Finite Group Databasebeta

← C3×#10604603 #14313727

Subgroups — C3×#10604603 #14313727

Order 1920.

524 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 104 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×#66049C211yesmaximal, characteristic
2C3×#65777C212yesmaximal, complemented
3C3×#64923C212yesmaximal, complemented
4C3×#64856C212yesmaximal, complemented
5#10604603C311yesmaximal, characteristic, direct product factor, Hall
6C2×C3×#711C2211yescharacteristic
7C2×C3×D4×D5C411yescharacteristic
8C2×C3×#704—22no—
9C3×C5×#127C411yescharacteristic
10C3×#4086C411yescharacteristic
11C3×#4085—22no—
12C3×#4083—22no—
13C3×#4082C2211yescharacteristic
14C3×#4021C2211yescharacteristic
15C3×#4018C411yescharacteristic
16C3×#4013—22no—
17C3×#4005C2214yescomplemented
18C3×#2134—51nomaximal, Hall
19#66049C2×C311yescharacteristic
20#65777C2×C312yescomplemented
21#64923C2×C312yescomplemented
22#64856C2×C312yescomplemented
23C23×C3×D5—21no—
24C2×C3×C5×D4—22no—
25C2×C3×C5×D4C2×C411yescharacteristic
26C2×C3×C5×D4C2×C411yescharacteristic
27C2×C3×C22⋊D5—22no—
28C2×C3×C22⋊D5—21no—
29C2×C3×C22⋊D5D412yes—
30C22×C3×Dic5D412yes—
31C3×#711—42no—
32C3×D4×D5—42no—
33C2×C3×D20C2×C411yescharacteristic
34C2×C3×C4×D5C2×C411yescharacteristic
35C2×C3×Dic10C2311yescharacteristic
36C3×#704—24no—
37C3×#704—42no—
38C2×C3×#170—42no—
39C3×C42×C5C2×C411yescharacteristic
40C3×C22⋊Dic5—22no—
41C3×#685—21no—
42C3×#685—22no—
43C3×#683—21no—
44C3×C4×Dic5C2×C411yescharacteristic
45C3×#535—51no—
46C3×#413—52no—
47C3×#355—52no—
48C3×#355—52no—
49C2×#711C22×C311yescharacteristic
50C2×D4×D5C3×C411yescharacteristic
51C2×#704—22no—
52C5×#127C3×C411yescharacteristic
53#4086C3×C411yescharacteristic
54#4085—22no—
55#4083—22no—
56#4082C22×C311yescharacteristic
57#4021C22×C311yescharacteristic
58#4018C3×C411yescharacteristic
59#4013—22no—
60#4005C22×C314yescomplemented
61#2134—51noSylow
62C23×C3×C5—21no—
63C23×C3×C5C22⋊C412yes—
64C22×C3×D5—21no—
65C22×C3×D5—42no—
66C22×C3×D5—82no—
67C22×C3×D5C22⋊C411yescharacteristic
68C3×C5×D4—41no—
69C3×C5×D4—41no—
70C3×C5×D4—82no—
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5C22×C411yescharacteristic
73C3×C22⋊D5—42no—
74C3×C22⋊D5—42no—
75C3×C22⋊D5—82no—
76C2×C3×Dic5—22no—
77C2×C3×Dic5—22no—
78C2×C3×Dic5—21no—
79C2×C3×Dic5C22⋊C411yescharacteristic
80C2×C3×Dic5C2×D412yes—
81C3×D20—41no—
82C3×C4×D5—22no—
83C3×Dic10—41no—
84C3×#170—44no—
85C2×C3×#41—51no—
86C22×C3×D4—51no—
87C2×C3×M16—102no—
88C3×#127—51no—
89C3×#127AGL(1,𝔽5)11yescharacteristic
90C3×#124—51no—
91C3×#124—51no—
92C3×#121—102no—
93C3×#120—102no—
94C3×#117—51no—
95C3×#101—54no—
96C3×#100—102no—
97C23×D5—21no—
98C2×C5×D4—22no—
99C2×C5×D4C2×C3×C411yescharacteristic
