Finite Group Databasebeta

← #455×D151 #34078437

Subgroups — #455×D151 #34078437

Order 19328.

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)×D151C211yesmaximal, characteristic
2#137×D151C212yesmaximal, complemented
3#124×D151C211yesmaximal, characteristic, complemented
4#23752392C211yesmaximal, characteristic, complemented
5#23752391C212yesmaximal, complemented
6#23752390C211yesmaximal, characteristic, complemented
7#23752389C211yesmaximal, characteristic, complemented
8#23752388C212yesmaximal, complemented
9#104×D151C212yesmaximal, complemented
10#100×D151C211yesmaximal, characteristic, complemented
11#455×C151C211yesmaximal, characteristic, complemented
12#18012785—22no—
13#18012785C2212yes—
14#18012784—22no—
15#18012784—22no—
16#18012784C2211yescharacteristic
17#41×D151—22no—
18#41×D151C2212yes—
19C2×Q8×D151C2211yescharacteristic, complemented
20C2×D4×D151—22no—
21C2×D4×D151—22no—
22C2×D4×D151C2211yescharacteristic
23#18012772C2212yescomplemented
24#18012771—22no—
25#18012770C2212yescomplemented
26#18012769C2212yescomplemented
27#18012768—22no—
28Q16×D151—22no—
29SD16×D151—22no—
30M16×D151C2212yescomplemented
31#18012728C2211yescharacteristic, complemented
32#18012727C2211yescharacteristic, complemented
33#18012726C2211yescharacteristic, complemented
34#18012725—22no—
35C22⋊C4×D151—22no—
36C42×D151C2211yescharacteristic, complemented
37#18012667C2212yescomplemented
38#18012666C2212yescomplemented
39#18012665C2212yescomplemented
40#18012656C2211yescharacteristic, complemented
41#18012655C2212yescomplemented
42H(5,𝔽2)×C151C2211yescharacteristic
43#137×C151C2212yescomplemented
44#124×C151C2211yescharacteristic, complemented
45#104×C151C2212yescomplemented
46#100×C151C2211yescharacteristic, complemented
47C23×D151—22no—
48C23×D151D412yes—
49#14559005—22no—
50#14559005D412yes—
51#14559004—24no—
52#14559004—22no—
53#14559004—22no—
54#14559004C2312yes—
55#14559003—24no—
56#14559003—22no—
57#14559003—22no—
58#14559003D412yes—
59C2×Dic302—21no—
60C2×Dic302C2311yescharacteristic, complemented
61Q8×D151—22no—
62Q8×D151—22no—
63Q8×D151D412yes—
64C2×D604—22no—
65C2×D604—22no—
66C2×D604C2311yescharacteristic
67C2×C22⋊D151—22no—
68C2×C22⋊D151—24no—
69C2×C22⋊D151—22no—
70C2×C22⋊D151D412yes—
71D4×D151—24no—
72D4×D151—24no—
73D4×D151—24no—
74D4×D151—22no—
75D4×D151—24no—
76D4×D151—22no—
77D4×D151—22no—
78D4×D151—22no—
79D4×D151—22no—
80D4×D151D412yes—
81C2×C4×D151—22no—
82C2×C4×D151—22no—
83C2×C4×D151—21no—
84C2×C4×D151—21no—
85C2×C4×D151C2311yescharacteristic
86Dic604—22no—
87#14558994—22no—
88#14558994—22no—
89#14558993—22no—
90#14558992—22no—
91#14558991—22no—
92#14558988C2312yescomplemented
93#14558987—22no—
94C8×D151—22no—
95C22⋊Dic151—22no—
96(C2×D151)⋊C4—22no—
97(C2×D151)⋊C4—22no—
98C4×Dic151—21no—
99C4×Dic151C2311yescharacteristic, complemented
100#41×C151—22no—
101#41×C151C2312yes—
102C2×Q8×C151C2311yescharacteristic, complemented
103C2×D4×C151—22no—
104C2×D4×C151—22no—
105C2×D4×C151C2311yescharacteristic
106Q16×C151—22no—
107SD16×C151—22no—
108M16×C151C2312yescomplemented
109C22⋊C4×C151—22no—
110C42×C151C2311yescharacteristic, complemented
111C22×D151—24no—
112C22×D151—22no—
113C22×D151—22no—
114C22×D151—22no—
115C22×D151—22no—
116C22×D151—44no—
117C22×D151—84no—
118C22×D151C2×D411yescharacteristic
119C22×D151C2×D412yes—
