Subgroups — C₅×#33435 #11956155

Order 1280.

674 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#504	C₂	1	2	yes	maximal, complemented
2	C₅×#2931	C₂	1	1	yes	maximal, characteristic
3	C₅×#2168	C₂	1	8	yes	maximal, complemented
4	C₅×#2150	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2113	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#346	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#131	C₂²	1	2	yes	—
8	C₅×#532	C₄	1	1	yes	characteristic
9	C₅×#504	—	2	8	no	—
10	C₂×C₅×M₃₂	C₂²	1	2	yes	—
11	C₂×C₅×M₃₂	C₂²	1	4	yes	—
12	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₅×C₁₆	C₂²	1	4	yes	—
14	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
15	C₅×#436	C₄	1	4	yes	—
16	C₅×C₈×D₄	C₂²	1	4	yes	—
17	C₅×#423	C₄	1	1	yes	characteristic
18	C₅×#408	C₄	1	2	yes	—
19	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₅×C₄⋊C₁₆	C₂²	1	4	yes	—
21	C₅×C₂²⋊C₁₆	C₂²	1	8	yes	—
22	C₅×#346	C₂²	1	4	yes	—
23	#33435	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂×C₅×#41	C₂×C₄	1	2	yes	—
25	C₅×#131	—	2	4	no	—
26	C₅×#131	—	2	4	no	—
27	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
28	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
29	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₅×C₈	C₂³	1	4	yes	—
31	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
32	C₅×C₄⋊Q₈	C₈	1	1	yes	characteristic
33	C₅×#127	C₈	1	1	yes	characteristic
34	C₅×#124	C₈	1	2	yes	—
35	C₅×#121	C₈	1	4	yes	—
36	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
37	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
38	C₅×M₃₂	—	2	4	no	—
39	C₅×M₃₂	—	2	8	no	—
40	C₂×C₅×C₁₆	—	2	2	no	—
41	C₂×C₅×C₁₆	—	2	8	no	—
42	C₂×C₅×C₁₆	D₄	1	4	yes	complemented
43	C₂×C₅×C₁₆	C₂³	1	2	yes	—
44	C₂×C₅×C₁₆	C₂³	1	4	yes	—
45	C₂×C₅×C₁₆	C₂³	1	2	yes	—
46	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
47	C₅×C₂²⋊C₈	C₂×C₄	1	8	yes	—
48	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
49	C₄×C₅×C₈	C₂³	1	2	yes	—
50	C₂×#504	C₂×C₅	1	2	yes	complemented
51	#2931	C₂×C₅	1	1	yes	characteristic
52	#2168	C₂×C₅	1	8	yes	complemented
53	#2150	C₂×C₅	1	1	yes	characteristic, complemented
54	#2113	C₂×C₅	1	2	yes	complemented
55	C₂×#346	C₂×C₅	1	1	yes	characteristic, complemented
56	C₅×#41	—	2	4	no	—
57	C₅×#41	—	2	4	no	—
58	C₂×C₅×Q₈	C₂×C₈	1	2	yes	—
59	C₂×C₅×D₄	C₂×C₈	1	4	yes	—
60	C₂×C₅×D₄	C₂×C₈	1	2	yes	—
61	C₂×C₅×D₄	C₂×C₈	1	4	yes	—
62	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
63	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
64	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
65	C₅×M₁₆	—	2	4	no	—
66	C₅×M₁₆	—	2	8	no	—
67	C₂×C₅×C₈	—	2	2	no	—
68	C₂×C₅×C₈	—	2	4	no	—
69	C₂×C₅×C₈	—	2	4	no	—
70	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
71	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
72	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
74	C₂×C₅×C₈	#41	1	2	yes	—
75	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
76	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	—
77	C₅×C₂²⋊C₄	C₂×C₈	1	8	yes	—
