Finite Group Databasebeta

← #14284018

Subgroups — #14284018

Order 1920.

452 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 88 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#11752471C211yesmaximal, characteristic
2#11750808C211yesmaximal, characteristic
3#11746844C211yesmaximal, characteristic
4C5×#4465C211yesmaximal, characteristic, complemented
5C3×#64685C211yesmaximal, characteristic, complemented
6#11745850C211yesmaximal, characteristic, complemented
7#11745849C211yesmaximal, characteristic, complemented
8#10599155—31nomaximal, Hall
9C2×#6705—21no—
10C42×D15C2211yescharacteristic
11C5×#870C2211yescharacteristic
12C3×#4016C2211yescharacteristic
13#91470C411yescharacteristic
14#91470C411yescharacteristic
15#91377—21no—
16#91377—21no—
17#91347C411yescharacteristic
18#91347C411yescharacteristic
19#91325—21no—
20#91325—21no—
21C2×#6651—21no—
22C3×C5×#97C2211yescharacteristic
23C8×Dic15—21no—
24#91087C2211yescharacteristic
25C5×#803C2211yescharacteristic
26C3×#3935C2211yescharacteristic
27#90951—21no—
28#68362—51nomaximal, Hall
29#66022—31no—
30#64996—31no—
31#64996—31no—
32C5×#330—31no—
33#64763—31no—
34#64685—31no—
35#64685D311yescharacteristic, complemented
36C2×C4×D15C2×C411yescharacteristic
37C2×C4×D15D411yescharacteristic
38C2×C4×D15D411yescharacteristic
39C2×#1204—21no—
40C2×#1204—21no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43C4×Dic15C2×C411yescharacteristic
44C4×Dic15D411yescharacteristic
45C4×Dic15D411yescharacteristic
46C2×C3⋊#168—21no—
47#6705—24no—
48C5×C4⋊Dic3C2×C411yescharacteristic
49C5×C4⋊Dic3C2×C411yescharacteristic
50C5×Dic3⋊C4—21no—
51C5×Dic3⋊C4—21no—
52C2×C5×C3⋊C8—21no—
53C3×C4⋊Dic5C2×C411yescharacteristic
54C3×C4⋊Dic5C2×C411yescharacteristic
55C3×#683—21no—
56C3×#683—21no—
57C2×C3×#168—21no—
58#6669—21no—
59#6669—21no—
60#6667—21no—
61#6667—21no—
62Dic3×Dic5—21no—
63Dic3×Dic5—21no—
64#6651—24no—
65#5688—51no—
66#4707—51no—
67#4707—51no—
68C3×#330—51no—
69#4543—51no—
70#4465—51no—
71#4465D511yescharacteristic, complemented
72C5×#125—31no—
73C2×#676—61no—
74C2×#676—61no—
75#4042—61no—
76#4042—61no—
77#4038—31no—
78#4038—31no—
79#4034—31no—
80#4034—31no—
81#4033—61no—
82#4033—61no—
83C42×D5—31no—
84#4016C2×D311yescharacteristic
85C5×#97—31no—
86C5×#97C2×D311yescharacteristic
87C8×Dic5—61no—
88C8×Dic5—61no—
89#3935—31no—
90#3935C2×D311yescharacteristic
91#1526—151noSylow
92C22×D15C22⋊C411yescharacteristic
93C2×C3×C4×C5C22×C411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15C22⋊C411yescharacteristic
97C2×Dic15C22⋊C411yescharacteristic
98C2×Dic15C22⋊C411yescharacteristic
99C4×D15—22no—
100C4×D15—22no—
101C4×D15—22no—
102C2×C5×Dic3—21no—
103C2×C5×Dic3—21no—
104C2×C3×Dic5—21no—
105C2×C3×Dic5—21no—
106#1204—42no—
107#1204—42no—
108C3×C5×C8—22no—
109C3⋊#168—22no—
110C3×#168—22no—
111C5×C3⋊C8—22no—
112C3×#125—51no—
