Finite Group Databasebeta

← C13×#13412 #15699751

Subgroups — C13×#13412 #15699751

Order 3328.

430 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3156C211yesmaximal, characteristic
2C2×C13×#362C211yesmaximal, characteristic, complemented
3C2×C13×#359C211yesmaximal, characteristic
4C13×#2139C211yesmaximal, characteristic
5C2×C13×#358C211yesmaximal, characteristic, complemented
6C13×#1952C211yesmaximal, characteristic, complemented
7C13×#1379C211yesmaximal, characteristic, complemented
8C2×C13×#137—21no—
9C2×C13×#135C2211yescharacteristic
10C22×C13×Q16C2211yescharacteristic
11C13×#536—21no—
12C2×C13×M32C2211yescharacteristic
13C22×C13×C16C2211yescharacteristic
14C13×#497—22no—
15C13×#495—21no—
16C13×#494—21no—
17C2×C13×#108C2211yescharacteristic
18C13×#428—21no—
19C2×C13×#107C2211yescharacteristic
20C13×#405C2211yescharacteristic
21C13×#362—22no—
22C13×#359—22no—
23C13×#358—22no—
24C13×#358—21no—
25C13×#357—21no—
26C13×#343—21no—
27C2×C13×#41—21no—
28C22×Q8×C13—21no—
29C13×#137—42no—
30C13×#137—42no—
31C13×#135—21no—
32C13×#135—21no—
33C13×#135—21no—
34C13×#135—21no—
35C2×C13×Q16—22no—
36C2×C13×Q16—21no—
37C2×C13×Q16—21no—
38C2×C13×Q16—21no—
39C2×C13×Q16—21no—
40C2×C13×Q16—21no—
41C2×C13×Q16D411yescharacteristic
42C2×C13×Q16D412yes—
43C2×C13×SD16—22no—
44C2×C13×SD16—21no—
45C2×C13×D8D411yescharacteristic
46C2×C13×M16—21no—
47C2×C13×M16D411yescharacteristic
48C22×C8×C13C2311yescharacteristic
49C13×C4⋊Q8—22no—
50C13×#124—22no—
51C13×#123—42no—
52C13×C22⋊Q8—41no—
53C13×C22⋊Q8—41no—
54C13×#117D411yescharacteristic
55C2×C13×C4⋊C4—21no—
56C13×M32—21no—
57C13×M32—21no—
58C2×C13×C16—21no—
59C2×C13×C16—21no—
60C2×C13×C16—21no—
61C2×C13×C16—21no—
62C13×#108—21no—
63C13×#108D412yes—
64C13×#107—21no—
65C13×#107—21no—
66C13×#107—41no—
67C13×#106—41no—
68C13×#97—21no—
69C4×C8×C13—21no—
70#13412C1311yesmaximal, characteristic, direct product factor, Sylow
71C13×#41—41no—
72C13×#41—41no—
73C13×#41—41no—
74C13×#41—41no—
75C2×Q8×C13—22no—
76C2×Q8×C13—21no—
77C2×Q8×C13—41no—
78C2×Q8×C13—41no—
79C2×Q8×C13—41no—
80C2×Q8×C13—41no—
81C2×Q8×C13—41no—
82C2×D4×C13—21no—
83C2×D4×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13—41no—
87C22×C4×C13C2×D411yescharacteristic
88C13×Q16—22no—
89C13×Q16—21no—
90C13×Q16—22no—
91C13×Q16—21no—
92C13×Q16—44no—
93C13×Q16—41no—
94C13×Q16—41no—
95C13×SD16—44no—
96C13×SD16—41no—
97C13×SD16—41no—
98C13×D8—21no—
99C13×D8—21no—
100C13×M16—21no—
101C13×M16—22no—
102C13×M16—41no—
103C13×M16SD1612yes—
104C2×C8×C13—21no—
105C2×C8×C13—41no—
106C2×C8×C13C2×D411yescharacteristic
107C2×C8×C13C2×D411yescharacteristic
108C2×C8×C13C2×D411yescharacteristic
109C2×C8×C13#4111yescharacteristic
110C2×C8×C13#4111yescharacteristic
111C2×C8×C13#4111yescharacteristic
112C13×C4⋊C4—42no—
113C13×C4⋊C4—42no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4—41no—
116C13×C4⋊C4D811yescharacteristic
