Finite Group Databasebeta

← C3×C5×#1934 #14274968

Subgroups — C3×C5×#1934 #14274968

Order 1920.

584 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#102C211yesmaximal, characteristic
2C2×C3×C5×#102C211yesmaximal, characteristic
3C2×C3×C4×C5×C8C211yesmaximal, characteristic, complemented
4C3×C5×#390C211yesmaximal, characteristic
5C3×C5×#389C211yesmaximal, characteristic, complemented
6C3×C5×#340C211yesmaximal, characteristic, complemented
7C3×C5×#340C211yesmaximal, characteristic, complemented
8C5×#1934C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C2×C3×C5×C4⋊C4—21no—
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C3×C5×C22⋊C4—21no—
17C2×C3×C5×C22⋊C4—21no—
18C2×C3×C42×C5C2211yescharacteristic
19C3×C5×#102—22no—
20C3×C5×#102C414yescomplemented
21C3×C4×C5×C8—22no—
22C3×C5×#95—21no—
23C3×#1934C511yesmaximal, characteristic, direct product factor, Hall
24C2×C5×#102C2×C311yescharacteristic
25C2×C5×#102C2×C311yescharacteristic
26C2×C4×C5×C8C2×C311yescharacteristic, complemented
27C5×#390C2×C311yescharacteristic
28C5×#389C2×C311yescharacteristic, complemented
29C5×#340C2×C311yescharacteristic, complemented
30C5×#340C2×C311yescharacteristic, complemented
31C24×C3×C5—21no—
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4C2×C412yes—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5D411yescharacteristic
42C22×C3×C4×C5D411yescharacteristic
43C22×C3×C4×C5C2311yescharacteristic
44C2×C3×C5×C8—21no—
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8—21no—
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8C2×C412yes—
49C2×C3×C5×C8D412yes—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4—42no—
56C3×C5×C4⋊C4C2×C412yes—
57C3×C5×C22⋊C4—42no—
58C3×C5×C22⋊C4—42no—
59C3×C42×C5—21no—
60C3×C42×C5—21no—
61C2×C3×#102C2×C511yescharacteristic
62C2×C3×#102C2×C511yescharacteristic
63C2×C3×C4×C8C2×C511yescharacteristic, complemented
64C3×#390C2×C511yescharacteristic
65C3×#389C2×C511yescharacteristic, complemented
66C3×#340C2×C511yescharacteristic, complemented
67C3×#340C2×C511yescharacteristic, complemented
68C22×C5×D4C22×C311yescharacteristic
69C22×C5×C8C22×C311yescharacteristic
70C22×C5×C8C22×C311yescharacteristic
71C2×C5×C4⋊C4—21no—
72C2×C5×C4⋊C4C22×C311yescharacteristic
73C2×C5×C4⋊C4C22×C311yescharacteristic
74C2×C5×C4⋊C4C22×C311yescharacteristic
75C2×C5×C22⋊C4—21no—
76C2×C5×C22⋊C4—21no—
77C2×C42×C5C22×C311yescharacteristic
78C5×#102—22no—
79C5×#102C3×C414yescomplemented
80C4×C5×C8—22no—
81C5×#95—21no—
82#1934C3×C511yescharacteristic, direct product factor, Sylow
83C23×C3×C5—22no—
84C23×C3×C5—41no—
85C23×C3×C5—41no—
86C23×C3×C5—41no—
87C23×C3×C5—41no—
88C23×C3×C5—41no—
89C23×C3×C5—41no—
90C23×C3×C5C2×D411yescharacteristic
91C3×C5×D4—22no—
92C3×C5×D4—22no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—22no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5D812yes—
109C2×C3×C4×C5SD1612yes—
110C2×C3×C4×C5C22×C411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116C3×C5×C8—22no—
117C3×C5×C8—22no—
118C22×C3×D4C22×C511yescharacteristic
119C22×C3×C8C22×C511yescharacteristic
120C22×C3×C8C22×C511yescharacteristic
