Finite Group Databasebeta

← C13×#12253 #15698592

Subgroups — C13×#12253 #15698592

Order 3328.

398 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2763C211yesmaximal, characteristic
2C13×#2062C211yesmaximal, characteristic
3C13×#1602C211yesmaximal, characteristic
4C13×#1602C211yesmaximal, characteristic
5C13×#1351C211yesmaximal, characteristic
6C13×#1351C211yesmaximal, characteristic
7C13×#1326C211yesmaximal, characteristic
8C13×#543C2211yescharacteristic
9C13×#451—21no—
10C13×#451—21no—
11C13×#400—21no—
12C13×#395—21no—
13C13×#393C2211yescharacteristic
14C13×#393C2211yescharacteristic
15C13×#391—21no—
16C13×#388—21no—
17C13×#385—21no—
18C13×#385—21no—
19C13×#385C2211yescharacteristic
20C13×#382—21no—
21C13×#342—21no—
22C13×#342C2211yescharacteristic
23C13×#328—21no—
24C13×#328—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C22×Q8×C13D411yescharacteristic
28C22×Q8×C13D411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C2×C13×Q16—41no—
31C2×C13×Q16—41no—
32C13×C22⋊Q8—21no—
33C13×C22⋊Q8—21no—
34C13×C22⋊Q8—41no—
35C13×C22⋊Q8—41no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—41no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4D411yescharacteristic
46C2×C13×C22⋊C4C2311yescharacteristic
47C2×C42×C13—21no—
48C13×#103—41no—
49C13×#103—41no—
50C13×C22⋊C8—21no—
51C13×C22⋊C8—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—41no—
60C13×#95D411yescharacteristic
61C13×#95D411yescharacteristic
62#12253C1311yesmaximal, characteristic, direct product factor, Sylow
63C24×C13C2×D411yescharacteristic
64C2×Q8×C13—21no—
65C2×Q8×C13—21no—
66C2×Q8×C13—42no—
67C2×Q8×C13—41no—
68C2×Q8×C13—41no—
69C2×Q8×C13—81no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—41no—
79C22×C4×C13—41no—
80C22×C4×C13—81no—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C13×Q16—82no—
84C13×Q16—82no—
85C2×C8×C13—41no—
86C2×C8×C13—41no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—81no—
92C13×C4⋊C4—81no—
93C13×C4⋊C4—81no—
94C13×C4⋊C4—81no—
95C13×C4⋊C4—82no—
96C13×C22⋊C4—21no—
97C13×C22⋊C4—22no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—81no—
104C13×C22⋊C4Q1612yescomplemented
105C42×C13—42no—
106#2763C2×C1311yescharacteristic
107#2062C2×C1311yescharacteristic
108#1602C2×C1311yescharacteristic
109#1602C2×C1311yescharacteristic
110#1351C2×C1311yescharacteristic
111#1351C2×C1311yescharacteristic
112#1326C2×C1311yescharacteristic
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13#12011yescharacteristic
118C23×C13C2×Q1611yescharacteristic
119C23×C13#13711yescharacteristic
120Q8×C13—42no—
121Q8×C13—42no—
122Q8×C13—81no—
123Q8×C13—81no—
124Q8×C13—81no—
125Q8×C13—81no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—42no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—42no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—81no—
153C2×C4×C13—81no—
154C2×C4×C13—81no—
155C2×C4×C13—81no—
156C2×C4×C13—81no—
157C8×C13—81no—
158C8×C13—81no—
159#543C22×C1311yescharacteristic
160#451—21no—
161#451—21no—
162#400—21no—
163#395—21no—
164#393C22×C1311yescharacteristic
165#393C22×C1311yescharacteristic
166#391—21no—
167#388—21no—
168#385—21no—
169#385—21no—
170#385C22×C1311yescharacteristic
171#382—21no—
172#342—21no—
173#342C22×C1311yescharacteristic
174#328—21no—
175#328—21no—
176#323C22×C1311yescharacteristic
177#323C22×C1311yescharacteristic
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—81no—
187C22×C13#45111yescharacteristic
188C22×C13#45611yescharacteristic
189C22×C13B(4,𝔽2)11yescharacteristic
190C4×C13—42no—
191C4×C13—41no—
192C4×C13—42no—
193C4×C13—41no—
194C4×C13—81no—
195C4×C13—81no—
196C4×C13—82no—
197C4×C13—81no—
198C4×C13—81no—
199C4×C13—81no—
200C4×C13—81no—
201C22×Q8D4×C1311yescharacteristic
202C22×Q8D4×C1311yescharacteristic
203C23×C4D4×C1311yescharacteristic
204C2×Q16—41no—
205C2×Q16—41no—
206C22⋊Q8—21no—
207C22⋊Q8—21no—
208C22⋊Q8—41no—
209C22⋊Q8—41no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—41no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4D4×C1311yescharacteristic
220C2×C22⋊C4C23×C1311yescharacteristic
221C2×C42—21no—
222#103—41no—
223#103—41no—
224C22⋊C8—21no—
225C22⋊C8—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—41no—
234#95D4×C1311yescharacteristic
235#95D4×C1311yescharacteristic
236C2×C13—21no—
237C2×C13—21no—
238C2×C13—41no—
239C2×C13—41no—
240C2×C13#160511yescharacteristic
241C2×C13#219711yescharacteristic
242C2×C13#219911yescharacteristic
243C24C2×D4×C1311yescharacteristic
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—42no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—81no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—81no—
261C22×C4C2×D4×C1311yescharacteristic
262C22×C4C2×D4×C1311yescharacteristic
263Q16—82no—
264Q16—82no—
265C2×C8—41no—
266C2×C8—41no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—81no—
272C4⋊C4—81no—
273C4⋊C4—81no—
274C4⋊C4—81no—
275C4⋊C4—82no—
276C22⋊C4—21no—
277C22⋊C4—22no—
278C22⋊C4—41no—
279C22⋊C4—42no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—81no—
284C22⋊C4C13×Q1612yescomplemented
285C42—42no—
286C13#1225311yescharacteristic, direct product factor, Sylow
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23C13×#12011yescharacteristic
292C23C2×C13×Q1611yescharacteristic
293C23C13×#13711yescharacteristic
294Q8—42no—
295Q8—42no—
296Q8—81no—
297Q8—81no—
298Q8—81no—
299Q8—81no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C8—81no—
332C8—81no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—81no—
342C22C13×#45111yescharacteristic
343C22C13×#45611yescharacteristic
344C22C13×B(4,𝔽2)11yescharacteristic
345C4—42no—
346C4—41no—
347C4—42no—
348C4—41no—
349C4—81no—
350C4—81no—
351C4—82no—
352C4—81no—
353C4—81no—
354C4—81no—
355C4—81no—
356C2—21no—
357C2—21no—
358C2—41no—
359C2—41no—
360C2C13×#160511yescharacteristic
361C2C13×#219711yescharacteristic
362C2C13×#219911yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC24×C13C2×D4
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C2×C13×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
62. #12253C13direct (N × H)
104. C13×C22⋊C4Q16semidirect
284. C22⋊C4C13×Q16semidirect
286. C13#12253direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27632
C13×#20622
C13×#16022
C13×#13512
C13×#13262
#1225313