Subgroups — #27165725

Order 12832.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₈₀₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₁₆₀₄	C₂	1	1	yes	maximal, characteristic
3	#20264343	C₂	1	4	yes	maximal, complemented
4	C₄²×C₄₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₄₀₁	C₂²	1	2	yes	—
6	Dic₈₀₂	—	2	2	no	—
7	D₁₆₀₄	—	2	2	no	—
8	C₂×Dic₄₀₁	C₂²	1	2	yes	—
9	C₂×C₄×C₄₀₁	C₂²	1	2	yes	—
10	C₂×C₄×C₄₀₁	C₂²	1	1	yes	characteristic
11	C₂²×C₄₀₁	C₂³	1	1	yes	characteristic
12	C₂×D₄₀₁	—	2	2	no	—
13	C₂×D₄₀₁	—	2	4	no	—
14	C₄×C₄₀₁	—	2	2	no	—
15	C₄×C₄₀₁	D₄	1	2	yes	—
16	Dic₄₀₁	—	2	2	no	—
17	C₂×C₄₀₁	C₂×D₄	1	1	yes	characteristic
18	C₂×C₄₀₁	#41	1	2	yes	—
19	D₄₀₁	—	4	2	no	—
20	C₄₀₁	#124	1	1	yes	characteristic, complemented, Sylow
21	#124	—	401	1	no	maximal, Sylow
22	C₂×Q₈	—	401	1	no	—
23	C₂×D₄	—	401	1	no	—
24	C₂²⋊C₄	—	401	4	no	—
25	C₄²	D₄₀₁	1	1	yes	characteristic, complemented
26	C₂³	—	401	2	no	—
27	Q₈	—	802	2	no	—
28	D₄	—	802	2	no	—
29	C₂×C₄	—	401	2	no	—
30	C₂×C₄	C₂×D₄₀₁	1	2	yes	—
31	C₂×C₄	C₂×D₄₀₁	1	1	yes	characteristic
32	C₂²	—	802	2	no	—
33	C₂²	—	802	4	no	—
34	C₂²	C₂²×D₄₀₁	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	802	2	no	—
37	C₄	D₁₆₀₄	1	2	yes	—
38	C₂	—	1604	2	no	—
39	C₂	C₂×D₁₆₀₄	1	1	yes	characteristic
40	C₂	#20264366	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.