Finite Group Databasebeta

← C5×#85475 #14511213

Subgroups — C5×#85475 #14511213

Order 1920.

490 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5927C212yesmaximal, complemented
2C5×#578⋊C3C211yesmaximal, characteristic, complemented
3C5×#5430C212yesmaximal, complemented
4C5×#5404C211yesmaximal, characteristic, complemented
5C5×#5403C211yesmaximal, characteristic, complemented
6C5×#3293—31nomaximal, Hall
7C5×2−1+4⋊C3C2212yes—
8C5×#985C2211yescharacteristic
9C5×#984C2212yes—
10C5×#983—22no—
11C2×C5×#226—22no—
12C5×#912—41nomaximal
13C5×#131⋊C3C2211yescharacteristic
14C5×GU(2,𝔽3)C2211yescharacteristic
15#85475C511yesmaximal, characteristic, direct product factor, Hall
16C5×#578—31no—
17C5×#578—32no—
18C5×#578D311yescharacteristic, complemented
19C5×#494—31no—
20C5×#473—31no—
21C5×#473—32no—
22C5×#473—31no—
23C5×#456—32no—
24C5×#456—32no—
25C5×#443—31no—
26C5×#443—31no—
27C5×#237—42no—
28C5×#41⋊C3C2311yescharacteristic
29C2×C5×SL(2,𝔽3)—22no—
30C5×GL(2,𝔽3)D411yescharacteristic
31C5×#226—22no—
32C5×#226D411yescharacteristic
33C3×C5×D8—41no—
34C5×#214—42no—
35C5×Dic12—41no—
36C5×D3×C8—41no—
37#5927C2×C512yescomplemented
38#578⋊C3C2×C511yescharacteristic, complemented
39#5430C2×C512yescomplemented
40#5404C2×C511yescharacteristic, complemented
41#5403C2×C511yescharacteristic, complemented
42C5×2−1+4—32no—
43C5×2−1+4C2×D312yes—
44C5×#137—32no—
45C5×#137—32no—
46C5×#137—32no—
47C5×#137—32no—
48C5×#137—62no—
49C5×#137—62no—
50C5×#137—62no—
51C5×#135—31no—
52C5×#135—31no—
53C5×#135—62no—
54C5×#135—61no—
55C2×C5×Q16—31no—
56C2×C5×Q16—32no—
57C2×C5×Q16—31no—
58C2×C5×Q16—62no—
59C2×C5×Q16—61no—
60C5×#131—32no—
61C5×#131—31no—
62C5×#131C2×D311yescharacteristic
63C5×C4⋊Q8—32no—
64C5×#108—31no—
65C5×#108—31no—
66C5×#104—31no—
67C5×#104—32no—
68C5×#104—31no—
69C5×#101—32no—
70C5×#101—32no—
71C4×C5×C8—31no—
72#3293—31noSylow
73C3×C5×D4—42no—
74C5×#67—82no—
75C2×C5×Dic3—82no—
76C4×C5×D3—41no—
77C5×Dic6—42no—
78C5×SL(2,𝔽3)C2×D411yescharacteristic
79C3×C5×C8—41no—
80C5×C3⋊C8—41no—
812−1+4⋊C3C22×C512yes—
82#985C22×C511yescharacteristic
83#984C22×C512yes—
84#983—22no—
85C2×#226—22no—
86#912—41no—
87#131⋊C3C22×C511yescharacteristic
88GU(2,𝔽3)C22×C511yescharacteristic
89C5×#41—31no—
90C5×#41—32no—
91C5×#41—62no—
92C5×#41—62no—
93C5×#41—62no—
94C5×#41—122no—
95C5×#41C22×D311yescharacteristic
96C2×C5×Q8—22no—
97C2×C5×Q8—32no—
98C2×C5×Q8—32no—
99C2×C5×Q8—62no—
100C2×C5×Q8—62no—
101C5×Q16—31no—
102C5×Q16—31no—
103C5×Q16—61no—
104C5×Q16—62no—
105C5×Q16—62no—
106C5×Q16—61no—
107C5×Q16—62no—
108C5×Q16—62no—
109C5×Q16—62no—
110C5×Q16—61no—
111C5×SD16—31no—
112C5×SD16—31no—
113C5×SD16—32no—
114C5×SD16—62no—
115C5×SD16—62no—
116C5×SD16—62no—
117C5×D8—31no—
118C5×D8S411yescharacteristic
119C5×M16—31no—
120C5×M16—32no—
121C5×M16—31no—
122C5×M16—62no—
123C5×M16—61no—
124C2×C5×C8—31no—
125C2×C5×C8—31no—
126C2×C5×C8—62no—
127C2×C5×C8—61no—
128C5×C4⋊C4—122no—
129C42×C5—31no—
130#578—31no—
131#578—32no—
132#578C5×D311yescharacteristic, complemented
133#494—31no—
134#473—31no—
135#473—32no—
136#473—31no—
137#456—32no—
138#456—32no—
139#443—31no—
140#443—31no—
141C22×C3×C5—82no—
142C2×C5×D3—41no—
143C3×C4×C5—41no—
144C5×Dic3—41no—
145C5×Dic3—82no—
146#237—42no—
147#41⋊C3C23×C511yescharacteristic
148C2×SL(2,𝔽3)—22no—
149GL(2,𝔽3)C5×D411yescharacteristic
150#226—22no—
151#226C5×D411yescharacteristic
152C3×D8—41no—
153#214—42no—
154Dic12—41no—
155D3×C8—41no—
156C5×Q8—31no—
157C5×Q8—32no—
158C5×Q8—62no—
159C5×Q8—62no—
160C5×Q8—62no—
161C5×Q8—122no—
