Subgroups — C₂×C₅×#3946 #13102360

Order 1600.

352 conjugacy classes of subgroups.

The subgroup lattice has 178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×#168	C₂	1	1	yes	maximal, characteristic
4	C₅×#3946	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₄×C₅²	C₂²	1	1	yes	characteristic
6	C₂²×C₅×Dic₅	C₄	1	1	yes	characteristic
7	C₂²×C₅×Dic₅	C₄	1	1	yes	characteristic
8	C₂×C₅²×C₈	—	2	2	no	—
9	C₂×C₅²×C₈	C₂²	1	2	yes	—
10	C₄×C₅×Dic₅	C₄	1	2	yes	—
11	C₄×C₅×Dic₅	C₂²	1	2	yes	—
12	C₂×C₅×#168	—	2	2	no	—
13	C₂×C₅×#168	C₂²	1	2	yes	—
14	C₂×C₅×C₄⋊C₈	—	5	1	no	maximal
15	C₂×#3946	C₅	1	1	yes	maximal, characteristic, direct product factor
16	C₂³×C₅²	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₅²	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₅²	D₄	1	2	yes	—
19	C₂×C₄×C₅²	Q₈	1	2	yes	—
20	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
21	C₂×C₅×Dic₅	—	2	2	no	—
22	C₂×C₅×Dic₅	C₈	1	4	yes	complemented
23	C₂×C₅×Dic₅	C₂×C₄	1	2	yes	—
24	C₂×C₅×Dic₅	C₂×C₄	1	2	yes	—
25	C₅²×C₈	—	2	2	no	—
26	C₅×#168	—	2	2	no	—
27	C₂²×C₅×C₈	—	2	2	no	—
28	C₂²×C₅×C₈	—	5	1	no	—
29	C₂²×C₅×C₈	D₅	1	1	yes	characteristic
30	C₂²×C₅×C₈	C₂×C₅	1	1	yes	characteristic
31	C₂×C₄²×C₅	—	5	1	no	—
32	C₂×C₄×Dic₅	C₂×C₅	1	1	yes	characteristic
33	C₂²×#168	C₂×C₅	1	1	yes	characteristic
34	C₅×C₄⋊C₈	—	5	4	no	—
35	#3946	C₂×C₅	1	4	yes	direct product factor
36	C₂²×C₅²	C₄⋊C₄	1	2	yes	—
37	C₂²×C₅²	C₂×C₈	1	2	yes	—
38	C₂²×C₅²	M₁₆	1	2	yes	—
39	C₂²×C₅²	C₂²×C₄	1	1	yes	characteristic
40	C₄×C₅²	C₄⋊C₄	1	2	yes	—
41	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
42	C₄×C₅²	C₂×Q₈	1	1	yes	characteristic
43	C₅×Dic₅	—	2	2	no	—
44	C₅×Dic₅	C₂×C₈	1	4	yes	complemented
45	C₂²×C₄×C₅	—	2	2	no	—
46	C₂²×C₄×C₅	—	5	1	no	—
47	C₂²×C₄×C₅	—	5	1	no	—
48	C₂²×C₄×C₅	C₂×D₅	1	1	yes	characteristic
49	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
50	C₂²×Dic₅	C₄×C₅	1	1	yes	characteristic
51	C₂²×Dic₅	C₄×C₅	1	1	yes	characteristic
52	C₂×C₅×C₈	—	2	8	no	—
53	C₂×C₅×C₈	—	2	2	no	—
54	C₂×C₅×C₈	—	2	2	no	—
55	C₂×C₅×C₈	—	2	4	no	—
56	C₂×C₅×C₈	—	5	2	no	—
57	C₂×C₅×C₈	—	10	2	no	—
58	C₂×C₅×C₈	C₂×D₅	1	2	yes	—
59	C₂×C₅×C₈	C₂²×C₅	1	2	yes	—
60	C₄²×C₅	—	5	2	no	—
61	C₄²×C₅	—	5	2	no	—
62	C₄×Dic₅	C₄×C₅	1	2	yes	—
63	C₄×Dic₅	C₂²×C₅	1	2	yes	—
64	C₂×#168	—	2	2	no	—
65	C₂×#168	C₂²×C₅	1	2	yes	—