78	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
79	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
80	C₄²×C₅	C₂²×C₄	1	2	yes	—
81	C₅×C₁₆	—	2	4	no	—
82	C₅×C₁₆	—	2	2	no	—
83	C₅×C₁₆	C₂×D₄	1	4	yes	—
84	C₂×#131	C₂²×C₅	1	2	yes	—
85	#532	C₄×C₅	1	1	yes	characteristic
86	#504	—	2	8	no	—
87	C₂×M₃₂	C₂²×C₅	1	2	yes	—
88	C₂×M₃₂	C₂²×C₅	1	4	yes	—
89	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
90	C₂²×C₁₆	C₂²×C₅	1	4	yes	—
91	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
92	#436	C₄×C₅	1	4	yes	—
93	C₈×D₄	C₂²×C₅	1	4	yes	—
94	#423	C₄×C₅	1	1	yes	characteristic
95	#408	C₄×C₅	1	2	yes	—
96	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
97	C₄⋊C₁₆	C₂²×C₅	1	4	yes	—
98	C₂²⋊C₁₆	C₂²×C₅	1	8	yes	—
99	#346	C₂²×C₅	1	4	yes	—
100	C₂³×C₅	C₂²×C₈	1	4	yes	—
101	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
102	C₅×Q₈	—	2	4	no	—
103	C₅×D₄	—	2	8	no	—
104	C₅×D₄	—	2	4	no	—
105	C₅×D₄	—	4	4	no	—
106	C₂×C₄×C₅	—	2	4	no	—
107	C₂×C₄×C₅	—	2	4	no	—
108	C₂×C₄×C₅	—	4	2	no	—
109	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
110	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
111	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
112	C₂×C₄×C₅	C₂²×C₈	1	4	yes	—
113	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
114	C₂×C₄×C₅	#131	1	2	yes	—
115	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
116	C₅×C₈	—	2	4	no	—
117	C₅×C₈	—	2	2	no	—
118	C₅×C₈	C₄×D₄	1	2	yes	—
119	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
120	C₅×C₈	C₂×#41	1	1	yes	characteristic
121	C₂×#41	C₂×C₄×C₅	1	2	yes	—
122	#131	—	2	4	no	—
123	#131	—	2	4	no	—
124	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
125	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
126	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
127	C₂²×C₈	C₂³×C₅	1	4	yes	—
128	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
129	C₄⋊Q₈	C₅×C₈	1	1	yes	characteristic
130	#127	C₅×C₈	1	1	yes	characteristic
131	#124	C₅×C₈	1	2	yes	—
132	#121	C₅×C₈	1	4	yes	—
133	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
134	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
135	M₃₂	—	2	4	no	—
136	M₃₂	—	2	8	no	—
137	C₂×C₁₆	—	2	2	no	—
138	C₂×C₁₆	—	2	8	no	—
139	C₂×C₁₆	C₅×D₄	1	4	yes	complemented
140	C₂×C₁₆	C₂³×C₅	1	2	yes	—
141	C₂×C₁₆	C₂³×C₅	1	4	yes	—
142	C₂×C₁₆	C₂³×C₅	1	2	yes	—
143	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
144	C₂²⋊C₈	C₂×C₄×C₅	1	8	yes	—
145	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
146	C₄×C₈	C₂³×C₅	1	2	yes	—
147	C₂²×C₅	—	2	2	no	—
148	C₂²×C₅	—	2	8	no	—
149	C₂²×C₅	—	2	4	no	—
150	C₂²×C₅	C₈×D₄	1	2	yes	—
151	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
152	C₄×C₅	—	2	2	no	—
153	C₄×C₅	—	2	2	no	—
154	C₄×C₅	—	2	4	no	—
155	C₄×C₅	C₈×D₄	1	2	yes	—
156	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
157	C₄×C₅	C₂×#131	1	1	yes	characteristic
158	#41	—	2	4	no	—
159	#41	—	2	4	no	—
160	C₂×Q₈	C₂×C₅×C₈	1	2	yes	—
161	C₂×D₄	C₂×C₅×C₈	1	4	yes	—
162	C₂×D₄	C₂×C₅×C₈	1	2	yes	—
