Finite Group Databasebeta

← #14291060

Subgroups — #14291060

Order 1920.

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

normal subgroups only

This group has 392 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
1C5×#5699C211yesmaximal, characteristic
2C3×#65354C211yesmaximal, characteristic, complemented
3#11747082C211yesmaximal, characteristic
4#11746969C211yesmaximal, characteristic, complemented
5#11746364C211yesmaximal, characteristic, complemented
6#11745850C211yesmaximal, characteristic, complemented
7#11745847C211yesmaximal, characteristic
8#10602749—31nomaximal, Hall
9C3×C5×#125C2211yescharacteristic
10C5×#898—21no—
11C5×#898—21no—
12C5×#897—21no—
13C5×#896—21no—
14C5×#894—21no—
15C5×#888—21no—
16C5×#875C2211yescharacteristic
17C5×#870C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19C2×#6661—21no—
20C2×#6656—21no—
21#91087C2211yescharacteristic
22#91087C2211yescharacteristic
23C3×#3940—21no—
24C3×#3939—21no—
25C3×#3935C2211yescharacteristic
26#90989—21no—
27#90986—21no—
28#71391—51nomaximal, Hall
29C5×#563—31no—
30#65354—31no—
31#65354D311yescharacteristic, complemented
32#65349—31no—
33#64763—31no—
34#64763—31no—
35#64760—31no—
36C2×C5×D12D411yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C5×Dic6—21no—
39C2×C5×Dic6D411yescharacteristic
40C2×C3×Dic10—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C42×C5C2311yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C5×(C2×D3)⋊C4—21no—
49C5×(C2×D3)⋊C4—21no—
50C5×(C2×D3)⋊C4—21no—
51C5×(C2×D3)⋊C4—21no—
52C5×(C2×D3)⋊C4—21no—
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3D411yescharacteristic
55C5×C4⋊Dic3D411yescharacteristic
56C5×Dic3⋊C4—21no—
57C5×Dic3⋊C4—21no—
58C5×Dic3⋊C4—21no—
59C4×C5×Dic3—21no—
60C3×C4⋊Dic5—21no—
61C3×C4⋊Dic5—21no—
62C2×C3×#168—21no—
63#6661—42no—
64#6656—42no—
65#5699D511yescharacteristic
66C3×#501—51no—
67#5086—51no—
68#5081—51no—
69#4543—51no—
70#4465—51no—
71#4464—51no—
72C5×C4⋊Q8—61no—
73C5×#126—61no—
74C5×#126—61no—
75C5×#125—31no—
76C5×#125C2×D311yescharacteristic
77C5×#124—31no—
78C5×#123—61no—
79C5×C22⋊Q8—61no—
80C5×C22⋊Q8—61no—
81C2×#689—61no—
82C2×#687—61no—
83#4015C2×D311yescharacteristic
84#3940—21no—
85#3940—61no—
86#3939—21no—
87#3939—61no—
88#3935—31no—
89#3935—31no—
90#3935C2×D311yescharacteristic
91#1660—151noSylow
92C22×C5×D3—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C5×Dic3—21no—
99C2×C5×Dic3—21no—
100C2×C5×Dic3—21no—
101C5×D12—41no—
102C4×C5×D3—81no—
103C5×Dic6—41no—
104C5×Dic6—81no—
105C2×C3×Dic5—41no—
106C3×Dic10—41no—
107C3×Dic10—41no—
108C3⋊#168—22no—
109C3⋊#168—22no—
110C3×#168—22no—
111C3×C4⋊Q8—51no—
112C3×#125C2×D511yescharacteristic
113C2×#216—101no—
114C2×#215—101no—
115#898—21no—
116#898—21no—
117#897—21no—
118#896—21no—
119#894—21no—
