Finite Group Databasebeta

← C3×C5×#1931 #14274965

Subgroups — C3×C5×#1931 #14274965

Order 1920.

464 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#428C211yesmaximal, characteristic, complemented
2C3×C5×#418C211yesmaximal, characteristic
3C2×C3×C5×#102C211yesmaximal, characteristic
4C2×C3×C5×#100C211yesmaximal, characteristic
5C3×C5×#405C211yesmaximal, characteristic, complemented
6C3×C5×#343C211yesmaximal, characteristic, complemented
7C3×C5×#341C211yesmaximal, characteristic, complemented
8C5×#1931C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×D4C2211yescharacteristic
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×#102—21no—
19C3×C5×#102—21no—
20C3×C5×#102—21no—
21C3×C5×#102—21no—
22C3×C5×#100C414yescomplemented
23C3×C5×#97—21no—
24C3×C4×C5×C8—21no—
25C3×#1931C511yesmaximal, characteristic, direct product factor, Hall
26C5×#428C2×C311yescharacteristic, complemented
27C5×#418C2×C311yescharacteristic
28C2×C5×#102C2×C311yescharacteristic
29C2×C5×#100C2×C311yescharacteristic
30C5×#405C2×C311yescharacteristic, complemented
31C5×#343C2×C311yescharacteristic, complemented
32C5×#341C2×C311yescharacteristic, complemented
33C24×C3×C5—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4C2×C412yes—
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, complemented
62C3×#418C2×C511yescharacteristic
63C2×C3×#102C2×C511yescharacteristic
64C2×C3×#100C2×C511yescharacteristic
65C3×#405C2×C511yescharacteristic, complemented
66C3×#343C2×C511yescharacteristic, complemented
67C3×#341C2×C511yescharacteristic, complemented
68C22×C5×D4C22×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×#102—21no—
78C5×#102—21no—
79C5×#102—21no—
80C5×#102—21no—
81C5×#100C3×C414yescomplemented
82C5×#97—21no—
83C4×C5×C8—21no—
84#1931C3×C511yescharacteristic, direct product factor, Sylow
85C23×C3×C5—22no—
86C23×C3×C5—41no—
87C23×C3×C5—41no—
88C23×C3×C5—81no—
89C23×C3×C5—81no—
90C23×C3×C5#4111yescharacteristic
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—41no—
98C2×C3×C4×C5—81no—
99C2×C3×C4×C5C22×C411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C3×C5×C8—22no—
106C3×C5×C8—22no—
107C3×C5×C8—21no—
108C3×C5×C8—21no—
109C3×C5×C8—41no—
110C22×C3×D4C22×C511yescharacteristic
111C2×C3×M16C22×C511yescharacteristic
112C2×C3×M16C22×C511yescharacteristic
113C2×C3×M16C22×C511yescharacteristic
114C22×C3×C8C22×C511yescharacteristic
115C3×#117C22×C511yescharacteristic
116C2×C3×C4⋊C4C22×C511yescharacteristic
117C3×#107—21no—
118C3×#106—21no—
119C3×#102—21no—
120C3×#102—21no—
121C3×#102—21no—
122C3×#102—21no—
123C3×#100C4×C514yescomplemented
124C3×#97—21no—
125C3×C4×C8—21no—
126C24×C5—21no—
127C2×C5×D4—21no—
128C2×C5×D4—21no—
129C2×C5×D4—21no—
130C2×C5×D4—21no—
131C2×C5×D4—21no—
132C2×C5×D4C2×C3×C412yes—
133C22×C4×C5—21no—
134C22×C4×C5C23×C311yescharacteristic
135C5×M16—21no—
136C5×M16—21no—
137C5×M16—21no—
138C5×M16—21no—
139C5×M16C2×C3×C412yes—
140C5×M16C2×C3×C412yes—
141C2×C5×C8—21no—
142C2×C5×C8—21no—
143C2×C5×C8—21no—
144C2×C5×C8—21no—
145C2×C5×C8—21no—
146C2×C5×C8C3×D411yescharacteristic
147C2×C5×C8C3×D411yescharacteristic
148C5×C4⋊C4—21no—
149C5×C4⋊C4—21no—
150C5×C4⋊C4C3×D411yescharacteristic
151C5×C4⋊C4C3×D411yescharacteristic
152C5×C22⋊C4—21no—
153C42×C5—21no—
154#428C2×C3×C511yescharacteristic, complemented
155#418C2×C3×C511yescharacteristic
156C2×#102C2×C3×C511yescharacteristic
157C2×#100C2×C3×C511yescharacteristic
