Finite Group Databasebeta

← C53×#62147 #27269659

Subgroups — C53×#62147 #27269659

Order 13568.

1734 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3503C211yesmaximal, characteristic, complemented
2C53×#3482C211yesmaximal, characteristic
3Q8×SD16×C53C212yesmaximal, complemented
4C53×#3363C212yesmaximal, complemented
5C53×#3356C216yesmaximal, complemented
6C53×#3331C216yesmaximal, complemented
7C53×#3255C213yesmaximal, complemented
8C53×#3229C213yesmaximal, complemented
9C53×#3107C213yesmaximal, complemented
10C53×#3079C213yesmaximal, complemented
11C53×#2991C211yesmaximal, characteristic, complemented
12Q82×C53C2212yes—
13C53×#557—21no—
14C53×#557C2211yescharacteristic
15C53×#556C2213yes—
16C53×#554C2216yes—
17C53×#552—23no—
18D4×Q8×C53—23no—
19D4×Q8×C53C2211yescharacteristic
20C53×#548—21no—
21C53×#547C2213yes—
22C53×#544—23no—
23C53×#533C2213yes—
24C53×#533C2213yes—
25C2×C4⋊Q8×C53C2213yes—
26C53×#529—23no—
27C53×#520—21no—
28C4×#41×C53C2213yes—
29C4×#41×C53C2211yescharacteristic
30C2×C4×Q8×C53—21no—
31C53×#498C2216yes—
32C53×#487C2216yes—
33C53×#485C2216yes—
34C53×#483C22112yes—
35C53×#477C2216yes—
36C53×#476C2216yes—
37C53×#475C2213yes—
38C53×#475C2216yes—
39C53×#475C2216yes—
40C53×#474C2213yes—
41C53×#470C22112yes—
42C53×#462C2213yes—
43C53×#462C2216yes—
44C53×#461C2211yescharacteristic
45C53×#452C2216yes—
46C8×Q8×C53C2212yes—
47C4×Q16×C53C2216yes—
48C4×SD16×C53C2216yes—
49C53×#436C2216yes—
50C53×#431C2213yes—
51C53×#428C2216yes—
52C53×#423C2213yes—
53C53×#417C2216yes—
54C2×#41×C53D411yescharacteristic
55C2×#41×C53C2313yes—
56C22×Q8×C53—21no—
57C22×Q8×C53—23no—
58C2×Q16×C53C2316yes—
59C2×SD16×C53C2312yes—
60C2×M16×C53C2316yes—
61C4⋊Q8×C53—26no—
62C4⋊Q8×C53—23no—
63C4⋊Q8×C53—23no—
64C4⋊Q8×C53C2316yes—
65C4⋊Q8×C53C2313yes—
66C4⋊Q8×C53C2313yes—
67C4⋊Q8×C53C2313yes—
68C4⋊Q8×C53C2311yescharacteristic
69#126×C53—26no—
70#125×C53—23no—
71#125×C53—26no—
72#125×C53—23no—
73#125×C53—23no—
74#124×C53—23no—
75#123×C53—26no—
76C22⋊Q8×C53—23no—
77C22⋊Q8×C53—212no—
78C22⋊Q8×C53—23no—
79C22⋊Q8×C53—23no—
80C22⋊Q8×C53C2316yes—
81C22⋊Q8×C53C2316yes—
82#121×C53—23no—
83C4×Q8×C53—23no—
84C4×Q8×C53—23no—
85C4×Q8×C53—23no—
86C4×Q8×C53—21no—
87C4×Q8×C53—22no—
88C4×Q8×C53D411yescharacteristic
89C4×Q8×C53C2311yescharacteristic
90C4×Q8×C53C2313yes—
91C4×Q8×C53C2313yes—
92C4×Q8×C53C2316yes—
93C4×D4×C53—26no—
94C4×D4×C53—23no—
95C4×D4×C53—23no—
96C4×D4×C53D413yes—
97C4×D4×C53C2311yescharacteristic
98C4×D4×C53C2313yes—
99C4×D4×C53C2313yes—
100#117×C53—23no—
101#117×C53—23no—
102#117×C53—23no—
103#117×C53D413yes—
104#117×C53C2313yes—
105C2×C4⋊C4×C53—23no—
106C2×C4⋊C4×C53—23no—
107C2×C4⋊C4×C53C2316yes—
108C2×C42×C53—23no—
109C2×C42×C53C2313yes—
110#107×C53C2316yes—
111#106×C53C2316yes—
112#106×C53C23112yes—
113C4⋊C8×C53C2313yes—
114C4⋊C8×C53C2316yes—
115C4⋊C8×C53C2311yescharacteristic
116#103×C53C2312yes—
