Finite Group Databasebeta

← C53×#13395 #27220907

Subgroups — C53×#13395 #27220907

Order 13568.

422 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3050C211yesmaximal, characteristic
2C53×#2155C211yesmaximal, characteristic, complemented
3C53×#2148C211yesmaximal, characteristic, complemented
4C53×#2143C211yesmaximal, characteristic, complemented
5C53×#2112C211yesmaximal, characteristic, complemented
6C53×#1810C211yesmaximal, characteristic, complemented
7C53×#1389C211yesmaximal, characteristic, complemented
8C2×#135×C53C2211yescharacteristic
9C23×C8×C53C2211yescharacteristic
10C53×#525—21no—
11C2×M32×C53C2211yescharacteristic
12C2×M32×C53C2211yescharacteristic
13C53×#467—21no—
14C53×#466—21no—
15C53×#465—22no—
16C2×#108×C53C2211yescharacteristic
17C2×#108×C53C2211yescharacteristic
18C53×#427C2211yescharacteristic
19C53×#416—21no—
20C53×#407—21no—
21C53×#365—22no—
22C53×#362—21no—
23C53×#361—21no—
24C53×#359—22no—
25C53×C22⋊C16—22no—
26C53×#341—21no—
27C2×#41×C53—21no—
28C23×C4×C53D411yescharacteristic
29#135×C53—21no—
30#135×C53—21no—
31#135×C53—21no—
32#135×C53—21no—
33C2×Q16×C53D411yescharacteristic
34C2×SD16×C53—21no—
35C2×D8×C53D411yescharacteristic
36C2×M16×C53—21no—
37C2×M16×C53—21no—
38C22×C8×C53—21no—
39C22×C8×C53—21no—
40C22×C8×C53—21no—
41C22×C8×C53—21no—
42C22×C8×C53—21no—
43C22×C8×C53—21no—
44C22×C8×C53D411yescharacteristic
45C22×C8×C53C2311yescharacteristic
46#123×C53—41no—
47C22⋊Q8×C53—22no—
48#121×C53—22no—
49#120×C53—41no—
50C4×D4×C53—42no—
51#117×C53—21no—
52M32×C53—21no—
53M32×C53—21no—
54M32×C53—21no—
55M32×C53—21no—
56C2×C16×C53—21no—
57C2×C16×C53D412yescomplemented
58#108×C53—21no—
59#108×C53—21no—
60#108×C53—21no—
61#108×C53—21no—
62#107×C53—21no—
63#106×C53D412yes—
64#103×C53—22no—
65#102×C53—22no—
66C22⋊C8×C53—42no—
67C24×C53SD1611yescharacteristic
68#41×C53—41no—
69#41×C53—41no—
70#41×C53—41no—
71#41×C53—41no—
72C2×Q8×C53—21no—
73C2×D4×C53—21no—
74C2×D4×C53—42no—
75C2×D4×C53—41no—
76C22×C4×C53—21no—
77C22×C4×C53—21no—
78C22×C4×C53—21no—
79C22×C4×C53—21no—
80C22×C4×C53—21no—
81C22×C4×C53—21no—
82C22×C4×C53—41no—
83C22×C4×C53SD1611yescharacteristic
84C22×C4×C53C2×D411yescharacteristic
85Q16×C53—21no—
86Q16×C53—21no—
87SD16×C53—41no—
88SD16×C53—41no—
89D8×C53—21no—
90D8×C53—21no—
91M16×C53—41no—
92M16×C53—41no—
93M16×C53—41no—
94M16×C53—41no—
95C2×C8×C53—21no—
96C2×C8×C53—21no—
97C2×C8×C53—21no—
98C2×C8×C53—41no—
99C2×C8×C53—41no—
100C2×C8×C53—41no—
101C2×C8×C53—41no—
102C2×C8×C53—41no—
103C2×C8×C53—41no—
104C2×C8×C53C2×D411yescharacteristic
105C2×C8×C53C2×D411yescharacteristic
106C2×C8×C53C2×D411yescharacteristic
107C2×C8×C53#4111yescharacteristic
108C2×C8×C53#4111yescharacteristic
109C2×C8×C53#4111yescharacteristic
110C4⋊C4×C53—22no—
111C4⋊C4×C53—42no—
112C22⋊C4×C53—42no—
113C22⋊C4×C53—42no—
114C22⋊C4×C53—41no—
115C42×C53—41no—
116C16×C53—22no—
117C16×C53—41no—