66	C₂×C₄⋊C₈	—	5	1	no	Sylow
67	C₂×C₅²	C₄⋊C₈	1	4	yes	complemented
68	C₂×C₅²	C₂×C₄⋊C₄	1	1	yes	characteristic
69	C₂×C₅²	C₂²×C₈	1	1	yes	characteristic
70	C₂×C₅²	C₂×M₁₆	1	1	yes	characteristic
71	C₂³×C₅	—	2	2	no	—
72	C₂³×C₅	C₄×D₅	1	1	yes	characteristic
73	C₂³×C₅	C₂×C₄×C₅	1	1	yes	characteristic
74	C₂×C₄×C₅	—	2	4	no	—
75	C₂×C₄×C₅	—	2	2	no	—
76	C₂×C₄×C₅	—	2	4	no	—
77	C₂×C₄×C₅	—	2	2	no	—
78	C₂×C₄×C₅	—	5	4	no	—
79	C₂×C₄×C₅	—	5	2	no	—
80	C₂×C₄×C₅	—	5	2	no	—
81	C₂×C₄×C₅	—	10	2	no	—
82	C₂×C₄×C₅	Dic₁₀	1	2	yes	—
83	C₂×C₄×C₅	C₄×D₅	1	1	yes	characteristic
84	C₂×C₄×C₅	C₂²⋊D₅	1	2	yes	—
85	C₂×C₄×C₅	C₂×C₄×C₅	1	1	yes	characteristic
86	C₂×C₄×C₅	C₅×D₄	1	2	yes	—
87	C₂×C₄×C₅	C₅×Q₈	1	2	yes	—
88	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
89	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
90	C₂×Dic₅	—	2	2	no	—
91	C₂×Dic₅	C₅×C₈	1	4	yes	complemented
92	C₂×Dic₅	C₂×C₄×C₅	1	2	yes	—
93	C₂×Dic₅	C₂×C₄×C₅	1	2	yes	—
94	C₅×C₈	—	2	8	no	—
95	C₅×C₈	—	2	2	no	—
96	C₅×C₈	—	2	2	no	—
97	C₅×C₈	—	10	2	no	—
98	#168	—	2	2	no	—
99	C₂²×C₈	—	5	1	no	—
100	C₂²×C₈	C₅×D₅	1	1	yes	characteristic
101	C₂×C₄²	—	5	1	no	—
102	C₄⋊C₈	—	5	4	no	—
103	C₅²	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
104	C₂²×C₅	—	2	2	no	—
105	C₂²×C₅	—	2	4	no	—
106	C₂²×C₅	—	2	4	no	—
107	C₂²×C₅	—	2	4	no	—
108	C₂²×C₅	C₈×D₅	1	2	yes	—
109	C₂²×C₅	#676	1	2	yes	—
110	C₂²×C₅	#683	1	2	yes	—
111	C₂²×C₅	C₅×C₄⋊C₄	1	2	yes	—
112	C₂²×C₅	C₂×C₅×C₈	1	2	yes	—
113	C₂²×C₅	C₅×M₁₆	1	2	yes	—
114	C₂²×C₅	C₂×C₄×D₅	1	1	yes	characteristic
115	C₂²×C₅	C₂²×C₄×C₅	1	1	yes	characteristic
116	C₄×C₅	—	2	2	no	—
117	C₄×C₅	—	2	2	no	—
118	C₄×C₅	—	2	4	no	—
119	C₄×C₅	—	5	4	no	—
120	C₄×C₅	—	10	2	no	—
121	C₄×C₅	#683	1	2	yes	—
122	C₄×C₅	C₅×C₄⋊C₄	1	2	yes	—
123	C₄×C₅	C₂×Dic₁₀	1	1	yes	characteristic
124	C₄×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
125	C₄×C₅	C₂×C₅×D₄	1	1	yes	characteristic
126	C₄×C₅	C₂×C₅×Q₈	1	1	yes	characteristic
127	Dic₅	—	2	2	no	—
128	Dic₅	C₂×C₅×C₈	1	4	yes	complemented
129	C₂²×C₄	—	5	1	no	—
130	C₂²×C₄	—	5	1	no	—
131	C₂²×C₄	C₂×C₅×D₅	1	1	yes	characteristic
132	C₂×C₈	—	2	2	no	—
133	C₂×C₈	—	5	2	no	—
134	C₂×C₈	—	10	2	no	—
135	C₂×C₈	C₂×C₅×D₅	1	2	yes	—
136	C₄²	—	5	2	no	—
137	C₄²	—	5	2	no	—
138	C₂×C₅	—	2	2	no	—
139	C₂×C₅	—	2	2	no	—
140	C₂×C₅	—	2	8	no	—
141	C₂×C₅	—	2	2	no	—
