Finite Group Databasebeta

← C13×#13445 #15699784

Subgroups — C13×#13445 #15699784

Order 3328.

432 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#509C211yesmaximal, characteristic
2C2×C13×#364C211yesmaximal, characteristic, complemented
3C2×C13×#361C211yesmaximal, characteristic, complemented
4C13×#2139C211yesmaximal, characteristic, complemented
5C13×#1974C211yesmaximal, characteristic, complemented
6C13×#1970C211yesmaximal, characteristic, complemented
7C13×#1387C211yesmaximal, characteristic, complemented
8C2×C13×#135C2211yescharacteristic
9C22×C13×D8C2211yescharacteristic
10C13×#509—22no—
11C13×#509—22no—
12C2×C13×SD32—21no—
13C2×C13×D16—21no—
14C2×C13×M32C2211yescharacteristic
15C2×C13×M32C2211yescharacteristic
16C2×C13×#108C2211yescharacteristic
17C2×C13×#107C2211yescharacteristic
18C2×C13×#104—21no—
19C2×C13×#102—21no—
20C13×#408—21no—
21C2×C4×C8×C13C2211yescharacteristic
22C13×#390—21no—
23C13×#364—22no—
24C13×#361—22no—
25C13×#358—21no—
26C13×#357—21no—
27C2×C13×#41—21no—
28C22×D4×C13—21no—
29C13×#135—21no—
30C13×#135—21no—
31C13×#135—21no—
32C13×#135—21no—
33C2×C13×Q16D411yescharacteristic
34C2×C13×SD16—21no—
35C2×C13×D8—21no—
36C2×C13×D8—21no—
37C2×C13×D8—21no—
38C2×C13×D8—21no—
39C2×C13×D8—21no—
40C2×C13×D8D411yescharacteristic
41C2×C13×D8D412yes—
42C2×C13×M16—21no—
43C22×C8×C13D411yescharacteristic
44C22×C8×C13C2311yescharacteristic
45C2×C13×C4⋊C4—21no—
46C2×C13×C22⋊C4—42no—
47C2×C42×C13D411yescharacteristic
48C13×SD32—24no—
49C13×D16—24no—
50C13×M32—21no—
51C13×M32—21no—
52C13×M32—21no—
53C13×M32D412yes—
54C2×C13×C16—21no—
55C2×C13×C16—21no—
56C13×#108—21no—
57C13×#108—21no—
58C13×#107—21no—
59C13×#107—21no—
60C13×#104—42no—
61C13×#102—42no—
62C13×C22⋊C8—42no—
63C4×C8×C13—21no—
64C4×C8×C13—21no—
65#13445C1311yesmaximal, characteristic, direct product factor, Sylow
66C24×C13—41no—
67C13×#41—41no—
68C13×#41—41no—
69C13×#41—41no—
70C13×#41—41no—
71C2×Q8×C13—21no—
72C2×D4×C13—22no—
73C2×D4×C13—21no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C2×D4×C13—41no—
79C2×D4×C13—41no—
80C22×C4×C13—21no—
81C22×C4×C13—41no—
82C22×C4×C13—41no—
83C22×C4×C13C2×D411yescharacteristic
84C13×Q16—21no—
85C13×Q16—21no—
86C13×SD16—41no—
87C13×SD16—41no—
88C13×D8—21no—
89C13×D8—22no—
90C13×D8—22no—
91C13×D8—21no—
92C13×D8—41no—
93C13×D8—41no—
94C13×M16—41no—
95C13×M16—41no—
96C2×C8×C13—21no—
97C2×C8×C13—21no—
98C2×C8×C13—41no—
99C2×C8×C13D812yes—
100C2×C8×C13C2×D411yescharacteristic
101C2×C8×C13C2×D411yescharacteristic
102C2×C8×C13C2×D411yescharacteristic
103C2×C8×C13#4111yescharacteristic
104C2×C8×C13#4111yescharacteristic
105C2×C8×C13#4111yescharacteristic
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C22⋊C4—84no—
109C42×C13—21no—
110C42×C13—21no—
111C13×C16—22no—
112C13×C16—41no—
113C2×#509C2×C1311yescharacteristic
114C2×#364C2×C1311yescharacteristic, complemented
