Finite Group Databasebeta

← C53×#13073 #27220585

Subgroups — C53×#13073 #27220585

Order 13568.

478 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#504C211yesmaximal, characteristic, complemented
2C2×C53×#472C211yesmaximal, characteristic
3C2×C53×#361C211yesmaximal, characteristic, complemented
4C2×C53×#357C211yesmaximal, characteristic, complemented
5C53×#1816C211yesmaximal, characteristic, complemented
6C53×#1387C211yesmaximal, characteristic, complemented
7C53×#1381C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C53—21no—
9C22×D8×C53C2211yescharacteristic
10C2×#131×C53C2211yescharacteristic
11C53×#504—22no—
12C53×#504—22no—
13C2×M32×C53—21no—
14C2×M32×C53C2211yescharacteristic
15C22×C16×C53—21no—
16C22×C16×C53C2211yescharacteristic
17C53×#472—22no—
18C53×#472C414yescomplemented
19C2×#108×C53C2211yescharacteristic
20C2×#108×C53C2211yescharacteristic
21C2×#107×C53C2211yescharacteristic
22C53×#417—21no—
23C2×#100×C53—21no—
24C53×#361—22no—
25C53×#357—21no—
26C53×#357—21no—
27C53×#343—21no—
28C2×#41×C53D411yescharacteristic
29C22×D4×C53—21no—
30AGL(1,ℤ/8)×C53—24no—
31AGL(1,ℤ/8)×C53—42no—
32C2×SD16×C53—41no—
33C2×D8×C53—21no—
34C2×D8×C53—21no—
35C2×D8×C53—21no—
36C2×D8×C53—21no—
37C2×D8×C53—21no—
38C2×D8×C53—41no—
39C2×D8×C53C2×C412yes—
40#131×C53—21no—
41#131×C53—21no—
42#131×C53C2×C412yes—
43#131×C53D412yes—
44C2×M16×C53—21no—
45C2×M16×C53—21no—
46C2×M16×C53—21no—
47C2×M16×C53D411yescharacteristic
48C22×C8×C53—21no—
49C22×C8×C53C2311yescharacteristic
50C2×C4⋊C4×C53—21no—
51M32×C53—24no—
52M32×C53—21no—
53M32×C53D412yes—
54C2×C16×C53—24no—
55C2×C16×C53—21no—
56C2×C16×C53—21no—
57C2×C16×C53—21no—
58C2×C16×C53D411yescharacteristic
59C2×C16×C53D411yescharacteristic
60#108×C53—21no—
61#108×C53—21no—
62#108×C53—21no—
63#108×C53C2×C412yes—
64#107×C53—21no—
65#107×C53—21no—
66#103×C53—41no—
67#102×C53—41no—
68#100×C53—24no—
69C24×C53—41no—
70#41×C53—21no—
71#41×C53—21no—
72#41×C53C22⋊C412yes—
73#41×C53SD1612yes—
74C2×Q8×C53D811yescharacteristic
75C2×D4×C53—21no—
76C2×D4×C53—22no—
77C2×D4×C53—41no—
78C2×D4×C53—41no—
79C2×D4×C53—41no—
80C2×D4×C53—41no—
81C2×D4×C53—41no—
82C2×D4×C53D811yescharacteristic
83C22×C4×C53—21no—
84C22×C4×C53—41no—
85C22×C4×C53C2×D411yescharacteristic
86SD16×C53—44no—
87D8×C53—22no—
88D8×C53—22no—
89D8×C53—44no—
90D8×C53—41no—
91D8×C53—41no—
92M16×C53—21no—
93M16×C53—22no—
94M16×C53—22no—
95M16×C53—22no—
96M16×C53—41no—
97M16×C53—41no—
98M16×C53—41no—
99M16×C53C22⋊C412yes—
100C2×C8×C53—21no—
101C2×C8×C53—22no—
102C2×C8×C53—22no—
103C2×C8×C53—41no—
104C2×C8×C53—41no—
105C2×C8×C53C22×C411yescharacteristic
106C2×C8×C53C2×D411yescharacteristic
107C2×C8×C53C2×D411yescharacteristic
108C2×C8×C53C2×D411yescharacteristic
109C2×C8×C53#4111yescharacteristic
110C2×C8×C53#4111yescharacteristic
111C4⋊C4×C53—41no—
112C4⋊C4×C53—41no—
113C16×C53—21no—
114C16×C53—22no—
115C16×C53—21no—
116C23×C53—21no—
117C23×C53—42no—
118C23×C53—81no—
119C23×C53—81no—
120C23×C53—161no—
121C23×C53—161no—
