Subgroups — #88129

Order 416.

76 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	C₂×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#6103	C₂	1	4	yes	maximal, complemented
5	C₂²×D₁₃	C₂²	1	2	yes	—
6	C₂×C₄×C₁₃	C₂²	1	2	yes	—
7	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×Dic₁₃	C₂²	1	2	yes	—
9	D₅₂	—	2	2	no	—
10	Dic₂₆	—	2	2	no	—
11	C₂²×C₁₃	C₂³	1	1	yes	characteristic
12	C₂×D₁₃	—	2	2	no	—
13	C₂×D₁₃	—	2	4	no	—
14	C₄×C₁₃	—	2	2	no	—
15	C₄×C₁₃	D₄	1	2	yes	—
16	Dic₁₃	—	2	2	no	—
17	#124	—	13	1	no	maximal, Sylow
18	C₂×C₁₃	C₂×D₄	1	1	yes	characteristic
19	C₂×C₁₃	#41	1	2	yes	—
20	D₁₃	—	4	2	no	—
21	C₂×Q₈	—	13	1	no	—
22	C₂×D₄	—	13	1	no	—
23	C₂²⋊C₄	—	13	4	no	—
24	C₄²	D₁₃	1	1	yes	characteristic, complemented
25	C₁₃	#124	1	1	yes	characteristic, complemented, Sylow
26	C₂³	—	13	2	no	—
27	Q₈	—	26	2	no	—
28	D₄	—	26	2	no	—
29	C₂×C₄	—	13	2	no	—
30	C₂×C₄	C₂×D₁₃	1	2	yes	—
31	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
32	C₂²	—	26	2	no	—
33	C₂²	—	26	4	no	—
34	C₂²	C₂²×D₁₃	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	26	2	no	—
37	C₄	D₅₂	1	2	yes	—
38	C₂	—	52	2	no	—
39	C₂	C₂×D₅₂	1	1	yes	characteristic
40	C₂	#6127	1	2	yes	—

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.