Finite Group Databasebeta

← C5×#67458 #14278146

Subgroups — C5×#67458 #14278146

Order 1920.

248 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 70 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×#4981C211yesmaximal, characteristic
2C3×C5×#324C211yesmaximal, characteristic
3C5×#4530C211yesmaximal, characteristic
4C5×#1346—31nomaximal, Hall
5C2×C3×C5×C4⋊C4C2211yescharacteristic
6C2×C5×C4⋊Dic3C411yescharacteristic
7C2×C5×Dic3⋊C4—21no—
8C2×C5×#208—21no—
9C3×C5×C22⋊C8—21no—
10C5×C3⋊#95—21no—
11C5×C3⋊#95C411yescharacteristic
12#67458C511yesmaximal, characteristic, direct product factor, Hall
13C5×#398—31no—
14C5×#343—31no—
15C5×#324D311yescharacteristic
16C22×C3×C4×C5C2×C411yescharacteristic
17C22×C3×C4×C5D411yescharacteristic
18C22×C3×C4×C5D411yescharacteristic
19C22×C5×Dic3—21no—
20C22×C5×Dic3—21no—
21C2×C3×C5×C8—41no—
22C3×C5×C4⋊C4—41no—
23C5×C4⋊Dic3—41no—
24C5×Dic3⋊C4—41no—
25C5×Dic3⋊C4—41no—
26C5×#208—22no—
27C5×#208—41no—
28C2×C5×C3⋊C8—41no—
29#4981C2×C511yescharacteristic
30C3×#324C2×C511yescharacteristic
31#4530C2×C511yescharacteristic
32C2×C5×M16—61no—
33C2×C5×C4⋊C4—31no—
34C2×C5×C4⋊C4—61no—
35C2×C5×C4⋊C4C2×D311yescharacteristic
36C5×C22⋊C8—21no—
37C5×#95—31no—
38C5×#95—61no—
39#1346—31noSylow
40C23×C3×C5C22⋊C411yescharacteristic
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5—21no—
45C2×C3×C4×C5—41no—
46C2×C3×C4×C5—41no—
47C2×C3×C4×C5D811yescharacteristic
48C2×C3×C4×C5SD1611yescharacteristic
49C2×C5×Dic3—22no—
50C2×C5×Dic3—41no—
51C2×C5×Dic3—41no—
52C2×C5×Dic3—41no—
53C2×C5×Dic3—41no—
54C2×C5×Dic3—41no—
55C3×C5×C8—81no—
56C5×C3⋊C8—42no—
57C2×C3×C4⋊C4C22×C511yescharacteristic
58C2×C4⋊Dic3C4×C511yescharacteristic
59C2×Dic3⋊C4—21no—
60C2×#208—21no—
61C3×C22⋊C8—21no—
62C3⋊#95—21no—
63C3⋊#95C4×C511yescharacteristic
64C22×C4×C5—61no—
65C22×C4×C5—61no—
66C22×C4×C5C4×D311yescharacteristic
67C22×C4×C5D1211yescharacteristic
68C22×C4×C5#6711yescharacteristic
69C5×M16—62no—
70C5×M16—121no—
71C2×C5×C8—41no—
72C2×C5×C8—121no—
73C5×C4⋊C4—41no—
74C5×C4⋊C4—121no—
75C5×C4⋊C4—121no—
76C5×C4⋊C4—121no—
77#398—31no—
78#343—31no—
79#324C5×D311yescharacteristic
80C22×C3×C5—21no—
81C22×C3×C5—21no—
82C22×C3×C5#9911yescharacteristic
83C22×C3×C5#10211yescharacteristic
84C22×C3×C5#10411yescharacteristic
85C3×C4×C5—21no—
86C3×C4×C5—21no—
87C3×C4×C5—41no—
88C3×C4×C5—41no—
89C5×Dic3—42no—
90C5×Dic3—81no—
91C22×C3×C4C2×C4×C511yescharacteristic
92C22×C3×C4C5×D411yescharacteristic
93C22×C3×C4C5×D411yescharacteristic
94C22×Dic3—21no—
95C22×Dic3—21no—
96C2×C3×C8—41no—
97C3×C4⋊C4—41no—
98C4⋊Dic3—41no—
99Dic3⋊C4—41no—
100Dic3⋊C4—41no—
101#208—22no—
102#208—41no—
103C2×C3⋊C8—41no—
104C23×C5(C2×D3)⋊C411yescharacteristic
105C2×C4×C5—21no—
106C2×C4×C5—21no—
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—41no—
110C2×C4×C5—41no—
111C2×C4×C5—62no—
112C2×C4×C5—121no—
113C2×C4×C5—121no—
114C2×C4×C5—121no—
115C2×C4×C5—121no—
116C2×C4×C5—121no—
117C2×C4×C5#20411yescharacteristic
118C2×C4×C5D2411yescharacteristic
119C5×C8—81no—
120C5×C8—122no—
