Finite Group Databasebeta

← C3×#10600510 #14288603

Subgroups — C3×#10600510 #14288603

Order 1920.

416 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 98 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×#65849C211yesmaximal, characteristic
2C3×C5×#400C211yesmaximal, characteristic, complemented
3C3×#65259C211yesmaximal, characteristic, complemented
4C3×#65257C211yesmaximal, characteristic
5C3×#64748C211yesmaximal, characteristic, complemented
6C3×#64672C211yesmaximal, characteristic, complemented
7C3×#64671C211yesmaximal, characteristic
8#10600510C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C3×#4076C2211yescharacteristic
12C3×#4075—21no—
13C3×C4×C22⋊D5—21no—
14C3×#4070C2211yescharacteristic
15C3×#4044—21no—
16C3×#4042—21no—
17C3×#4040—21no—
18C3×#4035—21no—
19C3×C5×#95—21no—
20C3×C5×#95—21no—
21C3×C5×#95C2211yescharacteristic
22C3×C22⋊#168C2211yescharacteristic
23C3×C22⋊#168C2211yescharacteristic
24C3×#3942—21no—
25C3×#3941—21no—
26C3×#3940—21no—
27C3×#3939—21no—
28C3×#1615—51nomaximal, Hall
29#65849C2×C311yescharacteristic
30C5×#400C2×C311yescharacteristic, complemented
31#65259C2×C311yescharacteristic, complemented
32#65257C2×C311yescharacteristic
33#64748C2×C311yescharacteristic, complemented
34#64672C2×C311yescharacteristic, complemented
35#64671C2×C311yescharacteristic
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5D411yescharacteristic
39C22×C3×C4×C5D411yescharacteristic
40C22×C3×C4×C5C2311yescharacteristic
41C2×C3×C22⋊D5—21no—
42C2×C3×D20D411yescharacteristic
43C2×C3×C4×D5—21no—
44C2×C3×Dic10D411yescharacteristic
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4—21no—
49C3×C22⋊Dic5—21no—
50C3×#685—21no—
51C3×#685—21no—
52C3×#685—21no—
53C3×#685—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C3×C4⋊Dic5D411yescharacteristic
56C3×#683—21no—
57C3×#683—21no—
58C3×#683—21no—
59C3×#683—21no—
60C3×C4×Dic5—21no—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C3×#539—51no—
64C3×#484—51no—
65C3×#481—51no—
66C3×#400D511yescharacteristic, complemented
67C3×#328—51no—
68C3×#327—51no—
69C3×#324—51no—
70C2×C5×C4⋊C4C22×C311yescharacteristic
71C2×C5×C4⋊C4C22×C311yescharacteristic
72#4076C22×C311yescharacteristic
73#4075—21no—
74C4×C22⋊D5—21no—
75#4070C22×C311yescharacteristic
76#4044—21no—
77#4042—21no—
78#4040—21no—
79#4035—21no—
80C5×#95—21no—
81C5×#95—21no—
82C5×#95C22×C311yescharacteristic
83C22⋊#168C22×C311yescharacteristic
84C22⋊#168C22×C311yescharacteristic
85#3942—21no—
86#3941—21no—
87#3940—21no—
88#3939—21no—
89#1615—51noSylow
90C23×C3×C5C2×D411yescharacteristic
91C22×C3×D5—21no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—42no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C3×C22⋊D5—41no—
106C3×C22⋊D5—41no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5—21no—
110C3×D20—41no—
111C3×C4×D5—81no—
112C3×Dic10—41no—
113C3×#168—41no—
114C3×#168—41no—
115C3×#126—101no—
116C3×#125—101no—
117C3×#123—101no—
118C3×#123—101no—
119C3×C22⋊Q8—51no—
120C3×C22⋊Q8—101no—
121C3×#121—51no—
122C3×C4×D4—101no—
123C2×C3×C4⋊C4C2×D511yescharacteristic
124C2×C3×C4⋊C4C2×D511yescharacteristic
125C3×#107—101no—
126C3×#106—101no—
127C3×#103—101no—
