Finite Group Databasebeta

← C3×#10587944 #13132638

Subgroups — C3×#10587944 #13132638

Order 1680.

160 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 64 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
1C3×C4×D35C211yesmaximal, characteristic, complemented
2C3×C4×C7×D5C211yesmaximal, characteristic, complemented
3C3×C4×C5×D7C211yesmaximal, characteristic, complemented
4C3×#63308C211yesmaximal, characteristic, complemented
5C3×#63307C211yesmaximal, characteristic, complemented
6C3×#63306C211yesmaximal, characteristic, complemented
7C3×#63305C211yesmaximal, characteristic, complemented
8#10587944C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×D35C2211yescharacteristic
10C2×C3×C7×D5C2211yescharacteristic
11C2×C3×C5×D7C2211yescharacteristic
12C3×C4×C5×C7C2211yescharacteristic
13C3×Dic35C2211yescharacteristic
14C3×C7×Dic5C2211yescharacteristic
15C3×C5×Dic7C2211yescharacteristic
16C3×#1157—51nomaximal, Hall
17C4×D35C2×C311yescharacteristic, complemented
18C4×C7×D5C2×C311yescharacteristic, complemented
19C4×C5×D7C2×C311yescharacteristic, complemented
20#63308C2×C311yescharacteristic, complemented
21#63307C2×C311yescharacteristic, complemented
22#63306C2×C311yescharacteristic, complemented
23#63305C2×C311yescharacteristic, complemented
24C3×#709—71nomaximal, Hall
25C2×C3×C5×C7C2311yescharacteristic
26C3×D35—21no—
27C3×C7×D5—21no—
28C3×C5×D7—21no—
29C2×C3×C4×C7—51no—
30C3×C22⋊D7—51no—
31C3×C22⋊D7—51no—
32C3×D28—51no—
33C3×C4×D7—51no—
34C3×C4×D7D511yescharacteristic, complemented
35C3×Dic14—51no—
36C2×D35C22×C311yescharacteristic
37C2×C7×D5C22×C311yescharacteristic
38C2×C5×D7C22×C311yescharacteristic
39C4×C5×C7C22×C311yescharacteristic
40Dic35C22×C311yescharacteristic
41C5×Dic7C22×C311yescharacteristic
42C7×Dic5C22×C311yescharacteristic
43C2×C3×C4×C5—71no—
44C3×C22⋊D5—71no—
45C3×C22⋊D5—71no—
46C3×D20—71no—
47C3×C4×D5—71no—
48C3×C4×D5D711yescharacteristic, complemented
49C3×Dic10—71no—
50#1157—51noHall
51C3×C5×C7#4111yescharacteristic, complemented, Hall
52C22×C3×C7—51no—
53C2×C3×D7—51no—
54C2×C3×D7C2×D511yescharacteristic
55C3×C4×C7—51no—
56C3×C4×C7C2×D511yescharacteristic
57C3×Dic7—51no—
58C3×Dic7C2×D511yescharacteristic
59#709—71noHall
60C2×C5×C7C23×C311yescharacteristic
61D35—21no—
62C5×D7—21no—
63C7×D5—21no—
64C22×C3×C5—71no—
65C2×C3×D5—71no—
66C2×C3×D5C2×D711yescharacteristic
67C3×C4×C5—71no—
68C3×C4×C5C2×D711yescharacteristic
69C3×Dic5—71no—
70C3×Dic5C2×D711yescharacteristic
71C2×C4×C7—51no—
72C22⋊D7—51no—
73C22⋊D7—51no—
74D28—51no—
75C4×D7—51no—
76C4×D7C3×D511yescharacteristic, complemented
77Dic14—51no—
78C3×#41—351noHall
79C2×C3×C7—101no—
80C2×C3×C7C22×D511yescharacteristic
81C3×D7—21no—
82C3×D7—101no—
83C2×C4×C5—71no—
