Subgroups — C₅×#2792 #10616387

Order 640.

384 conjugacy classes of subgroups.

The subgroup lattice has 202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#398	C₂	1	1	yes	maximal, characteristic
2	C₅×#398	C₂	1	2	yes	maximal
3	C₅×#395	C₂	1	2	yes	maximal
4	C₅×#395	C₂	1	1	yes	maximal, characteristic
5	C₅×#389	C₂	1	2	yes	maximal
6	C₅×#389	C₂	1	2	yes	maximal
7	C₅×#387	C₂	1	2	yes	maximal
8	C₅×#387	C₂	1	2	yes	maximal
9	C₅×#384	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₂×C₄²×C₅	C₂²	1	2	yes	—
23	C₅×#95	C₂²	1	1	yes	characteristic
24	C₅×#95	C₂²	1	2	yes	—
25	C₅×#95	C₂²	1	2	yes	—
26	C₅×#95	C₂²	1	2	yes	—
27	C₅×#95	C₂²	1	2	yes	—
28	C₅×#95	C₂²	1	2	yes	—
29	C₅×#95	C₂²	1	2	yes	—
30	C₅×#95	C₂²	1	1	yes	characteristic
31	#2792	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂×C₅×Q₈	—	4	1	no	—
33	C₂×C₅×Q₈	—	4	2	no	—
34	C₂²×C₄×C₅	C₂³	1	2	yes	—
35	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×C₄×C₅	C₂³	1	2	yes	—
38	C₂²×C₄×C₅	C₂³	1	2	yes	—
39	C₂²×C₄×C₅	C₂³	1	2	yes	—
40	C₂²×C₄×C₅	C₂³	1	2	yes	—
41	C₂²×C₄×C₅	C₂³	1	2	yes	—
42	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₅×C₄⋊C₄	—	2	4	no	—
44	C₅×C₄⋊C₄	—	4	2	no	—
45	C₅×C₄⋊C₄	—	4	2	no	—
46	C₅×C₄⋊C₄	—	4	2	no	—
47	C₅×C₄⋊C₄	—	4	1	no	—
48	C₅×C₄⋊C₄	—	4	2	no	—
49	C₅×C₄⋊C₄	—	4	1	no	—
50	C₅×C₄⋊C₄	—	4	1	no	—
51	C₅×C₄⋊C₄	—	4	2	no	—
52	C₅×C₄⋊C₄	Q₈	1	8	yes	complemented
53	C₄²×C₅	—	2	2	no	—
54	C₄²×C₅	—	4	2	no	—
55	#398	C₂×C₅	1	2	yes	—
56	#398	C₂×C₅	1	1	yes	characteristic
57	#395	C₂×C₅	1	1	yes	characteristic
58	#395	C₂×C₅	1	2	yes	—
59	#389	C₂×C₅	1	2	yes	—
60	#389	C₂×C₅	1	2	yes	—
61	#387	C₂×C₅	1	2	yes	—
62	#387	C₂×C₅	1	2	yes	—
63	#384	C₂×C₅	1	1	yes	characteristic
64	C₂³×C₅	C₂⁴	1	1	yes	characteristic
65	C₅×Q₈	—	4	4	no	—
66	C₂×C₄×C₅	—	2	2	no	—
67	C₂×C₄×C₅	—	2	2	no	—
68	C₂×C₄×C₅	—	2	2	no	—
69	C₂×C₄×C₅	—	2	2	no	—
70	C₂×C₄×C₅	—	2	1	no	—
71	C₂×C₄×C₅	—	2	2	no	—
72	C₂×C₄×C₅	—	2	1	no	—
73	C₂×C₄×C₅	—	2	2	no	—
74	C₂×C₄×C₅	—	2	2	no	—
75	C₂×C₄×C₅	—	2	2	no	—
76	C₂×C₄×C₅	—	2	2	no	—
77	C₂×C₄×C₅	—	2	2	no	—
78	C₂×C₄×C₅	—	2	1	no	—
79	C₂×C₄×C₅	—	2	2	no	—
80	C₂×C₄×C₅	—	2	2	no	—
81	C₂×C₄×C₅	—	2	1	no	—
82	C₂×C₄×C₅	—	2	2	no	—
83	C₂×C₄×C₅	—	2	2	no	—
84	C₂×C₄×C₅	—	2	2	no	—
85	C₂×C₄×C₅	—	2	2	no	—
86	C₂×C₄×C₅	—	2	2	no	—
87	C₂×C₄×C₅	C₂×Q₈	1	4	yes	—
88	C₂×C₄×C₅	C₂×Q₈	1	4	yes	—
89	C₂×C₄×C₅	C₂×Q₈	1	4	yes	—
90	C₂×C₄×C₅	#41	1	2	yes	—
91	C₂²×Q₈	C₂²×C₅	1	1	yes	characteristic
92	C₂×C₄⋊C₄	C₂²×C₅	1	2	yes	—
93	C₂×C₄⋊C₄	C₂²×C₅	1	2	yes	—
94	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
95	C₂×C₄⋊C₄	C₂²×C₅	1	2	yes	—
96	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
97	C₂×C₄⋊C₄	C₂²×C₅	1	2	yes	—
98	C₂×C₄⋊C₄	C₂²×C₅	1	2	yes	—
99	C₂×C₄⋊C₄	C₂²×C₅	1	2	yes	—
100	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
101	C₂×C₄⋊C₄	C₂²×C₅	1	2	yes	—
102	C₂×C₄²	C₂²×C₅	1	1	yes	characteristic
