Subgroups — C₂×#6105 #88187

Order 416.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#6105	C₂	1	4	yes	maximal, direct product factor
4	C₂×#1055	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₁₃	—	2	1	no	—
6	D₄×C₁₃	—	2	1	no	—
7	D₄×C₁₃	C₂²	1	2	yes	—
8	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₃	—	2	1	no	—
10	Dic₂₆	—	2	1	no	—
11	Dic₂₆	C₂²	1	2	yes	complemented
12	#1055	C₂²	1	2	yes	complemented
13	C₂²×C₁₃	—	2	2	no	—
14	C₂²×C₁₃	—	4	2	no	—
15	C₂²×C₁₃	D₄	1	1	yes	characteristic
16	C₄×C₁₃	D₄	1	1	yes	characteristic
17	C₄×C₁₃	C₂³	1	1	yes	characteristic
18	Dic₁₃	—	2	2	no	—
19	C₂×SD₁₆	—	13	1	no	maximal, Sylow
20	C₂×C₁₃	—	4	2	no	—
21	C₂×C₁₃	SD₁₆	1	2	yes	complemented
22	C₂×C₁₃	C₂×D₄	1	1	yes	characteristic
23	C₂×Q₈	—	13	1	no	—
24	C₂×D₄	D₁₃	1	1	yes	characteristic
25	SD₁₆	—	13	4	no	—
26	C₂×C₈	—	13	1	no	—
27	C₁₃	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
28	C₂³	—	2	1	no	—
29	Q₈	—	13	2	no	—
30	Q₈	—	26	1	no	—
31	D₄	—	2	1	no	—
32	D₄	C₂×D₁₃	1	2	yes	—
33	C₂×C₄	—	26	1	no	—
34	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
35	C₈	—	13	2	no	—
36	C₂²	—	2	2	no	—
37	C₂²	—	4	2	no	—
38	C₂²	C₂²⋊D₁₃	1	1	yes	characteristic
39	C₄	—	26	2	no	—
40	C₄	C₂²⋊D₁₃	1	1	yes	characteristic
41	C₄	C₂²×D₁₃	1	1	yes	characteristic
42	C₂	—	4	2	no	—
43	C₂	#6105	1	2	yes	direct product factor
44	C₂	C₂×C₂²⋊D₁₃	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.