Finite Group Databasebeta

← #585×D139 #31821210

Subgroups — #585×D139 #31821210

Order 17792.

5956 conjugacy classes of subgroups; only the 3203 normal subgroups are shown.

normal subgroups only

This group has 5956 conjugacy classes of subgroups — too many to draw. Only its 3203 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
1#22581790C216yesmaximal, complemented
2#22581789C2115yesmaximal, complemented
3#22581788C2110yesmaximal, complemented
42−1+4×D139C216yesmaximal, complemented
5H(5,𝔽2)×D139C2110yesmaximal, complemented
6C2×#41×D139C2115yesmaximal, complemented
7#585×C139C211yesmaximal, characteristic, complemented
8#17984890C22130yescomplemented
9#17984889C22160yescomplemented
10#17984888C22160yescomplemented
11#17984887C22190yescomplemented
12C2×#14555786C22115yescomplemented
13C2×#14555785C22145yescomplemented
14C2×#14555784C22145yescomplemented
15#41×D139C22120yescomplemented
16#41×D139C22160yescomplemented
17#41×D139C22160yescomplemented
18#41×D139C22160yescomplemented
19C2×Q8×D139C22115yescomplemented
20C2×D4×D139C22145yescomplemented
21C22×C4×D139C22115yescomplemented
222−1+4×C139C2216yescomplemented
23H(5,𝔽2)×C139C22110yescomplemented
24C2×#41×C139C22115yescomplemented
25C23×D139C23115yes—
26#14555786C23120yescomplemented
27#14555786C23160yescomplemented
28#14555785C23160yescomplemented
29#14555785C231180yescomplemented
30#14555784C23160yescomplemented
31#14555784C231180yescomplemented
32C2×Dic278C23145yescomplemented
33Q8×D139C23120yes—
34Q8×D139C23160yescomplemented
35C2×D556C23145yescomplemented
36C2×C22⋊D139C23190yescomplemented
37D4×D139C23160yes—
38D4×D139C231180yescomplemented
39C22×Dic139C23115yescomplemented
40C2×C4×D139C23115yes—
41C2×C4×D139C23145yes—
42C2×C4×D139C23145yescomplemented
43C2×C4×D139C23145yescomplemented
44#41×C139C23120yescomplemented
45#41×C139C23160yescomplemented
46C2×Q8×C139C23115yescomplemented
47C2×D4×C139C23145yescomplemented
48C22×C4×C139C23115yescomplemented
49C22×D139—430no—
50C22×D139C24115yes—
51C22×D139C24145yes—
52Dic278C24160yes—
53D556C24160yes—
54C22⋊D139C241120yes—
55C2×Dic139C24115yes—
56C2×Dic139C24145yes—
57C4×D139C2411yescharacteristic
58C4×D139C24115yes—
59C4×D139C24115yes—
60C4×D139C24115yes—
61C4×D139C24190yes—
62C23×C139C24115yes—
63Q8×C139C24120yes—
64D4×C139C24160yes—
65C2×C4×C139C24115yes—
66C2×C4×C139C24145yes—
67C22×C139—415no—
68C22×C139C25115yes—
69C2×D139—230no—
70C2×D139—445no—
71C2×D139C25115yes—
72C2×D139C2511yescharacteristic
73C4×C139C25115yes—
74C4×C139C2511yescharacteristic
75Dic139C2511yescharacteristic
76Dic139C25115yes—
77C2×C139—215no—
78C2×C139C2611yescharacteristic
79D139—215no—
80D139#58512yesdirect product factor
81C139C2×#58511yescharacteristic, complemented, Sylow
82C2×#585—1391nomaximal, Sylow
83#585—1396no—
84#585—13910no—
85#585—13915no—
86#585D13911yescharacteristic, direct product factor
87C2×2−1+4—1396no—
88C2×H(5,𝔽2)—13910no—
89C22×#41—13915no—
902−1+4—13960no—
912−1+4—13930no—
922−1+4C2×D13916yescomplemented
93H(5,𝔽2)—13960no—
94H(5,𝔽2)—13990no—
95H(5,𝔽2)C2×D139110yescomplemented
96C2×#41—13920no—
97C2×#41—13960no—
98C2×#41—13960no—
99C2×#41—13960no—
