Subgroups — C₅×#12664 #11935384

Order 1280.

334 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#364	C₂	1	1	yes	maximal, characteristic
2	C₅×#2108	C₂	1	2	yes	maximal
3	C₂×C₄×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₅×#1772	C₂	1	1	yes	maximal, characteristic
5	C₅×#1379	C₂	1	2	yes	maximal
6	C₂×C₅×M₃₂	C₂²	1	2	yes	—
7	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
8	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₅×#108	C₄	1	1	yes	characteristic
10	C₅×#427	C₄	1	1	yes	characteristic
11	C₅×#405	C₂²	1	2	yes	—
12	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₅×#364	C₄	1	4	yes	complemented
14	C₅×#346	—	2	2	no	—
15	C₄×C₅×C₁₆	—	2	2	no	—
16	C₄×C₅×C₁₆	C₄	1	4	yes	complemented
17	C₅×#339	C₄	1	2	yes	—
18	#12664	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
20	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
22	C₅×#117	C₂×C₄	1	2	yes	—
23	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
24	C₅×M₃₂	—	2	2	no	—
25	C₅×M₃₂	C₂×C₄	1	4	yes	—
26	C₂×C₅×C₁₆	—	2	2	no	—
27	C₂×C₅×C₁₆	—	2	1	no	—
28	C₂×C₅×C₁₆	—	2	1	no	—
29	C₂×C₅×C₁₆	C₂×C₄	1	2	yes	—
30	C₂×C₅×C₁₆	C₂×C₄	1	2	yes	—
31	C₂×C₅×C₁₆	D₄	1	1	yes	characteristic
32	C₂×C₅×C₁₆	D₄	1	1	yes	characteristic
33	C₂×C₅×C₁₆	Q₈	1	2	yes	—
34	C₅×#108	C₈	1	4	yes	—
35	C₅×#107	C₈	1	2	yes	—
36	C₅×#106	C₈	1	2	yes	—
37	C₅×#97	—	2	2	no	—
38	C₄×C₅×C₈	—	2	2	no	—
39	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
40	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
41	C₂×#364	C₂×C₅	1	1	yes	characteristic
42	#2108	C₂×C₅	1	2	yes	—
43	C₂×C₄×C₁₆	C₂×C₅	1	1	yes	characteristic
44	#1772	C₂×C₅	1	1	yes	characteristic
45	#1379	C₂×C₅	1	2	yes	—
46	C₂²×C₄×C₅	—	2	1	no	—
47	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
48	C₅×M₁₆	—	2	2	no	—
49	C₅×M₁₆	C₂×C₈	1	4	yes	—
50	C₂×C₅×C₈	—	2	2	no	—
51	C₂×C₅×C₈	C₄²	1	2	yes	—
52	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
53	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
54	C₂×C₅×C₈	C₂×C₈	1	2	yes	—
55	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
58	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
59	C₂×C₅×C₈	#41	1	1	yes	characteristic
60	C₂×C₅×C₈	#41	1	1	yes	characteristic
61	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	—
62	C₅×C₂²⋊C₄	—	2	2	no	—
63	C₄²×C₅	—	2	2	no	—
64	C₄²×C₅	—	2	1	no	—
65	C₄²×C₅	C₄²	1	2	yes	—
66	C₅×C₁₆	—	2	2	no	—
67	C₅×C₁₆	—	2	4	no	—
68	C₅×C₁₆	C₄⋊C₄	1	2	yes	—
69	C₅×C₁₆	C₄⋊C₄	1	2	yes	—
70	C₂×M₃₂	C₂²×C₅	1	2	yes	—
71	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
72	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
73	C₂×#108	C₄×C₅	1	1	yes	characteristic
74	#427	C₄×C₅	1	1	yes	characteristic
75	#405	C₂²×C₅	1	2	yes	—
76	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
77	#364	C₄×C₅	1	4	yes	complemented
78	#346	—	2	2	no	—
79	C₄×C₁₆	—	2	2	no	—
80	C₄×C₁₆	C₄×C₅	1	4	yes	complemented
81	#339	C₄×C₅	1	2	yes	—
82	C₂³×C₅	#131	1	1	yes	characteristic
83	C₂×C₄×C₅	—	2	4	no	—
84	C₂×C₄×C₅	—	2	2	no	—
85	C₂×C₄×C₅	—	2	4	no	—
86	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
87	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
88	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
89	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
90	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
91	C₂×C₄×C₅	#131	1	1	yes	characteristic
92	C₅×C₈	—	2	4	no	—
93	C₅×C₈	C₄×C₈	1	2	yes	—
94	C₅×C₈	C₄×C₈	1	2	yes	—
95	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
96	C₅×C₈	#117	1	1	yes	characteristic
97	C₅×C₈	C₄×D₄	1	1	yes	characteristic
98	C₅×C₈	C₄×Q₈	1	1	yes	characteristic
99	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
100	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
101	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
102	#117	C₂×C₄×C₅	1	2	yes	—
