Finite Group Databasebeta

← C5×#69155 #14316883

Subgroups — C5×#69155 #14316883

Order 1920.

452 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 82 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×#5672C211yesmaximal, characteristic, complemented
2C5×#5061C211yesmaximal, characteristic
3C5×#4742C212yesmaximal
4C3×C5×#354C211yesmaximal, characteristic, complemented
5C5×#4472C212yesmaximal, complemented
6C5×#2201—31nomaximal, Hall
7C5×#1004C2211yescharacteristic
8C3×C5×#124C2211yescharacteristic
9C5×#944—21no—
10C5×#942—21no—
11C5×#935C2212yes—
12C5×#886—22no—
13C5×#879—22no—
14C5×#878—22no—
15C5×#870—21no—
16C3×C5×#99C2212yes—
17C5×#833C2211yescharacteristic
18C5×#806—22no—
19C5×#805—21no—
20#69155C511yesmaximal, characteristic, direct product factor, Hall
21C5×#563—31no—
22C5×#458—32no—
23C5×#455—31no—
24C5×#354D311yescharacteristic, complemented
25C5×#352—32no—
26C2×C3×C5×Q8D411yescharacteristic
27C2×C3×C5×D4C2311yescharacteristic
28C2×C5×#67—22no—
29C22×C5×Dic3D412yes—
30C5×#237—41no—
31C5×D3×D4—41no—
32C5×#235—21no—
33C2×C5×Dic6—21no—
34C3×C5×C22⋊C4—22no—
35C3×C5×C22⋊C4—22no—
36C3×C42×C5D411yescharacteristic
37C5×#217—22no—
38C5×#217D412yes—
39C5×#216—41no—
40C5×#215—41no—
41C5×(C2×D3)⋊C4—42no—
42C5×C4⋊Dic3—21no—
43C5×C4⋊Dic3—21no—
44C5×C4⋊Dic3—42no—
45C5×Dic3⋊C4—22no—
46C5×Dic3⋊C4—22no—
47C5×Dic3⋊C4—22no—
48C4×C5×Dic3—21no—
49C5×#208—21no—
50#5672C2×C511yescharacteristic, complemented
51#5061C2×C511yescharacteristic
52#4742C2×C512yes—
53C3×#354C2×C511yescharacteristic, complemented
54#4472C2×C512yescomplemented
55C5×H(5,𝔽2)—31no—
56C5×#137—61no—
57C5×C4⋊Q8—61no—
58C5×#126—62no—
59C5×#125—61no—
60C5×#124C2×D311yescharacteristic
61C5×#123—32no—
62C5×#123—62no—
63C5×C22⋊Q8—62no—
64C5×#104—61no—
65C5×#100—31no—
66C5×#99—62no—
67C5×#99C2×D312yes—
68#2201—31noSylow
69C23×C3×C5C2×D412yes—
70C22×C5×D3—22no—
71C3×C5×Q8—41no—
72C3×C5×D4—41no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5—21no—
75C2×C3×C4×C5—42no—
76C2×C3×C4×C5C2×D411yescharacteristic
77C5×#67—42no—
78C5×#67—41no—
79C2×C5×Dic3—22no—
80C2×C5×Dic3—22no—
81C2×C5×Dic3—22no—
82C2×C5×Dic3—42no—
83C5×D12—21no—
84C4×C5×D3—41no—
85C5×Dic6—21no—
86C5×Dic6—81no—
87C5×C3⋊C8—41no—
88#1004C22×C511yescharacteristic
89C3×#124C22×C511yescharacteristic
90#944—21no—
91#942—21no—
92#935C22×C512yes—
93#886—22no—
94#879—22no—
95#878—22no—
96#870—21no—
97C3×#99C22×C512yes—
98#833C22×C511yescharacteristic
