Finite Group Databasebeta

← C5×#3025⋊C3 #14510983

Subgroups — C5×#3025⋊C3 #14510983

Order 1920.

342 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 36 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×#5950C211yesmaximal, characteristic, complemented
2C5×#458⋊C3C211yesmaximal, characteristic, complemented
3C5×B(4,𝔽2)⋊C3C211yesmaximal, characteristic, complemented
4C5×#3025C311yesmaximal, characteristic, complemented, Hall
5C5×#997C2211yescharacteristic
6C2×C4×C5×A4—41nomaximal
7#3025⋊C3C511yesmaximal, characteristic, direct product factor, Hall
8C5×#585C2×C311yescharacteristic, complemented
9C5×#525—31no—
10C5×#458—31no—
11C5×#458C2×C311yescharacteristic, complemented
12C5×B(4,𝔽2)—31no—
13C5×B(4,𝔽2)C2×C311yescharacteristic
14C5×#410—31no—
15C22×C5×A4—41no—
16C5×#41⋊C3—81no—
17C4×C5×A4—41no—
18C4×C5×A4—41no—
19C4×C5×A4—81no—
20#5950C2×C511yescharacteristic, complemented
21#458⋊C3C2×C511yescharacteristic, complemented
22B(4,𝔽2)⋊C3C2×C511yescharacteristic, complemented
23C5×2−1+4—61no—
24C5×H(5,𝔽2)—31no—
25C5×H(5,𝔽2)—61no—
26C5×H(5,𝔽2)C22×C311yescharacteristic
27C2×C5×#41—31no—
28C2×C5×#41—61no—
29C2×C5×#41—61no—
30C23×C4×C5A411yescharacteristic, complemented
31C5×#123—31no—
32C5×#123—31no—
33C5×C22⋊Q8—61no—
34C5×#121—61no—
35C5×#120—31no—
36C5×#120—31no—
37C4×C5×D4—61no—
38C4×C5×D4—61no—
39C5×#117—31no—
40C5×#99—32no—
41C5×#99—31no—
42C5×#99—31no—
43#3025C3×C511yescharacteristic, complemented, Sylow
44C2×C5×A4—42no—
45C2×C5×A4—41no—
46C2×C5×A4—81no—
47C2×C3×C4×C5—161no—
48C5×SL(2,𝔽3)—81no—
49#997C22×C511yescharacteristic
50C2×C4×A4—41no—
51C24×C5C2×A411yescharacteristic
52C5×#41—21no—
53C5×#41—62no—
54C5×#41—62no—
55C5×#41—61no—
56C5×#41—62no—
57C5×#41—61no—
58C5×#41—62no—
59C5×#41—62no—
60C5×#41—61no—
61C2×C5×Q8—31no—
62C2×C5×Q8—61no—
63C2×C5×Q8—61no—
64C2×C5×D4—31no—
65C2×C5×D4—31no—
66C2×C5×D4—31no—
67C2×C5×D4—61no—
68C2×C5×D4—62no—
69C2×C5×D4—61no—
70C2×C5×D4—61no—
71C2×C5×D4—61no—
72C2×C5×D4—61no—
73C2×C5×D4—61no—
74C22×C4×C5—21no—
75C22×C4×C5—31no—
76C22×C4×C5—31no—
77C22×C4×C5—61no—
78C22×C4×C5—61no—
79C22×C4×C5—61no—
80C22×C4×C5C2×A411yescharacteristic
81C22×C4×C5C2×A411yescharacteristic
82C5×C4⋊C4—61no—
83C5×C4⋊C4—61no—
84C5×C4⋊C4—61no—
85C5×C22⋊C4—31no—
86C5×C22⋊C4—31no—
87C5×C22⋊C4—61no—
88C5×C22⋊C4—61no—
89C5×C22⋊C4—61no—
90C5×C22⋊C4—61no—
91C42×C5—61no—
92#585C2×C3×C511yescharacteristic, complemented
93#525—31no—
94#458—31no—
95#458C2×C3×C511yescharacteristic, complemented
96B(4,𝔽2)—31no—
97B(4,𝔽2)C2×C3×C511yescharacteristic
98#410—31no—
99C22×C3×C5—161no—
100C5×A4—41no—
101C5×A4—81no—
102C3×C4×C5—161no—
103C3×C4×C5—161no—
104C22×A4—41no—
105#41⋊C3—81no—
106C4×A4—41no—
107C4×A4—41no—
108C4×A4—81no—
109C23×C5—21no—
110C23×C5—31no—
111C23×C5—31no—
112C23×C5—42no—
113C23×C5—61no—
114C23×C5—61no—
115C23×C5C22×A411yescharacteristic
116C5×Q8—21no—
117C5×Q8—62no—
118C5×Q8—61no—
119C5×D4—62no—
120C5×D4—62no—
121C5×D4—62no—
122C5×D4—61no—
123C5×D4—61no—
124C5×D4—62no—
125C5×D4—122no—
126C5×D4—122no—
127C2×C4×C5—31no—
128C2×C4×C5—31no—
129C2×C4×C5—31no—
130C2×C4×C5—31no—
131C2×C4×C5—41no—
132C2×C4×C5—61no—
133C2×C4×C5—61no—
134C2×C4×C5—61no—
135C2×C4×C5—62no—
136C2×C4×C5—61no—
137C2×C4×C5—61no—
138C2×C4×C5—61no—
139C2×C4×C5—61no—
140C2×C4×C5—61no—
141C2×C4×C5—61no—
142C2×C4×C5—121no—
1432−1+4—61no—
144H(5,𝔽2)—31no—
145H(5,𝔽2)—61no—