117#103×C53C2316yes—
118#103×C53C2316yes—
119#103×C53C23112yes—
120#102×C53C2316yes—
121C22⋊C8×C53C2316yes—
122C4×C8×C53C2316yes—
123#41×C53—24no—
124#41×C53—26no—
125#41×C53—43no—
126C2×Q8×C53—23no—
127C2×Q8×C53—23no—
128C2×Q8×C53—26no—
129C2×Q8×C53—44no—
130C2×Q8×C53—86no—
131C2×Q8×C53C2×D411yescharacteristic
132C2×Q8×C53C2413yes—
133C2×Q8×C53C2412yes—
134C2×D4×C53—23no—
135C2×D4×C53C2×D413yes—
136C2×D4×C53C2411yescharacteristic
137C22×C4×C53—26no—
138C22×C4×C53—21no—
139C22×C4×C53—23no—
140C22×C4×C53—23no—
141C22×C4×C53C2×D413yes—
142C22×C4×C53C2×D413yes—
143C22×C4×C53C2413yes—
144Q16×C53—46no—
145SD16×C53—24no—
146M16×C53—46no—
147C2×C8×C53C2412yes—
148C2×C8×C53C2416yes—
149C4⋊C4×C53—23no—
150C4⋊C4×C53—26no—
151C4⋊C4×C53—23no—
152C4⋊C4×C53—26no—
153C4⋊C4×C53—26no—
154C4⋊C4×C53—21no—
155C4⋊C4×C53—23no—
156C4⋊C4×C53—23no—
157C4⋊C4×C53—23no—
158C4⋊C4×C53—23no—
159C4⋊C4×C53—21no—
160C4⋊C4×C53—26no—
161C4⋊C4×C53—26no—
162C4⋊C4×C53C2×D413yes—
163C4⋊C4×C53C2×D413yes—
164C4⋊C4×C53C2416yes—
165C4⋊C4×C53C2413yes—
166C4⋊C4×C53C2411yescharacteristic
167C22⋊C4×C53—26no—
168C22⋊C4×C53—26no—
169C22⋊C4×C53—23no—
170C22⋊C4×C53—21no—
171C22⋊C4×C53—23no—
172C22⋊C4×C53C2×D416yes—
173C42×C53—23no—
174C42×C53—23no—
175C42×C53—23no—
176C42×C53—26no—
177C42×C53C2×D413yes—
178C42×C53C2×D413yes—
179C42×C53C2413yes—
180C42×C53C2411yescharacteristic
181C23×C53—21no—
182C23×C53C22×D413yes—
183Q8×C53—23no—
184Q8×C53—22no—
185Q8×C53—23no—
186Q8×C53—22no—
187Q8×C53—46no—
188Q8×C53—46no—
189Q8×C53—86no—
190Q8×C53#13714yes—
191D4×C53—26no—
192D4×C53—21no—
193D4×C53—46no—
194D4×C532−1+412yes—
195C2×C4×C53—26no—
196C2×C4×C53—26no—
197C2×C4×C53—23no—
198C2×C4×C53—23no—
199C2×C4×C53—26no—
200C2×C4×C53—23no—
201C2×C4×C53—23no—
202C2×C4×C53—21no—
203C2×C4×C53—22no—
204C2×C4×C53—46no—
205C2×C4×C53—46no—
206C2×C4×C53—42no—
207C2×C4×C53—86no—
208C2×C4×C53C22×D413yes—
209C2×C4×C53C22×D411yescharacteristic
210C2×C4×C53C22×D413yes—
211C2×C4×C53C22×D413yes—
212C2×C4×C53C22×D411yescharacteristic
213C2×C4×C53C2511yescharacteristic
214C8×C53—22no—
215C8×C53—26no—
216#62147C5311yesmaximal, characteristic, direct product factor, Sylow
217C22×C53—23no—
218C22×C53—22no—
219C22×C53—23no—
220C22×C53—23no—
221C22×C53—41no—
222C22×C53—41no—
223C22×C53C23×D411yescharacteristic
224C4×C53—23no—
225C4×C53—21no—
226C4×C53—23no—
227C4×C53—43no—
228C4×C53—42no—
229C4×C53—43no—
230C4×C53—41no—
231C4×C53—46no—
232C4×C53C2×#13716yes—
233C4×C53#57712yes—
234C4×C53C2×2−1+411yescharacteristic
235C4×C53#58511yescharacteristic
236#3503C2×C5311yescharacteristic, complemented
237#3482C2×C5311yescharacteristic
238Q8×SD16C2×C5312yescomplemented
239#3363C2×C5312yescomplemented
240#3356C2×C5316yescomplemented
241#3331C2×C5316yescomplemented
242#3255C2×C5313yescomplemented
243#3229C2×C5313yescomplemented
244#3107C2×C5313yescomplemented
245#3079C2×C5313yescomplemented
