Finite Group Databasebeta

← C3×#10598929 #14288615

Subgroups — C3×#10598929 #14288615

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×#65275C211yesmaximal, characteristic, complemented
3C3×#65024C211yesmaximal, characteristic
4C3×#65011C211yesmaximal, characteristic, complemented
5C3×C5×#324C211yesmaximal, characteristic, complemented
6C3×#64690C211yesmaximal, characteristic
7C3×#64687C211yesmaximal, characteristic, complemented
8#10598929C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10C3×#4076C2211yescharacteristic
11C3×#4075—21no—
12C3×C4×C22⋊D5—21no—
13C2×C3×C4⋊Dic5C2211yescharacteristic
14C3×#4070C2211yescharacteristic
15C3×#4044—21no—
16C3×#4042—21no—
17C3×#4040—21no—
18C3×#4035—21no—
19C3×C5×C22⋊C8C2211yescharacteristic
20C3×C5×C22⋊C8C2211yescharacteristic
21C3×#3963—21no—
22C3×#3963—21no—
23C3×#3963C2211yescharacteristic
24C3×#3953—21no—
25C3×#3950—21no—
26C3×#3949—21no—
27C3×#3948—21no—
28C3×#1615—51nomaximal, Hall
29#65849C2×C311yescharacteristic
30#65275C2×C311yescharacteristic, complemented
31#65024C2×C311yescharacteristic
32#65011C2×C311yescharacteristic, complemented
33C5×#324C2×C311yescharacteristic, complemented
34#64690C2×C311yescharacteristic
35#64687C2×C311yescharacteristic, complemented
36C22×C3×C4×C5D411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C2×C3×C22⋊D5—21no—
40C22×C3×Dic5—21no—
41C22×C3×Dic5—21no—
42C2×C3×D20D411yescharacteristic
43C2×C3×C4×D5—21no—
44C2×C3×Dic10D411yescharacteristic
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8—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⋊Dic5—21no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5D411yescharacteristic
57C3×C4⋊Dic5D411yescharacteristic
58C3×#683—21no—
59C3×#683—21no—
60C3×#683—21no—
61C3×#683—21no—
62C3×C4×Dic5—21no—
63C3×#539—51no—
64C3×#484—51no—
65C3×#481—51no—
66C3×#400—51no—
67C3×#328—51no—
68C3×#327—51no—
69C3×#324D511yescharacteristic, complemented
70C2×C5×C4⋊C4C22×C311yescharacteristic
71#4076C22×C311yescharacteristic
72#4075—21no—
73C4×C22⋊D5—21no—
74C2×C4⋊Dic5C22×C311yescharacteristic
75#4070C22×C311yescharacteristic
76#4044—21no—
77#4042—21no—
78#4040—21no—
79#4035—21no—
80C5×C22⋊C8C22×C311yescharacteristic
81C5×C22⋊C8C22×C311yescharacteristic
82#3963—21no—
83#3963—21no—
84#3963C22×C311yescharacteristic
85#3953—21no—
86#3950—21no—
87#3949—21no—
88#3948—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×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C3×C22⋊D5—41no—
101C3×C22⋊D5—41no—
102C2×C3×Dic5—21no—
103C2×C3×Dic5—21no—
104C2×C3×Dic5—21no—
105C2×C3×Dic5—41no—
106C2×C3×Dic5—41no—
107C2×C3×Dic5—42no—
108C2×C3×Dic5—41no—
109C2×C3×Dic5—41no—
110C3×D20—41no—
111C3×C4×D5—81no—
112C3×Dic10—41no—
113C3×C5×C8—41no—
114C3×C5×C8—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⋊C4—51no—
124C2×C3×C4⋊C4C2×D511yescharacteristic
125C3×#107—101no—
126C3×#106—101no—
127C3×#103—101no—
128C3×#102—101no—
129C3×C22⋊C8C2×D511yescharacteristic
130C3×C22⋊C8C2×D511yescharacteristic
131C3×#95—51no—
132C3×#95—101no—
133C3×#95—101no—
134C22×C4×C5C3×D411yescharacteristic
135C22×C4×C5C3×D411yescharacteristic
136C22×C4×C5C23×C311yescharacteristic
137C2×C22⋊D5—21no—
138C22×Dic5—21no—
139C22×Dic5—21no—
140C2×D20C3×D411yescharacteristic
141C2×C4×D5—21no—
142C2×Dic10C3×D411yescharacteristic
143C2×C5×C8—21no—
144C2×C5×C8—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⋊Dic5—21no—
153C4⋊Dic5—21no—
154C4⋊Dic5C3×D411yescharacteristic
155C4⋊Dic5C3×D411yescharacteristic
156#683—21no—
157#683—21no—
158#683—21no—
159#683—21no—
160C4×Dic5—21no—
161#539—51no—
162#484—51no—
163#481—51no—
164#400—51no—
165#328—51no—
166#327—51no—
167#324C3×D511yescharacteristic, complemented
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×Dic5—41no—
181C3×Dic5—41no—
182C3×Dic5—41no—
183C3×Dic5—81no—
184C3×Dic5—81no—
185C2×C3×Q8—51no—
186C2×C3×D4—51no—
187C2×C3×D4—101no—
188C22×C3×C4—101no—
189C22×C3×C4—101no—
190C22×C3×C4—101no—
191C22×C3×C4D2011yescharacteristic
