Finite Group Databasebeta

← C3×C5×#1932 #14274966

Subgroups — C3×C5×#1932 #14274966

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#430C211yesmaximal, characteristic, complemented
2C3×C5×#421C211yesmaximal, characteristic
3C2×C3×C5×#104C211yesmaximal, characteristic
4C3×C5×#413C211yesmaximal, characteristic
5C3×C4×C5×M16C211yesmaximal, characteristic, complemented
6C3×C5×#344C211yesmaximal, characteristic, complemented
7C3×C5×#339C211yesmaximal, characteristic, complemented
8C5×#1932C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C3×C5×M16C2211yescharacteristic
13C2×C3×C5×M16C2211yescharacteristic
14C3×C5×#117C2211yescharacteristic
15C2×C3×C42×C5C2211yescharacteristic
16C3×C5×#108—22no—
17C3×C5×#104—22no—
18C3×C5×#104—21no—
19C3×C5×#104—21no—
20C3×C5×#101C412yescomplemented
21C3×C5×#100C412yescomplemented
22C3×C5×#97—21no—
23C3×C4×C5×C8—21no—
24C3×#1932C511yesmaximal, characteristic, direct product factor, Hall
25C5×#430C2×C311yescharacteristic, complemented
26C5×#421C2×C311yescharacteristic
27C2×C5×#104C2×C311yescharacteristic
28C5×#413C2×C311yescharacteristic
29C4×C5×M16C2×C311yescharacteristic, complemented
30C5×#344C2×C311yescharacteristic, complemented
31C5×#339C2×C311yescharacteristic, complemented
32C3×C5×#41—21no—
33C3×C5×#41—21no—
34C3×C5×#41—21no—
35C3×C5×#41—21no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4C2×C411yescharacteristic
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5C2311yescharacteristic
42C3×C5×M16—21no—
43C3×C5×M16—21no—
44C3×C5×M16—21no—
45C3×C5×M16—21no—
46C3×C5×M16—21no—
47C3×C5×M16C2×C412yes—
48C3×C5×M16C2×C412yes—
49C3×C5×M16D412yes—
50C2×C3×C5×C8—21no—
51C2×C3×C5×C8—21no—
52C2×C3×C5×C8—21no—
53C2×C3×C5×C8—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C22⋊C4—21no—
56C3×C42×C5—21no—
57C3×C42×C5—21no—
58C3×C42×C5D411yescharacteristic
59C3×C42×C5D411yescharacteristic
60C3×#430C2×C511yescharacteristic, complemented
61C3×#421C2×C511yescharacteristic
62C2×C3×#104C2×C511yescharacteristic
63C3×#413C2×C511yescharacteristic
64C3×C4×M16C2×C511yescharacteristic, complemented
65C3×#344C2×C511yescharacteristic, complemented
66C3×#339C2×C511yescharacteristic, complemented
67C2×C5×#41C22×C311yescharacteristic
68C2×C5×M16C22×C311yescharacteristic
69C2×C5×M16C22×C311yescharacteristic
70C2×C5×M16C22×C311yescharacteristic
71C2×C5×M16C22×C311yescharacteristic
72C5×#117C22×C311yescharacteristic
73C2×C42×C5C22×C311yescharacteristic
74C5×#108—22no—
75C5×#104—22no—
76C5×#104—21no—
77C5×#104—21no—
78C5×#101C3×C412yescomplemented
79C5×#100C3×C412yescomplemented
80C5×#97—21no—
81C4×C5×C8—21no—
82#1932C3×C511yescharacteristic, direct product factor, Sylow
83C23×C3×C5—21no—
84C23×C3×C5#4111yescharacteristic
85C3×C5×Q8—21no—
86C3×C5×Q8—21no—
87C3×C5×D4—21no—
88C3×C5×D4—21no—
89C3×C5×D4—41no—
90C3×C5×D4—41no—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—42no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C3×C5×C8—22no—
105C3×C5×C8—22no—
106C3×C5×C8—22no—
107C3×C5×C8—41no—
108C2×C3×#41C22×C511yescharacteristic
109C2×C3×M16C22×C511yescharacteristic
110C2×C3×M16C22×C511yescharacteristic
111C2×C3×M16C22×C511yescharacteristic
112C2×C3×M16C22×C511yescharacteristic
113C3×#117C22×C511yescharacteristic
114C2×C3×C42C22×C511yescharacteristic
115C3×#108—22no—
116C3×#104—22no—
117C3×#104—21no—
118C3×#104—21no—
119C3×#101C4×C512yescomplemented
120C3×#100C4×C512yescomplemented
121C3×#97—21no—
122C3×C4×C8—21no—
123C5×#41—21no—
124C5×#41—21no—
125C5×#41—21no—
126C5×#41—21no—
127C2×C5×Q8C2×C3×C411yescharacteristic
128C2×C5×D4—21no—
