Finite Group Databasebeta

← C3×#10598570 #14279158

Subgroups — C3×#10598570 #14279158

Order 1920.

324 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 76 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×#65777C211yesmaximal, characteristic
2C3×#65776C211yesmaximal, characteristic
3C3×#65029C211yesmaximal, characteristic
4#10598570C311yesmaximal, characteristic, direct product factor, Hall
5C2×C3×#711C2211yescharacteristic
6C2×C3×#704—21no—
7C2×C3×#700C411yescharacteristic, complemented
8C2×C3×D5⋊C8C411yescharacteristic, complemented
9C3×#4023—21no—
10C3×#4013—21no—
11C3×C22⋊#170—21no—
12C3×C22⋊#170—21no—
13C3×#4005C412yescomplemented
14C3×C5×#99C411yescharacteristic
15C3×#3966C411yescharacteristic
16C3×#3938—21no—
17C3×#1395—51nomaximal, Hall
18#65777C2×C311yescharacteristic
19#65776C2×C311yescharacteristic
20#65029C2×C311yescharacteristic
21C2×C3×C5×D4C2×C411yescharacteristic
22C2×C3×C22⋊D5D411yescharacteristic
23C2×C3×C22⋊D5Q811yescharacteristic
24C22×C3×Dic5D411yescharacteristic
25C22×C3×Dic5D411yescharacteristic
26C3×#711—41no—
27C3×#711—41no—
28C2×C3×C4×D5C2×C411yescharacteristic
29C2×C3×Dic10C2×C411yescharacteristic
30C3×#704—22no—
31C3×#704—41no—
32C2×C3×#170—21no—
33C2×C3×#170—21no—
34C2×C3×#170—41no—
35C3×#700—41no—
36C3×D5⋊C8—41no—
37C3×C5×C22⋊C4—21no—
38C3×C22⋊Dic5—21no—
39C3×#683—41no—
40C3×C4×Dic5—41no—
41C3×#413—51no—
42C3×#410—51no—
43C3×#408—51no—
44C2×#711C22×C311yescharacteristic
45C2×#704—21no—
46C2×#700C3×C411yescharacteristic, complemented
47C2×D5⋊C8C3×C411yescharacteristic, complemented
48#4023—21no—
49#4013—21no—
50C22⋊#170—21no—
51C22⋊#170—21no—
52#4005C3×C412yescomplemented
53C5×#99C3×C411yescharacteristic
54#3966C3×C411yescharacteristic
55#3938—21no—
56#1395—51noSylow
57C23×C3×C5C22⋊C411yescharacteristic
58C23×C3×C5C4⋊C411yescharacteristic
59C22×C3×D5C4⋊C411yescharacteristic
60C3×C5×D4—41no—
61C2×C3×C4×C5—41no—
62C2×C3×C4×C5C4211yescharacteristic
63C3×C22⋊D5—41no—
64C3×C22⋊D5—41no—
65C2×C3×Dic5—21no—
66C2×C3×Dic5—21no—
67C2×C3×Dic5—21no—
68C2×C3×Dic5—21no—
69C2×C3×Dic5—41no—
70C2×C3×Dic5C22⋊C411yescharacteristic
71C2×C3×Dic5C22⋊C411yescharacteristic
72C2×C3×Dic5C4⋊C411yescharacteristic
73C3×C4×D5—21no—
74C3×C4×D5—21no—
75C3×Dic10—41no—
76C3×#170—42no—
77C3×#170—41no—
78C3×#170—41no—
79C2×C3×#41—51no—
80C2×C3×M16—51no—
81C2×C3×M16—101no—
82C22×C3×C8—51no—
83C3×#117—101no—
84C3×#101—52no—
85C3×#100—101no—
86C3×#99—51no—
87C3×#99—101no—
88C3×#99AGL(1,𝔽5)11yescharacteristic
89C3×C22⋊C8—101no—
90C3×C22⋊C8—101no—
91C2×C5×D4C2×C3×C411yescharacteristic
92C2×C22⋊D5C3×D411yescharacteristic
