Finite Group Databasebeta

← #455×D157 #34109463

Subgroups — #455×D157 #34109463

Order 20096.

760 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 135 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
1H(5,𝔽2)×D157C211yesmaximal, characteristic
2#137×D157C212yesmaximal, complemented
3#124×D157C211yesmaximal, characteristic, complemented
4#23757453C211yesmaximal, characteristic, complemented
5#23757452C212yesmaximal, complemented
6#23757451C211yesmaximal, characteristic, complemented
7#23757450C211yesmaximal, characteristic, complemented
8#23757449C212yesmaximal, complemented
9#104×D157C212yesmaximal, complemented
10#100×D157C211yesmaximal, characteristic, complemented
11#455×C157C211yesmaximal, characteristic, complemented
12#19097817—22no—
13#19097817C2212yes—
14#19097816—22no—
15#19097816—22no—
16#19097816C2211yescharacteristic
17#41×D157—22no—
18#41×D157C2212yes—
19C2×Q8×D157C2211yescharacteristic, complemented
20C2×D4×D157—22no—
21C2×D4×D157—22no—
22C2×D4×D157C2211yescharacteristic
23#19097804C2212yescomplemented
24#19097803—22no—
25#19097802C2212yescomplemented
26#19097801C2212yescomplemented
27#19097800—22no—
28Q16×D157—22no—
29SD16×D157—22no—
30M16×D157C2212yescomplemented
31#19097760C2211yescharacteristic, complemented
32#19097759C2211yescharacteristic, complemented
33#19097758C2211yescharacteristic, complemented
34#19097757—22no—
35C22⋊C4×D157—22no—
36C42×D157C2211yescharacteristic, complemented
37#19097699C2212yescomplemented
38#19097698C2212yescomplemented
39#19097697C2212yescomplemented
40#19097688C2211yescharacteristic, complemented
41#19097687C2212yescomplemented
42H(5,𝔽2)×C157C2211yescharacteristic
43#137×C157C2212yescomplemented
44#124×C157C2211yescharacteristic, complemented
45#104×C157C2212yescomplemented
46#100×C157C2211yescharacteristic, complemented
47C23×D157—22no—
48C23×D157D412yes—
49#14578955—22no—
50#14578955D412yes—
51#14578954—24no—
52#14578954—22no—
53#14578954—22no—
54#14578954C2312yes—
55#14578953—24no—
56#14578953—22no—
57#14578953—22no—
58#14578953D412yes—
59C2×Dic314—21no—
60C2×Dic314C2311yescharacteristic, complemented
61Q8×D157—22no—
62Q8×D157—22no—
63Q8×D157D412yes—
64C2×D628—22no—
65C2×D628—22no—
66C2×D628C2311yescharacteristic
67C2×C22⋊D157—22no—
68C2×C22⋊D157—24no—
69C2×C22⋊D157—22no—
70C2×C22⋊D157D412yes—
71D4×D157—24no—
72D4×D157—24no—
73D4×D157—24no—
74D4×D157—22no—
75D4×D157—24no—
76D4×D157—22no—
77D4×D157—22no—
78D4×D157—22no—
79D4×D157—22no—
80D4×D157D412yes—
81C2×C4×D157—22no—
82C2×C4×D157—22no—
83C2×C4×D157—21no—
84C2×C4×D157—21no—
85C2×C4×D157C2311yescharacteristic
86Dic628—22no—
87#14578944—22no—
88#14578944—22no—
89#14578943—22no—
90#14578942—22no—
91#14578941—22no—
92#14578938C2312yescomplemented
93#14578937—22no—
94C8×D157—22no—
95C22⋊Dic157—22no—
96#14578931—22no—
97#14578931—22no—
98C4×Dic157—21no—
99C4×Dic157C2311yescharacteristic, complemented
100#41×C157—22no—
101#41×C157C2312yes—
102C2×Q8×C157C2311yescharacteristic, complemented
103C2×D4×C157—22no—
104C2×D4×C157—22no—
105C2×D4×C157C2311yescharacteristic
106Q16×C157—22no—
107SD16×C157—22no—
108M16×C157C2312yescomplemented
109C22⋊C4×C157—22no—
110C42×C157C2311yescharacteristic, complemented
111C22×D157—24no—
112C22×D157—22no—
113C22×D157—22no—
114C22×D157—22no—
115C22×D157—22no—
116C22×D157—44no—
117C22×D157—84no—