113C2×ΓL(1,𝔽25)—101no—
114C2×ΓL(1,𝔽25)—101no—
115#896—101no—
116#896—101no—
117#892—51no—
118#892—51no—
119#888—51no—
120#888—51no—
121#887—101no—
122#887—101no—
123C42×D3—51no—
124#870C2×D511yescharacteristic
125C3×#97—51no—
126C3×#97C2×D511yescharacteristic
127C8×Dic3—101no—
128C8×Dic3—101no—
129#803—51no—
130#803C2×D511yescharacteristic
131C2×C4×D5—31no—
132C2×C4×D5—31no—
133C2×C4×D5—31no—
134C2×Dic10—61no—
135C2×Dic10—61no—
136C2×C5×C8—21no—
137C2×C5×C8—61no—
138C5×C4⋊C4—31no—
139C5×C4⋊C4—31no—
140C5×C4⋊C4—61no—
141C5×C4⋊C4—61no—
142C42×C5C22×D311yescharacteristic
143#685—61no—
144#685—61no—
145C4⋊Dic5C4×D311yescharacteristic
146C4⋊Dic5C4×D311yescharacteristic
147#683—21no—
148#683—21no—
149#683—61no—
150#683—61no—
151C4×Dic5—31no—
152C4×Dic5—31no—
153C4×Dic5—31no—
154C4×Dic5—61no—
155C4×Dic5—61no—
156C2×#168—21no—
157C2×#168—61no—
158#676—64no—
159#676—64no—
160#533—151no—
161C4×M16—151no—
162C4×M16—151no—
163#330—31no—
164#330—51no—
165#330—151no—
166#330—151no—
167C22×C3×C5C2×C22⋊C411yescharacteristic
168C2×D15—21no—
169C2×D15—21no—
170C2×D15—21no—
171C3×C4×C5—21no—
172C3×C4×C5—21no—
173C3×C4×C5—21no—
174Dic15#10112yes—
175Dic15#10412yes—
176Dic15#10412yes—
177C3×Dic5—41no—
178C3×Dic5—41no—
179C5×Dic3—41no—
180C5×Dic3—41no—
181C2×C4×D3—51no—
182C2×C4×D3—51no—
183C2×C4×D3—51no—
184C2×Dic6—101no—
185C2×Dic6—101no—
186C2×C3×C8—21no—
187C2×C3×C8—101no—
188C3×C4⋊C4—51no—
189C3×C4⋊C4—51no—
190C3×C4⋊C4—101no—
191C3×C4⋊C4—101no—
192C3×C42C22×D511yescharacteristic
193(C2×D3)⋊C4—101no—
194(C2×D3)⋊C4—101no—
195C4⋊Dic3C4×D511yescharacteristic
196C4⋊Dic3C4×D511yescharacteristic
197Dic3⋊C4—21no—
198Dic3⋊C4—21no—
199Dic3⋊C4—101no—
200Dic3⋊C4—101no—
201C4×Dic3—51no—
202C4×Dic3—51no—
203C4×Dic3—51no—
204C4×Dic3—101no—
205C4×Dic3—101no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—101no—
208ΓL(1,𝔽25)—104no—
209ΓL(1,𝔽25)—104no—
210C22×D5—31no—
211C2×C4×C5—61no—
212C2×C4×C5—61no—
213C2×C4×C5C2×C4×D311yescharacteristic
214C2×C4×C5D3×D411yescharacteristic
215C2×C4×C5D3×D411yescharacteristic
216C2×Dic5—21no—
217C2×Dic5—21no—
218C2×Dic5—31no—
219C2×Dic5—31no—
220C2×Dic5—31no—
221C4×D5—62no—
222C4×D5—62no—
223C4×D5—62no—
224Dic10—122no—
225Dic10—122no—
226C5×C8—22no—
227C5×C8—62no—
228#168—22no—
229#168—62no—
230C2×M16—301no—
231C2×M16—301no—
232C4⋊Q8—151no—
233C4⋊Q8—151no—
234#125—31no—
235#125—51no—
236C22⋊Q8—301no—
237C22⋊Q8—301no—
238C4×Q8—301no—
239C4×Q8—301no—
240#117—151no—
241#117—151no—
242C2×C42—151no—
243#97—31no—
244#97—51no—
245#97—151no—
246#97D3×D511yescharacteristic
247C4×C8—301no—
248C4×C8—301no—
249C2×C3×C5C2×#10111yescharacteristic
250C2×C3×C5C2×#10411yescharacteristic
251C2×C3×C5C2×#10411yescharacteristic
252D15—41no—
253C22×D3—51no—
254C2×C3×C4—101no—
255C2×C3×C4—101no—
256C2×C3×C4C2×C4×D511yescharacteristic
257C2×C3×C4D4×D511yescharacteristic
