Finite Group Databasebeta

← #14290993

Subgroups — #14290993

Order 1920.

364 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 70 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
1#11752488C211yesmaximal, characteristic, complemented
2C3×#65002C211yesmaximal, characteristic
3#11746897C211yesmaximal, characteristic
4#11746892C211yesmaximal, characteristic
5#11746286C211yesmaximal, characteristic, complemented
6C5×#4465C211yesmaximal, characteristic, complemented
7#11745849C211yesmaximal, characteristic, complemented
8#10599168—31nomaximal, Hall
9#91759C2211yescharacteristic
10C5×#870C2211yescharacteristic
11C3×#4020C2211yescharacteristic
12C3×#4016C2211yescharacteristic
13#91346—21no—
14#91343—21no—
15#91339—21no—
16#91336—21no—
17#91335—21no—
18#91334—21no—
19C3×C5×#97C2211yescharacteristic
20#91087C2211yescharacteristic
21C5×#803C2211yescharacteristic
22C3×#3953—21no—
23C3×#3953—21no—
24#90965—21no—
25#90965—21no—
26#90964—21no—
27#90964—21no—
28#71250—51nomaximal, Hall
29C5⋊#564—31no—
30#65356—31no—
31#65002—31no—
32#65002D311yescharacteristic
33C5×#330—31no—
34#64685—31no—
35#64685—31no—
36C2×C3×D20—21no—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41C4⋊Dic15D411yescharacteristic
42C4⋊Dic15D411yescharacteristic
43#6712—21no—
44#6712—21no—
45C2×C3⋊#168—21no—
46C5×C4⋊Dic3D411yescharacteristic
47C5×C4⋊Dic3D411yescharacteristic
48C5×Dic3⋊C4—21no—
49C5×Dic3⋊C4—21no—
50C2×C5×C3⋊C8—21no—
51C3×C4⋊Dic5D411yescharacteristic
52C3×C4⋊Dic5D411yescharacteristic
53C3×#683—21no—
54C3×#683—21no—
55Dic3⋊Dic5—21no—
56Dic3⋊Dic5—21no—
57#6669—21no—
58#6669—21no—
59#6668—21no—
60#6668—21no—
61Dic3×Dic5—21no—
62Dic3×Dic5—21no—
63C3⋊#564—51no—
64C3×#490—51no—
65#5071—51no—
66#5071—51no—
67#4543—51no—
68#4465—51no—
69#4465D511yescharacteristic, complemented
70C5×#125—31no—
71#4036—61no—
72#4036—61no—
73#4035—61no—
74#4035—61no—
75#4035—61no—
76#4035—61no—
77#4020C2×D311yescharacteristic
78#4016—31no—
79#4016C2×D311yescharacteristic
80C5×#97—31no—
81C5×#97C2×D311yescharacteristic
82#3953—21no—
83#3953—21no—
84#3953—61no—
85#3953—61no—
86#3941—61no—
87#3941—61no—
88#3935—31no—
89#1658—151noSylow
90C22×C3×D5—41no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×Dic15—21no—
95C2×Dic15—21no—
96C2×C5×Dic3—21no—
97C2×C5×Dic3—21no—
98C2×C3×Dic5—21no—
99C2×C3×Dic5—21no—
100C3×D20—42no—
101C3×D20—42no—
102C3×D20—42no—
103C3×C5×C8—41no—
104C3⋊#168—41no—
105C5×C3⋊C8—41no—
106C3×#127—51no—
107C3×#125—51no—
108#890—101no—
109#890—101no—
110#889—101no—
111#889—101no—
112#889—101no—
113#889—101no—
114#870—51no—
115#870C2×D511yescharacteristic
116C3×#102—101no—
117C3×#102—101no—
118C3×#97C2×D511yescharacteristic
119#832—101no—
120#832—101no—
121#832—101no—
122#832—101no—
123#803—51no—
124#803C2×D511yescharacteristic
125C2×D20—21no—
126C2×D20—21no—
127C2×D20—21no—
128C2×C5×C8—21no—
129C2×C5×C8—61no—
130C5×C4⋊C4—31no—
131C5×C4⋊C4—31no—
132C5×C4⋊C4—61no—
133C5×C4⋊C4—61no—
134C42×C5C22×D311yescharacteristic
135C4⋊Dic5—31no—
136C4⋊Dic5—31no—
137C4⋊Dic5—61no—
138C4⋊Dic5—61no—
139C4⋊Dic5#6711yescharacteristic
140C4⋊Dic5#6711yescharacteristic
141#683—21no—
142#683—21no—
143#683—61no—
144#683—61no—
145#683—61no—
146#683—61no—
147#683—61no—
148#683—61no—
149C4×Dic5—61no—
150C4×Dic5—61no—
151C2×#168—61no—
152#564—151no—
153#490—51no—
154#490—151no—
155#490—151no—
156#330—31no—
157#330—151no—
158#330—151no—
159C22×C3×C5#12011yescharacteristic
160C2×C3×D5—81no—
161C2×C3×D5—81no—
162C2×C3×D5—81no—
163C3×C4×C5—21no—
164C3×C4×C5—21no—
165C3×C4×C5—21no—
166Dic15—41no—
167Dic15—41no—
168C3×Dic5—41no—
169C3×Dic5—41no—
170C5×Dic3—41no—
171C5×Dic3—41no—
172C2×C3×D4—101no—
173C2×C3×D4—101no—
174C2×C3×D4—101no—
175C2×C3×C8—21no—
176C3×C4⋊C4—51no—
177C3×C4⋊C4—51no—
178C3×C4⋊C4—101no—
179C3×C4⋊C4—101no—
180C3×C42C22×D511yescharacteristic
181C4⋊Dic3—51no—
182C4⋊Dic3—51no—
