Finite Group Databasebeta

← C5×#71330 #14291034

Subgroups — C5×#71330 #14291034

Order 1920.

392 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 90 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
2C3×C5×#497C211yesmaximal, characteristic
3C5×#5081C212yesmaximal, complemented
4C5×#4540C211yesmaximal, characteristic
5C5×#4465C212yesmaximal, complemented
6C5×#1660—31nomaximal, Hall
7C2×C3×C5×Q16—21no—
8C2×C3×C5×SD16—21no—
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#124C2211yescharacteristic
11C5×#944—21no—
12C5×#935—21no—
13C5×#879—22no—
14C5×#878—22no—
15C5×#870C2212yes—
16C3×C5×#97C2211yescharacteristic
17C5×#808—22no—
18C5×#807—22no—
19C5×#803C2212yes—
20#71330C511yesmaximal, characteristic, direct product factor, Hall
21C5×#563—31no—
22C5×#501—32no—
23C5×#497D311yescharacteristic
24C5×#330—32no—
25C5×#329—31no—
26C2×C3×C5×Q8—21no—
27C2×C3×C5×Q8D411yescharacteristic
28C2×C3×C5×D4D411yescharacteristic
29C22×C5×Dic3—21no—
30C2×C5×Dic6—21no—
31C3×C5×Q16—42no—
32C3×C5×SD16—42no—
33C2×C3×C5×C8—21no—
34C3×C5×C4⋊C4—22no—
35C3×C5×C22⋊C4—22no—
36C3×C42×C5C2311yescharacteristic
37C5×#217—22no—
38C5×#217—21no—
39C5×C4⋊Dic3D412yes—
40C5×C4⋊Dic3D412yes—
41C5×Dic3⋊C4—22no—
42C5×Dic3⋊C4—22no—
43C5×Dic3⋊C4—22no—
44C4×C5×Dic3—21no—
45C2×C5×C3⋊C8—22no—
46#5672C2×C511yescharacteristic
47C3×#497C2×C511yescharacteristic
48#5081C2×C512yescomplemented
49#4540C2×C511yescharacteristic
50#4465C2×C512yescomplemented
51C2×C5×Q16—21no—
52C2×C5×SD16—21no—
53C5×C4⋊Q8—61no—
54C5×C4⋊Q8C2×D311yescharacteristic
55C5×#126—62no—
56C5×#125—32no—
57C5×#124C2×D311yescharacteristic
58C5×#123—61no—
59C5×C22⋊Q8—62no—
60C5×#107—62no—
61C5×#106—62no—
62C5×#97—32no—
63C5×#97C2×D311yescharacteristic
64#1660—31noSylow
65C23×C3×C5—21no—
66C3×C5×Q8—41no—
67C3×C5×Q8—41no—
68C3×C5×Q8—41no—
69C3×C5×D4—41no—
70C2×C3×C4×C5—21no—
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5C2×D412yes—
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C5×Dic3—22no—
75C2×C5×Dic3—22no—
76C2×C5×Dic3—81no—
77C5×Dic6—81no—
78C3×C5×C8—22no—
79C5×C3⋊C8—24no—
80C2×C3×Q16—21no—
81C2×C3×SD16—21no—
82C3×C4⋊Q8C22×C511yescharacteristic
83C3×#124C22×C511yescharacteristic
84#944—21no—
85#935—21no—
86#879—22no—
87#878—22no—
88#870C22×C512yes—
89C3×#97C22×C511yescharacteristic
90#808—22no—
91#807—22no—
92#803C22×C512yes—
93C2×C5×Q8—21no—
94C2×C5×Q8—61no—
95C2×C5×Q8#6711yescharacteristic
96C2×C5×D4#6711yescharacteristic
97C22×C4×C5—61no—
98C5×Q16—42no—
99C5×SD16—42no—
100C2×C5×C8—21no—
101C2×C5×C8—62no—
102C5×C4⋊C4—22no—
103C5×C4⋊C4—32no—
104C5×C4⋊C4—32no—
105C5×C4⋊C4—62no—
106C5×C4⋊C4—62no—
107C5×C4⋊C4—62no—
108C5×C22⋊C4—22no—
109C5×C22⋊C4—62no—
110C5×C22⋊C4—61no—
111C42×C5—61no—
112C42×C5C22×D311yescharacteristic
113#563—31no—
114#501—32no—
115#497C5×D311yescharacteristic
116#330—32no—
117#329—31no—
118C22×C3×C5—41no—
119C22×C3×C5—42no—
120C22×C3×C5#12011yescharacteristic
121C3×C4×C5—21no—
122C3×C4×C5—22no—
123C3×C4×C5—41no—
124C3×C4×C5—81no—
125C5×Dic3—42no—
126C5×Dic3—42no—
127C2×C3×Q8—21no—
128C2×C3×Q8C5×D411yescharacteristic
129C2×C3×D4C5×D411yescharacteristic
130C22×Dic3—21no—
131C2×Dic6—21no—
132C3×Q16—42no—
133C3×SD16—42no—
134C2×C3×C8—21no—
135C3×C4⋊C4—22no—