117C13×C4⋊C4D811yescharacteristic
118C13×C22⋊C4—21no—
119C13×C22⋊C4—42no—
120C13×C22⋊C4—42no—
121C42×C13—21no—
122C13×C16—41no—
123C13×C16—41no—
124#3156C2×C1311yescharacteristic
125C2×#362C2×C1311yescharacteristic, complemented
126C2×#359C2×C1311yescharacteristic
127#2139C2×C1311yescharacteristic
128C2×#358C2×C1311yescharacteristic, complemented
129#1952C2×C1311yescharacteristic, complemented
130#1379C2×C1311yescharacteristic, complemented
131C23×C13—41no—
132C23×C13AGL(1,ℤ/8)11yescharacteristic
133Q8×C13—41no—
134Q8×C13—42no—
135Q8×C13—42no—
136Q8×C13—41no—
137Q8×C13—81no—
138Q8×C13—81no—
139D4×C13—41no—
140D4×C13—41no—
141D4×C13—81no—
142D4×C13—81no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—42no—
146C2×C4×C13—41no—
147C2×C4×C13—81no—
148C2×C4×C13—81no—
149C2×C4×C13—81no—
150C2×C4×C13—81no—
151C2×C4×C13—81no—
152C2×C4×C13—161no—
153C2×C4×C13#12011yescharacteristic
154C2×C4×C13#12111yescharacteristic
155C2×C4×C13#12411yescharacteristic
156C2×C4×C13C2×D811yescharacteristic
157C2×C4×C13C2×SD1611yescharacteristic
158C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
159C8×C13—22no—
160C8×C13—42no—
161C8×C13#12111yescharacteristic
162C8×C13#12111yescharacteristic
163C8×C13#12311yescharacteristic
164C8×C13#12311yescharacteristic
165C2×#137—21no—
166C2×#135C22×C1311yescharacteristic
167C22×Q16C22×C1311yescharacteristic
168#536—21no—
169C2×M32C22×C1311yescharacteristic
170C22×C16C22×C1311yescharacteristic
171#497—22no—
172#495—21no—
173#494—21no—
174C2×#108C22×C1311yescharacteristic
175#428—21no—
176C2×#107C22×C1311yescharacteristic
177#405C22×C1311yescharacteristic
178#362—22no—
179#359—22no—
180#358—22no—
181#358—21no—
182#357—21no—
183#343—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—81no—
187C22×C13—81no—
188C22×C13—81no—
189C22×C13#44711yescharacteristic
190C22×C13#46011yescharacteristic
191C22×C13#49011yescharacteristic
192C4×C13—41no—
193C4×C13—41no—
194C4×C13—81no—
195C4×C13—82no—
196C4×C13—161no—
197C4×C13#39411yescharacteristic
198C4×C13#45011yescharacteristic
199C4×C13#45911yescharacteristic
200C4×C13#48611yescharacteristic
201C2×#41—21no—
202C22×Q8—21no—
203#137—42no—
204#137—42no—
205#135—21no—
206#135—21no—
207#135—21no—
208#135—21no—
209C2×Q16—22no—
210C2×Q16—21no—
211C2×Q16—21no—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×Q16D4×C1312yes—
216C2×Q16D4×C1311yescharacteristic
217C2×SD16—22no—
218C2×SD16—21no—
219C2×D8D4×C1311yescharacteristic
220C2×M16—21no—
221C2×M16D4×C1311yescharacteristic
222C22×C8C23×C1311yescharacteristic
223C4⋊Q8—22no—
224#124—22no—
225#123—42no—
226C22⋊Q8—41no—
227C22⋊Q8—41no—
228#117D4×C1311yescharacteristic
229C2×C4⋊C4—21no—
230M32—21no—
231M32—21no—
232C2×C16—21no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16—21no—
236#108—21no—
237#108D4×C1312yes—
238#107—21no—
239#107—21no—
240#107—41no—
241#106—41no—