118C22×D157C2×D411yescharacteristic
119C22×D157C2×D412yes—
120Dic314—22no—
121Dic314—22no—
122Dic314—42no—
123Dic314C2×D412yes—
124D628—24no—
125D628—22no—
126D628—22no—
127D628C2×D412yes—
128C22⋊D157—24no—
129C22⋊D157—24no—
130C22⋊D157—22no—
131C22⋊D157—22no—
132C22⋊D157—24no—
133C22⋊D157—22no—
134C2×Dic157—22no—
135C2×Dic157—22no—
136C2×Dic157—21no—
137C2×Dic157—21no—
138C2×Dic157C2×D411yescharacteristic
139C4×D157—24no—
140C4×D157—22no—
141C4×D157—22no—
142C4×D157—22no—
143C4×D157—42no—
144C4×D157—41no—
145C4×D157—41no—
146C4×D157C2×D412yes—
147C4×D157C2×D412yes—
148#11929434—22no—
149C23×C157—22no—
150C23×C157C2×D412yes—
151Q8×C157—22no—
152Q8×C157C2×D412yes—
153D4×C157—24no—
154D4×C157—22no—
155D4×C157—22no—
156D4×C157C2×D412yes—
157C2×C4×C157—22no—
158C2×C4×C157—22no—
159C2×C4×C157—21no—
160C2×C4×C157—21no—
161C2×C4×C157C2411yescharacteristic
162C8×C157—22no—
163C22×C157—22no—
164C22×C157—22no—
165C22×C157—42no—
166C22×C157—82no—
167C22×C157C22×D411yescharacteristic
168C2×D157—22no—
169C2×D157—22no—
170C2×D157—22no—
171C2×D157—44no—
172C2×D157—44no—
173C2×D157—42no—
174C2×D157—82no—
175C2×D157—84no—
176C2×D157—82no—
177C2×D157#12011yescharacteristic
178C2×D157#12011yescharacteristic
179C4×C157—22no—
180C4×C157—41no—
181C4×C157—41no—
182C4×C157C22×D412yes—
183Dic157—22no—
184Dic157—41no—
185Dic157—41no—
186Dic157#12012yes—
187C2×C157—21no—
188C2×C157—42no—
189C2×C157—42no—
190C2×C157C2×#12011yescharacteristic
191D157—21no—
192D157—42no—
193D157—42no—
194D157#45512yesdirect product factor
195C157C2×#45511yescharacteristic, complemented, Sylow
196C2×#455—1571nomaximal, Sylow
197C2×H(5,𝔽2)—1571no—
198C2×#137—1572no—
199C2×#124—1571no—
200#455—1571no—
201#455—1572no—
202#455—1571no—
203#455—1572no—
204#455—1571no—
205#455D15711yescharacteristic, direct product factor
206C2×#104—1572no—
207C2×#100—1571no—
208H(5,𝔽2)—3142no—
209H(5,𝔽2)—3142no—
210H(5,𝔽2)—3142no—
211H(5,𝔽2)—1572no—
212H(5,𝔽2)—1571no—
213H(5,𝔽2)C2×D15711yescharacteristic
214C2×#41—3142no—
215C2×#41—1572no—
216C22×Q8—1571no—
217C22×D4—3142no—
218C22×D4—3142no—
219C22×D4—1571no—
220#137—3142no—
221#137—3142no—
222#137—1572no—
223#137—1572no—
224#137—1572no—
225#137C2×D15712yescomplemented
226C2×Q16—3142no—
227C2×SD16—3142no—
228C2×M16—1572no—
229#124—3142no—
230#124—1571no—
231#124—1571no—
232#124—1571no—
233#124C2×D15711yescharacteristic, complemented
234C2×C22⋊C4—3142no—
235C2×C42—1571no—
236#104—1572no—
237#104—1572no—
238#104—1572no—
239#104C2×D15712yescomplemented
240#100—1571no—
241#100—1572no—
242#100C2×D15711yescharacteristic, complemented
243C24—3142no—
244C24—1572no—
245#41—22no—
246#41—3144no—
247#41—3142no—
248#41—3142no—
249#41—3144no—
250#41—3142no—
251#41—3142no—
252#41—3142no—
253#41—1572no—
254#41—1572no—
255#41—1572no—
256#41C22×D15712yes—
257C2×Q8—3141no—
258C2×Q8—3142no—
259C2×Q8—3142no—
260C2×Q8—1572no—
261C2×Q8—1571no—
262C2×Q8C22×D15711yescharacteristic, complemented
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—3142no—
266C2×D4—3142no—
267C2×D4—3144no—
268C2×D4—3144no—
269C2×D4—3144no—
270C2×D4—3142no—
271C2×D4—3144no—
272C2×D4—3142no—
273C2×D4—3142no—
274C2×D4—3144no—
275C2×D4—3142no—
276C2×D4—3142no—
277C2×D4—3142no—
278C2×D4—3142no—
279C2×D4—1572no—
280C2×D4—1572no—
281C2×D4—1571no—
282C2×D4C22×D15711yescharacteristic
283C22×C4—3142no—
284C22×C4—3142no—
285C22×C4—3141no—
