Subgroups — C₂×D₂₃₀₁ #22604201

Order 9204.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₃₀₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₃×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₇₆₇	—	3	1	no	maximal, Hall
4	C₃×C₁₃×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₅₉	D₃	1	1	yes	characteristic, complemented
6	D₇₆₇	—	3	2	no	—
7	C₁₃×C₅₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₁₇₇	—	13	1	no	maximal, Hall
9	C₂×C₃×C₅₉	D₁₃	1	1	yes	characteristic, complemented
10	D₁₇₇	—	13	2	no	—
11	C₂×D₅₉	—	39	1	no	Hall
12	C₃×C₅₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
13	C₂×D₃₉	—	59	1	no	maximal, Hall
14	C₂×C₅₉	D₃₉	1	1	yes	characteristic, complemented
15	D₅₉	—	39	2	no	—
16	C₂×C₃×C₁₃	D₅₉	1	1	yes	characteristic, complemented
17	D₃₉	—	59	2	no	—
18	C₅₉	C₂×D₃₉	1	1	yes	characteristic, complemented, Sylow
19	C₂×D₁₃	—	177	1	no	Hall
20	C₃×C₁₃	C₂×D₅₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₃	D₁₇₇	1	1	yes	characteristic, complemented
22	D₁₃	—	177	2	no	—
23	C₁₃	C₂×D₁₇₇	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₃	—	767	1	no	Hall
25	C₂×C₃	D₇₆₇	1	1	yes	characteristic, complemented
26	D₃	—	767	2	no	—
27	C₂²	—	2301	1	no	Sylow
28	C₃	C₂×D₇₆₇	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	2301	2	no	—
30	C₂	D₂₃₀₁	1	1	yes	characteristic, direct product factor

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