192C22×C3×C4D2011yescharacteristic
193C22×C3×C4C22×D511yescharacteristic
194C2×C3×C8—21no—
195C2×C3×C8—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—51no—
199C3×C4⋊C4—51no—
200C3×C4⋊C4—101no—
201C3×C4⋊C4—101no—
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×C5C2×C3×D411yescharacteristic
221C2×C4×C5C2×C3×D411yescharacteristic
222C22⋊D5—41no—
223C22⋊D5—41no—
224C2×Dic5—21no—
225C2×Dic5—21no—
226C2×Dic5—21no—
227C2×Dic5—41no—
228C2×Dic5—41no—
229C2×Dic5—42no—
230C2×Dic5—41no—
231C2×Dic5—41no—
232D20—41no—
233C4×D5—81no—
234Dic10—41no—
235C5×C8—41no—
236C5×C8—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⋊C4—51no—
246C2×C4⋊C4C2×C3×D511yescharacteristic
247#107—101no—
248#106—101no—
249#103—101no—
250#102—101no—
251C22⋊C8C2×C3×D511yescharacteristic
252C22⋊C8C2×C3×D511yescharacteristic
253#95—51no—
254#95—101no—
255#95—101no—
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×D2011yescharacteristic
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—101no—
275C2×C3×C4—101no—
276C2×C3×C4—101no—
277C2×C3×C4—201no—
278C2×C3×C4—201no—
279C2×C3×C4—202no—
280C2×C3×C4—201no—
281C2×C3×C4—201no—
282C2×C3×C4—401no—
283C2×C3×C4D4×D511yescharacteristic
284C2×C3×C4D4×D511yescharacteristic
285C3×C8—41no—
286C3×C8—41no—
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—
299Dic5—41no—
300Dic5—41no—
301Dic5—41no—
302Dic5—81no—
303Dic5—81no—
304C2×Q8—51no—
305C2×D4—51no—
306C2×D4—101no—
307C22×C4—101no—
308C22×C4—101no—
309C22×C4—101no—
310C22×C4C3×D2011yescharacteristic
311C22×C4C3×D2011yescharacteristic
312C22×C4C22×C3×D511yescharacteristic
313C2×C8—21no—
314C2×C8—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—51no—
318C4⋊C4—51no—
319C4⋊C4—101no—
320C4⋊C4—101no—
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#402811yescharacteristic
338C22×C3#405011yescharacteristic
339C22×C3#405511yescharacteristic
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—201no—
345C3×C4—201no—
346C3×C4—201no—
347C3×C4—401no—
348C3×C4—401no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5C3×#45211yescharacteristic
352C2×C5C3×#45411yescharacteristic
353C2×C5C3×#45811yescharacteristic
354D5—81no—
355C23—101no—
356C23C2×C3×D2011yescharacteristic
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—101no—
368C2×C4—101no—
369C2×C4—101no—
370C2×C4—201no—
371C2×C4—201no—
372C2×C4—202no—
373C2×C4—201no—
374C2×C4—201no—
375C2×C4—401no—
376C2×C4C3×D4×D511yescharacteristic
377C2×C4C3×D4×D511yescharacteristic
378C8—41no—
379C8—41no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—401no—
383C2×C3#6502211yescharacteristic
384C2×C3#6503111yescharacteristic
385C2×C3#6504211yescharacteristic
386C5C3×#161511yescharacteristic, complemented, Sylow
387C22—21no—
388C22—21no—
389C22—201no—
390C22—201no—
391C22—201no—
392C22C3×#402811yescharacteristic
393C22C3×#405011yescharacteristic
394C22C3×#405511yescharacteristic
395C4—21no—
396C4—21no—
397C4—41no—
398C4—41no—
399C4—201no—
400C4—201no—
401C4—201no—
402C4—401no—
403C4—401no—
404C3#1059892911yescharacteristic, direct product factor, Sylow
405C2—21no—
406C2—21no—
407C2—401no—
408C2C3×#6502211yescharacteristic
409C2C3×#6503111yescharacteristic
410C2C3×#6504211yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#324C2
socleC22×C3×C5#120
prime radicalC3×#4076C22
hypercenterC3×#324D5
hypocenterC5C3×#1615
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#324

Complements

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

NH ≅ G/Ntype
2. C3×#65275C2semidirect
4. C3×#65011C2semidirect
5. C3×C5×#324C2semidirect
7. C3×#64687C2semidirect
8. #10598929C3direct (N × H)
30. #65275C2×C3semidirect
32. #65011C2×C3semidirect
33. C5×#324C2×C3semidirect
35. #64687C2×C3semidirect
69. C3×#324D5semidirect
167. #324C3×D5semidirect
331. C3×C5#1615semidirect
386. C5C3×#1615semidirect
404. C3#10598929direct (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×#652752
C3×#650242
C3×#650112
C3×C5×#3242
C3×#646902
C3×#646872
#105989293
C3×#16155