Subgroups — C₂×C₁₃×#2104 #15710185

Order 3328.

822 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2104	C₂	1	8	yes	maximal, direct product factor
2	C₂×C₁₃×#342	C₂	1	7	yes	maximal
3	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	7	yes	—
4	C₁₃×#342	C₂²	1	28	yes	—
5	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
6	C₂³×C₄×C₁₃	—	2	7	no	—
7	C₂×C₁₃×C₂²⋊C₄	—	2	14	no	—
8	C₂×C₁₃×C₂²⋊C₄	—	2	14	no	—
9	C₂×C₁₃×C₂²⋊C₄	—	2	7	no	—
10	C₂×C₁₃×C₂²⋊C₄	C₂³	1	14	yes	—
11	C₂×#2104	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂⁴×C₁₃	—	8	2	no	—
13	C₂⁴×C₁₃	#41	1	7	yes	—
14	C₂⁴×C₁₃	#41	1	7	yes	—
15	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
16	C₂²×C₄×C₁₃	—	2	14	no	—
17	C₂²×C₄×C₁₃	—	4	7	no	—
18	C₂²×C₄×C₁₃	—	4	7	no	—
19	C₂²×C₄×C₁₃	—	8	14	no	—
20	C₁₃×C₂²⋊C₄	—	2	28	no	—
21	C₁₃×C₂²⋊C₄	—	4	14	no	—
22	#2104	C₂×C₁₃	1	8	yes	direct product factor
23	C₂×#342	C₂×C₁₃	1	7	yes	—
24	C₂³×C₁₃	—	4	14	no	—
25	C₂³×C₁₃	—	8	7	no	—
26	C₂³×C₁₃	—	8	1	no	—
27	C₂³×C₁₃	#126	1	7	yes	—
28	C₂³×C₁₃	#126	1	14	yes	—
29	C₂³×C₁₃	#126	1	7	yes	—
30	C₂³×C₁₃	C₂×#41	1	7	yes	—
31	C₂×C₄×C₁₃	—	4	14	no	—
32	C₂×C₄×C₁₃	—	8	14	no	—
33	C₂×C₄×C₁₃	—	8	14	no	—
34	C₂×C₄×C₁₃	—	8	14	no	—
35	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	7	yes	—
36	#342	C₂²×C₁₃	1	28	yes	—
37	C₂²×C₁₃	—	2	14	no	—
38	C₂²×C₁₃	—	4	7	no	—
39	C₂²×C₁₃	—	4	7	no	—
40	C₂²×C₁₃	—	4	14	no	—
41	C₂²×C₁₃	#401	1	7	yes	—
42	C₂²×C₁₃	#401	1	1	yes	characteristic
43	C₂²×C₁₃	C₂×#126	1	7	yes	—
44	C₄×C₁₃	—	8	14	no	—
45	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
46	C₂³×C₄	—	2	7	no	—
47	C₂×C₂²⋊C₄	—	2	14	no	—
48	C₂×C₂²⋊C₄	—	2	14	no	—
49	C₂×C₂²⋊C₄	—	2	7	no	—
50	C₂×C₂²⋊C₄	C₂³×C₁₃	1	14	yes	—
51	C₂×C₁₃	—	2	7	no	—
52	C₂×C₁₃	—	2	7	no	—
53	C₂×C₁₃	#2104	1	2	yes	direct product factor
54	C₂×C₁₃	C₂×#401	1	1	yes	characteristic
55	C₂⁴	—	8	2	no	—
56	C₂⁴	C₁₃×#41	1	7	yes	—
57	C₂⁴	C₁₃×#41	1	7	yes	—
58	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
59	C₂²×C₄	—	2	14	no	—
60	C₂²×C₄	—	4	7	no	—
61	C₂²×C₄	—	4	7	no	—
62	C₂²×C₄	—	8	14	no	—
63	C₂²⋊C₄	—	2	28	no	—
64	C₂²⋊C₄	—	4	14	no	—
65	C₁₃	C₂×#2104	1	1	yes	characteristic, direct product factor, Sylow
66	C₂³	—	4	14	no	—
67	C₂³	—	8	7	no	—
68	C₂³	—	8	1	no	—
69	C₂³	C₁₃×#126	1	7	yes	—
70	C₂³	C₁₃×#126	1	14	yes	—
71	C₂³	C₁₃×#126	1	7	yes	—
72	C₂³	C₂×C₁₃×#41	1	7	yes	—
73	C₂×C₄	—	4	14	no	—
74	C₂×C₄	—	8	14	no	—
75	C₂×C₄	—	8	14	no	—
76	C₂×C₄	—	8	14	no	—
77	C₂²	—	2	14	no	—
78	C₂²	—	4	7	no	—
79	C₂²	—	4	7	no	—
80	C₂²	—	4	14	no	—
81	C₂²	C₁₃×#401	1	7	yes	—
82	C₂²	C₁₃×#401	1	1	yes	characteristic
83	C₂²	C₂×C₁₃×#126	1	7	yes	—
84	C₄	—	8	14	no	—
85	C₂	—	2	7	no	—
86	C₂	—	2	7	no	—
87	C₂	C₁₃×#2104	1	2	yes	direct product factor
88	C₂	C₂×C₁₃×#401	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	#401
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂⁵×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2104	C₂	direct (N × H)
11. C₂×#2104	C₁₃	direct (N × H)
22. #2104	C₂×C₁₃	direct (N × H)
53. C₂×C₁₃	#2104	direct (N × H)
65. C₁₃	C₂×#2104	direct (N × H)
87. C₂	C₁₃×#2104	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2104	2
C₂×C₁₃×#342	2
C₂×#2104	13

Subgroups — C2×C13×#2104 #15710185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2104 #15710185