Finite Group Databasebeta

← #585×D101 #27185938

Subgroups — #585×D101 #27185938

Order 12928.

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#20266014C216yesmaximal, complemented
2#20266013C2115yesmaximal, complemented
3#20266012C2110yesmaximal, complemented
42−1+4×D101C216yesmaximal, complemented
5H(5,𝔽2)×D101C2110yesmaximal, complemented
6C2×#41×D101C2115yesmaximal, complemented
7#585×C101C211yesmaximal, characteristic, complemented
8#15692303C22130yescomplemented
9#15692302C22160yescomplemented
10#15692301C22160yescomplemented
11#15692300C22190yescomplemented
12C2×#13108075C22115yescomplemented
13C2×#13108074C22145yescomplemented
14C2×#13108073C22145yescomplemented
15#41×D101C22120yescomplemented
16#41×D101C22160yescomplemented
17#41×D101C22160yescomplemented
18#41×D101C22160yescomplemented
19C2×Q8×D101C22115yescomplemented
20C2×D4×D101C22145yescomplemented
21C22×C4×D101C22115yescomplemented
222−1+4×C101C2216yescomplemented
23H(5,𝔽2)×C101C22110yescomplemented
24C2×#41×C101C22115yescomplemented
25C23×D101C23115yes—
26#13108075C23120yescomplemented
27#13108075C23160yescomplemented
28#13108074C23160yescomplemented
29#13108074C231180yescomplemented
30#13108073C23160yescomplemented
31#13108073C231180yescomplemented
32C2×Dic202C23145yescomplemented
33Q8×D101C23120yes—
34Q8×D101C23160yescomplemented
35C2×D404C23145yescomplemented
36C2×C22⋊D101C23190yescomplemented
37D4×D101C23160yes—
38D4×D101C231180yescomplemented
39C22×Dic101C23115yescomplemented
40C2×C4×D101C23115yes—
41C2×C4×D101C23145yes—
42C2×C4×D101C23145yescomplemented
43C2×C4×D101C23145yescomplemented
44#41×C101C23120yescomplemented
45#41×C101C23160yescomplemented
46C2×Q8×C101C23115yescomplemented
47C2×D4×C101C23145yescomplemented
48C22×C4×C101C23115yescomplemented
49C23×C101C24115yes—
50C22×D101—430no—
51C22×D101C24115yes—
52C22×D101C24145yes—
53Q8×C101C24120yes—
54D4×C101C24160yes—
55C2×C4×C101C24115yes—
56C2×C4×C101C24145yes—
57C22⋊D101C241120yes—
58C2×Dic101C24115yes—
59C2×Dic101C24145yes—
60D404C24160yes—
61C4×D101C2411yescharacteristic
62C4×D101C24115yes—
63C4×D101C24115yes—
64C4×D101C24115yes—
65C4×D101C24190yes—
66Dic202C24160yes—
67C22×C101—415no—
68C22×C101C25115yes—
69C2×D101—230no—
70C2×D101—445no—
71C2×D101C25115yes—
72C2×D101C2511yescharacteristic
73C4×C101C25115yes—
74C4×C101C2511yescharacteristic
75Dic101C25115yes—
76Dic101C2511yescharacteristic
77C2×C101—215no—
78C2×C101C2611yescharacteristic
79D101—215no—
80D101#58512yesdirect product factor
81C2×#585—1011nomaximal, Sylow
82C101C2×#58511yescharacteristic, complemented, Sylow
83#585—1016no—
84#585—10110no—
85#585—10115no—
86#585D10111yescharacteristic, direct product factor
87C2×2−1+4—1016no—
88C2×H(5,𝔽2)—10110no—
89C22×#41—10115no—
902−1+4—10160no—
912−1+4—10130no—
922−1+4C2×D10116yescomplemented
93H(5,𝔽2)—10160no—
94H(5,𝔽2)—10190no—
95H(5,𝔽2)C2×D101110yescomplemented
96C2×#41—10120no—
97C2×#41—10160no—
98C2×#41—10160no—
99C2×#41—10160no—
100C2×#41—10115no—
101C2×#41—10145no—
102C2×#41—10145no—
103C2×#41C2×D101115yescomplemented
104C22×Q8—10115no—