158#405C2×C3×C511yescharacteristic, complemented
159#343C2×C3×C511yescharacteristic, complemented
160#341C2×C3×C511yescharacteristic, complemented
161C22×C3×C5—21no—
162C22×C3×C5—21no—
163C22×C3×C5—42no—
164C22×C3×C5—82no—
165C22×C3×C5—82no—
166C22×C3×C5—81no—
167C22×C3×C5—81no—
168C22×C3×C5#11711yescharacteristic
169C22×C3×C5#12111yescharacteristic
170C22×C3×C5#12611yescharacteristic
171C3×C4×C5—41no—
172C3×C4×C5—41no—
173C3×C4×C5—81no—
174C3×C4×C5C4×D411yescharacteristic
175C3×C4×C5C4×D411yescharacteristic
176C3×C4×C5#12311yescharacteristic
177C3×C4×C5#12411yescharacteristic
178C24×C3—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4C2×C4×C512yes—
185C22×C3×C4—21no—
186C22×C3×C4C23×C511yescharacteristic
187C3×M16—21no—
188C3×M16—21no—
189C3×M16—21no—
190C3×M16—21no—
191C3×M16C2×C4×C512yes—
192C3×M16C2×C4×C512yes—
193C2×C3×C8—21no—
194C2×C3×C8—21no—
195C2×C3×C8—21no—
196C2×C3×C8—21no—
197C2×C3×C8—21no—
198C2×C3×C8C5×D411yescharacteristic
199C2×C3×C8C5×D411yescharacteristic
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4C5×D411yescharacteristic
203C3×C4⋊C4C5×D411yescharacteristic
204C3×C22⋊C4—21no—
205C3×C42—21no—
206C23×C5—22no—
207C23×C5—41no—
208C23×C5—41no—
209C23×C5—81no—
210C23×C5—81no—
211C23×C5C3×#4111yescharacteristic
212C5×D4—22no—
213C5×D4—22no—
214C5×D4—41no—
215C5×D4—41no—
216C2×C4×C5—21no—
217C2×C4×C5—21no—
218C2×C4×C5—41no—
219C2×C4×C5—81no—
220C2×C4×C5C22×C3×C411yescharacteristic
221C2×C4×C5C2×C3×D411yescharacteristic
222C2×C4×C5C2×C3×D411yescharacteristic
223C2×C4×C5C3×#4111yescharacteristic
224C2×C4×C5C3×#4111yescharacteristic
225C2×C4×C5C3×#4111yescharacteristic
226C5×C8—22no—
227C5×C8—22no—
228C5×C8—21no—
229C5×C8—21no—
230C5×C8—41no—
231C22×D4C22×C3×C511yescharacteristic
232C2×M16C22×C3×C511yescharacteristic
233C2×M16C22×C3×C511yescharacteristic
234C2×M16C22×C3×C511yescharacteristic
235C22×C8C22×C3×C511yescharacteristic
236#117C22×C3×C511yescharacteristic
237C2×C4⋊C4C22×C3×C511yescharacteristic
238#107—21no—
239#106—21no—
240#102—21no—
241#102—21no—
242#102—21no—
243#102—21no—
244#100C3×C4×C514yescomplemented
245#97—21no—
246C4×C8—21no—
247C2×C3×C5—21no—
248C2×C3×C5—21no—
249C2×C3×C5—82no—
250C2×C3×C5#38811yescharacteristic
251C2×C3×C5#47111yescharacteristic
252C2×C3×C5#47211yescharacteristic
253C23×C3—22no—
254C23×C3—41no—
255C23×C3—41no—
256C23×C3—81no—
257C23×C3—81no—
258C23×C3C5×#4111yescharacteristic
259C3×D4—22no—
260C3×D4—22no—
261C3×D4—41no—
262C3×D4—41no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—41no—
266C2×C3×C4—81no—
267C2×C3×C4C22×C4×C511yescharacteristic
268C2×C3×C4C2×C5×D411yescharacteristic
269C2×C3×C4C2×C5×D411yescharacteristic
270C2×C3×C4C5×#4111yescharacteristic
271C2×C3×C4C5×#4111yescharacteristic
272C2×C3×C4C5×#4111yescharacteristic
273C3×C8—22no—
274C3×C8—22no—
275C3×C8—21no—
276C3×C8—21no—
277C3×C8—41no—
278C22×C5—21no—
279C22×C5—21no—
280C22×C5—42no—
281C22×C5—82no—
282C22×C5—82no—
283C22×C5—81no—
284C22×C5—81no—
285C22×C5C3×#11711yescharacteristic
286C22×C5C3×#12111yescharacteristic
287C22×C5C3×#12611yescharacteristic
288C4×C5—41no—
289C4×C5—41no—
290C4×C5—81no—
291C4×C5C3×C4×D411yescharacteristic
292C4×C5C3×C4×D411yescharacteristic
293C4×C5C3×#12311yescharacteristic
294C4×C5C3×#12411yescharacteristic
295C24—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4C2×C3×C4×C512yes—
302C22×C4—21no—
