Subgroups — C₂×#23778830 #35204153

Order 20288.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23778830	C₂	1	2	yes	maximal, direct product factor
2	C₂×#19099549	C₂	1	1	yes	maximal, characteristic
3	#19099549	C₄	1	1	yes	characteristic
4	#19099549	C₂²	1	1	yes	characteristic
5	C₂×C₈×C₃₁₇	C₄	1	1	yes	characteristic
6	C₂×C₄×C₃₁₇	C₈	1	1	yes	characteristic
7	C₈×C₃₁₇	C₈	1	1	yes	characteristic
8	C₈×C₃₁₇	C₂×C₄	1	1	yes	characteristic
9	C₂²×C₃₁₇	C₁₆	1	1	yes	characteristic
10	C₄×C₃₁₇	C₁₆	1	1	yes	characteristic
11	C₄×C₃₁₇	C₂×C₈	1	1	yes	characteristic
12	C₂×C₃₁₇	C₃₂	1	2	yes	complemented
13	C₂×C₃₁₇	C₂×C₁₆	1	1	yes	characteristic
14	C₃₁₇	C₂×C₃₂	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₃₂	—	317	1	no	maximal, Sylow
16	C₂×C₁₆	—	317	1	no	—
17	C₃₂	—	317	2	no	—
18	C₂×C₈	#11929639	1	1	yes	characteristic
19	C₁₆	—	317	1	no	—
20	C₁₆	—	317	1	no	—
21	C₂×C₄	#14579268	1	1	yes	characteristic
22	C₈	#14579268	1	1	yes	characteristic
23	C₈	C₂×#11929639	1	1	yes	characteristic
24	C₂²	#19099577	1	1	yes	characteristic
25	C₄	#19099577	1	1	yes	characteristic
26	C₄	C₂×#14579268	1	1	yes	characteristic
27	C₂	#23778830	1	2	yes	direct product factor
28	C₂	C₂×#19099577	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.