118C23×C53—21no—
119C23×C53—21no—
120C23×C53—21no—
121C23×C53—42no—
122C23×C53—41no—
123C23×C53C2×SD1611yescharacteristic
124Q8×C53—41no—
125Q8×C53—41no—
126D4×C53—41no—
127D4×C53—41no—
128D4×C53—84no—
129D4×C53—81no—
130D4×C53—81no—
131C2×C4×C53—21no—
132C2×C4×C53—21no—
133C2×C4×C53—21no—
134C2×C4×C53—41no—
135C2×C4×C53—41no—
136C2×C4×C53—41no—
137C2×C4×C53—41no—
138C2×C4×C53—41no—
139C2×C4×C53—42no—
140C2×C4×C53—81no—
141C2×C4×C53—81no—
142C2×C4×C53#12011yescharacteristic
143C2×C4×C53#12111yescharacteristic
144C2×C4×C53#12311yescharacteristic
145C2×C4×C53#13511yescharacteristic
146C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
148C8×C53—41no—
149C8×C53—81no—
150C8×C53—81no—
151C8×C53#12111yescharacteristic
152C8×C53#12111yescharacteristic
153C8×C53#12311yescharacteristic
154C8×C53#12411yescharacteristic
155#13395C5311yesmaximal, characteristic, direct product factor, Sylow
156C22×C53—22no—
157C22×C53—22no—
158C22×C53—22no—
159C22×C53—41no—
160C22×C53—41no—
161C22×C53—41no—
162C22×C53—41no—
163C22×C53—41no—
164C22×C53—82no—
165C22×C53—81no—
166C22×C53#45011yescharacteristic
167C22×C53#46511yescharacteristic
168C22×C53#48111yescharacteristic
169C4×C53—41no—
170C4×C53—82no—
171C4×C53—81no—
172C4×C53#39411yescharacteristic
173C4×C53#44911yescharacteristic
174C4×C53#46911yescharacteristic
175C4×C53#48211yescharacteristic
176#3050C2×C5311yescharacteristic
177#2155C2×C5311yescharacteristic, complemented
178#2148C2×C5311yescharacteristic, complemented
179#2143C2×C5311yescharacteristic, complemented
180#2112C2×C5311yescharacteristic, complemented
181#1810C2×C5311yescharacteristic, complemented
182#1389C2×C5311yescharacteristic, complemented
183C2×C53—21no—
184C2×C53—21no—
185C2×C53—21no—
186C2×C53—42no—
187C2×C53—161no—
188C2×C53#203411yescharacteristic
189C2×#135C22×C5311yescharacteristic
190C23×C8C22×C5311yescharacteristic
191#525—21no—
192C2×M32C22×C5311yescharacteristic
193C2×M32C22×C5311yescharacteristic
194#467—21no—
195#466—21no—
196#465—22no—
197C2×#108C22×C5311yescharacteristic
198C2×#108C22×C5311yescharacteristic
199#427C22×C5311yescharacteristic
200#416—21no—
201#407—21no—
202#365—22no—
203#362—21no—
204#361—21no—
205#359—22no—
206C22⋊C16—22no—
207#341—21no—
208C53#1339511yescharacteristic, direct product factor, Sylow
209C2×#41—21no—
210C23×C4D4×C5311yescharacteristic
211#135—21no—
212#135—21no—
213#135—21no—
214#135—21no—
215C2×Q16D4×C5311yescharacteristic
216C2×SD16—21no—
217C2×D8D4×C5311yescharacteristic
218C2×M16—21no—
219C2×M16—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8D4×C5311yescharacteristic
227C22×C8C23×C5311yescharacteristic
228#123—41no—
229C22⋊Q8—22no—
230#121—22no—
231#120—41no—
232C4×D4—42no—
233#117—21no—
234M32—21no—
235M32—21no—
236M32—21no—
237M32—21no—
238C2×C16—21no—
239C2×C16D4×C5312yescomplemented
240#108—21no—
241#108—21no—
242#108—21no—
