Subgroups — C₅×#12933 #11935653

Order 1280.

380 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2916	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#365	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#365	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2117	C₂	1	1	yes	maximal, characteristic
5	C₅×#1815	C₂	1	1	yes	maximal, characteristic
6	C₅×#1388	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1385	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#568	—	2	1	no	—
9	C₂×C₅×#131	C₂²	1	1	yes	characteristic
10	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
11	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
12	C₅×#430	—	2	2	no	—
13	C₅×#430	—	2	1	no	—
14	C₂×C₅×#108	—	2	2	no	—
15	C₂×C₅×#108	C₂²	1	1	yes	characteristic
16	C₂×C₅×#108	C₂²	1	1	yes	characteristic
17	C₂×C₅×#108	C₂²	1	1	yes	characteristic
18	C₂×C₅×#106	C₂²	1	1	yes	characteristic
19	C₅×#417	—	2	1	no	—
20	C₅×#365	—	2	2	no	—
21	C₅×#365	—	2	2	no	—
22	C₅×#350	C₄	1	4	yes	complemented
23	C₅×#343	—	2	1	no	—
24	#12933	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₅×#41	D₄	1	1	yes	characteristic
26	C₅×#131	—	2	1	no	—
27	C₅×#131	—	2	1	no	—
28	C₅×#131	—	4	2	no	—
29	C₅×#131	—	4	2	no	—
30	C₅×#131	C₂×C₄	1	2	yes	—
31	C₅×#131	Q₈	1	2	yes	—
32	C₂×C₅×M₁₆	—	2	1	no	—
33	C₂×C₅×M₁₆	—	2	4	no	—
34	C₂×C₅×M₁₆	—	2	1	no	—
35	C₂×C₅×M₁₆	—	2	1	no	—
36	C₂×C₅×M₁₆	—	2	1	no	—
37	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
38	C₂²×C₅×C₈	—	2	1	no	—
39	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
40	C₂×C₅×C₄⋊C₄	—	2	1	no	—
41	C₅×M₃₂	—	2	1	no	—
42	C₅×M₃₂	—	2	1	no	—
43	C₅×M₃₂	—	2	1	no	—
44	C₅×M₃₂	C₂×C₄	1	2	yes	—
45	C₂×C₅×C₁₆	—	2	1	no	—
46	C₂×C₅×C₁₆	C₂×C₄	1	2	yes	—
47	C₅×#108	—	2	4	no	—
48	C₅×#108	—	2	1	no	—
49	C₅×#108	—	2	1	no	—
50	C₅×#108	—	2	1	no	—
51	C₅×#108	—	2	1	no	—
52	C₅×#108	D₄	1	2	yes	—
53	C₅×#108	D₄	1	2	yes	—
54	C₅×#106	—	2	1	no	—
55	C₅×#106	—	2	1	no	—
56	C₅×#103	—	4	1	no	—
57	C₅×#102	—	4	1	no	—
58	#2916	C₂×C₅	1	1	yes	characteristic
59	C₂×#365	C₂×C₅	1	1	yes	characteristic, complemented
60	C₂×#365	C₂×C₅	1	1	yes	characteristic, complemented
61	#2117	C₂×C₅	1	1	yes	characteristic
62	#1815	C₂×C₅	1	1	yes	characteristic
63	#1388	C₂×C₅	1	1	yes	characteristic, complemented
64	#1385	C₂×C₅	1	1	yes	characteristic, complemented
65	C₅×#41	—	2	1	no	—
66	C₅×#41	—	2	1	no	—
67	C₅×#41	C₄⋊C₄	1	2	yes	—
68	C₅×#41	SD₁₆	1	2	yes	—
69	C₂×C₅×Q₈	SD₁₆	1	1	yes	characteristic
70	C₂×C₅×D₄	—	2	1	no	—
71	C₂×C₅×D₄	SD₁₆	1	1	yes	characteristic
72	C₂²×C₄×C₅	—	2	1	no	—
73	C₂²×C₄×C₅	—	4	1	no	—
74	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
75	C₅×M₁₆	—	2	1	no	—
76	C₅×M₁₆	—	2	2	no	—
77	C₅×M₁₆	—	2	2	no	—
78	C₅×M₁₆	—	2	2	no	—
79	C₅×M₁₆	—	2	2	no	—
80	C₅×M₁₆	—	4	4	no	—
81	C₅×M₁₆	—	4	1	no	—
82	C₅×M₁₆	—	4	1	no	—
83	C₅×M₁₆	—	4	1	no	—
84	C₅×M₁₆	—	4	1	no	—
85	C₅×M₁₆	C₄⋊C₄	1	2	yes	—
86	C₂×C₅×C₈	—	2	1	no	—
87	C₂×C₅×C₈	—	2	2	no	—
88	C₂×C₅×C₈	—	2	2	no	—
89	C₂×C₅×C₈	—	4	4	no	—
90	C₂×C₅×C₈	—	4	1	no	—
91	C₂×C₅×C₈	—	4	1	no	—
92	C₂×C₅×C₈	—	4	1	no	—
93	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
95	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