84C22⋊D5—71no—
85C22⋊D5—71no—
86D20—71no—
87C4×D5—71no—
88C4×D5C3×D711yescharacteristic, complemented
89Dic10—71no—
90C5×C7C3×#4111yescharacteristic, complemented, Hall
91C2×C3×C5—141no—
92C2×C3×C5C22×D711yescharacteristic
93C3×D5—21no—
94C3×D5—141no—
95C22×C7—51no—
96C2×D7—51no—
97C2×D7C2×C3×D511yescharacteristic
98C4×C7—51no—
99C4×C7C2×C3×D511yescharacteristic
100Dic7—51no—
101Dic7C2×C3×D511yescharacteristic
102C3×Q8—351no—
103C3×D4—351no—
104C3×D4—351no—
105C3×D4—351no—
106C2×C3×C4—51no—
107C2×C3×C4—71no—
108C2×C3×C4—351no—
109C3×C7#70911yescharacteristic, complemented, Hall
110C22×C5—71no—
111C2×D5—71no—
112C2×D5C2×C3×D711yescharacteristic
113C4×C5—71no—
114C4×C5C2×C3×D711yescharacteristic
115Dic5—71no—
116Dic5C2×C3×D711yescharacteristic
117#41—351noSylow
118C3×C5#115711yescharacteristic, complemented, Hall
119C2×C7—101no—
120C2×C7C22×C3×D511yescharacteristic
121D7—21no—
122D7—101no—
123C22×C3—51no—
124C22×C3—71no—
125C22×C3—351no—
126C3×C4—51no—
127C3×C4—71no—
128C3×C4—351no—
129C3×C4D5×D711yescharacteristic
130C2×C5—141no—
131C2×C5C22×C3×D711yescharacteristic
132D5—21no—
133D5—141no—
134Q8—351no—
135D4—351no—
136D4—351no—
137D4—351no—
138C2×C4—51no—
139C2×C4—71no—
140C2×C4—351no—
141C7C3×#70911yescharacteristic, complemented, Sylow
142C2×C3—101no—
143C2×C3—141no—
144C2×C3—701no—
145C2×C3C2×D5×D711yescharacteristic
146C5C3×#115711yescharacteristic, complemented, Sylow
147C22—51no—
148C22—71no—
149C22—351no—
150C4—51no—
151C4—71no—
152C4—351no—
153C4C3×D5×D711yescharacteristic
154C3#1058794411yescharacteristic, direct product factor, Sylow
155C2—101no—
156C2—141no—
157C2—701no—
158C2C2×C3×D5×D711yescharacteristic
subgroupG/H
center, hypercenterC3×C4D5×D7
commutator, cosocleC2×C5×C7C23×C3
FrattiniC2C2×C3×D5×D7
FittingC3×C4×C5×C7C22
socleC2×C3×C5×C7C23
hypocenterC5×C7C3×#41
LCSG ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
1. C3×C4×D35C2semidirect
2. C3×C4×C7×D5C2semidirect
3. C3×C4×C5×D7C2semidirect
4. C3×#63308C2semidirect
5. C3×#63307C2semidirect
6. C3×#63306C2semidirect
7. C3×#63305C2semidirect
8. #10587944C3direct (N × H)
17. C4×D35C2×C3semidirect
18. C4×C7×D5C2×C3semidirect
19. C4×C5×D7C2×C3semidirect
20. #63308C2×C3semidirect
21. #63307C2×C3semidirect
22. #63306C2×C3semidirect
23. #63305C2×C3semidirect
34. C3×C4×D7D5semidirect
48. C3×C4×D5D7semidirect
51. C3×C5×C7#41semidirect
76. C4×D7C3×D5semidirect
88. C4×D5C3×D7semidirect
90. C5×C7C3×#41semidirect
109. C3×C7#709semidirect
118. C3×C5#1157semidirect
141. C7C3×#709semidirect
146. C5C3×#1157semidirect
154. C3#10587944direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4×D352
C3×C4×C7×D52
C3×C4×C5×D72
C3×#633082
C3×#633072
C3×#633062
C3×#633052
#105879443
C3×#11575
C3×#7097