Subgroups — #88115

Order 416.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#261	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₁₃	—	2	1	no	—
5	C₂×#261	—	2	1	no	—
6	D₄×C₁₃	C₄	1	1	yes	characteristic, complemented
7	C₂²⋊D₁₃	—	2	1	no	—
8	D₅₂	C₄	1	1	yes	characteristic, complemented
9	C₄×D₁₃	C₂²	1	1	yes	characteristic
10	#1057	—	2	1	no	—
11	C₂²×C₁₃	—	2	1	no	—
12	C₂×D₁₃	—	2	1	no	—
13	C₂×D₁₃	—	4	1	no	—
14	C₂×D₁₃	—	4	1	no	—
15	C₂×D₁₃	D₄	1	1	yes	characteristic
16	#261	—	4	1	no	—
17	C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
18	Dic₁₃	D₄	1	1	yes	characteristic
19	#102	—	13	1	no	maximal, Sylow
20	C₂×C₁₃	—	4	1	no	—
21	C₂×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
22	D₁₃	—	4	1	no	—
23	D₁₃	D₈	1	1	yes	characteristic
24	D₁₃	SD₁₆	1	1	yes	characteristic
25	C₂×D₄	—	13	1	no	—
26	C₂×C₈	—	13	1	no	—
27	C₄⋊C₄	—	13	1	no	—
28	C₁₃	#102	1	1	yes	characteristic, complemented, Sylow
29	C₂³	—	26	1	no	—
30	D₄	—	13	1	no	—
31	D₄	—	26	1	no	—
32	D₄	#261	1	1	yes	characteristic, complemented
33	C₂×C₄	—	13	1	no	—
34	C₂×C₄	—	26	1	no	—
35	C₈	—	26	1	no	—
36	C₂²	—	2	1	no	—
37	C₂²	—	13	1	no	—
38	C₂²	—	26	1	no	—
39	C₂²	—	52	1	no	—
40	C₂²	—	52	1	no	—
41	C₄	—	13	1	no	—
42	C₄	—	52	1	no	—
43	C₄	C₂×#261	1	1	yes	characteristic
44	C₂	—	4	1	no	—
45	C₂	—	13	1	no	—
46	C₂	—	13	1	no	—
47	C₂	—	52	1	no	—
48	C₂	C₂²⋊#261	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.