129C2×C5×D4C2×C3×C411yescharacteristic
130C22×C4×C5—21no—
131C22×C4×C5—21no—
132C22×C4×C5C23×C311yescharacteristic
133C5×M16—21no—
134C5×M16—21no—
135C5×M16—21no—
136C5×M16—21no—
137C5×M16—21no—
138C5×M16C2×C3×C412yes—
139C5×M16C2×C3×C412yes—
140C5×M16C3×D412yes—
141C2×C5×C8—21no—
142C2×C5×C8—21no—
143C2×C5×C8—21no—
144C2×C5×C8—21no—
145C5×C4⋊C4—21no—
146C5×C22⋊C4—21no—
147C42×C5—21no—
148C42×C5—21no—
149C42×C5C3×D411yescharacteristic
150C42×C5C3×D411yescharacteristic
151#430C2×C3×C511yescharacteristic, complemented
152#421C2×C3×C511yescharacteristic
153C2×#104C2×C3×C511yescharacteristic
154#413C2×C3×C511yescharacteristic
155C4×M16C2×C3×C511yescharacteristic, complemented
156#344C2×C3×C511yescharacteristic, complemented
157#339C2×C3×C511yescharacteristic, complemented
158C22×C3×C5—41no—
159C22×C3×C5—41no—
160C22×C3×C5—81no—
161C22×C3×C5#11711yescharacteristic
162C22×C3×C5#12311yescharacteristic
163C22×C3×C5#12411yescharacteristic
164C3×C4×C5—22no—
165C3×C4×C5—41no—
166C3×C4×C5—41no—
167C3×C4×C5—81no—
168C3×C4×C5C4×D411yescharacteristic
169C3×C4×C5C4×D411yescharacteristic
170C3×C4×C5#12111yescharacteristic
171C3×C4×C5#12611yescharacteristic
172C3×#41—21no—
173C3×#41—21no—
174C3×#41—21no—
175C3×#41—21no—
176C2×C3×Q8C2×C4×C511yescharacteristic
177C2×C3×D4—21no—
178C2×C3×D4C2×C4×C511yescharacteristic
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4C23×C511yescharacteristic
182C3×M16—21no—
183C3×M16—21no—
184C3×M16—21no—
185C3×M16—21no—
186C3×M16—21no—
187C3×M16C2×C4×C512yes—
188C3×M16C2×C4×C512yes—
189C3×M16C5×D412yes—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C3×C4⋊C4—21no—
195C3×C22⋊C4—21no—
196C3×C42—21no—
197C3×C42—21no—
198C3×C42C5×D411yescharacteristic
199C3×C42C5×D411yescharacteristic
200C23×C5—21no—
201C23×C5C3×#4111yescharacteristic
202C5×Q8—21no—
203C5×Q8—21no—
204C5×D4—21no—
205C5×D4—21no—
206C5×D4—41no—
207C5×D4—41no—
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5—21no—
211C2×C4×C5—42no—
212C2×C4×C5—41no—
213C2×C4×C5—41no—
214C2×C4×C5—41no—
215C2×C4×C5C22×C3×C411yescharacteristic
216C2×C4×C5C2×C3×D411yescharacteristic
217C2×C4×C5C2×C3×D411yescharacteristic
218C2×C4×C5C3×#4111yescharacteristic
219C2×C4×C5C3×#4111yescharacteristic
220C2×C4×C5C3×#4111yescharacteristic
221C5×C8—22no—
222C5×C8—22no—
223C5×C8—22no—
224C5×C8—41no—
225C2×#41C22×C3×C511yescharacteristic
226C2×M16C22×C3×C511yescharacteristic
227C2×M16C22×C3×C511yescharacteristic
228C2×M16C22×C3×C511yescharacteristic
229C2×M16C22×C3×C511yescharacteristic
230#117C22×C3×C511yescharacteristic
231C2×C42C22×C3×C511yescharacteristic
232#108—22no—
233#104—22no—
234#104—21no—
235#104—21no—
236#101C3×C4×C512yescomplemented
237#100C3×C4×C512yescomplemented
238#97—21no—
239C4×C8—21no—
240C2×C3×C5—21no—
241C2×C3×C5—21no—
242C2×C3×C5—21no—
243C2×C3×C5—81no—
244C2×C3×C5#38811yescharacteristic
245C23×C3—21no—
246C23×C3C5×#4111yescharacteristic
247C3×Q8—21no—
248C3×Q8—21no—
249C3×D4—21no—
250C3×D4—21no—
251C3×D4—41no—
252C3×D4—41no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—42no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4C22×C4×C511yescharacteristic
261C2×C3×C4C2×C5×D411yescharacteristic
262C2×C3×C4C2×C5×D411yescharacteristic
263C2×C3×C4C5×#4111yescharacteristic
264C2×C3×C4C5×#4111yescharacteristic
265C2×C3×C4C5×#4111yescharacteristic
266C3×C8—22no—
267C3×C8—22no—
268C3×C8—22no—
269C3×C8—41no—
270C22×C5—41no—
271C22×C5—41no—
272C22×C5—81no—
273C22×C5C3×#11711yescharacteristic
274C22×C5C3×#12311yescharacteristic
275C22×C5C3×#12411yescharacteristic
276C4×C5—22no—
277C4×C5—41no—