243#108—21no—
244#107—21no—
245#106D4×C5312yes—
246#103—22no—
247#102—22no—
248C22⋊C8—42no—
249C24SD16×C5311yescharacteristic
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254C2×Q8—21no—
255C2×D4—21no—
256C2×D4—42no—
257C2×D4—41no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4SD16×C5311yescharacteristic
266C22×C4C2×D4×C5311yescharacteristic
267Q16—21no—
268Q16—21no—
269SD16—41no—
270SD16—41no—
271D8—21no—
272D8—21no—
273M16—41no—
274M16—41no—
275M16—41no—
276M16—41no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8C2×D4×C5311yescharacteristic
287C2×C8C2×D4×C5311yescharacteristic
288C2×C8C2×D4×C5311yescharacteristic
289C2×C8#41×C5311yescharacteristic
290C2×C8#41×C5311yescharacteristic
291C2×C8#41×C5311yescharacteristic
292C4⋊C4—22no—
293C4⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—41no—
297C42—41no—
298C16—22no—
299C16—41no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—42no—
304C23—41no—
305C23C2×SD16×C5311yescharacteristic
306Q8—41no—
307Q8—41no—
308D4—41no—
309D4—41no—
310D4—84no—
311D4—81no—
312D4—81no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4#120×C5311yescharacteristic
325C2×C4#121×C5311yescharacteristic
326C2×C4#123×C5311yescharacteristic
327C2×C4#135×C5311yescharacteristic
328C2×C4AGL(1,ℤ/8)×C5311yescharacteristic
329C2×C4AGL(1,ℤ/8)×C5311yescharacteristic
330C8—41no—
331C8—81no—
332C8—81no—
333C8#121×C5311yescharacteristic
334C8#121×C5311yescharacteristic
335C8#123×C5311yescharacteristic
336C8#124×C5311yescharacteristic
337C22—22no—
338C22—22no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—82no—
346C22—81no—
347C22C53×#45011yescharacteristic
348C22C53×#46511yescharacteristic
349C22C53×#48111yescharacteristic
350C4—41no—
351C4—82no—
352C4—81no—
353C4C53×#39411yescharacteristic
354C4C53×#44911yescharacteristic
355C4C53×#46911yescharacteristic
356C4C53×#48211yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—42no—
361C2—161no—
362C2C53×#203411yescharacteristic
subgroupG/H
centerC4×C53#469
commutator, Frattini, cosocleC22×C8C23×C53
socleC2×C53#2034
prime radicalC53×#3050C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C53 ◁ C22×C4×C53 ◁ C23×C8×C53 ◁ G

Complements

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

NH ≅ G/Ntype
2. C53×#2155C2semidirect
3. C53×#2148C2semidirect
4. C53×#2143C2semidirect
5. C53×#2112C2semidirect
6. C53×#1810C2semidirect
7. C53×#1389C2semidirect
57. C2×C16×C53D4semidirect
155. #13395C53direct (N × H)
177. #2155C2×C53semidirect
178. #2148C2×C53semidirect
179. #2143C2×C53semidirect
180. #2112C2×C53semidirect
181. #1810C2×C53semidirect
182. #1389C2×C53semidirect
208. C53#13395direct (N × H)
239. C2×C16D4×C53semidirect

Maximal subgroups

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

subgroupindex
C53×#30502
C53×#21552
C53×#21482
C53×#21432
C53×#21122
C53×#18102
C53×#13892
#1339553