Subgroups — #42117827

Order 27488.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₇₁₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊Dic₈₅₉	C₂	1	4	yes	maximal, complemented
3	C₄×Dic₈₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×C₈₅₉	C₂	1	1	yes	maximal, characteristic
5	Dic₁₇₁₈	—	2	2	no	—
6	C₂×Dic₈₅₉	C₂²	1	2	yes	—
7	C₂×Dic₈₅₉	C₂²	1	2	yes	—
8	C₂³×C₈₅₉	C₂²	1	2	yes	—
9	D₄×C₈₅₉	—	2	2	no	—
10	C₂×C₄×C₈₅₉	C₂²	1	1	yes	characteristic
11	C₂²×C₈₅₉	—	2	2	no	—
12	C₂²×C₈₅₉	—	2	4	no	—
13	C₂²×C₈₅₉	C₂³	1	1	yes	characteristic
14	C₄×C₈₅₉	D₄	1	2	yes	—
15	Dic₈₅₉	—	2	2	no	—
16	Dic₈₅₉	—	2	2	no	—
17	C₂×C₈₅₉	—	4	2	no	—
18	C₂×C₈₅₉	C₂×D₄	1	1	yes	characteristic
19	C₂×C₈₅₉	#41	1	2	yes	—
20	C₈₅₉	#124	1	1	yes	characteristic, complemented, Sylow
21	#124	—	859	1	no	maximal, Sylow
22	C₂×Q₈	—	859	1	no	—
23	C₂×D₄	D₈₅₉	1	1	yes	characteristic
24	C₂²⋊C₄	—	859	4	no	—
25	C₄²	—	859	1	no	—
26	C₂³	C₂×D₈₅₉	1	2	yes	—
27	Q₈	—	1718	2	no	—
28	D₄	—	2	2	no	—
29	C₂×C₄	—	859	2	no	—
30	C₂×C₄	—	859	2	no	—
31	C₂×C₄	C₂×D₈₅₉	1	1	yes	characteristic
32	C₂²	—	2	2	no	—
33	C₂²	—	2	4	no	—
34	C₂²	C₂²×D₈₅₉	1	1	yes	characteristic
35	C₄	—	1718	2	no	—
36	C₄	—	1718	2	no	—
37	C₄	C₂²⋊D₈₅₉	1	2	yes	—
38	C₂	—	4	2	no	—
39	C₂	C₂×C₂²⋊D₈₅₉	1	1	yes	characteristic
40	C₂	#28351700	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.