96	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
97	C₂×C₅×C₈	#41	1	1	yes	characteristic
98	C₂×C₅×C₈	#41	1	1	yes	characteristic
99	C₅×C₄⋊C₄	—	4	1	no	—
100	C₅×C₄⋊C₄	—	4	1	no	—
101	C₅×C₁₆	—	2	2	no	—
102	C₅×C₁₆	—	2	2	no	—
103	#568	—	2	1	no	—
104	C₂×#131	C₂²×C₅	1	1	yes	characteristic
105	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
106	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
107	#430	—	2	1	no	—
108	#430	—	2	2	no	—
109	C₂×#108	—	2	2	no	—
110	C₂×#108	C₂²×C₅	1	1	yes	characteristic
111	C₂×#108	C₂²×C₅	1	1	yes	characteristic
112	C₂×#108	C₂²×C₅	1	1	yes	characteristic
113	C₂×#106	C₂²×C₅	1	1	yes	characteristic
114	#417	—	2	1	no	—
115	#365	—	2	2	no	—
116	#365	—	2	2	no	—
117	#350	C₄×C₅	1	4	yes	complemented
118	#343	—	2	1	no	—
119	C₂³×C₅	—	2	1	no	—
120	C₂³×C₅	#137	1	1	yes	characteristic
121	C₅×Q₈	—	2	1	no	—
122	C₅×Q₈	#106	1	2	yes	—
123	C₅×D₄	—	2	2	no	—
124	C₅×D₄	—	2	2	no	—
125	C₅×D₄	—	2	1	no	—
126	C₅×D₄	#106	1	2	yes	—
127	C₂×C₄×C₅	—	2	1	no	—
128	C₂×C₄×C₅	—	2	2	no	—
129	C₂×C₄×C₅	—	2	2	no	—
130	C₂×C₄×C₅	—	8	1	no	—
131	C₂×C₄×C₅	—	16	1	no	—
132	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₅	#120	1	1	yes	characteristic
134	C₂×C₄×C₅	#123	1	1	yes	characteristic
135	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
136	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
137	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
138	C₅×C₈	—	2	2	no	—
139	C₅×C₈	—	4	2	no	—
140	C₅×C₈	—	4	2	no	—
141	C₅×C₈	—	8	1	no	—
142	C₅×C₈	C₄×D₄	1	1	yes	characteristic
143	C₅×C₈	C₄×D₄	1	1	yes	characteristic
144	C₅×C₈	C₂²⋊Q₈	1	1	yes	characteristic
145	C₅×C₈	C₂²⋊Q₈	1	1	yes	characteristic
146	C₂×#41	C₅×D₄	1	1	yes	characteristic
147	#131	—	2	1	no	—
148	#131	—	2	1	no	—
149	#131	—	4	2	no	—
150	#131	—	4	2	no	—
151	#131	C₂×C₄×C₅	1	2	yes	—
152	#131	C₅×Q₈	1	2	yes	—
153	C₂×M₁₆	—	2	1	no	—
154	C₂×M₁₆	—	2	4	no	—
155	C₂×M₁₆	—	2	1	no	—
156	C₂×M₁₆	—	2	1	no	—
157	C₂×M₁₆	—	2	1	no	—
158	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
159	C₂²×C₈	—	2	1	no	—
160	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
161	C₂×C₄⋊C₄	—	2	1	no	—
162	M₃₂	—	2	1	no	—
163	M₃₂	—	2	1	no	—
164	M₃₂	—	2	1	no	—
165	M₃₂	C₂×C₄×C₅	1	2	yes	—
166	C₂×C₁₆	—	2	1	no	—
167	C₂×C₁₆	C₂×C₄×C₅	1	2	yes	—
168	#108	—	2	4	no	—
169	#108	—	2	1	no	—
170	#108	—	2	1	no	—
171	#108	—	2	1	no	—
172	#108	—	2	1	no	—
173	#108	C₅×D₄	1	2	yes	—
174	#108	C₅×D₄	1	2	yes	—
175	#106	—	2	1	no	—
176	#106	—	2	1	no	—
177	#103	—	4	1	no	—
178	#102	—	4	1	no	—
179	C₂²×C₅	—	2	2	no	—
180	C₂²×C₅	—	4	1	no	—
181	C₂²×C₅	—	8	1	no	—
182	C₂²×C₅	#428	1	1	yes	characteristic
183	C₂²×C₅	#448	1	1	yes	characteristic
184	C₂²×C₅	#483	1	1	yes	characteristic
185	C₄×C₅	—	2	2	no	—
186	C₄×C₅	—	16	1	no	—
187	C₄×C₅	#385	1	1	yes	characteristic
188	C₄×C₅	C₂×#106	1	1	yes	characteristic
189	C₄×C₅	#450	1	1	yes	characteristic
190	C₄×C₅	#481	1	1	yes	characteristic
191	#41	—	2	1	no	—
192	#41	—	2	1	no	—
193	#41	C₅×C₄⋊C₄	1	2	yes	—
194	#41	C₅×SD₁₆	1	2	yes	—
195	C₂×Q₈	C₅×SD₁₆	1	1	yes	characteristic
196	C₂×D₄	—	2	1	no	—
197	C₂×D₄	C₅×SD₁₆	1	1	yes	characteristic
198	C₂²×C₄	—	2	1	no	—
199	C₂²×C₄	—	4	1	no	—