103	C₂×C₄²	C₂²×C₅	1	2	yes	—
104	#95	C₂²×C₅	1	1	yes	characteristic
105	#95	C₂²×C₅	1	2	yes	—
106	#95	C₂²×C₅	1	2	yes	—
107	#95	C₂²×C₅	1	2	yes	—
108	#95	C₂²×C₅	1	2	yes	—
109	#95	C₂²×C₅	1	2	yes	—
110	#95	C₂²×C₅	1	2	yes	—
111	#95	C₂²×C₅	1	1	yes	characteristic
112	C₂²×C₅	C₂²×Q₈	1	2	yes	—
113	C₂²×C₅	C₂×#41	1	1	yes	characteristic
114	C₂²×C₅	H(5,𝔽₂)	1	1	yes	characteristic
115	C₂²×C₅	H(5,𝔽₂)	1	2	yes	—
116	C₂²×C₅	2₋¹⁺⁴	1	1	yes	characteristic
117	C₄×C₅	—	2	2	no	—
118	C₄×C₅	—	2	4	no	—
119	C₄×C₅	—	2	4	no	—
120	C₄×C₅	—	2	4	no	—
121	C₄×C₅	—	4	2	no	—
122	C₄×C₅	—	4	2	no	—
123	C₄×C₅	—	4	1	no	—
124	C₄×C₅	—	4	1	no	—
125	C₄×C₅	—	4	2	no	—
126	C₂×Q₈	—	4	1	no	—
127	C₂×Q₈	—	4	2	no	—
128	C₂²×C₄	C₂³×C₅	1	2	yes	—
129	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
130	C₂²×C₄	C₂³×C₅	1	2	yes	—
131	C₂²×C₄	C₂³×C₅	1	2	yes	—
132	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
133	C₂²×C₄	C₂³×C₅	1	2	yes	—
134	C₂²×C₄	C₂³×C₅	1	2	yes	—
135	C₂²×C₄	C₂³×C₅	1	2	yes	—
136	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
137	C₄⋊C₄	—	2	4	no	—
138	C₄⋊C₄	—	4	2	no	—
139	C₄⋊C₄	—	4	2	no	—
140	C₄⋊C₄	—	4	2	no	—
141	C₄⋊C₄	—	4	1	no	—
142	C₄⋊C₄	—	4	2	no	—
143	C₄⋊C₄	—	4	1	no	—
144	C₄⋊C₄	—	4	1	no	—
145	C₄⋊C₄	—	4	2	no	—
146	C₄⋊C₄	C₅×Q₈	1	8	yes	complemented
147	C₄²	—	2	2	no	—
148	C₄²	—	4	2	no	—
149	C₂×C₅	#539	1	1	yes	characteristic
150	C₂×C₅	#544	1	2	yes	—
151	C₂×C₅	#554	1	2	yes	—
152	C₂×C₅	Q₈²	1	1	yes	characteristic
153	C₂×C₅	#560	1	1	yes	characteristic
154	C₂³	C₂⁴×C₅	1	1	yes	characteristic
155	Q₈	—	4	4	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	1	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	1	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	C₂×C₅×Q₈	1	4	yes	—
178	C₂×C₄	C₂×C₅×Q₈	1	4	yes	—
179	C₂×C₄	C₂×C₅×Q₈	1	4	yes	—
180	C₂×C₄	C₅×#41	1	2	yes	—
181	C₅	#2792	1	1	yes	characteristic, direct product factor, Sylow
182	C₂²	C₂²×C₅×Q₈	1	2	yes	—
183	C₂²	C₂×C₅×#41	1	1	yes	characteristic
184	C₂²	C₅×H(5,𝔽₂)	1	1	yes	characteristic
185	C₂²	C₅×H(5,𝔽₂)	1	2	yes	—
186	C₂²	C₅×2₋¹⁺⁴	1	1	yes	characteristic
187	C₄	—	2	2	no	—
188	C₄	—	2	4	no	—
189	C₄	—	2	4	no	—
190	C₄	—	2	4	no	—
191	C₄	—	4	2	no	—
192	C₄	—	4	1	no	—
193	C₄	—	4	2	no	—
194	C₄	—	4	2	no	—
195	C₄	—	4	1	no	—
196	C₂	C₅×#539	1	1	yes	characteristic
197	C₂	C₅×#544	1	2	yes	—
198	C₂	C₅×#554	1	2	yes	—
199	C₂	C₅×Q₈²	1	1	yes	characteristic
200	C₂	C₅×#560	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₅
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
31. #2792	C₅	direct (N × H)
52. C₅×C₄⋊C₄	Q₈	semidirect
146. C₄⋊C₄	C₅×Q₈	semidirect
181. C₅	#2792	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×#398	2
C₅×#395	2
C₅×#389	2
C₅×#387	2
C₅×#384	2
#2792	5

Subgroups — C5×#2792 #10616387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#2792 #10616387