100C2×C5×D4C2×C3×C411yescharacteristic
101C2×C22⋊D5—22no—
102C2×C22⋊D5—21no—
103C2×C22⋊D5C3×D412yes—
104C22×Dic5C3×D412yes—
105#711—42no—
106D4×D5—42no—
107C2×D20C2×C3×C411yescharacteristic
108C2×C4×D5C2×C3×C411yescharacteristic
109C2×Dic10C23×C311yescharacteristic
110#704—24no—
111#704—42no—
112C2×#170—42no—
113C42×C5C2×C3×C411yescharacteristic
114C22⋊Dic5—22no—
115#685—21no—
116#685—22no—
117#683—21no—
118C4×Dic5C2×C3×C411yescharacteristic
119#535—51no—
120#413—52no—
121#355—52no—
122#355—52no—
123C22×C3×C5—22no—
124C22×C3×C5—42no—
125C22×C3×C5—42no—
126C22×C3×C5—41no—
127C22×C3×C5C2×C22⋊C411yescharacteristic
128C2×C3×D5—21no—
129C2×C3×D5—41no—
130C2×C3×D5—42no—
131C2×C3×D5—41no—
132C2×C3×D5—84no—
133C3×C4×C5—21no—
134C3×C4×C5—41no—
135C3×Dic5—22no—
136C3×Dic5—41no—
137C3×Dic5#9912yes—
138C24×C3—101no—
139C3×#41—202no—
140C2×C3×Q8—51no—
141C2×C3×D4—22no—
142C2×C3×D4—52no—
143C2×C3×D4—51no—
144C2×C3×D4—101no—
145C2×C3×D4—102no—
146C2×C3×D4—202no—
147C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
148C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
149C22×C3×C4—52no—
150C22×C3×C4—51no—
151C3×M16—104no—
152C3×M16—202no—
153C2×C3×C8—202no—
154C3×C4⋊C4—101no—
155C3×C22⋊C4—102no—
156C3×C22⋊C4—101no—
157C3×C22⋊C4—102no—
158C3×C42—51no—
159C3×C42C2×AGL(1,𝔽5)11yescharacteristic
160C23×C5—21no—
161C23×C5C3×C22⋊C412yes—
162C22×D5—21no—
163C22×D5—42no—
164C22×D5—82no—
165C22×D5C3×C22⋊C411yescharacteristic
166C5×D4—41no—
167C5×D4—41no—
168C5×D4—82no—
169C2×C4×C5—21no—
170C2×C4×C5C22×C3×C411yescharacteristic
171C22⋊D5—42no—
172C22⋊D5—42no—
173C22⋊D5—82no—
174C2×Dic5—22no—
175C2×Dic5—22no—
176C2×Dic5—21no—
177C2×Dic5C3×C22⋊C411yescharacteristic
178C2×Dic5C2×C3×D412yes—
179D20—41no—
180C4×D5—22no—
181Dic10—41no—
182#170—44no—
183C2×#41—51no—
184C22×D4—51no—
185C2×M16—102no—
186#127—51no—
187#127C3×AGL(1,𝔽5)11yescharacteristic
188#124—51no—
189#124—51no—
190#121—102no—
191#120—102no—
192#117—51no—
193#101—54no—
194#100—102no—
195C2×C3×C5—21no—
196C2×C3×C5—42no—
197C2×C3×C5—81no—
198C2×C3×C5C2×#9911yescharacteristic
199C3×D5—41no—
200C3×D5—81no—
201C23×C3—21no—
202C23×C3—51no—
203C23×C3—101no—
204C23×C3—202no—
205C23×C3—402no—
206C23×C3C22⋊AGL(1,𝔽5)12yes—
207C3×Q8—201no—
208C3×D4—41no—
209C3×D4—41no—
210C3×D4—82no—
211C3×D4—201no—
212C3×D4—202no—
213C3×D4—202no—
214C3×D4—402no—
215C2×C3×C4—21no—
216C2×C3×C4—51no—
217C2×C3×C4—52no—
218C2×C3×C4—102no—
219C2×C3×C4—102no—
220C2×C3×C4—102no—
221C2×C3×C4—101no—
222C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
223C3×C8—204no—
224C22×C5—22no—
225C22×C5—42no—
226C22×C5—42no—
227C22×C5—41no—
228C22×C5C2×C3×C22⋊C411yescharacteristic
229C2×D5—21no—
230C2×D5—41no—
231C2×D5—42no—
232C2×D5—41no—
233C2×D5—84no—