246#2991C2×C5311yescharacteristic, complemented
247C2×C53—43no—
248C2×C53—42no—
249C2×C53#348911yescharacteristic
250C2×C53C22×#13711yescharacteristic
251C2×C53C2×#57711yescharacteristic
252Q82C22×C5312yes—
253#557—21no—
254#557C22×C5311yescharacteristic
255#556C22×C5313yes—
256#554C22×C5316yes—
257#552—23no—
258D4×Q8—23no—
259D4×Q8C22×C5311yescharacteristic
260#548—21no—
261#547C22×C5313yes—
262#544—23no—
263#533C22×C5313yes—
264#533C22×C5313yes—
265C2×C4⋊Q8C22×C5313yes—
266#529—23no—
267#520—21no—
268C4×#41C22×C5313yes—
269C4×#41C22×C5311yescharacteristic
270C2×C4×Q8—21no—
271#498C22×C5316yes—
272#487C22×C5316yes—
273#485C22×C5316yes—
274#483C22×C53112yes—
275#477C22×C5316yes—
276#476C22×C5316yes—
277#475C22×C5316yes—
278#475C22×C5316yes—
279#475C22×C5313yes—
280#474C22×C5313yes—
281#470C22×C53112yes—
282#462C22×C5316yes—
283#462C22×C5313yes—
284#461C22×C5311yescharacteristic
285#452C22×C5316yes—
286C8×Q8C22×C5312yes—
287C4×Q16C22×C5316yes—
288C4×SD16C22×C5316yes—
289#436C22×C5316yes—
290#431C22×C5313yes—
291#428C22×C5316yes—
292#423C22×C5313yes—
293#417C22×C5316yes—
294C53#6214711yescharacteristic, direct product factor, Sylow
295C2×#41D4×C5311yescharacteristic
296C2×#41C23×C5313yes—
297C22×Q8—21no—
298C22×Q8—23no—
299C2×Q16C23×C5316yes—
300C2×SD16C23×C5312yes—
301C2×M16C23×C5316yes—
302C4⋊Q8—26no—
303C4⋊Q8—23no—
304C4⋊Q8—23no—
305C4⋊Q8C23×C5311yescharacteristic
306C4⋊Q8C23×C5313yes—
307C4⋊Q8C23×C5313yes—
308C4⋊Q8C23×C5316yes—
309C4⋊Q8C23×C5313yes—
310#126—26no—
311#125—23no—
312#125—26no—
313#125—23no—
314#125—23no—
315#124—23no—
316#123—26no—
317C22⋊Q8—23no—
318C22⋊Q8—23no—
319C22⋊Q8—23no—
320C22⋊Q8—212no—
321C22⋊Q8C23×C5316yes—
322C22⋊Q8C23×C5316yes—
323#121—23no—
324C4×Q8—21no—
325C4×Q8—22no—
326C4×Q8—23no—
327C4×Q8—23no—
328C4×Q8—23no—
329C4×Q8D4×C5311yescharacteristic
330C4×Q8C23×C5313yes—
331C4×Q8C23×C5313yes—
332C4×Q8C23×C5316yes—
333C4×Q8C23×C5311yescharacteristic
334C4×D4—26no—
335C4×D4—23no—
336C4×D4—23no—
337C4×D4D4×C5313yes—
338C4×D4C23×C5311yescharacteristic
339C4×D4C23×C5313yes—
340C4×D4C23×C5313yes—
341#117—23no—
342#117—23no—
343#117—23no—
344#117D4×C5313yes—
345#117C23×C5313yes—
346C2×C4⋊C4—23no—
347C2×C4⋊C4—23no—
348C2×C4⋊C4C23×C5316yes—
349C2×C42—23no—
350C2×C42C23×C5313yes—
351#107C23×C5316yes—
352#106C23×C53112yes—
353#106C23×C5316yes—
354C4⋊C8C23×C5313yes—
355C4⋊C8C23×C5316yes—
356C4⋊C8C23×C5311yescharacteristic
357#103C23×C53112yes—
358#103C23×C5316yes—
359#103C23×C5312yes—
360#103C23×C5316yes—
361#102C23×C5316yes—
362C22⋊C8C23×C5316yes—
363C4×C8C23×C5316yes—
364#41—24no—
365#41—26no—
366#41—43no—
367C2×Q8—23no—
368C2×Q8—23no—
369C2×Q8—26no—
370C2×Q8—44no—
371C2×Q8—86no—
372C2×Q8C2×D4×C5311yescharacteristic
373C2×Q8C24×C5313yes—
374C2×Q8C24×C5312yes—
375C2×D4—23no—
376C2×D4C2×D4×C5313yes—
377C2×D4C24×C5311yescharacteristic
378C22×C4—26no—
379C22×C4—21no—
