Subgroups — C₂×C₅×#1373 #11934730

Order 1280.

230 conjugacy classes of subgroups.

The subgroup lattice has 162 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	2	yes	maximal
2	C₂×C₄×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₅×#1373	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₅×M₃₂	—	2	2	no	—
5	C₂²×C₅×C₁₆	C₄	1	1	yes	characteristic
6	C₂²×C₅×C₁₆	C₄	1	1	yes	characteristic
7	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₅×#364	—	2	2	no	—
9	C₅×#364	C₂²	1	4	yes	—
10	C₄×C₅×C₁₆	C₄	1	2	yes	—
11	C₄×C₅×C₁₆	C₂²	1	2	yes	—
12	C₂×#1373	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
15	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
16	C₅×M₃₂	—	2	4	no	—
17	C₅×M₃₂	—	4	2	no	—
18	C₂×C₅×C₁₆	—	2	1	no	—
19	C₂×C₅×C₁₆	—	2	1	no	—
20	C₂×C₅×C₁₆	—	4	2	no	—
21	C₂×C₅×C₁₆	C₈	1	2	yes	—
22	C₂×C₅×C₁₆	C₈	1	2	yes	—
23	C₂×C₅×C₁₆	C₂×C₄	1	2	yes	—
24	C₂×C₅×C₁₆	C₂×C₄	1	2	yes	—
25	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
26	C₄×C₅×C₈	D₄	1	1	yes	characteristic
27	C₄×C₅×C₈	Q₈	1	1	yes	characteristic
28	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
29	C₂×#364	C₂×C₅	1	2	yes	—
30	C₂×C₄×C₁₆	C₂×C₅	1	1	yes	characteristic
31	#1373	C₂×C₅	1	4	yes	direct product factor
32	C₂²×C₄×C₅	—	2	1	no	—
33	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
37	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
38	C₂×C₅×C₈	M₁₆	1	1	yes	characteristic
39	C₂×C₅×C₈	M₁₆	1	1	yes	characteristic
40	C₂×C₅×C₈	D₈	1	1	yes	characteristic
41	C₂×C₅×C₈	D₈	1	1	yes	characteristic
42	C₂×C₅×C₈	Q₁₆	1	1	yes	characteristic
43	C₂×C₅×C₈	Q₁₆	1	1	yes	characteristic
44	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
46	C₄²×C₅	—	2	1	no	—
47	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
48	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
49	C₅×C₁₆	—	2	2	no	—
50	C₅×C₁₆	—	4	4	no	—
51	C₅×C₁₆	C₂×C₈	1	4	yes	—
52	C₂×M₃₂	—	2	2	no	—
53	C₂²×C₁₆	C₄×C₅	1	1	yes	characteristic
54	C₂²×C₁₆	C₄×C₅	1	1	yes	characteristic
55	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
56	#364	—	2	2	no	—
57	#364	C₂²×C₅	1	4	yes	—
58	C₄×C₁₆	C₄×C₅	1	2	yes	—
59	C₄×C₁₆	C₂²×C₅	1	2	yes	—
60	C₂³×C₅	#108	1	1	yes	characteristic
61	C₂×C₄×C₅	—	2	4	no	—
62	C₂×C₄×C₅	—	2	1	no	—
63	C₂×C₄×C₅	—	2	1	no	—
64	C₂×C₄×C₅	C₄⋊C₈	1	1	yes	characteristic
65	C₂×C₄×C₅	C₄⋊C₈	1	1	yes	characteristic
66	C₂×C₄×C₅	#107	1	1	yes	characteristic
67	C₂×C₄×C₅	#107	1	1	yes	characteristic
68	C₂×C₄×C₅	#108	1	1	yes	characteristic
69	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
70	C₅×C₈	C₄⋊C₈	1	1	yes	characteristic
71	C₅×C₈	C₄⋊C₈	1	1	yes	characteristic
72	C₅×C₈	#107	1	1	yes	characteristic
73	C₅×C₈	#107	1	1	yes	characteristic
74	C₅×C₈	C₂²×C₈	1	1	yes	characteristic
75	C₅×C₈	C₂×M₁₆	1	1	yes	characteristic
76	C₅×C₈	C₂×D₈	1	1	yes	characteristic
77	C₅×C₈	C₂×Q₁₆	1	1	yes	characteristic
78	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
79	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
80	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
81	M₃₂	—	2	4	no	—
82	M₃₂	—	4	2	no	—
83	C₂×C₁₆	—	2	1	no	—
84	C₂×C₁₆	—	2	1	no	—
85	C₂×C₁₆	—	4	2	no	—
86	C₂×C₁₆	C₅×C₈	1	2	yes	—
87	C₂×C₁₆	C₅×C₈	1	2	yes	—
88	C₂×C₁₆	C₂×C₄×C₅	1	2	yes	—
89	C₂×C₁₆	C₂×C₄×C₅	1	2	yes	—
90	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
