Finite Group Databasebeta

← C3×#10602695 #14287862

Subgroups — C3×#10602695 #14287862

Order 1920.

532 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 114 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×C5×#544C211yesmaximal, characteristic, complemented
2C3×#65335C212yesmaximal
3C3×#65280C211yesmaximal, characteristic
4C3×#64758C212yesmaximal, complemented
5C3×#64748C211yesmaximal, characteristic, complemented
6#10602695C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×D20C2211yescharacteristic
8C3×C5×C4⋊Q8—22no—
9C3×C5×#125—22no—
10C3×C5×C22⋊Q8—21no—
11C3×C5×C22⋊Q8C2212yes—
12C3×C5×#117—21no—
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×C3×#688—22no—
15C2×C3×#685—21no—
16C2×C3×#685—21no—
17C3×#3963C2211yescharacteristic
18C3×C22⋊#168C2212yes—
19C3×#3941—22no—
20C3×#1599—51nomaximal, Hall
21C5×#544C2×C311yescharacteristic, complemented
22#65335C2×C312yes—
23#65280C2×C311yescharacteristic
24#64758C2×C312yescomplemented
25#64748C2×C311yescharacteristic, complemented
26C23×C3×D5—21no—
27C2×C3×C5×Q8—21no—
28C2×C3×C5×Q8D412yes—
29C22×C3×C4×C5D411yescharacteristic
30C22×C3×C4×C5D411yescharacteristic
31C22×C3×C4×C5C2311yescharacteristic
32C22×C3×Dic5—21no—
33C2×C3×D20—22no—
34C2×C3×D20—42no—
35C3×C5×C4⋊C4—21no—
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4—22no—
39C3×C5×C4⋊C4—22no—
40C3×C5×C4⋊C4—22no—
41C3×C5×C4⋊C4D412yes—
42C3×C5×C22⋊C4—22no—
43C3×C42×C5—22no—
44C3×#688—44no—
45C3×#685—42no—
46C3×#685—42no—
47C2×C3×#168—22no—
48C3×#544D511yescharacteristic, complemented
49C3×#450—52no—
50C3×#394—51no—
51C3×#328—52no—
52C3×#324—51no—
53C22×D20C22×C311yescharacteristic
54C5×C4⋊Q8—22no—
55C5×#125—22no—
56C5×C22⋊Q8—21no—
57C5×C22⋊Q8C22×C312yes—
58C5×#117—21no—
59C2×C5×C4⋊C4C22×C311yescharacteristic
60C2×#688—22no—
61C2×#685—21no—
62C2×#685—21no—
63#3963C22×C311yescharacteristic
64C22⋊#168C22×C312yes—
65#3941—22no—
66#1599—51noSylow
67C23×C3×C5C2×D411yescharacteristic
68C22×C3×D5—22no—
69C22×C3×D5—41no—
70C22×C3×D5—41no—
71C22×C3×D5—41no—
72C22×C3×D5—41no—
73C22×C3×D5—41no—
74C22×C3×D5—41no—
75C3×C5×Q8—42no—
76C3×C5×Q8—81no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—22no—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5—21no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5SD1612yescomplemented
85C2×C3×C4×C5C2×D412yes—
86C2×C3×Dic5—41no—
87C2×C3×Dic5—41no—
88C2×C3×Dic5—41no—
89C3×D20—24no—
90C3×D20—42no—
91C3×#168—42no—
92C22×C3×D4—51no—
93C2×C3×SD16—102no—
94C3×C4⋊Q8—22no—
95C3×#125—22no—
96C3×C22⋊Q8—21no—
97C3×C22⋊Q8C2×D512yes—
98C3×#117—21no—
99C2×C3×C4⋊C4C2×D511yescharacteristic
100C2×C3×C22⋊C4—101no—
101C2×C3×C22⋊C4—101no—
102C3×#102—102no—
103C3×C22⋊C8—52no—
104C3×#95—51no—
105C23×D5—21no—
106C2×C5×Q8—21no—
107C2×C5×Q8C3×D412yes—
108C22×C4×C5C3×D411yescharacteristic
109C22×C4×C5C3×D411yescharacteristic
110C22×C4×C5C23×C311yescharacteristic
111C22×Dic5—21no—