278C4×C5—41no—
279C4×C5—81no—
280C4×C5C3×C4×D411yescharacteristic
281C4×C5C3×C4×D411yescharacteristic
282C4×C5C3×#12111yescharacteristic
283C4×C5C3×#12611yescharacteristic
284#41—21no—
285#41—21no—
286#41—21no—
287#41—21no—
288C2×Q8C2×C3×C4×C511yescharacteristic
289C2×D4—21no—
290C2×D4C2×C3×C4×C511yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4C23×C3×C511yescharacteristic
294M16—21no—
295M16—21no—
296M16—21no—
297M16—21no—
298M16—21no—
299M16C2×C3×C4×C512yes—
300M16C2×C3×C4×C512yes—
301M16C3×C5×D412yes—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C4⋊C4—21no—
307C22⋊C4—21no—
308C42—21no—
309C42—21no—
310C42C3×C5×D411yescharacteristic
311C42C3×C5×D411yescharacteristic
312C3×C5#193211yescharacteristic, direct product factor, Hall
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—81no—
316C22×C3C5×#11711yescharacteristic
317C22×C3C5×#12311yescharacteristic
318C22×C3C5×#12411yescharacteristic
319C3×C4—22no—
320C3×C4—41no—
321C3×C4—41no—
322C3×C4—81no—
323C3×C4C4×C5×D411yescharacteristic
324C3×C4C4×C5×D411yescharacteristic
325C3×C4C5×#12111yescharacteristic
326C3×C4C5×#12611yescharacteristic
327C2×C5—21no—
328C2×C5—21no—
329C2×C5—21no—
330C2×C5—81no—
331C2×C5C3×#38811yescharacteristic
332C23—21no—
333C23C3×C5×#4111yescharacteristic
334Q8—21no—
335Q8—21no—
336D4—21no—
337D4—21no—
338D4—41no—
339D4—41no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4C22×C3×C4×C511yescharacteristic
348C2×C4C2×C3×C5×D411yescharacteristic
349C2×C4C2×C3×C5×D411yescharacteristic
350C2×C4C3×C5×#4111yescharacteristic
351C2×C4C3×C5×#4111yescharacteristic
352C2×C4C3×C5×#4111yescharacteristic
353C8—22no—
354C8—22no—
355C8—22no—
356C8—41no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—81no—
361C2×C3C5×#38811yescharacteristic
362C5C3×#193211yescharacteristic, direct product factor, Sylow
363C22—41no—
364C22—41no—
365C22—81no—
366C22C3×C5×#11711yescharacteristic
367C22C3×C5×#12311yescharacteristic
368C22C3×C5×#12411yescharacteristic
369C4—22no—
370C4—41no—
371C4—41no—
372C4—81no—
373C4C3×C4×C5×D411yescharacteristic
374C4C3×C4×C5×D411yescharacteristic
375C4C3×C5×#12111yescharacteristic
376C4C3×C5×#12611yescharacteristic
377C3C5×#193211yescharacteristic, direct product factor, Sylow
378C2—21no—
379C2—21no—
380C2—21no—
381C2—81no—
382C2C3×C5×#38811yescharacteristic
subgroupG/H
centerC3×C4×C5#121
commutatorC2×C4C22×C3×C4×C5
Frattini, cosocleC22×C4C23×C3×C5
socleC2×C3×C5#388
prime radicalC2×C3×C5×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C3×C4×C5 ◁ C22×C3×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×C5×#430C2semidirect
5. C3×C4×C5×M16C2semidirect
6. C3×C5×#344C2semidirect
7. C3×C5×#339C2semidirect
8. C5×#1932C3direct (N × H)
20. C3×C5×#101C4semidirect
21. C3×C5×#100C4semidirect
24. C3×#1932C5direct (N × H)
25. C5×#430C2×C3semidirect
29. C4×C5×M16C2×C3semidirect
30. C5×#344C2×C3semidirect
31. C5×#339C2×C3semidirect
60. C3×#430C2×C5semidirect
64. C3×C4×M16C2×C5semidirect
65. C3×#344C2×C5semidirect
66. C3×#339C2×C5semidirect
78. C5×#101C3×C4semidirect
79. C5×#100C3×C4semidirect
82. #1932C3×C5direct (N × H)
119. C3×#101C4×C5semidirect
120. C3×#100C4×C5semidirect
151. #430C2×C3×C5semidirect
155. C4×M16C2×C3×C5semidirect
156. #344C2×C3×C5semidirect
157. #339C2×C3×C5semidirect
236. #101C3×C4×C5semidirect
237. #100C3×C4×C5semidirect
312. C3×C5#1932direct (N × H)
362. C5C3×#1932direct (N × H)
377. C3C5×#1932direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4302
C3×C5×#4212
C2×C3×C5×#1042
C3×C5×#4132
C3×C4×C5×M162
C3×C5×#3442
C3×C5×#3392
C5×#19323
C3×#19325