Finite Group Databasebeta

← C13×#8907 #15695246

Subgroups — C13×#8907 #15695246

Order 3328.

376 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C13×M16C211yesmaximal, characteristic
2C13×#1950C211yesmaximal, characteristic
3C13×#1567C211yesmaximal, characteristic
4C13×#1487C211yesmaximal, characteristic
5C2×C13×Q8⋊C8C211yesmaximal, characteristic
6C13×#1301C211yesmaximal, characteristic
7C13×#1278C211yesmaximal, characteristic
8C2×C4×Q8×C13C2211yescharacteristic
9C13×#446—21no—
10C13×#446—22no—
11C8×Q8×C13—21no—
12C13×#431C2211yescharacteristic
13C2×C13×#108—21no—
14C13×#423—21no—
15C13×#423C2211yescharacteristic
16C13×#423C2211yescharacteristic
17C2×C13×C4⋊C8C2211yescharacteristic
18C4×C13×M16—21no—
19C4×C13×M16C2211yescharacteristic
20C2×C4×C8×C13C2211yescharacteristic
21C13×#341—21no—
22C13×#335—22no—
23C13×Q8⋊C8—21no—
24C13×Q8⋊C8—21no—
25C13×Q8⋊C8C411yescharacteristic
26C13×Q8⋊C8C411yescharacteristic
27C13×Q8⋊C8C411yescharacteristic
28C13×Q8⋊C8C411yescharacteristic
29C22×Q8×C13Q811yescharacteristic
30C2×C13×M16—21no—
31C2×C13×M16—21no—
32C2×C13×M16D411yescharacteristic
33C2×C13×M16D411yescharacteristic
34C22×C8×C13—21no—
35C22×C8×C13—21no—
36C4×Q8×C13—21no—
37C4×Q8×C13—21no—
38C4×Q8×C13C2×C411yescharacteristic
39C4×Q8×C13C2×C411yescharacteristic
40C4×Q8×C13D411yescharacteristic
41C4×Q8×C13D411yescharacteristic
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4Q811yescharacteristic
44C2×C42×C13—21no—
45C2×C42×C13C2311yescharacteristic
46C13×#108—42no—
47C13×C4⋊C8—22no—
48C13×C4⋊C8—22no—
49C13×C4⋊C8—21no—
50C13×C4⋊C8—21no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54C13×C4⋊C8C2×C411yescharacteristic
55C13×C4⋊C8C2×C411yescharacteristic
56C13×C4⋊C8D412yes—
57C13×C22⋊C8—21no—
58C13×#97—22no—
59C13×#97—21no—
60C4×C8×C13—22no—
61C4×C8×C13—21no—
62C4×C8×C13—21no—
63C4×C8×C13—21no—
64C4×C8×C13C2×C411yescharacteristic
65C4×C8×C13C2×C411yescharacteristic
66#8907C1311yesmaximal, characteristic, direct product factor, Sylow
67C2×Q8×C13—21no—
68C2×Q8×C13—22no—
69C2×Q8×C13—41no—
70C2×Q8×C13C4⋊C411yescharacteristic
71C2×Q8×C13C4⋊C411yescharacteristic
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×Q811yescharacteristic
76C22×C4×C13#4111yescharacteristic
77C13×M16—21no—
78C13×M16—21no—
79C13×M16—21no—
80C13×M16—41no—
81C13×M16—41no—
82C13×M16—41no—
83C13×M16—41no—
84C13×M16Q1612yes—
85C2×C8×C13—21no—
86C2×C8×C13—21no—
87C2×C8×C13—21no—
88C2×C8×C13—21no—
89C2×C8×C13—21no—
90C2×C8×C13—21no—
91C2×C8×C13—22no—
92C2×C8×C13—42no—
93C2×C8×C13—41no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C2×C8×C13—41no—
97C13×C4⋊C4—21no—
98C13×C4⋊C4—21no—
99C13×C4⋊C4—21no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4C4⋊C411yescharacteristic
103C13×C4⋊C4C4⋊C411yescharacteristic
104C42×C13—21no—
105C42×C13—21no—
106C42×C13—21no—
107C42×C13—21no—
108C42×C13C22×C411yescharacteristic
109C42×C13C2×D411yescharacteristic
110C42×C13C2×D411yescharacteristic
111C42×C13#4111yescharacteristic
112Q8×M16C2×C1311yescharacteristic
113#1950C2×C1311yescharacteristic
114#1567C2×C1311yescharacteristic
115#1487C2×C1311yescharacteristic
116C2×Q8⋊C8C2×C1311yescharacteristic
117#1301C2×C1311yescharacteristic
118#1278C2×C1311yescharacteristic
119C23×C13C22⋊Q811yescharacteristic
120Q8×C13—21no—
121Q8×C13—21no—
122Q8×C13—21no—
123Q8×C13—42no—
124Q8×C13#10812yescomplemented
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—41no—
132C2×C4×C13—42no—
133C2×C4×C13—81no—
134C2×C4×C13C2×C4⋊C411yescharacteristic
135C2×C4×C13C4×D411yescharacteristic
136C2×C4×C13C4×D411yescharacteristic
137C2×C4×C13#12011yescharacteristic
138C2×C4×C13C22⋊Q811yescharacteristic
139C2×C4×C13#12311yescharacteristic
140C2×C4×C13C2×Q1611yescharacteristic
141C2×C4×C13#13511yescharacteristic
142C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C13#13711yescharacteristic
144C8×C13—22no—
145C8×C13—22no—
146C8×C13—41no—
147C8×C13—41no—
148C8×C13—41no—
149C8×C13—41no—
150C8×C13—42no—
151C8×C13—81no—
152C8×C13—81no—
153C2×C4×Q8C22×C1311yescharacteristic
154#446—21no—
155#446—22no—
156C8×Q8—21no—
157#431C22×C1311yescharacteristic
158C2×#108—21no—
159#423—21no—
160#423C22×C1311yescharacteristic
161#423C22×C1311yescharacteristic
162C2×C4⋊C8C22×C1311yescharacteristic
