Finite Group Databasebeta

← #14291204

Subgroups — #14291204

Order 1920.

344 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C3×C5⋊#564C211yesmaximal, characteristic
2#11751165C211yesmaximal, characteristic
3#11746953C211yesmaximal, characteristic
4#11746936C211yesmaximal, characteristic
5C5×#4543C211yesmaximal, characteristic
6#11745849C211yesmaximal, characteristic
7#11745849C211yesmaximal, characteristic
8#10599169—31nomaximal, Hall
9C3×C5×#125C2211yescharacteristic
10#91758C2211yescharacteristic
11C3×#4036—21no—
12C3×#4036—21no—
13C3×#4035—21no—
14C3×#4035—21no—
15C3×#4035—21no—
16C3×#4035—21no—
17C3×#4016C2211yescharacteristic
18C3×#4016C2211yescharacteristic
19#91092—21no—
20#91091—21no—
21#91087C2211yescharacteristic
22C5×#803C2211yescharacteristic
23C5×#803C2211yescharacteristic
24#90990—21no—
25#90987—21no—
26#90974—21no—
27#90974—21no—
28#71961—51nomaximal, Hall
29C5⋊#564D311yescharacteristic
30#65354—31no—
31#64992—31no—
32#64991—31no—
33C5×#330—31no—
34#64685—31no—
35#64685—31no—
36C2×Dic30—21no—
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4D411yescharacteristic
40C3×C5×C4⋊C4D411yescharacteristic
41C3×C42×C5C2311yescharacteristic
42C4⋊Dic15—21no—
43C4⋊Dic15—21no—
44C2×C3⋊#168—21no—
45C2×C5×C3⋊C8—21no—
46C2×C5×C3⋊C8—21no—
47C3×C4⋊Dic5—21no—
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5D411yescharacteristic
50C3×C4⋊Dic5D411yescharacteristic
51C3×C4⋊Dic5D411yescharacteristic
52C3×C4⋊Dic5D411yescharacteristic
53C3×#683—21no—
54C3×#683—21no—
55C3×#683—21no—
56C3×#683—21no—
57C3×#683—21no—
58C3×#683—21no—
59C3×#683—21no—
60C3×#683—21no—
61C3×C4×Dic5—21no—
62C3×C4×Dic5—21no—
63C3×#564—51no—
64#5069—51no—
65#5064—51no—
66#5064—51no—
67#4543—51no—
68#4543—51no—
69#4543D511yescharacteristic
70C5×#125C2×D311yescharacteristic
71#4036—21no—
72#4036—21no—
73#4035—21no—
74#4035—21no—
75#4035—21no—
76#4035—21no—
77#4016C2×D311yescharacteristic
78#4016C2×D311yescharacteristic
79#4015—31no—
80C5×#97—31no—
81C5×#97—31no—
82#3950—61no—
83#3949—61no—
84#3948—61no—
85#3948—61no—
86#3940—61no—
87#3939—61no—
88#3935—31no—
89#1663—151noSylow
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×Dic15—41no—
96Dic30—42no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—21no—
99C2×C3×Dic5—21no—
100C2×C3×Dic5—21no—
101C3⋊#168—22no—
102C5×C3⋊C8—22no—
103C5×C3⋊C8—41no—
104C3×#125—51no—
105C3×#125—51no—
106C3×#125—101no—
107C3×#125—101no—
108C3×#125—101no—
109C3×#125—101no—
110C3×#125—101no—
111C3×#125—101no—
112C3×#125C2×D511yescharacteristic
113#869—51no—
114#810—101no—
115#810—101no—
116#808—101no—
117#808—101no—
118#807—101no—
119#807—101no—
120#803—51no—
121#803C2×D511yescharacteristic
122#803C2×D511yescharacteristic
123C2×Dic10—61no—
124C2×C5×C8—61no—
125C2×C5×C8—61no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4#6711yescharacteristic
129C5×C4⋊C4#6711yescharacteristic
130C42×C5C22×D311yescharacteristic
131C4⋊Dic5—21no—
132C4⋊Dic5—21no—
133C4⋊Dic5—61no—
134C4⋊Dic5—61no—
135C4⋊Dic5#6711yescharacteristic
136C4⋊Dic5#6711yescharacteristic
137C4⋊Dic5#6711yescharacteristic
138C4⋊Dic5#6711yescharacteristic
139#683—21no—
140#683—21no—
141#683—21no—
142#683—21no—
143#683—21no—
144#683—21no—
145#683—21no—
146#683—21no—
147C4×Dic5—21no—
148C4×Dic5—21no—
149C2×#168—61no—
150#564—51no—
151#501—151no—
152#501—151no—
153#491—151no—
154#330—31no—
155#330—151no—
156#330—151no—
157C22×C3×C5#12011yescharacteristic
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—41no—
162C3×C4×C5—41no—
163Dic15—81no—
164C3×Dic5—41no—
165C3×Dic5—41no—
166C3×Dic5—41no—
167C3×Dic5—41no—
168C2×Dic6—101no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—51no—
172C3×C4⋊C4—51no—