303C22×C4C23×C3×C511yescharacteristic
304M16—21no—
305M16—21no—
306M16—21no—
307M16—21no—
308M16C2×C3×C4×C512yes—
309M16C2×C3×C4×C512yes—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8C3×C5×D411yescharacteristic
316C2×C8C3×C5×D411yescharacteristic
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4C3×C5×D411yescharacteristic
320C4⋊C4C3×C5×D411yescharacteristic
321C22⋊C4—21no—
322C42—21no—
323C3×C5#193111yescharacteristic, direct product factor, Hall
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—42no—
327C22×C3—82no—
328C22×C3—82no—
329C22×C3—81no—
330C22×C3—81no—
331C22×C3C5×#11711yescharacteristic
332C22×C3C5×#12111yescharacteristic
333C22×C3C5×#12611yescharacteristic
334C3×C4—41no—
335C3×C4—41no—
336C3×C4—81no—
337C3×C4C4×C5×D411yescharacteristic
338C3×C4C4×C5×D411yescharacteristic
339C3×C4C5×#12311yescharacteristic
340C3×C4C5×#12411yescharacteristic
341C2×C5—21no—
342C2×C5—21no—
343C2×C5—82no—
344C2×C5C3×#38811yescharacteristic
345C2×C5C3×#47111yescharacteristic
346C2×C5C3×#47211yescharacteristic
347C23—22no—
348C23—41no—
349C23—41no—
350C23—81no—
351C23—81no—
352C23C3×C5×#4111yescharacteristic
353D4—22no—
354D4—22no—
355D4—41no—
356D4—41no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—81no—
361C2×C4C22×C3×C4×C511yescharacteristic
362C2×C4C2×C3×C5×D411yescharacteristic
363C2×C4C2×C3×C5×D411yescharacteristic
364C2×C4C3×C5×#4111yescharacteristic
365C2×C4C3×C5×#4111yescharacteristic
366C2×C4C3×C5×#4111yescharacteristic
367C8—22no—
368C8—22no—
369C8—21no—
370C8—21no—
371C8—41no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—82no—
375C2×C3C5×#38811yescharacteristic
376C2×C3C5×#47111yescharacteristic
377C2×C3C5×#47211yescharacteristic
378C5C3×#193111yescharacteristic, direct product factor, Sylow
379C22—21no—
380C22—21no—
381C22—42no—
382C22—82no—
383C22—82no—
384C22—81no—
385C22—81no—
386C22C3×C5×#11711yescharacteristic
387C22C3×C5×#12111yescharacteristic
388C22C3×C5×#12611yescharacteristic
389C4—41no—
390C4—41no—
391C4—81no—
392C4C3×C4×C5×D411yescharacteristic
393C4C3×C4×C5×D411yescharacteristic
394C4C3×C5×#12311yescharacteristic
395C4C3×C5×#12411yescharacteristic
396C3C5×#193111yescharacteristic, direct product factor, Sylow
397C2—21no—
398C2—21no—
399C2—82no—
400C2C3×C5×#38811yescharacteristic
401C2C3×C5×#47111yescharacteristic
402C2C3×C5×#47211yescharacteristic
subgroupG/H
center, socleC22×C3×C5#121
commutatorC2×C4C22×C3×C4×C5
Frattini, cosocleC22×C4C23×C3×C5
prime radicalC22×C3×C5×D4C22
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
1. C3×C5×#428C2semidirect
5. C3×C5×#405C2semidirect
6. C3×C5×#343C2semidirect
7. C3×C5×#341C2semidirect
8. C5×#1931C3direct (N × H)
22. C3×C5×#100C4semidirect
25. C3×#1931C5direct (N × H)
26. C5×#428C2×C3semidirect
30. C5×#405C2×C3semidirect
31. C5×#343C2×C3semidirect
32. C5×#341C2×C3semidirect
61. C3×#428C2×C5semidirect
65. C3×#405C2×C5semidirect
66. C3×#343C2×C5semidirect
67. C3×#341C2×C5semidirect
81. C5×#100C3×C4semidirect
84. #1931C3×C5direct (N × H)
123. C3×#100C4×C5semidirect
154. #428C2×C3×C5semidirect
158. #405C2×C3×C5semidirect
159. #343C2×C3×C5semidirect
160. #341C2×C3×C5semidirect
244. #100C3×C4×C5semidirect
323. C3×C5#1931direct (N × H)
378. C5C3×#1931direct (N × H)
396. C3C5×#1931direct (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×#4182
C2×C3×C5×#1022
C2×C3×C5×#1002
C3×C5×#4052
C3×C5×#3432
C3×C5×#3412
C5×#19313
C3×#19315