Finite Group Databasebeta

← C5×#85419 #14511157

Subgroups — C5×#85419 #14511157

Order 1920.

398 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 68 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×#557⋊C3C211yesmaximal, characteristic, complemented
2C5×#5395C212yesmaximal
3C4×C5×GL(2,𝔽3)C211yesmaximal, characteristic
4C5×C4⋊#226C211yesmaximal, characteristic, complemented
5C4×C5×#226C212yesmaximal, complemented
6C5×#3364—31nomaximal, Hall
7C2×C5×GL(2,𝔽3)C2211yescharacteristic
8C2×C5×#226C2212yes—
9C5×#892—41nomaximal
10C4×C5×SL(2,𝔽3)C2212yes—
11C4×C5×SL(2,𝔽3)C2211yescharacteristic
12C5×#859C2211yescharacteristic
13#85419C511yesmaximal, characteristic, direct product factor, Hall
14C5×#557D311yescharacteristic, complemented
15C5×#556—31no—
16C5×#488—32no—
17C5×#487—31no—
18C5×#479—32no—
19C5×#474—31no—
20C5×#464—32no—
21C5×#462—31no—
22C5×C8×Q8—31no—
23C4×C5×Q16—32no—
24C4×C5×SD16—31no—
25C2×C4×C5×D3—41no—
26C2×C5×SL(2,𝔽3)C2311yescharacteristic
27C5×GL(2,𝔽3)—21no—
28C5×#226—22no—
29C3×C5×C4⋊C4—41no—
30C5×(C2×D3)⋊C4—42no—
31C5×C4⋊Dic3—41no—
32C4×C5×Dic3—42no—
33#557⋊C3C2×C511yescharacteristic, complemented
34#5395C2×C512yes—
35C4×GL(2,𝔽3)C2×C511yescharacteristic
36C4⋊#226C2×C511yescharacteristic, complemented
37C4×#226C2×C512yescomplemented
38C2×C5×Q16—32no—
39C2×C5×SD16—31no—
40C5×C4⋊Q8—31no—
41C5×C4⋊Q8—31no—
42C5×#126—62no—
43C5×#125—32no—
44C5×#124—32no—
45C5×C22⋊Q8—61no—
46C4×C5×Q8—31no—
47C4×C5×Q8—32no—
48C4×C5×Q8C2×D311yescharacteristic
49C4×C5×Q8C2×D312yes—
50C4×C5×D4—31no—
51C5×#117—61no—
52C5×#107—32no—
53C5×#106—31no—
54C5×C4⋊C8—31no—
55C5×C4⋊C8—32no—
56C5×#103—32no—
57C5×#103—32no—
58C5×#103—32no—
59C5×#103—31no—
60C5×#102—31no—
61C5×#102—32no—
62C4×C5×C8—31no—
63C4×C5×C8—32no—
64#3364—31noSylow
65C22×C5×D3—41no—
66C2×C3×C4×C5—41no—
67C2×C3×C4×C5—42no—
68C2×C5×Dic3—41no—
69C2×C5×Dic3—42no—
70C4×C5×D3—44no—
71C5×SL(2,𝔽3)#4111yescharacteristic
72C2×GL(2,𝔽3)C22×C511yescharacteristic
73C2×#226C22×C512yes—
74#892—41no—
75C4×SL(2,𝔽3)C22×C512yes—
76C4×SL(2,𝔽3)C22×C511yescharacteristic
77#859C22×C511yescharacteristic
78C2×C5×Q8—31no—
79C2×C5×Q8—32no—
80C2×C5×Q8C22×D311yescharacteristic
81C2×C5×D4—31no—
82C22×C4×C5—61no—
83C5×Q16—62no—
84C5×Q16—62no—
85C5×SD16—61no—
86C5×SD16—61no—
87C2×C5×C8—31no—
88C2×C5×C8—32no—
89C2×C5×C8—31no—
90C5×C4⋊C4—31no—
91C5×C4⋊C4—32no—
92C5×C4⋊C4—32no—
93C5×C4⋊C4—31no—
94C5×C4⋊C4—61no—
95C5×C4⋊C4—62no—
96C5×C4⋊C4—61no—
97C5×C4⋊C4—61no—
98C5×C4⋊C4S411yescharacteristic
99C5×C22⋊C4—61no—
100C5×C22⋊C4—62no—
101C5×C22⋊C4—62no—
102C42×C5—31no—
103C42×C5—32no—
104C42×C5—62no—
105#557C5×D311yescharacteristic, complemented
106#556—31no—
107#488—32no—
108#487—31no—
109#479—32no—
110#474—31no—
111#464—32no—
112#462—31no—
113C8×Q8—31no—
114C4×Q16—32no—
115C4×SD16—31no—
116C22×C3×C5—41no—
117C2×C5×D3—42no—
118C2×C5×D3—81no—
119C2×C5×D3—81no—
120C3×C4×C5—42no—
121C3×C4×C5—82no—
122C5×Dic3—42no—
123C5×Dic3—82no—
124C2×C4×D3—41no—
125C2×SL(2,𝔽3)C23×C511yescharacteristic
126GL(2,𝔽3)—21no—
127#226—22no—
128C3×C4⋊C4—41no—
129(C2×D3)⋊C4—42no—
130C4⋊Dic3—41no—
131C4×Dic3—42no—
132C23×C5—61no—
133C5×Q8—31no—
134C5×Q8—62no—
135C5×Q8—62no—
136C5×Q8—62no—
137C5×Q8#23911yescharacteristic
