Finite Group Databasebeta

← C3×C5×#1930 #14274964

Subgroups — C3×C5×#1930 #14274964

Order 1920.

424 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#428C211yesmaximal, characteristic
2C3×C5×#419C211yesmaximal, characteristic
3C2×C3×C5×#103C211yesmaximal, characteristic
4C2×C3×C5×#101C211yesmaximal, characteristic
5C3×C5×#405C211yesmaximal, characteristic
6C3×C5×#343C211yesmaximal, characteristic
7C3×C5×#341C211yesmaximal, characteristic
8C5×#1930C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C3×C5×M16C2211yescharacteristic
13C22×C3×C5×C8C2211yescharacteristic
14C3×C5×#117C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C3×C5×#107—21no—
17C3×C5×#106—21no—
18C3×C5×#103—21no—
19C3×C5×#103—21no—
20C3×C5×#103—21no—
21C3×C5×#103—21no—
22C3×C5×#101C414yescomplemented
23C3×C5×#97—21no—
24C3×C4×C5×C8—21no—
25C3×#1930C511yesmaximal, characteristic, direct product factor, Hall
26C5×#428C2×C311yescharacteristic
27C5×#419C2×C311yescharacteristic
28C2×C5×#103C2×C311yescharacteristic
29C2×C5×#101C2×C311yescharacteristic
30C5×#405C2×C311yescharacteristic
31C5×#343C2×C311yescharacteristic
32C5×#341C2×C311yescharacteristic
33C2×C3×C5×Q8—21no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8C2×C412yes—
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×M16C2×C412yes—
47C3×C5×M16C2×C412yes—
48C2×C3×C5×C8—21no—
49C2×C3×C5×C8—21no—
50C2×C3×C5×C8—21no—
51C2×C3×C5×C8—21no—
52C2×C3×C5×C8—21no—
53C2×C3×C5×C8D411yescharacteristic
54C2×C3×C5×C8D411yescharacteristic
55C3×C5×C4⋊C4—21no—
56C3×C5×C4⋊C4—21no—
57C3×C5×C4⋊C4D411yescharacteristic
58C3×C5×C4⋊C4D411yescharacteristic
59C3×C5×C22⋊C4—21no—
60C3×C42×C5—21no—
61C3×#428C2×C511yescharacteristic
62C3×#419C2×C511yescharacteristic
63C2×C3×#103C2×C511yescharacteristic
64C2×C3×#101C2×C511yescharacteristic
65C3×#405C2×C511yescharacteristic
66C3×#343C2×C511yescharacteristic
67C3×#341C2×C511yescharacteristic
68C22×C5×Q8C22×C311yescharacteristic
69C2×C5×M16C22×C311yescharacteristic
70C2×C5×M16C22×C311yescharacteristic
71C2×C5×M16C22×C311yescharacteristic
72C22×C5×C8C22×C311yescharacteristic
73C5×#117C22×C311yescharacteristic
74C2×C5×C4⋊C4C22×C311yescharacteristic
75C5×#107—21no—
76C5×#106—21no—
77C5×#103—21no—
78C5×#103—21no—
79C5×#103—21no—
80C5×#103—21no—
81C5×#101C3×C414yescomplemented
82C5×#97—21no—
83C4×C5×C8—21no—
84#1930C3×C511yescharacteristic, direct product factor, Sylow
85C23×C3×C5#4111yescharacteristic
86C3×C5×Q8—22no—
87C3×C5×Q8—22no—
88C3×C5×Q8—41no—
89C3×C5×Q8—41no—
90C2×C3×C4×C5—22no—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—81no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5#4111yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C3×C5×C8—22no—
104C3×C5×C8—22no—
105C3×C5×C8—21no—
106C3×C5×C8—21no—
107C3×C5×C8—41no—
108C22×C3×Q8C22×C511yescharacteristic
109C2×C3×M16C22×C511yescharacteristic
110C2×C3×M16C22×C511yescharacteristic
111C2×C3×M16C22×C511yescharacteristic
112C22×C3×C8C22×C511yescharacteristic
113C3×#117C22×C511yescharacteristic
114C2×C3×C4⋊C4C22×C511yescharacteristic
115C3×#107—21no—
116C3×#106—21no—
117C3×#103—21no—
118C3×#103—21no—
119C3×#103—21no—
120C3×#103—21no—
121C3×#101C4×C514yescomplemented
122C3×#97—21no—
123C3×C4×C8—21no—
124C2×C5×Q8—21no—
125C2×C5×Q8—21no—
126C2×C5×Q8—21no—