120Dic302—22no—
121Dic302—22no—
122Dic302—42no—
123Dic302C2×D412yes—
124D604—24no—
125D604—22no—
126D604—22no—
127D604C2×D412yes—
128C22⋊D151—24no—
129C22⋊D151—24no—
130C22⋊D151—22no—
131C22⋊D151—22no—
132C22⋊D151—24no—
133C22⋊D151—22no—
134C2×Dic151—22no—
135C2×Dic151—22no—
136C2×Dic151—21no—
137C2×Dic151—21no—
138C2×Dic151C2×D411yescharacteristic
139C4×D151—24no—
140C4×D151—22no—
141C4×D151—22no—
142C4×D151—22no—
143C4×D151—42no—
144C4×D151—41no—
145C4×D151—41no—
146C4×D151C2×D412yes—
147C4×D151C2×D412yes—
148C151⋊C8—22no—
149C23×C151—22no—
150C23×C151C2×D412yes—
151Q8×C151—22no—
152Q8×C151C2×D412yes—
153D4×C151—24no—
154D4×C151—22no—
155D4×C151—22no—
156D4×C151C2×D412yes—
157C2×C4×C151—22no—
158C2×C4×C151—22no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151C2411yescharacteristic
162C8×C151—22no—
163C22×C151—22no—
164C22×C151—22no—
165C22×C151—42no—
166C22×C151—82no—
167C22×C151C22×D411yescharacteristic
168C2×D151—22no—
169C2×D151—22no—
170C2×D151—22no—
171C2×D151—44no—
172C2×D151—44no—
173C2×D151—42no—
174C2×D151—82no—
175C2×D151—84no—
176C2×D151—82no—
177C2×D151#12011yescharacteristic
178C2×D151#12011yescharacteristic
179C4×C151—22no—
180C4×C151—41no—
181C4×C151—41no—
182C4×C151C22×D412yes—
183Dic151—22no—
184Dic151—41no—
185Dic151—41no—
186Dic151#12012yes—
187C2×C151—21no—
188C2×C151—42no—
189C2×C151—42no—
190C2×C151C2×#12011yescharacteristic
191D151—21no—
192D151—42no—
193D151—42no—
194D151#45512yesdirect product factor
195C151C2×#45511yescharacteristic, complemented, Sylow
196C2×#455—1511nomaximal, Sylow
197C2×H(5,𝔽2)—1511no—
198C2×#137—1512no—
199C2×#124—1511no—
200#455—1511no—
201#455—1512no—
202#455—1511no—
203#455—1512no—
204#455—1511no—
205#455D15111yescharacteristic, direct product factor
206C2×#104—1512no—
207C2×#100—1511no—
208H(5,𝔽2)—3022no—
209H(5,𝔽2)—3022no—
210H(5,𝔽2)—3022no—
211H(5,𝔽2)—1512no—
212H(5,𝔽2)—1511no—
213H(5,𝔽2)C2×D15111yescharacteristic
214C2×#41—3022no—
215C2×#41—1512no—
216C22×Q8—1511no—
217C22×D4—3022no—
218C22×D4—3022no—
219C22×D4—1511no—
220#137—3022no—
221#137—3022no—
222#137—1512no—
223#137—1512no—
224#137—1512no—
225#137C2×D15112yescomplemented
226C2×Q16—3022no—
227C2×SD16—3022no—
228C2×M16—1512no—
229#124—3022no—
230#124—1511no—
231#124—1511no—
232#124—1511no—
233#124C2×D15111yescharacteristic, complemented
234C2×C22⋊C4—3022no—
235C2×C42—1511no—
236#104—1512no—
237#104—1512no—
238#104—1512no—
239#104C2×D15112yescomplemented
240#100—1511no—
241#100—1512no—
242#100C2×D15111yescharacteristic, complemented
243C24—3022no—
244C24—1512no—
245#41—22no—
246#41—3024no—
247#41—3022no—
248#41—3022no—
249#41—3024no—
250#41—3022no—
251#41—3022no—
252#41—3022no—
253#41—1512no—
254#41—1512no—
255#41—1512no—
256#41C22×D15112yes—
257C2×Q8—3021no—
258C2×Q8—3022no—
259C2×Q8—3022no—
260C2×Q8—1512no—
261C2×Q8—1511no—
262C2×Q8C22×D15111yescharacteristic, complemented
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—3022no—
266C2×D4—3022no—
267C2×D4—3024no—
268C2×D4—3024no—
269C2×D4—3024no—
270C2×D4—3022no—
271C2×D4—3024no—
272C2×D4—3022no—
273C2×D4—3022no—
274C2×D4—3024no—
275C2×D4—3022no—
276C2×D4—3022no—
277C2×D4—3022no—
278C2×D4—3022no—
279C2×D4—1512no—
280C2×D4—1512no—
281C2×D4—1511no—
282C2×D4C22×D15111yescharacteristic
283C22×C4—3022no—
284C22×C4—3022no—
285C22×C4—3021no—
286C22×C4—3021no—