122C23×C53#13511yescharacteristic
123Q8×C53—21no—
124Q8×C53#10212yes—
125D4×C53—22no—
126D4×C53—22no—
127D4×C53—21no—
128D4×C53—42no—
129D4×C53—42no—
130D4×C53—81no—
131D4×C53—81no—
132D4×C53#10212yes—
133C2×C4×C53—21no—
134C2×C4×C53—22no—
135C2×C4×C53—22no—
136C2×C4×C53—81no—
137C2×C4×C53—161no—
138C2×C4×C53C2×C22⋊C411yescharacteristic
139C2×C4×C53#12111yescharacteristic
140C2×C4×C53#12111yescharacteristic
141C2×C4×C53C2×D811yescharacteristic
142C2×C4×C53C2×SD1611yescharacteristic
143C2×C4×C53#13511yescharacteristic
144C8×C53—22no—
145C8×C53—42no—
146C8×C53—81no—
147C8×C53C4×D411yescharacteristic
148C8×C53C4×D411yescharacteristic
149C8×C53#12011yescharacteristic
150C8×C53#12311yescharacteristic
151#13073C5311yesmaximal, characteristic, direct product factor, Sylow
152C22×C53—21no—
153C22×C53—21no—
154C22×C53—22no—
155C22×C53—41no—
156C22×C53—41no—
157C22×C53—82no—
158C22×C53—162no—
159C22×C53—162no—
160C22×C53—161no—
161C22×C53—161no—
162C22×C53#41611yescharacteristic
163C22×C53#46511yescharacteristic
164C22×C53#46611yescharacteristic
165C4×C53—22no—
166C4×C53—161no—
167C4×C53#38611yescharacteristic
168C4×C53C2×#10211yescharacteristic
169C4×C53#46511yescharacteristic
170C4×C53#46611yescharacteristic
171C2×#504C2×C5311yescharacteristic, complemented
172C2×#472C2×C5311yescharacteristic
173C2×#361C2×C5311yescharacteristic, complemented
174C2×#357C2×C5311yescharacteristic, complemented
175#1816C2×C5311yescharacteristic, complemented
176#1387C2×C5311yescharacteristic, complemented
177#1381C2×C5311yescharacteristic, complemented
178C2×C53—21no—
179C2×C53—21no—
180C2×C53—42no—
181C2×C53—162no—
182C2×C53#189311yescharacteristic
183C2×C53#222111yescharacteristic
184C2×C53#222311yescharacteristic
185C2×AGL(1,ℤ/8)—21no—
186C22×D8C22×C5311yescharacteristic
187C2×#131C22×C5311yescharacteristic
188#504—22no—
189#504—22no—
190C2×M32—21no—
191C2×M32C22×C5311yescharacteristic
192C22×C16—21no—
193C22×C16C22×C5311yescharacteristic
194#472—22no—
195#472C4×C5314yescomplemented
196C2×#108C22×C5311yescharacteristic
197C2×#108C22×C5311yescharacteristic
198C2×#107C22×C5311yescharacteristic
199#417—21no—
200C2×#100—21no—
201#361—22no—
202#357—21no—
203#357—21no—
204#343—21no—
205C53#1307311yescharacteristic, direct product factor, Sylow
206C2×#41D4×C5311yescharacteristic
207C22×D4—21no—
208AGL(1,ℤ/8)—24no—
209AGL(1,ℤ/8)—42no—
210C2×SD16—41no—
211C2×D8—21no—
212C2×D8—21no—
213C2×D8—21no—
214C2×D8—21no—
215C2×D8—21no—
216C2×D8—41no—
217C2×D8C2×C4×C5312yes—
218#131—21no—
219#131—21no—
220#131C2×C4×C5312yes—
221#131D4×C5312yes—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16—21no—
225C2×M16D4×C5311yescharacteristic
226C22×C8—21no—
227C22×C8C23×C5311yescharacteristic
228C2×C4⋊C4—21no—
229M32—24no—
230M32—21no—
231M32D4×C5312yes—
232C2×C16—24no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16—21no—
236C2×C16D4×C5311yescharacteristic
237C2×C16D4×C5311yescharacteristic
238#108—21no—
239#108—21no—
240#108—21no—
241#108C2×C4×C5312yes—
242#107—21no—