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4C22×C511yescharacteristic
123C2×C3×C4⋊C4C22×C511yescharacteristic
124C2×C3×C4⋊C4C22×C511yescharacteristic
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4—21no—
127C2×C3×C42C22×C511yescharacteristic
128C3×#102—22no—
129C3×#102C4×C514yescomplemented
130C3×C4×C8—22no—
131C3×#95—21no—
132C24×C5—21no—
133C2×C5×D4—21no—
134C2×C5×D4—21no—
135C2×C5×D4—21no—
136C2×C5×D4—21no—
137C2×C5×D4—21no—
138C2×C5×D4C2×C3×C412yes—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5C3×D411yescharacteristic
143C22×C4×C5C3×D411yescharacteristic
144C22×C4×C5C23×C311yescharacteristic
145C2×C5×C8—21no—
146C2×C5×C8—21no—
147C2×C5×C8—21no—
148C2×C5×C8—21no—
149C2×C5×C8C2×C3×C412yes—
150C2×C5×C8C3×D412yes—
151C5×C4⋊C4—21no—
152C5×C4⋊C4—21no—
153C5×C4⋊C4—21no—
154C5×C4⋊C4—21no—
155C5×C4⋊C4—21no—
156C5×C4⋊C4—42no—
157C5×C4⋊C4C2×C3×C412yes—
158C5×C22⋊C4—42no—
159C5×C22⋊C4—42no—
160C42×C5—21no—
161C42×C5—21no—
162C2×#102C2×C3×C511yescharacteristic
163C2×#102C2×C3×C511yescharacteristic
164C2×C4×C8C2×C3×C511yescharacteristic, complemented
165#390C2×C3×C511yescharacteristic
166#389C2×C3×C511yescharacteristic, complemented
167#340C2×C3×C511yescharacteristic, complemented
168#340C2×C3×C511yescharacteristic, complemented
169C22×C3×C5—42no—
170C22×C3×C5—42no—
171C22×C3×C5—42no—
172C22×C3×C5—81no—
173C22×C3×C5—81no—
174C22×C3×C5—81no—
175C22×C3×C5—81no—
176C22×C3×C5C4×D411yescharacteristic
177C22×C3×C5#12111yescharacteristic
178C22×C3×C5#12411yescharacteristic
179C22×C3×C5C2×D811yescharacteristic
180C22×C3×C5C2×SD1611yescharacteristic
181C22×C3×C5#13511yescharacteristic
182C22×C3×C5#13511yescharacteristic
183C3×C4×C5—22no—
184C3×C4×C5—22no—
185C3×C4×C5—42no—
186C3×C4×C5—81no—
187C3×C4×C5—81no—
188C3×C4×C5#11711yescharacteristic
189C3×C4×C5C4×D411yescharacteristic
190C3×C4×C5#12311yescharacteristic
191C3×C4×C5#12611yescharacteristic
192C24×C3—21no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4C2×C4×C512yes—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4C5×D411yescharacteristic
203C22×C3×C4C5×D411yescharacteristic
204C22×C3×C4C23×C511yescharacteristic
205C2×C3×C8—21no—
206C2×C3×C8—21no—
207C2×C3×C8—21no—
208C2×C3×C8—21no—
209C2×C3×C8C2×C4×C512yes—
210C2×C3×C8C5×D412yes—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—42no—
217C3×C4⋊C4C2×C4×C512yes—
218C3×C22⋊C4—42no—
219C3×C22⋊C4—42no—
220C3×C42—21no—
221C3×C42—21no—
222C23×C5—22no—
223C23×C5—41no—
224C23×C5—41no—
225C23×C5—41no—
226C23×C5—41no—
227C23×C5—41no—
228C23×C5—41no—
229C23×C5C2×C3×D411yescharacteristic
230C5×D4—22no—
231C5×D4—22no—
232C5×D4—41no—
233C5×D4—41no—
234C2×C4×C5—21no—
235C2×C4×C5—21no—
236C2×C4×C5—21no—
237C2×C4×C5—21no—
238C2×C4×C5—22no—
239C2×C4×C5—41no—
240C2×C4×C5—41no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5—41no—
244C2×C4×C5—41no—
245C2×C4×C5—41no—
246C2×C4×C5—41no—
247C2×C4×C5C3×D812yes—
248C2×C4×C5C3×SD1612yes—
249C2×C4×C5C22×C3×C411yescharacteristic
250C2×C4×C5C2×C3×D411yescharacteristic
251C2×C4×C5C3×#4111yescharacteristic
252C2×C4×C5C3×#4111yescharacteristic
253C2×C4×C5C3×#4111yescharacteristic
