Finite Group Databasebeta

← C3×#10604661 #14285259

Subgroups — C3×#10604661 #14285259

Order 1920.

456 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 120 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
1C3×D5×C4⋊Q8C211yesmaximal, characteristic
2C3×#65684C211yesmaximal, characteristic
3C3×#65684C211yesmaximal, characteristic
4C3×#64873C214yesmaximal, complemented
5#10604661C311yesmaximal, characteristic, direct product factor, Hall
6C2×C3×Q8×D5—21no—
7C3×C5×C4⋊Q8C411yescharacteristic
8C3×#4090—21no—
9C3×D5×C4⋊C4—21no—
10C3×D5×C4⋊C4C412yes—
11C3×#4034—21no—
12C3×#4034C2212yes—
13C3×C42×D5C2211yescharacteristic
14C3×#4015C411yescharacteristic
15C3×#4004C2212yes—
16C3×#4004C2212yes—
17C3×#4003—21no—
18C3×#4003—21no—
19C3×#4002—21no—
20C3×#4002—21no—
21C3×#1556—51nomaximal, Hall
22D5×C4⋊Q8C2×C311yescharacteristic
23#65684C2×C311yescharacteristic
24#65684C2×C311yescharacteristic
25#64873C2×C314yescomplemented
26C2×C3×C5×Q8—21no—
27C3×Q8×D5—44no—
28C2×C3×C4×D5—22no—
29C2×C3×C4×D5C2×C411yescharacteristic
30C2×C3×C4×D5D411yescharacteristic
31C2×C3×C4×D5D411yescharacteristic
32C2×C3×Dic10—21no—
33C2×C3×Dic10—22no—
34C2×C3×#170—22no—
35C2×C3×#170—22no—
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4C2×C412yes—
38C3×C42×C5C2×C411yescharacteristic
39C3×C4⋊Dic5—21no—
40C3×C4⋊Dic5C2×C412yes—
41C3×#683—22no—
42C3×#683—22no—
43C3×C4×Dic5D411yescharacteristic
44C3×C4×Dic5D411yescharacteristic
45C3×C4×Dic5C2311yescharacteristic
46C2×C3×C4⋊Q8—51no—
47C3×#432—51no—
48C3×#432—51no—
49C3×#332—54no—
50C2×Q8×D5—21no—
51C5×C4⋊Q8C3×C411yescharacteristic
52#4090—21no—
53D5×C4⋊C4—21no—
54D5×C4⋊C4C3×C412yes—
55#4034—21no—
56#4034C22×C312yes—
57C42×D5C22×C311yescharacteristic
58#4015C3×C411yescharacteristic
59#4004C22×C312yes—
60#4004C22×C312yes—
61#4003—21no—
62#4003—21no—
63#4002—21no—
64#4002—21no—
65#1556—51noSylow
66C22×C3×D5C22⋊C411yescharacteristic
67C3×C5×Q8—42no—
68C2×C3×C4×C5—22no—
69C2×C3×C4×C5C22⋊C411yescharacteristic
70C2×C3×C4×C5C22⋊C411yescharacteristic
71C2×C3×C4×C5C22×C411yescharacteristic
72C2×C3×Dic5—22no—
73C2×C3×Dic5C22⋊C411yescharacteristic
74C2×C3×Dic5C2×D411yescharacteristic
75C2×C3×Dic5C2×D411yescharacteristic
76C3×C4×D5—22no—
77C3×C4×D5—22no—
78C3×C4×D5—22no—
79C3×C4×D5—44no—
80C3×Dic10—42no—
81C3×Dic10—44no—
82C3×#170—42no—
83C3×#170—42no—
84C22×C3×Q8—101no—
85C3×C4⋊Q8—52no—
86C3×C4⋊Q8—51no—
87C3×C4⋊Q8—101no—
88C3×C4⋊Q8—101no—
89C3×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
90C2×C3×C4⋊C4—52no—
91C2×C3×C4⋊C4—101no—
92C2×C3×C42—51no—
93C3×C4⋊C8—52no—
94C3×C4⋊C8—52no—
95C3×C22⋊C8—101no—
96C3×C22⋊C8—101no—
97C3×#97—101no—
98C3×#97—101no—
99C2×C5×Q8—21no—
100Q8×D5—44no—
101C2×C4×D5—22no—
102C2×C4×D5C2×C3×C411yescharacteristic
103C2×C4×D5C3×D411yescharacteristic
104C2×C4×D5C3×D411yescharacteristic
105C2×Dic10—21no—
106C2×Dic10—22no—
107C2×#170—22no—
108C2×#170—22no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4C2×C3×C412yes—
111C42×C5C2×C3×C411yescharacteristic
112C4⋊Dic5—21no—
113C4⋊Dic5C2×C3×C412yes—
114#683—22no—
115#683—22no—
116C4×Dic5C3×D411yescharacteristic
117C4×Dic5C3×D411yescharacteristic
118C4×Dic5C23×C311yescharacteristic
119C2×C4⋊Q8—51no—
120#432—51no—
121#432—51no—
122#332—54no—
123C22×C3×C5C2×C22⋊C411yescharacteristic
124C2×C3×D5—21no—
125C2×C3×D5—21no—
126C2×C3×D5#10112yes—
127C3×C4×C5—21no—
128C3×C4×C5—21no—
129C3×C4×C5—21no—
130C3×C4×C5—42no—
131C3×Dic5—21no—
132C3×Dic5—42no—
133C3×Dic5AGL(1,ℤ/8)12yes—
134C3×Dic5#13712yes—
135C2×C3×Q8—21no—
136C2×C3×Q8—102no—
137C2×C3×Q8—101no—
138C2×C3×Q8—204no—
139C22×C3×C4—51no—
140C22×C3×C4—51no—
141C22×C3×C4—51no—
142C22×C3×C4—102no—
143C2×C3×C8—102no—
144C2×C3×C8—102no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—52no—
147C3×C4⋊C4—102no—
148C3×C4⋊C4—102no—
