Subgroups — #88048

Order 416.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#1055	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₁₃	—	2	1	no	—
5	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×Dic₁₃	—	2	1	no	—
7	#1055	C₄	1	2	yes	complemented
8	C₂²×C₁₃	D₄	1	1	yes	characteristic
9	C₄×C₁₃	—	4	1	no	—
10	C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
11	C₄×C₁₃	Q₈	1	1	yes	characteristic
12	Dic₁₃	—	4	1	no	—
13	#106	—	13	1	no	maximal, Sylow
14	C₂×C₁₃	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₁₃	SD₁₆	1	1	yes	characteristic
16	C₂×C₁₃	SD₁₆	1	1	yes	characteristic
17	C₂×C₈	—	13	1	no	—
18	C₄⋊C₄	—	13	1	no	—
19	C₄⋊C₄	D₁₃	1	1	yes	characteristic
20	C₁₃	#106	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₄	—	2	1	no	—
22	C₂×C₄	—	26	1	no	—
23	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
24	C₈	—	13	2	no	—
25	C₂²	C₂²⋊D₁₃	1	1	yes	characteristic
26	C₄	—	4	1	no	—
27	C₄	—	52	1	no	—
28	C₄	Dic₂₆	1	1	yes	characteristic
29	C₄	C₄×D₁₃	1	1	yes	characteristic
30	C₂	#6101	1	1	yes	characteristic
31	C₂	#6105	1	1	yes	characteristic
32	C₂	#6106	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. #1055	C₄	semidirect
20. C₁₃	#106	semidirect

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