Subgroups — #41×D₁₃ #88255

Order 416.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	#6131	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#6129	C₂	1	3	yes	maximal, complemented
5	D₄×D₁₃	C₂	1	3	yes	maximal, complemented
6	#6127	C₂	1	3	yes	maximal, complemented
7	C₂×C₄×D₁₃	C₂	1	3	yes	maximal, complemented
8	C₂²×D₁₃	C₂²	1	3	yes	—
9	Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
10	D₄×C₁₃	C₂²	1	3	yes	complemented
11	C₂×C₄×C₁₃	C₂²	1	3	yes	complemented
12	C₂²⋊D₁₃	C₂²	1	6	yes	complemented
13	C₂×Dic₁₃	C₂²	1	3	yes	complemented
14	D₅₂	C₂²	1	3	yes	complemented
15	C₄×D₁₃	C₂²	1	1	yes	characteristic
16	C₄×D₁₃	C₂²	1	3	yes	—
17	C₄×D₁₃	C₂²	1	3	yes	complemented
18	C₄×D₁₃	C₂²	1	3	yes	complemented
19	Dic₂₆	C₂²	1	3	yes	complemented
20	C₂²×C₁₃	C₂³	1	3	yes	—
21	C₂×D₁₃	—	2	6	no	—
22	C₂×D₁₃	C₂³	1	3	yes	—
23	C₂×D₁₃	C₂³	1	1	yes	characteristic
24	C₄×C₁₃	C₂³	1	3	yes	—
25	C₄×C₁₃	C₂³	1	1	yes	characteristic
26	Dic₁₃	C₂³	1	3	yes	—
27	Dic₁₃	C₂³	1	1	yes	characteristic
28	C₂×#41	—	13	1	no	maximal, Sylow
29	C₂×C₁₃	—	2	3	no	—
30	C₂×C₁₃	C₂⁴	1	1	yes	characteristic
31	D₁₃	—	2	3	no	—
32	D₁₃	#41	1	2	yes	direct product factor
33	#41	—	13	1	no	—
34	#41	—	13	3	no	—
35	#41	—	13	3	no	—
36	#41	D₁₃	1	1	yes	characteristic, direct product factor
37	C₂×Q₈	—	13	1	no	—
38	C₂×D₄	—	13	3	no	—
39	C₂²×C₄	—	13	3	no	—
40	C₁₃	C₂×#41	1	1	yes	characteristic, complemented, Sylow
41	C₂³	—	13	3	no	—
42	Q₈	—	13	3	no	—
43	Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
44	D₄	—	13	6	no	—
45	D₄	—	13	3	no	—
46	D₄	C₂×D₁₃	1	3	yes	complemented
47	C₂×C₄	—	13	3	no	—
48	C₂×C₄	—	13	3	no	—
49	C₂×C₄	—	13	3	no	—
50	C₂×C₄	—	13	1	no	—
51	C₂×C₄	—	13	3	no	—
52	C₂×C₄	C₂×D₁₃	1	3	yes	complemented
53	C₂²	—	13	1	no	—
54	C₂²	—	13	3	no	—
55	C₂²	—	26	6	no	—
56	C₂²	C₂²×D₁₃	1	3	yes	—
57	C₄	—	13	1	no	—
58	C₄	—	13	3	no	—
59	C₄	C₂²×D₁₃	1	3	yes	—
60	C₄	C₂²×D₁₃	1	1	yes	characteristic
61	C₂	—	2	3	no	—
62	C₂	—	13	2	no	—
63	C₂	—	26	3	no	—
64	C₂	C₂³×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₁₃
commutator, socle, cosocle	C₂×C₁₃	C₂⁴
Frattini	C₂	C₂³×D₁₃
Fitting	C₁₃×#41	C₂
hypercenter	#41	D₁₃
hypocenter	C₁₃	C₂×#41
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. C₁₃×#41	C₂	semidirect
2. #6131	C₂	semidirect
3. Q₈×D₁₃	C₂	semidirect
4. #6129	C₂	semidirect
5. D₄×D₁₃	C₂	semidirect
6. #6127	C₂	semidirect
7. C₂×C₄×D₁₃	C₂	semidirect
9. Q₈×C₁₃	C₂²	semidirect
10. D₄×C₁₃	C₂²	semidirect
11. C₂×C₄×C₁₃	C₂²	semidirect
12. C₂²⋊D₁₃	C₂²	semidirect
13. C₂×Dic₁₃	C₂²	semidirect
14. D₅₂	C₂²	semidirect
17. C₄×D₁₃	C₂²	semidirect
18. C₄×D₁₃	C₂²	semidirect
19. Dic₂₆	C₂²	semidirect
32. D₁₃	#41	direct (N × H)
36. #41	D₁₃	direct (N × H)
40. C₁₃	C₂×#41	semidirect
43. Q₈	C₂×D₁₃	semidirect
46. D₄	C₂×D₁₃	semidirect
52. C₂×C₄	C₂×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#41	2
#6131	2
Q₈×D₁₃	2
#6129	2
D₄×D₁₃	2
#6127	2
C₂×C₄×D₁₃	2
C₂×#41	13

Subgroups — #41×D13 #88255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #41×D₁₃ #88255