254C2×C4×C5C3×#4111yescharacteristic
255C5×C8—22no—
256C5×C8—22no—
257C22×D4C22×C3×C511yescharacteristic
258C22×C8C22×C3×C511yescharacteristic
259C22×C8C22×C3×C511yescharacteristic
260C2×C4⋊C4—21no—
261C2×C4⋊C4C22×C3×C511yescharacteristic
262C2×C4⋊C4C22×C3×C511yescharacteristic
263C2×C4⋊C4C22×C3×C511yescharacteristic
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C42C22×C3×C511yescharacteristic
267#102—22no—
268#102C3×C4×C514yescomplemented
269C4×C8—22no—
270#95—21no—
271C2×C3×C5—82no—
272C2×C3×C5#38811yescharacteristic
273C2×C3×C5C4×D811yescharacteristic
274C2×C3×C5C4×SD1611yescharacteristic
275C2×C3×C5#46511yescharacteristic
276C2×C3×C5#46611yescharacteristic
277C2×C3×C5#48611yescharacteristic
278C2×C3×C5#48811yescharacteristic
279C23×C3—22no—
280C23×C3—41no—
281C23×C3—41no—
282C23×C3—41no—
283C23×C3—41no—
284C23×C3—41no—
285C23×C3—41no—
286C23×C3C2×C5×D411yescharacteristic
287C3×D4—22no—
288C3×D4—22no—
289C3×D4—41no—
290C3×D4—41no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—22no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4C5×D812yes—
305C2×C3×C4C5×SD1612yes—
306C2×C3×C4C22×C4×C511yescharacteristic
307C2×C3×C4C2×C5×D411yescharacteristic
308C2×C3×C4C5×#4111yescharacteristic
309C2×C3×C4C5×#4111yescharacteristic
310C2×C3×C4C5×#4111yescharacteristic
311C2×C3×C4C5×#4111yescharacteristic
312C3×C8—22no—
313C3×C8—22no—
314C22×C5—42no—
315C22×C5—42no—
316C22×C5—42no—
317C22×C5—81no—
318C22×C5—81no—
319C22×C5—81no—
320C22×C5—81no—
321C22×C5C3×C4×D411yescharacteristic
322C22×C5C3×#12111yescharacteristic
323C22×C5C3×#12411yescharacteristic
324C22×C5C2×C3×D811yescharacteristic
325C22×C5C2×C3×SD1611yescharacteristic
326C22×C5C3×#13511yescharacteristic
327C22×C5C3×#13511yescharacteristic
328C4×C5—22no—
329C4×C5—22no—
330C4×C5—42no—
331C4×C5—81no—
332C4×C5—81no—
333C4×C5C3×#11711yescharacteristic
334C4×C5C3×C4×D411yescharacteristic
335C4×C5C3×#12311yescharacteristic
336C4×C5C3×#12611yescharacteristic
337C24—21no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4C2×C3×C4×C512yes—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4C3×C5×D411yescharacteristic
348C22×C4C3×C5×D411yescharacteristic
349C22×C4C23×C3×C511yescharacteristic
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8C2×C3×C4×C512yes—
355C2×C8C3×C5×D412yes—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—42no—
362C4⋊C4C2×C3×C4×C512yes—
363C22⋊C4—42no—
364C22⋊C4—42no—
365C42—21no—
366C42—21no—
367C3×C5#193411yescharacteristic, direct product factor, Hall
368C22×C3—42no—
369C22×C3—42no—
370C22×C3—42no—
371C22×C3—81no—
372C22×C3—81no—
373C22×C3—81no—
374C22×C3—81no—
375C22×C3C4×C5×D411yescharacteristic
376C22×C3C5×#12111yescharacteristic
377C22×C3C5×#12411yescharacteristic
378C22×C3C2×C5×D811yescharacteristic
379C22×C3C2×C5×SD1611yescharacteristic
380C22×C3C5×#13511yescharacteristic
381C22×C3C5×#13511yescharacteristic
382C3×C4—22no—
383C3×C4—22no—
384C3×C4—42no—
385C3×C4—81no—
386C3×C4—81no—
387C3×C4C5×#11711yescharacteristic
388C3×C4C4×C5×D411yescharacteristic
389C3×C4C5×#12311yescharacteristic
390C3×C4C5×#12611yescharacteristic
391C2×C5—82no—
