Finite Group Databasebeta

← C5×#67548 #14279392

Subgroups — C5×#67548 #14279392

Order 1920.

216 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 46 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
1C5×#5058C211yesmaximal, characteristic
2C3×C5×#355C211yesmaximal, characteristic, complemented
3C5×#4541C211yesmaximal, characteristic, complemented
4C5×#1406—31nomaximal, Hall
5C3×C5×#124C2211yescharacteristic
6C2×C5×#215—21no—
7C2×C5×#213—21no—
8C5×#874C411yescharacteristic, complemented
9C3×C5×#101—21no—
10C5×#834—21no—
11C5×#803C411yescharacteristic, complemented
12#67548C511yesmaximal, characteristic, direct product factor, Hall
13C5×#496—31no—
14C5×#355D311yescharacteristic, complemented
15C5×#354—31no—
16C2×C3×C5×Q8D411yescharacteristic
17C2×C3×C5×D4D411yescharacteristic
18C2×C5×D12—21no—
19C2×C5×D12—41no—
20C3×C5×M16—41no—
21C3×C5×C22⋊C4—41no—
22C3×C42×C5C2×C411yescharacteristic
23C5×#217—41no—
24C5×#215—42no—
25C5×#213—42no—
26C2×C5×C3⋊C8—21no—
27#5058C2×C511yescharacteristic
28C3×#355C2×C511yescharacteristic, complemented
29#4541C2×C511yescharacteristic, complemented
30C2×C5×SD16—61no—
31C2×C5×D8—61no—
32C5×#127—31no—
33C5×#124C2×D311yescharacteristic
34C5×#101—21no—
35C5×#99—61no—
36C5×#97—31no—
37#1406—31noSylow
38C23×C3×C5—21no—
39C22×C5×D3—41no—
40C3×C5×Q8—41no—
41C3×C5×D4—41no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5C22⋊C411yescharacteristic
45C2×C5×Dic3—81no—
46C5×D12—41no—
47C5×D12—41no—
48C5×D12—82no—
49C3×C5×C8—81no—
50C5×C3⋊C8—22no—
51C3×#124C22×C511yescharacteristic
52C2×#215—21no—
53C2×#213—21no—
54#874C4×C511yescharacteristic, complemented
55C3×#101—21no—
56#834—21no—
57#803C4×C511yescharacteristic, complemented
58C2×C5×Q8#6711yescharacteristic
59C2×C5×D4—61no—
60C2×C5×D4—121no—
61C2×C5×D4D1211yescharacteristic
62C5×SD16—122no—
63C5×D8—122no—
64C5×M16—41no—
65C2×C5×C8—61no—
66C5×C22⋊C4—41no—
67C5×C22⋊C4—121no—
68C42×C5C4×D311yescharacteristic
69#496—31no—
70#355C5×D311yescharacteristic, complemented
71#354—31no—
72C22×C3×C5—41no—
73C22×C3×C5—81no—
74C22×C3×C5#9911yescharacteristic
75C2×C5×D3—82no—
76C2×C5×D3—81no—
77C3×C4×C5—21no—
78C3×C4×C5—41no—
79C3×C4×C5—41no—
80C5×Dic3—161no—
81C2×C3×Q8C5×D411yescharacteristic
82C2×C3×D4C5×D411yescharacteristic
83C2×D12—21no—
84C2×D12—41no—
85C3×M16—41no—
86C3×C22⋊C4—41no—
87C3×C42C2×C4×C511yescharacteristic
88#217—41no—
89#215—42no—
90#213—42no—
91C2×C3⋊C8—21no—
92C23×C5—21no—
93C23×C5—121no—
94C5×Q8—41no—
95C5×D4—41no—
96C5×D4—121no—
97C5×D4—121no—
98C5×D4—242no—
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5—241no—
102C2×C4×C5(C2×D3)⋊C411yescharacteristic
103C5×C8—62no—
104C5×C8—81no—
105C2×SD16—61no—
106C2×D8—61no—
107#127—31no—
108#124C2×C5×D311yescharacteristic
109#101—21no—
110#99—61no—
111#97—31no—
112C2×C3×C5—21no—
113C2×C3×C5—81no—
114C2×C3×C5#35311yescharacteristic
115C5×D3—161no—
116C23×C3—21no—
117C22×D3—41no—
118C3×Q8—41no—
119C3×D4—41no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4C5×C22⋊C411yescharacteristic
123C2×Dic3—81no—
124D12—41no—
125D12—41no—
126D12—82no—
127C3×C8—81no—
128C3⋊C8—22no—
129C22×C5—41no—
130C22×C5—81no—
131C22×C5—242no—
132C22×C5—241no—
133C22×C5#80611yescharacteristic
134C4×C5—21no—
135C4×C5—41no—
136C4×C5—41no—
137C4×C5—481no—
138C2×Q8C5×#6711yescharacteristic
139C2×D4—61no—
140C2×D4—121no—
141C2×D4C5×D1211yescharacteristic
142SD16—122no—
143D8—122no—
144M16—41no—
145C2×C8—61no—
146C22⋊C4—41no—
147C22⋊C4—121no—
148C42C4×C5×D311yescharacteristic
149C3×C5#140611yescharacteristic, complemented, Hall
150C22×C3—41no—
151C22×C3—81no—
152C22×C3C5×#9911yescharacteristic
153C2×D3—82no—
154C2×D3—81no—
155C3×C4—21no—
156C3×C4—41no—
157C3×C4—41no—
158Dic3—161no—
159C2×C5—21no—
160C2×C5—81no—
161C2×C5—481no—
162C2×C5#447411yescharacteristic
163C23—21no—
164C23—121no—
165Q8—41no—
166D4—41no—
167D4—121no—
168D4—121no—
169D4—242no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—241no—
173C2×C4C5×(C2×D3)⋊C411yescharacteristic
174C8—62no—
175C8—81no—
176C2×C3—21no—
177C2×C3—81no—
178C2×C3C5×#35311yescharacteristic
179D3—161no—
180C5#6754811yescharacteristic, direct product factor, Sylow
181C22—41no—
182C22—81no—
183C22—242no—
184C22—241no—
185C22C5×#80611yescharacteristic
186C4—21no—
187C4—41no—
188C4—41no—
189C4—481no—
190C3C5×#140611yescharacteristic, complemented, Sylow
191C2—21no—
192C2—81no—
193C2—481no—
194C2C5×#447411yescharacteristic
subgroupG/H
centerC2×C5#4474
commutatorC3×C42C2×C4×C5
Frattini#124C2×C5×D3
FittingC3×C5×#355C2
socleC2×C3×C5#353
prime radicalC5×#5058C2
cosocleC3×#124C22×C5
hypercenterC5×#355D3
hypocenterC3C5×#1406
LCSG ▷ C3×C42 ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C5 ◁ C2×C4×C5 ◁ C5×#124 ◁ C5×#355

Complements

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

NH ≅ G/Ntype
2. C3×C5×#355C2semidirect
3. C5×#4541C2semidirect
8. C5×#874C4semidirect
11. C5×#803C4semidirect
12. #67548C5direct (N × H)
14. C5×#355D3semidirect
28. C3×#355C2×C5semidirect
29. #4541C2×C5semidirect
54. #874C4×C5semidirect
57. #803C4×C5semidirect
70. #355C5×D3semidirect
149. C3×C5#1406semidirect
180. C5#67548direct (N × H)
190. C3C5×#1406semidirect

Maximal subgroups

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

subgroupindex
C5×#50582
C3×C5×#3552
C5×#45412
C5×#14063
#675485