115C2×#361C2×C1311yescharacteristic, complemented
116#2139C2×C1311yescharacteristic, complemented
117#1974C2×C1311yescharacteristic, complemented
118#1970C2×C1311yescharacteristic, complemented
119#1387C2×C1311yescharacteristic, complemented
120C23×C13—41no—
121C23×C13—42no—
122C23×C13—82no—
123C23×C13—82no—
124C23×C13—81no—
125C23×C13—81no—
126C23×C13AGL(1,ℤ/8)11yescharacteristic
127Q8×C13—41no—
128Q8×C13—41no—
129D4×C13—42no—
130D4×C13—41no—
131D4×C13—42no—
132D4×C13—41no—
133D4×C13—81no—
134D4×C13—81no—
135D4×C13—81no—
136D4×C13—81no—
137C2×C4×C13—22no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—81no—
142C2×C4×C13—81no—
143C2×C4×C13—82no—
144C2×C4×C13—81no—
145C2×C4×C13#12111yescharacteristic
146C2×C4×C13#12111yescharacteristic
147C2×C4×C13#12111yescharacteristic
148C2×C4×C13C2×D811yescharacteristic
149C2×C4×C13#13511yescharacteristic
150C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
151C8×C13—22no—
152C8×C13—81no—
153C8×C13#12011yescharacteristic
154C8×C13#12311yescharacteristic
155C8×C13#12311yescharacteristic
156C8×C13#12411yescharacteristic
157C2×#135C22×C1311yescharacteristic
158C22×D8C22×C1311yescharacteristic
159#509—22no—
160#509—22no—
161C2×SD32—21no—
162C2×D16—21no—
163C2×M32C22×C1311yescharacteristic
164C2×M32C22×C1311yescharacteristic
165C2×#108C22×C1311yescharacteristic
166C2×#107C22×C1311yescharacteristic
167C2×#104—21no—
168C2×#102—21no—
169#408—21no—
170C2×C4×C8C22×C1311yescharacteristic
171#390—21no—
172#364—22no—
173#361—22no—
174#358—21no—
175#357—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—84no—
179C22×C13—81no—
180C22×C13—82no—
181C22×C13—81no—
182C22×C13—81no—
183C22×C13—162no—
184C22×C13—161no—
185C22×C13—161no—
186C22×C13#45911yescharacteristic
187C22×C13#46311yescharacteristic
188C22×C13#46911yescharacteristic
189C4×C13—42no—
190C4×C13—81no—
191C4×C13—161no—
192C4×C13#39411yescharacteristic
193C4×C13#45911yescharacteristic
194C4×C13#46311yescharacteristic
195C4×C13#46611yescharacteristic
196C2×#41—21no—
197C22×D4—21no—
198#135—21no—
199#135—21no—
200#135—21no—
201#135—21no—
202C2×Q16D4×C1311yescharacteristic
203C2×SD16—21no—
204C2×D8—21no—
205C2×D8—21no—
206C2×D8—21no—
207C2×D8—21no—
208C2×D8—21no—
209C2×D8D4×C1312yes—
210C2×D8D4×C1311yescharacteristic
211C2×M16—21no—
212C22×C8D4×C1311yescharacteristic
213C22×C8C23×C1311yescharacteristic
214C2×C4⋊C4—21no—
215C2×C22⋊C4—42no—
216C2×C42D4×C1311yescharacteristic
217SD32—24no—
218D16—24no—
219M32—21no—
220M32—21no—
221M32—21no—
222M32D4×C1312yes—
223C2×C16—21no—
224C2×C16—21no—
225#108—21no—
226#108—21no—
227#107—21no—
228#107—21no—
229#104—42no—
230#102—42no—
231C22⋊C8—42no—
232C4×C8—21no—
233C4×C8—21no—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—161no—
237C2×C13—162no—
238C2×C13#205411yescharacteristic
239C2×C13#221211yescharacteristic
240C2×C13#221311yescharacteristic