112C2×D20—22no—
113C2×D20—42no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—22no—
118C5×C4⋊C4—22no—
119C5×C4⋊C4—22no—
120C5×C4⋊C4C3×D412yes—
121C5×C22⋊C4—22no—
122C42×C5—22no—
123#688—44no—
124#685—42no—
125#685—42no—
126C2×#168—22no—
127#544C3×D511yescharacteristic, complemented
128#450—52no—
129#394—51no—
130#328—52no—
131#324—51no—
132C22×C3×C5—21no—
133C22×C3×C5—21no—
134C22×C3×C5#12011yescharacteristic
135C22×C3×C5C2×SD1611yescharacteristic
136C22×C3×C5#13711yescharacteristic
137C2×C3×D5—42no—
138C2×C3×D5—42no—
139C2×C3×D5—42no—
140C2×C3×D5—81no—
141C2×C3×D5—81no—
142C2×C3×D5—81no—
143C2×C3×D5—81no—
144C3×C4×C5—22no—
145C3×C4×C5—22no—
146C3×C4×C5—42no—
147C3×C4×C5—41no—
148C3×C4×C5—42no—
149C3×Dic5—81no—
150C24×C3—101no—
151C2×C3×Q8—21no—
152C2×C3×Q8C22⋊D512yes—
153C2×C3×D4—102no—
154C2×C3×D4—202no—
155C22×C3×C4—101no—
156C22×C3×C4C22⋊D511yescharacteristic
157C22×C3×C4C22⋊D511yescharacteristic
158C22×C3×C4C22×D511yescharacteristic
159C3×SD16—204no—
160C2×C3×C8—102no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—22no—
165C3×C4⋊C4—22no—
166C3×C4⋊C4—22no—
167C3×C4⋊C4C22⋊D512yes—
168C3×C22⋊C4—22no—
169C3×C22⋊C4—202no—
170C3×C22⋊C4—202no—
171C3×C42—22no—
172C23×C5C2×C3×D411yescharacteristic
173C22×D5—22no—
174C22×D5—41no—
175C22×D5—41no—
176C22×D5—41no—
177C22×D5—41no—
178C22×D5—41no—
179C22×D5—41no—
180C5×Q8—42no—
181C5×Q8—81no—
182C2×C4×C5—21no—
183C2×C4×C5—21no—
184C2×C4×C5—22no—
185C2×C4×C5—22no—
186C2×C4×C5—21no—
187C2×C4×C5—41no—
188C2×C4×C5—41no—
189C2×C4×C5C3×SD1612yescomplemented
190C2×C4×C5C2×C3×D412yes—
191C2×Dic5—41no—
192C2×Dic5—41no—
193C2×Dic5—41no—
194D20—24no—
195D20—42no—
196#168—42no—
197C22×D4—51no—
198C2×SD16—102no—
199C4⋊Q8—22no—
200#125—22no—
201C22⋊Q8—21no—
202C22⋊Q8C2×C3×D512yes—
203#117—21no—
204C2×C4⋊C4C2×C3×D511yescharacteristic
205C2×C22⋊C4—101no—
206C2×C22⋊C4—101no—
207#102—102no—
208C22⋊C8—52no—
209#95—51no—
210C2×C3×C5—21no—
211C2×C3×C5—21no—
212C2×C3×C5#44811yescharacteristic
213C2×C3×C5#45411yescharacteristic
214C2×C3×C5B(4,𝔽2)11yescharacteristic
215C3×D5—82no—
216C23×C3—102no—
217C23×C3—201no—
218C23×C3—201no—
219C23×C3—201no—
220C23×C3—201no—
221C23×C3—201no—
222C23×C3—201no—
223C23×C3C2×C22⋊D511yescharacteristic
224C3×Q8—42no—
225C3×Q8—81no—
226C3×D4—104no—
227C3×D4—202no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—21no—
233C2×C3×C4—41no—
234C2×C3×C4—41no—
235C2×C3×C4—201no—
236C2×C3×C4—201no—
237C2×C3×C4—201no—
238C2×C3×C4#68812yescomplemented
239C2×C3×C4C2×C22⋊D512yes—
240C3×C8—202no—
241C22×C5—21no—
242C22×C5—21no—
243C22×C5C3×#12011yescharacteristic
244C22×C5C2×C3×SD1611yescharacteristic
245C22×C5C3×#13711yescharacteristic
246C2×D5—42no—
247C2×D5—42no—
248C2×D5—42no—
249C2×D5—81no—
250C2×D5—81no—
251C2×D5—81no—
252C2×D5—81no—
253C4×C5—22no—
254C4×C5—22no—
255C4×C5—42no—
256C4×C5—41no—
257C4×C5—42no—
258Dic5—81no—
259C24—101no—