380C22×C4—23no—
381C22×C4—23no—
382C22×C4C2×D4×C5313yes—
383C22×C4C2×D4×C5313yes—
384C22×C4C24×C5313yes—
385Q16—46no—
386SD16—24no—
387M16—46no—
388C2×C8C24×C5312yes—
389C2×C8C24×C5316yes—
390C4⋊C4—23no—
391C4⋊C4—26no—
392C4⋊C4—23no—
393C4⋊C4—26no—
394C4⋊C4—26no—
395C4⋊C4—21no—
396C4⋊C4—23no—
397C4⋊C4—23no—
398C4⋊C4—23no—
399C4⋊C4—23no—
400C4⋊C4—21no—
401C4⋊C4—26no—
402C4⋊C4—26no—
403C4⋊C4C2×D4×C5313yes—
404C4⋊C4C2×D4×C5313yes—
405C4⋊C4C24×C5316yes—
406C4⋊C4C24×C5313yes—
407C4⋊C4C24×C5311yescharacteristic
408C22⋊C4—26no—
409C22⋊C4—26no—
410C22⋊C4—23no—
411C22⋊C4—21no—
412C22⋊C4—23no—
413C22⋊C4C2×D4×C5316yes—
414C42—23no—
415C42—23no—
416C42—23no—
417C42—26no—
418C42C2×D4×C5313yes—
419C42C2×D4×C5313yes—
420C42C24×C5313yes—
421C42C24×C5311yescharacteristic
422C23—21no—
423C23C22×D4×C5313yes—
424Q8—22no—
425Q8—23no—
426Q8—22no—
427Q8—23no—
428Q8—46no—
429Q8—46no—
430Q8—86no—
431Q8#137×C5314yes—
432D4—26no—
433D4—21no—
434D4—46no—
435D42−1+4×C5312yes—
436C2×C4—26no—
437C2×C4—26no—
438C2×C4—23no—
439C2×C4—23no—
440C2×C4—21no—
441C2×C4—22no—
442C2×C4—23no—
443C2×C4—23no—
444C2×C4—26no—
445C2×C4—46no—
446C2×C4—46no—
447C2×C4—42no—
448C2×C4—86no—
449C2×C4C22×D4×C5313yes—
450C2×C4C22×D4×C5311yescharacteristic
451C2×C4C22×D4×C5313yes—
452C2×C4C22×D4×C5313yes—
453C2×C4C22×D4×C5311yescharacteristic
454C2×C4C25×C5311yescharacteristic
455C8—22no—
456C8—26no—
457C22—23no—
458C22—22no—
459C22—23no—
460C22—23no—
461C22—41no—
462C22—41no—
463C22C23×D4×C5311yescharacteristic
464C4—23no—
465C4—21no—
466C4—23no—
467C4—43no—
468C4—42no—
469C4—43no—
470C4—41no—
471C4—46no—
472C4C2×#137×C5316yes—
473C4C53×#57712yes—
474C4C2×2−1+4×C5311yescharacteristic
475C4C53×#58511yescharacteristic
476C2—43no—
477C2—42no—
478C2C53×#348911yescharacteristic
479C2C22×#137×C5311yescharacteristic
480C2C2×C53×#57711yescharacteristic
subgroupG/H
center, socleC22×C53C23×D4
commutator, Frattini, cosocleC2×C4C25×C53
prime radicalC53×#3482C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C53 ◁ C4×#41×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C53×#3503C2semidirect
3. Q8×SD16×C53C2semidirect
4. C53×#3363C2semidirect
5. C53×#3356C2semidirect
6. C53×#3331C2semidirect
7. C53×#3255C2semidirect
8. C53×#3229C2semidirect
9. C53×#3107C2semidirect
10. C53×#3079C2semidirect
11. C53×#2991C2semidirect
216. #62147C53direct (N × H)
236. #3503C2×C53semidirect
238. Q8×SD16C2×C53semidirect
239. #3363C2×C53semidirect
240. #3356C2×C53semidirect
241. #3331C2×C53semidirect
242. #3255C2×C53semidirect
243. #3229C2×C53semidirect
244. #3107C2×C53semidirect
245. #3079C2×C53semidirect
246. #2991C2×C53semidirect
294. C53#62147direct (N × H)

Maximal subgroups

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

subgroupindex
C53×#35032
C53×#34822
Q8×SD16×C532
C53×#33632
C53×#33562
C53×#33312
C53×#32552
C53×#32292
C53×#31072
C53×#30792
C53×#29912
#6214753