Subgroups — #88049

Order 416.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₂	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#1055	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₁₃	—	2	1	no	—
5	C₂×C₄×C₁₃	—	2	1	no	—
6	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
7	D₅₂	—	2	1	no	—
8	D₅₂	C₄	1	2	yes	complemented
9	#1055	—	2	1	no	—
10	C₂²×C₁₃	D₄	1	1	yes	characteristic
11	C₂×D₁₃	—	2	2	no	—
12	C₂×D₁₃	—	4	1	no	—
13	C₂×D₁₃	—	4	1	no	—
14	C₄×C₁₃	—	4	1	no	—
15	C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₄×C₁₃	D₄	1	1	yes	characteristic
17	#102	—	13	1	no	maximal, Sylow
18	C₂×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₁₃	D₈	1	1	yes	characteristic
20	C₂×C₁₃	SD₁₆	1	1	yes	characteristic
21	D₁₃	—	4	2	no	—
22	C₂×D₄	—	13	1	no	—
23	C₂×C₈	—	13	1	no	—
24	C₄⋊C₄	D₁₃	1	1	yes	characteristic, complemented
25	C₁₃	#102	1	1	yes	characteristic, complemented, Sylow
26	C₂³	—	26	1	no	—
27	D₄	—	13	2	no	—
28	D₄	—	26	1	no	—
29	C₂×C₄	—	2	1	no	—
30	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
31	C₈	—	26	1	no	—
32	C₂²	—	26	2	no	—
33	C₂²	—	52	1	no	—
34	C₂²	—	52	1	no	—
35	C₂²	C₂²⋊D₁₃	1	1	yes	characteristic
36	C₄	—	4	1	no	—
37	C₄	C₄×D₁₃	1	1	yes	characteristic
38	C₄	D₅₂	1	1	yes	characteristic
39	C₂	—	52	2	no	—
40	C₂	#6103	1	1	yes	characteristic
41	C₂	#6104	1	1	yes	characteristic
42	C₂	#6106	1	1	yes	characteristic

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

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