93C2×C22⋊D5C3×Q811yescharacteristic
94C22×Dic5C3×D411yescharacteristic
95C22×Dic5C3×D411yescharacteristic
96#711—41no—
97#711—41no—
98C2×C4×D5C2×C3×C411yescharacteristic
99C2×Dic10C2×C3×C411yescharacteristic
100#704—22no—
101#704—41no—
102C2×#170—21no—
103C2×#170—21no—
104C2×#170—41no—
105#700—41no—
106D5⋊C8—41no—
107C5×C22⋊C4—21no—
108C22⋊Dic5—21no—
109#683—41no—
110C4×Dic5—41no—
111#413—51no—
112#410—51no—
113#408—51no—
114C22×C3×C5—21no—
115C22×C3×C5—21no—
116C22×C3×C5—41no—
117C22×C3×C5—41no—
118C22×C3×C5#9511yescharacteristic
119C2×C3×D5—21no—
120C2×C3×D5—41no—
121C3×C4×C5—21no—
122C3×C4×C5—81no—
123C3×Dic5—21no—
124C3×Dic5—21no—
125C3×Dic5—81no—
126C3×Dic5#9911yescharacteristic
127C3×Dic5#9911yescharacteristic
128C3×#41—201no—
129C3×#41—201no—
130C2×C3×Q8—51no—
131C2×C3×D4—51no—
132C2×C3×D4—51no—
133C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
134C22×C3×C4—51no—
135C22×C3×C4—51no—
136C22×C3×C4—51no—
137C3×M16—102no—
138C3×M16—201no—
139C3×M16—201no—
140C2×C3×C8—101no—
141C2×C3×C8—101no—
142C2×C3×C8—201no—
143C2×C3×C8—201no—
144C3×C4⋊C4—201no—
145C3×C22⋊C4—21no—
146C3×C22⋊C4—101no—
147C3×C42—201no—
148C23×C5C3×C22⋊C411yescharacteristic
149C23×C5C3×C4⋊C411yescharacteristic
150C22×D5C3×C4⋊C411yescharacteristic
151C5×D4—41no—
152C2×C4×C5—41no—
153C2×C4×C5C3×C4211yescharacteristic
154C22⋊D5—41no—
155C22⋊D5—41no—
156C2×Dic5—21no—
157C2×Dic5—21no—
158C2×Dic5—21no—
159C2×Dic5—21no—
160C2×Dic5—41no—
161C2×Dic5C3×C22⋊C411yescharacteristic
162C2×Dic5C3×C22⋊C411yescharacteristic
163C2×Dic5C3×C4⋊C411yescharacteristic
164C4×D5—21no—
165C4×D5—21no—
166Dic10—41no—
167#170—42no—
168#170—41no—
169#170—41no—
170C2×#41—51no—
171C2×M16—51no—
172C2×M16—101no—
173C22×C8—51no—
174#117—101no—
175#101—52no—
176#100—101no—
177#99—51no—
178#99—101no—
179#99C3×AGL(1,𝔽5)11yescharacteristic
180C22⋊C8—101no—
181C22⋊C8—101no—
182C2×C3×C5—21no—
183C2×C3×C5—41no—
184C2×C3×C5—41no—
185C2×C3×C5#34211yescharacteristic
186C3×D5—41no—
187C23×C3—51no—
188C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
189C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
190C3×Q8—201no—
191C3×D4—41no—
192C3×D4—201no—
193C3×D4—201no—
194C2×C3×C4—41no—
195C2×C3×C4—51no—
196C2×C3×C4—51no—
197C2×C3×C4—51no—
198C2×C3×C4—101no—
199C2×C3×C4—101no—
200C2×C3×C4—101no—
201C2×C3×C4—101no—
202C2×C3×C4—101no—
203C2×C3×C4—101no—
204C2×C3×C4—201no—
205C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
206C3×C8—201no—
207C3×C8—201no—
208C3×C8—202no—
209C22×C5—21no—
210C22×C5—21no—
211C22×C5—41no—
212C22×C5—41no—
213C22×C5C3×#9511yescharacteristic
214C2×D5—21no—
215C2×D5—41no—