138C5×D4—61no—
139C5×D4—61no—
140C2×C4×C5—31no—
141C2×C4×C5—31no—
142C2×C4×C5—32no—
143C2×C4×C5—61no—
144C2×C4×C5—62no—
145C2×C4×C5—122no—
146C2×C4×C5C2×S412yes—
147C2×C4×C5C2×S411yescharacteristic
148C5×C8—61no—
149C5×C8—61no—
150C5×C8—62no—
151C2×Q16—32no—
152C2×SD16—31no—
153C4⋊Q8—31no—
154C4⋊Q8—31no—
155#126—62no—
156#125—32no—
157#124—32no—
158C22⋊Q8—61no—
159C4×Q8—31no—
160C4×Q8—32no—
161C4×Q8C2×C5×D311yescharacteristic
162C4×Q8C2×C5×D312yes—
163C4×D4—31no—
164#117—61no—
165#107—32no—
166#106—31no—
167C4⋊C8—31no—
168C4⋊C8—32no—
169#103—32no—
170#103—32no—
171#103—32no—
172#103—31no—
173#102—31no—
174#102—32no—
175C4×C8—31no—
176C4×C8—32no—
177C2×C3×C5—41no—
178C2×C3×C5—41no—
179C2×C3×C5—41no—
180C5×D3—82no—
181C22×D3—41no—
182C2×C3×C4—41no—
183C2×C3×C4—42no—
184C2×Dic3—41no—
185C2×Dic3—42no—
186C4×D3—44no—
187SL(2,𝔽3)C5×#4111yescharacteristic
188C22×C5—121no—
189C22×C5—121no—
190C22×C5—121no—
191C22×C5C22×S411yescharacteristic
192C4×C5—22no—
193C4×C5—31no—
194C4×C5—31no—
195C4×C5—62no—
196C4×C5—61no—
197C4×C5—122no—
198C4×C5—121no—
199C4×C5#98512yes—
200C2×Q8—31no—
201C2×Q8—32no—
202C2×Q8C22×C5×D311yescharacteristic
203C2×D4—31no—
204C22×C4—61no—
205Q16—62no—
206Q16—62no—
207SD16—61no—
208SD16—61no—
209C2×C8—31no—
210C2×C8—32no—
211C2×C8—31no—
212C4⋊C4—31no—
213C4⋊C4—32no—
214C4⋊C4—32no—
215C4⋊C4—31no—
216C4⋊C4—61no—
217C4⋊C4—62no—
218C4⋊C4—61no—
219C4⋊C4—61no—
220C4⋊C4C5×S411yescharacteristic
221C22⋊C4—61no—
222C22⋊C4—62no—
223C22⋊C4—62no—
224C42—31no—
225C42—32no—
226C42—62no—
227C3×C5—41noHall
228C22×C3—41no—
229C2×D3—42no—
230C2×D3—81no—
231C2×D3—81no—
232C3×C4—42no—
233C3×C4—82no—
234Dic3—42no—
235Dic3—82no—
236C2×C5—241no—
237C2×C5#591911yescharacteristic
238C2×C5C2×#98511yescharacteristic
239C2×C5#592711yescharacteristic
240C23—61no—
241Q8—31no—
242Q8—62no—
243Q8—62no—
244Q8—62no—
245Q8C5×#23911yescharacteristic
246D4—61no—
247D4—61no—
248C2×C4—31no—
249C2×C4—31no—
250C2×C4—32no—
251C2×C4—61no—
252C2×C4—62no—
253C2×C4—122no—
254C2×C4C2×C5×S412yes—
255C2×C4C2×C5×S411yescharacteristic
256C8—61no—
257C8—62no—
258C8—61no—
259C2×C3—41no—
260C2×C3—41no—
261C2×C3—41no—
262D3—82no—
263C5#8541911yescharacteristic, direct product factor, Sylow
264C22—121no—
265C22—121no—
266C22—121no—
267C22C22×C5×S411yescharacteristic
268C4—22no—
269C4—31no—
270C4—31no—
271C4—62no—
272C4—61no—
273C4—122no—
274C4—121no—
275C4C5×#98512yes—
276C3—41noSylow
277C2—241no—
278C2C5×#591911yescharacteristic
279C2C2×C5×#98511yescharacteristic
280C2C5×#592711yescharacteristic
subgroupG/H
center, socleC22×C5C22×S4
commutator, cosocleC2×SL(2,𝔽3)C23×C5
FrattiniC22C22×C5×S4
FittingC5×#557D3
prime radicalC2×C5×GL(2,𝔽3)C22
hypercenterC5×C4⋊C4S4
hypocenterSL(2,𝔽3)C5×#41
LCSG ▷ C2×SL(2,𝔽3) ▷ SL(2,𝔽3)
UCSC1 ◁ C22×C5 ◁ C5×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C5×#557⋊C3C2semidirect
4. C5×C4⋊#226C2semidirect
5. C4×C5×#226C2semidirect
13. #85419C5direct (N × H)
14. C5×#557D3semidirect
33. #557⋊C3C2×C5semidirect
36. C4⋊#226C2×C5semidirect
37. C4×#226C2×C5semidirect
105. #557C5×D3semidirect
263. C5#85419direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#557⋊C32
C5×#53952
C4×C5×GL(2,𝔽3)2
C5×C4⋊#2262
C4×C5×#2262
C5×#33643
C5×#8924
#854195