136C3×C22⋊C4—22no—
137C3×C42C23×C511yescharacteristic
138#217—22no—
139#217—21no—
140C4⋊Dic3C5×D412yes—
141C4⋊Dic3C5×D412yes—
142Dic3⋊C4—22no—
143Dic3⋊C4—22no—
144Dic3⋊C4—22no—
145C4×Dic3—21no—
146C2×C3⋊C8—22no—
147C23×C5—21no—
148C5×Q8—41no—
149C5×Q8—41no—
150C5×Q8—41no—
151C5×Q8—241no—
152C5×D4—41no—
153C2×C4×C5—21no—
154C2×C4×C5—41no—
155C2×C4×C5—62no—
156C2×C4×C5—62no—
157C2×C4×C5—241no—
158C2×C4×C5D3×D412yes—
159C2×C4×C5C2×#6711yescharacteristic
160C5×C8—22no—
161C5×C8—64no—
162C2×Q16—21no—
163C2×SD16—21no—
164C4⋊Q8—61no—
165C4⋊Q8C2×C5×D311yescharacteristic
166#126—62no—
167#125—32no—
168#124C2×C5×D311yescharacteristic
169#123—61no—
170C22⋊Q8—62no—
171#107—62no—
172#106—62no—
173#97—32no—
174#97C2×C5×D311yescharacteristic
175C2×C3×C5—81no—
176C2×C3×C5#45311yescharacteristic
177C2×C3×C5#45612yes—
178C23×C3—21no—
179C3×Q8—41no—
180C3×Q8—41no—
181C3×Q8—41no—
182C3×D4—41no—
183C2×C3×C4—21no—
184C2×C3×C4—41no—
185C2×C3×C4C2×C5×D412yes—
186C2×C3×C4C2×C5×D411yescharacteristic
187C2×Dic3—22no—
188C2×Dic3—22no—
189C2×Dic3—81no—
190Dic6—81no—
191C3×C8—22no—
192C3⋊C8—24no—
193C22×C5—42no—
194C22×C5—41no—
195C22×C5#93711yescharacteristic
196C4×C5—22no—
197C4×C5—21no—
198C4×C5—41no—
199C4×C5—81no—
200C4×C5—122no—
201C4×C5—122no—
202C2×Q8—21no—
203C2×Q8—61no—
204C2×Q8C5×#6711yescharacteristic
205C2×D4C5×#6711yescharacteristic
206C22×C4—61no—
207Q16—42no—
208SD16—42no—
209C2×C8—21no—
210C2×C8—62no—
211C4⋊C4—22no—
212C4⋊C4—32no—
213C4⋊C4—32no—
214C4⋊C4—62no—
215C4⋊C4—62no—
216C4⋊C4—62no—
217C22⋊C4—22no—
218C22⋊C4—62no—
219C22⋊C4—61no—
220C42—61no—
221C42C22×C5×D311yescharacteristic
222C3×C5#166011yescharacteristic, complemented, Hall
223C22×C3—41no—
224C22×C3—42no—
225C22×C3C5×#12011yescharacteristic
226C3×C4—21no—
227C3×C4—22no—
228C3×C4—41no—
229C3×C4—81no—
230Dic3—42no—
231Dic3—42no—
232C2×C5—81no—
233C2×C5#507711yescharacteristic
234C2×C5#520512yes—
235C23—21no—
236Q8—41no—
237Q8—41no—
238Q8—41no—
239Q8—241no—
240D4—41no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—62no—
244C2×C4—62no—
245C2×C4—241no—
246C2×C4C5×D3×D412yes—
247C2×C4C2×C5×#6711yescharacteristic
248C8—22no—
249C8—64no—
250C2×C3—81no—
251C2×C3C5×#45311yescharacteristic
252C2×C3C5×#45612yes—
253C5#7133011yescharacteristic, direct product factor, Sylow
254C22—42no—
255C22—41no—
256C22C5×#93711yescharacteristic
257C4—22no—
258C4—21no—
259C4—41no—
260C4—81no—
261C4—122no—
262C4—122no—
263C3C5×#166011yescharacteristic, complemented, Sylow
264C2—81no—
265C2C5×#507711yescharacteristic
266C2C5×#520512yes—
subgroupG/H
centerC22×C5#937
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#497C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC5×#497D3
hypocenterC3C5×#1660
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#497

Complements

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

NH ≅ G/Ntype
3. C5×#5081C2semidirect
5. C5×#4465C2semidirect
20. #71330C5direct (N × H)
48. #5081C2×C5semidirect
50. #4465C2×C5semidirect
222. C3×C5#1660semidirect
253. C5#71330direct (N × H)
263. C3C5×#1660semidirect

Maximal subgroups

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

subgroupindex
C5×#56722
C3×C5×#4972
C5×#50812
C5×#45402
C5×#44652
C5×#16603
#713305