Finite Group Databasebeta

← C5×#67798 #14279412

Subgroups — C5×#67798 #14279412

Order 1920.

196 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 50 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×C5×#497C211yesmaximal, characteristic
2C5×#4542C211yesmaximal, characteristic
3C5×#4541C211yesmaximal, characteristic
4C5×#1407—31nomaximal, Hall
5C2×C3×C5×Q16—21no—
6C2×C3×C5×SD16—21no—
7C3×C5×C4⋊Q8C411yescharacteristic, complemented
8C3×C5×#124C2211yescharacteristic
9C3×C5×#97C411yescharacteristic, complemented
10C5×#836—21no—
11C5×#834—21no—
12#67798C511yesmaximal, characteristic, direct product factor, Hall
13C5×#497D311yescharacteristic
14C5×#355—31no—
15C5×#354—31no—
16C2×C3×C5×Q8—21no—
17C2×C3×C5×Q8D411yescharacteristic
18C2×C3×C5×D4D411yescharacteristic
19C3×C5×Q16—42no—
20C3×C5×SD16—42no—
21C2×C3×C5×C8—21no—
22C3×C5×C4⋊C4—41no—
23C3×C5×C22⋊C4—41no—
24C3×C42×C5C2×C411yescharacteristic
25C5×#217—41no—
26C5×#208—41no—
27C3×#497C2×C511yescharacteristic
28#4542C2×C511yescharacteristic
29#4541C2×C511yescharacteristic
30C2×C5×Q16—21no—
31C2×C5×SD16—21no—
32C5×C4⋊Q8Dic311yescharacteristic, complemented
33C5×#124C2×D311yescharacteristic
34C5×#101—61no—
35C5×#99—61no—
36C5×#97Dic311yescharacteristic, complemented
37#1407—31noSylow
38C23×C3×C5—21no—
39C3×C5×Q8—41no—
40C3×C5×Q8—41no—
41C3×C5×Q8—41no—
42C3×C5×D4—41no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5—21no—
45C2×C3×C4×C5—41no—
46C2×C3×C4×C5C22⋊C411yescharacteristic
47C2×C5×Dic3—81no—
48C3×C5×C8—22no—
49C5×C3⋊C8—81no—
50C2×C3×Q16—21no—
51C2×C3×SD16—21no—
52C3×C4⋊Q8C4×C511yescharacteristic, complemented
53C3×#124C22×C511yescharacteristic
54C3×#97C4×C511yescharacteristic, complemented
55#836—21no—
56#834—21no—
57C2×C5×Q8—21no—
58C2×C5×Q8#6711yescharacteristic
59C2×C5×D4#6711yescharacteristic
60C5×Q16—42no—
61C5×SD16—42no—
62C5×M16—121no—
63C2×C5×C8—21no—
64C5×C4⋊C4—41no—
65C5×C22⋊C4—41no—
66C5×C22⋊C4—121no—
67C42×C5C2×Dic311yescharacteristic
68#497C5×D311yescharacteristic
69#355—31no—
70#354—31no—
71C22×C3×C5—41no—
72C22×C3×C5—81no—
73C22×C3×C5#9911yescharacteristic
74C3×C4×C5—21no—
75C3×C4×C5—41no—
76C3×C4×C5—41no—
77C3×C4×C5—81no—
78C5×Dic3—161no—
79C2×C3×Q8—21no—
80C2×C3×Q8C5×D411yescharacteristic
81C2×C3×D4C5×D411yescharacteristic
82C3×Q16—42no—
83C3×SD16—42no—
84C2×C3×C8—21no—
85C3×C4⋊C4—41no—
86C3×C22⋊C4—41no—
87C3×C42C2×C4×C511yescharacteristic
88#217—41no—
89#208—41no—
90C23×C5—21no—
91C5×Q8—41no—
92C5×Q8—41no—
93C5×Q8—41no—
94C5×D4—41no—
95C2×C4×C5—21no—
96C2×C4×C5—21no—
97C2×C4×C5—41no—
98C2×C4×C5—241no—
99C2×C4×C5#21711yescharacteristic
100C5×C8—22no—
101C5×C8—241no—
102C2×Q16—21no—
103C2×SD16—21no—
104C4⋊Q8C5×Dic311yescharacteristic, complemented
105#124C2×C5×D311yescharacteristic
106#101—61no—
107#99—61no—
108#97C5×Dic311yescharacteristic, complemented
109C2×C3×C5—21no—
110C2×C3×C5—81no—
111C2×C3×C5#35311yescharacteristic
112C23×C3—21no—
113C3×Q8—41no—
114C3×Q8—41no—
115C3×Q8—41no—
116C3×D4—41no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—41no—
120C2×C3×C4C5×C22⋊C411yescharacteristic
121C2×Dic3—81no—
122C3×C8—22no—
123C3⋊C8—81no—
124C22×C5—41no—
125C22×C5—81no—
126C22×C5#83411yescharacteristic
127C4×C5—21no—
128C4×C5—41no—
129C4×C5—41no—
130C4×C5—81no—
131C4×C5—481no—
132C2×Q8—21no—
133C2×Q8C5×#6711yescharacteristic
134C2×D4C5×#6711yescharacteristic
135Q16—42no—
136SD16—42no—
137M16—121no—
138C2×C8—21no—
139C4⋊C4—41no—
140C22⋊C4—41no—
141C22⋊C4—121no—
142C42C2×C5×Dic311yescharacteristic
143C3×C5#140711yescharacteristic, complemented, Hall
144C22×C3—41no—
145C22×C3—81no—
146C22×C3C5×#9911yescharacteristic
147C3×C4—21no—
148C3×C4—41no—
149C3×C4—41no—
150C3×C4—81no—
151Dic3—161no—
152C2×C5—21no—
153C2×C5—81no—
154C2×C5#454511yescharacteristic
155C23—21no—
156Q8—41no—
157Q8—41no—
158Q8—41no—
159D4—41no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—241no—
164C2×C4C5×#21711yescharacteristic
165C8—22no—
166C8—241no—
167C2×C3—21no—
168C2×C3—81no—
169C2×C3C5×#35311yescharacteristic
170C5#6779811yescharacteristic, direct product factor, Sylow
171C22—41no—
172C22—81no—
173C22C5×#83411yescharacteristic
174C4—21no—
175C4—41no—
176C4—41no—
177C4—81no—
178C4—481no—
179C3C5×#140711yescharacteristic, complemented, Sylow
180C2—21no—
181C2—81no—
182C2C5×#454511yescharacteristic
subgroupG/H
centerC2×C5#4545
commutatorC3×C42C2×C4×C5
Frattini#124C2×C5×D3
FittingC3×C5×#497C2
socleC2×C3×C5#353
prime radicalC2×C3×C5×D4D4
cosocleC3×#124C22×C5
hypercenterC5×#497D3
hypocenterC3C5×#1407
LCSG ▷ C3×C42 ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C5 ◁ C2×C4×C5 ◁ C5×#124 ◁ C5×#497

Complements

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

NH ≅ G/Ntype
7. C3×C5×C4⋊Q8C4semidirect
9. C3×C5×#97C4semidirect
12. #67798C5direct (N × H)
32. C5×C4⋊Q8Dic3semidirect
36. C5×#97Dic3semidirect
52. C3×C4⋊Q8C4×C5semidirect
54. C3×#97C4×C5semidirect
104. C4⋊Q8C5×Dic3semidirect
108. #97C5×Dic3semidirect
143. C3×C5#1407semidirect
170. C5#67798direct (N × H)
179. C3C5×#1407semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4972
C5×#45422
C5×#45412
C5×#14073
#677985