Finite Group Databasebeta

← C5×#70534 #14303592

Subgroups — C5×#70534 #14303592

Order 1920.

372 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#424C211yesmaximal, characteristic
2C5×#5101C211yesmaximal, characteristic
3C5×#4998C211yesmaximal, characteristic
4C5×#4558C211yesmaximal, characteristic
5C5×#4555C211yesmaximal, characteristic
6C5×#4550C211yesmaximal, characteristic
7C5×#4532C211yesmaximal, characteristic
8C5×#1922—31nomaximal, Hall
9C2×C3×C5×M16C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C5×#926C2211yescharacteristic
13C2×C4×C5×Dic3C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C22×C5×C3⋊C8C2211yescharacteristic
16C3×C5×C4⋊C8—21no—
17C3×C5×C4⋊C8—21no—
18C5×#815—21no—
19C5×C8×Dic3—21no—
20C5×#808C411yescharacteristic, complemented
21C5×#808C411yescharacteristic, complemented
22C5×#807C411yescharacteristic, complemented
23C5×#807C411yescharacteristic, complemented
24#70534C511yesmaximal, characteristic, direct product factor, Hall
25C5×#427—31no—
26C5×#424D311yescharacteristic
27C5×#405—31no—
28C5×#341—31no—
29C5×#339—31no—
30C5×#339—31no—
31C5×#336—31no—
32C22×C3×C4×C5C2311yescharacteristic
33C22×C5×Dic3—21no—
34C3×C5×M16—21no—
35C3×C5×M16—21no—
36C2×C3×C5×C8—21no—
37C2×C3×C5×C8—21no—
38C2×C3×C5×C8—21no—
39C2×C3×C5×C8D411yescharacteristic
40C2×C3×C5×C8D411yescharacteristic
41C3×C5×C4⋊C4C2×C411yescharacteristic
42C3×C5×C4⋊C4C2×C411yescharacteristic
43C3×C5×C22⋊C4—21no—
44C3×C42×C5—21no—
45C5×#217—21no—
46C5×C4⋊Dic3C2×C411yescharacteristic
47C5×C4⋊Dic3C2×C411yescharacteristic
48C4×C5×Dic3—21no—
49C4×C5×Dic3—21no—
50C4×C5×Dic3—21no—
51C5×#208—21no—
52C5×#208Q812yes—
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8—21no—
55C2×C5×C3⋊C8—21no—
56C2×C5×C3⋊C8C2×C411yescharacteristic
57C2×C5×C3⋊C8C2×C411yescharacteristic
58C3×#424C2×C511yescharacteristic
59#5101C2×C511yescharacteristic
60#4998C2×C511yescharacteristic
61#4558C2×C511yescharacteristic
62#4555C2×C511yescharacteristic
63#4550C2×C511yescharacteristic
64#4532C2×C511yescharacteristic
65C2×C5×M16—31no—
66C2×C5×M16C2×D311yescharacteristic
67C22×C5×C8—31no—
68C22×C5×C8C2×D311yescharacteristic
69C5×#117—31no—
70C5×#117C2×D311yescharacteristic
71C2×C42×C5—31no—
72C5×#107—31no—
73C5×#107—31no—
74C5×#106—31no—
75C5×#106—31no—
76C5×C4⋊C8—21no—
77C5×C4⋊C8—21no—
78C5×#97—61no—
79C4×C5×C8—61no—
80#1922—31noSylow
81C23×C3×C5#4111yescharacteristic
82C2×C3×C4×C5—21no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5C22×C411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×Q811yescharacteristic
87C2×C3×C4×C5#4111yescharacteristic
88C2×C3×C4×C5#4111yescharacteristic
89C2×C3×C4×C5#4111yescharacteristic
90C2×C5×Dic3—22no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—21no—
93C2×C5×Dic3—41no—
94C2×C5×Dic3—41no—
95C3×C5×C8—21no—
96C3×C5×C8—21no—
97C3×C5×C8—41no—
98C5×C3⋊C8—21no—
99C5×C3⋊C8—21no—
100C5×C3⋊C8—22no—
101C2×C3×M16C22×C511yescharacteristic
102C22×C3×C8C22×C511yescharacteristic
103C3×#117C22×C511yescharacteristic
104#926C22×C511yescharacteristic
105C2×C4×Dic3C22×C511yescharacteristic
106C2×#208C22×C511yescharacteristic
107C22×C3⋊C8C22×C511yescharacteristic
108C3×C4⋊C8—21no—
109C3×C4⋊C8—21no—
110#815—21no—
111C8×Dic3—21no—
112#808C4×C511yescharacteristic, complemented
