Subgroups — C₂×#14584199 #19150607

Order 5628.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14584199	C₂	1	2	yes	maximal, direct product factor
2	C₂×#13064105	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₇×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#13064105	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
6	D₇×C₆₇	C₂×C₃	1	2	yes	complemented
7	C₂²×C₆₇⋊C₃	—	7	1	no	maximal, Hall
8	C₇×C₆₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₆₇⋊C₃	—	7	2	no	—
10	C₂×C₆₇⋊C₃	—	7	1	no	—
11	C₂²×C₆₇	—	7	1	no	Hall
12	C₆₇⋊C₃	—	7	1	no	Hall
13	C₂×C₆₇	—	7	2	no	—
14	C₂×C₆₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
15	C₂×AGL(1,𝔽₇)	—	67	1	no	maximal, Hall
16	C₆₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
17	C₂×ΓL(1,𝔽₈)	—	67	1	no	—
18	AGL(1,𝔽₇)	—	67	2	no	—
19	C₂×D₇	C₆₇⋊C₃	1	1	yes	characteristic, complemented, Hall
20	ΓL(1,𝔽₈)	—	67	1	no	Hall
21	C₂×C₇	C₂×C₆₇⋊C₃	1	1	yes	characteristic, complemented
22	D₇	C₂×C₆₇⋊C₃	1	2	yes	complemented
23	C₂²×C₃	—	469	1	no	Hall
24	C₇	C₂²×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃	—	469	2	no	—
26	C₂×C₃	—	469	1	no	—
27	C₂²	—	7	1	no	Sylow
28	C₃	—	469	1	no	Sylow
29	C₂	—	7	2	no	—
30	C₂	#14584199	1	1	yes	characteristic, direct product factor

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