91	C₄×C₈	C₅×D₄	1	1	yes	characteristic
92	C₄×C₈	C₅×Q₈	1	1	yes	characteristic
93	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
94	C₂²×C₅	—	2	2	no	—
95	C₂²×C₅	#335	1	1	yes	characteristic
96	C₂²×C₅	#335	1	1	yes	characteristic
97	C₂²×C₅	C₂×#108	1	1	yes	characteristic
98	C₄×C₅	—	2	2	no	—
99	C₄×C₅	—	2	2	no	—
100	C₄×C₅	#335	1	1	yes	characteristic
101	C₄×C₅	#335	1	1	yes	characteristic
102	C₄×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
103	C₄×C₅	C₂×#107	1	1	yes	characteristic
104	C₂²×C₄	—	2	1	no	—
105	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₈	C₂×C₅×C₈	1	1	yes	characteristic
109	C₂×C₈	C₂×C₅×C₈	1	1	yes	characteristic
110	C₂×C₈	C₅×M₁₆	1	1	yes	characteristic
111	C₂×C₈	C₅×M₁₆	1	1	yes	characteristic
112	C₂×C₈	C₅×D₈	1	1	yes	characteristic
113	C₂×C₈	C₅×D₈	1	1	yes	characteristic
114	C₂×C₈	C₅×Q₁₆	1	1	yes	characteristic
115	C₂×C₈	C₅×Q₁₆	1	1	yes	characteristic
116	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
117	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
118	C₄²	—	2	1	no	—
119	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
120	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
121	C₁₆	—	2	2	no	—
122	C₁₆	—	4	4	no	—
123	C₁₆	C₂×C₅×C₈	1	4	yes	—
124	C₂×C₅	—	2	1	no	—
125	C₂×C₅	—	2	1	no	—
126	C₂×C₅	#1373	1	2	yes	direct product factor
127	C₂×C₅	C₂×#335	1	1	yes	characteristic
128	C₂³	C₅×#108	1	1	yes	characteristic
129	C₂×C₄	—	2	4	no	—
130	C₂×C₄	—	2	1	no	—
131	C₂×C₄	—	2	1	no	—
132	C₂×C₄	C₅×C₄⋊C₈	1	1	yes	characteristic
133	C₂×C₄	C₅×C₄⋊C₈	1	1	yes	characteristic
134	C₂×C₄	C₅×#107	1	1	yes	characteristic
135	C₂×C₄	C₅×#107	1	1	yes	characteristic
136	C₂×C₄	C₅×#108	1	1	yes	characteristic
137	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
138	C₈	C₅×C₄⋊C₈	1	1	yes	characteristic
139	C₈	C₅×C₄⋊C₈	1	1	yes	characteristic
140	C₈	C₅×#107	1	1	yes	characteristic
141	C₈	C₅×#107	1	1	yes	characteristic
142	C₈	C₂²×C₅×C₈	1	1	yes	characteristic
143	C₈	C₂×C₅×M₁₆	1	1	yes	characteristic
144	C₈	C₂×C₅×D₈	1	1	yes	characteristic
145	C₈	C₂×C₅×Q₁₆	1	1	yes	characteristic
146	C₅	C₂×#1373	1	1	yes	characteristic, direct product factor, Sylow
147	C₂²	—	2	2	no	—
148	C₂²	C₅×#335	1	1	yes	characteristic
149	C₂²	C₅×#335	1	1	yes	characteristic
150	C₂²	C₂×C₅×#108	1	1	yes	characteristic
151	C₄	—	2	2	no	—
152	C₄	—	2	2	no	—
153	C₄	C₅×#335	1	1	yes	characteristic
154	C₄	C₅×#335	1	1	yes	characteristic
155	C₄	C₂×C₅×C₄⋊C₈	1	1	yes	characteristic
156	C₄	C₂×C₅×#107	1	1	yes	characteristic
157	C₂	—	2	1	no	—
158	C₂	—	2	1	no	—
159	C₂	C₅×#1373	1	2	yes	direct product factor
160	C₂	C₂×C₅×#335	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅×C₈	D₈
commutator	C₈	C₂²×C₅×C₈
Frattini, cosocle	C₄×C₈	C₂³×C₅
socle	C₂²×C₅	#335
prime radical	C₂³×C₅	#108
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ C₂²×C₅×C₈ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#1373	C₂	direct (N × H)
12. C₂×#1373	C₅	direct (N × H)
31. #1373	C₂×C₅	direct (N × H)
126. C₂×C₅	#1373	direct (N × H)
146. C₅	C₂×#1373	direct (N × H)
159. C₂	C₅×#1373	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
C₂×C₄×C₅×C₁₆	2
C₅×#1373	2
C₂×#1373	5

Subgroups — C2×C5×#1373 #11934730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1373 #11934730