258C2×C3×C4D4×D511yescharacteristic
259C2×Dic3—21no—
260C2×Dic3—21no—
261C2×Dic3—51no—
262C2×Dic3—51no—
263C2×Dic3—51no—
264C4×D3—102no—
265C4×D3—102no—
266C4×D3—102no—
267Dic6—202no—
268Dic6—202no—
269C3×C8—22no—
270C3×C8—102no—
271C3⋊C8—22no—
272C3⋊C8—102no—
273C22×C5D3×C22⋊C411yescharacteristic
274C2×D5—61no—
275C2×D5—61no—
276C2×D5—61no—
277C4×C5—21no—
278C4×C5—21no—
279C4×C5—21no—
280C4×C5—121no—
281C4×C5—121no—
282Dic5—32no—
283Dic5—32no—
284Dic5—32no—
285Dic5—41no—
286Dic5—41no—
287C2×Q8—301no—
288C2×Q8—301no—
289C22×C4—151no—
290C22×C4—151no—
291C22×C4—151no—
292M16—304no—
293M16—304no—
294C2×C8—21no—
295C2×C8—61no—
296C2×C8—101no—
297C2×C8—301no—
298C4⋊C4—31no—
299C4⋊C4—31no—
300C4⋊C4—51no—
301C4⋊C4—51no—
302C4⋊C4—61no—
303C4⋊C4—61no—
304C4⋊C4—101no—
305C4⋊C4—101no—
306C4⋊C4—301no—
307C4⋊C4—301no—
308C22⋊C4—301no—
309C22⋊C4—301no—
310C42—151no—
311C42—151no—
312C42—151no—
313C42—301no—
314C42—301no—
315C42C2×D3×D511yescharacteristic
316C3×C5#152611yescharacteristic, complemented, Hall
317C22×C3D5×C22⋊C411yescharacteristic
318C2×D3—101no—
319C2×D3—101no—
320C2×D3—101no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—201no—
325C3×C4—201no—
326Dic3—41no—
327Dic3—41no—
328Dic3—52no—
329Dic3—52no—
330Dic3—52no—
331C2×C5D3×#10111yescharacteristic
332C2×C5D3×#10411yescharacteristic
333C2×C5D3×#10411yescharacteristic
334D5—121no—
335C23—151no—
336Q8—602no—
337Q8—602no—
338C2×C4—61no—
339C2×C4—61no—
340C2×C4—101no—
341C2×C4—101no—
342C2×C4—151no—
343C2×C4—151no—
344C2×C4—151no—
345C2×C4—302no—
346C2×C4—302no—
347C2×C4—302no—
348C2×C4C4×D3×D511yescharacteristic
349C2×C4#677711yescharacteristic
350C2×C4#679011yescharacteristic
351C8—22no—
352C8—62no—
353C8—102no—
354C8—302no—
355C2×C3D5×#10111yescharacteristic
356C2×C3D5×#10411yescharacteristic
357C2×C3D5×#10411yescharacteristic
358D3—201no—
359C5#6836211yescharacteristic, complemented, Sylow
360C22—301no—
361C22—301no—
362C22—301no—
363C22#9147311yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—121no—
368C4—121no—
369C4—152no—
370C4—152no—
371C4—152no—
372C4—201no—
373C4—201no—
374C3#1059915511yescharacteristic, complemented, Sylow
375C2—601no—
376C2#1174711211yescharacteristic
377C2#1174822711yescharacteristic
378C2#1174823611yescharacteristic
subgroupG/H
centerC22#91473
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C42×C5C23
hypercenter#97D3×D5
hypocenterC3×C5#1526
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
4. C5×#4465C2semidirect
5. C3×#64685C2semidirect
6. #11745850C2semidirect
7. #11745849C2semidirect
35. #64685D3semidirect
71. #4465D5semidirect
316. C3×C5#1526semidirect
359. C5#68362semidirect
374. C3#10599155semidirect

Maximal subgroups

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

subgroupindex
#117524712
#117508082
#117468442
C5×#44652
C3×#646852
#117458502
#117458492
#105991553
#683625