163	C₂×D₄	C₂×C₅×C₈	1	4	yes	—
164	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
165	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
166	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
167	M₁₆	—	2	4	no	—
168	M₁₆	—	2	8	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	2	4	no	—
171	C₂×C₈	—	2	4	no	—
172	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
173	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
174	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
175	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
176	C₂×C₈	C₅×#41	1	2	yes	—
177	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
178	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	—
179	C₂²⋊C₄	C₂×C₅×C₈	1	8	yes	—
180	C₄²	C₂×C₅×C₈	1	1	yes	characteristic
181	C₄²	C₂×C₅×C₈	1	1	yes	characteristic
182	C₄²	C₂²×C₄×C₅	1	2	yes	—
183	C₁₆	—	2	4	no	—
184	C₁₆	—	2	2	no	—
185	C₁₆	C₂×C₅×D₄	1	4	yes	—
186	C₂×C₅	—	2	2	no	—
187	C₂×C₅	—	4	4	no	—
188	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
189	C₂×C₅	#3407	1	2	yes	—
190	C₂³	C₂²×C₅×C₈	1	4	yes	—
191	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
192	Q₈	—	2	4	no	—
193	D₄	—	2	8	no	—
194	D₄	—	2	4	no	—
195	D₄	—	4	4	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
200	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
201	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
202	C₂×C₄	C₂²×C₅×C₈	1	4	yes	—
203	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
204	C₂×C₄	C₅×#131	1	2	yes	—
205	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
206	C₈	—	2	4	no	—
207	C₈	—	2	2	no	—
208	C₈	C₄×C₅×D₄	1	2	yes	—
209	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
210	C₈	C₂×C₅×#41	1	1	yes	characteristic
211	C₅	#33435	1	1	yes	characteristic, direct product factor, Sylow
212	C₂²	—	2	2	no	—
213	C₂²	—	2	8	no	—
214	C₂²	—	2	4	no	—
215	C₂²	C₅×C₈×D₄	1	2	yes	—
216	C₂²	C₂³×C₅×C₈	1	1	yes	characteristic
217	C₄	—	2	2	no	—
218	C₄	—	2	2	no	—
219	C₄	—	2	4	no	—
220	C₄	C₅×C₈×D₄	1	2	yes	—
221	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
222	C₄	C₂×C₅×#131	1	1	yes	characteristic
223	C₂	—	2	2	no	—
224	C₂	—	4	4	no	—
225	C₂	C₂×C₅×C₈×D₄	1	1	yes	characteristic
226	C₂	C₅×#3407	1	2	yes	—

	subgroup	G/H
center	C₂×C₅×C₈	C₂⁴
commutator	C₂²	C₂³×C₅×C₈
Frattini, cosocle	C₂×C₈	C₂⁴×C₅
socle	C₂²×C₅	C₂³×C₈
prime radical	C₅×#532	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#504	C₂	semidirect
3. C₅×#2168	C₂	semidirect
4. C₅×#2150	C₂	semidirect
5. C₅×#2113	C₂	semidirect
6. C₂×C₅×#346	C₂	semidirect
23. #33435	C₅	direct (N × H)
42. C₂×C₅×C₁₆	D₄	semidirect
50. C₂×#504	C₂×C₅	semidirect
52. #2168	C₂×C₅	semidirect
53. #2150	C₂×C₅	semidirect
54. #2113	C₂×C₅	semidirect
55. C₂×#346	C₂×C₅	semidirect
139. C₂×C₁₆	C₅×D₄	semidirect
211. C₅	#33435	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#504	2
C₅×#2931	2
C₅×#2168	2
C₅×#2150	2
C₅×#2113	2
C₂×C₅×#346	2
#33435	5

Subgroups — C5×#33435 #11956155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33435 #11956155