173C3×C4⋊C4—51no—
174C3×C4⋊C4—51no—
175C3×C4⋊C4—101no—
176C3×C4⋊C4—101no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4—101no—
179C3×C4⋊C4—101no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4—101no—
182C3×C4⋊C4—101no—
183C3×C4⋊C4—101no—
184C3×C4⋊C4—101no—
185C3×C4⋊C4D2011yescharacteristic
186C3×C4⋊C4D2011yescharacteristic
187C3×C42—101no—
188C3×C42—101no—
189C3×C42C22×D511yescharacteristic
190C4⋊Dic3—101no—
191C4⋊Dic3—101no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—101no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5C2×#6711yescharacteristic
198C2×C4×C5C2×#6711yescharacteristic
199C2×C4×C5C2×#6711yescharacteristic
200C2×Dic5—21no—
201C2×Dic5—21no—
202C2×Dic5—21no—
203C2×Dic5—21no—
204C2×Dic5—121no—
205Dic10—122no—
206C5×C8—62no—
207C5×C8—121no—
208#168—62no—
209C4⋊Q8—151no—
210#125—51no—
211#125—51no—
212#125—101no—
213#125—101no—
214#125—101no—
215#125—101no—
216#125—101no—
217#125—101no—
218#125D3×D511yescharacteristic
219#107—301no—
220#107—301no—
221#106—301no—
222#106—301no—
223#103—301no—
224#103—301no—
225#97—31no—
226#97—31no—
227#97—151no—
228C2×C3×C5#45411yescharacteristic
229C2×C3×C5#45611yescharacteristic
230C2×C3×C5#45611yescharacteristic
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—101no—
234C2×C3×C4—101no—
235C2×C3×C4—101no—
236C2×C3×C4—101no—
237C2×C3×C4C2×D2011yescharacteristic
238C2×C3×C4D4×D511yescharacteristic
239C2×C3×C4D4×D511yescharacteristic
240C2×Dic3—201no—
241Dic6—202no—
242C3⋊C8—22no—
243C3⋊C8—41no—
244C3⋊C8—102no—
245C22×C5#95311yescharacteristic
246C4×C5—21no—
247C4×C5—21no—
248C4×C5—21no—
249C4×C5—41no—
250C4×C5—41no—
251Dic5—41no—
252Dic5—41no—
253Dic5—41no—
254Dic5—41no—
255Dic5—241no—
256C2×Q8—301no—
257C2×C8—61no—
258C2×C8—61no—
259C2×C8—301no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—51no—
263C4⋊C4—51no—
264C4⋊C4—51no—
265C4⋊C4—51no—
266C4⋊C4—101no—
267C4⋊C4—101no—
268C4⋊C4—101no—
269C4⋊C4—101no—
270C4⋊C4—101no—
271C4⋊C4—101no—
272C4⋊C4—101no—
273C4⋊C4—101no—
274C4⋊C4—101no—
275C4⋊C4—101no—
276C4⋊C4—301no—
277C4⋊C4—301no—
278C4⋊C4#120211yescharacteristic
279C4⋊C4#120211yescharacteristic
280C42—101no—
281C42—101no—
282C42C2×D3×D511yescharacteristic
283C3×C5#166311yescharacteristic, complemented, Hall
284C22×C3#402811yescharacteristic
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—41no—
289C3×C4—41no—
290C3×C4—201no—
291C3×C4—201no—
292C3×C4—201no—
293C3×C4—201no—
294Dic3—401no—
295C2×C5#524511yescharacteristic
296C2×C5#524611yescharacteristic
297C2×C5#524611yescharacteristic
298Q8—602no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—101no—
302C2×C4—101no—
303C2×C4—101no—
304C2×C4—101no—
305C2×C4—601no—
306C2×C4C2×#120211yescharacteristic
307C2×C4D5×#6711yescharacteristic
308C2×C4D5×#6711yescharacteristic
309C8—62no—
310C8—121no—
311C8—302no—
312C2×C3#6504111yescharacteristic
313C2×C3#6511511yescharacteristic
314C2×C3#6511611yescharacteristic
315C5#7196111yescharacteristic, complemented, Sylow
316C22#9156411yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—201no—
323C4—201no—
324C4—201no—
325C4—201no—
326C4—1201no—
327C3#1059916911yescharacteristic, complemented, Sylow
328C2#1174939111yescharacteristic
329C2#1174945711yescharacteristic
330C2#1174946411yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socle, prime radicalC22×C3×C5#120
hypercenter#125D3×D5
hypocenterC3×C5#1663
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
283. C3×C5#1663semidirect
315. C5#71961semidirect
327. C3#10599169semidirect

Maximal subgroups

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

subgroupindex
C3×C5⋊#5642
#117511652
#117469532
#117469362
C5×#45432
#117458492
#105991693
#719615