216C4×C5—21no—
217C4×C5—81no—
218Dic5—21no—
219Dic5—21no—
220Dic5—81no—
221Dic5C3×#9911yescharacteristic
222Dic5C3×#9911yescharacteristic
223#41—201no—
224#41—201no—
225C2×Q8—51no—
226C2×D4—51no—
227C2×D4—51no—
228C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
229C22×C4—51no—
230C22×C4—51no—
231C22×C4—51no—
232M16—102no—
233M16—201no—
234M16—201no—
235C2×C8—101no—
236C2×C8—101no—
237C2×C8—201no—
238C2×C8—201no—
239C4⋊C4—201no—
240C22⋊C4—21no—
241C22⋊C4—101no—
242C42—201no—
243C3×C5#139511yescharacteristic, complemented, Hall
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—41no—
247C22×C3—41no—
248C22×C3—101no—
249C22×C3—201no—
250C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
251C3×C4—21no—
252C3×C4—51no—
253C3×C4—51no—
254C3×C4—81no—
255C3×C4—101no—
256C3×C4—101no—
257C3×C4—401no—
258C2×C5—21no—
259C2×C5—41no—
260C2×C5—41no—
261C2×C5C3×#34211yescharacteristic
262D5—41no—
263C23—51no—
264C23C3×C4⋊AGL(1,𝔽5)11yescharacteristic
265C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
266Q8—201no—
267D4—41no—
268D4—201no—
269D4—201no—
270C2×C4—41no—
271C2×C4—51no—
272C2×C4—51no—
273C2×C4—51no—
274C2×C4—101no—
275C2×C4—101no—
276C2×C4—101no—
277C2×C4—101no—
278C2×C4—101no—
279C2×C4—101no—
280C2×C4—201no—
281C2×C4C3×C4×AGL(1,𝔽5)11yescharacteristic
282C8—201no—
283C8—201no—
284C8—202no—
285C2×C3—21no—
286C2×C3—41no—
287C2×C3—41no—
288C2×C3—201no—
289C2×C3#6486611yescharacteristic
290C5C3×#139511yescharacteristic, complemented, Sylow
291C22—21no—
292C22—21no—
293C22—41no—
294C22—41no—
295C22—101no—
296C22—201no—
297C22C3×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
298C4—21no—
299C4—51no—
300C4—51no—
301C4—81no—
302C4—101no—
303C4—101no—
304C4—401no—
305C3#1059857011yescharacteristic, direct product factor, Sylow
306C2—21no—
307C2—41no—
308C2—41no—
309C2—201no—
310C2C3×#6486611yescharacteristic
subgroupG/H
centerC2×C3#64866
commutatorC2×C4×C5C3×C42
FrattiniC2×D4C2×C3×AGL(1,𝔽5)
FittingC3×C5×#99C4
socleC2×C3×C5#342
prime radicalC2×C3×#711C22
cosocleC2×#711C22×C3
hypercenterC3×#99AGL(1,𝔽5)
hypocenterC5C3×#1395
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#99

Complements

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

NH ≅ G/Ntype
4. #10598570C3direct (N × H)
7. C2×C3×#700C4semidirect
8. C2×C3×D5⋊C8C4semidirect
13. C3×#4005C4semidirect
46. C2×#700C3×C4semidirect
47. C2×D5⋊C8C3×C4semidirect
52. #4005C3×C4semidirect
243. C3×C5#1395semidirect
290. C5C3×#1395semidirect
305. C3#10598570direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#657772
C3×#657762
C3×#650292
#105985703
C3×#13955