120#888—21no—
121#875C2×D511yescharacteristic
122#870C2×D511yescharacteristic
123C3×#107—101no—
124C3×#106—101no—
125C3×#97—51no—
126#808—101no—
127#807—101no—
128#803—51no—
129#803—51no—
130C2×C5×Q8—31no—
131C2×C5×Q8—61no—
132C2×C5×D4—31no—
133C22×C4×C5—61no—
134C2×Dic10—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—31no—
138C5×C4⋊C4—31no—
139C5×C4⋊C4—61no—
140C5×C4⋊C4—61no—
141C5×C4⋊C4—61no—
142C5×C4⋊C4—61no—
143C5×C4⋊C4#6711yescharacteristic
144C5×C4⋊C4#6711yescharacteristic
145C5×C22⋊C4—61no—
146C5×C22⋊C4—61no—
147C5×C22⋊C4—61no—
148C5×C22⋊C4—61no—
149C5×C22⋊C4—61no—
150C42×C5—61no—
151C42×C5C22×D311yescharacteristic
152#689—122no—
153#687—122no—
154C4⋊Dic5—21no—
155C4⋊Dic5—21no—
156C2×#168—21no—
157C2×#168—61no—
158C2×#168—61no—
159#563—31no—
160#501—51no—
161#501—151no—
162#497—151no—
163#330—151no—
164#330—151no—
165#329—151no—
166C22×C3×C5#12011yescharacteristic
167C2×C5×D3—41no—
168C2×C5×D3—41no—
169C2×C5×D3—41no—
170C3×C4×C5—21no—
171C3×C4×C5—21no—
172C3×C4×C5—21no—
173C3×C4×C5—41no—
174C3×C4×C5—41no—
175C3×Dic5—81no—
176C5×Dic3—41no—
177C5×Dic3—41no—
178C5×Dic3—41no—
179C2×C3×Q8—101no—
180C2×D12C22⋊D511yescharacteristic
181C2×C4×D3—21no—
182C2×Dic6—21no—
183C2×Dic6C22⋊D511yescharacteristic
184C2×C3×C8—101no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—101no—
188C3×C4⋊C4—101no—
189C3×C4⋊C4C22⋊D511yescharacteristic
190C3×C4⋊C4C22⋊D511yescharacteristic
191C3×C42C22×D511yescharacteristic
192#216—202no—
193#215—202no—
194(C2×D3)⋊C4—21no—
195(C2×D3)⋊C4—21no—
196(C2×D3)⋊C4—21no—
197(C2×D3)⋊C4—21no—
198(C2×D3)⋊C4—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3C22⋊D511yescharacteristic
201C4⋊Dic3C22⋊D511yescharacteristic
202Dic3⋊C4—21no—
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205C4×Dic3—21no—
206C2×C3⋊C8—101no—
207C2×C3⋊C8—101no—
208C23×C5—61no—
209C5×Q8—121no—
210C5×Q8—241no—
211C5×D4—121no—
212C2×C4×C5—21no—
213C2×C4×C5—21no—
214C2×C4×C5—61no—
215C2×C4×C5—61no—
216C2×C4×C5—61no—
217C2×C4×C5—241no—
218C2×C4×C5D3×D411yescharacteristic
219C2×C4×C5D3×D411yescharacteristic
220C2×C4×C5C2×#6711yescharacteristic
221C2×Dic5—41no—
222Dic10—41no—
223Dic10—41no—
224#168—22no—
225#168—62no—
226#168—62no—
227C2×Q16—301no—
228C2×SD16—301no—
229C4⋊Q8—51no—
230C4⋊Q8—61no—
231#126—61no—
232#126—61no—
233#125—31no—
234#125D3×D511yescharacteristic
235#124—31no—
236#123—61no—
237C22⋊Q8—61no—
238C22⋊Q8—61no—
239#107—101no—
240#107—301no—
241#106—101no—
242#106—301no—
243#97—51no—
244#97—151no—
245#97—151no—
246C2×C3×C5#45311yescharacteristic
247C2×C3×C5#45611yescharacteristic
248C2×C3×C5#45611yescharacteristic
249C5×D3—81no—
250C22×D3—21no—
251C3×Q8—201no—
252C3×Q8—201no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—201no—
256C2×C3×C4C2×C22⋊D511yescharacteristic