146H(5,𝔽2)C22×C3×C511yescharacteristic
147C2×#41—31no—
148C2×#41—61no—
149C2×#41—61no—
150C23×C4C5×A411yescharacteristic, complemented
151#123—31no—
152#123—31no—
153C22⋊Q8—61no—
154#121—61no—
155#120—31no—
156#120—31no—
157C4×D4—61no—
158C4×D4—61no—
159#117—31no—
160#99—32no—
161#99—31no—
162#99—31no—
163C2×C3×C5—162no—
164C2×C3×C5—161no—
165C2×A4—42no—
166C2×A4—41no—
167C2×A4—81no—
168C2×C3×C4—161no—
169SL(2,𝔽3)—81no—
170C22×C5—31no—
171C22×C5—41no—
172C22×C5—41no—
173C22×C5—62no—
174C22×C5—61no—
175C22×C5—61no—
176C22×C5—81no—
177C22×C5—121no—
178C22×C5—121no—
179C22×C5—121no—
180C22×C5—241no—
181C4×C5—31no—
182C4×C5—41no—
183C4×C5—61no—
184C4×C5—61no—
185C4×C5—121no—
186C4×C5—121no—
187C4×C5#120⋊C311yescharacteristic
188C24C2×C5×A411yescharacteristic
189#41—21no—
190#41—62no—
191#41—62no—
192#41—61no—
193#41—62no—
194#41—61no—
195#41—62no—
196#41—62no—
197#41—61no—
198C2×Q8—31no—
199C2×Q8—61no—
200C2×Q8—61no—
201C2×D4—31no—
202C2×D4—31no—
203C2×D4—31no—
204C2×D4—61no—
205C2×D4—62no—
206C2×D4—61no—
207C2×D4—61no—
208C2×D4—61no—
209C2×D4—61no—
210C2×D4—61no—
211C22×C4—21no—
212C22×C4—31no—
213C22×C4—31no—
214C22×C4—61no—
215C22×C4—61no—
216C22×C4—61no—
217C22×C4C2×C5×A411yescharacteristic
218C22×C4C2×C5×A411yescharacteristic
219C4⋊C4—61no—
220C4⋊C4—61no—
221C4⋊C4—61no—
222C22⋊C4—31no—
223C22⋊C4—31no—
224C22⋊C4—61no—
225C22⋊C4—61no—
226C22⋊C4—61no—
227C22⋊C4—61no—
228C42—61no—
229C3×C5—161noHall
230C22×C3—161no—
231A4—41no—
232A4—81no—
233C3×C4—161no—
234C3×C4—161no—
235C2×C5—42no—
236C2×C5—61no—
237C2×C5—121no—
238C2×C5—121no—
239C2×C5C2×#120⋊C311yescharacteristic
240C23—21no—
241C23—31no—
242C23—31no—
243C23—42no—
244C23—61no—
245C23—61no—
246C23C22×C5×A411yescharacteristic
247Q8—21no—
248Q8—62no—
249Q8—61no—
250D4—62no—
251D4—62no—
252D4—62no—
253D4—61no—
254D4—61no—
255D4—62no—
256D4—122no—
257D4—122no—
258C2×C4—31no—
259C2×C4—31no—
260C2×C4—31no—
261C2×C4—31no—
262C2×C4—41no—
263C2×C4—61no—
264C2×C4—61no—
265C2×C4—61no—
266C2×C4—62no—
267C2×C4—61no—
268C2×C4—61no—
269C2×C4—61no—
270C2×C4—61no—
271C2×C4—61no—
272C2×C4—61no—
273C2×C4—121no—
274C2×C3—162no—
275C2×C3—161no—
276C5#3025⋊C311yescharacteristic, direct product factor, Sylow
277C22—31no—
278C22—41no—
279C22—41no—
280C22—62no—
281C22—61no—
282C22—61no—
283C22—81no—
284C22—121no—
285C22—121no—
286C22—121no—
287C22—241no—
288C4—31no—
289C4—41no—
290C4—61no—
291C4—61no—
292C4—121no—
293C4—121no—
294C4C5×#120⋊C311yescharacteristic
295C3—161noSylow
296C2—42no—
297C2—61no—
298C2—121no—
299C2—121no—
300C2C2×C5×#120⋊C311yescharacteristic
subgroupG/H
center, hypercenterC4×C5#120⋊C3
commutator, cosocle, hypocenterH(5,𝔽2)C22×C3×C5
FrattiniC23C22×C5×A4
FittingC5×#3025C3
socleC2×C5C2×#120⋊C3
LCSG ▷ H(5,𝔽2)
UCSC1 ◁ C4×C5

Complements

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

NH ≅ G/Ntype
1. C5×#5950C2semidirect
2. C5×#458⋊C3C2semidirect
3. C5×B(4,𝔽2)⋊C3C2semidirect
4. C5×#3025C3semidirect
7. #3025⋊C3C5direct (N × H)
8. C5×#585C2×C3semidirect
11. C5×#458C2×C3semidirect
20. #5950C2×C5semidirect
21. #458⋊C3C2×C5semidirect
22. B(4,𝔽2)⋊C3C2×C5semidirect
30. C23×C4×C5A4semidirect
43. #3025C3×C5semidirect
92. #585C2×C3×C5semidirect
95. #458C2×C3×C5semidirect
150. C23×C4C5×A4semidirect
276. C5#3025⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#59502
C5×#458⋊C32
C5×B(4,𝔽2)⋊C32
C5×#30253
C2×C4×C5×A44
#3025⋊C35