286C22×C4—3141no—
287C22×C4—1571no—
288Q16—22no—
289Q16—3142no—
290Q16—3142no—
291Q16—3142no—
292SD16—22no—
293SD16—3142no—
294SD16—3142no—
295SD16—3142no—
296M16—3142no—
297M16—1572no—
298M16C22×D15712yescomplemented
299C2×C8—3142no—
300C22⋊C4—22no—
301C22⋊C4—3142no—
302C22⋊C4—3142no—
303C22⋊C4—3142no—
304C42—3141no—
305C42—1571no—
306C42C22×D15711yescharacteristic, complemented
307C23—22no—
308C23—3142no—
309C23—3144no—
310C23—3142no—
311C23—3142no—
312C23—3142no—
313C23—6284no—
314C23—1571no—
315C23—1572no—
316C23—12564no—
317C23D4×D15712yes—
318Q8—22no—
319Q8—3142no—
320Q8—3142no—
321Q8—6282no—
322Q8—1572no—
323Q8D4×D15712yes—
324D4—24no—
325D4—22no—
326D4—22no—
327D4—3144no—
328D4—3142no—
329D4—3144no—
330D4—3144no—
331D4—3142no—
332D4—3142no—
333D4—3144no—
334D4—3142no—
335D4—3142no—
336D4—1572no—
337D4D4×D15712yes—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—3144no—
343C2×C4—3142no—
344C2×C4—3142no—
345C2×C4—3142no—
346C2×C4—3142no—
347C2×C4—3142no—
348C2×C4—3141no—
349C2×C4—3141no—
350C2×C4—6282no—
351C2×C4—6281no—
352C2×C4—6281no—
353C2×C4—1571no—
354C2×C4—1572no—
355C2×C4—1572no—
356C2×C4C23×D15711yescharacteristic
357C8—22no—
358C8—3142no—
359C22—22no—
360C22—22no—
361C22—42no—
362C22—82no—
363C22—3142no—
364C22—3142no—
365C22—3142no—
366C22—6282no—
367C22—6284no—
368C22—6284no—
369C22—1571no—
370C22—1571no—
371C22—12562no—
372C22—12562no—
373C22—12564no—
374C22C2×D4×D15711yescharacteristic
375C4—22no—
376C4—41no—
377C4—41no—
378C4—3142no—
379C4—6281no—
380C4—6281no—
381C4—1572no—
382C4C2×D4×D15712yes—
383C2—21no—
384C2—42no—
385C2—42no—
386C2—3141no—
387C2—6282no—
388C2—6282no—
389C2—1572no—
390C2#120×D15711yescharacteristic
subgroupG/H
centerC2#120×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#455×C157C2
socleC2×C157C2×#120
prime radicalH(5,𝔽2)×D157C2
hypercenter#455D157
hypocenterC157C2×#455
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
2. #137×D157C2semidirect
3. #124×D157C2semidirect
4. #23757453C2semidirect
5. #23757452C2semidirect
6. #23757451C2semidirect
7. #23757450C2semidirect
8. #23757449C2semidirect
9. #104×D157C2semidirect
10. #100×D157C2semidirect
11. #455×C157C2semidirect
19. C2×Q8×D157C22semidirect
23. #19097804C22semidirect
25. #19097802C22semidirect
26. #19097801C22semidirect
30. M16×D157C22semidirect
31. #19097760C22semidirect
32. #19097759C22semidirect
33. #19097758C22semidirect
36. C42×D157C22semidirect
37. #19097699C22semidirect
38. #19097698C22semidirect
39. #19097697C22semidirect
40. #19097688C22semidirect
41. #19097687C22semidirect
43. #137×C157C22semidirect
44. #124×C157C22semidirect
45. #104×C157C22semidirect
46. #100×C157C22semidirect
60. C2×Dic314C23semidirect
92. #14578938C23semidirect
99. C4×Dic157C23semidirect
102. C2×Q8×C157C23semidirect
108. M16×C157C23semidirect
110. C42×C157C23semidirect
194. D157#455direct (N × H)
195. C157C2×#455semidirect
205. #455D157direct (N × H)
225. #137C2×D157semidirect
233. #124C2×D157semidirect
239. #104C2×D157semidirect
242. #100C2×D157semidirect
262. C2×Q8C22×D157semidirect
298. M16C22×D157semidirect
306. C42C22×D157semidirect

Maximal subgroups

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

subgroupindex
H(5,𝔽2)×D1572
#137×D1572
#124×D1572
#237574532
#237574522
#237574512
#237574502
#237574492
#104×D1572
#100×D1572
#455×C1572
C2×#455157