149C3×C4⋊C4—101no—
150C3×C4⋊C4C2×AGL(1,𝔽5)12yes—
151C3×C42—51no—
152C3×C42—51no—
153C3×C42—51no—
154C3×C42C2×AGL(1,𝔽5)11yescharacteristic
155C22×D5C3×C22⋊C411yescharacteristic
156C5×Q8—42no—
157C2×C4×C5—22no—
158C2×C4×C5C3×C22⋊C411yescharacteristic
159C2×C4×C5C3×C22⋊C411yescharacteristic
160C2×C4×C5C22×C3×C411yescharacteristic
161C2×Dic5—22no—
162C2×Dic5C3×C22⋊C411yescharacteristic
163C2×Dic5C2×C3×D411yescharacteristic
164C2×Dic5C2×C3×D411yescharacteristic
165C4×D5—22no—
166C4×D5—22no—
167C4×D5—22no—
168C4×D5—44no—
169Dic10—42no—
170Dic10—44no—
171#170—42no—
172#170—42no—
173C22×Q8—101no—
174C4⋊Q8—52no—
175C4⋊Q8—51no—
176C4⋊Q8—101no—
177C4⋊Q8—101no—
178C4⋊Q8C3×AGL(1,𝔽5)11yescharacteristic
179C2×C4⋊C4—52no—
180C2×C4⋊C4—101no—
181C2×C42—51no—
182C4⋊C8—52no—
183C4⋊C8—52no—
184C22⋊C8—101no—
185C22⋊C8—101no—
186#97—101no—
187#97—101no—
188C2×C3×C5C2×#10111yescharacteristic
189C2×C3×C5#41811yescharacteristic
190C2×C3×C5#41911yescharacteristic
191C3×D5—22no—
192C23×C3—51no—
193C3×Q8—42no—
194C3×Q8—202no—
195C3×Q8—204no—
196C2×C3×C4—22no—
197C2×C3×C4—51no—
198C2×C3×C4—51no—
199C2×C3×C4—51no—
200C2×C3×C4—102no—
201C2×C3×C4—102no—
202C2×C3×C4—102no—
203C2×C3×C4—102no—
204C2×C3×C4—204no—
205C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
206C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
207C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
208C3×C8—202no—
209C3×C8—202no—
210C22×C5C2×C3×C22⋊C411yescharacteristic
211C2×D5—21no—
212C2×D5—21no—
213C2×D5C3×#10112yes—
214C4×C5—21no—
215C4×C5—21no—
216C4×C5—21no—
217C4×C5—42no—
218Dic5—21no—
219Dic5—42no—
220Dic5C3×AGL(1,ℤ/8)12yes—
221Dic5C3×#13712yes—
222C2×Q8—21no—
223C2×Q8—102no—
224C2×Q8—101no—
225C2×Q8—204no—
226C22×C4—51no—
227C22×C4—51no—
228C22×C4—51no—
229C22×C4—102no—
230C2×C8—102no—
231C2×C8—102no—
232C4⋊C4—21no—
233C4⋊C4—52no—
234C4⋊C4—102no—
235C4⋊C4—102no—
236C4⋊C4—101no—
237C4⋊C4C2×C3×AGL(1,𝔽5)12yes—
238C42—51no—
239C42—51no—
240C42—51no—
241C42C2×C3×AGL(1,𝔽5)11yescharacteristic
242C3×C5#155611yescharacteristic, complemented, Hall
243C22×C3—52no—
244C22×C3—101no—
245C22×C3—101no—
246C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—42no—
251C3×C4—52no—
252C3×C4—52no—
253C3×C4—101no—
254C3×C4—202no—
255C2×C5C2×C3×#10111yescharacteristic
256C2×C5C3×#41811yescharacteristic
257C2×C5C3×#41911yescharacteristic
258D5—22no—
259C23—51no—
260Q8—42no—
261Q8—202no—
262Q8—204no—
263C2×C4—22no—
264C2×C4—51no—
265C2×C4—51no—
266C2×C4—51no—
267C2×C4—102no—
268C2×C4—102no—
269C2×C4—102no—
270C2×C4—102no—
271C2×C4—204no—
272C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
273C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
274C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
275C8—202no—
276C8—202no—
277C2×C3—102no—
278C2×C3#6576711yescharacteristic
279C2×C3#6578211yescharacteristic
280C2×C3D5⋊#10111yescharacteristic
281C5C3×#155611yescharacteristic, complemented, Sylow
282C22—52no—
283C22—101no—
284C22—101no—
285C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
286C4—21no—
287C4—21no—
288C4—21no—
289C4—42no—
290C4—52no—
291C4—52no—
292C4—101no—
293C4—202no—
294C3#1060466111yescharacteristic, direct product factor, Sylow
295C2—102no—
296C2C3×#6576711yescharacteristic
297C2C3×#6578211yescharacteristic
298C2C3×D5⋊#10111yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×C4⋊Q8C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC4×Dic5C23×C3
hypercenterC3×C4⋊Q8AGL(1,𝔽5)
hypocenterC5C3×#1556
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. C3×#64873C2semidirect
5. #10604661C3direct (N × H)
25. #64873C2×C3semidirect
242. C3×C5#1556semidirect
281. C5C3×#1556semidirect
294. C3#10604661direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×C4⋊Q82
C3×#656842
C3×#648732
#106046613
C3×#15565