163C4×M16—21no—
164C4×M16C22×C1311yescharacteristic
165C2×C4×C8C22×C1311yescharacteristic
166#341—21no—
167#335—22no—
168Q8⋊C8—21no—
169Q8⋊C8—21no—
170Q8⋊C8C4×C1311yescharacteristic
171Q8⋊C8C4×C1311yescharacteristic
172Q8⋊C8C4×C1311yescharacteristic
173Q8⋊C8C4×C1311yescharacteristic
174C22×C13—21no—
175C22×C13—21no—
176C22×C13#38511yescharacteristic
177C22×C13#47711yescharacteristic
178C22×C13#47911yescharacteristic
179C4×C13—21no—
180C4×C13—22no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—41no—
186C4×C13C2×#10811yescharacteristic
187C4×C13#43011yescharacteristic
188C4×C13C4×Q1611yescharacteristic
189C4×C13#44011yescharacteristic
190C4×C13#44911yescharacteristic
191C4×C13#45111yescharacteristic
192C22×Q8Q8×C1311yescharacteristic
193C2×M16—21no—
194C2×M16—21no—
195C2×M16D4×C1311yescharacteristic
196C2×M16D4×C1311yescharacteristic
197C22×C8—21no—
198C22×C8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201C4×Q8C2×C4×C1311yescharacteristic
202C4×Q8C2×C4×C1311yescharacteristic
203C4×Q8D4×C1311yescharacteristic
204C4×Q8D4×C1311yescharacteristic
205C2×C4⋊C4—21no—
206C2×C4⋊C4Q8×C1311yescharacteristic
207C2×C42—21no—
208C2×C42C23×C1311yescharacteristic
209#108—42no—
210C4⋊C8—22no—
211C4⋊C8—22no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8C2×C4×C1311yescharacteristic
218C4⋊C8C2×C4×C1311yescharacteristic
219C4⋊C8D4×C1312yes—
220C22⋊C8—21no—
221#97—22no—
222#97—21no—
223C4×C8—22no—
224C4×C8—21no—
225C4×C8—21no—
226C4×C8—21no—
227C4×C8C2×C4×C1311yescharacteristic
228C4×C8C2×C4×C1311yescharacteristic
229C2×C13—21no—
230C2×C13—21no—
231C2×C13#185511yescharacteristic
232C2×C13#186111yescharacteristic
233C2×C13#186311yescharacteristic
234C2×Q8—21no—
235C2×Q8—22no—
236C2×Q8—41no—
237C2×Q8C13×C4⋊C411yescharacteristic
238C2×Q8C13×C4⋊C411yescharacteristic
239C22×C4—21no—
240C22×C4—21no—
241C22×C4C2×D4×C1311yescharacteristic
242C22×C4C2×Q8×C1311yescharacteristic
243C22×C4C13×#4111yescharacteristic
244M16—21no—
245M16—21no—
246M16—21no—
247M16—41no—
248M16—41no—
249M16—41no—
250M16—41no—
251M16C13×Q1612yes—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—22no—
259C2×C8—42no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4C13×C4⋊C411yescharacteristic
270C4⋊C4C13×C4⋊C411yescharacteristic
271C42—21no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42C22×C4×C1311yescharacteristic
276C42C2×D4×C1311yescharacteristic
277C42C2×D4×C1311yescharacteristic
278C42C13×#4111yescharacteristic
279C13#890711yescharacteristic, direct product factor, Sylow
280C23C13×C22⋊Q811yescharacteristic
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—42no—
285Q8C13×#10812yescomplemented
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—81no—
295C2×C4C2×C13×C4⋊C411yescharacteristic
296C2×C4C4×D4×C1311yescharacteristic
297C2×C4C4×D4×C1311yescharacteristic
298C2×C4C13×#12011yescharacteristic
299C2×C4C13×C22⋊Q811yescharacteristic
300C2×C4C13×#12311yescharacteristic
301C2×C4C2×C13×Q1611yescharacteristic
302C2×C4C13×#13511yescharacteristic
303C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
304C2×C4C13×#13711yescharacteristic
305C8—22no—
306C8—22no—
307C8—41no—
308C8—41no—
309C8—41no—
310C8—41no—
311C8—42no—
312C8—81no—
313C8—81no—
314C22—21no—
315C22—21no—
316C22C13×#38511yescharacteristic
317C22C13×#47711yescharacteristic
318C22C13×#47911yescharacteristic
319C4—21no—
320C4—22no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4C2×C13×#10811yescharacteristic
327C4C13×#43011yescharacteristic
328C4C4×C13×Q1611yescharacteristic
329C4C13×#44011yescharacteristic
330C4C13×#44911yescharacteristic
331C4C13×#45111yescharacteristic
332C2—21no—
333C2—21no—
334C2C13×#185511yescharacteristic
335C2C13×#186111yescharacteristic
336C2C13×#186311yescharacteristic
subgroupG/H
centerC2×C4×C13#120
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
socleC22×C13#385
prime radicalC23×C13C22⋊Q8
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
66. #8907C13direct (N × H)
124. Q8×C13#108semidirect
279. C13#8907direct (N × H)
285. Q8C13×#108semidirect

Maximal subgroups

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

subgroupindex
Q8×C13×M162
C13×#19502
C13×#15672
C13×#14872
C2×C13×Q8⋊C82
C13×#13012
C13×#12782
#890713