127C2×C5×Q8—21no—
128C2×C5×Q8—21no—
129C2×C5×Q8C2×C3×C412yes—
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×M16C2×C3×C412yes—
138C5×M16C2×C3×C412yes—
139C2×C5×C8—21no—
140C2×C5×C8—21no—
141C2×C5×C8—21no—
142C2×C5×C8—21no—
143C2×C5×C8—21no—
144C2×C5×C8C3×D411yescharacteristic
145C2×C5×C8C3×D411yescharacteristic
146C5×C4⋊C4—21no—
147C5×C4⋊C4—21no—
148C5×C4⋊C4C3×D411yescharacteristic
149C5×C4⋊C4C3×D411yescharacteristic
150C5×C22⋊C4—21no—
151C42×C5—21no—
152#428C2×C3×C511yescharacteristic
153#419C2×C3×C511yescharacteristic
154C2×#103C2×C3×C511yescharacteristic
155C2×#101C2×C3×C511yescharacteristic
156#405C2×C3×C511yescharacteristic
157#343C2×C3×C511yescharacteristic
158#341C2×C3×C511yescharacteristic
159C22×C3×C5—21no—
160C22×C3×C5—21no—
161C22×C3×C5#11711yescharacteristic
162C22×C3×C5#12111yescharacteristic
163C22×C3×C5#12611yescharacteristic
164C3×C4×C5—42no—
165C3×C4×C5—41no—
166C3×C4×C5—41no—
167C3×C4×C5—81no—
168C3×C4×C5C4×D411yescharacteristic
169C3×C4×C5C4×D411yescharacteristic
170C3×C4×C5#12311yescharacteristic
171C3×C4×C5#12411yescharacteristic
172C2×C3×Q8—21no—
173C2×C3×Q8—21no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×Q8—21no—
177C2×C3×Q8C2×C4×C512yes—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4C23×C511yescharacteristic
181C3×M16—21no—
182C3×M16—21no—
183C3×M16—21no—
184C3×M16—21no—
185C3×M16C2×C4×C512yes—
186C3×M16C2×C4×C512yes—
187C2×C3×C8—21no—
188C2×C3×C8—21no—
189C2×C3×C8—21no—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C2×C3×C8C5×D411yescharacteristic
193C2×C3×C8C5×D411yescharacteristic
194C3×C4⋊C4—21no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4C5×D411yescharacteristic
197C3×C4⋊C4C5×D411yescharacteristic
198C3×C22⋊C4—21no—
199C3×C42—21no—
200C23×C5C3×#4111yescharacteristic
201C5×Q8—22no—
202C5×Q8—22no—
203C5×Q8—41no—
204C5×Q8—41no—
205C2×C4×C5—22no—
206C2×C4×C5—21no—
207C2×C4×C5—21no—
208C2×C4×C5—41no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5—81no—
212C2×C4×C5C22×C3×C411yescharacteristic
213C2×C4×C5C2×C3×D411yescharacteristic
214C2×C4×C5C2×C3×D411yescharacteristic
215C2×C4×C5C3×#4111yescharacteristic
216C2×C4×C5C3×#4111yescharacteristic
217C2×C4×C5C3×#4111yescharacteristic
218C5×C8—22no—
219C5×C8—22no—
220C5×C8—21no—
221C5×C8—21no—
222C5×C8—41no—
223C22×Q8C22×C3×C511yescharacteristic
224C2×M16C22×C3×C511yescharacteristic
225C2×M16C22×C3×C511yescharacteristic
226C2×M16C22×C3×C511yescharacteristic
227C22×C8C22×C3×C511yescharacteristic
228#117C22×C3×C511yescharacteristic
229C2×C4⋊C4C22×C3×C511yescharacteristic
230#107—21no—
231#106—21no—
232#103—21no—
233#103—21no—
234#103—21no—
235#103—21no—
236#101C3×C4×C514yescomplemented
237#97—21no—
238C4×C8—21no—
239C2×C3×C5—21no—
240C2×C3×C5—21no—
241C2×C3×C5#38811yescharacteristic
242C2×C3×C5#47111yescharacteristic
243C2×C3×C5#47311yescharacteristic
244C23×C3C5×#4111yescharacteristic
245C3×Q8—22no—
246C3×Q8—22no—
247C3×Q8—41no—
248C3×Q8—41no—
249C2×C3×C4—22no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—81no—
256C2×C3×C4C22×C4×C511yescharacteristic
257C2×C3×C4C2×C5×D411yescharacteristic
258C2×C3×C4C2×C5×D411yescharacteristic
259C2×C3×C4C5×#4111yescharacteristic
260C2×C3×C4C5×#4111yescharacteristic
261C2×C3×C4C5×#4111yescharacteristic
262C3×C8—22no—
263C3×C8—22no—