128C3×#102—101no—
129C3×C22⋊C8—51no—
130C3×C22⋊C8—51no—
131C3×#95—21no—
132C3×#95—21no—
133C3×#95C2×D511yescharacteristic
134C22×C4×C5—21no—
135C22×C4×C5—21no—
136C22×C4×C5C3×D411yescharacteristic
137C22×C4×C5C3×D411yescharacteristic
138C22×C4×C5C23×C311yescharacteristic
139C2×C22⋊D5—21no—
140C2×D20C3×D411yescharacteristic
141C2×C4×D5—21no—
142C2×Dic10C3×D411yescharacteristic
143C5×C4⋊C4—21no—
144C5×C4⋊C4—21no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4—21no—
147C22⋊Dic5—21no—
148#685—21no—
149#685—21no—
150#685—21no—
151#685—21no—
152C4⋊Dic5C3×D411yescharacteristic
153C4⋊Dic5C3×D411yescharacteristic
154#683—21no—
155#683—21no—
156#683—21no—
157#683—21no—
158C4×Dic5—21no—
159C2×#168—21no—
160C2×#168—21no—
161#539—51no—
162#484—51no—
163#481—51no—
164#400C3×D511yescharacteristic, complemented
165#328—51no—
166#327—51no—
167#324—51no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5#12011yescharacteristic
171C22×C3×C5#13511yescharacteristic
172C22×C3×C5#13711yescharacteristic
173C2×C3×D5—41no—
174C2×C3×D5—41no—
175C2×C3×D5—41no—
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—41no—
179C3×C4×C5—41no—
180C3×C4×C5—81no—
181C3×C4×C5—81no—
182C3×Dic5—41no—
183C3×Dic5—41no—
184C3×Dic5—41no—
185C2×C3×Q8—51no—
186C2×C3×D4—51no—
187C2×C3×D4—101no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—101no—
191C22×C3×C4C22⋊D511yescharacteristic
192C22×C3×C4C22⋊D511yescharacteristic
193C22×C3×C4C22×D511yescharacteristic
194C2×C3×C8—101no—
195C2×C3×C8—101no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—51no—
201C3×C4⋊C4—51no—
202C3×C4⋊C4—101no—
203C3×C4⋊C4—101no—
204C3×C4⋊C4—101no—
205C3×C4⋊C4—101no—
206C3×C22⋊C4—101no—
207C3×C22⋊C4—101no—
208C3×C22⋊C4—101no—
209C3×C22⋊C4—101no—
210C3×C22⋊C4—101no—
211C3×C42—101no—
212C23×C5C2×C3×D411yescharacteristic
213C22×D5—21no—
214C2×C4×C5—21no—
215C2×C4×C5—21no—
216C2×C4×C5—21no—
217C2×C4×C5—21no—
218C2×C4×C5—41no—
219C2×C4×C5—41no—
220C2×C4×C5—41no—
221C2×C4×C5—41no—
222C2×C4×C5—42no—
223C2×C4×C5—41no—
224C2×C4×C5—41no—
225C2×C4×C5C2×C3×D411yescharacteristic
226C2×C4×C5C2×C3×D411yescharacteristic
227C22⋊D5—41no—
228C22⋊D5—41no—
229C2×Dic5—21no—
230C2×Dic5—21no—
231C2×Dic5—21no—
232D20—41no—
233C4×D5—81no—
234Dic10—41no—
235#168—41no—
236#168—41no—
237#126—101no—
238#125—101no—
239#123—101no—
240#123—101no—
241C22⋊Q8—51no—
242C22⋊Q8—101no—
243#121—51no—
244C4×D4—101no—
245C2×C4⋊C4C2×C3×D511yescharacteristic
246C2×C4⋊C4C2×C3×D511yescharacteristic
247#107—101no—
248#106—101no—
249#103—101no—
250#102—101no—
251C22⋊C8—51no—
252C22⋊C8—51no—
253#95—21no—
254#95—21no—
255#95C2×C3×D511yescharacteristic
256C2×C3×C5—21no—
257C2×C3×C5—21no—
258C2×C3×C5#45211yescharacteristic
259C2×C3×C5#45411yescharacteristic
260C2×C3×C5#45811yescharacteristic
261C3×D5—81no—
262C23×C3—101no—
263C23×C3C2×C22⋊D511yescharacteristic
264C3×Q8—201no—
265C3×D4—201no—
266C3×D4—201no—
267C3×D4—201no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—42no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—101no—
280C2×C3×C4—101no—
281C2×C3×C4—101no—
282C2×C3×C4—401no—
283C2×C3×C4D4×D511yescharacteristic
284C2×C3×C4D4×D511yescharacteristic
285C3×C8—201no—
286C3×C8—201no—