99#806—22no—
100#805—21no—
101C5×#41—61no—
102C5×#41—121no—
103C2×C5×Q8—61no—
104C2×C5×Q8D1211yescharacteristic
105C2×C5×D4—62no—
106C2×C5×D4—121no—
107C2×C5×D4C22×D311yescharacteristic
108C22×C4×C5—32no—
109C5×Q16—121no—
110C5×SD16—121no—
111C5×M16—61no—
112C5×C4⋊C4—61no—
113C5×C4⋊C4—62no—
114C5×C4⋊C4—62no—
115C5×C4⋊C4—61no—
116C5×C4⋊C4—62no—
117C5×C4⋊C4—122no—
118C5×C22⋊C4—22no—
119C5×C22⋊C4—22no—
120C5×C22⋊C4—32no—
121C5×C22⋊C4—62no—
122C5×C22⋊C4—122no—
123C42×C5—61no—
124C42×C5D1211yescharacteristic
125#563—31no—
126#458—32no—
127#455—31no—
128#354C5×D311yescharacteristic, complemented
129#352—32no—
130C22×C3×C5—22no—
131C22×C3×C5—42no—
132C22×C3×C5#12011yescharacteristic
133C2×C5×D3—41no—
134C2×C5×D3—82no—
135C3×C4×C5—21no—
136C3×C4×C5—41no—
137C3×C4×C5—41no—
138C3×C4×C5—82no—
139C5×Dic3—42no—
140C5×Dic3—41no—
141C5×Dic3—42no—
142C2×C3×Q8C5×D411yescharacteristic
143C2×C3×D4C23×C511yescharacteristic
144C2×#67—22no—
145C22×Dic3C5×D412yes—
146#237—41no—
147D3×D4—41no—
148#235—21no—
149C2×Dic6—21no—
150C3×C22⋊C4—22no—
151C3×C22⋊C4—22no—
152C3×C42C5×D411yescharacteristic
153#217—22no—
154#217C5×D412yes—
155#216—41no—
156#215—41no—
157(C2×D3)⋊C4—42no—
158C4⋊Dic3—21no—
159C4⋊Dic3—21no—
160C4⋊Dic3—42no—
161Dic3⋊C4—22no—
162Dic3⋊C4—22no—
163Dic3⋊C4—22no—
164C4×Dic3—21no—
165#208—21no—
166C23×C5—62no—
167C23×C5D3×D412yes—
168C5×Q8—41no—
169C5×Q8—61no—
170C5×Q8—241no—
171C5×D4—41no—
172C5×D4—61no—
173C5×D4—122no—
174C5×D4—121no—
175C2×C4×C5—21no—
176C2×C4×C5—21no—
177C2×C4×C5—42no—
178C2×C4×C5—62no—
179C2×C4×C5—62no—
180C2×C4×C5—62no—
181C2×C4×C5—121no—
182C2×C4×C5—122no—
183C2×C4×C5C2×D1211yescharacteristic
184C5×C8—121no—
185H(5,𝔽2)—31no—
186#137—61no—
187C4⋊Q8—61no—
188#126—62no—
189#125—61no—
190#124C2×C5×D311yescharacteristic
191#123—32no—
192#123—62no—
193C22⋊Q8—62no—
194#104—61no—
195#100—31no—
196#99—62no—
197#99C2×C5×D312yes—
198C2×C3×C5—21no—
199C2×C3×C5—42no—
200C2×C3×C5B(4,𝔽2)11yescharacteristic
201C5×D3—81no—
202C23×C3C2×C5×D412yes—
203C22×D3—22no—
204C3×Q8—41no—
205C3×D4—41no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—42no—
209C2×C3×C4C2×C5×D411yescharacteristic
210#67—42no—
211#67—41no—
212C2×Dic3—22no—
213C2×Dic3—22no—
214C2×Dic3—22no—
215C2×Dic3—42no—
216D12—21no—
217C4×D3—41no—
218Dic6—21no—
219Dic6—81no—
220C3⋊C8—41no—
221C22×C5—22no—
222C22×C5—42no—
223C22×C5—121no—
224C22×C5—242no—
225C22×C5#88211yescharacteristic
226C4×C5—21no—
227C4×C5—41no—