121C2×M16—61no—
122C2×C4⋊C4—31no—
123C2×C4⋊C4—61no—
124C2×C4⋊C4C2×C5×D311yescharacteristic
125C22⋊C8—21no—
126#95—31no—
127#95—61no—
128C2×C3×C5—21no—
129C2×C3×C5—21no—
130C2×C3×C5#32711yescharacteristic
131C2×C3×C5#35211yescharacteristic
132C2×C3×C5#35611yescharacteristic
133C23×C3C5×C22⋊C411yescharacteristic
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—41no—
139C2×C3×C4—41no—
140C2×C3×C4C5×D811yescharacteristic
141C2×C3×C4C5×SD1611yescharacteristic
142C2×Dic3—22no—
143C2×Dic3—41no—
144C2×Dic3—41no—
145C2×Dic3—41no—
146C2×Dic3—41no—
147C2×Dic3—41no—
148C3×C8—81no—
149C3⋊C8—42no—
150C22×C5—21no—
151C22×C5—21no—
152C22×C5#80611yescharacteristic
153C22×C5#82111yescharacteristic
154C22×C5#82511yescharacteristic
155C4×C5—21no—
156C4×C5—21no—
157C4×C5—41no—
158C4×C5—41no—
159C4×C5—122no—
160C4×C5—241no—
161C22×C4—61no—
162C22×C4—61no—
163C22×C4C4×C5×D311yescharacteristic
164C22×C4C5×D1211yescharacteristic
165C22×C4C5×#6711yescharacteristic
166M16—62no—
167M16—121no—
168C2×C8—41no—
169C2×C8—121no—
170C4⋊C4—41no—
171C4⋊C4—121no—
172C4⋊C4—121no—
173C4⋊C4—121no—
174C3×C5#134611yescharacteristic, complemented, Hall
175C22×C3—21no—
176C22×C3—21no—
177C22×C3C5×#9911yescharacteristic
178C22×C3C5×#10211yescharacteristic
179C22×C3C5×#10411yescharacteristic
180C3×C4—21no—
181C3×C4—21no—
182C3×C4—41no—
183C3×C4—41no—
184Dic3—42no—
185Dic3—81no—
186C2×C5—21no—
187C2×C5—21no—
188C2×C5#447011yescharacteristic
189C2×C5#447211yescharacteristic
190C2×C5#447811yescharacteristic
191C23C5×(C2×D3)⋊C411yescharacteristic
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—62no—
199C2×C4—121no—
200C2×C4—121no—
201C2×C4—121no—
202C2×C4—121no—
203C2×C4—121no—
204C2×C4C5×#20411yescharacteristic
205C2×C4C5×D2411yescharacteristic
206C8—81no—
207C8—122no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3C5×#32711yescharacteristic
211C2×C3C5×#35211yescharacteristic
212C2×C3C5×#35611yescharacteristic
213C5#6745811yescharacteristic, direct product factor, Sylow
214C22—21no—
215C22—21no—
216C22C5×#80611yescharacteristic
217C22C5×#82111yescharacteristic
218C22C5×#82511yescharacteristic
219C4—21no—
220C4—21no—
221C4—41no—
222C4—41no—
223C4—122no—
224C4—241no—
225C3C5×#134611yescharacteristic, complemented, Sylow
226C2—21no—
227C2—21no—
228C2C5×#447011yescharacteristic
229C2C5×#447211yescharacteristic
230C2C5×#447811yescharacteristic
subgroupG/H
centerC22×C5#806
commutatorC22×C3×C4C2×C4×C5
FrattiniC2×C4⋊C4C2×C5×D3
FittingC3×C5×#324C2
socleC22×C3×C5#99
prime radicalC23×C3×C5C22⋊C4
cosocleC2×C3×C4⋊C4C22×C5
hypercenterC5×#324D3
hypocenterC3C5×#1346
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C23×C5 ◁ C2×C5×C4⋊C4 ◁ C5×#324

Complements

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

NH ≅ G/Ntype
12. #67458C5direct (N × H)
174. C3×C5#1346semidirect
213. C5#67458direct (N × H)
225. C3C5×#1346semidirect

Maximal subgroups

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

subgroupindex
C5×#49812
C3×C5×#3242
C5×#45302
C5×#13463
#674585