162C5×Q8D3×D411yescharacteristic
163C5×D4—31no—
164C5×D4—31no—
165C5×D4—62no—
166C5×D4—61no—
167C5×D4—122no—
168C5×D4C2×S412yes—
169C2×C4×C5—31no—
170C2×C4×C5—62no—
171C2×C4×C5—61no—
172C2×C4×C5—61no—
173C2×C4×C5—62no—
174C2×C4×C5—62no—
175C2×C4×C5—122no—
176C2×C4×C5—122no—
177C5×C8—31no—
178C5×C8—31no—
179C5×C8—31no—
180C5×C8—62no—
181C5×C8—61no—
182C5×C8C2×S411yescharacteristic
1832−1+4—32no—
1842−1+4C2×C5×D312yes—
185#137—32no—
186#137—32no—
187#137—32no—
188#137—32no—
189#137—62no—
190#137—62no—
191#137—62no—
192#135—31no—
193#135—31no—
194#135—62no—
195#135—61no—
196C2×Q16—31no—
197C2×Q16—32no—
198C2×Q16—31no—
199C2×Q16—62no—
200C2×Q16—61no—
201#131—32no—
202#131—31no—
203#131C2×C5×D311yescharacteristic
204C4⋊Q8—32no—
205#108—31no—
206#108—31no—
207#104—31no—
208#104—32no—
209#104—31no—
210#101—32no—
211#101—32no—
212C4×C8—31no—
213C2×C3×C5—41no—
214C2×C3×C5—162no—
215C5×D3—81no—
216C3×D4—42no—
217#67—82no—
218C2×Dic3—82no—
219C4×D3—41no—
220Dic6—42no—
221SL(2,𝔽3)C2×C5×D411yescharacteristic
222C3×C8—41no—
223C3⋊C8—41no—
224C22×C5—22no—
225C22×C5—31no—
226C22×C5—61no—
227C4×C5—31no—
228C4×C5—62no—
229C4×C5—61no—
230C4×C5—62no—
231C4×C5—122no—
232C4×C5C22×S411yescharacteristic
233#41—31no—
234#41—32no—
235#41—62no—
236#41—62no—
237#41—62no—
238#41—122no—
239#41C22×C5×D311yescharacteristic
240C2×Q8—22no—
241C2×Q8—32no—
242C2×Q8—32no—
243C2×Q8—62no—
244C2×Q8—62no—
245Q16—31no—
246Q16—31no—
247Q16—61no—
248Q16—62no—
249Q16—62no—
250Q16—61no—
251Q16—62no—
252Q16—62no—
253Q16—62no—
254Q16—61no—
255SD16—31no—
256SD16—31no—
257SD16—32no—
258SD16—62no—
259SD16—62no—
260SD16—62no—
261D8—31no—
262D8C5×S411yescharacteristic
263M16—31no—
264M16—32no—
265M16—31no—
266M16—62no—
267M16—61no—
268C2×C8—31no—
269C2×C8—31no—
270C2×C8—62no—
271C2×C8—61no—
272C4⋊C4—122no—
273C42—31no—
274C3×C5—41noHall
275C22×C3—82no—
276C2×D3—41no—
277C3×C4—41no—
278Dic3—41no—
279Dic3—82no—
280C2×C5—42no—
281C2×C5—61no—
282C2×C5—121no—
283C2×C5D4×S411yescharacteristic
284Q8—31no—
285Q8—32no—
286Q8—62no—
287Q8—62no—
288Q8—62no—
289Q8—122no—
290Q8C5×D3×D411yescharacteristic
291D4—31no—
292D4—31no—
293D4—62no—
294D4—61no—
295D4—122no—
296D4C2×C5×S412yes—
297C2×C4—31no—
298C2×C4—62no—
299C2×C4—61no—
300C2×C4—61no—
301C2×C4—62no—
302C2×C4—62no—
303C2×C4—122no—
304C2×C4—122no—
305C8—31no—
306C8—31no—
307C8—31no—
308C8—62no—
309C8—61no—
310C8C2×C5×S411yescharacteristic
311C2×C3—41no—
312C2×C3—162no—
313D3—81no—
314C5#8547511yescharacteristic, direct product factor, Sylow
315C22—22no—
316C22—31no—
317C22—61no—
318C4—31no—
319C4—62no—
320C4—62no—
321C4—61no—
322C4—122no—
323C4C22×C5×S411yescharacteristic
324C3—41noSylow
325C2—42no—
326C2—61no—
327C2—121no—
328C2C5×D4×S411yescharacteristic
subgroupG/H
center, socleC2×C5D4×S4
commutator, cosocle#41⋊C3C23×C5
FrattiniC4C22×C5×S4
FittingC5×#578D3
hypercenterC5×D8S4
hypocenterSL(2,𝔽3)C2×C5×D4
LCSG ▷ #41⋊C3 ▷ SL(2,𝔽3)
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×D8

Complements

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

NH ≅ G/Ntype
1. C5×#5927C2semidirect
2. C5×#578⋊C3C2semidirect
3. C5×#5430C2semidirect
4. C5×#5404C2semidirect
5. C5×#5403C2semidirect
15. #85475C5direct (N × H)
18. C5×#578D3semidirect
37. #5927C2×C5semidirect
38. #578⋊C3C2×C5semidirect
39. #5430C2×C5semidirect
40. #5404C2×C5semidirect
41. #5403C2×C5semidirect
132. #578C5×D3semidirect
314. C5#85475direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#59272
C5×#578⋊C32
C5×#54302
C5×#54042
C5×#54032
C5×#32933
C5×#9124
#854755