no—
166D4×C13—41no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—22no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—42no—
173C2×C4×C13—42no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—42no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—41no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—81no—
193C2×C4×C13—81no—
194C2×C4×C13—81no—
195C2×C4×C13—81no—
196C2×C4×C13—81no—
197C2×C4×C13—81no—
198C2×C4×C13—81no—
199C2×C4×C13—81no—
200C2×C4×C13—81no—
201C2×C4×C13—81no—
202C2×C4×C13—81no—
203C2×C4×C13#12111yescharacteristic
204C2×C4×C13#12311yescharacteristic
205C8×C13—81no—
206C2×#124C22×C1311yescharacteristic
207C2×#123C22×C1311yescharacteristic
208#518C22×C1311yescharacteristic
209#419—21no—
210C2×#100C22×C1311yescharacteristic
211C2×#99C22×C1311yescharacteristic
212C2×#99C22×C1311yescharacteristic
213#397—21no—
214#397—21no—
215#395—21no—
216#387—21no—
217#386C22×C1311yescharacteristic
218#385—21no—
219#385—21no—
220#381—21no—
221#380—21no—
222#354—22no—
223#352—22no—
224#342—21no—
225#342—21no—
226#339—21no—
227C22×C13—21no—
228C22×C13—21no—
229C22×C13—21no—
230C22×C13—21no—
231C22×C13—21no—
232C22×C13—21no—
233C22×C13—41no—
234C22×C13—41no—
235C22×C13—41no—
236C22×C13—41no—
237C22×C13—41no—
238C22×C13—41no—
239C22×C13—41no—
240C22×C13—41no—
241C22×C13—81no—
242C22×C13—81no—
243C22×C13#39411yescharacteristic
244C22×C13B(4,𝔽2)11yescharacteristic
245C22×C13#45811yescharacteristic
246C4×C13—21no—
247C4×C13—21no—
248C4×C13—42no—
249C4×C13—81no—
250C4×C13—81no—
251C4×C13—81no—
252C4×C13—82no—
253C4×C13—81no—
254C4×C13—81no—
255C4×C13—81no—
256C4×C13—81no—
257C4×C13—161no—
258C22×Q8D4×C1311yescharacteristic
259C22×D4C23×C1311yescharacteristic
260C23×C4D4×C1311yescharacteristic
261C23×C4D4×C1311yescharacteristic
262C2×M16—21no—
263#124—21no—
264#124—21no—
265#124—21no—
266#124—21no—
267#123—21no—
268#123—21no—
269#123—21no—
270#123—21no—
271C4×D4—41no—
272C4×D4—41no—
273#117—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—41no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4D4×C1311yescharacteristic
288C2×C22⋊C4D4×C1311yescharacteristic
289C2×C42D4×C1311yescharacteristic
290#103—41no—
291#103—41no—
292#100—21no—
293#100—21no—
294#99—21no—
295#99—21no—
296#99—21no—
297#99D4×C1312yes—
298#95—21no—
299#95—21no—
300#95—21no—
301#95—21no—
302#95—21no—
303#95—21no—
304#95—41no—
305#95—41no—
306#95—41no—
307C2×C13—21no—
308C2×C13—21no—
309C2×C13—41no—
310C2×C13—41no—
311C2×C13—41no—
312C2×C13—41no—
313C2×C13#204411yescharacteristic
314C2×C13#219711yescharacteristic
315C2×C13#220111yescharacteristic
316C24C2×D4×C1311yescharacteristic
317C24C2×D4×C1311yescharacteristic
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—41no—
321C2×Q8—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4C2×D4×C1311yescharacteristic
325C2×D4C13×#4111yescharacteristic
326C2×D4C13×#4111yescharacteristic
327C2×D4C13×#4111yescharacteristic
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—42no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4C2×D4×C1311yescharacteristic
347M16—41no—
348M16—41no—
349C2×C8—41no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—42no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—81no—
356C4⋊C4—81no—
357C4⋊C4—82no—
358C22⋊C4—22no—
359C22⋊C4—21no—
360C22⋊C4—21no—
361C22⋊C4—42no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C22⋊C4—41no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C42—21no—
376C42—21no—
377C42—41no—
378C13#1342511yescharacteristic, direct product factor, Sylow
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23C13×#12011yescharacteristic
388C23C13×#12111yescharacteristic
389C23C13×#12111yescharacteristic
390C23C13×#12311yescharacteristic
391C23C13×#12411yescharacteristic
392Q8—42no—
393Q8—81no—
394D4—41no—
395D4—41no—
396D4—41no—
397D4—41no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4—81no—
434C2×C4C13×#12111yescharacteristic
435C2×C4C13×#12311yescharacteristic
436C8—81no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—81no—
452C22—81no—
453C22C13×#39411yescharacteristic
454C22C13×B(4,𝔽2)11yescharacteristic
455C22C13×#45811yescharacteristic
456C4—21no—
457C4—21no—
458C4—42no—
459C4—81no—
460C4—81no—
461C4—81no—
462C4—82no—
463C4—81no—
464C4—81no—
465C4—81no—
466C4—81no—
467C4—161no—
468C2—21no—
469C2—21no—
470C2—41no—
471C2—41no—
472C2—41no—
473C2—41no—
474C2C13×#204411yescharacteristic
475C2C13×#219711yescharacteristic
476C2C13×#220111yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C13
prime radicalC22×D4×C13C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C22×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
78. #13425C13direct (N × H)
378. C13#13425direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27172
C2×C13×#3542
C2×C13×#3522
C13×#18902
C13×#18852
C13×#18672
C13×#13902
#1342513