200	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
201	M₁₆	—	2	1	no	—
202	M₁₆	—	2	2	no	—
203	M₁₆	—	2	2	no	—
204	M₁₆	—	2	2	no	—
205	M₁₆	—	2	2	no	—
206	M₁₆	—	4	4	no	—
207	M₁₆	—	4	1	no	—
208	M₁₆	—	4	1	no	—
209	M₁₆	—	4	1	no	—
210	M₁₆	—	4	1	no	—
211	M₁₆	C₅×C₄⋊C₄	1	2	yes	—
212	C₂×C₈	—	2	1	no	—
213	C₂×C₈	—	2	2	no	—
214	C₂×C₈	—	2	2	no	—
215	C₂×C₈	—	4	4	no	—
216	C₂×C₈	—	4	1	no	—
217	C₂×C₈	—	4	1	no	—
218	C₂×C₈	—	4	1	no	—
219	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
220	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
221	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
222	C₂×C₈	C₂×C₅×Q₈	1	1	yes	characteristic
223	C₂×C₈	C₅×#41	1	1	yes	characteristic
224	C₂×C₈	C₅×#41	1	1	yes	characteristic
225	C₄⋊C₄	—	4	1	no	—
226	C₄⋊C₄	—	4	1	no	—
227	C₁₆	—	2	2	no	—
228	C₁₆	—	2	2	no	—
229	C₂×C₅	—	2	1	no	—
230	C₂×C₅	—	2	1	no	—
231	C₂×C₅	—	2	1	no	—
232	C₂×C₅	—	4	2	no	—
233	C₂×C₅	#1853	1	1	yes	characteristic
234	C₂³	—	2	1	no	—
235	C₂³	C₅×#137	1	1	yes	characteristic
236	Q₈	—	2	1	no	—
237	Q₈	C₅×#106	1	2	yes	—
238	D₄	—	2	2	no	—
239	D₄	—	2	2	no	—
240	D₄	—	2	1	no	—
241	D₄	C₅×#106	1	2	yes	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	2	2	no	—
245	C₂×C₄	—	8	1	no	—
246	C₂×C₄	—	16	1	no	—
247	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
248	C₂×C₄	C₅×#120	1	1	yes	characteristic
249	C₂×C₄	C₅×#123	1	1	yes	characteristic
250	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
251	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
252	C₂×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
253	C₈	—	2	2	no	—
254	C₈	—	4	2	no	—
255	C₈	—	4	2	no	—
256	C₈	—	8	1	no	—
257	C₈	C₄×C₅×D₄	1	1	yes	characteristic
258	C₈	C₄×C₅×D₄	1	1	yes	characteristic
259	C₈	C₅×C₂²⋊Q₈	1	1	yes	characteristic
260	C₈	C₅×C₂²⋊Q₈	1	1	yes	characteristic
261	C₅	#12933	1	1	yes	characteristic, direct product factor, Sylow
262	C₂²	—	2	2	no	—
263	C₂²	—	4	1	no	—
264	C₂²	—	8	1	no	—
265	C₂²	C₅×#428	1	1	yes	characteristic
266	C₂²	C₅×#448	1	1	yes	characteristic
267	C₂²	C₅×#483	1	1	yes	characteristic
268	C₄	—	2	2	no	—
269	C₄	—	16	1	no	—
270	C₄	C₅×#385	1	1	yes	characteristic
271	C₄	C₂×C₅×#106	1	1	yes	characteristic
272	C₄	C₅×#450	1	1	yes	characteristic
273	C₄	C₅×#481	1	1	yes	characteristic
274	C₂	—	2	1	no	—
275	C₂	—	2	1	no	—
276	C₂	—	2	1	no	—
277	C₂	—	4	2	no	—
278	C₂	C₅×#1853	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	#1853
commutator	C₂×C₈	C₂²×C₄×C₅
Frattini, cosocle	C₂²×C₈	C₂³×C₅
prime radical	C₂×C₅×#41	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#131 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#365	C₂	semidirect
3. C₂×C₅×#365	C₂	semidirect
6. C₅×#1388	C₂	semidirect
7. C₅×#1385	C₂	semidirect
22. C₅×#350	C₄	semidirect
24. #12933	C₅	direct (N × H)
59. C₂×#365	C₂×C₅	semidirect
60. C₂×#365	C₂×C₅	semidirect
63. #1388	C₂×C₅	semidirect
64. #1385	C₂×C₅	semidirect
117. #350	C₄×C₅	semidirect
261. C₅	#12933	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2916	2
C₂×C₅×#365	2
C₅×#2117	2
C₅×#1815	2
C₅×#1388	2
C₅×#1385	2
#12933	5

Subgroups — C5×#12933 #11935653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#12933 #11935653