Subgroups — #88135

Order 416.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	#6103	C₂	1	1	yes	maximal, characteristic, complemented
6	#6101	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×C₁₃	C₂²	1	1	yes	characteristic
9	C₂²×D₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂²⋊D₁₃	C₄	1	4	yes	complemented
13	C₂×Dic₁₃	—	2	2	no	—
14	C₂×Dic₁₃	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₃	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₃	C₂²	1	1	yes	characteristic
17	C₄×D₁₃	—	2	2	no	—
18	C₂²×C₁₃	—	2	1	no	—
19	C₂²×C₁₃	—	2	1	no	—
20	C₂²×C₁₃	C₂×C₄	1	2	yes	complemented
21	C₂²×C₁₃	C₂³	1	1	yes	characteristic
22	C₂×D₁₃	—	2	1	no	—
23	C₂×D₁₃	—	2	1	no	—
24	C₂×D₁₃	C₂×C₄	1	2	yes	complemented
25	C₄×C₁₃	—	2	1	no	—
26	C₄×C₁₃	—	2	1	no	—
27	Dic₁₃	—	2	1	no	—
28	Dic₁₃	C₂×C₄	1	2	yes	complemented
29	Dic₁₃	D₄	1	2	yes	complemented
30	C₄×D₄	—	13	1	no	maximal, Sylow
31	C₂×C₁₃	—	2	2	no	—
32	C₂×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₁₃	C₂×D₄	1	1	yes	characteristic
34	C₂×C₁₃	#41	1	1	yes	characteristic
35	D₁₃	—	2	2	no	—
36	C₂×D₄	—	13	1	no	—
37	C₂²×C₄	—	13	1	no	—
38	C₂²×C₄	—	13	1	no	—
39	C₄⋊C₄	—	13	1	no	—
40	C₂²⋊C₄	—	13	1	no	—
41	C₂²⋊C₄	D₁₃	1	1	yes	characteristic, complemented
42	C₄²	—	13	1	no	—
43	C₁₃	C₄×D₄	1	1	yes	characteristic, complemented, Sylow
44	C₂³	—	13	1	no	—
45	C₂³	C₂×D₁₃	1	1	yes	characteristic
46	D₄	—	13	4	no	—
47	C₂×C₄	—	13	1	no	—
48	C₂×C₄	—	13	1	no	—
49	C₂×C₄	—	13	1	no	—
50	C₂×C₄	—	26	2	no	—
51	C₂×C₄	—	26	2	no	—
52	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
53	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
54	C₂²	—	2	1	no	—
55	C₂²	—	2	1	no	—
56	C₂²	—	13	2	no	—
57	C₂²	—	26	1	no	—
58	C₂²	—	26	1	no	—
59	C₂²	C₄×D₁₃	1	2	yes	complemented
60	C₂²	C₂²×D₁₃	1	1	yes	characteristic
61	C₄	—	2	1	no	—
62	C₄	—	2	1	no	—
63	C₄	—	13	2	no	—
64	C₄	—	13	2	no	—
65	C₄	—	26	1	no	—
66	C₂	—	2	2	no	—
67	C₂	—	26	2	no	—
68	C₂	C₂×C₄×D₁₃	1	1	yes	characteristic
69	C₂	D₄×D₁₃	1	1	yes	characteristic
70	C₂	#6129	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₁₃
commutator	C₂×C₁₃	C₂²×C₄
Fitting	C₁₃×C₂²⋊C₄	C₂
socle, cosocle	C₂²×C₁₃	C₂³
prime radical	C₂×C₂²⋊D₁₃	C₂
hypercenter	C₂²⋊C₄	D₁₃
hypocenter	C₁₃	C₄×D₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₁₃	C₂	semidirect
3. C₂×C₄×D₁₃	C₂	semidirect
4. C₁₃×C₂²⋊C₄	C₂	semidirect
5. #6103	C₂	semidirect
6. #6101	C₂	semidirect
7. C₄×Dic₁₃	C₂	semidirect
12. C₂²⋊D₁₃	C₄	semidirect
20. C₂²×C₁₃	C₂×C₄	semidirect
24. C₂×D₁₃	C₂×C₄	semidirect
28. Dic₁₃	C₂×C₄	semidirect
29. Dic₁₃	D₄	semidirect
41. C₂²⋊C₄	D₁₃	semidirect
43. C₁₃	C₄×D₄	semidirect
59. C₂²	C₄×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂²⋊D₁₃	2
C₂²×Dic₁₃	2
C₂×C₄×D₁₃	2
C₁₃×C₂²⋊C₄	2
#6103	2
#6101	2
C₄×Dic₁₃	2
C₄×D₄	13