260C2×Q8—21no—
261C2×Q8C3×C22⋊D512yes—
262C2×D4—102no—
263C2×D4—202no—
264C22×C4—101no—
265C22×C4C3×C22⋊D511yescharacteristic
266C22×C4C3×C22⋊D511yescharacteristic
267C22×C4C22×C3×D511yescharacteristic
268SD16—204no—
269C2×C8—102no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4C3×C22⋊D512yes—
277C22⋊C4—22no—
278C22⋊C4—202no—
279C22⋊C4—202no—
280C42—22no—
281C3×C5#159911yescharacteristic, complemented, Hall
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—202no—
285C22×C3—202no—
286C22×C3—202no—
287C22×C3—401no—
288C22×C3—401no—
289C22×C3—401no—
290C22×C3—401no—
291C22×C3C2×#68811yescharacteristic
292C22×C3#408811yescharacteristic
293C22×C3#409911yescharacteristic
294C3×C4—22no—
295C3×C4—22no—
296C3×C4—41no—
297C3×C4—42no—
298C3×C4—42no—
299C3×C4—401no—
300C2×C5—21no—
301C2×C5—21no—
302C2×C5C3×#44811yescharacteristic
303C2×C5C3×#45411yescharacteristic
304C2×C5C3×B(4,𝔽2)11yescharacteristic
305D5—82no—
306C23—102no—
307C23—201no—
308C23—201no—
309C23—201no—
310C23—201no—
311C23—201no—
312C23—201no—
313C23C2×C3×C22⋊D511yescharacteristic
314Q8—42no—
315Q8—81no—
316D4—104no—
317D4—202no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—201no—
326C2×C4—201no—
327C2×C4—201no—
328C2×C4C3×#68812yescomplemented
329C2×C4C2×C3×C22⋊D512yes—
330C8—202no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—402no—
334C2×C3#6551611yescharacteristic
335C2×C3#6553311yescharacteristic
336C2×C3#6553411yescharacteristic
337C5C3×#159911yescharacteristic, complemented, Sylow
338C22—21no—
339C22—21no—
340C22—202no—
341C22—202no—
342C22—202no—
343C22—401no—
344C22—401no—
345C22—401no—
346C22—401no—
347C22C2×C3×#68811yescharacteristic
348C22C3×#408811yescharacteristic
349C22C3×#409911yescharacteristic
350C4—22no—
351C4—22no—
352C4—41no—
353C4—42no—
354C4—42no—
355C4—401no—
356C3#1060269511yescharacteristic, direct product factor, Sylow
357C2—21no—
358C2—21no—
359C2—402no—
360C2C3×#6551611yescharacteristic
361C2C3×#6553311yescharacteristic
362C2C3×#6553411yescharacteristic
subgroupG/H
centerC22×C3#4099
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#544C2
socleC22×C3×C5#120
prime radicalC22×C3×D20C22
hypercenterC3×#544D5
hypocenterC5C3×#1599
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#544

Complements

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

NH ≅ G/Ntype
1. C3×C5×#544C2semidirect
4. C3×#64758C2semidirect
5. C3×#64748C2semidirect
6. #10602695C3direct (N × H)
21. C5×#544C2×C3semidirect
24. #64758C2×C3semidirect
25. #64748C2×C3semidirect
48. C3×#544D5semidirect
84. C2×C3×C4×C5SD16semidirect
127. #544C3×D5semidirect
189. C2×C4×C5C3×SD16semidirect
238. C2×C3×C4#688semidirect
281. C3×C5#1599semidirect
328. C2×C4C3×#688semidirect
337. C5C3×#1599semidirect
356. C3#10602695direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5442
C3×#653352
C3×#652802
C3×#647582
C3×#647482
#106026953
C3×#15995