100C2×#41—13915no—
101C2×#41—13945no—
102C2×#41—13945no—
103C2×#41C2×D139115yescomplemented
104C22×Q8—13915no—
105C22×D4—13945no—
106C23×C4—13915no—
107C24—13915no—
108#41—13920no—
109#41—13960no—
110#41—13960no—
111#41—139180no—
112#41—13960no—
113#41—139180no—
114#41C22×D139120yescomplemented
115#41C22×D139160yescomplemented
116C2×Q8—13920no—
117C2×Q8—13960no—
118C2×Q8—13945no—
119C2×Q8C22×D139115yescomplemented
120C2×D4—13990no—
121C2×D4—13960no—
122C2×D4—139180no—
123C2×D4—13945no—
124C2×D4C22×D139145yescomplemented
125C22×C4—13915no—
126C22×C4—13915no—
127C22×C4—13945no—
128C22×C4—13945no—
129C22×C4—13945no—
130C22×C4C22×D139115yescomplemented
131C23—55630no—
132C23—13915no—
133C23—13945no—
134C23C23×D139115yes—
135Q8—13960no—
136Q8C23×D139120yes—
137D4—139120no—
138D4—13960no—
139D4C23×D139160yes—
140C2×C4—13915no—
141C2×C4—13945no—
142C2×C4—13915no—
143C2×C4—13915no—
144C2×C4—13990no—
145C2×C4—1391no—
146C2×C4—13915no—
147C2×C4C23×D139145yes—
148C2×C4C23×D139115yes—
149C22—415no—
150C22—27830no—
151C22—55645no—
152C22—13915no—
153C22—1391no—
154C22C24×D139115yes—
155C4—1391no—
156C4—13915no—
157C4C24×D139115yes—
158C4C24×D13911yescharacteristic
159C2—215no—
160C2—27815no—
161C2—1392no—
162C2C25×D13911yescharacteristic
subgroupG/H
centerC4C24×D139
commutator, socle, cosocleC2×C139C26
FrattiniC2C25×D139
Fitting#585×C139C2
hypercenter#585D139
hypocenterC139C2×#585
LCSG ▷ C2×C139 ▷ C139
UCSC1 ◁ C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #22581790C2semidirect
2. #22581789C2semidirect
3. #22581788C2semidirect
4. 2−1+4×D139C2semidirect
5. H(5,𝔽2)×D139C2semidirect
6. C2×#41×D139C2semidirect
7. #585×C139C2semidirect
8. #17984890C22semidirect
9. #17984889C22semidirect
10. #17984888C22semidirect
11. #17984887C22semidirect
12. C2×#14555786C22semidirect
13. C2×#14555785C22semidirect
14. C2×#14555784C22semidirect
15. #41×D139C22semidirect
16. #41×D139C22semidirect
17. #41×D139C22semidirect
18. #41×D139C22semidirect
19. C2×Q8×D139C22semidirect
20. C2×D4×D139C22semidirect
21. C22×C4×D139C22semidirect
22. 2−1+4×C139C22semidirect
23. H(5,𝔽2)×C139C22semidirect
24. C2×#41×C139C22semidirect
26. #14555786C23semidirect
27. #14555786C23semidirect
28. #14555785C23semidirect
29. #14555785C23semidirect
30. #14555784C23semidirect
31. #14555784C23semidirect
32. C2×Dic278C23semidirect
34. Q8×D139C23semidirect
35. C2×D556C23semidirect
36. C2×C22⋊D139C23semidirect
38. D4×D139C23semidirect
39. C22×Dic139C23semidirect
42. C2×C4×D139C23semidirect
43. C2×C4×D139C23semidirect
44. #41×C139C23semidirect
45. #41×C139C23semidirect
46. C2×Q8×C139C23semidirect
47. C2×D4×C139C23semidirect
48. C22×C4×C139C23semidirect
80. D139#585direct (N × H)
81. C139C2×#585semidirect
86. #585D139direct (N × H)
92. 2−1+4C2×D139semidirect
95. H(5,𝔽2)C2×D139semidirect
103. C2×#41C2×D139semidirect
114. #41C22×D139semidirect
115. #41C22×D139semidirect
119. C2×Q8C22×D139semidirect
124. C2×D4C22×D139semidirect
130. C22×C4C22×D139semidirect

Maximal subgroups

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

subgroupindex
#225817902
#225817892
#225817882
2−1+4×D1392
H(5,𝔽2)×D1392
C2×#41×D1392
#585×C1392
C2×#585139