Subgroups — C₂×D₆₃₉₉ #72235321

Order 25596.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₃₉₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×D₂₁₃₃	—	3	1	no	maximal
3	D₂₁₃₃	—	3	2	no	—
4	C₂×C₇₉×C₈₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₇×C₇₉	D₃	1	1	yes	characteristic
6	C₇₉×C₈₁	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×D₇₁₁	—	9	1	no	—
8	C₂₇×C₇₉	C₂×D₃	1	1	yes	characteristic
9	C₂×C₉×C₇₉	D₉	1	1	yes	characteristic
10	D₇₁₁	—	9	2	no	—
11	C₂×D₂₃₇	—	27	1	no	—
12	C₉×C₇₉	C₂×D₉	1	1	yes	characteristic
13	C₂×C₃×C₇₉	D₂₇	1	1	yes	characteristic
14	D₂₃₇	—	27	2	no	—
15	C₂×D₈₁	—	79	1	no	maximal, Hall
16	C₂×D₇₉	—	81	1	no	Hall
17	C₃×C₇₉	C₂×D₂₇	1	1	yes	characteristic
18	C₂×C₈₁	D₇₉	1	1	yes	characteristic, complemented
19	D₈₁	—	79	2	no	—
20	C₂×C₇₉	D₈₁	1	1	yes	characteristic, complemented
21	D₇₉	—	81	2	no	—
22	C₂×D₂₇	—	237	1	no	—
23	C₈₁	C₂×D₇₉	1	1	yes	characteristic, complemented, Sylow
24	C₇₉	C₂×D₈₁	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₂₇	D₂₃₇	1	1	yes	characteristic
26	D₂₇	—	237	2	no	—
27	C₂×D₉	—	711	1	no	—
28	C₂₇	C₂×D₂₃₇	1	1	yes	characteristic
29	C₂×C₉	D₇₁₁	1	1	yes	characteristic
30	D₉	—	711	2	no	—
31	C₂×D₃	—	2133	1	no	—
32	C₉	C₂×D₇₁₁	1	1	yes	characteristic
33	C₂×C₃	D₂₁₃₃	1	1	yes	characteristic
34	D₃	—	2133	2	no	—
35	C₂²	—	6399	1	no	Sylow
36	C₃	C₂×D₂₁₃₃	1	1	yes	characteristic
37	C₂	—	6399	2	no	—
38	C₂	D₆₃₉₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₆₃₉₉
commutator, cosocle, hypocenter	C₇₉×C₈₁	C₂²
Frattini	C₂₇	C₂×D₂₃₇
Fitting	C₂×C₇₉×C₈₁	C₂
socle	C₂×C₃×C₇₉	D₂₇
LCS	G ▷ C₇₉×C₈₁
UCS	C₁ ◁ C₂

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.