Subgroups — C₂×#16864412 #22575539

Order 8608.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864412	C₂	1	4	yes	maximal, direct product factor
2	C₂×#14524137	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×D₂₆₉	C₂	1	1	yes	maximal, characteristic
4	#14524137	C₂²	1	4	yes	complemented
5	C₂²×D₂₆₉	C₄	1	1	yes	characteristic
6	C₂×Dic₂₆₉	C₂²	1	1	yes	characteristic
7	C₄×D₂₆₉	C₄	1	2	yes	—
8	C₄×D₂₆₉	C₂²	1	2	yes	—
9	C₂×C₄×C₂₆₉	C₄	1	1	yes	characteristic
10	C₂²×C₂₆₉	C₂×C₄	1	1	yes	characteristic
11	C₂×D₂₆₉	—	2	2	no	—
12	C₂×D₂₆₉	C₂×C₄	1	2	yes	—
13	C₄×C₂₆₉	C₂×C₄	1	2	yes	—
14	Dic₂₆₉	C₂×C₄	1	1	yes	characteristic
15	Dic₂₆₉	C₂³	1	1	yes	characteristic
16	C₂×C₂₆₉	M₁₆	1	2	yes	complemented
17	C₂×C₂₆₉	C₂²×C₄	1	1	yes	characteristic
18	D₂₆₉	—	2	2	no	—
19	C₂₆₉	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
20	C₂×M₁₆	—	269	1	no	maximal, Sylow
21	C₂²×C₄	—	269	1	no	—
22	M₁₆	—	269	4	no	—
23	C₂×C₈	—	269	2	no	—
24	C₂³	—	269	1	no	—
25	C₂×C₄	—	269	1	no	—
26	C₂×C₄	—	269	2	no	—
27	C₂×C₄	—	269	2	no	—
28	C₂×C₄	#11761640	1	1	yes	characteristic
29	C₈	—	269	4	no	—
30	C₂²	—	269	2	no	—
31	C₂²	—	538	2	no	—
32	C₂²	C₂×#11761640	1	1	yes	characteristic
33	C₄	—	269	1	no	—
34	C₄	—	269	1	no	—
35	C₄	C₂×#11761640	1	2	yes	—
36	C₂	—	538	2	no	—
37	C₂	#16864412	1	2	yes	direct product factor
38	C₂	C₂²×#11761640	1	1	yes	characteristic

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