Subgroups — C₄×C₁₃×#564 #15720694

Order 3328.

1800 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#564	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2382	C₂	1	15	yes	maximal
3	C₄×C₁₃×#125	C₂	1	15	yes	maximal
4	C₁₃×#564	C₄	1	16	yes	direct product factor
5	C₂×C₁₃×#125	C₂²	1	15	yes	—
6	C₁₃×#389	C₂²	1	30	yes	—
7	C₁₃×#387	C₂²	1	60	yes	—
8	C₁₃×#382	C₂²	1	15	yes	—
9	C₄×C₁₃×C₄⋊C₄	C₂²	1	30	yes	—
10	C₄³×C₁₃	C₂²	1	5	yes	—
11	C₁₃×#125	C₂×C₄	1	120	yes	—
12	C₂×C₁₃×C₄⋊C₄	C₂³	1	30	yes	—
13	C₂×C₁₃×C₄⋊C₄	C₂³	1	30	yes	—
14	C₂×C₄²×C₁₃	C₂³	1	15	yes	—
15	C₂×C₄²×C₁₃	C₂³	1	15	yes	—
16	C₂×C₄²×C₁₃	C₂³	1	5	yes	—
17	C₁₃×#95	C₂³	1	60	yes	—
18	C₄×#564	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₄×C₁₃	C₂⁴	1	15	yes	—
20	C₂²×C₄×C₁₃	C₂⁴	1	15	yes	—
21	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
22	C₁₃×C₄⋊C₄	—	4	30	no	—
23	C₁₃×C₄⋊C₄	C₂²×C₄	1	120	yes	—
24	C₄²×C₁₃	—	2	30	no	—
25	C₄²×C₁₃	—	4	15	no	—
26	C₄²×C₁₃	C₂²×C₄	1	20	yes	—
27	C₂×#564	C₂×C₁₃	1	1	yes	characteristic
28	#2382	C₂×C₁₃	1	15	yes	—
29	C₄×#125	C₂×C₁₃	1	15	yes	—
30	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
31	C₂×C₄×C₁₃	—	2	15	no	—
32	C₂×C₄×C₁₃	—	2	15	no	—
33	C₂×C₄×C₁₃	—	2	15	no	—
34	C₂×C₄×C₁₃	—	2	30	no	—
35	C₂×C₄×C₁₃	C₂³×C₄	1	30	yes	—
36	C₂×C₄×C₁₃	2₋¹⁺⁴	1	6	yes	—
37	#564	C₄×C₁₃	1	16	yes	direct product factor
38	C₂×#125	C₂²×C₁₃	1	15	yes	—
39	#389	C₂²×C₁₃	1	30	yes	—
40	#387	C₂²×C₁₃	1	60	yes	—
41	#382	C₂²×C₁₃	1	15	yes	—
42	C₄×C₄⋊C₄	C₂²×C₁₃	1	30	yes	—
43	C₄³	C₂²×C₁₃	1	5	yes	—
44	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
45	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	3	yes	—
46	C₂²×C₁₃	#585	1	3	yes	—
47	C₄×C₁₃	—	2	30	no	—
48	C₄×C₁₃	—	4	15	no	—
49	C₄×C₁₃	#564	1	4	yes	direct product factor
50	#125	C₂×C₄×C₁₃	1	120	yes	—
51	C₂×C₄⋊C₄	C₂³×C₁₃	1	30	yes	—
52	C₂×C₄⋊C₄	C₂³×C₁₃	1	30	yes	—
53	C₂×C₄²	C₂³×C₁₃	1	15	yes	—
54	C₂×C₄²	C₂³×C₁₃	1	15	yes	—
55	C₂×C₄²	C₂³×C₁₃	1	5	yes	—
56	#95	C₂³×C₁₃	1	60	yes	—
57	C₂×C₁₃	C₄×2₋¹⁺⁴	1	3	yes	—
58	C₂×C₁₃	C₂×#564	1	1	yes	characteristic
59	C₂×C₁₃	#3531	1	3	yes	—
60	C₂²×C₄	C₂⁴×C₁₃	1	15	yes	—
61	C₂²×C₄	C₂⁴×C₁₃	1	15	yes	—
62	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
63	C₄⋊C₄	—	4	30	no	—
64	C₄⋊C₄	C₂²×C₄×C₁₃	1	120	yes	—
65	C₄²	—	2	30	no	—
66	C₄²	—	4	15	no	—
67	C₄²	C₂²×C₄×C₁₃	1	20	yes	—
68	C₁₃	C₄×#564	1	1	yes	characteristic, direct product factor, Sylow
69	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
70	C₂×C₄	—	2	15	no	—
71	C₂×C₄	—	2	15	no	—
72	C₂×C₄	—	2	15	no	—
73	C₂×C₄	—	2	30	no	—
74	C₂×C₄	C₂³×C₄×C₁₃	1	30	yes	—
75	C₂×C₄	C₁₃×2₋¹⁺⁴	1	6	yes	—
76	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
77	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	3	yes	—
78	C₂²	C₁₃×#585	1	3	yes	—
79	C₄	—	2	30	no	—
80	C₄	—	4	15	no	—
81	C₄	C₁₃×#564	1	4	yes	direct product factor
82	C₂	C₄×C₁₃×2₋¹⁺⁴	1	3	yes	—
83	C₂	C₂×C₁₃×#564	1	1	yes	characteristic
84	C₂	C₁₃×#3531	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle, prime radical	C₂³×C₁₃	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#564	C₄	direct (N × H)
18. C₄×#564	C₁₃	direct (N × H)
37. #564	C₄×C₁₃	direct (N × H)
49. C₄×C₁₃	#564	direct (N × H)
68. C₁₃	C₄×#564	direct (N × H)
81. C₄	C₁₃×#564	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×C₁₃×#564	2
C₁₃×#2382	2
C₄×C₁₃×#125	2
C₄×#564	13

Subgroups — C4×C13×#564 #15720694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₃×#564 #15720694