241C24—41no—
242#41—41no—
243#41—41no—
244#41—41no—
245#41—41no—
246C2×Q8—21no—
247C2×D4—22no—
248C2×D4—21no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—41no—
255C22×C4—21no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4C2×D4×C1311yescharacteristic
259Q16—21no—
260Q16—21no—
261SD16—41no—
262SD16—41no—
263D8—21no—
264D8—22no—
265D8—22no—
266D8—21no—
267D8—41no—
268D8—41no—
269M16—41no—
270M16—41no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—41no—
274C2×C8C13×D812yes—
275C2×C8C2×D4×C1311yescharacteristic
276C2×C8C2×D4×C1311yescharacteristic
277C2×C8C2×D4×C1311yescharacteristic
278C2×C8C13×#4111yescharacteristic
279C2×C8C13×#4111yescharacteristic
280C2×C8C13×#4111yescharacteristic
281C4⋊C4—41no—
282C4⋊C4—41no—
283C22⋊C4—84no—
284C42—21no—
285C42—21no—
286C16—22no—
287C16—41no—
288C13#1344511yescharacteristic, direct product factor, Sylow
289C23—41no—
290C23—42no—
291C23—82no—
292C23—82no—
293C23—81no—
294C23—81no—
295C23C13×AGL(1,ℤ/8)11yescharacteristic
296Q8—41no—
297Q8—41no—
298D4—42no—
299D4—41no—
300D4—42no—
301D4—41no—
302D4—81no—
303D4—81no—
304D4—81no—
305D4—81no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—82no—
313C2×C4—81no—
314C2×C4C13×#12111yescharacteristic
315C2×C4C13×#12111yescharacteristic
316C2×C4C13×#12111yescharacteristic
317C2×C4C2×C13×D811yescharacteristic
318C2×C4C13×#13511yescharacteristic
319C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
320C8—22no—
321C8—81no—
322C8C13×#12011yescharacteristic
323C8C13×#12311yescharacteristic
324C8C13×#12311yescharacteristic
325C8C13×#12411yescharacteristic
326C22—21no—
327C22—21no—
328C22—84no—
329C22—81no—
330C22—82no—
331C22—81no—
332C22—81no—
333C22—162no—
334C22—161no—
335C22—161no—
336C22C13×#45911yescharacteristic
337C22C13×#46311yescharacteristic
338C22C13×#46911yescharacteristic
339C4—42no—
340C4—81no—
341C4—161no—
342C4C13×#39411yescharacteristic
343C4C13×#45911yescharacteristic
344C4C13×#46311yescharacteristic
345C4C13×#46611yescharacteristic
346C2—21no—
347C2—21no—
348C2—162no—
349C2—161no—
350C2C13×#205411yescharacteristic
351C2C13×#221211yescharacteristic
352C2C13×#221311yescharacteristic
subgroupG/H
center, socleC22×C13#459
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC2×C13×#509C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×C8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#364C2semidirect
3. C2×C13×#361C2semidirect
4. C13×#2139C2semidirect
5. C13×#1974C2semidirect
6. C13×#1970C2semidirect
7. C13×#1387C2semidirect
65. #13445C13direct (N × H)
114. C2×#364C2×C13semidirect
115. C2×#361C2×C13semidirect
116. #2139C2×C13semidirect
117. #1974C2×C13semidirect
118. #1970C2×C13semidirect
119. #1387C2×C13semidirect
288. C13#13445direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5092
C2×C13×#3642
C2×C13×#3612
C13×#21392
C13×#19742
C13×#19702
C13×#13872
#1344513