257C2×C3×C4C2×C22⋊D511yescharacteristic
258C2×C3×C4C2×C22⋊D511yescharacteristic
259C2×Dic3—21no—
260C2×Dic3—21no—
261C2×Dic3—21no—
262D12—41no—
263C4×D3—81no—
264Dic6—41no—
265Dic6—81no—
266C3×C8—102no—
267C3⋊C8—102no—
268C3⋊C8—102no—
269C22×C5—121no—
270C22×C5—121no—
271C22×C5—121no—
272C22×C5#93711yescharacteristic
273C4×C5—21no—
274C4×C5—21no—
275C4×C5—21no—
276C4×C5—41no—
277C4×C5—41no—
278C4×C5—121no—
279C4×C5—121no—
280C4×C5—121no—
281Dic5—81no—
282C2×Q8—31no—
283C2×Q8—61no—
284C2×Q8—101no—
285C2×D4—31no—
286C22×C4—61no—
287Q16—602no—
288SD16—602no—
289C2×C8—101no—
290C2×C8—301no—
291C2×C8—301no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—31no—
295C4⋊C4—31no—
296C4⋊C4—61no—
297C4⋊C4—61no—
298C4⋊C4—61no—
299C4⋊C4—61no—
300C4⋊C4—101no—
301C4⋊C4—101no—
302C4⋊C4#120111yescharacteristic
303C4⋊C4#120111yescharacteristic
304C22⋊C4—61no—
305C22⋊C4—61no—
306C22⋊C4—61no—
307C22⋊C4—61no—
308C22⋊C4—61no—
309C42—61no—
310C42C2×D3×D511yescharacteristic
311C3×C5#166011yescharacteristic, complemented, Hall
312C22×C3#409911yescharacteristic
313C2×D3—41no—
314C2×D3—41no—
315C2×D3—41no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—41no—
320C3×C4—41no—
321C3×C4—401no—
322Dic3—41no—
323Dic3—41no—
324Dic3—41no—
325C2×C5—241no—
326C2×C5#509511yescharacteristic
327C2×C5#519811yescharacteristic
328C2×C5#520511yescharacteristic
329C23—61no—
330Q8—121no—
331Q8—201no—
332Q8—201no—
333Q8—241no—
334D4—121no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—61no—
338C2×C4—61no—
339C2×C4—61no—
340C2×C4—201no—
341C2×C4—241no—
342C2×C4C2×#120111yescharacteristic
343C2×C4D3×C22⋊D511yescharacteristic
344C2×C4D3×C22⋊D511yescharacteristic
345C8—102no—
346C8—302no—
347C8—302no—
348C2×C3#6553011yescharacteristic
349C2×C3#6553511yescharacteristic
350C2×C3#6553511yescharacteristic
351D3—81no—
352C5#7139111yescharacteristic, complemented, Sylow
353C22—121no—
354C22—121no—
355C22—121no—
356C22#9156811yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—121no—
363C4—121no—
364C4—121no—
365C4—401no—
366C3#1060274911yescharacteristic, complemented, Sylow
367C2—241no—
368C2#1174939311yescharacteristic
369C2#1174941911yescharacteristic
370C2#1174946511yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5#120
prime radicalC2×C5×D12D4
hypercenter#125D3×D5
hypocenterC3×C5#1660
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
2. C3×#65354C2semidirect
4. #11746969C2semidirect
5. #11746364C2semidirect
6. #11745850C2semidirect
31. #65354D3semidirect
311. C3×C5#1660semidirect
352. C5#71391semidirect
366. C3#10602749semidirect

Maximal subgroups

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

subgroupindex
C5×#56992
C3×#653542
#117470822
#117469692
#117463642
#117458502
#117458472
#106027493
#713915