392C2×C5C3×#38811yescharacteristic
393C2×C5C3×C4×D811yescharacteristic
394C2×C5C3×C4×SD1611yescharacteristic
395C2×C5C3×#46511yescharacteristic
396C2×C5C3×#46611yescharacteristic
397C2×C5C3×#48611yescharacteristic
398C2×C5C3×#48811yescharacteristic
399C23—22no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23C2×C3×C5×D411yescharacteristic
407D4—22no—
408D4—22no—
409D4—41no—
410D4—41no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—22no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4C3×C5×D812yes—
425C2×C4C3×C5×SD1612yes—
426C2×C4C22×C3×C4×C511yescharacteristic
427C2×C4C2×C3×C5×D411yescharacteristic
428C2×C4C3×C5×#4111yescharacteristic
429C2×C4C3×C5×#4111yescharacteristic
430C2×C4C3×C5×#4111yescharacteristic
431C2×C4C3×C5×#4111yescharacteristic
432C8—22no—
433C8—22no—
434C2×C3—82no—
435C2×C3C5×#38811yescharacteristic
436C2×C3C4×C5×D811yescharacteristic
437C2×C3C4×C5×SD1611yescharacteristic
438C2×C3C5×#46511yescharacteristic
439C2×C3C5×#46611yescharacteristic
440C2×C3C5×#48611yescharacteristic
441C2×C3C5×#48811yescharacteristic
442C5C3×#193411yescharacteristic, direct product factor, Sylow
443C22—42no—
444C22—42no—
445C22—42no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22C3×C4×C5×D411yescharacteristic
451C22C3×C5×#12111yescharacteristic
452C22C3×C5×#12411yescharacteristic
453C22C2×C3×C5×D811yescharacteristic
454C22C2×C3×C5×SD1611yescharacteristic
455C22C3×C5×#13511yescharacteristic
456C22C3×C5×#13511yescharacteristic
457C4—22no—
458C4—22no—
459C4—42no—
460C4—81no—
461C4—81no—
462C4C3×C5×#11711yescharacteristic
463C4C3×C4×C5×D411yescharacteristic
464C4C3×C5×#12311yescharacteristic
465C4C3×C5×#12611yescharacteristic
466C3C5×#193411yescharacteristic, direct product factor, Sylow
467C2—82no—
468C2C3×C5×#38811yescharacteristic
469C2C3×C4×C5×D811yescharacteristic
470C2C3×C4×C5×SD1611yescharacteristic
471C2C3×C5×#46511yescharacteristic
472C2C3×C5×#46611yescharacteristic
473C2C3×C5×#48611yescharacteristic
474C2C3×C5×#48811yescharacteristic
subgroupG/H
center, socleC23×C3×C5C2×D4
commutatorC2×C4C22×C3×C4×C5
Frattini, cosocleC22×C4C23×C3×C5
prime radicalC22×C3×C5×D4C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ C2×C3×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C3×C4×C5×C8C2semidirect
5. C3×C5×#389C2semidirect
6. C3×C5×#340C2semidirect
7. C3×C5×#340C2semidirect
8. C5×#1934C3direct (N × H)
20. C3×C5×#102C4semidirect
23. C3×#1934C5direct (N × H)
26. C2×C4×C5×C8C2×C3semidirect
28. C5×#389C2×C3semidirect
29. C5×#340C2×C3semidirect
30. C5×#340C2×C3semidirect
63. C2×C3×C4×C8C2×C5semidirect
65. C3×#389C2×C5semidirect
66. C3×#340C2×C5semidirect
67. C3×#340C2×C5semidirect
79. C5×#102C3×C4semidirect
82. #1934C3×C5direct (N × H)
129. C3×#102C4×C5semidirect
164. C2×C4×C8C2×C3×C5semidirect
166. #389C2×C3×C5semidirect
167. #340C2×C3×C5semidirect
168. #340C2×C3×C5semidirect
268. #102C3×C4×C5semidirect
367. C3×C5#1934direct (N × H)
442. C5C3×#1934direct (N × H)
466. C3C5×#1934direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1022
C2×C3×C4×C5×C82
C3×C5×#3902
C3×C5×#3892
C3×C5×#3402
C5×#19343
C3×#19345