113#808C4×C511yescharacteristic, complemented
114#807C4×C511yescharacteristic, complemented
115#807C4×C511yescharacteristic, complemented
116C22×C4×C5—61no—
117C22×C4×C5C22×D311yescharacteristic
118C5×M16—21no—
119C5×M16—21no—
120C5×M16—32no—
121C5×M16—61no—
122C2×C5×C8—21no—
123C2×C5×C8—21no—
124C2×C5×C8—21no—
125C2×C5×C8—31no—
126C2×C5×C8—31no—
127C2×C5×C8—61no—
128C2×C5×C8—61no—
129C2×C5×C8—61no—
130C2×C5×C8#6711yescharacteristic
131C2×C5×C8#6711yescharacteristic
132C5×C4⋊C4—31no—
133C5×C4⋊C4—31no—
134C5×C4⋊C4C4×D311yescharacteristic
135C5×C4⋊C4C4×D311yescharacteristic
136C5×C22⋊C4—21no—
137C5×C22⋊C4—61no—
138C42×C5—21no—
139C42×C5—61no—
140C42×C5—61no—
141C42×C5—61no—
142#427—31no—
143#424C5×D311yescharacteristic
144#405—31no—
145#341—31no—
146#339—31no—
147#339—31no—
148#336—31no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5C4×D411yescharacteristic
152C22×C3×C5#12511yescharacteristic
153C22×C3×C5#12611yescharacteristic
154C3×C4×C5—41no—
155C3×C4×C5—41no—
156C3×C4×C5#11711yescharacteristic
157C3×C4×C5C4×Q811yescharacteristic
158C3×C4×C5C22⋊Q811yescharacteristic
159C3×C4×C5#12311yescharacteristic
160C5×Dic3—42no—
161C5×Dic3—41no—
162C5×Dic3—41no—
163C22×C3×C4C23×C511yescharacteristic
164C22×Dic3—21no—
165C3×M16—21no—
166C3×M16—21no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8C5×D411yescharacteristic
171C2×C3×C8C5×D411yescharacteristic
172C3×C4⋊C4C2×C4×C511yescharacteristic
173C3×C4⋊C4C2×C4×C511yescharacteristic
174C3×C22⋊C4—21no—
175C3×C42—21no—
176#217—21no—
177C4⋊Dic3C2×C4×C511yescharacteristic
178C4⋊Dic3C2×C4×C511yescharacteristic
179C4×Dic3—21no—
180C4×Dic3—21no—
181C4×Dic3—21no—
182#208—21no—
183#208C5×Q812yes—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8C2×C4×C511yescharacteristic
188C2×C3⋊C8C2×C4×C511yescharacteristic
189C23×C5#23511yescharacteristic
190C2×C4×C5—21no—
191C2×C4×C5—21no—
192C2×C4×C5—62no—
193C2×C4×C5—61no—
194C2×C4×C5—61no—
195C2×C4×C5—121no—
196C2×C4×C5—121no—
197C2×C4×C5C2×C4×D311yescharacteristic
198C2×C4×C5#23711yescharacteristic
199C2×C4×C5#23711yescharacteristic
200C2×C4×C5D3×Q811yescharacteristic
201C2×C4×C5#23911yescharacteristic
202C2×C4×C5C2×#6711yescharacteristic
203C5×C8—21no—
204C5×C8—21no—
205C5×C8—41no—
206C5×C8—61no—
207C5×C8—61no—
208C5×C8—62no—
209C2×M16—31no—
210C2×M16C2×C5×D311yescharacteristic
211C22×C8—31no—
212C22×C8C2×C5×D311yescharacteristic
213#117—31no—
214#117C2×C5×D311yescharacteristic
215C2×C42—31no—
216#107—31no—
217#107—31no—
218#106—31no—
219#106—31no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222#97—61no—
223C4×C8—61no—
224C2×C3×C5—21no—
225C2×C3×C5—21no—
226C2×C3×C5#38711yescharacteristic
227C2×C3×C5#44311yescharacteristic
228C2×C3×C5#44411yescharacteristic
229C23×C3C5×#4111yescharacteristic
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4C22×C4×C511yescharacteristic
233C2×C3×C4C2×C5×D411yescharacteristic
234C2×C3×C4C2×C5×Q811yescharacteristic
235C2×C3×C4C5×#4111yescharacteristic
236C2×C3×C4C5×#4111yescharacteristic
237C2×C3×C4C5×#4111yescharacteristic
238C2×Dic3—22no—
239C2×Dic3—21no—
240C2×Dic3—21no—
241C2×Dic3—41no—
242C2×Dic3—41no—
243C3×C8—21no—
244C3×C8—21no—
245C3×C8—41no—
246C3⋊C8—21no—
247C3⋊C8—21no—
248C3⋊C8—22no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5#88911yescharacteristic