228C4×C5—41no—
229C4×C5—82no—
230C4×C5—122no—
231C4×C5—121no—
232C4×C5—122no—
233#41—61no—
234#41—121no—
235C2×Q8—61no—
236C2×Q8C5×D1211yescharacteristic
237C2×D4—62no—
238C2×D4—121no—
239C2×D4C22×C5×D311yescharacteristic
240C22×C4—32no—
241Q16—121no—
242SD16—121no—
243M16—61no—
244C4⋊C4—61no—
245C4⋊C4—62no—
246C4⋊C4—62no—
247C4⋊C4—61no—
248C4⋊C4—62no—
249C4⋊C4—122no—
250C22⋊C4—22no—
251C22⋊C4—22no—
252C22⋊C4—32no—
253C22⋊C4—62no—
254C22⋊C4—122no—
255C42—61no—
256C42C5×D1211yescharacteristic
257C3×C5#220111yescharacteristic, complemented, Hall
258C22×C3—22no—
259C22×C3—42no—
260C22×C3C5×#12011yescharacteristic
261C2×D3—41no—
262C2×D3—82no—
263C3×C4—21no—
264C3×C4—41no—
265C3×C4—41no—
266C3×C4—82no—
267Dic3—42no—
268Dic3—41no—
269Dic3—42no—
270C2×C5—21no—
271C2×C5—42no—
272C2×C5—241no—
273C2×C5#474111yescharacteristic
274C23—62no—
275C23C5×D3×D412yes—
276Q8—41no—
277Q8—61no—
278Q8—241no—
279D4—41no—
280D4—61no—
281D4—122no—
282D4—121no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—42no—
286C2×C4—62no—
287C2×C4—62no—
288C2×C4—62no—
289C2×C4—121no—
290C2×C4—122no—
291C2×C4C2×C5×D1211yescharacteristic
292C8—121no—
293C2×C3—21no—
294C2×C3—42no—
295C2×C3C5×B(4,𝔽2)11yescharacteristic
296D3—81no—
297C5#6915511yescharacteristic, direct product factor, Sylow
298C22—22no—
299C22—42no—
300C22—121no—
301C22—242no—
302C22C5×#88211yescharacteristic
303C4—21no—
304C4—41no—
305C4—41no—
306C4—82no—
307C4—122no—
308C4—121no—
309C4—122no—
310C3C5×#220111yescharacteristic, complemented, Sylow
311C2—21no—
312C2—42no—
313C2—241no—
314C2C5×#474111yescharacteristic
subgroupG/H
centerC2×C5#4741
commutator, cosocleC2×C3×D4C23×C5
FrattiniC2×D4C22×C5×D3
FittingC3×C5×#354C2
socleC2×C3×C5B(4,𝔽2)
prime radicalC5×#1004C22
hypercenterC5×#354D3
hypocenterC3C5×#2201
LCSG ▷ C2×C3×D4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C5 ◁ C2×C5×D4 ◁ C5×#354

Complements

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

NH ≅ G/Ntype
1. C5×#5672C2semidirect
4. C3×C5×#354C2semidirect
5. C5×#4472C2semidirect
20. #69155C5direct (N × H)
24. C5×#354D3semidirect
50. #5672C2×C5semidirect
53. C3×#354C2×C5semidirect
54. #4472C2×C5semidirect
128. #354C5×D3semidirect
257. C3×C5#2201semidirect
297. C5#69155direct (N × H)
310. C3C5×#2201semidirect

Maximal subgroups

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

subgroupindex
C5×#56722
C5×#50612
C5×#47422
C3×C5×#3542
C5×#44722
C5×#22013
#691555