243#107—21no—
244#103—41no—
245#102—41no—
246#100—24no—
247C24—41no—
248#41—21no—
249#41—21no—
250#41C22⋊C4×C5312yes—
251#41SD16×C5312yes—
252C2×Q8D8×C5311yescharacteristic
253C2×D4—21no—
254C2×D4—22no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4D8×C5311yescharacteristic
261C22×C4—21no—
262C22×C4—41no—
263C22×C4C2×D4×C5311yescharacteristic
264SD16—44no—
265D8—22no—
266D8—22no—
267D8—44no—
268D8—41no—
269D8—41no—
270M16—21no—
271M16—22no—
272M16—22no—
273M16—22no—
274M16—41no—
275M16—41no—
276M16—41no—
277M16C22⋊C4×C5312yes—
278C2×C8—21no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8C22×C4×C5311yescharacteristic
284C2×C8C2×D4×C5311yescharacteristic
285C2×C8C2×D4×C5311yescharacteristic
286C2×C8C2×D4×C5311yescharacteristic
287C2×C8#41×C5311yescharacteristic
288C2×C8#41×C5311yescharacteristic
289C4⋊C4—41no—
290C4⋊C4—41no—
291C16—21no—
292C16—22no—
293C16—21no—
294C23—21no—
295C23—42no—
296C23—81no—
297C23—81no—
298C23—161no—
299C23—161no—
300C23#135×C5311yescharacteristic
301Q8—21no—
302Q8#102×C5312yes—
303D4—22no—
304D4—22no—
305D4—21no—
306D4—42no—
307D4—42no—
308D4—81no—
309D4—81no—
310D4#102×C5312yes—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—81no—
315C2×C4—161no—
316C2×C4C2×C22⋊C4×C5311yescharacteristic
317C2×C4#121×C5311yescharacteristic
318C2×C4#121×C5311yescharacteristic
319C2×C4C2×D8×C5311yescharacteristic
320C2×C4C2×SD16×C5311yescharacteristic
321C2×C4#135×C5311yescharacteristic
322C8—22no—
323C8—42no—
324C8—81no—
325C8C4×D4×C5311yescharacteristic
326C8C4×D4×C5311yescharacteristic
327C8#120×C5311yescharacteristic
328C8#123×C5311yescharacteristic
329C22—21no—
330C22—21no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—82no—
335C22—162no—
336C22—162no—
337C22—161no—
338C22—161no—
339C22C53×#41611yescharacteristic
340C22C53×#46511yescharacteristic
341C22C53×#46611yescharacteristic
342C4—22no—
343C4—161no—
344C4C53×#38611yescharacteristic
345C4C2×#102×C5311yescharacteristic
346C4C53×#46511yescharacteristic
347C4C53×#46611yescharacteristic
348C2—21no—
349C2—21no—
350C2—42no—
351C2—162no—
352C2C53×#189311yescharacteristic
353C2C53×#222111yescharacteristic
354C2C53×#222311yescharacteristic
subgroupG/H
center, socleC22×C53#466
commutatorC2×C8C22×C4×C53
Frattini, cosocleC22×C8C23×C53
prime radicalC2×C53×#472C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C53 ◁ C22×C4×C53 ◁ C2×#131×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C53×#504C2semidirect
3. C2×C53×#361C2semidirect
4. C2×C53×#357C2semidirect
5. C53×#1816C2semidirect
6. C53×#1387C2semidirect
7. C53×#1381C2semidirect
18. C53×#472C4semidirect
151. #13073C53direct (N × H)
171. C2×#504C2×C53semidirect
173. C2×#361C2×C53semidirect
174. C2×#357C2×C53semidirect
175. #1816C2×C53semidirect
176. #1387C2×C53semidirect
177. #1381C2×C53semidirect
195. #472C4×C53semidirect
205. C53#13073direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C53×#5042
C2×C53×#4722
C2×C53×#3612
C2×C53×#3572
C53×#18162
C53×#13872
C53×#13812
#1307353