242#97—21no—
243C4×C8—21no—
244C2×C13—21no—
245C2×C13—21no—
246C2×C13—161no—
247C2×C13#204111yescharacteristic
248C2×C13#219311yescharacteristic
249C2×C13#219511yescharacteristic
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254C2×Q8—22no—
255C2×Q8—21no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×D4—21no—
262C2×D4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4C2×D4×C1311yescharacteristic
267Q16—22no—
268Q16—21no—
269Q16—22no—
270Q16—21no—
271Q16—44no—
272Q16—41no—
273Q16—41no—
274SD16—44no—
275SD16—41no—
276SD16—41no—
277D8—21no—
278D8—21no—
279M16—21no—
280M16—22no—
281M16—41no—
282M16C13×SD1612yes—
283C2×C8—21no—
284C2×C8—41no—
285C2×C8C2×D4×C1311yescharacteristic
286C2×C8C2×D4×C1311yescharacteristic
287C2×C8C2×D4×C1311yescharacteristic
288C2×C8C13×#4111yescharacteristic
289C2×C8C13×#4111yescharacteristic
290C2×C8C13×#4111yescharacteristic
291C4⋊C4—42no—
292C4⋊C4—42no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4C13×D811yescharacteristic
296C4⋊C4C13×D811yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C42—21no—
301C16—41no—
302C16—41no—
303C13#1341211yescharacteristic, direct product factor, Sylow
304C23—41no—
305C23C13×AGL(1,ℤ/8)11yescharacteristic
306Q8—41no—
307Q8—42no—
308Q8—42no—
309Q8—41no—
310Q8—81no—
311Q8—81no—
312D4—41no—
313D4—41no—
314D4—81no—
315D4—81no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—161no—
326C2×C4C13×#12011yescharacteristic
327C2×C4C13×#12111yescharacteristic
328C2×C4C13×#12411yescharacteristic
329C2×C4C2×C13×D811yescharacteristic
330C2×C4C2×C13×SD1611yescharacteristic
331C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
332C8—22no—
333C8—42no—
334C8C13×#12111yescharacteristic
335C8C13×#12111yescharacteristic
336C8C13×#12311yescharacteristic
337C8C13×#12311yescharacteristic
338C22—21no—
339C22—21no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22C13×#44711yescharacteristic
344C22C13×#46011yescharacteristic
345C22C13×#49011yescharacteristic
346C4—41no—
347C4—41no—
348C4—81no—
349C4—82no—
350C4—161no—
351C4C13×#39411yescharacteristic
352C4C13×#45011yescharacteristic
353C4C13×#45911yescharacteristic
354C4C13×#48611yescharacteristic
355C2—21no—
356C2—21no—
357C2—161no—
358C2C13×#204111yescharacteristic
359C2C13×#219311yescharacteristic
360C2C13×#219511yescharacteristic
subgroupG/H
center, socleC22×C13#447
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC2×C13×#135C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#362C2semidirect
5. C2×C13×#358C2semidirect
6. C13×#1952C2semidirect
7. C13×#1379C2semidirect
70. #13412C13direct (N × H)
125. C2×#362C2×C13semidirect
128. C2×#358C2×C13semidirect
129. #1952C2×C13semidirect
130. #1379C2×C13semidirect
303. C13#13412direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31562
C2×C13×#3622
C2×C13×#3592
C13×#21392
C2×C13×#3582
C13×#19522
C13×#13792
#1341213