Finite Group Databasebeta

← C3×#10599951 #14313409

Subgroups — C3×#10599951 #14313409

Order 1920.

516 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 110 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×#66002C211yesmaximal, characteristic
2C3×#65029C212yesmaximal, complemented
3C3×C5×#354C211yesmaximal, characteristic, complemented
4C3×#64761C211yesmaximal, characteristic, complemented
5C3×#64694C212yesmaximal, complemented
6#10599951C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#713C411yescharacteristic, complemented
8C2×C3×#711C2211yescharacteristic
9C3×C5×#124C2211yescharacteristic
10C3×#4090C411yescharacteristic, complemented
11C3×#4086C2211yescharacteristic
12C3×#4030—22no—
13C3×#4027—22no—
14C3×#4023—22no—
15C3×#4021C411yescharacteristic, complemented
16C3×C42×D5C411yescharacteristic, complemented
17C3×C5×#99C2212yes—
18C3×#3966C2212yes—
19C3×#3938—22no—
20C3×#2126—51nomaximal, Hall
21#66002C2×C311yescharacteristic
22#65029C2×C312yescomplemented
23C5×#354C2×C311yescharacteristic, complemented
24#64761C2×C311yescharacteristic, complemented
25#64694C2×C312yescomplemented
26C2×C3×C5×Q8C2×C411yescharacteristic
27C2×C3×C5×D4C2311yescharacteristic
28C2×C3×C22⋊D5—22no—
29C2×C3×C22⋊D5D412yes—
30C22×C3×Dic5D412yes—
31C3×#713—41no—
32C3×#713—41no—
33C3×#711—41no—
34C3×#711—41no—
35C2×C3×D20—21no—
36C2×C3×D20C2×C411yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5C2×C411yescharacteristic
40C2×C3×Dic10C2×C411yescharacteristic
41C3×C5×C22⋊C4—22no—
42C3×C5×C22⋊C4—22no—
43C3×C42×C5C2×C411yescharacteristic
44C3×C22⋊Dic5—22no—
45C3×#685—22no—
46C3×#683—22no—
47C3×#683—42no—
48C3×C4×Dic5—21no—
49C3×C4×Dic5—42no—
50C3×C4×Dic5C2×C411yescharacteristic
51C3×#532—51no—
52C3×#410—52no—
53C3×#354—51no—
54C3×#354D511yescharacteristic, complemented
55C3×#353—52no—
56C2×#713C3×C411yescharacteristic, complemented
57C2×#711C22×C311yescharacteristic
58C5×#124C22×C311yescharacteristic
59#4090C3×C411yescharacteristic, complemented
60#4086C22×C311yescharacteristic
61#4030—22no—
62#4027—22no—
63#4023—22no—
64#4021C3×C411yescharacteristic, complemented
65C42×D5C3×C411yescharacteristic, complemented
66C5×#99C22×C312yes—
67#3966C22×C312yes—
68#3938—22no—
69#2126—51noSylow
70C23×C3×C5C2×D412yes—
71C22×C3×D5—21no—
72C22×C3×D5C22⋊C411yescharacteristic
73C3×C5×Q8—41no—
74C3×C5×D4—41no—
75C2×C3×C4×C5—21no—
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5—42no—
78C2×C3×C4×C5C22×C411yescharacteristic
79C3×C22⋊D5—42no—
80C3×C22⋊D5—44no—
81C2×C3×Dic5—21no—
82C2×C3×Dic5—22no—
83C2×C3×Dic5—22no—
84C2×C3×Dic5—42no—
85C2×C3×Dic5C22⋊C412yes—
86C2×C3×Dic5C22⋊C411yescharacteristic
87C3×D20—41no—
88C3×D20—42no—
89C3×C4×D5—21no—
90C3×C4×D5—21no—
91C3×C4×D5—42no—
92C3×C4×D5—41no—
93C3×C4×D5—41no—
94C3×Dic10—41no—
95C2×C3×#41—51no—
96C2×C3×#41—51no—
97C3×C4⋊Q8—51no—
98C3×#127—51no—
99C3×#124—51no—
100C3×#124C2×D511yescharacteristic
101C3×#121—102no—
102C3×C4×D4—102no—
103C3×#117—102no—
104C2×C3×C42—51no—
105C3×#99—52no—
106C3×#99—102no—