252C22×C5#89811yescharacteristic
253C22×C5C4×#6711yescharacteristic
254C4×C5—41no—
255C4×C5—41no—
256C4×C5—122no—
257C4×C5—121no—
258C4×C5—121no—
259C4×C5#88711yescharacteristic
260C4×C5#89211yescharacteristic
261C4×C5#93511yescharacteristic
262C4×C5#94611yescharacteristic
263C22×C4—61no—
264C22×C4C22×C5×D311yescharacteristic
265M16—21no—
266M16—21no—
267M16—32no—
268M16—61no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—31no—
273C2×C8—31no—
274C2×C8—61no—
275C2×C8—61no—
276C2×C8—61no—
277C2×C8C5×#6711yescharacteristic
278C2×C8C5×#6711yescharacteristic
279C4⋊C4—31no—
280C4⋊C4—31no—
281C4⋊C4C4×C5×D311yescharacteristic
282C4⋊C4C4×C5×D311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—61no—
285C42—21no—
286C42—61no—
287C42—61no—
288C42—61no—
289C3×C5#192211yescharacteristic, complemented, Hall
290C22×C3—21no—
291C22×C3—21no—
292C22×C3C4×C5×D411yescharacteristic
293C22×C3C5×#12511yescharacteristic
294C22×C3C5×#12611yescharacteristic
295C3×C4—41no—
296C3×C4—41no—
297C3×C4C5×#11711yescharacteristic
298C3×C4C4×C5×Q811yescharacteristic
299C3×C4C5×C22⋊Q811yescharacteristic
300C3×C4C5×#12311yescharacteristic
301Dic3—42no—
302Dic3—41no—
303Dic3—41no—
304C2×C5—21no—
305C2×C5—21no—
306C2×C5#497811yescharacteristic
307C2×C5#514411yescharacteristic
308C2×C5#514511yescharacteristic
309C23C5×#23511yescharacteristic
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—62no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—121no—
316C2×C4—121no—
317C2×C4C2×C4×C5×D311yescharacteristic
318C2×C4C5×#23711yescharacteristic
319C2×C4C5×#23711yescharacteristic
320C2×C4C5×D3×Q811yescharacteristic
321C2×C4C5×#23911yescharacteristic
322C2×C4C2×C5×#6711yescharacteristic
323C8—21no—
324C8—21no—
325C8—41no—
326C8—61no—
327C8—61no—
328C8—62no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3C5×#38711yescharacteristic
332C2×C3C5×#44311yescharacteristic
333C2×C3C5×#44411yescharacteristic
334C5#7053411yescharacteristic, direct product factor, Sylow
335C22—21no—
336C22—21no—
337C22C5×#88911yescharacteristic
338C22C5×#89811yescharacteristic
339C22C4×C5×#6711yescharacteristic
340C4—41no—
341C4—41no—
342C4—122no—
343C4—121no—
344C4—121no—
345C4C5×#88711yescharacteristic
346C4C5×#89211yescharacteristic
347C4C5×#93511yescharacteristic
348C4C5×#94611yescharacteristic
349C3C5×#192211yescharacteristic, complemented, Sylow
350C2—21no—
351C2—21no—
352C2C5×#497811yescharacteristic
353C2C5×#514411yescharacteristic
354C2C5×#514511yescharacteristic
subgroupG/H
centerC2×C4×C5C2×#67
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#424C2
socleC22×C3×C5C4×D4
prime radicalC23×C3×C5#41
cosocleC22×C3×C4C23×C5
hypercenterC5×#424D3
hypocenterC3C5×#1922
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C5×C8 ◁ C5×#424

Complements

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

NH ≅ G/Ntype
20. C5×#808C4semidirect
21. C5×#808C4semidirect
22. C5×#807C4semidirect
23. C5×#807C4semidirect
24. #70534C5direct (N × H)
112. #808C4×C5semidirect
113. #808C4×C5semidirect
114. #807C4×C5semidirect
115. #807C4×C5semidirect
289. C3×C5#1922semidirect
334. C5#70534direct (N × H)
349. C3C5×#1922semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4242
C5×#51012
C5×#49982
C5×#45582
C5×#45552
C5×#45502
C5×#45322
C5×#19223
#705345