287C22×C4—1511no—
288Q16—22no—
289Q16—3022no—
290Q16—3022no—
291Q16—3022no—
292SD16—22no—
293SD16—3022no—
294SD16—3022no—
295SD16—3022no—
296M16—3022no—
297M16—1512no—
298M16C22×D15112yescomplemented
299C2×C8—3022no—
300C22⋊C4—22no—
301C22⋊C4—3022no—
302C22⋊C4—3022no—
303C22⋊C4—3022no—
304C42—3021no—
305C42—1511no—
306C42C22×D15111yescharacteristic, complemented
307C23—22no—
308C23—3022no—
309C23—3024no—
310C23—3022no—
311C23—3022no—
312C23—3022no—
313C23—6044no—
314C23—1511no—
315C23—1512no—
316C23—12084no—
317C23D4×D15112yes—
318Q8—22no—
319Q8—3022no—
320Q8—3022no—
321Q8—6042no—
322Q8—1512no—
323Q8D4×D15112yes—
324D4—24no—
325D4—22no—
326D4—22no—
327D4—3024no—
328D4—3022no—
329D4—3024no—
330D4—3024no—
331D4—3022no—
332D4—3022no—
333D4—3024no—
334D4—3022no—
335D4—3022no—
336D4—1512no—
337D4D4×D15112yes—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—3024no—
343C2×C4—3022no—
344C2×C4—3022no—
345C2×C4—3022no—
346C2×C4—3022no—
347C2×C4—3022no—
348C2×C4—3021no—
349C2×C4—3021no—
350C2×C4—6042no—
351C2×C4—6041no—
352C2×C4—6041no—
353C2×C4—1511no—
354C2×C4—1512no—
355C2×C4—1512no—
356C2×C4C23×D15111yescharacteristic
357C8—22no—
358C8—3022no—
359C22—22no—
360C22—22no—
361C22—42no—
362C22—82no—
363C22—3022no—
364C22—3022no—
365C22—3022no—
366C22—6042no—
367C22—6044no—
368C22—6044no—
369C22—1511no—
370C22—1511no—
371C22—12082no—
372C22—12082no—
373C22—12084no—
374C22C2×D4×D15111yescharacteristic
375C4—22no—
376C4—41no—
377C4—41no—
378C4—3022no—
379C4—6041no—
380C4—6041no—
381C4—1512no—
382C4C2×D4×D15112yes—
383C2—21no—
384C2—42no—
385C2—42no—
386C2—3021no—
387C2—6042no—
388C2—6042no—
389C2—1512no—
390C2#120×D15111yescharacteristic
subgroupG/H
centerC2#120×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#455×C151C2
socleC2×C151C2×#120
prime radicalH(5,𝔽2)×D151C2
hypercenter#455D151
hypocenterC151C2×#455
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
2. #137×D151C2semidirect
3. #124×D151C2semidirect
4. #23752392C2semidirect
5. #23752391C2semidirect
6. #23752390C2semidirect
7. #23752389C2semidirect
8. #23752388C2semidirect
9. #104×D151C2semidirect
10. #100×D151C2semidirect
11. #455×C151C2semidirect
19. C2×Q8×D151C22semidirect
23. #18012772C22semidirect
25. #18012770C22semidirect
26. #18012769C22semidirect
30. M16×D151C22semidirect
31. #18012728C22semidirect
32. #18012727C22semidirect
33. #18012726C22semidirect
36. C42×D151C22semidirect
37. #18012667C22semidirect
38. #18012666C22semidirect
39. #18012665C22semidirect
40. #18012656C22semidirect
41. #18012655C22semidirect
43. #137×C151C22semidirect
44. #124×C151C22semidirect
45. #104×C151C22semidirect
46. #100×C151C22semidirect
60. C2×Dic302C23semidirect
92. #14558988C23semidirect
99. C4×Dic151C23semidirect
102. C2×Q8×C151C23semidirect
108. M16×C151C23semidirect
110. C42×C151C23semidirect
194. D151#455direct (N × H)
195. C151C2×#455semidirect
205. #455D151direct (N × H)
225. #137C2×D151semidirect
233. #124C2×D151semidirect
239. #104C2×D151semidirect
242. #100C2×D151semidirect
262. C2×Q8C22×D151semidirect
298. M16C22×D151semidirect
306. C42C22×D151semidirect

Maximal subgroups

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

subgroupindex
H(5,𝔽2)×D1512
#137×D1512
#124×D1512
#237523922
#237523912
#237523902
#237523892
#237523882
#104×D1512
#100×D1512
#455×C1512
C2×#455151