264C3×C8—21no—
265C3×C8—21no—
266C3×C8—41no—
267C22×C5—21no—
268C22×C5—21no—
269C22×C5C3×#11711yescharacteristic
270C22×C5C3×#12111yescharacteristic
271C22×C5C3×#12611yescharacteristic
272C4×C5—42no—
273C4×C5—41no—
274C4×C5—41no—
275C4×C5—81no—
276C4×C5C3×C4×D411yescharacteristic
277C4×C5C3×C4×D411yescharacteristic
278C4×C5C3×#12311yescharacteristic
279C4×C5C3×#12411yescharacteristic
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8C2×C3×C4×C512yes—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4C23×C3×C511yescharacteristic
289M16—21no—
290M16—21no—
291M16—21no—
292M16—21no—
293M16C2×C3×C4×C512yes—
294M16C2×C3×C4×C512yes—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8C3×C5×D411yescharacteristic
301C2×C8C3×C5×D411yescharacteristic
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4C3×C5×D411yescharacteristic
305C4⋊C4C3×C5×D411yescharacteristic
306C22⋊C4—21no—
307C42—21no—
308C3×C5#193011yescharacteristic, direct product factor, Hall
309C22×C3—21no—
310C22×C3—21no—
311C22×C3C5×#11711yescharacteristic
312C22×C3C5×#12111yescharacteristic
313C22×C3C5×#12611yescharacteristic
314C3×C4—42no—
315C3×C4—41no—
316C3×C4—41no—
317C3×C4—81no—
318C3×C4C4×C5×D411yescharacteristic
319C3×C4C4×C5×D411yescharacteristic
320C3×C4C5×#12311yescharacteristic
321C3×C4C5×#12411yescharacteristic
322C2×C5—21no—
323C2×C5—21no—
324C2×C5C3×#38811yescharacteristic
325C2×C5C3×#47111yescharacteristic
326C2×C5C3×#47311yescharacteristic
327C23C3×C5×#4111yescharacteristic
328Q8—22no—
329Q8—22no—
330Q8—41no—
331Q8—41no—
332C2×C4—22no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—81no—
339C2×C4C22×C3×C4×C511yescharacteristic
340C2×C4C2×C3×C5×D411yescharacteristic
341C2×C4C2×C3×C5×D411yescharacteristic
342C2×C4C3×C5×#4111yescharacteristic
343C2×C4C3×C5×#4111yescharacteristic
344C2×C4C3×C5×#4111yescharacteristic
345C8—22no—
346C8—22no—
347C8—21no—
348C8—21no—
349C8—41no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3C5×#38811yescharacteristic
353C2×C3C5×#47111yescharacteristic
354C2×C3C5×#47311yescharacteristic
355C5C3×#193011yescharacteristic, direct product factor, Sylow
356C22—21no—
357C22—21no—
358C22C3×C5×#11711yescharacteristic
359C22C3×C5×#12111yescharacteristic
360C22C3×C5×#12611yescharacteristic
361C4—41no—
362C4—41no—
363C4—42no—
364C4—81no—
365C4C3×C4×C5×D411yescharacteristic
366C4C3×C4×C5×D411yescharacteristic
367C4C3×C5×#12311yescharacteristic
368C4C3×C5×#12411yescharacteristic
369C3C5×#193011yescharacteristic, direct product factor, Sylow
370C2—21no—
371C2—21no—
372C2C3×C5×#38811yescharacteristic
373C2C3×C5×#47111yescharacteristic
374C2C3×C5×#47311yescharacteristic
subgroupG/H
center, socleC22×C3×C5#121
commutatorC2×C4C22×C3×C4×C5
Frattini, cosocleC22×C4C23×C3×C5
prime radicalC23×C3×C5#41
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
8. C5×#1930C3direct (N × H)
22. C3×C5×#101C4semidirect
25. C3×#1930C5direct (N × H)
81. C5×#101C3×C4semidirect
84. #1930C3×C5direct (N × H)
121. C3×#101C4×C5semidirect
236. #101C3×C4×C5semidirect
308. C3×C5#1930direct (N × H)
355. C5C3×#1930direct (N × H)
369. C3C5×#1930direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4282
C3×C5×#4192
C2×C3×C5×#1032
C2×C3×C5×#1012
C3×C5×#4052
C3×C5×#3432
C3×C5×#3412
C5×#19303
C3×#19305