105C22×D4—10145no—
106C23×C4—10115no—
107C24—10115no—
108#41—10120no—
109#41—10160no—
110#41—10160no—
111#41—101180no—
112#41—10160no—
113#41—101180no—
114#41C22×D101120yescomplemented
115#41C22×D101160yescomplemented
116C2×Q8—10120no—
117C2×Q8—10160no—
118C2×Q8—10145no—
119C2×Q8C22×D101115yescomplemented
120C2×D4—10190no—
121C2×D4—10160no—
122C2×D4—101180no—
123C2×D4—10145no—
124C2×D4C22×D101145yescomplemented
125C22×C4—10115no—
126C22×C4—10115no—
127C22×C4—10145no—
128C22×C4—10145no—
129C22×C4—10145no—
130C22×C4C22×D101115yescomplemented
131C23—10145no—
132C23—10115no—
133C23—40430no—
134C23C23×D101115yes—
135Q8—10160no—
136Q8C23×D101120yes—
137D4—101120no—
138D4—10160no—
139D4C23×D101160yes—
140C2×C4—10115no—
141C2×C4—10145no—
142C2×C4—10115no—
143C2×C4—10115no—
144C2×C4—10190no—
145C2×C4—1011no—
146C2×C4—10115no—
147C2×C4C23×D101145yes—
148C2×C4C23×D101115yes—
149C22—415no—
150C22—1011no—
151C22—10115no—
152C22—40445no—
153C22—20230no—
154C22C24×D101115yes—
155C4—1011no—
156C4—10115no—
157C4C24×D101115yes—
158C4C24×D10111yescharacteristic
159C2—215no—
160C2—1012no—
161C2—20215no—
162C2C25×D10111yescharacteristic
subgroupG/H
centerC4C24×D101
commutator, socle, cosocleC2×C101C26
FrattiniC2C25×D101
Fitting#585×C101C2
hypercenter#585D101
hypocenterC101C2×#585
LCSG ▷ C2×C101 ▷ C101
UCSC1 ◁ C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #20266014C2semidirect
2. #20266013C2semidirect
3. #20266012C2semidirect
4. 2−1+4×D101C2semidirect
5. H(5,𝔽2)×D101C2semidirect
6. C2×#41×D101C2semidirect
7. #585×C101C2semidirect
8. #15692303C22semidirect
9. #15692302C22semidirect
10. #15692301C22semidirect
11. #15692300C22semidirect
12. C2×#13108075C22semidirect
13. C2×#13108074C22semidirect
14. C2×#13108073C22semidirect
15. #41×D101C22semidirect
16. #41×D101C22semidirect
17. #41×D101C22semidirect
18. #41×D101C22semidirect
19. C2×Q8×D101C22semidirect
20. C2×D4×D101C22semidirect
21. C22×C4×D101C22semidirect
22. 2−1+4×C101C22semidirect
23. H(5,𝔽2)×C101C22semidirect
24. C2×#41×C101C22semidirect
26. #13108075C23semidirect
27. #13108075C23semidirect
28. #13108074C23semidirect
29. #13108074C23semidirect
30. #13108073C23semidirect
31. #13108073C23semidirect
32. C2×Dic202C23semidirect
34. Q8×D101C23semidirect
35. C2×D404C23semidirect
36. C2×C22⋊D101C23semidirect
38. D4×D101C23semidirect
39. C22×Dic101C23semidirect
42. C2×C4×D101C23semidirect
43. C2×C4×D101C23semidirect
44. #41×C101C23semidirect
45. #41×C101C23semidirect
46. C2×Q8×C101C23semidirect
47. C2×D4×C101C23semidirect
48. C22×C4×C101C23semidirect
80. D101#585direct (N × H)
82. C101C2×#585semidirect
86. #585D101direct (N × H)
92. 2−1+4C2×D101semidirect
95. H(5,𝔽2)C2×D101semidirect
103. C2×#41C2×D101semidirect
114. #41C22×D101semidirect
115. #41C22×D101semidirect
119. C2×Q8C22×D101semidirect
124. C2×D4C22×D101semidirect
130. C22×C4C22×D101semidirect

Maximal subgroups

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

subgroupindex
#202660142
#202660132
#202660122
2−1+4×D1012
H(5,𝔽2)×D1012
C2×#41×D1012
#585×C1012
C2×#585101