287C22×C5—21no—
288C22×C5—21no—
289C22×C5C3×#12011yescharacteristic
290C22×C5C3×#13511yescharacteristic
291C22×C5C3×#13711yescharacteristic
292C2×D5—41no—
293C2×D5—41no—
294C2×D5—41no—
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—41no—
298C4×C5—41no—
299C4×C5—81no—
300C4×C5—81no—
301Dic5—41no—
302Dic5—41no—
303Dic5—41no—
304C2×Q8—51no—
305C2×D4—51no—
306C2×D4—101no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—101no—
310C22×C4C3×C22⋊D511yescharacteristic
311C22×C4C3×C22⋊D511yescharacteristic
312C22×C4C22×C3×D511yescharacteristic
313C2×C8—101no—
314C2×C8—101no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—51no—
320C4⋊C4—51no—
321C4⋊C4—101no—
322C4⋊C4—101no—
323C4⋊C4—101no—
324C4⋊C4—101no—
325C22⋊C4—101no—
326C22⋊C4—101no—
327C22⋊C4—101no—
328C22⋊C4—101no—
329C22⋊C4—101no—
330C42—101no—
331C3×C5#161511yescharacteristic, complemented, Hall
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—201no—
335C22×C3—201no—
336C22×C3—201no—
337C22×C3#408311yescharacteristic
338C22×C3#408811yescharacteristic
339C22×C3#409611yescharacteristic
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—81no—
345C3×C4—81no—
346C3×C4—201no—
347C3×C4—201no—
348C3×C4—201no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5C3×#45211yescharacteristic
352C2×C5C3×#45411yescharacteristic
353C2×C5C3×#45811yescharacteristic
354D5—81no—
355C23—101no—
356C23C2×C3×C22⋊D511yescharacteristic
357Q8—201no—
358D4—201no—
359D4—201no—
360D4—201no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—101no—
373C2×C4—101no—
374C2×C4—101no—
375C2×C4—401no—
376C2×C4C3×D4×D511yescharacteristic
377C2×C4C3×D4×D511yescharacteristic
378C8—201no—
379C8—201no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—401no—
383C2×C3#6533611yescharacteristic
384C2×C3#6534211yescharacteristic
385C2×C3#6535111yescharacteristic
386C5C3×#161511yescharacteristic, complemented, Sylow
387C22—21no—
388C22—21no—
389C22—201no—
390C22—201no—
391C22—201no—
392C22C3×#408311yescharacteristic
393C22C3×#408811yescharacteristic
394C22C3×#409611yescharacteristic
395C4—21no—
396C4—21no—
397C4—41no—
398C4—41no—
399C4—81no—
400C4—81no—
401C4—201no—
402C4—201no—
403C4—201no—
404C3#1060051011yescharacteristic, direct product factor, Sylow
405C2—21no—
406C2—21no—
407C2—401no—
408C2C3×#6533611yescharacteristic
409C2C3×#6534211yescharacteristic
410C2C3×#6535111yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#400C2
socleC22×C3×C5#120
prime radicalC3×#4076C22
hypercenterC3×#400D5
hypocenterC5C3×#1615
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#400

Complements

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

NH ≅ G/Ntype
2. C3×C5×#400C2semidirect
3. C3×#65259C2semidirect
5. C3×#64748C2semidirect
6. C3×#64672C2semidirect
8. #10600510C3direct (N × H)
30. C5×#400C2×C3semidirect
31. #65259C2×C3semidirect
33. #64748C2×C3semidirect
34. #64672C2×C3semidirect
66. C3×#400D5semidirect
164. #400C3×D5semidirect
331. C3×C5#1615semidirect
386. C5C3×#1615semidirect
404. C3#10600510direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658492
C3×C5×#4002
C3×#652592
C3×#652572
C3×#647482
C3×#646722
C3×#646712
#106005103
C3×#16155