234C4×C5—21no—
235C4×C5—41no—
236Dic5—22no—
237Dic5—41no—
238Dic5C3×#9912yes—
239C24—101no—
240#41—202no—
241C2×Q8—51no—
242C2×D4—22no—
243C2×D4—52no—
244C2×D4—51no—
245C2×D4—101no—
246C2×D4—102no—
247C2×D4—202no—
248C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
249C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
250C22×C4—52no—
251C22×C4—51no—
252M16—104no—
253M16—202no—
254C2×C8—202no—
255C4⋊C4—101no—
256C22⋊C4—102no—
257C22⋊C4—101no—
258C22⋊C4—102no—
259C42—51no—
260C42C2×C3×AGL(1,𝔽5)11yescharacteristic
261C3×C5#213411yescharacteristic, complemented, Hall
262C22×C3—22no—
263C22×C3—42no—
264C22×C3—42no—
265C22×C3—41no—
266C22×C3—101no—
267C22×C3—201no—
268C22×C3—202no—
269C22×C3—201no—
270C22×C3—404no—
271C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
272C3×C4—21no—
273C3×C4—41no—
274C3×C4—52no—
275C3×C4—102no—
276C3×C4—201no—
277C2×C5—21no—
278C2×C5—42no—
279C2×C5—81no—
280C2×C5C2×C3×#9911yescharacteristic
281D5—41no—
282D5—81no—
283C23—21no—
284C23—51no—
285C23—101no—
286C23—202no—
287C23—402no—
288C23C3×C22⋊AGL(1,𝔽5)12yes—
289Q8—201no—
290D4—41no—
291D4—41no—
292D4—82no—
293D4—201no—
294D4—202no—
295D4—202no—
296D4—402no—
297C2×C4—21no—
298C2×C4—51no—
299C2×C4—52no—
300C2×C4—102no—
301C2×C4—102no—
302C2×C4—102no—
303C2×C4—101no—
304C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
305C8—204no—
306C2×C3—21no—
307C2×C3—42no—
308C2×C3—81no—
309C2×C3—201no—
310C2×C3—401no—
311C2×C3D5⋊#9911yescharacteristic
312C5C3×#213411yescharacteristic, complemented, Sylow
313C22—22no—
314C22—42no—
315C22—42no—
316C22—41no—
317C22—101no—
318C22—201no—
319C22—202no—
320C22—201no—
321C22—404no—
322C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
323C4—21no—
324C4—41no—
325C4—52no—
326C4—102no—
327C4—201no—
328C3#1060460311yescharacteristic, direct product factor, Sylow
329C2—21no—
330C2—42no—
331C2—81no—
332C2—201no—
333C2—401no—
334C2C3×D5⋊#9911yescharacteristic
subgroupG/H
centerC2×C3D5⋊#99
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#127C4
socleC2×C3×C5C2×#99
prime radicalC3×#66049C2
cosocleC2×Dic10C23×C3
hypercenterC3×#127AGL(1,𝔽5)
hypocenterC5C3×#2134
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#127

Complements

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

NH ≅ G/Ntype
2. C3×#65777C2semidirect
3. C3×#64923C2semidirect
4. C3×#64856C2semidirect
5. #10604603C3direct (N × H)
17. C3×#4005C22semidirect
20. #65777C2×C3semidirect
21. #64923C2×C3semidirect
22. #64856C2×C3semidirect
60. #4005C22×C3semidirect
261. C3×C5#2134semidirect
312. C5C3×#2134semidirect
328. C3#10604603direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660492
C3×#657772
C3×#649232
C3×#648562
#106046033
C3×#21345