183C4⋊Dic3—101no—
184C4⋊Dic3—101no—
185C4⋊Dic3D2011yescharacteristic
186C4⋊Dic3D2011yescharacteristic
187Dic3⋊C4—21no—
188Dic3⋊C4—21no—
189Dic3⋊C4—101no—
190Dic3⋊C4—101no—
191Dic3⋊C4—101no—
192Dic3⋊C4—101no—
193Dic3⋊C4—101no—
194Dic3⋊C4—101no—
195C4×Dic3—101no—
196C4×Dic3—101no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—101no—
199C22×D5—41no—
200C2×C4×C5—61no—
201C2×C4×C5—61no—
202C2×C4×C5D3×D411yescharacteristic
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5C2×#6711yescharacteristic
205C2×Dic5—21no—
206C2×Dic5—21no—
207C2×Dic5—61no—
208C2×Dic5—61no—
209D20—42no—
210D20—42no—
211D20—42no—
212C5×C8—41no—
213C5×C8—121no—
214#168—121no—
215#127—51no—
216#125—31no—
217#125—51no—
218#125—151no—
219#125—301no—
220#125—301no—
221#125—301no—
222#125—301no—
223#125—301no—
224#125—301no—
225#102—101no—
226#102—101no—
227#102—301no—
228#102—301no—
229#102—301no—
230#102—301no—
231#97—31no—
232#97—151no—
233#97D3×D511yescharacteristic
234C2×C3×C5#45411yescharacteristic
235C2×C3×C5#45411yescharacteristic
236C2×C3×C5#45411yescharacteristic
237C3×D5—161no—
238C23×C3—201no—
239C3×D4—202no—
240C3×D4—202no—
241C3×D4—202no—
242C2×C3×C4—101no—
243C2×C3×C4—101no—
244C2×C3×C4C2×D2011yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4D4×D511yescharacteristic
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—101no—
250C2×Dic3—101no—
251C3×C8—41no—
252C3⋊C8—41no—
253C3⋊C8—201no—
254C22×C5#93711yescharacteristic
255C2×D5—81no—
256C2×D5—81no—
257C2×D5—81no—
258C4×C5—21no—
259C4×C5—21no—
260C4×C5—21no—
261C4×C5—121no—
262C4×C5—121no—
263Dic5—41no—
264Dic5—41no—
265Dic5—121no—
266Dic5—121no—
267C2×D4—101no—
268C2×D4—101no—
269C2×D4—101no—
270C2×C8—21no—
271C2×C8—61no—
272C2×C8—301no—
273C4⋊C4—31no—
274C4⋊C4—31no—
275C4⋊C4—51no—
276C4⋊C4—51no—
277C4⋊C4—61no—
278C4⋊C4—61no—
279C4⋊C4—101no—
280C4⋊C4—101no—
281C4⋊C4—151no—
282C4⋊C4—151no—
283C4⋊C4—301no—
284C4⋊C4—301no—
285C4⋊C4—301no—
286C4⋊C4—301no—
287C4⋊C4—301no—
288C4⋊C4—301no—
289C4⋊C4—301no—
290C4⋊C4—301no—
291C42—301no—
292C42—301no—
293C42C2×D3×D511yescharacteristic
294C3×C5#165811yescharacteristic, complemented, Hall
295C22×C3—401no—
296C22×C3—401no—
297C22×C3—401no—
298C22×C3#402811yescharacteristic
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—201no—
303C3×C4—201no—
304Dic3—41no—
305Dic3—41no—
306Dic3—201no—
307Dic3—201no—
308C2×C5#506211yescharacteristic
309C2×C5#520111yescharacteristic
310C2×C5#520111yescharacteristic
311D5—161no—
312C23—201no—
313D4—202no—
314D4—202no—
315D4—202no—
316C2×C4—61no—
317C2×C4—61no—
318C2×C4—101no—
319C2×C4—101no—
320C2×C4—301no—
321C2×C4—301no—
322C2×C4D3×D2011yescharacteristic
323C2×C4#677711yescharacteristic
324C2×C4D5×#6711yescharacteristic
325C8—41no—
326C8—121no—
327C8—601no—
328C2×C3—801no—
329C2×C3#6504211yescharacteristic
330C2×C3#6511611yescharacteristic
331C2×C3#6511611yescharacteristic
332C5#7125011yescharacteristic, complemented, Sylow
333C22—401no—
334C22—401no—
335C22—401no—
336C22#9147411yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—121no—
341C4—121no—
342C4—201no—
343C4—201no—
344C4—601no—
345C4—601no—
346C3#1059916811yescharacteristic, complemented, Sylow
347C2—801no—
348C2#1174712111yescharacteristic
349C2#1174825411yescharacteristic
350C2#1174825511yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5#120
prime radicalC3×#4020C22
hypercenter#97D3×D5
hypocenterC3×C5#1658
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. #11752488C2semidirect
5. #11746286C2semidirect
6. C5×#4465C2semidirect
7. #11745849C2semidirect
69. #4465D5semidirect
294. C3×C5#1658semidirect
332. C5#71250semidirect
346. C3#10599168semidirect

Maximal subgroups

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

subgroupindex
#117524882
C3×#650022
#117468972
#117468922
#117462862
C5×#44652
#117458492
#105991683
#712505