107C3×#99C2×D512yes—
108C2×C5×Q8C2×C3×C411yescharacteristic
109C2×C5×D4C23×C311yescharacteristic
110C2×C22⋊D5—22no—
111C2×C22⋊D5C3×D412yes—
112C22×Dic5C3×D412yes—
113#713—41no—
114#713—41no—
115#711—41no—
116#711—41no—
117C2×D20—21no—
118C2×D20C2×C3×C411yescharacteristic
119C2×C4×D5—21no—
120C2×C4×D5—21no—
121C2×C4×D5C2×C3×C411yescharacteristic
122C2×Dic10C2×C3×C411yescharacteristic
123C5×C22⋊C4—22no—
124C5×C22⋊C4—22no—
125C42×C5C2×C3×C411yescharacteristic
126C22⋊Dic5—22no—
127#685—22no—
128#683—22no—
129#683—42no—
130C4×Dic5—21no—
131C4×Dic5—42no—
132C4×Dic5C2×C3×C411yescharacteristic
133#532—51no—
134#410—52no—
135#354—51no—
136#354C3×D511yescharacteristic, complemented
137#353—52no—
138C22×C3×C5—22no—
139C22×C3×C5—42no—
140C22×C3×C5C2×C22⋊C411yescharacteristic
141C2×C3×D5—21no—
142C2×C3×D5—41no—
143C2×C3×D5—42no—
144C2×C3×D5—41no—
145C3×C4×C5—21no—
146C3×C4×C5—41no—
147C3×C4×C5—41no—
148C3×C4×C5—82no—
149C3×Dic5—22no—
150C3×Dic5—22no—
151C3×Dic5—82no—
152C3×Dic5#9911yescharacteristic
153C3×Dic5#9911yescharacteristic
154C3×#41—201no—
155C3×#41—201no—
156C3×#41—201no—
157C3×#41—201no—
158C2×C3×Q8—51no—
159C2×C3×Q8C4×D511yescharacteristic
160C2×C3×D4—52no—
161C2×C3×D4—51no—
162C2×C3×D4—101no—
163C2×C3×D4—102no—
164C2×C3×D4C22×D511yescharacteristic
165C22×C3×C4—52no—
166C22×C3×C4—51no—
167C22×C3×C4—101no—
168C22×C3×C4—101no—
169C3×C4⋊C4—102no—
170C3×C4⋊C4—202no—
171C3×C22⋊C4—22no—
172C3×C22⋊C4—22no—
173C3×C22⋊C4—102no—
174C3×C22⋊C4—102no—
175C3×C42—51no—
176C3×C42—101no—
177C3×C42—202no—
178C3×C42C4×D511yescharacteristic
179C23×C5C2×C3×D412yes—
180C22×D5—21no—
181C22×D5C3×C22⋊C411yescharacteristic
182C5×Q8—41no—
183C5×D4—41no—
184C2×C4×C5—21no—
185C2×C4×C5—21no—
186C2×C4×C5—42no—
187C2×C4×C5C22×C3×C411yescharacteristic
188C22⋊D5—42no—
189C22⋊D5—44no—
190C2×Dic5—21no—
191C2×Dic5—22no—
192C2×Dic5—22no—
193C2×Dic5—42no—
194C2×Dic5C3×C22⋊C412yes—
195C2×Dic5C3×C22⋊C411yescharacteristic
196D20—41no—
197D20—42no—
198C4×D5—21no—
199C4×D5—21no—
200C4×D5—42no—
201C4×D5—41no—
202C4×D5—41no—
203Dic10—41no—
204C2×#41—51no—
205C2×#41—51no—
206C4⋊Q8—51no—
207#127—51no—
208#124—51no—
209#124C2×C3×D511yescharacteristic
210#121—102no—
211C4×D4—102no—
212#117—102no—
213C2×C42—51no—
214#99—52no—
215#99—102no—
216#99C2×C3×D512yes—
217C2×C3×C5—21no—
218C2×C3×C5—42no—
219C2×C3×C5C2×#9911yescharacteristic
220C3×D5—41no—
221C3×D5—81no—
222C23×C3—51no—
223C23×C3—101no—
224C23×C3D4×D512yes—
225C3×Q8—41no—
226C3×Q8—201no—
227C3×D4—41no—
228C3×D4—201no—
229C3×D4—202no—
230C3×D4—202no—
231C3×D4—204no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—42no—
235C2×C3×C4—51no—
236C2×C3×C4—52no—
237C2×C3×C4—101no—
238C2×C3×C4—101no—
239C2×C3×C4—102no—
240C2×C3×C4—102no—
241C2×C3×C4—101no—
242C2×C3×C4—201no—
243C2×C3×C4—201no—
244C2×C3×C4—202no—
245C2×C3×C4—202no—
246C2×C3×C4C2×C4×D511yescharacteristic
247C22×C5—22no—
248C22×C5—42no—
249C22×C5C2×C3×C22⋊C411yescharacteristic
250C2×D5—21no—
251C2×D5—41no—
252C2×D5—42no—
253C2×D5—41no—
254C4×C5—21no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5—82no—