142	C₂×C₅	#3946	1	4	yes	direct product factor
143	C₂×C₅	C₅×C₄⋊C₈	1	4	yes	complemented
144	C₂×C₅	C₂×C₈×D₅	1	1	yes	characteristic
145	C₂×C₅	C₂×#676	1	1	yes	characteristic
146	C₂×C₅	C₂×#683	1	1	yes	characteristic
147	C₂×C₅	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₅	C₂²×C₅×C₈	1	1	yes	characteristic
149	C₂×C₅	C₂×C₅×M₁₆	1	1	yes	characteristic
150	C₂³	C₄×C₅×D₅	1	1	yes	characteristic
151	C₂×C₄	—	5	2	no	—
152	C₂×C₄	—	5	4	no	—
153	C₂×C₄	—	5	2	no	—
154	C₂×C₄	—	10	2	no	—
155	C₂×C₄	C₅×Dic₁₀	1	2	yes	—
156	C₂×C₄	C₄×C₅×D₅	1	1	yes	characteristic
157	C₂×C₄	C₅×C₂²⋊D₅	1	2	yes	—
158	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
159	C₈	—	2	2	no	—
160	C₈	—	10	2	no	—
161	C₅	—	2	2	no	—
162	C₅	C₂×#3946	1	1	yes	characteristic, direct product factor
163	C₅	C₂×C₅×C₄⋊C₈	1	1	yes	characteristic, complemented
164	C₂²	C₅×C₈×D₅	1	2	yes	—
165	C₂²	C₅×#676	1	2	yes	—
166	C₂²	C₅×#683	1	2	yes	—
167	C₂²	C₂×C₄×C₅×D₅	1	1	yes	characteristic
168	C₄	—	5	4	no	—
169	C₄	—	10	2	no	—
170	C₄	C₅×#683	1	2	yes	—
171	C₄	C₂×C₅×Dic₁₀	1	1	yes	characteristic
172	C₄	C₂×C₅×C₂²⋊D₅	1	1	yes	characteristic
173	C₂	C₅×#3946	1	4	yes	direct product factor
174	C₂	C₂×C₅×C₈×D₅	1	1	yes	characteristic
175	C₂	C₂×C₅×#676	1	1	yes	characteristic
176	C₂	C₂×C₅×#683	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₅
commutator	C₂×C₅	C₂²×C₅×C₈
Frattini	C₂×C₄	C₂²×C₅×D₅
Fitting	C₂²×C₅²×C₈	C₂
socle, prime radical	C₂³×C₅²	C₂×C₄
cosocle	C₂×C₄×C₅	C₂³×C₅
hypercenter	C₂²×C₅×C₈	D₅
hypocenter	C₅	C₂×C₅×C₄⋊C₈
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×C₈

Complements

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

N	H ≅ G/N	type
4. C₅×#3946	C₂	direct (N × H)
15. C₂×#3946	C₅	direct (N × H)
22. C₂×C₅×Dic₅	C₈	semidirect
35. #3946	C₂×C₅	direct (N × H)
44. C₅×Dic₅	C₂×C₈	semidirect
67. C₂×C₅²	C₄⋊C₈	semidirect
91. C₂×Dic₅	C₅×C₈	semidirect
103. C₅²	C₂×C₄⋊C₈	semidirect
128. Dic₅	C₂×C₅×C₈	semidirect
142. C₂×C₅	#3946	direct (N × H)
143. C₂×C₅	C₅×C₄⋊C₈	semidirect
162. C₅	C₂×#3946	direct (N × H)
163. C₅	C₂×C₅×C₄⋊C₈	semidirect
173. C₂	C₅×#3946	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅²×C₈	2
C₂×C₄×C₅×Dic₅	2
C₂²×C₅×#168	2
C₅×#3946	2
C₂×C₅×C₄⋊C₈	5
C₂×#3946	5

Subgroups — C2×C5×#3946 #13102360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3946 #13102360