103	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
104	M₃₂	—	2	2	no	—
105	M₃₂	C₂×C₄×C₅	1	4	yes	—
106	C₂×C₁₆	—	2	2	no	—
107	C₂×C₁₆	—	2	1	no	—
108	C₂×C₁₆	—	2	1	no	—
109	C₂×C₁₆	C₂×C₄×C₅	1	2	yes	—
110	C₂×C₁₆	C₂×C₄×C₅	1	2	yes	—
111	C₂×C₁₆	C₅×D₄	1	1	yes	characteristic
112	C₂×C₁₆	C₅×D₄	1	1	yes	characteristic
113	C₂×C₁₆	C₅×Q₈	1	2	yes	—
114	#108	C₅×C₈	1	4	yes	—
115	#107	C₅×C₈	1	2	yes	—
116	#106	C₅×C₈	1	2	yes	—
117	#97	—	2	2	no	—
118	C₄×C₈	—	2	2	no	—
119	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
120	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
121	C₂²×C₅	—	2	2	no	—
122	C₂²×C₅	#405	1	1	yes	characteristic
123	C₂²×C₅	C₈×D₄	1	1	yes	characteristic
124	C₂²×C₅	C₈×Q₈	1	1	yes	characteristic
125	C₄×C₅	—	2	4	no	—
126	C₄×C₅	—	4	4	no	—
127	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
128	C₄×C₅	C₂×C₄×C₈	1	1	yes	characteristic
129	C₄×C₅	C₈×D₄	1	1	yes	characteristic
130	C₄×C₅	C₈×Q₈	1	1	yes	characteristic
131	C₂²×C₄	—	2	1	no	—
132	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
133	M₁₆	—	2	2	no	—
134	M₁₆	C₂×C₅×C₈	1	4	yes	—
135	C₂×C₈	—	2	2	no	—
136	C₂×C₈	C₄²×C₅	1	2	yes	—
137	C₂×C₈	C₂×C₅×C₈	1	1	yes	characteristic
138	C₂×C₈	C₂×C₅×C₈	1	1	yes	characteristic
139	C₂×C₈	C₂×C₅×C₈	1	2	yes	—
140	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
141	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
142	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
143	C₂×C₈	C₂×C₅×Q₈	1	1	yes	characteristic
144	C₂×C₈	C₅×#41	1	1	yes	characteristic
145	C₂×C₈	C₅×#41	1	1	yes	characteristic
146	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	—
147	C₂²⋊C₄	—	2	2	no	—
148	C₄²	—	2	2	no	—
149	C₄²	—	2	1	no	—
150	C₄²	C₄²×C₅	1	2	yes	—
151	C₁₆	—	2	2	no	—
152	C₁₆	—	2	4	no	—
153	C₁₆	C₅×C₄⋊C₄	1	2	yes	—
154	C₁₆	C₅×C₄⋊C₄	1	2	yes	—
155	C₂×C₅	—	2	1	no	—
156	C₂×C₅	—	2	1	no	—
157	C₂×C₅	C₈×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₅	#2170	1	2	yes	—
159	C₂³	C₅×#131	1	1	yes	characteristic
160	C₂×C₄	—	2	4	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	4	no	—
163	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
164	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
165	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
166	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
167	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
168	C₂×C₄	C₅×#131	1	1	yes	characteristic
169	C₈	—	2	4	no	—
170	C₈	C₄×C₅×C₈	1	2	yes	—
171	C₈	C₄×C₅×C₈	1	2	yes	—
172	C₈	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
173	C₈	C₅×#117	1	1	yes	characteristic
174	C₈	C₄×C₅×D₄	1	1	yes	characteristic
175	C₈	C₄×C₅×Q₈	1	1	yes	characteristic
176	C₅	#12664	1	1	yes	characteristic, direct product factor, Sylow
177	C₂²	—	2	2	no	—
178	C₂²	C₅×#405	1	1	yes	characteristic
179	C₂²	C₅×C₈×D₄	1	1	yes	characteristic
180	C₂²	C₅×C₈×Q₈	1	1	yes	characteristic
181	C₄	—	2	4	no	—
182	C₄	—	4	4	no	—
183	C₄	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
184	C₄	C₂×C₄×C₅×C₈	1	1	yes	characteristic
185	C₄	C₅×C₈×D₄	1	1	yes	characteristic
186	C₄	C₅×C₈×Q₈	1	1	yes	characteristic
187	C₂	—	2	1	no	—
188	C₂	—	2	1	no	—
189	C₂	C₅×C₈×C₄⋊C₄	1	1	yes	characteristic
190	C₂	C₅×#2170	1	2	yes	—

	subgroup	G/H
center	C₂×C₅×C₁₆	D₄
commutator	C₄	C₂×C₄×C₅×C₈
Frattini, cosocle	C₂²×C₈	C₂³×C₅
socle	C₂²×C₅	C₈×D₄
prime radical	C₂³×C₅	#131
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₁₆ ◁ C₂²×C₅×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₅×#364	C₄	semidirect
16. C₄×C₅×C₁₆	C₄	semidirect
18. #12664	C₅	direct (N × H)
77. #364	C₄×C₅	semidirect
80. C₄×C₁₆	C₄×C₅	semidirect
176. C₅	#12664	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×#364	2
C₅×#2108	2
C₂×C₄×C₅×C₁₆	2
C₅×#1772	2
C₅×#1379	2
#12664	5

Subgroups — C5×#12664 #11935384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#12664 #11935384