258Dic5—22no—
259Dic5—22no—
260Dic5—82no—
261Dic5C3×#9911yescharacteristic
262Dic5C3×#9911yescharacteristic
263#41—201no—
264#41—201no—
265#41—201no—
266#41—201no—
267C2×Q8—51no—
268C2×Q8C3×C4×D511yescharacteristic
269C2×D4—52no—
270C2×D4—51no—
271C2×D4—101no—
272C2×D4—102no—
273C2×D4C22×C3×D511yescharacteristic
274C22×C4—52no—
275C22×C4—51no—
276C22×C4—101no—
277C22×C4—101no—
278C4⋊C4—102no—
279C4⋊C4—202no—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—102no—
283C22⋊C4—102no—
284C42—51no—
285C42—101no—
286C42—202no—
287C42C3×C4×D511yescharacteristic
288C3×C5#212611yescharacteristic, complemented, Hall
289C22×C3—22no—
290C22×C3—42no—
291C22×C3—101no—
292C22×C3—201no—
293C22×C3—202no—
294C22×C3—201no—
295C22×C3D5×C22⋊C411yescharacteristic
296C3×C4—21no—
297C3×C4—41no—
298C3×C4—41no—
299C3×C4—51no—
300C3×C4—51no—
301C3×C4—82no—
302C3×C4—102no—
303C3×C4—102no—
304C3×C4—402no—
305C2×C5—21no—
306C2×C5—42no—
307C2×C5C2×C3×#9911yescharacteristic
308D5—41no—
309D5—81no—
310C23—51no—
311C23—101no—
312C23C3×D4×D512yes—
313Q8—41no—
314Q8—201no—
315D4—41no—
316D4—201no—
317D4—202no—
318D4—202no—
319D4—204no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—51no—
324C2×C4—52no—
325C2×C4—101no—
326C2×C4—101no—
327C2×C4—102no—
328C2×C4—102no—
329C2×C4—101no—
330C2×C4—201no—
331C2×C4—201no—
332C2×C4—202no—
333C2×C4—202no—
334C2×C4C2×C3×C4×D511yescharacteristic
335C2×C3—21no—
336C2×C3—42no—
337C2×C3—201no—
338C2×C3—401no—
339C2×C3D5×#9911yescharacteristic
340C5C3×#212611yescharacteristic, complemented, Sylow
341C22—22no—
342C22—42no—
343C22—101no—
344C22—201no—
345C22—202no—
346C22—201no—
347C22C3×D5×C22⋊C411yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—51no—
352C4—51no—
353C4—82no—
354C4—102no—
355C4—102no—
356C4—402no—
357C3#1059995111yescharacteristic, direct product factor, Sylow
358C2—21no—
359C2—42no—
360C2—201no—
361C2—401no—
362C2C3×D5×#9911yescharacteristic
subgroupG/H
centerC2×C3D5×#99
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×D4C22×C3×D5
FittingC3×C5×#354C2
socleC2×C3×C5C2×#99
prime radicalC3×#66002C2
cosocleC2×C5×D4C23×C3
hypercenterC3×#354D5
hypocenterC5C3×#2126
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#354

Complements

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

NH ≅ G/Ntype
2. C3×#65029C2semidirect
3. C3×C5×#354C2semidirect
4. C3×#64761C2semidirect
5. C3×#64694C2semidirect
6. #10599951C3direct (N × H)
7. C2×C3×#713C4semidirect
10. C3×#4090C4semidirect
15. C3×#4021C4semidirect
16. C3×C42×D5C4semidirect
22. #65029C2×C3semidirect
23. C5×#354C2×C3semidirect
24. #64761C2×C3semidirect
25. #64694C2×C3semidirect
54. C3×#354D5semidirect
56. C2×#713C3×C4semidirect
59. #4090C3×C4semidirect
64. #4021C3×C4semidirect
65. C42×D5C3×C4semidirect
136. #354C3×D5semidirect
288. C3×C5#2126semidirect
340. C5C3×#2126semidirect
357. C3#10599951direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660022
C3×#650292
C3×C5×#3542
C3×#647612
C3×#646942
#105999513
C3×#21265